1,1,149,0,0.2196891,"\int x^3 \left(d+e x^2\right) \left(a+c x^4\right)^5 \, dx","Int[x^3*(d + e*x^2)*(a + c*x^4)^5,x]","\frac{5}{8} a^2 c^3 d x^{16}+\frac{5}{6} a^3 c^2 d x^{12}+\frac{5}{9} a^2 c^3 e x^{18}+\frac{5}{7} a^3 c^2 e x^{14}+\frac{5}{8} a^4 c d x^8+\frac{1}{2} a^4 c e x^{10}+\frac{1}{4} a^5 d x^4+\frac{1}{6} a^5 e x^6+\frac{1}{4} a c^4 d x^{20}+\frac{5}{22} a c^4 e x^{22}+\frac{1}{24} c^5 d x^{24}+\frac{1}{26} c^5 e x^{26}","\frac{5}{8} a^2 c^3 d x^{16}+\frac{5}{6} a^3 c^2 d x^{12}+\frac{5}{9} a^2 c^3 e x^{18}+\frac{5}{7} a^3 c^2 e x^{14}+\frac{5}{8} a^4 c d x^8+\frac{1}{2} a^4 c e x^{10}+\frac{1}{4} a^5 d x^4+\frac{1}{6} a^5 e x^6+\frac{1}{4} a c^4 d x^{20}+\frac{5}{22} a c^4 e x^{22}+\frac{1}{24} c^5 d x^{24}+\frac{1}{26} c^5 e x^{26}",1,"(a^5*d*x^4)/4 + (a^5*e*x^6)/6 + (5*a^4*c*d*x^8)/8 + (a^4*c*e*x^10)/2 + (5*a^3*c^2*d*x^12)/6 + (5*a^3*c^2*e*x^14)/7 + (5*a^2*c^3*d*x^16)/8 + (5*a^2*c^3*e*x^18)/9 + (a*c^4*d*x^20)/4 + (5*a*c^4*e*x^22)/22 + (c^5*d*x^24)/24 + (c^5*e*x^26)/26","A",3,2,20,0.1000,1,"{1252, 766}"
2,1,149,0,0.0977514,"\int x^2 \left(d+e x^2\right) \left(a+c x^4\right)^5 \, dx","Int[x^2*(d + e*x^2)*(a + c*x^4)^5,x]","\frac{2}{3} a^2 c^3 d x^{15}+\frac{10}{11} a^3 c^2 d x^{11}+\frac{10}{17} a^2 c^3 e x^{17}+\frac{10}{13} a^3 c^2 e x^{13}+\frac{5}{7} a^4 c d x^7+\frac{5}{9} a^4 c e x^9+\frac{1}{3} a^5 d x^3+\frac{1}{5} a^5 e x^5+\frac{5}{19} a c^4 d x^{19}+\frac{5}{21} a c^4 e x^{21}+\frac{1}{23} c^5 d x^{23}+\frac{1}{25} c^5 e x^{25}","\frac{2}{3} a^2 c^3 d x^{15}+\frac{10}{11} a^3 c^2 d x^{11}+\frac{10}{17} a^2 c^3 e x^{17}+\frac{10}{13} a^3 c^2 e x^{13}+\frac{5}{7} a^4 c d x^7+\frac{5}{9} a^4 c e x^9+\frac{1}{3} a^5 d x^3+\frac{1}{5} a^5 e x^5+\frac{5}{19} a c^4 d x^{19}+\frac{5}{21} a c^4 e x^{21}+\frac{1}{23} c^5 d x^{23}+\frac{1}{25} c^5 e x^{25}",1,"(a^5*d*x^3)/3 + (a^5*e*x^5)/5 + (5*a^4*c*d*x^7)/7 + (5*a^4*c*e*x^9)/9 + (10*a^3*c^2*d*x^11)/11 + (10*a^3*c^2*e*x^13)/13 + (2*a^2*c^3*d*x^15)/3 + (10*a^2*c^3*e*x^17)/17 + (5*a*c^4*d*x^19)/19 + (5*a*c^4*e*x^21)/21 + (c^5*d*x^23)/23 + (c^5*e*x^25)/25","A",2,1,20,0.05000,1,"{1262}"
3,1,89,0,0.0770721,"\int x \left(d+e x^2\right) \left(a+c x^4\right)^5 \, dx","Int[x*(d + e*x^2)*(a + c*x^4)^5,x]","\frac{5}{7} a^2 c^3 d x^{14}+a^3 c^2 d x^{10}+\frac{5}{6} a^4 c d x^6+\frac{1}{2} a^5 d x^2+\frac{5}{18} a c^4 d x^{18}+\frac{e \left(a+c x^4\right)^6}{24 c}+\frac{1}{22} c^5 d x^{22}","\frac{5}{7} a^2 c^3 d x^{14}+a^3 c^2 d x^{10}+\frac{5}{6} a^4 c d x^6+\frac{1}{2} a^5 d x^2+\frac{5}{18} a c^4 d x^{18}+\frac{e \left(a+c x^4\right)^6}{24 c}+\frac{1}{22} c^5 d x^{22}",1,"(a^5*d*x^2)/2 + (5*a^4*c*d*x^6)/6 + a^3*c^2*d*x^10 + (5*a^2*c^3*d*x^14)/7 + (5*a*c^4*d*x^18)/18 + (c^5*d*x^22)/22 + (e*(a + c*x^4)^6)/(24*c)","A",4,3,18,0.1667,1,"{1248, 641, 194}"
4,1,141,0,0.0819144,"\int \left(d+e x^2\right) \left(a+c x^4\right)^5 \, dx","Int[(d + e*x^2)*(a + c*x^4)^5,x]","\frac{10}{13} a^2 c^3 d x^{13}+\frac{10}{9} a^3 c^2 d x^9+\frac{2}{3} a^2 c^3 e x^{15}+\frac{10}{11} a^3 c^2 e x^{11}+a^4 c d x^5+\frac{5}{7} a^4 c e x^7+a^5 d x+\frac{1}{3} a^5 e x^3+\frac{5}{17} a c^4 d x^{17}+\frac{5}{19} a c^4 e x^{19}+\frac{1}{21} c^5 d x^{21}+\frac{1}{23} c^5 e x^{23}","\frac{10}{13} a^2 c^3 d x^{13}+\frac{10}{9} a^3 c^2 d x^9+\frac{2}{3} a^2 c^3 e x^{15}+\frac{10}{11} a^3 c^2 e x^{11}+a^4 c d x^5+\frac{5}{7} a^4 c e x^7+a^5 d x+\frac{1}{3} a^5 e x^3+\frac{5}{17} a c^4 d x^{17}+\frac{5}{19} a c^4 e x^{19}+\frac{1}{21} c^5 d x^{21}+\frac{1}{23} c^5 e x^{23}",1,"a^5*d*x + (a^5*e*x^3)/3 + a^4*c*d*x^5 + (5*a^4*c*e*x^7)/7 + (10*a^3*c^2*d*x^9)/9 + (10*a^3*c^2*e*x^11)/11 + (10*a^2*c^3*d*x^13)/13 + (2*a^2*c^3*e*x^15)/3 + (5*a*c^4*d*x^17)/17 + (5*a*c^4*e*x^19)/19 + (c^5*d*x^21)/21 + (c^5*e*x^23)/23","A",2,1,17,0.05882,1,"{1154}"
5,1,142,0,0.1112886,"\int \frac{\left(d+e x^2\right) \left(a+c x^4\right)^5}{x} \, dx","Int[((d + e*x^2)*(a + c*x^4)^5)/x,x]","\frac{5}{6} a^2 c^3 d x^{12}+\frac{5}{4} a^3 c^2 d x^8+\frac{5}{7} a^2 c^3 e x^{14}+a^3 c^2 e x^{10}+\frac{5}{4} a^4 c d x^4+\frac{5}{6} a^4 c e x^6+a^5 d \log (x)+\frac{1}{2} a^5 e x^2+\frac{5}{16} a c^4 d x^{16}+\frac{5}{18} a c^4 e x^{18}+\frac{1}{20} c^5 d x^{20}+\frac{1}{22} c^5 e x^{22}","\frac{5}{6} a^2 c^3 d x^{12}+\frac{5}{4} a^3 c^2 d x^8+\frac{5}{7} a^2 c^3 e x^{14}+a^3 c^2 e x^{10}+\frac{5}{4} a^4 c d x^4+\frac{5}{6} a^4 c e x^6+a^5 d \log (x)+\frac{1}{2} a^5 e x^2+\frac{5}{16} a c^4 d x^{16}+\frac{5}{18} a c^4 e x^{18}+\frac{1}{20} c^5 d x^{20}+\frac{1}{22} c^5 e x^{22}",1,"(a^5*e*x^2)/2 + (5*a^4*c*d*x^4)/4 + (5*a^4*c*e*x^6)/6 + (5*a^3*c^2*d*x^8)/4 + a^3*c^2*e*x^10 + (5*a^2*c^3*d*x^12)/6 + (5*a^2*c^3*e*x^14)/7 + (5*a*c^4*d*x^16)/16 + (5*a*c^4*e*x^18)/18 + (c^5*d*x^20)/20 + (c^5*e*x^22)/22 + a^5*d*Log[x]","A",3,2,20,0.1000,1,"{1252, 766}"
6,1,139,0,0.081904,"\int \frac{\left(d+e x^2\right) \left(a+c x^4\right)^5}{x^2} \, dx","Int[((d + e*x^2)*(a + c*x^4)^5)/x^2,x]","\frac{10}{11} a^2 c^3 d x^{11}+\frac{10}{7} a^3 c^2 d x^7+\frac{10}{13} a^2 c^3 e x^{13}+\frac{10}{9} a^3 c^2 e x^9+\frac{5}{3} a^4 c d x^3+a^4 c e x^5-\frac{a^5 d}{x}+a^5 e x+\frac{1}{3} a c^4 d x^{15}+\frac{5}{17} a c^4 e x^{17}+\frac{1}{19} c^5 d x^{19}+\frac{1}{21} c^5 e x^{21}","\frac{10}{11} a^2 c^3 d x^{11}+\frac{10}{7} a^3 c^2 d x^7+\frac{10}{13} a^2 c^3 e x^{13}+\frac{10}{9} a^3 c^2 e x^9+\frac{5}{3} a^4 c d x^3+a^4 c e x^5-\frac{a^5 d}{x}+a^5 e x+\frac{1}{3} a c^4 d x^{15}+\frac{5}{17} a c^4 e x^{17}+\frac{1}{19} c^5 d x^{19}+\frac{1}{21} c^5 e x^{21}",1,"-((a^5*d)/x) + a^5*e*x + (5*a^4*c*d*x^3)/3 + a^4*c*e*x^5 + (10*a^3*c^2*d*x^7)/7 + (10*a^3*c^2*e*x^9)/9 + (10*a^2*c^3*d*x^11)/11 + (10*a^2*c^3*e*x^13)/13 + (a*c^4*d*x^15)/3 + (5*a*c^4*e*x^17)/17 + (c^5*d*x^19)/19 + (c^5*e*x^21)/21","A",2,1,20,0.05000,1,"{1262}"
7,1,142,0,0.1212429,"\int \frac{\left(d+e x^2\right) \left(a+c x^4\right)^5}{x^3} \, dx","Int[((d + e*x^2)*(a + c*x^4)^5)/x^3,x]","a^2 c^3 d x^{10}+\frac{5}{3} a^3 c^2 d x^6+\frac{5}{6} a^2 c^3 e x^{12}+\frac{5}{4} a^3 c^2 e x^8+\frac{5}{2} a^4 c d x^2+\frac{5}{4} a^4 c e x^4-\frac{a^5 d}{2 x^2}+a^5 e \log (x)+\frac{5}{14} a c^4 d x^{14}+\frac{5}{16} a c^4 e x^{16}+\frac{1}{18} c^5 d x^{18}+\frac{1}{20} c^5 e x^{20}","a^2 c^3 d x^{10}+\frac{5}{3} a^3 c^2 d x^6+\frac{5}{6} a^2 c^3 e x^{12}+\frac{5}{4} a^3 c^2 e x^8+\frac{5}{2} a^4 c d x^2+\frac{5}{4} a^4 c e x^4-\frac{a^5 d}{2 x^2}+a^5 e \log (x)+\frac{5}{14} a c^4 d x^{14}+\frac{5}{16} a c^4 e x^{16}+\frac{1}{18} c^5 d x^{18}+\frac{1}{20} c^5 e x^{20}",1,"-(a^5*d)/(2*x^2) + (5*a^4*c*d*x^2)/2 + (5*a^4*c*e*x^4)/4 + (5*a^3*c^2*d*x^6)/3 + (5*a^3*c^2*e*x^8)/4 + a^2*c^3*d*x^10 + (5*a^2*c^3*e*x^12)/6 + (5*a*c^4*d*x^14)/14 + (5*a*c^4*e*x^16)/16 + (c^5*d*x^18)/18 + (c^5*e*x^20)/20 + a^5*e*Log[x]","A",3,2,20,0.1000,1,"{1252, 766}"
8,1,67,0,0.0501683,"\int x^5 \left(2+3 x^2\right) \sqrt{5+x^4} \, dx","Int[x^5*(2 + 3*x^2)*Sqrt[5 + x^4],x]","\frac{3}{10} \left(x^4+5\right)^{3/2} x^4-\frac{5}{8} \sqrt{x^4+5} x^2-\frac{1}{4} \left(4-x^2\right) \left(x^4+5\right)^{3/2}-\frac{25}{8} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)","\frac{3}{10} \left(x^4+5\right)^{3/2} x^4-\frac{5}{8} \sqrt{x^4+5} x^2-\frac{1}{4} \left(4-x^2\right) \left(x^4+5\right)^{3/2}-\frac{25}{8} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)",1,"(-5*x^2*Sqrt[5 + x^4])/8 + (3*x^4*(5 + x^4)^(3/2))/10 - ((4 - x^2)*(5 + x^4)^(3/2))/4 - (25*ArcSinh[x^2/Sqrt[5]])/8","A",5,5,20,0.2500,1,"{1252, 833, 780, 195, 215}"
9,1,51,0,0.0307754,"\int x^3 \left(2+3 x^2\right) \sqrt{5+x^4} \, dx","Int[x^3*(2 + 3*x^2)*Sqrt[5 + x^4],x]","-\frac{15}{16} \sqrt{x^4+5} x^2+\frac{1}{24} \left(9 x^2+8\right) \left(x^4+5\right)^{3/2}-\frac{75}{16} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)","-\frac{15}{16} \sqrt{x^4+5} x^2+\frac{1}{24} \left(9 x^2+8\right) \left(x^4+5\right)^{3/2}-\frac{75}{16} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)",1,"(-15*x^2*Sqrt[5 + x^4])/16 + ((8 + 9*x^2)*(5 + x^4)^(3/2))/24 - (75*ArcSinh[x^2/Sqrt[5]])/16","A",4,4,20,0.2000,1,"{1252, 780, 195, 215}"
10,1,44,0,0.0214319,"\int x \left(2+3 x^2\right) \sqrt{5+x^4} \, dx","Int[x*(2 + 3*x^2)*Sqrt[5 + x^4],x]","\frac{1}{2} \sqrt{x^4+5} x^2+\frac{1}{2} \left(x^4+5\right)^{3/2}+\frac{5}{2} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)","\frac{1}{2} \sqrt{x^4+5} x^2+\frac{1}{2} \left(x^4+5\right)^{3/2}+\frac{5}{2} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)",1,"(x^2*Sqrt[5 + x^4])/2 + (5 + x^4)^(3/2)/2 + (5*ArcSinh[x^2/Sqrt[5]])/2","A",4,4,18,0.2222,1,"{1248, 641, 195, 215}"
11,1,58,0,0.05466,"\int \frac{\left(2+3 x^2\right) \sqrt{5+x^4}}{x} \, dx","Int[((2 + 3*x^2)*Sqrt[5 + x^4])/x,x]","\frac{1}{4} \sqrt{x^4+5} \left(3 x^2+4\right)+\frac{15}{4} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)-\sqrt{5} \tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)","\frac{1}{4} \sqrt{x^4+5} \left(3 x^2+4\right)+\frac{15}{4} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)-\sqrt{5} \tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)",1,"((4 + 3*x^2)*Sqrt[5 + x^4])/4 + (15*ArcSinh[x^2/Sqrt[5]])/4 - Sqrt[5]*ArcTanh[Sqrt[5 + x^4]/Sqrt[5]]","A",7,7,20,0.3500,1,"{1252, 815, 844, 215, 266, 63, 207}"
12,1,59,0,0.0557464,"\int \frac{\left(2+3 x^2\right) \sqrt{5+x^4}}{x^3} \, dx","Int[((2 + 3*x^2)*Sqrt[5 + x^4])/x^3,x]","-\frac{\sqrt{x^4+5} \left(2-3 x^2\right)}{2 x^2}+\sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)-\frac{3}{2} \sqrt{5} \tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)","-\frac{\sqrt{x^4+5} \left(2-3 x^2\right)}{2 x^2}+\sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)-\frac{3}{2} \sqrt{5} \tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)",1,"-((2 - 3*x^2)*Sqrt[5 + x^4])/(2*x^2) + ArcSinh[x^2/Sqrt[5]] - (3*Sqrt[5]*ArcTanh[Sqrt[5 + x^4]/Sqrt[5]])/2","A",7,7,20,0.3500,1,"{1252, 813, 844, 215, 266, 63, 207}"
13,1,63,0,0.0548039,"\int \frac{\left(2+3 x^2\right) \sqrt{5+x^4}}{x^5} \, dx","Int[((2 + 3*x^2)*Sqrt[5 + x^4])/x^5,x]","-\frac{\sqrt{x^4+5} \left(3 x^2+1\right)}{2 x^4}+\frac{3}{2} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)}{2 \sqrt{5}}","-\frac{\sqrt{x^4+5} \left(3 x^2+1\right)}{2 x^4}+\frac{3}{2} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)}{2 \sqrt{5}}",1,"-((1 + 3*x^2)*Sqrt[5 + x^4])/(2*x^4) + (3*ArcSinh[x^2/Sqrt[5]])/2 - ArcTanh[Sqrt[5 + x^4]/Sqrt[5]]/(2*Sqrt[5])","A",7,7,20,0.3500,1,"{1252, 811, 844, 215, 266, 63, 207}"
14,1,58,0,0.0466886,"\int \frac{\left(2+3 x^2\right) \sqrt{5+x^4}}{x^7} \, dx","Int[((2 + 3*x^2)*Sqrt[5 + x^4])/x^7,x]","-\frac{\left(x^4+5\right)^{3/2}}{15 x^6}-\frac{3 \sqrt{x^4+5}}{4 x^4}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)}{4 \sqrt{5}}","-\frac{\left(x^4+5\right)^{3/2}}{15 x^6}-\frac{3 \sqrt{x^4+5}}{4 x^4}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)}{4 \sqrt{5}}",1,"(-3*Sqrt[5 + x^4])/(4*x^4) - (5 + x^4)^(3/2)/(15*x^6) - (3*ArcTanh[Sqrt[5 + x^4]/Sqrt[5]])/(4*Sqrt[5])","A",6,6,20,0.3000,1,"{1252, 807, 266, 47, 63, 207}"
15,1,208,0,0.1241845,"\int x^4 \left(2+3 x^2\right) \sqrt{5+x^4} \, dx","Int[x^4*(2 + 3*x^2)*Sqrt[5 + x^4],x]","\frac{1}{21} \left(7 x^2+6\right) \sqrt{x^4+5} x^5+\frac{2}{3} \sqrt{x^4+5} x^3-\frac{10 \sqrt{x^4+5} x}{x^2+\sqrt{5}}+\frac{20}{21} \sqrt{x^4+5} x-\frac{5 \sqrt[4]{5} \left(21+2 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{21 \sqrt{x^4+5}}+\frac{10 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}","\frac{1}{21} \left(7 x^2+6\right) \sqrt{x^4+5} x^5+\frac{2}{3} \sqrt{x^4+5} x^3-\frac{10 \sqrt{x^4+5} x}{x^2+\sqrt{5}}+\frac{20}{21} \sqrt{x^4+5} x-\frac{5 \sqrt[4]{5} \left(21+2 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{21 \sqrt{x^4+5}}+\frac{10 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}",1,"(20*x*Sqrt[5 + x^4])/21 + (2*x^3*Sqrt[5 + x^4])/3 - (10*x*Sqrt[5 + x^4])/(Sqrt[5] + x^2) + (x^5*(6 + 7*x^2)*Sqrt[5 + x^4])/21 + (10*5^(1/4)*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticE[2*ArcTan[x/5^(1/4)], 1/2])/Sqrt[5 + x^4] - (5*5^(1/4)*(21 + 2*Sqrt[5])*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticF[2*ArcTan[x/5^(1/4)], 1/2])/(21*Sqrt[5 + x^4])","A",6,5,20,0.2500,1,"{1274, 1280, 1198, 220, 1196}"
16,1,192,0,0.096707,"\int x^2 \left(2+3 x^2\right) \sqrt{5+x^4} \, dx","Int[x^2*(2 + 3*x^2)*Sqrt[5 + x^4],x]","\frac{1}{35} \left(15 x^2+14\right) \sqrt{x^4+5} x^3+\frac{4 \sqrt{x^4+5} x}{x^2+\sqrt{5}}+\frac{10}{7} \sqrt{x^4+5} x+\frac{\sqrt[4]{5} \left(14-5 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{7 \sqrt{x^4+5}}-\frac{4 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}","\frac{1}{35} \left(15 x^2+14\right) \sqrt{x^4+5} x^3+\frac{4 \sqrt{x^4+5} x}{x^2+\sqrt{5}}+\frac{10}{7} \sqrt{x^4+5} x+\frac{\sqrt[4]{5} \left(14-5 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{7 \sqrt{x^4+5}}-\frac{4 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}",1,"(10*x*Sqrt[5 + x^4])/7 + (4*x*Sqrt[5 + x^4])/(Sqrt[5] + x^2) + (x^3*(14 + 15*x^2)*Sqrt[5 + x^4])/35 - (4*5^(1/4)*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticE[2*ArcTan[x/5^(1/4)], 1/2])/Sqrt[5 + x^4] + (5^(1/4)*(14 - 5*Sqrt[5])*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticF[2*ArcTan[x/5^(1/4)], 1/2])/(7*Sqrt[5 + x^4])","A",5,5,20,0.2500,1,"{1274, 1280, 1198, 220, 1196}"
17,1,176,0,0.0635536,"\int \left(2+3 x^2\right) \sqrt{5+x^4} \, dx","Int[(2 + 3*x^2)*Sqrt[5 + x^4],x]","\frac{1}{15} \left(9 x^2+10\right) \sqrt{x^4+5} x+\frac{6 \sqrt{x^4+5} x}{x^2+\sqrt{5}}+\frac{\sqrt[4]{5} \left(9+2 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{3 \sqrt{x^4+5}}-\frac{6 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}","\frac{1}{15} \left(9 x^2+10\right) \sqrt{x^4+5} x+\frac{6 \sqrt{x^4+5} x}{x^2+\sqrt{5}}+\frac{\sqrt[4]{5} \left(9+2 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{3 \sqrt{x^4+5}}-\frac{6 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}",1,"(6*x*Sqrt[5 + x^4])/(Sqrt[5] + x^2) + (x*(10 + 9*x^2)*Sqrt[5 + x^4])/15 - (6*5^(1/4)*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticE[2*ArcTan[x/5^(1/4)], 1/2])/Sqrt[5 + x^4] + (5^(1/4)*(9 + 2*Sqrt[5])*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticF[2*ArcTan[x/5^(1/4)], 1/2])/(3*Sqrt[5 + x^4])","A",4,4,17,0.2353,1,"{1177, 1198, 220, 1196}"
18,1,171,0,0.0670011,"\int \frac{\left(2+3 x^2\right) \sqrt{5+x^4}}{x^2} \, dx","Int[((2 + 3*x^2)*Sqrt[5 + x^4])/x^2,x]","\frac{4 \sqrt{x^4+5} x}{x^2+\sqrt{5}}-\frac{\left(2-x^2\right) \sqrt{x^4+5}}{x}+\frac{\sqrt[4]{5} \left(2+\sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}-\frac{4 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}","\frac{4 \sqrt{x^4+5} x}{x^2+\sqrt{5}}-\frac{\left(2-x^2\right) \sqrt{x^4+5}}{x}+\frac{\sqrt[4]{5} \left(2+\sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}-\frac{4 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}",1,"-(((2 - x^2)*Sqrt[5 + x^4])/x) + (4*x*Sqrt[5 + x^4])/(Sqrt[5] + x^2) - (4*5^(1/4)*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticE[2*ArcTan[x/5^(1/4)], 1/2])/Sqrt[5 + x^4] + (5^(1/4)*(2 + Sqrt[5])*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticF[2*ArcTan[x/5^(1/4)], 1/2])/Sqrt[5 + x^4]","A",4,4,20,0.2000,1,"{1272, 1198, 220, 1196}"
19,1,192,0,0.0893237,"\int \frac{\left(2+3 x^2\right) \sqrt{5+x^4}}{x^4} \, dx","Int[((2 + 3*x^2)*Sqrt[5 + x^4])/x^4,x]","\frac{6 \sqrt{x^4+5} x}{x^2+\sqrt{5}}-\frac{6 \sqrt{x^4+5}}{x}-\frac{\left(2-9 x^2\right) \sqrt{x^4+5}}{3 x^3}+\frac{\left(2+9 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{5} \sqrt{x^4+5}}-\frac{6 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}","\frac{6 \sqrt{x^4+5} x}{x^2+\sqrt{5}}-\frac{6 \sqrt{x^4+5}}{x}-\frac{\left(2-9 x^2\right) \sqrt{x^4+5}}{3 x^3}+\frac{\left(2+9 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{5} \sqrt{x^4+5}}-\frac{6 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}",1,"(-6*Sqrt[5 + x^4])/x - ((2 - 9*x^2)*Sqrt[5 + x^4])/(3*x^3) + (6*x*Sqrt[5 + x^4])/(Sqrt[5] + x^2) - (6*5^(1/4)*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticE[2*ArcTan[x/5^(1/4)], 1/2])/Sqrt[5 + x^4] + ((2 + 9*Sqrt[5])*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticF[2*ArcTan[x/5^(1/4)], 1/2])/(3*5^(1/4)*Sqrt[5 + x^4])","A",5,5,20,0.2500,1,"{1272, 1282, 1198, 220, 1196}"
20,1,83,0,0.0588598,"\int x^5 \left(2+3 x^2\right) \left(5+x^4\right)^{3/2} \, dx","Int[x^5*(2 + 3*x^2)*(5 + x^4)^(3/2),x]","\frac{3}{14} \left(x^4+5\right)^{5/2} x^4-\frac{5}{24} \left(x^4+5\right)^{3/2} x^2-\frac{25}{16} \sqrt{x^4+5} x^2-\frac{1}{42} \left(18-7 x^2\right) \left(x^4+5\right)^{5/2}-\frac{125}{16} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)","\frac{3}{14} \left(x^4+5\right)^{5/2} x^4-\frac{5}{24} \left(x^4+5\right)^{3/2} x^2-\frac{25}{16} \sqrt{x^4+5} x^2-\frac{1}{42} \left(18-7 x^2\right) \left(x^4+5\right)^{5/2}-\frac{125}{16} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)",1,"(-25*x^2*Sqrt[5 + x^4])/16 - (5*x^2*(5 + x^4)^(3/2))/24 + (3*x^4*(5 + x^4)^(5/2))/14 - ((18 - 7*x^2)*(5 + x^4)^(5/2))/42 - (125*ArcSinh[x^2/Sqrt[5]])/16","A",6,5,20,0.2500,1,"{1252, 833, 780, 195, 215}"
21,1,67,0,0.039551,"\int x^3 \left(2+3 x^2\right) \left(5+x^4\right)^{3/2} \, dx","Int[x^3*(2 + 3*x^2)*(5 + x^4)^(3/2),x]","\frac{1}{20} \left(5 x^2+4\right) \left(x^4+5\right)^{5/2}-\frac{5}{16} x^2 \left(x^4+5\right)^{3/2}-\frac{75}{32} x^2 \sqrt{x^4+5}-\frac{375}{32} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)","\frac{1}{20} \left(5 x^2+4\right) \left(x^4+5\right)^{5/2}-\frac{5}{16} x^2 \left(x^4+5\right)^{3/2}-\frac{75}{32} x^2 \sqrt{x^4+5}-\frac{375}{32} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)",1,"(-75*x^2*Sqrt[5 + x^4])/32 - (5*x^2*(5 + x^4)^(3/2))/16 + ((4 + 5*x^2)*(5 + x^4)^(5/2))/20 - (375*ArcSinh[x^2/Sqrt[5]])/32","A",5,4,20,0.2000,1,"{1252, 780, 195, 215}"
22,1,60,0,0.030477,"\int x \left(2+3 x^2\right) \left(5+x^4\right)^{3/2} \, dx","Int[x*(2 + 3*x^2)*(5 + x^4)^(3/2),x]","\frac{3}{10} \left(x^4+5\right)^{5/2}+\frac{1}{4} x^2 \left(x^4+5\right)^{3/2}+\frac{15}{8} x^2 \sqrt{x^4+5}+\frac{75}{8} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)","\frac{3}{10} \left(x^4+5\right)^{5/2}+\frac{1}{4} x^2 \left(x^4+5\right)^{3/2}+\frac{15}{8} x^2 \sqrt{x^4+5}+\frac{75}{8} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)",1,"(15*x^2*Sqrt[5 + x^4])/8 + (x^2*(5 + x^4)^(3/2))/4 + (3*(5 + x^4)^(5/2))/10 + (75*ArcSinh[x^2/Sqrt[5]])/8","A",5,4,18,0.2222,1,"{1248, 641, 195, 215}"
23,1,78,0,0.0746282,"\int \frac{\left(2+3 x^2\right) \left(5+x^4\right)^{3/2}}{x} \, dx","Int[((2 + 3*x^2)*(5 + x^4)^(3/2))/x,x]","\frac{1}{24} \left(9 x^2+8\right) \left(x^4+5\right)^{3/2}+\frac{5}{16} \left(9 x^2+16\right) \sqrt{x^4+5}+\frac{225}{16} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)-5 \sqrt{5} \tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)","\frac{1}{24} \left(9 x^2+8\right) \left(x^4+5\right)^{3/2}+\frac{5}{16} \left(9 x^2+16\right) \sqrt{x^4+5}+\frac{225}{16} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)-5 \sqrt{5} \tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)",1,"(5*(16 + 9*x^2)*Sqrt[5 + x^4])/16 + ((8 + 9*x^2)*(5 + x^4)^(3/2))/24 + (225*ArcSinh[x^2/Sqrt[5]])/16 - 5*Sqrt[5]*ArcTanh[Sqrt[5 + x^4]/Sqrt[5]]","A",8,7,20,0.3500,1,"{1252, 815, 844, 215, 266, 63, 207}"
24,1,81,0,0.0748548,"\int \frac{\left(2+3 x^2\right) \left(5+x^4\right)^{3/2}}{x^3} \, dx","Int[((2 + 3*x^2)*(5 + x^4)^(3/2))/x^3,x]","-\frac{\left(2-x^2\right) \left(x^4+5\right)^{3/2}}{2 x^2}+\frac{3}{2} \left(x^2+5\right) \sqrt{x^4+5}+\frac{15}{2} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)-\frac{15}{2} \sqrt{5} \tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)","-\frac{\left(2-x^2\right) \left(x^4+5\right)^{3/2}}{2 x^2}+\frac{3}{2} \left(x^2+5\right) \sqrt{x^4+5}+\frac{15}{2} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)-\frac{15}{2} \sqrt{5} \tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)",1,"(3*(5 + x^2)*Sqrt[5 + x^4])/2 - ((2 - x^2)*(5 + x^4)^(3/2))/(2*x^2) + (15*ArcSinh[x^2/Sqrt[5]])/2 - (15*Sqrt[5]*ArcTanh[Sqrt[5 + x^4]/Sqrt[5]])/2","A",8,8,20,0.4000,1,"{1252, 813, 815, 844, 215, 266, 63, 207}"
25,1,86,0,0.0773522,"\int \frac{\left(2+3 x^2\right) \left(5+x^4\right)^{3/2}}{x^5} \, dx","Int[((2 + 3*x^2)*(5 + x^4)^(3/2))/x^5,x]","-\frac{\left(2-3 x^2\right) \left(x^4+5\right)^{3/2}}{4 x^4}-\frac{3 \left(15-2 x^2\right) \sqrt{x^4+5}}{4 x^2}+\frac{45}{4} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)-\frac{3}{2} \sqrt{5} \tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)","-\frac{\left(2-3 x^2\right) \left(x^4+5\right)^{3/2}}{4 x^4}-\frac{3 \left(15-2 x^2\right) \sqrt{x^4+5}}{4 x^2}+\frac{45}{4} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)-\frac{3}{2} \sqrt{5} \tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)",1,"(-3*(15 - 2*x^2)*Sqrt[5 + x^4])/(4*x^2) - ((2 - 3*x^2)*(5 + x^4)^(3/2))/(4*x^4) + (45*ArcSinh[x^2/Sqrt[5]])/4 - (3*Sqrt[5]*ArcTanh[Sqrt[5 + x^4]/Sqrt[5]])/2","A",8,7,20,0.3500,1,"{1252, 813, 844, 215, 266, 63, 207}"
26,1,82,0,0.0749648,"\int \frac{\left(2+3 x^2\right) \left(5+x^4\right)^{3/2}}{x^7} \, dx","Int[((2 + 3*x^2)*(5 + x^4)^(3/2))/x^7,x]","-\frac{\left(9 x^2+4\right) \left(x^4+5\right)^{3/2}}{12 x^6}-\frac{\left(4-9 x^2\right) \sqrt{x^4+5}}{4 x^2}+\sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)-\frac{9}{4} \sqrt{5} \tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)","-\frac{\left(9 x^2+4\right) \left(x^4+5\right)^{3/2}}{12 x^6}-\frac{\left(4-9 x^2\right) \sqrt{x^4+5}}{4 x^2}+\sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)-\frac{9}{4} \sqrt{5} \tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)",1,"-((4 - 9*x^2)*Sqrt[5 + x^4])/(4*x^2) - ((4 + 9*x^2)*(5 + x^4)^(3/2))/(12*x^6) + ArcSinh[x^2/Sqrt[5]] - (9*Sqrt[5]*ArcTanh[Sqrt[5 + x^4]/Sqrt[5]])/4","A",8,8,20,0.4000,1,"{1252, 811, 813, 844, 215, 266, 63, 207}"
27,1,235,0,0.1344442,"\int x^4 \left(2+3 x^2\right) \left(5+x^4\right)^{3/2} \, dx","Int[x^4*(2 + 3*x^2)*(5 + x^4)^(3/2),x]","\frac{1}{143} \left(33 x^2+26\right) \left(x^4+5\right)^{3/2} x^5+\frac{10 \left(77 x^2+78\right) \sqrt{x^4+5} x^5}{1001}+\frac{20}{13} \sqrt{x^4+5} x^3-\frac{300 \sqrt{x^4+5} x}{13 \left(x^2+\sqrt{5}\right)}+\frac{200}{77} \sqrt{x^4+5} x-\frac{50 \sqrt[4]{5} \left(231+26 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{1001 \sqrt{x^4+5}}+\frac{300 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{13 \sqrt{x^4+5}}","\frac{1}{143} \left(33 x^2+26\right) \left(x^4+5\right)^{3/2} x^5+\frac{10 \left(77 x^2+78\right) \sqrt{x^4+5} x^5}{1001}+\frac{20}{13} \sqrt{x^4+5} x^3-\frac{300 \sqrt{x^4+5} x}{13 \left(x^2+\sqrt{5}\right)}+\frac{200}{77} \sqrt{x^4+5} x-\frac{50 \sqrt[4]{5} \left(231+26 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{1001 \sqrt{x^4+5}}+\frac{300 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{13 \sqrt{x^4+5}}",1,"(200*x*Sqrt[5 + x^4])/77 + (20*x^3*Sqrt[5 + x^4])/13 - (300*x*Sqrt[5 + x^4])/(13*(Sqrt[5] + x^2)) + (10*x^5*(78 + 77*x^2)*Sqrt[5 + x^4])/1001 + (x^5*(26 + 33*x^2)*(5 + x^4)^(3/2))/143 + (300*5^(1/4)*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticE[2*ArcTan[x/5^(1/4)], 1/2])/(13*Sqrt[5 + x^4]) - (50*5^(1/4)*(231 + 26*Sqrt[5])*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticF[2*ArcTan[x/5^(1/4)], 1/2])/(1001*Sqrt[5 + x^4])","A",7,5,20,0.2500,1,"{1274, 1280, 1198, 220, 1196}"
28,1,219,0,0.1198781,"\int x^2 \left(2+3 x^2\right) \left(5+x^4\right)^{3/2} \, dx","Int[x^2*(2 + 3*x^2)*(5 + x^4)^(3/2),x]","\frac{1}{99} \left(27 x^2+22\right) \left(x^4+5\right)^{3/2} x^3+\frac{2}{231} \left(135 x^2+154\right) \sqrt{x^4+5} x^3+\frac{40 \sqrt{x^4+5} x}{3 \left(x^2+\sqrt{5}\right)}+\frac{300}{77} \sqrt{x^4+5} x+\frac{10 \sqrt[4]{5} \left(154-45 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{231 \sqrt{x^4+5}}-\frac{40 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{3 \sqrt{x^4+5}}","\frac{1}{99} \left(27 x^2+22\right) \left(x^4+5\right)^{3/2} x^3+\frac{2}{231} \left(135 x^2+154\right) \sqrt{x^4+5} x^3+\frac{40 \sqrt{x^4+5} x}{3 \left(x^2+\sqrt{5}\right)}+\frac{300}{77} \sqrt{x^4+5} x+\frac{10 \sqrt[4]{5} \left(154-45 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{231 \sqrt{x^4+5}}-\frac{40 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{3 \sqrt{x^4+5}}",1,"(300*x*Sqrt[5 + x^4])/77 + (40*x*Sqrt[5 + x^4])/(3*(Sqrt[5] + x^2)) + (2*x^3*(154 + 135*x^2)*Sqrt[5 + x^4])/231 + (x^3*(22 + 27*x^2)*(5 + x^4)^(3/2))/99 - (40*5^(1/4)*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticE[2*ArcTan[x/5^(1/4)], 1/2])/(3*Sqrt[5 + x^4]) + (10*5^(1/4)*(154 - 45*Sqrt[5])*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticF[2*ArcTan[x/5^(1/4)], 1/2])/(231*Sqrt[5 + x^4])","A",6,5,20,0.2500,1,"{1274, 1280, 1198, 220, 1196}"
29,1,197,0,0.0817294,"\int \left(2+3 x^2\right) \left(5+x^4\right)^{3/2} \, dx","Int[(2 + 3*x^2)*(5 + x^4)^(3/2),x]","\frac{1}{21} x \left(7 x^2+6\right) \left(x^4+5\right)^{3/2}+\frac{2}{7} x \left(7 x^2+10\right) \sqrt{x^4+5}+\frac{20 x \sqrt{x^4+5}}{x^2+\sqrt{5}}+\frac{10 \sqrt[4]{5} \left(7+2 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{7 \sqrt{x^4+5}}-\frac{20 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}","\frac{1}{21} x \left(7 x^2+6\right) \left(x^4+5\right)^{3/2}+\frac{2}{7} x \left(7 x^2+10\right) \sqrt{x^4+5}+\frac{20 x \sqrt{x^4+5}}{x^2+\sqrt{5}}+\frac{10 \sqrt[4]{5} \left(7+2 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{7 \sqrt{x^4+5}}-\frac{20 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}",1,"(20*x*Sqrt[5 + x^4])/(Sqrt[5] + x^2) + (2*x*(10 + 7*x^2)*Sqrt[5 + x^4])/7 + (x*(6 + 7*x^2)*(5 + x^4)^(3/2))/21 - (20*5^(1/4)*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticE[2*ArcTan[x/5^(1/4)], 1/2])/Sqrt[5 + x^4] + (10*5^(1/4)*(7 + 2*Sqrt[5])*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticF[2*ArcTan[x/5^(1/4)], 1/2])/(7*Sqrt[5 + x^4])","A",5,4,17,0.2353,1,"{1177, 1198, 220, 1196}"
30,1,199,0,0.0883871,"\int \frac{\left(2+3 x^2\right) \left(5+x^4\right)^{3/2}}{x^2} \, dx","Int[((2 + 3*x^2)*(5 + x^4)^(3/2))/x^2,x]","-\frac{\left(14-3 x^2\right) \left(x^4+5\right)^{3/2}}{7 x}+\frac{6}{35} x \left(14 x^2+25\right) \sqrt{x^4+5}+\frac{24 x \sqrt{x^4+5}}{x^2+\sqrt{5}}+\frac{6 \sqrt[4]{5} \left(14+5 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{7 \sqrt{x^4+5}}-\frac{24 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}","-\frac{\left(14-3 x^2\right) \left(x^4+5\right)^{3/2}}{7 x}+\frac{6}{35} x \left(14 x^2+25\right) \sqrt{x^4+5}+\frac{24 x \sqrt{x^4+5}}{x^2+\sqrt{5}}+\frac{6 \sqrt[4]{5} \left(14+5 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{7 \sqrt{x^4+5}}-\frac{24 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}",1,"(24*x*Sqrt[5 + x^4])/(Sqrt[5] + x^2) + (6*x*(25 + 14*x^2)*Sqrt[5 + x^4])/35 - ((14 - 3*x^2)*(5 + x^4)^(3/2))/(7*x) - (24*5^(1/4)*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticE[2*ArcTan[x/5^(1/4)], 1/2])/Sqrt[5 + x^4] + (6*5^(1/4)*(14 + 5*Sqrt[5])*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticF[2*ArcTan[x/5^(1/4)], 1/2])/(7*Sqrt[5 + x^4])","A",5,5,20,0.2500,1,"{1272, 1177, 1198, 220, 1196}"
31,1,201,0,0.0859568,"\int \frac{\left(2+3 x^2\right) \left(5+x^4\right)^{3/2}}{x^4} \, dx","Int[((2 + 3*x^2)*(5 + x^4)^(3/2))/x^4,x]","-\frac{\left(10-9 x^2\right) \left(x^4+5\right)^{3/2}}{15 x^3}-\frac{2 \left(27-2 x^2\right) \sqrt{x^4+5}}{3 x}+\frac{36 x \sqrt{x^4+5}}{x^2+\sqrt{5}}+\frac{2 \sqrt[4]{5} \left(27+2 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{3 \sqrt{x^4+5}}-\frac{36 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}","-\frac{\left(10-9 x^2\right) \left(x^4+5\right)^{3/2}}{15 x^3}-\frac{2 \left(27-2 x^2\right) \sqrt{x^4+5}}{3 x}+\frac{36 x \sqrt{x^4+5}}{x^2+\sqrt{5}}+\frac{2 \sqrt[4]{5} \left(27+2 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{3 \sqrt{x^4+5}}-\frac{36 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}",1,"(-2*(27 - 2*x^2)*Sqrt[5 + x^4])/(3*x) + (36*x*Sqrt[5 + x^4])/(Sqrt[5] + x^2) - ((10 - 9*x^2)*(5 + x^4)^(3/2))/(15*x^3) - (36*5^(1/4)*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticE[2*ArcTan[x/5^(1/4)], 1/2])/Sqrt[5 + x^4] + (2*5^(1/4)*(27 + 2*Sqrt[5])*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticF[2*ArcTan[x/5^(1/4)], 1/2])/(3*Sqrt[5 + x^4])","A",5,4,20,0.2000,1,"{1272, 1198, 220, 1196}"
32,1,67,0,0.0575545,"\int \frac{x^7 \left(2+3 x^2\right)}{\sqrt{5+x^4}} \, dx","Int[(x^7*(2 + 3*x^2))/Sqrt[5 + x^4],x]","\frac{3}{8} \sqrt{x^4+5} x^6+\frac{1}{3} \sqrt{x^4+5} x^4-\frac{5}{48} \left(27 x^2+32\right) \sqrt{x^4+5}+\frac{225}{16} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)","\frac{3}{8} \sqrt{x^4+5} x^6+\frac{1}{3} \sqrt{x^4+5} x^4-\frac{5}{48} \left(27 x^2+32\right) \sqrt{x^4+5}+\frac{225}{16} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)",1,"(x^4*Sqrt[5 + x^4])/3 + (3*x^6*Sqrt[5 + x^4])/8 - (5*(32 + 27*x^2)*Sqrt[5 + x^4])/48 + (225*ArcSinh[x^2/Sqrt[5]])/16","A",5,4,20,0.2000,1,"{1252, 833, 780, 215}"
33,1,51,0,0.0417361,"\int \frac{x^5 \left(2+3 x^2\right)}{\sqrt{5+x^4}} \, dx","Int[(x^5*(2 + 3*x^2))/Sqrt[5 + x^4],x]","\frac{1}{2} \sqrt{x^4+5} x^4-\frac{1}{2} \left(10-x^2\right) \sqrt{x^4+5}-\frac{5}{2} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)","\frac{1}{2} \sqrt{x^4+5} x^4-\frac{1}{2} \left(10-x^2\right) \sqrt{x^4+5}-\frac{5}{2} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)",1,"(x^4*Sqrt[5 + x^4])/2 - ((10 - x^2)*Sqrt[5 + x^4])/2 - (5*ArcSinh[x^2/Sqrt[5]])/2","A",4,4,20,0.2000,1,"{1252, 833, 780, 215}"
34,1,35,0,0.0258202,"\int \frac{x^3 \left(2+3 x^2\right)}{\sqrt{5+x^4}} \, dx","Int[(x^3*(2 + 3*x^2))/Sqrt[5 + x^4],x]","\frac{1}{4} \left(3 x^2+4\right) \sqrt{x^4+5}-\frac{15}{4} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)","\frac{1}{4} \left(3 x^2+4\right) \sqrt{x^4+5}-\frac{15}{4} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)",1,"((4 + 3*x^2)*Sqrt[5 + x^4])/4 - (15*ArcSinh[x^2/Sqrt[5]])/4","A",3,3,20,0.1500,1,"{1252, 780, 215}"
35,1,24,0,0.0168086,"\int \frac{x \left(2+3 x^2\right)}{\sqrt{5+x^4}} \, dx","Int[(x*(2 + 3*x^2))/Sqrt[5 + x^4],x]","\frac{3 \sqrt{x^4+5}}{2}+\sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)","\frac{3 \sqrt{x^4+5}}{2}+\sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)",1,"(3*Sqrt[5 + x^4])/2 + ArcSinh[x^2/Sqrt[5]]","A",3,3,18,0.1667,1,"{1248, 641, 215}"
36,1,38,0,0.0382031,"\int \frac{2+3 x^2}{x \sqrt{5+x^4}} \, dx","Int[(2 + 3*x^2)/(x*Sqrt[5 + x^4]),x]","\frac{3}{2} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)}{\sqrt{5}}","\frac{3}{2} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)}{\sqrt{5}}",1,"(3*ArcSinh[x^2/Sqrt[5]])/2 - ArcTanh[Sqrt[5 + x^4]/Sqrt[5]]/Sqrt[5]","A",6,6,20,0.3000,1,"{1252, 844, 215, 266, 63, 207}"
37,1,42,0,0.0372282,"\int \frac{2+3 x^2}{x^3 \sqrt{5+x^4}} \, dx","Int[(2 + 3*x^2)/(x^3*Sqrt[5 + x^4]),x]","-\frac{\sqrt{x^4+5}}{5 x^2}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)}{2 \sqrt{5}}","-\frac{\sqrt{x^4+5}}{5 x^2}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)}{2 \sqrt{5}}",1,"-Sqrt[5 + x^4]/(5*x^2) - (3*ArcTanh[Sqrt[5 + x^4]/Sqrt[5]])/(2*Sqrt[5])","A",5,5,20,0.2500,1,"{1252, 807, 266, 63, 207}"
38,1,58,0,0.0512227,"\int \frac{2+3 x^2}{x^5 \sqrt{5+x^4}} \, dx","Int[(2 + 3*x^2)/(x^5*Sqrt[5 + x^4]),x]","-\frac{3 \sqrt{x^4+5}}{10 x^2}-\frac{\sqrt{x^4+5}}{10 x^4}+\frac{\tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)}{10 \sqrt{5}}","-\frac{3 \sqrt{x^4+5}}{10 x^2}-\frac{\sqrt{x^4+5}}{10 x^4}+\frac{\tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)}{10 \sqrt{5}}",1,"-Sqrt[5 + x^4]/(10*x^4) - (3*Sqrt[5 + x^4])/(10*x^2) + ArcTanh[Sqrt[5 + x^4]/Sqrt[5]]/(10*Sqrt[5])","A",6,6,20,0.3000,1,"{1252, 835, 807, 266, 63, 207}"
39,1,185,0,0.0850326,"\int \frac{x^4 \left(2+3 x^2\right)}{\sqrt{5+x^4}} \, dx","Int[(x^4*(2 + 3*x^2))/Sqrt[5 + x^4],x]","\frac{3}{5} \sqrt{x^4+5} x^3-\frac{9 \sqrt{x^4+5} x}{x^2+\sqrt{5}}+\frac{2}{3} \sqrt{x^4+5} x-\frac{\sqrt[4]{5} \left(27+2 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{6 \sqrt{x^4+5}}+\frac{9 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}","\frac{3}{5} \sqrt{x^4+5} x^3-\frac{9 \sqrt{x^4+5} x}{x^2+\sqrt{5}}+\frac{2}{3} \sqrt{x^4+5} x-\frac{\sqrt[4]{5} \left(27+2 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{6 \sqrt{x^4+5}}+\frac{9 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}",1,"(2*x*Sqrt[5 + x^4])/3 + (3*x^3*Sqrt[5 + x^4])/5 - (9*x*Sqrt[5 + x^4])/(Sqrt[5] + x^2) + (9*5^(1/4)*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticE[2*ArcTan[x/5^(1/4)], 1/2])/Sqrt[5 + x^4] - (5^(1/4)*(27 + 2*Sqrt[5])*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticF[2*ArcTan[x/5^(1/4)], 1/2])/(6*Sqrt[5 + x^4])","A",5,4,20,0.2000,1,"{1280, 1198, 220, 1196}"
40,1,166,0,0.0663092,"\int \frac{x^2 \left(2+3 x^2\right)}{\sqrt{5+x^4}} \, dx","Int[(x^2*(2 + 3*x^2))/Sqrt[5 + x^4],x]","\frac{2 \sqrt{x^4+5} x}{x^2+\sqrt{5}}+\sqrt{x^4+5} x+\frac{\sqrt[4]{5} \left(2-\sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{2 \sqrt{x^4+5}}-\frac{2 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}","\frac{2 \sqrt{x^4+5} x}{x^2+\sqrt{5}}+\sqrt{x^4+5} x+\frac{\sqrt[4]{5} \left(2-\sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{2 \sqrt{x^4+5}}-\frac{2 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}",1,"x*Sqrt[5 + x^4] + (2*x*Sqrt[5 + x^4])/(Sqrt[5] + x^2) - (2*5^(1/4)*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticE[2*ArcTan[x/5^(1/4)], 1/2])/Sqrt[5 + x^4] + (5^(1/4)*(2 - Sqrt[5])*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticF[2*ArcTan[x/5^(1/4)], 1/2])/(2*Sqrt[5 + x^4])","A",4,4,20,0.2000,1,"{1280, 1198, 220, 1196}"
41,1,155,0,0.0455755,"\int \frac{2+3 x^2}{\sqrt{5+x^4}} \, dx","Int[(2 + 3*x^2)/Sqrt[5 + x^4],x]","\frac{3 \sqrt{x^4+5} x}{x^2+\sqrt{5}}+\frac{\left(2+3 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{5} \sqrt{x^4+5}}-\frac{3 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}","\frac{3 \sqrt{x^4+5} x}{x^2+\sqrt{5}}+\frac{\left(2+3 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{5} \sqrt{x^4+5}}-\frac{3 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{\sqrt{x^4+5}}",1,"(3*x*Sqrt[5 + x^4])/(Sqrt[5] + x^2) - (3*5^(1/4)*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticE[2*ArcTan[x/5^(1/4)], 1/2])/Sqrt[5 + x^4] + ((2 + 3*Sqrt[5])*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticF[2*ArcTan[x/5^(1/4)], 1/2])/(2*5^(1/4)*Sqrt[5 + x^4])","A",3,3,17,0.1765,1,"{1198, 220, 1196}"
42,1,173,0,0.062236,"\int \frac{2+3 x^2}{x^2 \sqrt{5+x^4}} \, dx","Int[(2 + 3*x^2)/(x^2*Sqrt[5 + x^4]),x]","\frac{2 \sqrt{x^4+5} x}{5 \left(x^2+\sqrt{5}\right)}-\frac{2 \sqrt{x^4+5}}{5 x}+\frac{\left(2+3 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{2\ 5^{3/4} \sqrt{x^4+5}}-\frac{2 \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{5^{3/4} \sqrt{x^4+5}}","\frac{2 \sqrt{x^4+5} x}{5 \left(x^2+\sqrt{5}\right)}-\frac{2 \sqrt{x^4+5}}{5 x}+\frac{\left(2+3 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{2\ 5^{3/4} \sqrt{x^4+5}}-\frac{2 \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{5^{3/4} \sqrt{x^4+5}}",1,"(-2*Sqrt[5 + x^4])/(5*x) + (2*x*Sqrt[5 + x^4])/(5*(Sqrt[5] + x^2)) - (2*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticE[2*ArcTan[x/5^(1/4)], 1/2])/(5^(3/4)*Sqrt[5 + x^4]) + ((2 + 3*Sqrt[5])*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticF[2*ArcTan[x/5^(1/4)], 1/2])/(2*5^(3/4)*Sqrt[5 + x^4])","A",4,4,20,0.2000,1,"{1282, 1198, 220, 1196}"
43,1,189,0,0.0860867,"\int \frac{2+3 x^2}{x^4 \sqrt{5+x^4}} \, dx","Int[(2 + 3*x^2)/(x^4*Sqrt[5 + x^4]),x]","\frac{3 \sqrt{x^4+5} x}{5 \left(x^2+\sqrt{5}\right)}-\frac{3 \sqrt{x^4+5}}{5 x}-\frac{2 \sqrt{x^4+5}}{15 x^3}-\frac{\left(2-9 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{30 \sqrt[4]{5} \sqrt{x^4+5}}-\frac{3 \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{5^{3/4} \sqrt{x^4+5}}","\frac{3 \sqrt{x^4+5} x}{5 \left(x^2+\sqrt{5}\right)}-\frac{3 \sqrt{x^4+5}}{5 x}-\frac{2 \sqrt{x^4+5}}{15 x^3}-\frac{\left(2-9 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{30 \sqrt[4]{5} \sqrt{x^4+5}}-\frac{3 \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{5^{3/4} \sqrt{x^4+5}}",1,"(-2*Sqrt[5 + x^4])/(15*x^3) - (3*Sqrt[5 + x^4])/(5*x) + (3*x*Sqrt[5 + x^4])/(5*(Sqrt[5] + x^2)) - (3*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticE[2*ArcTan[x/5^(1/4)], 1/2])/(5^(3/4)*Sqrt[5 + x^4]) - ((2 - 9*Sqrt[5])*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticF[2*ArcTan[x/5^(1/4)], 1/2])/(30*5^(1/4)*Sqrt[5 + x^4])","A",5,4,20,0.2000,1,"{1282, 1198, 220, 1196}"
44,1,58,0,0.0457434,"\int \frac{x^7 \left(2+3 x^2\right)}{\left(5+x^4\right)^{3/2}} \, dx","Int[(x^7*(2 + 3*x^2))/(5 + x^4)^(3/2),x]","-\frac{\left(3 x^2+2\right) x^4}{2 \sqrt{x^4+5}}+\frac{1}{4} \left(9 x^2+8\right) \sqrt{x^4+5}-\frac{45}{4} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)","-\frac{\left(3 x^2+2\right) x^4}{2 \sqrt{x^4+5}}+\frac{1}{4} \left(9 x^2+8\right) \sqrt{x^4+5}-\frac{45}{4} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)",1,"-(x^4*(2 + 3*x^2))/(2*Sqrt[5 + x^4]) + ((8 + 9*x^2)*Sqrt[5 + x^4])/4 - (45*ArcSinh[x^2/Sqrt[5]])/4","A",4,4,20,0.2000,1,"{1252, 819, 780, 215}"
45,1,45,0,0.0386738,"\int \frac{x^5 \left(2+3 x^2\right)}{\left(5+x^4\right)^{3/2}} \, dx","Int[(x^5*(2 + 3*x^2))/(5 + x^4)^(3/2),x]","-\frac{\left(3 x^2+2\right) x^2}{2 \sqrt{x^4+5}}+3 \sqrt{x^4+5}+\sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)","-\frac{\left(3 x^2+2\right) x^2}{2 \sqrt{x^4+5}}+3 \sqrt{x^4+5}+\sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)",1,"-(x^2*(2 + 3*x^2))/(2*Sqrt[5 + x^4]) + 3*Sqrt[5 + x^4] + ArcSinh[x^2/Sqrt[5]]","A",4,4,20,0.2000,1,"{1252, 819, 641, 215}"
46,1,35,0,0.0265763,"\int \frac{x^3 \left(2+3 x^2\right)}{\left(5+x^4\right)^{3/2}} \, dx","Int[(x^3*(2 + 3*x^2))/(5 + x^4)^(3/2),x]","\frac{3}{2} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)-\frac{3 x^2+2}{2 \sqrt{x^4+5}}","\frac{3}{2} \sinh ^{-1}\left(\frac{x^2}{\sqrt{5}}\right)-\frac{3 x^2+2}{2 \sqrt{x^4+5}}",1,"-(2 + 3*x^2)/(2*Sqrt[5 + x^4]) + (3*ArcSinh[x^2/Sqrt[5]])/2","A",3,3,20,0.1500,1,"{1252, 778, 215}"
47,1,20,0,0.0156476,"\int \frac{x \left(2+3 x^2\right)}{\left(5+x^4\right)^{3/2}} \, dx","Int[(x*(2 + 3*x^2))/(5 + x^4)^(3/2),x]","-\frac{15-2 x^2}{10 \sqrt{x^4+5}}","-\frac{15-2 x^2}{10 \sqrt{x^4+5}}",1,"-(15 - 2*x^2)/(10*Sqrt[5 + x^4])","A",2,2,18,0.1111,1,"{1248, 637}"
48,1,46,0,0.0432416,"\int \frac{2+3 x^2}{x \left(5+x^4\right)^{3/2}} \, dx","Int[(2 + 3*x^2)/(x*(5 + x^4)^(3/2)),x]","\frac{3 x^2+2}{10 \sqrt{x^4+5}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)}{5 \sqrt{5}}","\frac{3 x^2+2}{10 \sqrt{x^4+5}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)}{5 \sqrt{5}}",1,"(2 + 3*x^2)/(10*Sqrt[5 + x^4]) - ArcTanh[Sqrt[5 + x^4]/Sqrt[5]]/(5*Sqrt[5])","A",6,6,20,0.3000,1,"{1252, 823, 12, 266, 63, 207}"
49,1,65,0,0.055294,"\int \frac{2+3 x^2}{x^3 \left(5+x^4\right)^{3/2}} \, dx","Int[(2 + 3*x^2)/(x^3*(5 + x^4)^(3/2)),x]","\frac{3 x^2+2}{10 x^2 \sqrt{x^4+5}}-\frac{2 \sqrt{x^4+5}}{25 x^2}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)}{10 \sqrt{5}}","\frac{3 x^2+2}{10 x^2 \sqrt{x^4+5}}-\frac{2 \sqrt{x^4+5}}{25 x^2}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{x^4+5}}{\sqrt{5}}\right)}{10 \sqrt{5}}",1,"(2 + 3*x^2)/(10*x^2*Sqrt[5 + x^4]) - (2*Sqrt[5 + x^4])/(25*x^2) - (3*ArcTanh[Sqrt[5 + x^4]/Sqrt[5]])/(10*Sqrt[5])","A",6,6,20,0.3000,1,"{1252, 823, 807, 266, 63, 207}"
50,1,196,0,0.0852553,"\int \frac{x^4 \left(2+3 x^2\right)}{\left(5+x^4\right)^{3/2}} \, dx","Int[(x^4*(2 + 3*x^2))/(5 + x^4)^(3/2),x]","-\frac{\left(15-2 x^2\right) x^3}{10 \sqrt{x^4+5}}+\frac{9 \sqrt{x^4+5} x}{2 \left(x^2+\sqrt{5}\right)}-\frac{1}{5} \sqrt{x^4+5} x+\frac{\left(2+9 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{5} \sqrt{x^4+5}}-\frac{9 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{2 \sqrt{x^4+5}}","-\frac{\left(15-2 x^2\right) x^3}{10 \sqrt{x^4+5}}+\frac{9 \sqrt{x^4+5} x}{2 \left(x^2+\sqrt{5}\right)}-\frac{1}{5} \sqrt{x^4+5} x+\frac{\left(2+9 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{5} \sqrt{x^4+5}}-\frac{9 \sqrt[4]{5} \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{2 \sqrt{x^4+5}}",1,"-(x^3*(15 - 2*x^2))/(10*Sqrt[5 + x^4]) - (x*Sqrt[5 + x^4])/5 + (9*x*Sqrt[5 + x^4])/(2*(Sqrt[5] + x^2)) - (9*5^(1/4)*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticE[2*ArcTan[x/5^(1/4)], 1/2])/(2*Sqrt[5 + x^4]) + ((2 + 9*Sqrt[5])*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticF[2*ArcTan[x/5^(1/4)], 1/2])/(4*5^(1/4)*Sqrt[5 + x^4])","A",5,5,20,0.2500,1,"{1276, 1280, 1198, 220, 1196}"
51,1,177,0,0.0691724,"\int \frac{x^2 \left(2+3 x^2\right)}{\left(5+x^4\right)^{3/2}} \, dx","Int[(x^2*(2 + 3*x^2))/(5 + x^4)^(3/2),x]","-\frac{\sqrt{x^4+5} x}{5 \left(x^2+\sqrt{5}\right)}-\frac{\left(15-2 x^2\right) x}{10 \sqrt{x^4+5}}-\frac{\left(2-3 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{4\ 5^{3/4} \sqrt{x^4+5}}+\frac{\left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{5^{3/4} \sqrt{x^4+5}}","-\frac{\sqrt{x^4+5} x}{5 \left(x^2+\sqrt{5}\right)}-\frac{\left(15-2 x^2\right) x}{10 \sqrt{x^4+5}}-\frac{\left(2-3 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{4\ 5^{3/4} \sqrt{x^4+5}}+\frac{\left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{5^{3/4} \sqrt{x^4+5}}",1,"-(x*(15 - 2*x^2))/(10*Sqrt[5 + x^4]) - (x*Sqrt[5 + x^4])/(5*(Sqrt[5] + x^2)) + ((Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticE[2*ArcTan[x/5^(1/4)], 1/2])/(5^(3/4)*Sqrt[5 + x^4]) - ((2 - 3*Sqrt[5])*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticF[2*ArcTan[x/5^(1/4)], 1/2])/(4*5^(3/4)*Sqrt[5 + x^4])","A",4,4,20,0.2000,1,"{1276, 1198, 220, 1196}"
52,1,180,0,0.0614915,"\int \frac{2+3 x^2}{\left(5+x^4\right)^{3/2}} \, dx","Int[(2 + 3*x^2)/(5 + x^4)^(3/2),x]","-\frac{3 \sqrt{x^4+5} x}{10 \left(x^2+\sqrt{5}\right)}+\frac{\left(3 x^2+2\right) x}{10 \sqrt{x^4+5}}+\frac{\left(2-3 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{20 \sqrt[4]{5} \sqrt{x^4+5}}+\frac{3 \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{2\ 5^{3/4} \sqrt{x^4+5}}","-\frac{3 \sqrt{x^4+5} x}{10 \left(x^2+\sqrt{5}\right)}+\frac{\left(3 x^2+2\right) x}{10 \sqrt{x^4+5}}+\frac{\left(2-3 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{20 \sqrt[4]{5} \sqrt{x^4+5}}+\frac{3 \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{2\ 5^{3/4} \sqrt{x^4+5}}",1,"(x*(2 + 3*x^2))/(10*Sqrt[5 + x^4]) - (3*x*Sqrt[5 + x^4])/(10*(Sqrt[5] + x^2)) + (3*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticE[2*ArcTan[x/5^(1/4)], 1/2])/(2*5^(3/4)*Sqrt[5 + x^4]) + ((2 - 3*Sqrt[5])*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticF[2*ArcTan[x/5^(1/4)], 1/2])/(20*5^(1/4)*Sqrt[5 + x^4])","A",4,4,17,0.2353,1,"{1179, 1198, 220, 1196}"
53,1,196,0,0.081502,"\int \frac{2+3 x^2}{x^2 \left(5+x^4\right)^{3/2}} \, dx","Int[(2 + 3*x^2)/(x^2*(5 + x^4)^(3/2)),x]","\frac{3 \sqrt{x^4+5} x}{25 \left(x^2+\sqrt{5}\right)}-\frac{3 \sqrt{x^4+5}}{25 x}+\frac{3 x^2+2}{10 \sqrt{x^4+5} x}+\frac{3 \left(2+\sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{20\ 5^{3/4} \sqrt{x^4+5}}-\frac{3 \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{5\ 5^{3/4} \sqrt{x^4+5}}","\frac{3 \sqrt{x^4+5} x}{25 \left(x^2+\sqrt{5}\right)}-\frac{3 \sqrt{x^4+5}}{25 x}+\frac{3 x^2+2}{10 \sqrt{x^4+5} x}+\frac{3 \left(2+\sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{20\ 5^{3/4} \sqrt{x^4+5}}-\frac{3 \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{5\ 5^{3/4} \sqrt{x^4+5}}",1,"(2 + 3*x^2)/(10*x*Sqrt[5 + x^4]) - (3*Sqrt[5 + x^4])/(25*x) + (3*x*Sqrt[5 + x^4])/(25*(Sqrt[5] + x^2)) - (3*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticE[2*ArcTan[x/5^(1/4)], 1/2])/(5*5^(3/4)*Sqrt[5 + x^4]) + (3*(2 + Sqrt[5])*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticF[2*ArcTan[x/5^(1/4)], 1/2])/(20*5^(3/4)*Sqrt[5 + x^4])","A",5,5,20,0.2500,1,"{1278, 1282, 1198, 220, 1196}"
54,1,214,0,0.1078471,"\int \frac{2+3 x^2}{x^4 \left(5+x^4\right)^{3/2}} \, dx","Int[(2 + 3*x^2)/(x^4*(5 + x^4)^(3/2)),x]","\frac{9 \sqrt{x^4+5} x}{50 \left(x^2+\sqrt{5}\right)}-\frac{9 \sqrt{x^4+5}}{50 x}-\frac{\sqrt{x^4+5}}{15 x^3}+\frac{3 x^2+2}{10 \sqrt{x^4+5} x^3}+\frac{\left(27-2 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{60\ 5^{3/4} \sqrt{x^4+5}}-\frac{9 \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{10\ 5^{3/4} \sqrt{x^4+5}}","\frac{9 \sqrt{x^4+5} x}{50 \left(x^2+\sqrt{5}\right)}-\frac{9 \sqrt{x^4+5}}{50 x}-\frac{\sqrt{x^4+5}}{15 x^3}+\frac{3 x^2+2}{10 \sqrt{x^4+5} x^3}+\frac{\left(27-2 \sqrt{5}\right) \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{60\ 5^{3/4} \sqrt{x^4+5}}-\frac{9 \left(x^2+\sqrt{5}\right) \sqrt{\frac{x^4+5}{\left(x^2+\sqrt{5}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{x}{\sqrt[4]{5}}\right)|\frac{1}{2}\right)}{10\ 5^{3/4} \sqrt{x^4+5}}",1,"(2 + 3*x^2)/(10*x^3*Sqrt[5 + x^4]) - Sqrt[5 + x^4]/(15*x^3) - (9*Sqrt[5 + x^4])/(50*x) + (9*x*Sqrt[5 + x^4])/(50*(Sqrt[5] + x^2)) - (9*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticE[2*ArcTan[x/5^(1/4)], 1/2])/(10*5^(3/4)*Sqrt[5 + x^4]) + ((27 - 2*Sqrt[5])*(Sqrt[5] + x^2)*Sqrt[(5 + x^4)/(Sqrt[5] + x^2)^2]*EllipticF[2*ArcTan[x/5^(1/4)], 1/2])/(60*5^(3/4)*Sqrt[5 + x^4])","A",6,5,20,0.2500,1,"{1278, 1282, 1198, 220, 1196}"
55,1,269,0,0.1607825,"\int (f x)^m \left(d+e x^2\right) \left(1+2 x^2+x^4\right)^5 \, dx","Int[(f*x)^m*(d + e*x^2)*(1 + 2*x^2 + x^4)^5,x]","\frac{(10 d+e) (f x)^{m+3}}{f^3 (m+3)}+\frac{5 (9 d+2 e) (f x)^{m+5}}{f^5 (m+5)}+\frac{15 (8 d+3 e) (f x)^{m+7}}{f^7 (m+7)}+\frac{30 (7 d+4 e) (f x)^{m+9}}{f^9 (m+9)}+\frac{42 (6 d+5 e) (f x)^{m+11}}{f^{11} (m+11)}+\frac{42 (5 d+6 e) (f x)^{m+13}}{f^{13} (m+13)}+\frac{30 (4 d+7 e) (f x)^{m+15}}{f^{15} (m+15)}+\frac{15 (3 d+8 e) (f x)^{m+17}}{f^{17} (m+17)}+\frac{5 (2 d+9 e) (f x)^{m+19}}{f^{19} (m+19)}+\frac{(d+10 e) (f x)^{m+21}}{f^{21} (m+21)}+\frac{d (f x)^{m+1}}{f (m+1)}+\frac{e (f x)^{m+23}}{f^{23} (m+23)}","\frac{(10 d+e) (f x)^{m+3}}{f^3 (m+3)}+\frac{5 (9 d+2 e) (f x)^{m+5}}{f^5 (m+5)}+\frac{15 (8 d+3 e) (f x)^{m+7}}{f^7 (m+7)}+\frac{30 (7 d+4 e) (f x)^{m+9}}{f^9 (m+9)}+\frac{42 (6 d+5 e) (f x)^{m+11}}{f^{11} (m+11)}+\frac{42 (5 d+6 e) (f x)^{m+13}}{f^{13} (m+13)}+\frac{30 (4 d+7 e) (f x)^{m+15}}{f^{15} (m+15)}+\frac{15 (3 d+8 e) (f x)^{m+17}}{f^{17} (m+17)}+\frac{5 (2 d+9 e) (f x)^{m+19}}{f^{19} (m+19)}+\frac{(d+10 e) (f x)^{m+21}}{f^{21} (m+21)}+\frac{d (f x)^{m+1}}{f (m+1)}+\frac{e (f x)^{m+23}}{f^{23} (m+23)}",1,"(d*(f*x)^(1 + m))/(f*(1 + m)) + ((10*d + e)*(f*x)^(3 + m))/(f^3*(3 + m)) + (5*(9*d + 2*e)*(f*x)^(5 + m))/(f^5*(5 + m)) + (15*(8*d + 3*e)*(f*x)^(7 + m))/(f^7*(7 + m)) + (30*(7*d + 4*e)*(f*x)^(9 + m))/(f^9*(9 + m)) + (42*(6*d + 5*e)*(f*x)^(11 + m))/(f^11*(11 + m)) + (42*(5*d + 6*e)*(f*x)^(13 + m))/(f^13*(13 + m)) + (30*(4*d + 7*e)*(f*x)^(15 + m))/(f^15*(15 + m)) + (15*(3*d + 8*e)*(f*x)^(17 + m))/(f^17*(17 + m)) + (5*(2*d + 9*e)*(f*x)^(19 + m))/(f^19*(19 + m)) + ((d + 10*e)*(f*x)^(21 + m))/(f^21*(21 + m)) + (e*(f*x)^(23 + m))/(f^23*(23 + m))","A",3,2,25,0.08000,1,"{28, 448}"
56,1,63,0,0.1967009,"\int x^5 \left(d+e x^2\right) \left(1+2 x^2+x^4\right)^5 \, dx","Int[x^5*(d + e*x^2)*(1 + 2*x^2 + x^4)^5,x]","\frac{1}{26} \left(x^2+1\right)^{13} (d-3 e)-\frac{1}{24} \left(x^2+1\right)^{12} (2 d-3 e)+\frac{1}{22} \left(x^2+1\right)^{11} (d-e)+\frac{1}{28} e \left(x^2+1\right)^{14}","\frac{1}{26} \left(x^2+1\right)^{13} (d-3 e)-\frac{1}{24} \left(x^2+1\right)^{12} (2 d-3 e)+\frac{1}{22} \left(x^2+1\right)^{11} (d-e)+\frac{1}{28} e \left(x^2+1\right)^{14}",1,"((d - e)*(1 + x^2)^11)/22 - ((2*d - 3*e)*(1 + x^2)^12)/24 + ((d - 3*e)*(1 + x^2)^13)/26 + (e*(1 + x^2)^14)/28","A",4,3,23,0.1304,1,"{28, 446, 76}"
57,1,153,0,0.1165503,"\int x^4 \left(d+e x^2\right) \left(1+2 x^2+x^4\right)^5 \, dx","Int[x^4*(d + e*x^2)*(1 + 2*x^2 + x^4)^5,x]","\frac{1}{25} x^{25} (d+10 e)+\frac{5}{23} x^{23} (2 d+9 e)+\frac{5}{7} x^{21} (3 d+8 e)+\frac{30}{19} x^{19} (4 d+7 e)+\frac{42}{17} x^{17} (5 d+6 e)+\frac{14}{5} x^{15} (6 d+5 e)+\frac{30}{13} x^{13} (7 d+4 e)+\frac{15}{11} x^{11} (8 d+3 e)+\frac{5}{9} x^9 (9 d+2 e)+\frac{1}{7} x^7 (10 d+e)+\frac{d x^5}{5}+\frac{e x^{27}}{27}","\frac{1}{25} x^{25} (d+10 e)+\frac{5}{23} x^{23} (2 d+9 e)+\frac{5}{7} x^{21} (3 d+8 e)+\frac{30}{19} x^{19} (4 d+7 e)+\frac{42}{17} x^{17} (5 d+6 e)+\frac{14}{5} x^{15} (6 d+5 e)+\frac{30}{13} x^{13} (7 d+4 e)+\frac{15}{11} x^{11} (8 d+3 e)+\frac{5}{9} x^9 (9 d+2 e)+\frac{1}{7} x^7 (10 d+e)+\frac{d x^5}{5}+\frac{e x^{27}}{27}",1,"(d*x^5)/5 + ((10*d + e)*x^7)/7 + (5*(9*d + 2*e)*x^9)/9 + (15*(8*d + 3*e)*x^11)/11 + (30*(7*d + 4*e)*x^13)/13 + (14*(6*d + 5*e)*x^15)/5 + (42*(5*d + 6*e)*x^17)/17 + (30*(4*d + 7*e)*x^19)/19 + (5*(3*d + 8*e)*x^21)/7 + (5*(2*d + 9*e)*x^23)/23 + ((d + 10*e)*x^25)/25 + (e*x^27)/27","A",3,2,23,0.08696,1,"{28, 448}"
58,1,45,0,0.1233962,"\int x^3 \left(d+e x^2\right) \left(1+2 x^2+x^4\right)^5 \, dx","Int[x^3*(d + e*x^2)*(1 + 2*x^2 + x^4)^5,x]","\frac{1}{24} \left(x^2+1\right)^{12} (d-2 e)-\frac{1}{22} \left(x^2+1\right)^{11} (d-e)+\frac{1}{26} e \left(x^2+1\right)^{13}","\frac{1}{24} \left(x^2+1\right)^{12} (d-2 e)-\frac{1}{22} \left(x^2+1\right)^{11} (d-e)+\frac{1}{26} e \left(x^2+1\right)^{13}",1,"-((d - e)*(1 + x^2)^11)/22 + ((d - 2*e)*(1 + x^2)^12)/24 + (e*(1 + x^2)^13)/26","A",4,3,23,0.1304,1,"{28, 446, 76}"
59,1,153,0,0.0845725,"\int x^2 \left(d+e x^2\right) \left(1+2 x^2+x^4\right)^5 \, dx","Int[x^2*(d + e*x^2)*(1 + 2*x^2 + x^4)^5,x]","\frac{1}{23} x^{23} (d+10 e)+\frac{5}{21} x^{21} (2 d+9 e)+\frac{15}{19} x^{19} (3 d+8 e)+\frac{30}{17} x^{17} (4 d+7 e)+\frac{14}{5} x^{15} (5 d+6 e)+\frac{42}{13} x^{13} (6 d+5 e)+\frac{30}{11} x^{11} (7 d+4 e)+\frac{5}{3} x^9 (8 d+3 e)+\frac{5}{7} x^7 (9 d+2 e)+\frac{1}{5} x^5 (10 d+e)+\frac{d x^3}{3}+\frac{e x^{25}}{25}","\frac{1}{23} x^{23} (d+10 e)+\frac{5}{21} x^{21} (2 d+9 e)+\frac{15}{19} x^{19} (3 d+8 e)+\frac{30}{17} x^{17} (4 d+7 e)+\frac{14}{5} x^{15} (5 d+6 e)+\frac{42}{13} x^{13} (6 d+5 e)+\frac{30}{11} x^{11} (7 d+4 e)+\frac{5}{3} x^9 (8 d+3 e)+\frac{5}{7} x^7 (9 d+2 e)+\frac{1}{5} x^5 (10 d+e)+\frac{d x^3}{3}+\frac{e x^{25}}{25}",1,"(d*x^3)/3 + ((10*d + e)*x^5)/5 + (5*(9*d + 2*e)*x^7)/7 + (5*(8*d + 3*e)*x^9)/3 + (30*(7*d + 4*e)*x^11)/11 + (42*(6*d + 5*e)*x^13)/13 + (14*(5*d + 6*e)*x^15)/5 + (30*(4*d + 7*e)*x^17)/17 + (15*(3*d + 8*e)*x^19)/19 + (5*(2*d + 9*e)*x^21)/21 + ((d + 10*e)*x^23)/23 + (e*x^25)/25","A",3,2,23,0.08696,1,"{28, 448}"
60,1,29,0,0.0493032,"\int x \left(d+e x^2\right) \left(1+2 x^2+x^4\right)^5 \, dx","Int[x*(d + e*x^2)*(1 + 2*x^2 + x^4)^5,x]","\frac{1}{22} \left(x^2+1\right)^{11} (d-e)+\frac{1}{24} e \left(x^2+1\right)^{12}","\frac{1}{22} \left(x^2+1\right)^{11} (d-e)+\frac{1}{24} e \left(x^2+1\right)^{12}",1,"((d - e)*(1 + x^2)^11)/22 + (e*(1 + x^2)^12)/24","A",4,3,21,0.1429,1,"{28, 444, 43}"
61,1,143,0,0.0742943,"\int \left(d+e x^2\right) \left(1+2 x^2+x^4\right)^5 \, dx","Int[(d + e*x^2)*(1 + 2*x^2 + x^4)^5,x]","\frac{1}{21} x^{21} (d+10 e)+\frac{5}{19} x^{19} (2 d+9 e)+\frac{15}{17} x^{17} (3 d+8 e)+2 x^{15} (4 d+7 e)+\frac{42}{13} x^{13} (5 d+6 e)+\frac{42}{11} x^{11} (6 d+5 e)+\frac{10}{3} x^9 (7 d+4 e)+\frac{15}{7} x^7 (8 d+3 e)+x^5 (9 d+2 e)+\frac{1}{3} x^3 (10 d+e)+d x+\frac{e x^{23}}{23}","\frac{1}{21} x^{21} (d+10 e)+\frac{5}{19} x^{19} (2 d+9 e)+\frac{15}{17} x^{17} (3 d+8 e)+2 x^{15} (4 d+7 e)+\frac{42}{13} x^{13} (5 d+6 e)+\frac{42}{11} x^{11} (6 d+5 e)+\frac{10}{3} x^9 (7 d+4 e)+\frac{15}{7} x^7 (8 d+3 e)+x^5 (9 d+2 e)+\frac{1}{3} x^3 (10 d+e)+d x+\frac{e x^{23}}{23}",1,"d*x + ((10*d + e)*x^3)/3 + (9*d + 2*e)*x^5 + (15*(8*d + 3*e)*x^7)/7 + (10*(7*d + 4*e)*x^9)/3 + (42*(6*d + 5*e)*x^11)/11 + (42*(5*d + 6*e)*x^13)/13 + 2*(4*d + 7*e)*x^15 + (15*(3*d + 8*e)*x^17)/17 + (5*(2*d + 9*e)*x^19)/19 + ((d + 10*e)*x^21)/21 + (e*x^23)/23","A",3,2,20,0.1000,1,"{28, 373}"
62,1,93,0,0.0547076,"\int \frac{\left(d+e x^2\right) \left(1+2 x^2+x^4\right)^5}{x} \, dx","Int[((d + e*x^2)*(1 + 2*x^2 + x^4)^5)/x,x]","\frac{d x^{20}}{20}+\frac{5 d x^{18}}{9}+\frac{45 d x^{16}}{16}+\frac{60 d x^{14}}{7}+\frac{35 d x^{12}}{2}+\frac{126 d x^{10}}{5}+\frac{105 d x^8}{4}+20 d x^6+\frac{45 d x^4}{4}+5 d x^2+d \log (x)+\frac{1}{22} e \left(x^2+1\right)^{11}","\frac{d x^{20}}{20}+\frac{5 d x^{18}}{9}+\frac{45 d x^{16}}{16}+\frac{60 d x^{14}}{7}+\frac{35 d x^{12}}{2}+\frac{126 d x^{10}}{5}+\frac{105 d x^8}{4}+20 d x^6+\frac{45 d x^4}{4}+5 d x^2+d \log (x)+\frac{1}{22} e \left(x^2+1\right)^{11}",1,"5*d*x^2 + (45*d*x^4)/4 + 20*d*x^6 + (105*d*x^8)/4 + (126*d*x^10)/5 + (35*d*x^12)/2 + (60*d*x^14)/7 + (45*d*x^16)/16 + (5*d*x^18)/9 + (d*x^20)/20 + (e*(1 + x^2)^11)/22 + d*Log[x]","A",5,4,23,0.1739,1,"{28, 446, 80, 43}"
63,1,141,0,0.0821492,"\int \frac{\left(d+e x^2\right) \left(1+2 x^2+x^4\right)^5}{x^2} \, dx","Int[((d + e*x^2)*(1 + 2*x^2 + x^4)^5)/x^2,x]","\frac{1}{19} x^{19} (d+10 e)+\frac{5}{17} x^{17} (2 d+9 e)+x^{15} (3 d+8 e)+\frac{30}{13} x^{13} (4 d+7 e)+\frac{42}{11} x^{11} (5 d+6 e)+\frac{14}{3} x^9 (6 d+5 e)+\frac{30}{7} x^7 (7 d+4 e)+3 x^5 (8 d+3 e)+\frac{5}{3} x^3 (9 d+2 e)+x (10 d+e)-\frac{d}{x}+\frac{e x^{21}}{21}","\frac{1}{19} x^{19} (d+10 e)+\frac{5}{17} x^{17} (2 d+9 e)+x^{15} (3 d+8 e)+\frac{30}{13} x^{13} (4 d+7 e)+\frac{42}{11} x^{11} (5 d+6 e)+\frac{14}{3} x^9 (6 d+5 e)+\frac{30}{7} x^7 (7 d+4 e)+3 x^5 (8 d+3 e)+\frac{5}{3} x^3 (9 d+2 e)+x (10 d+e)-\frac{d}{x}+\frac{e x^{21}}{21}",1,"-(d/x) + (10*d + e)*x + (5*(9*d + 2*e)*x^3)/3 + 3*(8*d + 3*e)*x^5 + (30*(7*d + 4*e)*x^7)/7 + (14*(6*d + 5*e)*x^9)/3 + (42*(5*d + 6*e)*x^11)/11 + (30*(4*d + 7*e)*x^13)/13 + (3*d + 8*e)*x^15 + (5*(2*d + 9*e)*x^17)/17 + ((d + 10*e)*x^19)/19 + (e*x^21)/21","A",3,2,23,0.08696,1,"{28, 448}"
64,1,147,0,0.1355365,"\int \frac{\left(d+e x^2\right) \left(1+2 x^2+x^4\right)^5}{x^3} \, dx","Int[((d + e*x^2)*(1 + 2*x^2 + x^4)^5)/x^3,x]","\frac{1}{18} x^{18} (d+10 e)+\frac{5}{16} x^{16} (2 d+9 e)+\frac{15}{14} x^{14} (3 d+8 e)+\frac{5}{2} x^{12} (4 d+7 e)+\frac{21}{5} x^{10} (5 d+6 e)+\frac{21}{4} x^8 (6 d+5 e)+5 x^6 (7 d+4 e)+\frac{15}{4} x^4 (8 d+3 e)+\frac{5}{2} x^2 (9 d+2 e)+(10 d+e) \log (x)-\frac{d}{2 x^2}+\frac{e x^{20}}{20}","\frac{1}{18} x^{18} (d+10 e)+\frac{5}{16} x^{16} (2 d+9 e)+\frac{15}{14} x^{14} (3 d+8 e)+\frac{5}{2} x^{12} (4 d+7 e)+\frac{21}{5} x^{10} (5 d+6 e)+\frac{21}{4} x^8 (6 d+5 e)+5 x^6 (7 d+4 e)+\frac{15}{4} x^4 (8 d+3 e)+\frac{5}{2} x^2 (9 d+2 e)+(10 d+e) \log (x)-\frac{d}{2 x^2}+\frac{e x^{20}}{20}",1,"-d/(2*x^2) + (5*(9*d + 2*e)*x^2)/2 + (15*(8*d + 3*e)*x^4)/4 + 5*(7*d + 4*e)*x^6 + (21*(6*d + 5*e)*x^8)/4 + (21*(5*d + 6*e)*x^10)/5 + (5*(4*d + 7*e)*x^12)/2 + (15*(3*d + 8*e)*x^14)/14 + (5*(2*d + 9*e)*x^16)/16 + ((d + 10*e)*x^18)/18 + (e*x^20)/20 + (10*d + e)*Log[x]","A",4,3,23,0.1304,1,"{28, 446, 76}"
65,1,203,0,0.073443,"\int (f x)^m \left(1+x^2\right) \left(1+2 x^2+x^4\right)^5 \, dx","Int[(f*x)^m*(1 + x^2)*(1 + 2*x^2 + x^4)^5,x]","\frac{11 (f x)^{m+3}}{f^3 (m+3)}+\frac{55 (f x)^{m+5}}{f^5 (m+5)}+\frac{165 (f x)^{m+7}}{f^7 (m+7)}+\frac{330 (f x)^{m+9}}{f^9 (m+9)}+\frac{462 (f x)^{m+11}}{f^{11} (m+11)}+\frac{462 (f x)^{m+13}}{f^{13} (m+13)}+\frac{330 (f x)^{m+15}}{f^{15} (m+15)}+\frac{165 (f x)^{m+17}}{f^{17} (m+17)}+\frac{55 (f x)^{m+19}}{f^{19} (m+19)}+\frac{11 (f x)^{m+21}}{f^{21} (m+21)}+\frac{(f x)^{m+23}}{f^{23} (m+23)}+\frac{(f x)^{m+1}}{f (m+1)}","\frac{11 (f x)^{m+3}}{f^3 (m+3)}+\frac{55 (f x)^{m+5}}{f^5 (m+5)}+\frac{165 (f x)^{m+7}}{f^7 (m+7)}+\frac{330 (f x)^{m+9}}{f^9 (m+9)}+\frac{462 (f x)^{m+11}}{f^{11} (m+11)}+\frac{462 (f x)^{m+13}}{f^{13} (m+13)}+\frac{330 (f x)^{m+15}}{f^{15} (m+15)}+\frac{165 (f x)^{m+17}}{f^{17} (m+17)}+\frac{55 (f x)^{m+19}}{f^{19} (m+19)}+\frac{11 (f x)^{m+21}}{f^{21} (m+21)}+\frac{(f x)^{m+23}}{f^{23} (m+23)}+\frac{(f x)^{m+1}}{f (m+1)}",1,"(f*x)^(1 + m)/(f*(1 + m)) + (11*(f*x)^(3 + m))/(f^3*(3 + m)) + (55*(f*x)^(5 + m))/(f^5*(5 + m)) + (165*(f*x)^(7 + m))/(f^7*(7 + m)) + (330*(f*x)^(9 + m))/(f^9*(9 + m)) + (462*(f*x)^(11 + m))/(f^11*(11 + m)) + (462*(f*x)^(13 + m))/(f^13*(13 + m)) + (330*(f*x)^(15 + m))/(f^15*(15 + m)) + (165*(f*x)^(17 + m))/(f^17*(17 + m)) + (55*(f*x)^(19 + m))/(f^19*(19 + m)) + (11*(f*x)^(21 + m))/(f^21*(21 + m)) + (f*x)^(23 + m)/(f^23*(23 + m))","A",3,2,23,0.08696,1,"{28, 270}"
66,1,34,0,0.0467126,"\int x^5 \left(1+x^2\right) \left(1+2 x^2+x^4\right)^5 \, dx","Int[x^5*(1 + x^2)*(1 + 2*x^2 + x^4)^5,x]","\frac{1}{28} \left(x^2+1\right)^{14}-\frac{1}{13} \left(x^2+1\right)^{13}+\frac{1}{24} \left(x^2+1\right)^{12}","\frac{1}{28} \left(x^2+1\right)^{14}-\frac{1}{13} \left(x^2+1\right)^{13}+\frac{1}{24} \left(x^2+1\right)^{12}",1,"(1 + x^2)^12/24 - (1 + x^2)^13/13 + (1 + x^2)^14/28","A",4,3,21,0.1429,1,"{28, 266, 43}"
67,1,83,0,0.0314287,"\int x^4 \left(1+x^2\right) \left(1+2 x^2+x^4\right)^5 \, dx","Int[x^4*(1 + x^2)*(1 + 2*x^2 + x^4)^5,x]","\frac{x^{27}}{27}+\frac{11 x^{25}}{25}+\frac{55 x^{23}}{23}+\frac{55 x^{21}}{7}+\frac{330 x^{19}}{19}+\frac{462 x^{17}}{17}+\frac{154 x^{15}}{5}+\frac{330 x^{13}}{13}+15 x^{11}+\frac{55 x^9}{9}+\frac{11 x^7}{7}+\frac{x^5}{5}","\frac{x^{27}}{27}+\frac{11 x^{25}}{25}+\frac{55 x^{23}}{23}+\frac{55 x^{21}}{7}+\frac{330 x^{19}}{19}+\frac{462 x^{17}}{17}+\frac{154 x^{15}}{5}+\frac{330 x^{13}}{13}+15 x^{11}+\frac{55 x^9}{9}+\frac{11 x^7}{7}+\frac{x^5}{5}",1,"x^5/5 + (11*x^7)/7 + (55*x^9)/9 + 15*x^11 + (330*x^13)/13 + (154*x^15)/5 + (462*x^17)/17 + (330*x^19)/19 + (55*x^21)/7 + (55*x^23)/23 + (11*x^25)/25 + x^27/27","A",3,2,21,0.09524,1,"{28, 270}"
68,1,23,0,0.0219489,"\int x^3 \left(1+x^2\right) \left(1+2 x^2+x^4\right)^5 \, dx","Int[x^3*(1 + x^2)*(1 + 2*x^2 + x^4)^5,x]","\frac{1}{26} \left(x^2+1\right)^{13}-\frac{1}{24} \left(x^2+1\right)^{12}","\frac{1}{26} \left(x^2+1\right)^{13}-\frac{1}{24} \left(x^2+1\right)^{12}",1,"-(1 + x^2)^12/24 + (1 + x^2)^13/26","A",4,3,21,0.1429,1,"{28, 266, 43}"
69,1,83,0,0.0268132,"\int x^2 \left(1+x^2\right) \left(1+2 x^2+x^4\right)^5 \, dx","Int[x^2*(1 + x^2)*(1 + 2*x^2 + x^4)^5,x]","\frac{x^{25}}{25}+\frac{11 x^{23}}{23}+\frac{55 x^{21}}{21}+\frac{165 x^{19}}{19}+\frac{330 x^{17}}{17}+\frac{154 x^{15}}{5}+\frac{462 x^{13}}{13}+30 x^{11}+\frac{55 x^9}{3}+\frac{55 x^7}{7}+\frac{11 x^5}{5}+\frac{x^3}{3}","\frac{x^{25}}{25}+\frac{11 x^{23}}{23}+\frac{55 x^{21}}{21}+\frac{165 x^{19}}{19}+\frac{330 x^{17}}{17}+\frac{154 x^{15}}{5}+\frac{462 x^{13}}{13}+30 x^{11}+\frac{55 x^9}{3}+\frac{55 x^7}{7}+\frac{11 x^5}{5}+\frac{x^3}{3}",1,"x^3/3 + (11*x^5)/5 + (55*x^7)/7 + (55*x^9)/3 + 30*x^11 + (462*x^13)/13 + (154*x^15)/5 + (330*x^17)/17 + (165*x^19)/19 + (55*x^21)/21 + (11*x^23)/23 + x^25/25","A",3,2,21,0.09524,1,"{28, 270}"
70,1,11,0,0.0023995,"\int x \left(1+x^2\right) \left(1+2 x^2+x^4\right)^5 \, dx","Int[x*(1 + x^2)*(1 + 2*x^2 + x^4)^5,x]","\frac{1}{24} \left(x^2+1\right)^{12}","\frac{1}{24} \left(x^2+1\right)^{12}",1,"(1 + x^2)^12/24","A",2,2,19,0.1053,1,"{28, 261}"
71,1,73,0,0.0217871,"\int \left(1+x^2\right) \left(1+2 x^2+x^4\right)^5 \, dx","Int[(1 + x^2)*(1 + 2*x^2 + x^4)^5,x]","\frac{x^{23}}{23}+\frac{11 x^{21}}{21}+\frac{55 x^{19}}{19}+\frac{165 x^{17}}{17}+22 x^{15}+\frac{462 x^{13}}{13}+42 x^{11}+\frac{110 x^9}{3}+\frac{165 x^7}{7}+11 x^5+\frac{11 x^3}{3}+x","\frac{x^{23}}{23}+\frac{11 x^{21}}{21}+\frac{55 x^{19}}{19}+\frac{165 x^{17}}{17}+22 x^{15}+\frac{462 x^{13}}{13}+42 x^{11}+\frac{110 x^9}{3}+\frac{165 x^7}{7}+11 x^5+\frac{11 x^3}{3}+x",1,"x + (11*x^3)/3 + 11*x^5 + (165*x^7)/7 + (110*x^9)/3 + 42*x^11 + (462*x^13)/13 + 22*x^15 + (165*x^17)/17 + (55*x^19)/19 + (11*x^21)/21 + x^23/23","A",3,2,18,0.1111,1,"{28, 194}"
72,1,80,0,0.0332073,"\int \frac{\left(1+x^2\right) \left(1+2 x^2+x^4\right)^5}{x} \, dx","Int[((1 + x^2)*(1 + 2*x^2 + x^4)^5)/x,x]","\frac{x^{22}}{22}+\frac{11 x^{20}}{20}+\frac{55 x^{18}}{18}+\frac{165 x^{16}}{16}+\frac{165 x^{14}}{7}+\frac{77 x^{12}}{2}+\frac{231 x^{10}}{5}+\frac{165 x^8}{4}+\frac{55 x^6}{2}+\frac{55 x^4}{4}+\frac{11 x^2}{2}+\log (x)","\frac{x^{22}}{22}+\frac{11 x^{20}}{20}+\frac{55 x^{18}}{18}+\frac{165 x^{16}}{16}+\frac{165 x^{14}}{7}+\frac{77 x^{12}}{2}+\frac{231 x^{10}}{5}+\frac{165 x^8}{4}+\frac{55 x^6}{2}+\frac{55 x^4}{4}+\frac{11 x^2}{2}+\log (x)",1,"(11*x^2)/2 + (55*x^4)/4 + (55*x^6)/2 + (165*x^8)/4 + (231*x^10)/5 + (77*x^12)/2 + (165*x^14)/7 + (165*x^16)/16 + (55*x^18)/18 + (11*x^20)/20 + x^22/22 + Log[x]","A",4,3,21,0.1429,1,"{28, 266, 43}"
73,1,73,0,0.0247976,"\int \frac{\left(1+x^2\right) \left(1+2 x^2+x^4\right)^5}{x^2} \, dx","Int[((1 + x^2)*(1 + 2*x^2 + x^4)^5)/x^2,x]","\frac{x^{21}}{21}+\frac{11 x^{19}}{19}+\frac{55 x^{17}}{17}+11 x^{15}+\frac{330 x^{13}}{13}+42 x^{11}+\frac{154 x^9}{3}+\frac{330 x^7}{7}+33 x^5+\frac{55 x^3}{3}+11 x-\frac{1}{x}","\frac{x^{21}}{21}+\frac{11 x^{19}}{19}+\frac{55 x^{17}}{17}+11 x^{15}+\frac{330 x^{13}}{13}+42 x^{11}+\frac{154 x^9}{3}+\frac{330 x^7}{7}+33 x^5+\frac{55 x^3}{3}+11 x-\frac{1}{x}",1,"-x^(-1) + 11*x + (55*x^3)/3 + 33*x^5 + (330*x^7)/7 + (154*x^9)/3 + 42*x^11 + (330*x^13)/13 + 11*x^15 + (55*x^17)/17 + (11*x^19)/19 + x^21/21","A",3,2,21,0.09524,1,"{28, 270}"
74,1,80,0,0.0396765,"\int \frac{\left(1+x^2\right) \left(1+2 x^2+x^4\right)^5}{x^3} \, dx","Int[((1 + x^2)*(1 + 2*x^2 + x^4)^5)/x^3,x]","\frac{x^{20}}{20}+\frac{11 x^{18}}{18}+\frac{55 x^{16}}{16}+\frac{165 x^{14}}{14}+\frac{55 x^{12}}{2}+\frac{231 x^{10}}{5}+\frac{231 x^8}{4}+55 x^6+\frac{165 x^4}{4}+\frac{55 x^2}{2}-\frac{1}{2 x^2}+11 \log (x)","\frac{x^{20}}{20}+\frac{11 x^{18}}{18}+\frac{55 x^{16}}{16}+\frac{165 x^{14}}{14}+\frac{55 x^{12}}{2}+\frac{231 x^{10}}{5}+\frac{231 x^8}{4}+55 x^6+\frac{165 x^4}{4}+\frac{55 x^2}{2}-\frac{1}{2 x^2}+11 \log (x)",1,"-1/(2*x^2) + (55*x^2)/2 + (165*x^4)/4 + 55*x^6 + (231*x^8)/4 + (231*x^10)/5 + (55*x^12)/2 + (165*x^14)/14 + (55*x^16)/16 + (11*x^18)/18 + x^20/20 + 11*Log[x]","A",4,3,21,0.1429,1,"{28, 266, 43}"
75,1,145,0,0.0901167,"\int \frac{x^2 \left(d+e x^2\right)}{\sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[(x^2*(d + e*x^2))/Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{x \left(a+b x^2\right) (b d-a e)}{b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\sqrt{a} \left(a+b x^2\right) (b d-a e) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{e x^3 \left(a+b x^2\right)}{3 b \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{x \left(a+b x^2\right) (b d-a e)}{b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\sqrt{a} \left(a+b x^2\right) (b d-a e) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{e x^3 \left(a+b x^2\right)}{3 b \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"((b*d - a*e)*x*(a + b*x^2))/(b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (e*x^3*(a + b*x^2))/(3*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (Sqrt[a]*(b*d - a*e)*(a + b*x^2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(b^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,4,33,0.1212,1,"{1250, 459, 321, 205}"
76,1,83,0,0.072228,"\int \frac{x \left(d+e x^2\right)}{\sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[(x*(d + e*x^2))/Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{\left(a+b x^2\right) (b d-a e) \log \left(a+b x^2\right)}{2 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{e \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 b^2}","\frac{\left(a+b x^2\right) (b d-a e) \log \left(a+b x^2\right)}{2 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{e \sqrt{a^2+2 a b x^2+b^2 x^4}}{2 b^2}",1,"(e*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*b^2) + ((b*d - a*e)*(a + b*x^2)*Log[a + b*x^2])/(2*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,4,31,0.1290,1,"{1247, 640, 608, 31}"
77,1,97,0,0.0470934,"\int \frac{d+e x^2}{\sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[(d + e*x^2)/Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{\left(a+b x^2\right) (b d-a e) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{e x \left(a+b x^2\right)}{b \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{\left(a+b x^2\right) (b d-a e) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{e x \left(a+b x^2\right)}{b \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(e*x*(a + b*x^2))/(b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + ((b*d - a*e)*(a + b*x^2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[a]*b^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",3,3,30,0.1000,1,"{1148, 388, 205}"
78,1,92,0,0.0717011,"\int \frac{d+e x^2}{x \sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[(d + e*x^2)/(x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]),x]","\frac{d \log (x) \left(a+b x^2\right)}{a \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\left(a+b x^2\right) (b d-a e) \log \left(a+b x^2\right)}{2 a b \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{d \log (x) \left(a+b x^2\right)}{a \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\left(a+b x^2\right) (b d-a e) \log \left(a+b x^2\right)}{2 a b \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(d*(a + b*x^2)*Log[x])/(a*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - ((b*d - a*e)*(a + b*x^2)*Log[a + b*x^2])/(2*a*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,3,33,0.09091,1,"{1250, 446, 72}"
79,1,101,0,0.0629733,"\int \frac{d+e x^2}{x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[(d + e*x^2)/(x^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]),x]","-\frac{\left(a+b x^2\right) (b d-a e) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} \sqrt{b} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d \left(a+b x^2\right)}{a x \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{\left(a+b x^2\right) (b d-a e) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} \sqrt{b} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d \left(a+b x^2\right)}{a x \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"-((d*(a + b*x^2))/(a*x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])) - ((b*d - a*e)*(a + b*x^2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",3,3,33,0.09091,1,"{1250, 453, 205}"
80,1,137,0,0.0981535,"\int \frac{d+e x^2}{x^3 \sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[(d + e*x^2)/(x^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]),x]","-\frac{\log (x) \left(a+b x^2\right) (b d-a e)}{a^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\left(a+b x^2\right) (b d-a e) \log \left(a+b x^2\right)}{2 a^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d \left(a+b x^2\right)}{2 a x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{\log (x) \left(a+b x^2\right) (b d-a e)}{a^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\left(a+b x^2\right) (b d-a e) \log \left(a+b x^2\right)}{2 a^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d \left(a+b x^2\right)}{2 a x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"-(d*(a + b*x^2))/(2*a*x^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - ((b*d - a*e)*(a + b*x^2)*Log[x])/(a^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + ((b*d - a*e)*(a + b*x^2)*Log[a + b*x^2])/(2*a^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,3,33,0.09091,1,"{1250, 446, 77}"
81,1,153,0,0.1192007,"\int \frac{x^2 \left(d+e x^2\right)}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[(x^2*(d + e*x^2))/(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{x (b d-5 a e)}{8 a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{x (b d-a e)}{4 b^2 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\left(a+b x^2\right) (3 a e+b d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{3/2} b^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{x (b d-5 a e)}{8 a b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{x (b d-a e)}{4 b^2 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\left(a+b x^2\right) (3 a e+b d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{3/2} b^{5/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"((b*d - 5*a*e)*x)/(8*a*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - ((b*d - a*e)*x)/(4*b^2*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + ((b*d + 3*a*e)*(a + b*x^2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(3/2)*b^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,4,33,0.1212,1,"{1250, 455, 385, 205}"
82,1,77,0,0.0657618,"\int \frac{x \left(d+e x^2\right)}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[(x*(d + e*x^2))/(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","-\frac{b d-a e}{4 b^2 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{e}{2 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{b d-a e}{4 b^2 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{e}{2 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"-e/(2*b^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (b*d - a*e)/(4*b^2*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",3,3,31,0.09677,1,"{1247, 640, 607}"
83,1,156,0,0.0894809,"\int \frac{d+e x^2}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[(d + e*x^2)/(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{x (a e+3 b d)}{8 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{x (b d-a e)}{4 a b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\left(a+b x^2\right) (a e+3 b d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{5/2} b^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{x (a e+3 b d)}{8 a^2 b \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{x (b d-a e)}{4 a b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\left(a+b x^2\right) (a e+3 b d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{5/2} b^{3/2} \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"((3*b*d + a*e)*x)/(8*a^2*b*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + ((b*d - a*e)*x)/(4*a*b*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + ((3*b*d + a*e)*(a + b*x^2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(5/2)*b^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,4,30,0.1333,1,"{1148, 385, 199, 205}"
84,1,161,0,0.1182656,"\int \frac{d+e x^2}{x \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[(d + e*x^2)/(x*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)),x]","\frac{b d-a e}{4 a b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{d}{2 a^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{d \log (x) \left(a+b x^2\right)}{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d \left(a+b x^2\right) \log \left(a+b x^2\right)}{2 a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{b d-a e}{4 a b \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{d}{2 a^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{d \log (x) \left(a+b x^2\right)}{a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d \left(a+b x^2\right) \log \left(a+b x^2\right)}{2 a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"d/(2*a^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (b*d - a*e)/(4*a*b*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + (d*(a + b*x^2)*Log[x])/(a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*(a + b*x^2)*Log[a + b*x^2])/(2*a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,3,33,0.09091,1,"{1250, 446, 77}"
85,1,190,0,0.1854387,"\int \frac{d+e x^2}{x^2 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[(d + e*x^2)/(x^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)),x]","-\frac{x (7 b d-3 a e)}{8 a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{x (b d-a e)}{4 a^2 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3 \left(a+b x^2\right) (5 b d-a e) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{7/2} \sqrt{b} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d \left(a+b x^2\right)}{a^3 x \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{x (7 b d-3 a e)}{8 a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{x (b d-a e)}{4 a^2 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{3 \left(a+b x^2\right) (5 b d-a e) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{7/2} \sqrt{b} \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d \left(a+b x^2\right)}{a^3 x \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"-((7*b*d - 3*a*e)*x)/(8*a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - ((b*d - a*e)*x)/(4*a^2*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*(a + b*x^2))/(a^3*x*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (3*(5*b*d - a*e)*(a + b*x^2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(7/2)*Sqrt[b]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",5,4,33,0.1212,1,"{1250, 456, 453, 205}"
86,1,223,0,0.1837834,"\int \frac{d+e x^2}{x^3 \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[(d + e*x^2)/(x^3*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2)),x]","-\frac{b d-a e}{4 a^2 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{2 b d-a e}{2 a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\log (x) \left(a+b x^2\right) (3 b d-a e)}{a^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\left(a+b x^2\right) (3 b d-a e) \log \left(a+b x^2\right)}{2 a^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d \left(a+b x^2\right)}{2 a^3 x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}","-\frac{b d-a e}{4 a^2 \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{2 b d-a e}{2 a^3 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{\log (x) \left(a+b x^2\right) (3 b d-a e)}{a^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{\left(a+b x^2\right) (3 b d-a e) \log \left(a+b x^2\right)}{2 a^4 \sqrt{a^2+2 a b x^2+b^2 x^4}}-\frac{d \left(a+b x^2\right)}{2 a^3 x^2 \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"-(2*b*d - a*e)/(2*a^3*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (b*d - a*e)/(4*a^2*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - (d*(a + b*x^2))/(2*a^3*x^2*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) - ((3*b*d - a*e)*(a + b*x^2)*Log[x])/(a^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + ((3*b*d - a*e)*(a + b*x^2)*Log[a + b*x^2])/(2*a^4*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",4,3,33,0.09091,1,"{1250, 446, 77}"
87,1,400,0,0.242838,"\int (f x)^m \left(d+e x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{5/2} \, dx","Int[(f*x)^m*(d + e*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(5/2),x]","\frac{a^4 \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+3} (a e+5 b d)}{f^3 (m+3) \left(a+b x^2\right)}+\frac{5 a^3 b \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+5} (a e+2 b d)}{f^5 (m+5) \left(a+b x^2\right)}+\frac{10 a^2 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+7} (a e+b d)}{f^7 (m+7) \left(a+b x^2\right)}+\frac{5 a b^3 \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+9} (2 a e+b d)}{f^9 (m+9) \left(a+b x^2\right)}+\frac{b^4 \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+11} (5 a e+b d)}{f^{11} (m+11) \left(a+b x^2\right)}+\frac{a^5 d \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+1}}{f (m+1) \left(a+b x^2\right)}+\frac{b^5 e \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+13}}{f^{13} (m+13) \left(a+b x^2\right)}","\frac{a^4 \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+3} (a e+5 b d)}{f^3 (m+3) \left(a+b x^2\right)}+\frac{5 a^3 b \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+5} (a e+2 b d)}{f^5 (m+5) \left(a+b x^2\right)}+\frac{10 a^2 b^2 \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+7} (a e+b d)}{f^7 (m+7) \left(a+b x^2\right)}+\frac{5 a b^3 \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+9} (2 a e+b d)}{f^9 (m+9) \left(a+b x^2\right)}+\frac{b^4 \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+11} (5 a e+b d)}{f^{11} (m+11) \left(a+b x^2\right)}+\frac{a^5 d \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+1}}{f (m+1) \left(a+b x^2\right)}+\frac{b^5 e \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+13}}{f^{13} (m+13) \left(a+b x^2\right)}",1,"(a^5*d*(f*x)^(1 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(f*(1 + m)*(a + b*x^2)) + (a^4*(5*b*d + a*e)*(f*x)^(3 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(f^3*(3 + m)*(a + b*x^2)) + (5*a^3*b*(2*b*d + a*e)*(f*x)^(5 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(f^5*(5 + m)*(a + b*x^2)) + (10*a^2*b^2*(b*d + a*e)*(f*x)^(7 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(f^7*(7 + m)*(a + b*x^2)) + (5*a*b^3*(b*d + 2*a*e)*(f*x)^(9 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(f^9*(9 + m)*(a + b*x^2)) + (b^4*(b*d + 5*a*e)*(f*x)^(11 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(f^11*(11 + m)*(a + b*x^2)) + (b^5*e*(f*x)^(13 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(f^13*(13 + m)*(a + b*x^2))","A",3,2,35,0.05714,1,"{1250, 448}"
88,1,276,0,0.1528632,"\int (f x)^m \left(d+e x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^{3/2} \, dx","Int[(f*x)^m*(d + e*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{a^2 \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+3} (a e+3 b d)}{f^3 (m+3) \left(a+b x^2\right)}+\frac{3 a b \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+5} (a e+b d)}{f^5 (m+5) \left(a+b x^2\right)}+\frac{b^2 \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+7} (3 a e+b d)}{f^7 (m+7) \left(a+b x^2\right)}+\frac{a^3 d \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+1}}{f (m+1) \left(a+b x^2\right)}+\frac{b^3 e \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+9}}{f^9 (m+9) \left(a+b x^2\right)}","\frac{a^2 \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+3} (a e+3 b d)}{f^3 (m+3) \left(a+b x^2\right)}+\frac{3 a b \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+5} (a e+b d)}{f^5 (m+5) \left(a+b x^2\right)}+\frac{b^2 \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+7} (3 a e+b d)}{f^7 (m+7) \left(a+b x^2\right)}+\frac{a^3 d \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+1}}{f (m+1) \left(a+b x^2\right)}+\frac{b^3 e \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+9}}{f^9 (m+9) \left(a+b x^2\right)}",1,"(a^3*d*(f*x)^(1 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(f*(1 + m)*(a + b*x^2)) + (a^2*(3*b*d + a*e)*(f*x)^(3 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(f^3*(3 + m)*(a + b*x^2)) + (3*a*b*(b*d + a*e)*(f*x)^(5 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(f^5*(5 + m)*(a + b*x^2)) + (b^2*(b*d + 3*a*e)*(f*x)^(7 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(f^7*(7 + m)*(a + b*x^2)) + (b^3*e*(f*x)^(9 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(f^9*(9 + m)*(a + b*x^2))","A",3,2,35,0.05714,1,"{1250, 448}"
89,1,153,0,0.0762581,"\int (f x)^m \left(d+e x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4} \, dx","Int[(f*x)^m*(d + e*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{\sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+3} (a e+b d)}{f^3 (m+3) \left(a+b x^2\right)}+\frac{a d \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+1}}{f (m+1) \left(a+b x^2\right)}+\frac{b e \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+5}}{f^5 (m+5) \left(a+b x^2\right)}","\frac{\sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+3} (a e+b d)}{f^3 (m+3) \left(a+b x^2\right)}+\frac{a d \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+1}}{f (m+1) \left(a+b x^2\right)}+\frac{b e \sqrt{a^2+2 a b x^2+b^2 x^4} (f x)^{m+5}}{f^5 (m+5) \left(a+b x^2\right)}",1,"(a*d*(f*x)^(1 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(f*(1 + m)*(a + b*x^2)) + ((b*d + a*e)*(f*x)^(3 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(f^3*(3 + m)*(a + b*x^2)) + (b*e*(f*x)^(5 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(f^5*(5 + m)*(a + b*x^2))","A",3,2,35,0.05714,1,"{1250, 448}"
90,1,134,0,0.0883244,"\int \frac{(f x)^m \left(d+e x^2\right)}{\sqrt{a^2+2 a b x^2+b^2 x^4}} \, dx","Int[((f*x)^m*(d + e*x^2))/Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{\left(a+b x^2\right) (f x)^{m+1} (b d-a e) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a b f (m+1) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{e \left(a+b x^2\right) (f x)^{m+1}}{b f (m+1) \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{\left(a+b x^2\right) (f x)^{m+1} (b d-a e) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a b f (m+1) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{e \left(a+b x^2\right) (f x)^{m+1}}{b f (m+1) \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"(e*(f*x)^(1 + m)*(a + b*x^2))/(b*f*(1 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + ((b*d - a*e)*(f*x)^(1 + m)*(a + b*x^2)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a*b*f*(1 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",3,3,35,0.08571,1,"{1250, 459, 364}"
91,1,154,0,0.119163,"\int \frac{(f x)^m \left(d+e x^2\right)}{\left(a^2+2 a b x^2+b^2 x^4\right)^{3/2}} \, dx","Int[((f*x)^m*(d + e*x^2))/(a^2 + 2*a*b*x^2 + b^2*x^4)^(3/2),x]","\frac{\left(a+b x^2\right) (f x)^{m+1} (a e (m+1)+b d (3-m)) \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{4 a^3 b f (m+1) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{(f x)^{m+1} (b d-a e)}{4 a b f \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}","\frac{\left(a+b x^2\right) (f x)^{m+1} (a e (m+1)+b d (3-m)) \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{4 a^3 b f (m+1) \sqrt{a^2+2 a b x^2+b^2 x^4}}+\frac{(f x)^{m+1} (b d-a e)}{4 a b f \left(a+b x^2\right) \sqrt{a^2+2 a b x^2+b^2 x^4}}",1,"((b*d - a*e)*(f*x)^(1 + m))/(4*a*b*f*(a + b*x^2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]) + ((b*d*(3 - m) + a*e*(1 + m))*(f*x)^(1 + m)*(a + b*x^2)*Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(4*a^3*b*f*(1 + m)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])","A",3,3,35,0.08571,1,"{1250, 457, 364}"
92,1,34,0,0.0289665,"\int x \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^p \, dx","Int[x*(a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^p,x]","\frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{p+1}}{4 b (p+1)}","\frac{\left(a^2+2 a b x^2+b^2 x^4\right)^{p+1}}{4 b (p+1)}",1,"(a^2 + 2*a*b*x^2 + b^2*x^4)^(1 + p)/(4*b*(1 + p))","A",2,2,29,0.06897,1,"{1247, 629}"
93,1,86,0,0.0887778,"\int x^3 \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^p \, dx","Int[x^3*(a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^p,x]","\frac{\left(a+b x^2\right)^3 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{2 b^2 (2 p+3)}-\frac{a \left(a+b x^2\right)^2 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{4 b^2 (p+1)}","\frac{\left(a+b x^2\right)^3 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{2 b^2 (2 p+3)}-\frac{a \left(a+b x^2\right)^2 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{4 b^2 (p+1)}",1,"-(a*(a + b*x^2)^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^p)/(4*b^2*(1 + p)) + ((a + b*x^2)^3*(a^2 + 2*a*b*x^2 + b^2*x^4)^p)/(2*b^2*(3 + 2*p))","A",5,4,31,0.1290,1,"{1249, 770, 21, 43}"
94,1,128,0,0.1289929,"\int x^5 \left(a+b x^2\right) \left(a^2+2 a b x^2+b^2 x^4\right)^p \, dx","Int[x^5*(a + b*x^2)*(a^2 + 2*a*b*x^2 + b^2*x^4)^p,x]","\frac{\left(a+b x^2\right)^4 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{4 b^3 (p+2)}-\frac{a \left(a+b x^2\right)^3 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{b^3 (2 p+3)}+\frac{a^2 \left(a+b x^2\right)^2 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{4 b^3 (p+1)}","\frac{\left(a+b x^2\right)^4 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{4 b^3 (p+2)}-\frac{a \left(a+b x^2\right)^3 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{b^3 (2 p+3)}+\frac{a^2 \left(a+b x^2\right)^2 \left(a^2+2 a b x^2+b^2 x^4\right)^p}{4 b^3 (p+1)}",1,"(a^2*(a + b*x^2)^2*(a^2 + 2*a*b*x^2 + b^2*x^4)^p)/(4*b^3*(1 + p)) - (a*(a + b*x^2)^3*(a^2 + 2*a*b*x^2 + b^2*x^4)^p)/(b^3*(3 + 2*p)) + ((a + b*x^2)^4*(a^2 + 2*a*b*x^2 + b^2*x^4)^p)/(4*b^3*(2 + p))","A",5,4,31,0.1290,1,"{1249, 770, 21, 43}"
95,1,166,0,0.3934878,"\int x^3 \left(A+B x^2\right) \left(a+b x^2+c x^4\right)^3 \, dx","Int[x^3*(A + B*x^2)*(a + b*x^2 + c*x^4)^3,x]","\frac{1}{6} a^2 x^6 (a B+3 A b)+\frac{1}{4} a^3 A x^4+\frac{1}{12} x^{12} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{3}{14} c x^{14} \left(a B c+A b c+b^2 B\right)+\frac{1}{10} x^{10} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{3}{8} a x^8 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{16} c^2 x^{16} (A c+3 b B)+\frac{1}{18} B c^3 x^{18}","\frac{1}{6} a^2 x^6 (a B+3 A b)+\frac{1}{4} a^3 A x^4+\frac{1}{12} x^{12} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{3}{14} c x^{14} \left(a B c+A b c+b^2 B\right)+\frac{1}{10} x^{10} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{3}{8} a x^8 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{16} c^2 x^{16} (A c+3 b B)+\frac{1}{18} B c^3 x^{18}",1,"(a^3*A*x^4)/4 + (a^2*(3*A*b + a*B)*x^6)/6 + (3*a*(a*b*B + A*(b^2 + a*c))*x^8)/8 + ((3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^10)/10 + ((b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^12)/12 + (3*c*(b^2*B + A*b*c + a*B*c)*x^14)/14 + (c^2*(3*b*B + A*c)*x^16)/16 + (B*c^3*x^18)/18","A",3,2,25,0.08000,1,"{1251, 765}"
96,1,166,0,0.1535066,"\int x^2 \left(A+B x^2\right) \left(a+b x^2+c x^4\right)^3 \, dx","Int[x^2*(A + B*x^2)*(a + b*x^2 + c*x^4)^3,x]","\frac{1}{5} a^2 x^5 (a B+3 A b)+\frac{1}{3} a^3 A x^3+\frac{1}{11} x^{11} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{3}{13} c x^{13} \left(a B c+A b c+b^2 B\right)+\frac{1}{9} x^9 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{3}{7} a x^7 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{15} c^2 x^{15} (A c+3 b B)+\frac{1}{17} B c^3 x^{17}","\frac{1}{5} a^2 x^5 (a B+3 A b)+\frac{1}{3} a^3 A x^3+\frac{1}{11} x^{11} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{3}{13} c x^{13} \left(a B c+A b c+b^2 B\right)+\frac{1}{9} x^9 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{3}{7} a x^7 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{15} c^2 x^{15} (A c+3 b B)+\frac{1}{17} B c^3 x^{17}",1,"(a^3*A*x^3)/3 + (a^2*(3*A*b + a*B)*x^5)/5 + (3*a*(a*b*B + A*(b^2 + a*c))*x^7)/7 + ((3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^9)/9 + ((b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^11)/11 + (3*c*(b^2*B + A*b*c + a*B*c)*x^13)/13 + (c^2*(3*b*B + A*c)*x^15)/15 + (B*c^3*x^17)/17","A",2,1,25,0.04000,1,"{1261}"
97,1,166,0,0.2867619,"\int x \left(A+B x^2\right) \left(a+b x^2+c x^4\right)^3 \, dx","Int[x*(A + B*x^2)*(a + b*x^2 + c*x^4)^3,x]","\frac{1}{4} a^2 x^4 (a B+3 A b)+\frac{1}{2} a^3 A x^2+\frac{1}{10} x^{10} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{1}{4} c x^{12} \left(a B c+A b c+b^2 B\right)+\frac{1}{8} x^8 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{1}{2} a x^6 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{14} c^2 x^{14} (A c+3 b B)+\frac{1}{16} B c^3 x^{16}","\frac{1}{4} a^2 x^4 (a B+3 A b)+\frac{1}{2} a^3 A x^2+\frac{1}{10} x^{10} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{1}{4} c x^{12} \left(a B c+A b c+b^2 B\right)+\frac{1}{8} x^8 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{1}{2} a x^6 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{14} c^2 x^{14} (A c+3 b B)+\frac{1}{16} B c^3 x^{16}",1,"(a^3*A*x^2)/2 + (a^2*(3*A*b + a*B)*x^4)/4 + (a*(a*b*B + A*(b^2 + a*c))*x^6)/2 + ((3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^8)/8 + ((b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^10)/10 + (c*(b^2*B + A*b*c + a*B*c)*x^12)/4 + (c^2*(3*b*B + A*c)*x^14)/14 + (B*c^3*x^16)/16","A",3,2,23,0.08696,1,"{1247, 631}"
98,1,161,0,0.1177798,"\int \left(A+B x^2\right) \left(a+b x^2+c x^4\right)^3 \, dx","Int[(A + B*x^2)*(a + b*x^2 + c*x^4)^3,x]","\frac{1}{3} a^2 x^3 (a B+3 A b)+a^3 A x+\frac{1}{9} x^9 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{3}{11} c x^{11} \left(a B c+A b c+b^2 B\right)+\frac{1}{7} x^7 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{3}{5} a x^5 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{13} c^2 x^{13} (A c+3 b B)+\frac{1}{15} B c^3 x^{15}","\frac{1}{3} a^2 x^3 (a B+3 A b)+a^3 A x+\frac{1}{9} x^9 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{3}{11} c x^{11} \left(a B c+A b c+b^2 B\right)+\frac{1}{7} x^7 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{3}{5} a x^5 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{13} c^2 x^{13} (A c+3 b B)+\frac{1}{15} B c^3 x^{15}",1,"a^3*A*x + (a^2*(3*A*b + a*B)*x^3)/3 + (3*a*(a*b*B + A*(b^2 + a*c))*x^5)/5 + ((3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^7)/7 + ((b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^9)/9 + (3*c*(b^2*B + A*b*c + a*B*c)*x^11)/11 + (c^2*(3*b*B + A*c)*x^13)/13 + (B*c^3*x^15)/15","A",2,1,22,0.04545,1,"{1153}"
99,1,162,0,0.227069,"\int \frac{\left(A+B x^2\right) \left(a+b x^2+c x^4\right)^3}{x} \, dx","Int[((A + B*x^2)*(a + b*x^2 + c*x^4)^3)/x,x]","\frac{1}{2} a^2 x^2 (a B+3 A b)+a^3 A \log (x)+\frac{1}{8} x^8 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{3}{10} c x^{10} \left(a B c+A b c+b^2 B\right)+\frac{1}{6} x^6 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{3}{4} a x^4 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{12} c^2 x^{12} (A c+3 b B)+\frac{1}{14} B c^3 x^{14}","\frac{1}{2} a^2 x^2 (a B+3 A b)+a^3 A \log (x)+\frac{1}{8} x^8 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{3}{10} c x^{10} \left(a B c+A b c+b^2 B\right)+\frac{1}{6} x^6 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{3}{4} a x^4 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{12} c^2 x^{12} (A c+3 b B)+\frac{1}{14} B c^3 x^{14}",1,"(a^2*(3*A*b + a*B)*x^2)/2 + (3*a*(a*b*B + A*(b^2 + a*c))*x^4)/4 + ((3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^6)/6 + ((b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^8)/8 + (3*c*(b^2*B + A*b*c + a*B*c)*x^10)/10 + (c^2*(3*b*B + A*c)*x^12)/12 + (B*c^3*x^14)/14 + a^3*A*Log[x]","A",3,2,25,0.08000,1,"{1251, 765}"
100,1,156,0,0.1080457,"\int \frac{\left(A+B x^2\right) \left(a+b x^2+c x^4\right)^3}{x^2} \, dx","Int[((A + B*x^2)*(a + b*x^2 + c*x^4)^3)/x^2,x]","a^2 x (a B+3 A b)-\frac{a^3 A}{x}+\frac{1}{7} x^7 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{1}{3} c x^9 \left(a B c+A b c+b^2 B\right)+\frac{1}{5} x^5 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+a x^3 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{11} c^2 x^{11} (A c+3 b B)+\frac{1}{13} B c^3 x^{13}","a^2 x (a B+3 A b)-\frac{a^3 A}{x}+\frac{1}{7} x^7 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{1}{3} c x^9 \left(a B c+A b c+b^2 B\right)+\frac{1}{5} x^5 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+a x^3 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{11} c^2 x^{11} (A c+3 b B)+\frac{1}{13} B c^3 x^{13}",1,"-((a^3*A)/x) + a^2*(3*A*b + a*B)*x + a*(a*b*B + A*(b^2 + a*c))*x^3 + ((3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^5)/5 + ((b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^7)/7 + (c*(b^2*B + A*b*c + a*B*c)*x^9)/3 + (c^2*(3*b*B + A*c)*x^11)/11 + (B*c^3*x^13)/13","A",2,1,25,0.04000,1,"{1261}"
101,1,162,0,0.22608,"\int \frac{\left(A+B x^2\right) \left(a+b x^2+c x^4\right)^3}{x^3} \, dx","Int[((A + B*x^2)*(a + b*x^2 + c*x^4)^3)/x^3,x]","a^2 \log (x) (a B+3 A b)-\frac{a^3 A}{2 x^2}+\frac{1}{6} x^6 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{3}{8} c x^8 \left(a B c+A b c+b^2 B\right)+\frac{1}{4} x^4 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{3}{2} a x^2 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{10} c^2 x^{10} (A c+3 b B)+\frac{1}{12} B c^3 x^{12}","a^2 \log (x) (a B+3 A b)-\frac{a^3 A}{2 x^2}+\frac{1}{6} x^6 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{3}{8} c x^8 \left(a B c+A b c+b^2 B\right)+\frac{1}{4} x^4 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{3}{2} a x^2 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{10} c^2 x^{10} (A c+3 b B)+\frac{1}{12} B c^3 x^{12}",1,"-(a^3*A)/(2*x^2) + (3*a*(a*b*B + A*(b^2 + a*c))*x^2)/2 + ((3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^4)/4 + ((b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^6)/6 + (3*c*(b^2*B + A*b*c + a*B*c)*x^8)/8 + (c^2*(3*b*B + A*c)*x^10)/10 + (B*c^3*x^12)/12 + a^2*(3*A*b + a*B)*Log[x]","A",3,2,25,0.08000,1,"{1251, 765}"
102,1,133,0,0.2067239,"\int \frac{x^5 \left(A+B x^2\right)}{a+b x^2+c x^4} \, dx","Int[(x^5*(A + B*x^2))/(a + b*x^2 + c*x^4),x]","\frac{\left(-a B c-A b c+b^2 B\right) \log \left(a+b x^2+c x^4\right)}{4 c^3}+\frac{\left(2 a A c^2-3 a b B c-A b^2 c+b^3 B\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^3 \sqrt{b^2-4 a c}}-\frac{x^2 (b B-A c)}{2 c^2}+\frac{B x^4}{4 c}","\frac{\left(-a B c-A b c+b^2 B\right) \log \left(a+b x^2+c x^4\right)}{4 c^3}+\frac{\left(2 a A c^2-3 a b B c-A b^2 c+b^3 B\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^3 \sqrt{b^2-4 a c}}-\frac{x^2 (b B-A c)}{2 c^2}+\frac{B x^4}{4 c}",1,"-((b*B - A*c)*x^2)/(2*c^2) + (B*x^4)/(4*c) + ((b^3*B - A*b^2*c - 3*a*b*B*c + 2*a*A*c^2)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^3*Sqrt[b^2 - 4*a*c]) + ((b^2*B - A*b*c - a*B*c)*Log[a + b*x^2 + c*x^4])/(4*c^3)","A",7,6,25,0.2400,1,"{1251, 800, 634, 618, 206, 628}"
103,1,97,0,0.1160545,"\int \frac{x^3 \left(A+B x^2\right)}{a+b x^2+c x^4} \, dx","Int[(x^3*(A + B*x^2))/(a + b*x^2 + c*x^4),x]","-\frac{\left(-2 a B c-A b c+b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^2 \sqrt{b^2-4 a c}}-\frac{(b B-A c) \log \left(a+b x^2+c x^4\right)}{4 c^2}+\frac{B x^2}{2 c}","-\frac{\left(-2 a B c-A b c+b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^2 \sqrt{b^2-4 a c}}-\frac{(b B-A c) \log \left(a+b x^2+c x^4\right)}{4 c^2}+\frac{B x^2}{2 c}",1,"(B*x^2)/(2*c) - ((b^2*B - A*b*c - 2*a*B*c)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^2*Sqrt[b^2 - 4*a*c]) - ((b*B - A*c)*Log[a + b*x^2 + c*x^4])/(4*c^2)","A",6,6,25,0.2400,1,"{1251, 773, 634, 618, 206, 628}"
104,1,71,0,0.0702653,"\int \frac{x \left(A+B x^2\right)}{a+b x^2+c x^4} \, dx","Int[(x*(A + B*x^2))/(a + b*x^2 + c*x^4),x]","\frac{(b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c \sqrt{b^2-4 a c}}+\frac{B \log \left(a+b x^2+c x^4\right)}{4 c}","\frac{(b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c \sqrt{b^2-4 a c}}+\frac{B \log \left(a+b x^2+c x^4\right)}{4 c}",1,"((b*B - 2*A*c)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c*Sqrt[b^2 - 4*a*c]) + (B*Log[a + b*x^2 + c*x^4])/(4*c)","A",5,5,23,0.2174,1,"{1247, 634, 618, 206, 628}"
105,1,78,0,0.1386586,"\int \frac{A+B x^2}{x \left(a+b x^2+c x^4\right)} \, dx","Int[(A + B*x^2)/(x*(a + b*x^2 + c*x^4)),x]","\frac{(A b-2 a B) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a \sqrt{b^2-4 a c}}-\frac{A \log \left(a+b x^2+c x^4\right)}{4 a}+\frac{A \log (x)}{a}","\frac{(A b-2 a B) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a \sqrt{b^2-4 a c}}-\frac{A \log \left(a+b x^2+c x^4\right)}{4 a}+\frac{A \log (x)}{a}",1,"((A*b - 2*a*B)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a*Sqrt[b^2 - 4*a*c]) + (A*Log[x])/a - (A*Log[a + b*x^2 + c*x^4])/(4*a)","A",7,6,25,0.2400,1,"{1251, 800, 634, 618, 206, 628}"
106,1,112,0,0.2454909,"\int \frac{A+B x^2}{x^3 \left(a+b x^2+c x^4\right)} \, dx","Int[(A + B*x^2)/(x^3*(a + b*x^2 + c*x^4)),x]","-\frac{\left(-2 a A c-a b B+A b^2\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \sqrt{b^2-4 a c}}+\frac{(A b-a B) \log \left(a+b x^2+c x^4\right)}{4 a^2}-\frac{\log (x) (A b-a B)}{a^2}-\frac{A}{2 a x^2}","-\frac{\left(-2 a A c-a b B+A b^2\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \sqrt{b^2-4 a c}}+\frac{(A b-a B) \log \left(a+b x^2+c x^4\right)}{4 a^2}-\frac{\log (x) (A b-a B)}{a^2}-\frac{A}{2 a x^2}",1,"-A/(2*a*x^2) - ((A*b^2 - a*b*B - 2*a*A*c)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^2*Sqrt[b^2 - 4*a*c]) - ((A*b - a*B)*Log[x])/a^2 + ((A*b - a*B)*Log[a + b*x^2 + c*x^4])/(4*a^2)","A",7,6,25,0.2400,1,"{1251, 800, 634, 618, 206, 628}"
107,1,261,0,1.4885077,"\int \frac{x^4 \left(A+B x^2\right)}{a+b x^2+c x^4} \, dx","Int[(x^4*(A + B*x^2))/(a + b*x^2 + c*x^4),x]","\frac{\left(-\frac{2 a A c^2-3 a b B c-A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}-a B c-A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{2 a A c^2-3 a b B c-A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}-a B c-A b c+b^2 B\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{x (b B-A c)}{c^2}+\frac{B x^3}{3 c}","\frac{\left(-\frac{2 a A c^2-3 a b B c-A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}-a B c-A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{2 a A c^2-3 a b B c-A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}-a B c-A b c+b^2 B\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{x (b B-A c)}{c^2}+\frac{B x^3}{3 c}",1,"-(((b*B - A*c)*x)/c^2) + (B*x^3)/(3*c) + ((b^2*B - A*b*c - a*B*c - (b^3*B - A*b^2*c - 3*a*b*B*c + 2*a*A*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b^2*B - A*b*c - a*B*c + (b^3*B - A*b^2*c - 3*a*b*B*c + 2*a*A*c^2)/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",5,3,25,0.1200,1,"{1279, 1166, 205}"
108,1,208,0,0.5277673,"\int \frac{x^2 \left(A+B x^2\right)}{a+b x^2+c x^4} \, dx","Int[(x^2*(A + B*x^2))/(a + b*x^2 + c*x^4),x]","-\frac{\left(-\frac{-2 a B c-A b c+b^2 B}{\sqrt{b^2-4 a c}}-A c+b B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{-2 a B c-A b c+b^2 B}{\sqrt{b^2-4 a c}}-A c+b B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{B x}{c}","-\frac{\left(-\frac{-2 a B c-A b c+b^2 B}{\sqrt{b^2-4 a c}}-A c+b B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{-2 a B c-A b c+b^2 B}{\sqrt{b^2-4 a c}}-A c+b B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{B x}{c}",1,"(B*x)/c - ((b*B - A*c - (b^2*B - A*b*c - 2*a*B*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((b*B - A*c + (b^2*B - A*b*c - 2*a*B*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,25,0.1200,1,"{1279, 1166, 205}"
109,1,172,0,0.2014376,"\int \frac{A+B x^2}{a+b x^2+c x^4} \, dx","Int[(A + B*x^2)/(a + b*x^2 + c*x^4),x]","\frac{\left(B-\frac{b B-2 A c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{b B-2 A c}{\sqrt{b^2-4 a c}}+B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{\left(B-\frac{b B-2 A c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{b B-2 A c}{\sqrt{b^2-4 a c}}+B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"((B - (b*B - 2*A*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((B + (b*B - 2*A*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",3,2,22,0.09091,1,"{1166, 205}"
110,1,189,0,0.4003989,"\int \frac{A+B x^2}{x^2 \left(a+b x^2+c x^4\right)} \, dx","Int[(A + B*x^2)/(x^2*(a + b*x^2 + c*x^4)),x]","-\frac{\sqrt{c} \left(\frac{A b-2 a B}{\sqrt{b^2-4 a c}}+A\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(A-\frac{A b-2 a B}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{A}{a x}","-\frac{\sqrt{c} \left(\frac{A b-2 a B}{\sqrt{b^2-4 a c}}+A\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(A-\frac{A b-2 a B}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{A}{a x}",1,"-(A/(a*x)) - (Sqrt[c]*(A + (A*b - 2*a*B)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(A - (A*b - 2*a*B)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,25,0.1200,1,"{1281, 1166, 205}"
111,1,271,0,0.6527116,"\int \frac{A+B x^2}{x^4 \left(a+b x^2+c x^4\right)} \, dx","Int[(A + B*x^2)/(x^4*(a + b*x^2 + c*x^4)),x]","-\frac{\sqrt{c} \left(a B \left(\sqrt{b^2-4 a c}+b\right)-A \left(b \sqrt{b^2-4 a c}-2 a c+b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a^2 \sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(a B \left(b-\sqrt{b^2-4 a c}\right)-A \left(-b \sqrt{b^2-4 a c}-2 a c+b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a^2 \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{A b-a B}{a^2 x}-\frac{A}{3 a x^3}","-\frac{\sqrt{c} \left(a B \left(\sqrt{b^2-4 a c}+b\right)-A \left(b \sqrt{b^2-4 a c}-2 a c+b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a^2 \sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(a B \left(b-\sqrt{b^2-4 a c}\right)-A \left(-b \sqrt{b^2-4 a c}-2 a c+b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a^2 \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{A b-a B}{a^2 x}-\frac{A}{3 a x^3}",1,"-A/(3*a*x^3) + (A*b - a*B)/(a^2*x) - (Sqrt[c]*(a*B*(b + Sqrt[b^2 - 4*a*c]) - A*(b^2 - 2*a*c + b*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^2*Sqrt[b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(a*B*(b - Sqrt[b^2 - 4*a*c]) - A*(b^2 - 2*a*c - b*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^2*Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,3,25,0.1200,1,"{1281, 1166, 205}"
112,1,212,0,0.3812391,"\int \frac{x^7 \left(A+B x^2\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x^7*(A + B*x^2))/(a + b*x^2 + c*x^4)^2,x]","-\frac{\left(12 a^2 B c^2+6 a A b c^2-12 a b^2 B c-A b^3 c+2 b^4 B\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^3 \left(b^2-4 a c\right)^{3/2}}+\frac{x^2 \left(-6 a B c-A b c+2 b^2 B\right)}{2 c^2 \left(b^2-4 a c\right)}-\frac{x^4 \left(x^2 \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{2 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{(2 b B-A c) \log \left(a+b x^2+c x^4\right)}{4 c^3}","-\frac{\left(12 a^2 B c^2+6 a A b c^2-12 a b^2 B c-A b^3 c+2 b^4 B\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^3 \left(b^2-4 a c\right)^{3/2}}+\frac{x^2 \left(-6 a B c-A b c+2 b^2 B\right)}{2 c^2 \left(b^2-4 a c\right)}-\frac{x^4 \left(x^2 \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{2 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{(2 b B-A c) \log \left(a+b x^2+c x^4\right)}{4 c^3}",1,"((2*b^2*B - A*b*c - 6*a*B*c)*x^2)/(2*c^2*(b^2 - 4*a*c)) - (x^4*(a*(b*B - 2*A*c) + (b^2*B - A*b*c - 2*a*B*c)*x^2))/(2*c*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((2*b^4*B - A*b^3*c - 12*a*b^2*B*c + 6*a*A*b*c^2 + 12*a^2*B*c^2)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^3*(b^2 - 4*a*c)^(3/2)) - ((2*b*B - A*c)*Log[a + b*x^2 + c*x^4])/(4*c^3)","A",7,7,25,0.2800,1,"{1251, 818, 773, 634, 618, 206, 628}"
113,1,147,0,0.1746673,"\int \frac{x^5 \left(A+B x^2\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x^5*(A + B*x^2))/(a + b*x^2 + c*x^4)^2,x]","\frac{\left(4 a A c^2-6 a b B c+b^3 B\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^2 \left(b^2-4 a c\right)^{3/2}}-\frac{x^2 \left(x^2 \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{2 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{B \log \left(a+b x^2+c x^4\right)}{4 c^2}","\frac{\left(4 a A c^2-6 a b B c+b^3 B\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^2 \left(b^2-4 a c\right)^{3/2}}-\frac{x^2 \left(x^2 \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{2 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{B \log \left(a+b x^2+c x^4\right)}{4 c^2}",1,"-(x^2*(a*(b*B - 2*A*c) + (b^2*B - A*b*c - 2*a*B*c)*x^2))/(2*c*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((b^3*B - 6*a*b*B*c + 4*a*A*c^2)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^2*(b^2 - 4*a*c)^(3/2)) + (B*Log[a + b*x^2 + c*x^4])/(4*c^2)","A",6,6,25,0.2400,1,"{1251, 818, 634, 618, 206, 628}"
114,1,107,0,0.1134405,"\int \frac{x^3 \left(A+B x^2\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x^3*(A + B*x^2))/(a + b*x^2 + c*x^4)^2,x]","-\frac{x^2 \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)}{2 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{(A b-2 a B) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}","-\frac{x^2 \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)}{2 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{(A b-2 a B) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}",1,"-(a*(b*B - 2*A*c) + (b^2*B - A*b*c - 2*a*B*c)*x^2)/(2*c*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((A*b - 2*a*B)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",4,4,25,0.1600,1,"{1251, 777, 618, 206}"
115,1,94,0,0.0876177,"\int \frac{x \left(A+B x^2\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x*(A + B*x^2))/(a + b*x^2 + c*x^4)^2,x]","-\frac{-2 a B+x^2 (-(b B-2 A c))+A b}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{(b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}","-\frac{-2 a B+x^2 (-(b B-2 A c))+A b}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{(b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}",1,"-(A*b - 2*a*B - (b*B - 2*A*c)*x^2)/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((b*B - 2*A*c)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",4,4,23,0.1739,1,"{1247, 638, 618, 206}"
116,1,150,0,0.3306703,"\int \frac{A+B x^2}{x \left(a+b x^2+c x^4\right)^2} \, dx","Int[(A + B*x^2)/(x*(a + b*x^2 + c*x^4)^2),x]","\frac{\left(4 a^2 B c+A \left(b^3-6 a b c\right)\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \left(b^2-4 a c\right)^{3/2}}-\frac{A \log \left(a+b x^2+c x^4\right)}{4 a^2}+\frac{A \log (x)}{a^2}-\frac{-A \left(b^2-2 a c\right)+c x^2 (-(A b-2 a B))+a b B}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","\frac{\left(4 a^2 B c+A \left(b^3-6 a b c\right)\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \left(b^2-4 a c\right)^{3/2}}-\frac{A \log \left(a+b x^2+c x^4\right)}{4 a^2}+\frac{A \log (x)}{a^2}-\frac{-A \left(b^2-2 a c\right)+c x^2 (-(A b-2 a B))+a b B}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"-(a*b*B - A*(b^2 - 2*a*c) - (A*b - 2*a*B)*c*x^2)/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((4*a^2*B*c + A*(b^3 - 6*a*b*c))*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^2*(b^2 - 4*a*c)^(3/2)) + (A*Log[x])/a^2 - (A*Log[a + b*x^2 + c*x^4])/(4*a^2)","A",8,7,25,0.2800,1,"{1251, 822, 800, 634, 618, 206, 628}"
117,1,223,0,0.4189066,"\int \frac{A+B x^2}{x^3 \left(a+b x^2+c x^4\right)^2} \, dx","Int[(A + B*x^2)/(x^3*(a + b*x^2 + c*x^4)^2),x]","\frac{\left(a b B \left(b^2-6 a c\right)-2 A \left(6 a^2 c^2-6 a b^2 c+b^4\right)\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^3 \left(b^2-4 a c\right)^{3/2}}-\frac{-6 a A c-a b B+2 A b^2}{2 a^2 x^2 \left(b^2-4 a c\right)}+\frac{(2 A b-a B) \log \left(a+b x^2+c x^4\right)}{4 a^3}-\frac{\log (x) (2 A b-a B)}{a^3}-\frac{-A \left(b^2-2 a c\right)+c x^2 (-(A b-2 a B))+a b B}{2 a x^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","\frac{\left(a b B \left(b^2-6 a c\right)-2 A \left(6 a^2 c^2-6 a b^2 c+b^4\right)\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^3 \left(b^2-4 a c\right)^{3/2}}-\frac{-6 a A c-a b B+2 A b^2}{2 a^2 x^2 \left(b^2-4 a c\right)}+\frac{(2 A b-a B) \log \left(a+b x^2+c x^4\right)}{4 a^3}-\frac{\log (x) (2 A b-a B)}{a^3}-\frac{-A \left(b^2-2 a c\right)+c x^2 (-(A b-2 a B))+a b B}{2 a x^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"-(2*A*b^2 - a*b*B - 6*a*A*c)/(2*a^2*(b^2 - 4*a*c)*x^2) - (a*b*B - A*(b^2 - 2*a*c) - (A*b - 2*a*B)*c*x^2)/(2*a*(b^2 - 4*a*c)*x^2*(a + b*x^2 + c*x^4)) + ((a*b*B*(b^2 - 6*a*c) - 2*A*(b^4 - 6*a*b^2*c + 6*a^2*c^2))*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^3*(b^2 - 4*a*c)^(3/2)) - ((2*A*b - a*B)*Log[x])/a^3 + ((2*A*b - a*B)*Log[a + b*x^2 + c*x^4])/(4*a^3)","A",8,7,25,0.2800,1,"{1251, 822, 800, 634, 618, 206, 628}"
118,1,425,0,3.6747207,"\int \frac{x^6 \left(A+B x^2\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x^6*(A + B*x^2))/(a + b*x^2 + c*x^4)^2,x]","-\frac{\left(-\frac{20 a^2 B c^2+8 a A b c^2-19 a b^2 B c-A b^3 c+3 b^4 B}{\sqrt{b^2-4 a c}}+6 a A c^2-13 a b B c-A b^2 c+3 b^3 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{20 a^2 B c^2+8 a A b c^2-19 a b^2 B c-A b^3 c+3 b^4 B}{\sqrt{b^2-4 a c}}+6 a A c^2-13 a b B c-A b^2 c+3 b^3 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x \left(-10 a B c-A b c+3 b^2 B\right)}{2 c^2 \left(b^2-4 a c\right)}-\frac{x^5 \left(-2 a B+x^2 (-(b B-2 A c))+A b\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{x^3 (b B-2 A c)}{2 c \left(b^2-4 a c\right)}","-\frac{\left(-\frac{20 a^2 B c^2+8 a A b c^2-19 a b^2 B c-A b^3 c+3 b^4 B}{\sqrt{b^2-4 a c}}+6 a A c^2-13 a b B c-A b^2 c+3 b^3 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{20 a^2 B c^2+8 a A b c^2-19 a b^2 B c-A b^3 c+3 b^4 B}{\sqrt{b^2-4 a c}}+6 a A c^2-13 a b B c-A b^2 c+3 b^3 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x \left(-10 a B c-A b c+3 b^2 B\right)}{2 c^2 \left(b^2-4 a c\right)}-\frac{x^5 \left(-2 a B+x^2 (-(b B-2 A c))+A b\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{x^3 (b B-2 A c)}{2 c \left(b^2-4 a c\right)}",1,"((3*b^2*B - A*b*c - 10*a*B*c)*x)/(2*c^2*(b^2 - 4*a*c)) - ((b*B - 2*A*c)*x^3)/(2*c*(b^2 - 4*a*c)) - (x^5*(A*b - 2*a*B - (b*B - 2*A*c)*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - ((3*b^3*B - A*b^2*c - 13*a*b*B*c + 6*a*A*c^2 - (3*b^4*B - A*b^3*c - 19*a*b^2*B*c + 8*a*A*b*c^2 + 20*a^2*B*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((3*b^3*B - A*b^2*c - 13*a*b*B*c + 6*a*A*c^2 + (3*b^4*B - A*b^3*c - 19*a*b^2*B*c + 8*a*A*b*c^2 + 20*a^2*B*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,4,25,0.1600,1,"{1275, 1279, 1166, 205}"
119,1,336,0,1.7169674,"\int \frac{x^4 \left(A+B x^2\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x^4*(A + B*x^2))/(a + b*x^2 + c*x^4)^2,x]","\frac{\left(-\frac{4 a A c^2-8 a b B c+A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}-6 a B c+A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} c^{3/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{4 a A c^2-8 a b B c+A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}-6 a B c+A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} c^{3/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{x^3 \left(-2 a B+x^2 (-(b B-2 A c))+A b\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{x (b B-2 A c)}{2 c \left(b^2-4 a c\right)}","\frac{\left(-\frac{4 a A c^2-8 a b B c+A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}-6 a B c+A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} c^{3/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{4 a A c^2-8 a b B c+A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}-6 a B c+A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} c^{3/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{x^3 \left(-2 a B+x^2 (-(b B-2 A c))+A b\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}-\frac{x (b B-2 A c)}{2 c \left(b^2-4 a c\right)}",1,"-((b*B - 2*A*c)*x)/(2*c*(b^2 - 4*a*c)) - (x^3*(A*b - 2*a*B - (b*B - 2*A*c)*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((b^2*B + A*b*c - 6*a*B*c - (b^3*B + A*b^2*c - 8*a*b*B*c + 4*a*A*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b^2*B + A*b*c - 6*a*B*c + (b^3*B + A*b^2*c - 8*a*b*B*c + 4*a*A*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,25,0.1600,1,"{1275, 1279, 1166, 205}"
120,1,276,0,0.5531889,"\int \frac{x^2 \left(A+B x^2\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(x^2*(A + B*x^2))/(a + b*x^2 + c*x^4)^2,x]","-\frac{x \left(-2 a B+x^2 (-(b B-2 A c))+A b\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\left(-\frac{4 a B c-4 A b c+b^2 B}{\sqrt{b^2-4 a c}}-2 A c+b B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{4 a B c-4 A b c+b^2 B}{\sqrt{b^2-4 a c}}-2 A c+b B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}","-\frac{x \left(-2 a B+x^2 (-(b B-2 A c))+A b\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\left(-\frac{4 a B c-4 A b c+b^2 B}{\sqrt{b^2-4 a c}}-2 A c+b B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{4 a B c-4 A b c+b^2 B}{\sqrt{b^2-4 a c}}-2 A c+b B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}",1,"-(x*(A*b - 2*a*B - (b*B - 2*A*c)*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((b*B - 2*A*c - (b^2*B - 4*A*b*c + 4*a*B*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b*B - 2*A*c + (b^2*B - 4*A*b*c + 4*a*B*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,25,0.1200,1,"{1275, 1166, 205}"
121,1,293,0,0.8463818,"\int \frac{A+B x^2}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(A + B*x^2)/(a + b*x^2 + c*x^4)^2,x]","\frac{x \left(c x^2 (A b-2 a B)-2 a A c-a b B+A b^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(\frac{A \left(b^2-12 a c\right)+4 a b B}{\sqrt{b^2-4 a c}}-2 a B+A b\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{-12 a A c+4 a b B+A b^2}{\sqrt{b^2-4 a c}}-2 a B+A b\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 (A b-2 a B)-2 a A c-a b B+A b^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(\frac{A \left(b^2-12 a c\right)+4 a b B}{\sqrt{b^2-4 a c}}-2 a B+A b\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{-12 a A c+4 a b B+A b^2}{\sqrt{b^2-4 a c}}-2 a B+A b\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*(A*b^2 - a*b*B - 2*a*A*c + (A*b - 2*a*B)*c*x^2))/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(A*b - 2*a*B + (4*a*b*B + A*(b^2 - 12*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(A*b - 2*a*B - (A*b^2 + 4*a*b*B - 12*a*A*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,22,0.1364,1,"{1178, 1166, 205}"
122,1,389,0,1.2199202,"\int \frac{A+B x^2}{x^2 \left(a+b x^2+c x^4\right)^2} \, dx","Int[(A + B*x^2)/(x^2*(a + b*x^2 + c*x^4)^2),x]","-\frac{-10 a A c-a b B+3 A b^2}{2 a^2 x \left(b^2-4 a c\right)}+\frac{\sqrt{c} \left(a B \left(b \sqrt{b^2-4 a c}-12 a c+b^2\right)-A \left(3 b^2 \sqrt{b^2-4 a c}-10 a c \sqrt{b^2-4 a c}-16 a b c+3 b^3\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(\frac{a B \left(b^2-12 a c\right)-A \left(3 b^3-16 a b c\right)}{\sqrt{b^2-4 a c}}-10 a A c-a b B+3 A 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^2 \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{-A \left(b^2-2 a c\right)+c x^2 (-(A b-2 a B))+a b B}{2 a x \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","-\frac{-10 a A c-a b B+3 A b^2}{2 a^2 x \left(b^2-4 a c\right)}+\frac{\sqrt{c} \left(a B \left(b \sqrt{b^2-4 a c}-12 a c+b^2\right)-A \left(3 b^2 \sqrt{b^2-4 a c}-10 a c \sqrt{b^2-4 a c}-16 a b c+3 b^3\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(\frac{a B \left(b^2-12 a c\right)-A \left(3 b^3-16 a b c\right)}{\sqrt{b^2-4 a c}}-10 a A c-a b B+3 A 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^2 \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{-A \left(b^2-2 a c\right)+c x^2 (-(A b-2 a B))+a b B}{2 a x \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"-(3*A*b^2 - a*b*B - 10*a*A*c)/(2*a^2*(b^2 - 4*a*c)*x) - (a*b*B - A*(b^2 - 2*a*c) - (A*b - 2*a*B)*c*x^2)/(2*a*(b^2 - 4*a*c)*x*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(a*B*(b^2 - 12*a*c + b*Sqrt[b^2 - 4*a*c]) - A*(3*b^3 - 16*a*b*c + 3*b^2*Sqrt[b^2 - 4*a*c] - 10*a*c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^2*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(3*A*b^2 - a*b*B - 10*a*A*c + (a*B*(b^2 - 12*a*c) - A*(3*b^3 - 16*a*b*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^2*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,25,0.1600,1,"{1277, 1281, 1166, 205}"
123,1,522,0,1.3646225,"\int \frac{A+B x^2}{x^4 \left(a+b x^2+c x^4\right)^2} \, dx","Int[(A + B*x^2)/(x^4*(a + b*x^2 + c*x^4)^2),x]","-\frac{\sqrt{c} \left(a B \left(3 b^2 \sqrt{b^2-4 a c}-10 a c \sqrt{b^2-4 a c}-16 a b c+3 b^3\right)-A \left(28 a^2 c^2+5 b^3 \sqrt{b^2-4 a c}-29 a b^2 c-19 a b c \sqrt{b^2-4 a c}+5 b^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^3 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(a B \left(-3 b^2 \sqrt{b^2-4 a c}+10 a c \sqrt{b^2-4 a c}-16 a b c+3 b^3\right)-A \left(28 a^2 c^2-5 b^3 \sqrt{b^2-4 a c}-29 a b^2 c+19 a b c \sqrt{b^2-4 a c}+5 b^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a^3 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{-14 a A c-3 a b B+5 A b^2}{6 a^2 x^3 \left(b^2-4 a c\right)}-\frac{a B \left(3 b^2-10 a c\right)-A \left(5 b^3-19 a b c\right)}{2 a^3 x \left(b^2-4 a c\right)}-\frac{-A \left(b^2-2 a c\right)+c x^2 (-(A b-2 a B))+a b B}{2 a x^3 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","-\frac{\sqrt{c} \left(a B \left(3 b^2 \sqrt{b^2-4 a c}-10 a c \sqrt{b^2-4 a c}-16 a b c+3 b^3\right)-A \left(28 a^2 c^2+5 b^3 \sqrt{b^2-4 a c}-29 a b^2 c-19 a b c \sqrt{b^2-4 a c}+5 b^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a^3 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(a B \left(-3 b^2 \sqrt{b^2-4 a c}+10 a c \sqrt{b^2-4 a c}-16 a b c+3 b^3\right)-A \left(28 a^2 c^2-5 b^3 \sqrt{b^2-4 a c}-29 a b^2 c+19 a b c \sqrt{b^2-4 a c}+5 b^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a^3 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{-14 a A c-3 a b B+5 A b^2}{6 a^2 x^3 \left(b^2-4 a c\right)}-\frac{a B \left(3 b^2-10 a c\right)-A \left(5 b^3-19 a b c\right)}{2 a^3 x \left(b^2-4 a c\right)}-\frac{-A \left(b^2-2 a c\right)+c x^2 (-(A b-2 a B))+a b B}{2 a x^3 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"-(5*A*b^2 - 3*a*b*B - 14*a*A*c)/(6*a^2*(b^2 - 4*a*c)*x^3) - (a*B*(3*b^2 - 10*a*c) - A*(5*b^3 - 19*a*b*c))/(2*a^3*(b^2 - 4*a*c)*x) - (a*b*B - A*(b^2 - 2*a*c) - (A*b - 2*a*B)*c*x^2)/(2*a*(b^2 - 4*a*c)*x^3*(a + b*x^2 + c*x^4)) - (Sqrt[c]*(a*B*(3*b^3 - 16*a*b*c + 3*b^2*Sqrt[b^2 - 4*a*c] - 10*a*c*Sqrt[b^2 - 4*a*c]) - A*(5*b^4 - 29*a*b^2*c + 28*a^2*c^2 + 5*b^3*Sqrt[b^2 - 4*a*c] - 19*a*b*c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^3*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(a*B*(3*b^3 - 16*a*b*c - 3*b^2*Sqrt[b^2 - 4*a*c] + 10*a*c*Sqrt[b^2 - 4*a*c]) - A*(5*b^4 - 29*a*b^2*c + 28*a^2*c^2 - 5*b^3*Sqrt[b^2 - 4*a*c] + 19*a*b*c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a^3*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,4,25,0.1600,1,"{1277, 1281, 1166, 205}"
124,1,365,0,1.4545898,"\int \frac{x^{11} \left(A+B x^2\right)}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[(x^11*(A + B*x^2))/(a + b*x^2 + c*x^4)^3,x]","-\frac{x^4 \left(x^2 \left(20 a^2 B c^2+10 a A b c^2-20 a b^2 B c-A b^3 c+3 b^4 B\right)+a \left(16 a A c^2-18 a b B c-A b^2 c+3 b^3 B\right)\right)}{4 c^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{x^2 \left(30 a^2 B c^2+7 a A b c^2-21 a b^2 B c-A b^3 c+3 b^4 B\right)}{2 c^3 \left(b^2-4 a c\right)^2}-\frac{\left(-30 a^2 A b c^3+90 a^2 b^2 B c^2-60 a^3 B c^3+10 a A b^3 c^2-30 a b^4 B c-A b^5 c+3 b^6 B\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^4 \left(b^2-4 a c\right)^{5/2}}-\frac{x^8 \left(x^2 \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{4 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{(3 b B-A c) \log \left(a+b x^2+c x^4\right)}{4 c^4}","-\frac{x^4 \left(x^2 \left(20 a^2 B c^2+10 a A b c^2-20 a b^2 B c-A b^3 c+3 b^4 B\right)+a \left(16 a A c^2-18 a b B c-A b^2 c+3 b^3 B\right)\right)}{4 c^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{x^2 \left(30 a^2 B c^2+7 a A b c^2-21 a b^2 B c-A b^3 c+3 b^4 B\right)}{2 c^3 \left(b^2-4 a c\right)^2}-\frac{\left(-30 a^2 A b c^3+90 a^2 b^2 B c^2-60 a^3 B c^3+10 a A b^3 c^2-30 a b^4 B c-A b^5 c+3 b^6 B\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^4 \left(b^2-4 a c\right)^{5/2}}-\frac{x^8 \left(x^2 \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{4 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{(3 b B-A c) \log \left(a+b x^2+c x^4\right)}{4 c^4}",1,"((3*b^4*B - A*b^3*c - 21*a*b^2*B*c + 7*a*A*b*c^2 + 30*a^2*B*c^2)*x^2)/(2*c^3*(b^2 - 4*a*c)^2) - (x^8*(a*(b*B - 2*A*c) + (b^2*B - A*b*c - 2*a*B*c)*x^2))/(4*c*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) - (x^4*(a*(3*b^3*B - A*b^2*c - 18*a*b*B*c + 16*a*A*c^2) + (3*b^4*B - A*b^3*c - 20*a*b^2*B*c + 10*a*A*b*c^2 + 20*a^2*B*c^2)*x^2))/(4*c^2*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) - ((3*b^6*B - A*b^5*c - 30*a*b^4*B*c + 10*a*A*b^3*c^2 + 90*a^2*b^2*B*c^2 - 30*a^2*A*b*c^3 - 60*a^3*B*c^3)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^4*(b^2 - 4*a*c)^(5/2)) - ((3*b*B - A*c)*Log[a + b*x^2 + c*x^4])/(4*c^4)","A",8,7,25,0.2800,1,"{1251, 818, 773, 634, 618, 206, 628}"
125,1,254,0,0.4041942,"\int \frac{x^9 \left(A+B x^2\right)}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[(x^9*(A + B*x^2))/(a + b*x^2 + c*x^4)^3,x]","-\frac{x^2 \left(x^2 \left(16 a^2 B c^2+6 a A b c^2-15 a b^2 B c+2 b^4 B\right)+2 a \left(6 a A c^2-7 a b B c+b^3 B\right)\right)}{4 c^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{\left(-12 a^2 A c^3+30 a^2 b B c^2-10 a b^3 B c+b^5 B\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^3 \left(b^2-4 a c\right)^{5/2}}-\frac{x^6 \left(x^2 \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{4 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{B \log \left(a+b x^2+c x^4\right)}{4 c^3}","-\frac{x^2 \left(x^2 \left(16 a^2 B c^2+6 a A b c^2-15 a b^2 B c+2 b^4 B\right)+2 a \left(6 a A c^2-7 a b B c+b^3 B\right)\right)}{4 c^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{\left(-12 a^2 A c^3+30 a^2 b B c^2-10 a b^3 B c+b^5 B\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^3 \left(b^2-4 a c\right)^{5/2}}-\frac{x^6 \left(x^2 \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{4 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{B \log \left(a+b x^2+c x^4\right)}{4 c^3}",1,"-(x^6*(a*(b*B - 2*A*c) + (b^2*B - A*b*c - 2*a*B*c)*x^2))/(4*c*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) - (x^2*(2*a*(b^3*B - 7*a*b*B*c + 6*a*A*c^2) + (2*b^4*B - 15*a*b^2*B*c + 6*a*A*b*c^2 + 16*a^2*B*c^2)*x^2))/(4*c^2*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + ((b^5*B - 10*a*b^3*B*c + 30*a^2*b*B*c^2 - 12*a^2*A*c^3)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^3*(b^2 - 4*a*c)^(5/2)) + (B*Log[a + b*x^2 + c*x^4])/(4*c^3)","A",7,6,25,0.2400,1,"{1251, 818, 634, 618, 206, 628}"
126,1,146,0,0.1386866,"\int \frac{x^7 \left(A+B x^2\right)}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[(x^7*(A + B*x^2))/(a + b*x^2 + c*x^4)^3,x]","-\frac{x^6 \left(-2 a B+x^2 (-(b B-2 A c))+A b\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 x^2 \left(2 a+b x^2\right) (A b-2 a B)}{4 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{3 a (A b-2 a B) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}","-\frac{x^6 \left(-2 a B+x^2 (-(b B-2 A c))+A b\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 x^2 \left(2 a+b x^2\right) (A b-2 a B)}{4 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{3 a (A b-2 a B) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}",1,"-(x^6*(A*b - 2*a*B - (b*B - 2*A*c)*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (3*(A*b - 2*a*B)*x^2*(2*a + b*x^2))/(4*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (3*a*(A*b - 2*a*B)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",5,5,25,0.2000,1,"{1251, 804, 722, 618, 206}"
127,1,185,0,0.2619682,"\int \frac{x^5 \left(A+B x^2\right)}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[(x^5*(A + B*x^2))/(a + b*x^2 + c*x^4)^3,x]","-\frac{x^2 \left(4 a A c^2+2 a b B c-4 A b^2 c+b^3 B\right)+a \left(8 a B c-6 A b c+b^2 B\right)}{4 c \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{x^4 \left(-2 a B+x^2 (-(b B-2 A c))+A b\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{\left(3 a b B-A \left(2 a c+b^2\right)\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}","-\frac{x^2 \left(4 a A c^2+2 a b B c-4 A b^2 c+b^3 B\right)+a \left(8 a B c-6 A b c+b^2 B\right)}{4 c \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{x^4 \left(-2 a B+x^2 (-(b B-2 A c))+A b\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{\left(3 a b B-A \left(2 a c+b^2\right)\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}",1,"-(x^4*(A*b - 2*a*B - (b*B - 2*A*c)*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) - (a*(b^2*B - 6*A*b*c + 8*a*B*c) + (b^3*B - 4*A*b^2*c + 2*a*b*B*c + 4*a*A*c^2)*x^2)/(4*c*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + ((3*a*b*B - A*(b^2 + 2*a*c))*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",5,5,25,0.2000,1,"{1251, 820, 777, 618, 206}"
128,1,170,0,0.1631014,"\int \frac{x^3 \left(A+B x^2\right)}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[(x^3*(A + B*x^2))/(a + b*x^2 + c*x^4)^3,x]","\frac{\left(b+2 c x^2\right) \left(2 a B c-3 A b c+b^2 B\right)}{4 c \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{x^2 \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)}{4 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{\left(2 a B c-3 A b c+b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}","\frac{\left(b+2 c x^2\right) \left(2 a B c-3 A b c+b^2 B\right)}{4 c \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{x^2 \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)}{4 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{\left(2 a B c-3 A b c+b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}",1,"-(a*(b*B - 2*A*c) + (b^2*B - A*b*c - 2*a*B*c)*x^2)/(4*c*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + ((b^2*B - 3*A*b*c + 2*a*B*c)*(b + 2*c*x^2))/(4*c*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) - ((b^2*B - 3*A*b*c + 2*a*B*c)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",5,5,25,0.2000,1,"{1251, 777, 614, 618, 206}"
129,1,139,0,0.1235909,"\int \frac{x \left(A+B x^2\right)}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[(x*(A + B*x^2))/(a + b*x^2 + c*x^4)^3,x]","-\frac{3 \left(b+2 c x^2\right) (b B-2 A c)}{4 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{-2 a B+x^2 (-(b B-2 A c))+A b}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 c (b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}","-\frac{3 \left(b+2 c x^2\right) (b B-2 A c)}{4 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{-2 a B+x^2 (-(b B-2 A c))+A b}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 c (b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}",1,"-(A*b - 2*a*B - (b*B - 2*A*c)*x^2)/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) - (3*(b*B - 2*A*c)*(b + 2*c*x^2))/(4*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (3*c*(b*B - 2*A*c)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",5,5,23,0.2174,1,"{1247, 638, 614, 618, 206}"
130,1,252,0,0.5434414,"\int \frac{A+B x^2}{x \left(a+b x^2+c x^4\right)^3} \, dx","Int[(A + B*x^2)/(x*(a + b*x^2 + c*x^4)^3),x]","\frac{2 c x^2 \left(6 a^2 B c+A \left(b^3-7 a b c\right)\right)+A \left(16 a^2 c^2-15 a b^2 c+2 b^4\right)+6 a^2 b B c}{4 a^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{\left(12 a^3 B c^2-A \left(30 a^2 b c^2-10 a b^3 c+b^5\right)\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^3 \left(b^2-4 a c\right)^{5/2}}-\frac{A \log \left(a+b x^2+c x^4\right)}{4 a^3}+\frac{A \log (x)}{a^3}-\frac{-A \left(b^2-2 a c\right)+c x^2 (-(A b-2 a B))+a b B}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}","\frac{2 c x^2 \left(6 a^2 B c+A \left(b^3-7 a b c\right)\right)+A \left(16 a^2 c^2-15 a b^2 c+2 b^4\right)+6 a^2 b B c}{4 a^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{\left(12 a^3 B c^2-A \left(30 a^2 b c^2-10 a b^3 c+b^5\right)\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^3 \left(b^2-4 a c\right)^{5/2}}-\frac{A \log \left(a+b x^2+c x^4\right)}{4 a^3}+\frac{A \log (x)}{a^3}-\frac{-A \left(b^2-2 a c\right)+c x^2 (-(A b-2 a B))+a b B}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}",1,"-(a*b*B - A*(b^2 - 2*a*c) - (A*b - 2*a*B)*c*x^2)/(4*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (6*a^2*b*B*c + A*(2*b^4 - 15*a*b^2*c + 16*a^2*c^2) + 2*c*(6*a^2*B*c + A*(b^3 - 7*a*b*c))*x^2)/(4*a^2*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) - ((12*a^3*B*c^2 - A*(b^5 - 10*a*b^3*c + 30*a^2*b*c^2))*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^3*(b^2 - 4*a*c)^(5/2)) + (A*Log[x])/a^3 - (A*Log[a + b*x^2 + c*x^4])/(4*a^3)","A",9,7,25,0.2800,1,"{1251, 822, 800, 634, 618, 206, 628}"
131,1,363,0,0.7710474,"\int \frac{A+B x^2}{x^3 \left(a+b x^2+c x^4\right)^3} \, dx","Int[(A + B*x^2)/(x^3*(a + b*x^2 + c*x^4)^3),x]","\frac{a b B \left(b^2-7 a c\right)-3 A \left(10 a^2 c^2-7 a b^2 c+b^4\right)}{2 a^3 x^2 \left(b^2-4 a c\right)^2}-\frac{-A \left(20 a^2 c^2-20 a b^2 c+3 b^4\right)+c x^2 \left(a B \left(b^2-16 a c\right)-3 A \left(b^3-6 a b c\right)\right)+a b B \left(b^2-10 a c\right)}{4 a^2 x^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{\left(a b B \left(30 a^2 c^2-10 a b^2 c+b^4\right)-3 A \left(30 a^2 b^2 c^2-20 a^3 c^3-10 a b^4 c+b^6\right)\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^4 \left(b^2-4 a c\right)^{5/2}}+\frac{(3 A b-a B) \log \left(a+b x^2+c x^4\right)}{4 a^4}-\frac{\log (x) (3 A b-a B)}{a^4}-\frac{-A \left(b^2-2 a c\right)+c x^2 (-(A b-2 a B))+a b B}{4 a x^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}","\frac{a b B \left(b^2-7 a c\right)-3 A \left(10 a^2 c^2-7 a b^2 c+b^4\right)}{2 a^3 x^2 \left(b^2-4 a c\right)^2}-\frac{-A \left(20 a^2 c^2-20 a b^2 c+3 b^4\right)+c x^2 \left(a B \left(b^2-16 a c\right)-3 A \left(b^3-6 a b c\right)\right)+a b B \left(b^2-10 a c\right)}{4 a^2 x^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{\left(a b B \left(30 a^2 c^2-10 a b^2 c+b^4\right)-3 A \left(30 a^2 b^2 c^2-20 a^3 c^3-10 a b^4 c+b^6\right)\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^4 \left(b^2-4 a c\right)^{5/2}}+\frac{(3 A b-a B) \log \left(a+b x^2+c x^4\right)}{4 a^4}-\frac{\log (x) (3 A b-a B)}{a^4}-\frac{-A \left(b^2-2 a c\right)+c x^2 (-(A b-2 a B))+a b B}{4 a x^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}",1,"(a*b*B*(b^2 - 7*a*c) - 3*A*(b^4 - 7*a*b^2*c + 10*a^2*c^2))/(2*a^3*(b^2 - 4*a*c)^2*x^2) - (a*b*B - A*(b^2 - 2*a*c) - (A*b - 2*a*B)*c*x^2)/(4*a*(b^2 - 4*a*c)*x^2*(a + b*x^2 + c*x^4)^2) - (a*b*B*(b^2 - 10*a*c) - A*(3*b^4 - 20*a*b^2*c + 20*a^2*c^2) + c*(a*B*(b^2 - 16*a*c) - 3*A*(b^3 - 6*a*b*c))*x^2)/(4*a^2*(b^2 - 4*a*c)^2*x^2*(a + b*x^2 + c*x^4)) + ((a*b*B*(b^4 - 10*a*b^2*c + 30*a^2*c^2) - 3*A*(b^6 - 10*a*b^4*c + 30*a^2*b^2*c^2 - 20*a^3*c^3))*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^4*(b^2 - 4*a*c)^(5/2)) - ((3*A*b - a*B)*Log[x])/a^4 + ((3*A*b - a*B)*Log[a + b*x^2 + c*x^4])/(4*a^4)","A",9,7,25,0.2800,1,"{1251, 822, 800, 634, 618, 206, 628}"
132,1,554,0,11.1945421,"\int \frac{x^8 \left(A+B x^2\right)}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[(x^8*(A + B*x^2))/(a + b*x^2 + c*x^4)^3,x]","\frac{\left(-\frac{-40 a^2 A c^3+132 a^2 b B c^2-18 a A b^2 c^2-33 a b^3 B c+A b^4 c+3 b^5 B}{\sqrt{b^2-4 a c}}+84 a^2 B c^2-16 a A b c^2-27 a b^2 B c+A b^3 c+3 b^4 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} c^{5/2} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{-40 a^2 A c^3+132 a^2 b B c^2-18 a A b^2 c^2-33 a b^3 B c+A b^4 c+3 b^5 B}{\sqrt{b^2-4 a c}}+84 a^2 B c^2-16 a A b c^2-27 a b^2 B c+A b^3 c+3 b^4 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} c^{5/2} \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{x \left(20 a A c^2-24 a b B c+A b^2 c+3 b^3 B\right)}{8 c^2 \left(b^2-4 a c\right)^2}-\frac{x^7 \left(-2 a B+x^2 (-(b B-2 A c))+A b\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{x^5 \left(x^2 \left(-28 a B c+12 A b c+b^2 B\right)-4 a A c-12 a b B+7 A b^2\right)}{8 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{x^3 \left(-28 a B c+12 A b c+b^2 B\right)}{8 c \left(b^2-4 a c\right)^2}","\frac{\left(-\frac{-40 a^2 A c^3+132 a^2 b B c^2-18 a A b^2 c^2-33 a b^3 B c+A b^4 c+3 b^5 B}{\sqrt{b^2-4 a c}}+84 a^2 B c^2-16 a A b c^2-27 a b^2 B c+A b^3 c+3 b^4 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} c^{5/2} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{-40 a^2 A c^3+132 a^2 b B c^2-18 a A b^2 c^2-33 a b^3 B c+A b^4 c+3 b^5 B}{\sqrt{b^2-4 a c}}+84 a^2 B c^2-16 a A b c^2-27 a b^2 B c+A b^3 c+3 b^4 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} c^{5/2} \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{x \left(20 a A c^2-24 a b B c+A b^2 c+3 b^3 B\right)}{8 c^2 \left(b^2-4 a c\right)^2}-\frac{x^7 \left(-2 a B+x^2 (-(b B-2 A c))+A b\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{x^5 \left(x^2 \left(-28 a B c+12 A b c+b^2 B\right)-4 a A c-12 a b B+7 A b^2\right)}{8 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{x^3 \left(-28 a B c+12 A b c+b^2 B\right)}{8 c \left(b^2-4 a c\right)^2}",1,"-((3*b^3*B + A*b^2*c - 24*a*b*B*c + 20*a*A*c^2)*x)/(8*c^2*(b^2 - 4*a*c)^2) + ((b^2*B + 12*A*b*c - 28*a*B*c)*x^3)/(8*c*(b^2 - 4*a*c)^2) - (x^7*(A*b - 2*a*B - (b*B - 2*A*c)*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) - (x^5*(7*A*b^2 - 12*a*b*B - 4*a*A*c + (b^2*B + 12*A*b*c - 28*a*B*c)*x^2))/(8*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + ((3*b^4*B + A*b^3*c - 27*a*b^2*B*c - 16*a*A*b*c^2 + 84*a^2*B*c^2 - (3*b^5*B + A*b^4*c - 33*a*b^3*B*c - 18*a*A*b^2*c^2 + 132*a^2*b*B*c^2 - 40*a^2*A*c^3)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((3*b^4*B + A*b^3*c - 27*a*b^2*B*c - 16*a*A*b*c^2 + 84*a^2*B*c^2 + (3*b^5*B + A*b^4*c - 33*a*b^3*B*c - 18*a*A*b^2*c^2 + 132*a^2*b*B*c^2 - 40*a^2*A*c^3)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",7,4,25,0.1600,1,"{1275, 1279, 1166, 205}"
133,1,461,0,4.6215832,"\int \frac{x^6 \left(A+B x^2\right)}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[(x^6*(A + B*x^2))/(a + b*x^2 + c*x^4)^3,x]","\frac{\left(-\frac{-40 a^2 B c^2+36 a A b c^2-18 a b^2 B c+3 A b^3 c+b^4 B}{\sqrt{b^2-4 a c}}+12 a A c^2-16 a b B c+3 A b^2 c+b^3 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} c^{3/2} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{-40 a^2 B c^2+36 a A b c^2-18 a b^2 B c+3 A b^3 c+b^4 B}{\sqrt{b^2-4 a c}}+12 a A c^2-16 a b B c+3 A b^2 c+b^3 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} c^{3/2} \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{x^5 \left(-2 a B+x^2 (-(b B-2 A c))+A b\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{x^3 \left(-x^2 \left(20 a B c-12 A b c+b^2 B\right)+4 a A c-12 a b B+5 A b^2\right)}{8 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{x \left(20 a B c-12 A b c+b^2 B\right)}{8 c \left(b^2-4 a c\right)^2}","\frac{\left(-\frac{-40 a^2 B c^2+36 a A b c^2-18 a b^2 B c+3 A b^3 c+b^4 B}{\sqrt{b^2-4 a c}}+12 a A c^2-16 a b B c+3 A b^2 c+b^3 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} c^{3/2} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{-40 a^2 B c^2+36 a A b c^2-18 a b^2 B c+3 A b^3 c+b^4 B}{\sqrt{b^2-4 a c}}+12 a A c^2-16 a b B c+3 A b^2 c+b^3 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} c^{3/2} \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{x^5 \left(-2 a B+x^2 (-(b B-2 A c))+A b\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{x^3 \left(-x^2 \left(20 a B c-12 A b c+b^2 B\right)+4 a A c-12 a b B+5 A b^2\right)}{8 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{x \left(20 a B c-12 A b c+b^2 B\right)}{8 c \left(b^2-4 a c\right)^2}",1,"-((b^2*B - 12*A*b*c + 20*a*B*c)*x)/(8*c*(b^2 - 4*a*c)^2) - (x^5*(A*b - 2*a*B - (b*B - 2*A*c)*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) - (x^3*(5*A*b^2 - 12*a*b*B + 4*a*A*c - (b^2*B - 12*A*b*c + 20*a*B*c)*x^2))/(8*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + ((b^3*B + 3*A*b^2*c - 16*a*b*B*c + 12*a*A*c^2 - (b^4*B + 3*A*b^3*c - 18*a*b^2*B*c + 36*a*A*b*c^2 - 40*a^2*B*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b^3*B + 3*A*b^2*c - 16*a*b*B*c + 12*a*A*c^2 + (b^4*B + 3*A*b^3*c - 18*a*b^2*B*c + 36*a*A*b*c^2 - 40*a^2*B*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,4,25,0.1600,1,"{1275, 1279, 1166, 205}"
134,1,380,0,1.4147772,"\int \frac{x^4 \left(A+B x^2\right)}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[(x^4*(A + B*x^2))/(a + b*x^2 + c*x^4)^3,x]","\frac{3 \left(-\frac{-8 a A c^2+12 a b B c-6 A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}+4 a B c-4 A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{3 \left(\frac{-8 a A c^2+12 a b B c-6 A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}+4 a B c-4 A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{x^3 \left(-2 a B+x^2 (-(b B-2 A c))+A b\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 x \left(x^2 \left(4 a B c-4 A b c+b^2 B\right)-A \left(4 a c+b^2\right)+4 a b B\right)}{8 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}","\frac{3 \left(-\frac{-8 a A c^2+12 a b B c-6 A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}+4 a B c-4 A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{3 \left(\frac{-8 a A c^2+12 a b B c-6 A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}+4 a B c-4 A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{x^3 \left(-2 a B+x^2 (-(b B-2 A c))+A b\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 x \left(x^2 \left(4 a B c-4 A b c+b^2 B\right)-A \left(4 a c+b^2\right)+4 a b B\right)}{8 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}",1,"-(x^3*(A*b - 2*a*B - (b*B - 2*A*c)*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (3*x*(4*a*b*B - A*(b^2 + 4*a*c) + (b^2*B - 4*A*b*c + 4*a*B*c)*x^2))/(8*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (3*(b^2*B - 4*A*b*c + 4*a*B*c - (b^3*B - 6*A*b^2*c + 12*a*b*B*c - 8*a*A*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (3*(b^2*B - 4*A*b*c + 4*a*B*c + (b^3*B - 6*A*b^2*c + 12*a*b*B*c - 8*a*A*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,3,25,0.1200,1,"{1275, 1166, 205}"
135,1,438,0,1.0902432,"\int \frac{x^2 \left(A+B x^2\right)}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[(x^2*(A + B*x^2))/(a + b*x^2 + c*x^4)^3,x]","-\frac{x \left(-2 a B+x^2 (-(b B-2 A c))+A b\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{x \left(c x^2 \left(12 a b B-A \left(20 a c+b^2\right)\right)-A \left(8 a b c+b^3\right)+a B \left(7 b^2-4 a c\right)\right)}{8 a \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(A \left(b^2 \sqrt{b^2-4 a c}+20 a c \sqrt{b^2-4 a c}-52 a b c+b^3\right)+6 a B \left(-2 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(A \left(-b^2 \sqrt{b^2-4 a c}-20 a c \sqrt{b^2-4 a c}-52 a b c+b^3\right)+6 a B \left(2 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a \left(b^2-4 a c\right)^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}","-\frac{x \left(-2 a B+x^2 (-(b B-2 A c))+A b\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{x \left(c x^2 \left(12 a b B-A \left(20 a c+b^2\right)\right)-A \left(8 a b c+b^3\right)+a B \left(7 b^2-4 a c\right)\right)}{8 a \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(A \left(b^2 \sqrt{b^2-4 a c}+20 a c \sqrt{b^2-4 a c}-52 a b c+b^3\right)+6 a B \left(-2 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(A \left(-b^2 \sqrt{b^2-4 a c}-20 a c \sqrt{b^2-4 a c}-52 a b c+b^3\right)+6 a B \left(2 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a \left(b^2-4 a c\right)^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"-(x*(A*b - 2*a*B - (b*B - 2*A*c)*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) - (x*(a*B*(7*b^2 - 4*a*c) - A*(b^3 + 8*a*b*c) + c*(12*a*b*B - A*(b^2 + 20*a*c))*x^2))/(8*a*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(6*a*B*(3*b^2 + 4*a*c - 2*b*Sqrt[b^2 - 4*a*c]) + A*(b^3 - 52*a*b*c + b^2*Sqrt[b^2 - 4*a*c] + 20*a*c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a*(b^2 - 4*a*c)^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(6*a*B*(3*b^2 + 4*a*c + 2*b*Sqrt[b^2 - 4*a*c]) + A*(b^3 - 52*a*b*c - b^2*Sqrt[b^2 - 4*a*c] - 20*a*c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a*(b^2 - 4*a*c)^(5/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,25,0.1600,1,"{1275, 1178, 1166, 205}"
136,1,460,0,1.3533557,"\int \frac{A+B x^2}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[(A + B*x^2)/(a + b*x^2 + c*x^4)^3,x]","\frac{x \left(A \left(28 a^2 c^2-25 a b^2 c+3 b^4\right)+c x^2 \left(3 A \left(b^3-8 a b c\right)+a B \left(20 a c+b^2\right)\right)+a b B \left(8 a c+b^2\right)\right)}{8 a^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(\frac{3 A \left(56 a^2 c^2-10 a b^2 c+b^4\right)+a b B \left(b^2-52 a c\right)}{\sqrt{b^2-4 a c}}+3 A \left(b^3-8 a b c\right)+a B \left(20 a c+b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^2 \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\frac{3 A \left(56 a^2 c^2-10 a b^2 c+b^4\right)+a b B \left(b^2-52 a c\right)}{\sqrt{b^2-4 a c}}+3 A \left(b^3-8 a b c\right)+a B \left(20 a c+b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a^2 \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x \left(c x^2 (A b-2 a B)-2 a A c-a b B+A b^2\right)}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}","\frac{x \left(A \left(28 a^2 c^2-25 a b^2 c+3 b^4\right)+c x^2 \left(3 A \left(b^3-8 a b c\right)+a B \left(20 a c+b^2\right)\right)+a b B \left(8 a c+b^2\right)\right)}{8 a^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(\frac{3 A \left(56 a^2 c^2-10 a b^2 c+b^4\right)+a b B \left(b^2-52 a c\right)}{\sqrt{b^2-4 a c}}+3 A \left(b^3-8 a b c\right)+a B \left(20 a c+b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^2 \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\frac{3 A \left(56 a^2 c^2-10 a b^2 c+b^4\right)+a b B \left(b^2-52 a c\right)}{\sqrt{b^2-4 a c}}+3 A \left(b^3-8 a b c\right)+a B \left(20 a c+b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a^2 \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x \left(c x^2 (A b-2 a B)-2 a A c-a b B+A b^2\right)}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}",1,"(x*(A*b^2 - a*b*B - 2*a*A*c + (A*b - 2*a*B)*c*x^2))/(4*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (x*(a*b*B*(b^2 + 8*a*c) + A*(3*b^4 - 25*a*b^2*c + 28*a^2*c^2) + c*(a*B*(b^2 + 20*a*c) + 3*A*(b^3 - 8*a*b*c))*x^2))/(8*a^2*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(a*B*(b^2 + 20*a*c) + 3*A*(b^3 - 8*a*b*c) + (a*b*B*(b^2 - 52*a*c) + 3*A*(b^4 - 10*a*b^2*c + 56*a^2*c^2))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^2*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(a*B*(b^2 + 20*a*c) + 3*A*(b^3 - 8*a*b*c) - (a*b*B*(b^2 - 52*a*c) + 3*A*(b^4 - 10*a*b^2*c + 56*a^2*c^2))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^2*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,3,22,0.1364,1,"{1178, 1166, 205}"
137,1,25,0,0.0183348,"\int \frac{x \left(-7+4 x^2\right)}{4-5 x^2+x^4} \, dx","Int[(x*(-7 + 4*x^2))/(4 - 5*x^2 + x^4),x]","\frac{1}{2} \log \left(1-x^2\right)+\frac{3}{2} \log \left(4-x^2\right)","\frac{1}{2} \log \left(1-x^2\right)+\frac{3}{2} \log \left(4-x^2\right)",1,"Log[1 - x^2]/2 + (3*Log[4 - x^2])/2","A",4,3,21,0.1429,1,"{1247, 632, 31}"
138,1,25,0,0.0293958,"\int \frac{-7 x+4 x^3}{4-5 x^2+x^4} \, dx","Int[(-7*x + 4*x^3)/(4 - 5*x^2 + x^4),x]","\frac{1}{2} \log \left(1-x^2\right)+\frac{3}{2} \log \left(4-x^2\right)","\frac{1}{2} \log \left(1-x^2\right)+\frac{3}{2} \log \left(4-x^2\right)",1,"Log[1 - x^2]/2 + (3*Log[4 - x^2])/2","A",5,4,22,0.1818,1,"{1593, 1247, 632, 31}"
139,1,37,0,0.0350982,"\int \frac{x \left(2+x^2\right)}{1+x^2+x^4} \, dx","Int[(x*(2 + x^2))/(1 + x^2 + x^4),x]","\frac{1}{4} \log \left(x^4+x^2+1\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)","\frac{1}{4} \log \left(x^4+x^2+1\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)",1,"(Sqrt[3]*ArcTan[(1 + 2*x^2)/Sqrt[3]])/2 + Log[1 + x^2 + x^4]/4","A",5,5,17,0.2941,1,"{1247, 634, 618, 204, 628}"
140,1,37,0,0.0417176,"\int \frac{2 x+x^3}{1+x^2+x^4} \, dx","Int[(2*x + x^3)/(1 + x^2 + x^4),x]","\frac{1}{4} \log \left(x^4+x^2+1\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)","\frac{1}{4} \log \left(x^4+x^2+1\right)+\frac{1}{2} \sqrt{3} \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)",1,"(Sqrt[3]*ArcTan[(1 + 2*x^2)/Sqrt[3]])/2 + Log[1 + x^2 + x^4]/4","A",6,6,18,0.3333,1,"{1593, 1247, 634, 618, 204, 628}"
141,1,45,0,0.0485355,"\int \frac{11 x+2 x^3}{\left(3+2 x^2+x^4\right)^2} \, dx","Int[(11*x + 2*x^3)/(3 + 2*x^2 + x^4)^2,x]","\frac{9 x^2+5}{8 \left(x^4+2 x^2+3\right)}+\frac{9 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{8 \sqrt{2}}","\frac{9 x^2+5}{8 \left(x^4+2 x^2+3\right)}+\frac{9 \tan ^{-1}\left(\frac{x^2+1}{\sqrt{2}}\right)}{8 \sqrt{2}}",1,"(5 + 9*x^2)/(8*(3 + 2*x^2 + x^4)) + (9*ArcTan[(1 + x^2)/Sqrt[2]])/(8*Sqrt[2])","A",5,5,22,0.2273,1,"{1593, 1247, 638, 618, 204}"
142,1,102,0,0.079444,"\int x^5 \left(2+3 x^2\right) \sqrt{3+5 x^2+x^4} \, dx","Int[x^5*(2 + 3*x^2)*Sqrt[3 + 5*x^2 + x^4],x]","\frac{3}{10} \left(x^4+5 x^2+3\right)^{3/2} x^4+\frac{1}{480} \left(1837-510 x^2\right) \left(x^4+5 x^2+3\right)^{3/2}-\frac{1633}{256} \left(2 x^2+5\right) \sqrt{x^4+5 x^2+3}+\frac{21229}{512} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)","\frac{3}{10} \left(x^4+5 x^2+3\right)^{3/2} x^4+\frac{1}{480} \left(1837-510 x^2\right) \left(x^4+5 x^2+3\right)^{3/2}-\frac{1633}{256} \left(2 x^2+5\right) \sqrt{x^4+5 x^2+3}+\frac{21229}{512} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)",1,"(-1633*(5 + 2*x^2)*Sqrt[3 + 5*x^2 + x^4])/256 + (3*x^4*(3 + 5*x^2 + x^4)^(3/2))/10 + ((1837 - 510*x^2)*(3 + 5*x^2 + x^4)^(3/2))/480 + (21229*ArcTanh[(5 + 2*x^2)/(2*Sqrt[3 + 5*x^2 + x^4])])/512","A",6,6,25,0.2400,1,"{1251, 832, 779, 612, 621, 206}"
143,1,81,0,0.0562794,"\int x^3 \left(2+3 x^2\right) \sqrt{3+5 x^2+x^4} \, dx","Int[x^3*(2 + 3*x^2)*Sqrt[3 + 5*x^2 + x^4],x]","-\frac{1}{48} \left(59-18 x^2\right) \left(x^4+5 x^2+3\right)^{3/2}+\frac{259}{128} \left(2 x^2+5\right) \sqrt{x^4+5 x^2+3}-\frac{3367}{256} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)","-\frac{1}{48} \left(59-18 x^2\right) \left(x^4+5 x^2+3\right)^{3/2}+\frac{259}{128} \left(2 x^2+5\right) \sqrt{x^4+5 x^2+3}-\frac{3367}{256} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)",1,"(259*(5 + 2*x^2)*Sqrt[3 + 5*x^2 + x^4])/128 - ((59 - 18*x^2)*(3 + 5*x^2 + x^4)^(3/2))/48 - (3367*ArcTanh[(5 + 2*x^2)/(2*Sqrt[3 + 5*x^2 + x^4])])/256","A",5,5,25,0.2000,1,"{1251, 779, 612, 621, 206}"
144,1,74,0,0.0435766,"\int x \left(2+3 x^2\right) \sqrt{3+5 x^2+x^4} \, dx","Int[x*(2 + 3*x^2)*Sqrt[3 + 5*x^2 + x^4],x]","\frac{1}{2} \left(x^4+5 x^2+3\right)^{3/2}-\frac{11}{16} \left(2 x^2+5\right) \sqrt{x^4+5 x^2+3}+\frac{143}{32} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)","\frac{1}{2} \left(x^4+5 x^2+3\right)^{3/2}-\frac{11}{16} \left(2 x^2+5\right) \sqrt{x^4+5 x^2+3}+\frac{143}{32} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)",1,"(-11*(5 + 2*x^2)*Sqrt[3 + 5*x^2 + x^4])/16 + (3 + 5*x^2 + x^4)^(3/2)/2 + (143*ArcTanh[(5 + 2*x^2)/(2*Sqrt[3 + 5*x^2 + x^4])])/32","A",5,5,23,0.2174,1,"{1247, 640, 612, 621, 206}"
145,1,94,0,0.08329,"\int \frac{\left(2+3 x^2\right) \sqrt{3+5 x^2+x^4}}{x} \, dx","Int[((2 + 3*x^2)*Sqrt[3 + 5*x^2 + x^4])/x,x]","\frac{1}{8} \sqrt{x^4+5 x^2+3} \left(6 x^2+23\right)+\frac{1}{16} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)-\sqrt{3} \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)","\frac{1}{8} \sqrt{x^4+5 x^2+3} \left(6 x^2+23\right)+\frac{1}{16} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)-\sqrt{3} \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)",1,"((23 + 6*x^2)*Sqrt[3 + 5*x^2 + x^4])/8 + ArcTanh[(5 + 2*x^2)/(2*Sqrt[3 + 5*x^2 + x^4])]/16 - Sqrt[3]*ArcTanh[(6 + 5*x^2)/(2*Sqrt[3]*Sqrt[3 + 5*x^2 + x^4])]","A",7,6,25,0.2400,1,"{1251, 814, 843, 621, 206, 724}"
146,1,97,0,0.0830542,"\int \frac{\left(2+3 x^2\right) \sqrt{3+5 x^2+x^4}}{x^3} \, dx","Int[((2 + 3*x^2)*Sqrt[3 + 5*x^2 + x^4])/x^3,x]","-\frac{\sqrt{x^4+5 x^2+3} \left(2-3 x^2\right)}{2 x^2}+\frac{19}{4} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)-\frac{7 \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{\sqrt{3}}","-\frac{\sqrt{x^4+5 x^2+3} \left(2-3 x^2\right)}{2 x^2}+\frac{19}{4} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)-\frac{7 \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{\sqrt{3}}",1,"-((2 - 3*x^2)*Sqrt[3 + 5*x^2 + x^4])/(2*x^2) + (19*ArcTanh[(5 + 2*x^2)/(2*Sqrt[3 + 5*x^2 + x^4])])/4 - (7*ArcTanh[(6 + 5*x^2)/(2*Sqrt[3]*Sqrt[3 + 5*x^2 + x^4])])/Sqrt[3]","A",7,6,25,0.2400,1,"{1251, 812, 843, 621, 206, 724}"
147,1,99,0,0.0834549,"\int \frac{\left(2+3 x^2\right) \sqrt{3+5 x^2+x^4}}{x^5} \, dx","Int[((2 + 3*x^2)*Sqrt[3 + 5*x^2 + x^4])/x^5,x]","-\frac{\sqrt{x^4+5 x^2+3} \left(23 x^2+6\right)}{12 x^4}+\frac{3}{2} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)-\frac{77 \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{24 \sqrt{3}}","-\frac{\sqrt{x^4+5 x^2+3} \left(23 x^2+6\right)}{12 x^4}+\frac{3}{2} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)-\frac{77 \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{24 \sqrt{3}}",1,"-((6 + 23*x^2)*Sqrt[3 + 5*x^2 + x^4])/(12*x^4) + (3*ArcTanh[(5 + 2*x^2)/(2*Sqrt[3 + 5*x^2 + x^4])])/2 - (77*ArcTanh[(6 + 5*x^2)/(2*Sqrt[3]*Sqrt[3 + 5*x^2 + x^4])])/(24*Sqrt[3])","A",7,6,25,0.2400,1,"{1251, 810, 843, 621, 206, 724}"
148,1,90,0,0.0681416,"\int \frac{\left(2+3 x^2\right) \sqrt{3+5 x^2+x^4}}{x^7} \, dx","Int[((2 + 3*x^2)*Sqrt[3 + 5*x^2 + x^4])/x^7,x]","-\frac{\left(x^4+5 x^2+3\right)^{3/2}}{9 x^6}-\frac{\left(5 x^2+6\right) \sqrt{x^4+5 x^2+3}}{18 x^4}+\frac{13 \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{36 \sqrt{3}}","-\frac{\left(x^4+5 x^2+3\right)^{3/2}}{9 x^6}-\frac{\left(5 x^2+6\right) \sqrt{x^4+5 x^2+3}}{18 x^4}+\frac{13 \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{36 \sqrt{3}}",1,"-((6 + 5*x^2)*Sqrt[3 + 5*x^2 + x^4])/(18*x^4) - (3 + 5*x^2 + x^4)^(3/2)/(9*x^6) + (13*ArcTanh[(6 + 5*x^2)/(2*Sqrt[3]*Sqrt[3 + 5*x^2 + x^4])])/(36*Sqrt[3])","A",5,5,25,0.2000,1,"{1251, 806, 720, 724, 206}"
149,1,111,0,0.0861399,"\int \frac{\left(2+3 x^2\right) \sqrt{3+5 x^2+x^4}}{x^9} \, dx","Int[((2 + 3*x^2)*Sqrt[3 + 5*x^2 + x^4])/x^9,x]","-\frac{11 \left(x^4+5 x^2+3\right)^{3/2}}{216 x^6}-\frac{\left(x^4+5 x^2+3\right)^{3/2}}{12 x^8}+\frac{67 \left(5 x^2+6\right) \sqrt{x^4+5 x^2+3}}{1728 x^4}-\frac{871 \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{3456 \sqrt{3}}","-\frac{11 \left(x^4+5 x^2+3\right)^{3/2}}{216 x^6}-\frac{\left(x^4+5 x^2+3\right)^{3/2}}{12 x^8}+\frac{67 \left(5 x^2+6\right) \sqrt{x^4+5 x^2+3}}{1728 x^4}-\frac{871 \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{3456 \sqrt{3}}",1,"(67*(6 + 5*x^2)*Sqrt[3 + 5*x^2 + x^4])/(1728*x^4) - (3 + 5*x^2 + x^4)^(3/2)/(12*x^8) - (11*(3 + 5*x^2 + x^4)^(3/2))/(216*x^6) - (871*ArcTanh[(6 + 5*x^2)/(2*Sqrt[3]*Sqrt[3 + 5*x^2 + x^4])])/(3456*Sqrt[3])","A",6,6,25,0.2400,1,"{1251, 834, 806, 720, 724, 206}"
150,1,132,0,0.1086238,"\int \frac{\left(2+3 x^2\right) \sqrt{3+5 x^2+x^4}}{x^{11}} \, dx","Int[((2 + 3*x^2)*Sqrt[3 + 5*x^2 + x^4])/x^11,x]","\frac{173 \left(x^4+5 x^2+3\right)^{3/2}}{3240 x^6}-\frac{\left(x^4+5 x^2+3\right)^{3/2}}{36 x^8}-\frac{\left(x^4+5 x^2+3\right)^{3/2}}{15 x^{10}}-\frac{161 \left(5 x^2+6\right) \sqrt{x^4+5 x^2+3}}{5184 x^4}+\frac{2093 \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{10368 \sqrt{3}}","\frac{173 \left(x^4+5 x^2+3\right)^{3/2}}{3240 x^6}-\frac{\left(x^4+5 x^2+3\right)^{3/2}}{36 x^8}-\frac{\left(x^4+5 x^2+3\right)^{3/2}}{15 x^{10}}-\frac{161 \left(5 x^2+6\right) \sqrt{x^4+5 x^2+3}}{5184 x^4}+\frac{2093 \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{10368 \sqrt{3}}",1,"(-161*(6 + 5*x^2)*Sqrt[3 + 5*x^2 + x^4])/(5184*x^4) - (3 + 5*x^2 + x^4)^(3/2)/(15*x^10) - (3 + 5*x^2 + x^4)^(3/2)/(36*x^8) + (173*(3 + 5*x^2 + x^4)^(3/2))/(3240*x^6) + (2093*ArcTanh[(6 + 5*x^2)/(2*Sqrt[3]*Sqrt[3 + 5*x^2 + x^4])])/(10368*Sqrt[3])","A",7,6,25,0.2400,1,"{1251, 834, 806, 720, 724, 206}"
151,1,322,0,0.273842,"\int x^4 \left(2+3 x^2\right) \sqrt{3+5 x^2+x^4} \, dx","Int[x^4*(2 + 3*x^2)*Sqrt[3 + 5*x^2 + x^4],x]","\frac{1}{21} \left(7 x^2+11\right) \sqrt{x^4+5 x^2+3} x^5-\frac{26}{35} \sqrt{x^4+5 x^2+3} x^3+\frac{13}{3} \sqrt{x^4+5 x^2+3} x-\frac{1924 \left(2 x^2+\sqrt{13}+5\right) x}{105 \sqrt{x^4+5 x^2+3}}-\frac{13 \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{6 \left(5+\sqrt{13}\right)} \sqrt{x^4+5 x^2+3}}+\frac{962 \sqrt{\frac{2}{3} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{105 \sqrt{x^4+5 x^2+3}}","\frac{1}{21} \left(7 x^2+11\right) \sqrt{x^4+5 x^2+3} x^5-\frac{26}{35} \sqrt{x^4+5 x^2+3} x^3+\frac{13}{3} \sqrt{x^4+5 x^2+3} x-\frac{1924 \left(2 x^2+\sqrt{13}+5\right) x}{105 \sqrt{x^4+5 x^2+3}}-\frac{13 \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{6 \left(5+\sqrt{13}\right)} \sqrt{x^4+5 x^2+3}}+\frac{962 \sqrt{\frac{2}{3} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{105 \sqrt{x^4+5 x^2+3}}",1,"(-1924*x*(5 + Sqrt[13] + 2*x^2))/(105*Sqrt[3 + 5*x^2 + x^4]) + (13*x*Sqrt[3 + 5*x^2 + x^4])/3 - (26*x^3*Sqrt[3 + 5*x^2 + x^4])/35 + (x^5*(11 + 7*x^2)*Sqrt[3 + 5*x^2 + x^4])/21 + (962*Sqrt[(2*(5 + Sqrt[13]))/3]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(105*Sqrt[3 + 5*x^2 + x^4]) - (13*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(Sqrt[6*(5 + Sqrt[13])]*Sqrt[3 + 5*x^2 + x^4])","A",6,5,25,0.2000,1,"{1273, 1279, 1189, 1099, 1135}"
152,1,305,0,0.2028032,"\int x^2 \left(2+3 x^2\right) \sqrt{3+5 x^2+x^4} \, dx","Int[x^2*(2 + 3*x^2)*Sqrt[3 + 5*x^2 + x^4],x]","\frac{1}{35} \left(15 x^2+29\right) \sqrt{x^4+5 x^2+3} x^3-\frac{4}{3} \sqrt{x^4+5 x^2+3} x+\frac{1247 \left(2 x^2+\sqrt{13}+5\right) x}{210 \sqrt{x^4+5 x^2+3}}+\frac{2 \sqrt{\frac{2}{3 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{x^4+5 x^2+3}}-\frac{1247 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{210 \sqrt{x^4+5 x^2+3}}","\frac{1}{35} \left(15 x^2+29\right) \sqrt{x^4+5 x^2+3} x^3-\frac{4}{3} \sqrt{x^4+5 x^2+3} x+\frac{1247 \left(2 x^2+\sqrt{13}+5\right) x}{210 \sqrt{x^4+5 x^2+3}}+\frac{2 \sqrt{\frac{2}{3 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{x^4+5 x^2+3}}-\frac{1247 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{210 \sqrt{x^4+5 x^2+3}}",1,"(1247*x*(5 + Sqrt[13] + 2*x^2))/(210*Sqrt[3 + 5*x^2 + x^4]) - (4*x*Sqrt[3 + 5*x^2 + x^4])/3 + (x^3*(29 + 15*x^2)*Sqrt[3 + 5*x^2 + x^4])/35 - (1247*Sqrt[(5 + Sqrt[13])/6]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(210*Sqrt[3 + 5*x^2 + x^4]) + (2*Sqrt[2/(3*(5 + Sqrt[13]))]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/Sqrt[3 + 5*x^2 + x^4]","A",5,5,25,0.2000,1,"{1273, 1279, 1189, 1099, 1135}"
153,1,279,0,0.122301,"\int \left(2+3 x^2\right) \sqrt{3+5 x^2+x^4} \, dx","Int[(2 + 3*x^2)*Sqrt[3 + 5*x^2 + x^4],x]","-\frac{23 x \left(2 x^2+\sqrt{13}+5\right)}{15 \sqrt{x^4+5 x^2+3}}+\frac{1}{15} x \left(9 x^2+25\right) \sqrt{x^4+5 x^2+3}+\frac{\sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{6 \left(5+\sqrt{13}\right)} \sqrt{x^4+5 x^2+3}}+\frac{23 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{15 \sqrt{x^4+5 x^2+3}}","-\frac{23 x \left(2 x^2+\sqrt{13}+5\right)}{15 \sqrt{x^4+5 x^2+3}}+\frac{1}{15} x \left(9 x^2+25\right) \sqrt{x^4+5 x^2+3}+\frac{\sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{6 \left(5+\sqrt{13}\right)} \sqrt{x^4+5 x^2+3}}+\frac{23 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{15 \sqrt{x^4+5 x^2+3}}",1,"(-23*x*(5 + Sqrt[13] + 2*x^2))/(15*Sqrt[3 + 5*x^2 + x^4]) + (x*(25 + 9*x^2)*Sqrt[3 + 5*x^2 + x^4])/15 + (23*Sqrt[(5 + Sqrt[13])/6]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(15*Sqrt[3 + 5*x^2 + x^4]) + (Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(Sqrt[6*(5 + Sqrt[13])]*Sqrt[3 + 5*x^2 + x^4])","A",4,4,22,0.1818,1,"{1176, 1189, 1099, 1135}"
154,1,284,0,0.1284876,"\int \frac{\left(2+3 x^2\right) \sqrt{3+5 x^2+x^4}}{x^2} \, dx","Int[((2 + 3*x^2)*Sqrt[3 + 5*x^2 + x^4])/x^2,x]","-\frac{\sqrt{x^4+5 x^2+3} \left(2-x^2\right)}{x}+\frac{9 x \left(2 x^2+\sqrt{13}+5\right)}{2 \sqrt{x^4+5 x^2+3}}+\frac{8 \sqrt{\frac{2}{3 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{x^4+5 x^2+3}}-\frac{3 \sqrt{\frac{3}{2} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{2 \sqrt{x^4+5 x^2+3}}","-\frac{\sqrt{x^4+5 x^2+3} \left(2-x^2\right)}{x}+\frac{9 x \left(2 x^2+\sqrt{13}+5\right)}{2 \sqrt{x^4+5 x^2+3}}+\frac{8 \sqrt{\frac{2}{3 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{x^4+5 x^2+3}}-\frac{3 \sqrt{\frac{3}{2} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{2 \sqrt{x^4+5 x^2+3}}",1,"(9*x*(5 + Sqrt[13] + 2*x^2))/(2*Sqrt[3 + 5*x^2 + x^4]) - ((2 - x^2)*Sqrt[3 + 5*x^2 + x^4])/x - (3*Sqrt[(3*(5 + Sqrt[13]))/2]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(2*Sqrt[3 + 5*x^2 + x^4]) + (8*Sqrt[2/(3*(5 + Sqrt[13]))]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/Sqrt[3 + 5*x^2 + x^4]","A",4,4,25,0.1600,1,"{1271, 1189, 1099, 1135}"
155,1,305,0,0.1583044,"\int \frac{\left(2+3 x^2\right) \sqrt{3+5 x^2+x^4}}{x^4} \, dx","Int[((2 + 3*x^2)*Sqrt[3 + 5*x^2 + x^4])/x^4,x]","-\frac{\sqrt{x^4+5 x^2+3} \left(2-9 x^2\right)}{3 x^3}-\frac{64 \sqrt{x^4+5 x^2+3}}{9 x}+\frac{32 x \left(2 x^2+\sqrt{13}+5\right)}{9 \sqrt{x^4+5 x^2+3}}+\frac{49 \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{3 \sqrt{6 \left(5+\sqrt{13}\right)} \sqrt{x^4+5 x^2+3}}-\frac{16 \sqrt{\frac{2}{3} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{9 \sqrt{x^4+5 x^2+3}}","-\frac{\sqrt{x^4+5 x^2+3} \left(2-9 x^2\right)}{3 x^3}-\frac{64 \sqrt{x^4+5 x^2+3}}{9 x}+\frac{32 x \left(2 x^2+\sqrt{13}+5\right)}{9 \sqrt{x^4+5 x^2+3}}+\frac{49 \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{3 \sqrt{6 \left(5+\sqrt{13}\right)} \sqrt{x^4+5 x^2+3}}-\frac{16 \sqrt{\frac{2}{3} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{9 \sqrt{x^4+5 x^2+3}}",1,"(32*x*(5 + Sqrt[13] + 2*x^2))/(9*Sqrt[3 + 5*x^2 + x^4]) - (64*Sqrt[3 + 5*x^2 + x^4])/(9*x) - ((2 - 9*x^2)*Sqrt[3 + 5*x^2 + x^4])/(3*x^3) - (16*Sqrt[(2*(5 + Sqrt[13]))/3]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(9*Sqrt[3 + 5*x^2 + x^4]) + (49*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(3*Sqrt[6*(5 + Sqrt[13])]*Sqrt[3 + 5*x^2 + x^4])","A",5,5,25,0.2000,1,"{1271, 1281, 1189, 1099, 1135}"
156,1,127,0,0.0958111,"\int x^5 \left(2+3 x^2\right) \left(3+5 x^2+x^4\right)^{3/2} \, dx","Int[x^5*(2 + 3*x^2)*(3 + 5*x^2 + x^4)^(3/2),x]","\frac{3}{14} \left(x^4+5 x^2+3\right)^{5/2} x^4+\frac{\left(3313-1070 x^2\right) \left(x^4+5 x^2+3\right)^{5/2}}{1680}-\frac{2183}{768} \left(2 x^2+5\right) \left(x^4+5 x^2+3\right)^{3/2}+\frac{28379 \left(2 x^2+5\right) \sqrt{x^4+5 x^2+3}}{2048}-\frac{368927 \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)}{4096}","\frac{3}{14} \left(x^4+5 x^2+3\right)^{5/2} x^4+\frac{\left(3313-1070 x^2\right) \left(x^4+5 x^2+3\right)^{5/2}}{1680}-\frac{2183}{768} \left(2 x^2+5\right) \left(x^4+5 x^2+3\right)^{3/2}+\frac{28379 \left(2 x^2+5\right) \sqrt{x^4+5 x^2+3}}{2048}-\frac{368927 \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)}{4096}",1,"(28379*(5 + 2*x^2)*Sqrt[3 + 5*x^2 + x^4])/2048 - (2183*(5 + 2*x^2)*(3 + 5*x^2 + x^4)^(3/2))/768 + (3*x^4*(3 + 5*x^2 + x^4)^(5/2))/14 + ((3313 - 1070*x^2)*(3 + 5*x^2 + x^4)^(5/2))/1680 - (368927*ArcTanh[(5 + 2*x^2)/(2*Sqrt[3 + 5*x^2 + x^4])])/4096","A",7,6,25,0.2400,1,"{1251, 832, 779, 612, 621, 206}"
157,1,106,0,0.0718341,"\int x^3 \left(2+3 x^2\right) \left(3+5 x^2+x^4\right)^{3/2} \, dx","Int[x^3*(2 + 3*x^2)*(3 + 5*x^2 + x^4)^(3/2),x]","-\frac{1}{40} \left(27-10 x^2\right) \left(x^4+5 x^2+3\right)^{5/2}+\frac{123}{128} \left(2 x^2+5\right) \left(x^4+5 x^2+3\right)^{3/2}-\frac{4797 \left(2 x^2+5\right) \sqrt{x^4+5 x^2+3}}{1024}+\frac{62361 \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)}{2048}","-\frac{1}{40} \left(27-10 x^2\right) \left(x^4+5 x^2+3\right)^{5/2}+\frac{123}{128} \left(2 x^2+5\right) \left(x^4+5 x^2+3\right)^{3/2}-\frac{4797 \left(2 x^2+5\right) \sqrt{x^4+5 x^2+3}}{1024}+\frac{62361 \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)}{2048}",1,"(-4797*(5 + 2*x^2)*Sqrt[3 + 5*x^2 + x^4])/1024 + (123*(5 + 2*x^2)*(3 + 5*x^2 + x^4)^(3/2))/128 - ((27 - 10*x^2)*(3 + 5*x^2 + x^4)^(5/2))/40 + (62361*ArcTanh[(5 + 2*x^2)/(2*Sqrt[3 + 5*x^2 + x^4])])/2048","A",6,5,25,0.2000,1,"{1251, 779, 612, 621, 206}"
158,1,99,0,0.0583216,"\int x \left(2+3 x^2\right) \left(3+5 x^2+x^4\right)^{3/2} \, dx","Int[x*(2 + 3*x^2)*(3 + 5*x^2 + x^4)^(3/2),x]","\frac{3}{10} \left(x^4+5 x^2+3\right)^{5/2}-\frac{11}{32} \left(2 x^2+5\right) \left(x^4+5 x^2+3\right)^{3/2}+\frac{429}{256} \left(2 x^2+5\right) \sqrt{x^4+5 x^2+3}-\frac{5577}{512} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)","\frac{3}{10} \left(x^4+5 x^2+3\right)^{5/2}-\frac{11}{32} \left(2 x^2+5\right) \left(x^4+5 x^2+3\right)^{3/2}+\frac{429}{256} \left(2 x^2+5\right) \sqrt{x^4+5 x^2+3}-\frac{5577}{512} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)",1,"(429*(5 + 2*x^2)*Sqrt[3 + 5*x^2 + x^4])/256 - (11*(5 + 2*x^2)*(3 + 5*x^2 + x^4)^(3/2))/32 + (3*(3 + 5*x^2 + x^4)^(5/2))/10 - (5577*ArcTanh[(5 + 2*x^2)/(2*Sqrt[3 + 5*x^2 + x^4])])/512","A",6,5,23,0.2174,1,"{1247, 640, 612, 621, 206}"
159,1,119,0,0.1059212,"\int \frac{\left(2+3 x^2\right) \left(3+5 x^2+x^4\right)^{3/2}}{x} \, dx","Int[((2 + 3*x^2)*(3 + 5*x^2 + x^4)^(3/2))/x,x]","\frac{1}{48} \left(18 x^2+61\right) \left(x^4+5 x^2+3\right)^{3/2}+\frac{1}{128} \left(199-74 x^2\right) \sqrt{x^4+5 x^2+3}+\frac{2401}{256} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)-3 \sqrt{3} \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)","\frac{1}{48} \left(18 x^2+61\right) \left(x^4+5 x^2+3\right)^{3/2}+\frac{1}{128} \left(199-74 x^2\right) \sqrt{x^4+5 x^2+3}+\frac{2401}{256} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)-3 \sqrt{3} \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)",1,"((199 - 74*x^2)*Sqrt[3 + 5*x^2 + x^4])/128 + ((61 + 18*x^2)*(3 + 5*x^2 + x^4)^(3/2))/48 + (2401*ArcTanh[(5 + 2*x^2)/(2*Sqrt[3 + 5*x^2 + x^4])])/256 - 3*Sqrt[3]*ArcTanh[(6 + 5*x^2)/(2*Sqrt[3]*Sqrt[3 + 5*x^2 + x^4])]","A",8,6,25,0.2400,1,"{1251, 814, 843, 621, 206, 724}"
160,1,122,0,0.106506,"\int \frac{\left(2+3 x^2\right) \left(3+5 x^2+x^4\right)^{3/2}}{x^3} \, dx","Int[((2 + 3*x^2)*(3 + 5*x^2 + x^4)^(3/2))/x^3,x]","-\frac{\left(2-x^2\right) \left(x^4+5 x^2+3\right)^{3/2}}{2 x^2}+\frac{3}{16} \left(18 x^2+109\right) \sqrt{x^4+5 x^2+3}+\frac{609}{32} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)-12 \sqrt{3} \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)","-\frac{\left(2-x^2\right) \left(x^4+5 x^2+3\right)^{3/2}}{2 x^2}+\frac{3}{16} \left(18 x^2+109\right) \sqrt{x^4+5 x^2+3}+\frac{609}{32} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)-12 \sqrt{3} \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)",1,"(3*(109 + 18*x^2)*Sqrt[3 + 5*x^2 + x^4])/16 - ((2 - x^2)*(3 + 5*x^2 + x^4)^(3/2))/(2*x^2) + (609*ArcTanh[(5 + 2*x^2)/(2*Sqrt[3 + 5*x^2 + x^4])])/32 - 12*Sqrt[3]*ArcTanh[(6 + 5*x^2)/(2*Sqrt[3]*Sqrt[3 + 5*x^2 + x^4])]","A",8,7,25,0.2800,1,"{1251, 812, 814, 843, 621, 206, 724}"
161,1,127,0,0.1089554,"\int \frac{\left(2+3 x^2\right) \left(3+5 x^2+x^4\right)^{3/2}}{x^5} \, dx","Int[((2 + 3*x^2)*(3 + 5*x^2 + x^4)^(3/2))/x^5,x]","-\frac{\left(2-3 x^2\right) \left(x^4+5 x^2+3\right)^{3/2}}{4 x^4}-\frac{3 \left(28-19 x^2\right) \sqrt{x^4+5 x^2+3}}{8 x^2}+\frac{453}{16} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)-\frac{127}{8} \sqrt{3} \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)","-\frac{\left(2-3 x^2\right) \left(x^4+5 x^2+3\right)^{3/2}}{4 x^4}-\frac{3 \left(28-19 x^2\right) \sqrt{x^4+5 x^2+3}}{8 x^2}+\frac{453}{16} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)-\frac{127}{8} \sqrt{3} \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)",1,"(-3*(28 - 19*x^2)*Sqrt[3 + 5*x^2 + x^4])/(8*x^2) - ((2 - 3*x^2)*(3 + 5*x^2 + x^4)^(3/2))/(4*x^4) + (453*ArcTanh[(5 + 2*x^2)/(2*Sqrt[3 + 5*x^2 + x^4])])/16 - (127*Sqrt[3]*ArcTanh[(6 + 5*x^2)/(2*Sqrt[3]*Sqrt[3 + 5*x^2 + x^4])])/8","A",8,6,25,0.2400,1,"{1251, 812, 843, 621, 206, 724}"
162,1,127,0,0.1068616,"\int \frac{\left(2+3 x^2\right) \left(3+5 x^2+x^4\right)^{3/2}}{x^7} \, dx","Int[((2 + 3*x^2)*(3 + 5*x^2 + x^4)^(3/2))/x^7,x]","-\frac{\left(7 x^2+2\right) \left(x^4+5 x^2+3\right)^{3/2}}{6 x^6}-\frac{\left(67-32 x^2\right) \sqrt{x^4+5 x^2+3}}{12 x^2}+\frac{49}{4} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)-\frac{527 \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{24 \sqrt{3}}","-\frac{\left(7 x^2+2\right) \left(x^4+5 x^2+3\right)^{3/2}}{6 x^6}-\frac{\left(67-32 x^2\right) \sqrt{x^4+5 x^2+3}}{12 x^2}+\frac{49}{4} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)-\frac{527 \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{24 \sqrt{3}}",1,"-((67 - 32*x^2)*Sqrt[3 + 5*x^2 + x^4])/(12*x^2) - ((2 + 7*x^2)*(3 + 5*x^2 + x^4)^(3/2))/(6*x^6) + (49*ArcTanh[(5 + 2*x^2)/(2*Sqrt[3 + 5*x^2 + x^4])])/4 - (527*ArcTanh[(6 + 5*x^2)/(2*Sqrt[3]*Sqrt[3 + 5*x^2 + x^4])])/(24*Sqrt[3])","A",8,7,25,0.2800,1,"{1251, 810, 812, 843, 621, 206, 724}"
163,1,356,0,0.2564759,"\int x^4 \left(2+3 x^2\right) \left(3+5 x^2+x^4\right)^{3/2} \, dx","Int[x^4*(2 + 3*x^2)*(3 + 5*x^2 + x^4)^(3/2),x]","\frac{1}{143} \left(33 x^2+71\right) \left(x^4+5 x^2+3\right)^{3/2} x^5-\frac{1}{429} \left(272 x^2+283\right) \sqrt{x^4+5 x^2+3} x^5+\frac{1251}{715} \sqrt{x^4+5 x^2+3} x^3-\frac{4210}{429} \sqrt{x^4+5 x^2+3} x+\frac{176723 \left(2 x^2+\sqrt{13}+5\right) x}{4290 \sqrt{x^4+5 x^2+3}}+\frac{2105 \sqrt{\frac{2}{3 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{143 \sqrt{x^4+5 x^2+3}}-\frac{176723 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{4290 \sqrt{x^4+5 x^2+3}}","\frac{1}{143} \left(33 x^2+71\right) \left(x^4+5 x^2+3\right)^{3/2} x^5-\frac{1}{429} \left(272 x^2+283\right) \sqrt{x^4+5 x^2+3} x^5+\frac{1251}{715} \sqrt{x^4+5 x^2+3} x^3-\frac{4210}{429} \sqrt{x^4+5 x^2+3} x+\frac{176723 \left(2 x^2+\sqrt{13}+5\right) x}{4290 \sqrt{x^4+5 x^2+3}}+\frac{2105 \sqrt{\frac{2}{3 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{143 \sqrt{x^4+5 x^2+3}}-\frac{176723 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{4290 \sqrt{x^4+5 x^2+3}}",1,"(176723*x*(5 + Sqrt[13] + 2*x^2))/(4290*Sqrt[3 + 5*x^2 + x^4]) - (4210*x*Sqrt[3 + 5*x^2 + x^4])/429 + (1251*x^3*Sqrt[3 + 5*x^2 + x^4])/715 - (x^5*(283 + 272*x^2)*Sqrt[3 + 5*x^2 + x^4])/429 + (x^5*(71 + 33*x^2)*(3 + 5*x^2 + x^4)^(3/2))/143 - (176723*Sqrt[(5 + Sqrt[13])/6]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(4290*Sqrt[3 + 5*x^2 + x^4]) + (2105*Sqrt[2/(3*(5 + Sqrt[13]))]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(143*Sqrt[3 + 5*x^2 + x^4])","A",7,5,25,0.2000,1,"{1273, 1279, 1189, 1099, 1135}"
164,1,331,0,0.2138383,"\int x^2 \left(2+3 x^2\right) \left(3+5 x^2+x^4\right)^{3/2} \, dx","Int[x^2*(2 + 3*x^2)*(3 + 5*x^2 + x^4)^(3/2),x]","\frac{1}{99} \left(27 x^2+67\right) \left(x^4+5 x^2+3\right)^{3/2} x^3-\frac{\left(890 x^2+911\right) \sqrt{x^4+5 x^2+3} x^3}{1155}+\frac{353}{99} \sqrt{x^4+5 x^2+3} x-\frac{49949 \left(2 x^2+\sqrt{13}+5\right) x}{3465 \sqrt{x^4+5 x^2+3}}-\frac{353 \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{33 \sqrt{6 \left(5+\sqrt{13}\right)} \sqrt{x^4+5 x^2+3}}+\frac{49949 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{3465 \sqrt{x^4+5 x^2+3}}","\frac{1}{99} \left(27 x^2+67\right) \left(x^4+5 x^2+3\right)^{3/2} x^3-\frac{\left(890 x^2+911\right) \sqrt{x^4+5 x^2+3} x^3}{1155}+\frac{353}{99} \sqrt{x^4+5 x^2+3} x-\frac{49949 \left(2 x^2+\sqrt{13}+5\right) x}{3465 \sqrt{x^4+5 x^2+3}}-\frac{353 \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{33 \sqrt{6 \left(5+\sqrt{13}\right)} \sqrt{x^4+5 x^2+3}}+\frac{49949 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{3465 \sqrt{x^4+5 x^2+3}}",1,"(-49949*x*(5 + Sqrt[13] + 2*x^2))/(3465*Sqrt[3 + 5*x^2 + x^4]) + (353*x*Sqrt[3 + 5*x^2 + x^4])/99 - (x^3*(911 + 890*x^2)*Sqrt[3 + 5*x^2 + x^4])/1155 + (x^3*(67 + 27*x^2)*(3 + 5*x^2 + x^4)^(3/2))/99 + (49949*Sqrt[(5 + Sqrt[13])/6]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(3465*Sqrt[3 + 5*x^2 + x^4]) - (353*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(33*Sqrt[6*(5 + Sqrt[13])]*Sqrt[3 + 5*x^2 + x^4])","A",6,5,25,0.2000,1,"{1273, 1279, 1189, 1099, 1135}"
165,1,308,0,0.1527722,"\int \left(2+3 x^2\right) \left(3+5 x^2+x^4\right)^{3/2} \, dx","Int[(2 + 3*x^2)*(3 + 5*x^2 + x^4)^(3/2),x]","\frac{1}{3} x \left(x^2+3\right) \left(x^4+5 x^2+3\right)^{3/2}-\frac{1}{15} x \left(12 x^2+5\right) \sqrt{x^4+5 x^2+3}+\frac{203 x \left(2 x^2+\sqrt{13}+5\right)}{30 \sqrt{x^4+5 x^2+3}}+\frac{5 \sqrt{\frac{2}{3 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{x^4+5 x^2+3}}-\frac{203 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{30 \sqrt{x^4+5 x^2+3}}","\frac{1}{3} x \left(x^2+3\right) \left(x^4+5 x^2+3\right)^{3/2}-\frac{1}{15} x \left(12 x^2+5\right) \sqrt{x^4+5 x^2+3}+\frac{203 x \left(2 x^2+\sqrt{13}+5\right)}{30 \sqrt{x^4+5 x^2+3}}+\frac{5 \sqrt{\frac{2}{3 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{x^4+5 x^2+3}}-\frac{203 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{30 \sqrt{x^4+5 x^2+3}}",1,"(203*x*(5 + Sqrt[13] + 2*x^2))/(30*Sqrt[3 + 5*x^2 + x^4]) - (x*(5 + 12*x^2)*Sqrt[3 + 5*x^2 + x^4])/15 + (x*(3 + x^2)*(3 + 5*x^2 + x^4)^(3/2))/3 - (203*Sqrt[(5 + Sqrt[13])/6]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(30*Sqrt[3 + 5*x^2 + x^4]) + (5*Sqrt[2/(3*(5 + Sqrt[13]))]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/Sqrt[3 + 5*x^2 + x^4]","A",5,4,22,0.1818,1,"{1176, 1189, 1099, 1135}"
166,1,312,0,0.1506561,"\int \frac{\left(2+3 x^2\right) \left(3+5 x^2+x^4\right)^{3/2}}{x^2} \, dx","Int[((2 + 3*x^2)*(3 + 5*x^2 + x^4)^(3/2))/x^2,x]","-\frac{\left(14-3 x^2\right) \left(x^4+5 x^2+3\right)^{3/2}}{7 x}+\frac{1}{35} x \left(129 x^2+655\right) \sqrt{x^4+5 x^2+3}+\frac{412 x \left(2 x^2+\sqrt{13}+5\right)}{35 \sqrt{x^4+5 x^2+3}}+\frac{19 \sqrt{\frac{3}{2 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{x^4+5 x^2+3}}-\frac{206 \sqrt{\frac{2}{3} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{35 \sqrt{x^4+5 x^2+3}}","-\frac{\left(14-3 x^2\right) \left(x^4+5 x^2+3\right)^{3/2}}{7 x}+\frac{1}{35} x \left(129 x^2+655\right) \sqrt{x^4+5 x^2+3}+\frac{412 x \left(2 x^2+\sqrt{13}+5\right)}{35 \sqrt{x^4+5 x^2+3}}+\frac{19 \sqrt{\frac{3}{2 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{x^4+5 x^2+3}}-\frac{206 \sqrt{\frac{2}{3} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{35 \sqrt{x^4+5 x^2+3}}",1,"(412*x*(5 + Sqrt[13] + 2*x^2))/(35*Sqrt[3 + 5*x^2 + x^4]) + (x*(655 + 129*x^2)*Sqrt[3 + 5*x^2 + x^4])/35 - ((14 - 3*x^2)*(3 + 5*x^2 + x^4)^(3/2))/(7*x) - (206*Sqrt[(2*(5 + Sqrt[13]))/3]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(35*Sqrt[3 + 5*x^2 + x^4]) + (19*Sqrt[3/(2*(5 + Sqrt[13]))]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/Sqrt[3 + 5*x^2 + x^4]","A",5,5,25,0.2000,1,"{1271, 1176, 1189, 1099, 1135}"
167,1,314,0,0.1641342,"\int \frac{\left(2+3 x^2\right) \left(3+5 x^2+x^4\right)^{3/2}}{x^4} \, dx","Int[((2 + 3*x^2)*(3 + 5*x^2 + x^4)^(3/2))/x^4,x]","-\frac{\left(10-9 x^2\right) \left(x^4+5 x^2+3\right)^{3/2}}{15 x^3}-\frac{13 \left(24-5 x^2\right) \sqrt{x^4+5 x^2+3}}{15 x}+\frac{949 x \left(2 x^2+\sqrt{13}+5\right)}{30 \sqrt{x^4+5 x^2+3}}+\frac{65 \sqrt{\frac{2}{3 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{x^4+5 x^2+3}}-\frac{949 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{30 \sqrt{x^4+5 x^2+3}}","-\frac{\left(10-9 x^2\right) \left(x^4+5 x^2+3\right)^{3/2}}{15 x^3}-\frac{13 \left(24-5 x^2\right) \sqrt{x^4+5 x^2+3}}{15 x}+\frac{949 x \left(2 x^2+\sqrt{13}+5\right)}{30 \sqrt{x^4+5 x^2+3}}+\frac{65 \sqrt{\frac{2}{3 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{x^4+5 x^2+3}}-\frac{949 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{30 \sqrt{x^4+5 x^2+3}}",1,"(949*x*(5 + Sqrt[13] + 2*x^2))/(30*Sqrt[3 + 5*x^2 + x^4]) - (13*(24 - 5*x^2)*Sqrt[3 + 5*x^2 + x^4])/(15*x) - ((10 - 9*x^2)*(3 + 5*x^2 + x^4)^(3/2))/(15*x^3) - (949*Sqrt[(5 + Sqrt[13])/6]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(30*Sqrt[3 + 5*x^2 + x^4]) + (65*Sqrt[2/(3*(5 + Sqrt[13]))]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/Sqrt[3 + 5*x^2 + x^4]","A",5,4,25,0.1600,1,"{1271, 1189, 1099, 1135}"
168,1,331,0,0.2027514,"\int \frac{\left(2+3 x^2\right) \left(3+5 x^2+x^4\right)^{3/2}}{x^6} \, dx","Int[((2 + 3*x^2)*(3 + 5*x^2 + x^4)^(3/2))/x^6,x]","-\frac{\left(2-5 x^2\right) \left(x^4+5 x^2+3\right)^{3/2}}{5 x^5}-\frac{\left(40-87 x^2\right) \sqrt{x^4+5 x^2+3}}{5 x^3}-\frac{722 \sqrt{x^4+5 x^2+3}}{15 x}+\frac{361 x \left(2 x^2+\sqrt{13}+5\right)}{15 \sqrt{x^4+5 x^2+3}}+\frac{103 \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{6 \left(5+\sqrt{13}\right)} \sqrt{x^4+5 x^2+3}}-\frac{361 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{15 \sqrt{x^4+5 x^2+3}}","-\frac{\left(2-5 x^2\right) \left(x^4+5 x^2+3\right)^{3/2}}{5 x^5}-\frac{\left(40-87 x^2\right) \sqrt{x^4+5 x^2+3}}{5 x^3}-\frac{722 \sqrt{x^4+5 x^2+3}}{15 x}+\frac{361 x \left(2 x^2+\sqrt{13}+5\right)}{15 \sqrt{x^4+5 x^2+3}}+\frac{103 \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{6 \left(5+\sqrt{13}\right)} \sqrt{x^4+5 x^2+3}}-\frac{361 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{15 \sqrt{x^4+5 x^2+3}}",1,"(361*x*(5 + Sqrt[13] + 2*x^2))/(15*Sqrt[3 + 5*x^2 + x^4]) - (722*Sqrt[3 + 5*x^2 + x^4])/(15*x) - ((40 - 87*x^2)*Sqrt[3 + 5*x^2 + x^4])/(5*x^3) - ((2 - 5*x^2)*(3 + 5*x^2 + x^4)^(3/2))/(5*x^5) - (361*Sqrt[(5 + Sqrt[13])/6]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(15*Sqrt[3 + 5*x^2 + x^4]) + (103*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(Sqrt[6*(5 + Sqrt[13])]*Sqrt[3 + 5*x^2 + x^4])","A",6,5,25,0.2000,1,"{1271, 1281, 1189, 1099, 1135}"
169,1,153,0,0.2028793,"\int \frac{x^5 \left(A+B x^2\right)}{\sqrt{a+b x^2+c x^4}} \, dx","Int[(x^5*(A + B*x^2))/Sqrt[a + b*x^2 + c*x^4],x]","\frac{\sqrt{a+b x^2+c x^4} \left(-16 a B c-2 c x^2 (5 b B-6 A c)-18 A b c+15 b^2 B\right)}{48 c^3}-\frac{\left(8 a A c^2-12 a b B c-6 A b^2 c+5 b^3 B\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{32 c^{7/2}}+\frac{B x^4 \sqrt{a+b x^2+c x^4}}{6 c}","\frac{\sqrt{a+b x^2+c x^4} \left(-16 a B c-2 c x^2 (5 b B-6 A c)-18 A b c+15 b^2 B\right)}{48 c^3}-\frac{\left(8 a A c^2-12 a b B c-6 A b^2 c+5 b^3 B\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{32 c^{7/2}}+\frac{B x^4 \sqrt{a+b x^2+c x^4}}{6 c}",1,"(B*x^4*Sqrt[a + b*x^2 + c*x^4])/(6*c) + ((15*b^2*B - 18*A*b*c - 16*a*B*c - 2*c*(5*b*B - 6*A*c)*x^2)*Sqrt[a + b*x^2 + c*x^4])/(48*c^3) - ((5*b^3*B - 6*A*b^2*c - 12*a*b*B*c + 8*a*A*c^2)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(32*c^(7/2))","A",5,5,27,0.1852,1,"{1251, 832, 779, 621, 206}"
170,1,100,0,0.0927491,"\int \frac{x^3 \left(A+B x^2\right)}{\sqrt{a+b x^2+c x^4}} \, dx","Int[(x^3*(A + B*x^2))/Sqrt[a + b*x^2 + c*x^4],x]","\frac{\left(-4 a B c-4 A b c+3 b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{16 c^{5/2}}-\frac{\sqrt{a+b x^2+c x^4} \left(-4 A c+3 b B-2 B c x^2\right)}{8 c^2}","\frac{\left(-4 a B c-4 A b c+3 b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{16 c^{5/2}}-\frac{\sqrt{a+b x^2+c x^4} \left(-4 A c+3 b B-2 B c x^2\right)}{8 c^2}",1,"-((3*b*B - 4*A*c - 2*B*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(8*c^2) + ((3*b^2*B - 4*A*b*c - 4*a*B*c)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(16*c^(5/2))","A",4,4,27,0.1481,1,"{1251, 779, 621, 206}"
171,1,76,0,0.0639266,"\int \frac{x \left(A+B x^2\right)}{\sqrt{a+b x^2+c x^4}} \, dx","Int[(x*(A + B*x^2))/Sqrt[a + b*x^2 + c*x^4],x]","\frac{B \sqrt{a+b x^2+c x^4}}{2 c}-\frac{(b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 c^{3/2}}","\frac{B \sqrt{a+b x^2+c x^4}}{2 c}-\frac{(b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 c^{3/2}}",1,"(B*Sqrt[a + b*x^2 + c*x^4])/(2*c) - ((b*B - 2*A*c)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(4*c^(3/2))","A",4,4,25,0.1600,1,"{1247, 640, 621, 206}"
172,1,90,0,0.0939564,"\int \frac{A+B x^2}{x \sqrt{a+b x^2+c x^4}} \, dx","Int[(A + B*x^2)/(x*Sqrt[a + b*x^2 + c*x^4]),x]","\frac{B \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{c}}-\frac{A \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{a}}","\frac{B \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{c}}-\frac{A \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{a}}",1,"-(A*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(2*Sqrt[a]) + (B*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(2*Sqrt[c])","A",6,5,27,0.1852,1,"{1251, 843, 621, 206, 724}"
173,1,80,0,0.0828435,"\int \frac{A+B x^2}{x^3 \sqrt{a+b x^2+c x^4}} \, dx","Int[(A + B*x^2)/(x^3*Sqrt[a + b*x^2 + c*x^4]),x]","\frac{(A b-2 a B) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{4 a^{3/2}}-\frac{A \sqrt{a+b x^2+c x^4}}{2 a x^2}","\frac{(A b-2 a B) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{4 a^{3/2}}-\frac{A \sqrt{a+b x^2+c x^4}}{2 a x^2}",1,"-(A*Sqrt[a + b*x^2 + c*x^4])/(2*a*x^2) + ((A*b - 2*a*B)*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(4*a^(3/2))","A",4,4,27,0.1481,1,"{1251, 806, 724, 206}"
174,1,124,0,0.145204,"\int \frac{A+B x^2}{x^5 \sqrt{a+b x^2+c x^4}} \, dx","Int[(A + B*x^2)/(x^5*Sqrt[a + b*x^2 + c*x^4]),x]","-\frac{\left(-4 a A c-4 a b B+3 A b^2\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{16 a^{5/2}}+\frac{(3 A b-4 a B) \sqrt{a+b x^2+c x^4}}{8 a^2 x^2}-\frac{A \sqrt{a+b x^2+c x^4}}{4 a x^4}","-\frac{\left(-4 a A c-4 a b B+3 A b^2\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{16 a^{5/2}}+\frac{(3 A b-4 a B) \sqrt{a+b x^2+c x^4}}{8 a^2 x^2}-\frac{A \sqrt{a+b x^2+c x^4}}{4 a x^4}",1,"-(A*Sqrt[a + b*x^2 + c*x^4])/(4*a*x^4) + ((3*A*b - 4*a*B)*Sqrt[a + b*x^2 + c*x^4])/(8*a^2*x^2) - ((3*A*b^2 - 4*a*b*B - 4*a*A*c)*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(16*a^(5/2))","A",5,5,27,0.1852,1,"{1251, 834, 806, 724, 206}"
175,1,177,0,0.2386139,"\int \frac{A+B x^2}{x^7 \sqrt{a+b x^2+c x^4}} \, dx","Int[(A + B*x^2)/(x^7*Sqrt[a + b*x^2 + c*x^4]),x]","-\frac{\sqrt{a+b x^2+c x^4} \left(-16 a A c-18 a b B+15 A b^2\right)}{48 a^3 x^2}+\frac{\left(8 a^2 B c-12 a A b c-6 a b^2 B+5 A b^3\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{32 a^{7/2}}+\frac{(5 A b-6 a B) \sqrt{a+b x^2+c x^4}}{24 a^2 x^4}-\frac{A \sqrt{a+b x^2+c x^4}}{6 a x^6}","-\frac{\sqrt{a+b x^2+c x^4} \left(-16 a A c-18 a b B+15 A b^2\right)}{48 a^3 x^2}+\frac{\left(8 a^2 B c-12 a A b c-6 a b^2 B+5 A b^3\right) \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{32 a^{7/2}}+\frac{(5 A b-6 a B) \sqrt{a+b x^2+c x^4}}{24 a^2 x^4}-\frac{A \sqrt{a+b x^2+c x^4}}{6 a x^6}",1,"-(A*Sqrt[a + b*x^2 + c*x^4])/(6*a*x^6) + ((5*A*b - 6*a*B)*Sqrt[a + b*x^2 + c*x^4])/(24*a^2*x^4) - ((15*A*b^2 - 18*a*b*B - 16*a*A*c)*Sqrt[a + b*x^2 + c*x^4])/(48*a^3*x^2) + ((5*A*b^3 - 6*a*b^2*B - 12*a*A*b*c + 8*a^2*B*c)*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(32*a^(7/2))","A",6,5,27,0.1852,1,"{1251, 834, 806, 724, 206}"
176,1,403,0,0.2836676,"\int \frac{x^4 \left(A+B x^2\right)}{\sqrt{a+b x^2+c x^4}} \, dx","Int[(x^4*(A + B*x^2))/Sqrt[a + b*x^2 + c*x^4],x]","\frac{x \sqrt{a+b x^2+c x^4} \left(-9 a B c-10 A b c+8 b^2 B\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(\sqrt{a} \sqrt{c} (4 b B-5 A c)-9 a B c-10 A b c+8 b^2 B\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} \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(-9 a B c-10 A b c+8 b^2 B\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{x \sqrt{a+b x^2+c x^4} (4 b B-5 A c)}{15 c^2}+\frac{B x^3 \sqrt{a+b x^2+c x^4}}{5 c}","\frac{x \sqrt{a+b x^2+c x^4} \left(-9 a B c-10 A b c+8 b^2 B\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(\sqrt{a} \sqrt{c} (4 b B-5 A c)-9 a B c-10 A b c+8 b^2 B\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} \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(-9 a B c-10 A b c+8 b^2 B\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{x \sqrt{a+b x^2+c x^4} (4 b B-5 A c)}{15 c^2}+\frac{B x^3 \sqrt{a+b x^2+c x^4}}{5 c}",1,"-((4*b*B - 5*A*c)*x*Sqrt[a + b*x^2 + c*x^4])/(15*c^2) + (B*x^3*Sqrt[a + b*x^2 + c*x^4])/(5*c) + ((8*b^2*B - 10*A*b*c - 9*a*B*c)*x*Sqrt[a + b*x^2 + c*x^4])/(15*c^(5/2)*(Sqrt[a] + Sqrt[c]*x^2)) - (a^(1/4)*(8*b^2*B - 10*A*b*c - 9*a*B*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(15*c^(11/4)*Sqrt[a + b*x^2 + c*x^4]) + (a^(1/4)*(8*b^2*B - 10*A*b*c - 9*a*B*c + Sqrt[a]*Sqrt[c]*(4*b*B - 5*A*c))*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(30*c^(11/4)*Sqrt[a + b*x^2 + c*x^4])","A",5,4,27,0.1481,1,"{1279, 1197, 1103, 1195}"
177,1,336,0,0.1492332,"\int \frac{x^2 \left(A+B x^2\right)}{\sqrt{a+b x^2+c x^4}} \, dx","Int[(x^2*(A + B*x^2))/Sqrt[a + b*x^2 + c*x^4],x]","-\frac{x \sqrt{a+b x^2+c x^4} (2 b B-3 A c)}{3 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+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{a} B \sqrt{c}-3 A c+2 b B\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{\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}} (2 b B-3 A c) 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{B x \sqrt{a+b x^2+c x^4}}{3 c}","-\frac{x \sqrt{a+b x^2+c x^4} (2 b B-3 A c)}{3 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+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{a} B \sqrt{c}-3 A c+2 b B\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{\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}} (2 b B-3 A c) 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{B x \sqrt{a+b x^2+c x^4}}{3 c}",1,"(B*x*Sqrt[a + b*x^2 + c*x^4])/(3*c) - ((2*b*B - 3*A*c)*x*Sqrt[a + b*x^2 + c*x^4])/(3*c^(3/2)*(Sqrt[a] + Sqrt[c]*x^2)) + (a^(1/4)*(2*b*B - 3*A*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(3*c^(7/4)*Sqrt[a + b*x^2 + c*x^4]) - (a^(1/4)*(2*b*B + Sqrt[a]*B*Sqrt[c] - 3*A*c)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(6*c^(7/4)*Sqrt[a + b*x^2 + c*x^4])","A",4,4,27,0.1481,1,"{1279, 1197, 1103, 1195}"
178,1,283,0,0.0828396,"\int \frac{A+B x^2}{\sqrt{a+b x^2+c x^4}} \, dx","Int[(A + B*x^2)/Sqrt[a + b*x^2 + c*x^4],x]","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x^2\right) \left(\frac{A \sqrt{c}}{\sqrt{a}}+B\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 c^{3/4} \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{a} B \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{c^{3/4} \sqrt{a+b x^2+c x^4}}+\frac{B 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) \left(\frac{A \sqrt{c}}{\sqrt{a}}+B\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 c^{3/4} \sqrt{a+b x^2+c x^4}}-\frac{\sqrt[4]{a} B \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{c^{3/4} \sqrt{a+b x^2+c x^4}}+\frac{B x \sqrt{a+b x^2+c x^4}}{\sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}",1,"(B*x*Sqrt[a + b*x^2 + c*x^4])/(Sqrt[c]*(Sqrt[a] + Sqrt[c]*x^2)) - (a^(1/4)*B*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(c^(3/4)*Sqrt[a + b*x^2 + c*x^4]) + (a^(1/4)*(B + (A*Sqrt[c])/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])/(2*c^(3/4)*Sqrt[a + b*x^2 + c*x^4])","A",3,3,24,0.1250,1,"{1197, 1103, 1195}"
179,1,312,0,0.1313998,"\int \frac{A+B x^2}{x^2 \sqrt{a+b x^2+c x^4}} \, dx","Int[(A + B*x^2)/(x^2*Sqrt[a + b*x^2 + c*x^4]),x]","\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \left(\sqrt{a} B+A \sqrt{c}\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 a^{3/4} \sqrt[4]{c} \sqrt{a+b x^2+c x^4}}-\frac{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)}{a^{3/4} \sqrt{a+b x^2+c x^4}}-\frac{A \sqrt{a+b x^2+c x^4}}{a x}+\frac{A \sqrt{c} x \sqrt{a+b x^2+c x^4}}{a \left(\sqrt{a}+\sqrt{c} x^2\right)}","\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \left(\sqrt{a} B+A \sqrt{c}\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 a^{3/4} \sqrt[4]{c} \sqrt{a+b x^2+c x^4}}-\frac{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)}{a^{3/4} \sqrt{a+b x^2+c x^4}}-\frac{A \sqrt{a+b x^2+c x^4}}{a x}+\frac{A \sqrt{c} x \sqrt{a+b x^2+c x^4}}{a \left(\sqrt{a}+\sqrt{c} x^2\right)}",1,"-((A*Sqrt[a + b*x^2 + c*x^4])/(a*x)) + (A*Sqrt[c]*x*Sqrt[a + b*x^2 + c*x^4])/(a*(Sqrt[a] + Sqrt[c]*x^2)) - (A*c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(a^(3/4)*Sqrt[a + b*x^2 + c*x^4]) + ((Sqrt[a]*B + A*Sqrt[c])*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(2*a^(3/4)*c^(1/4)*Sqrt[a + b*x^2 + c*x^4])","A",4,4,27,0.1481,1,"{1281, 1197, 1103, 1195}"
180,1,376,0,0.2273372,"\int \frac{A+B x^2}{x^4 \sqrt{a+b x^2+c x^4}} \, dx","Int[(A + B*x^2)/(x^4*Sqrt[a + b*x^2 + c*x^4]),x]","\frac{(2 A b-3 a B) \sqrt{a+b x^2+c x^4}}{3 a^2 x}-\frac{\sqrt{c} x (2 A b-3 a B) \sqrt{a+b x^2+c x^4}}{3 a^2 \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{a} A \sqrt{c}-3 a B+2 A b\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 a^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{\sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) (2 A b-3 a B) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 a^{7/4} \sqrt{a+b x^2+c x^4}}-\frac{A \sqrt{a+b x^2+c x^4}}{3 a x^3}","\frac{(2 A b-3 a B) \sqrt{a+b x^2+c x^4}}{3 a^2 x}-\frac{\sqrt{c} x (2 A b-3 a B) \sqrt{a+b x^2+c x^4}}{3 a^2 \left(\sqrt{a}+\sqrt{c} x^2\right)}-\frac{\sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{a} A \sqrt{c}-3 a B+2 A b\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 a^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{\sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) (2 A b-3 a B) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 a^{7/4} \sqrt{a+b x^2+c x^4}}-\frac{A \sqrt{a+b x^2+c x^4}}{3 a x^3}",1,"-(A*Sqrt[a + b*x^2 + c*x^4])/(3*a*x^3) + ((2*A*b - 3*a*B)*Sqrt[a + b*x^2 + c*x^4])/(3*a^2*x) - ((2*A*b - 3*a*B)*Sqrt[c]*x*Sqrt[a + b*x^2 + c*x^4])/(3*a^2*(Sqrt[a] + Sqrt[c]*x^2)) + ((2*A*b - 3*a*B)*c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(3*a^(7/4)*Sqrt[a + b*x^2 + c*x^4]) - ((2*A*b - 3*a*B + Sqrt[a]*A*Sqrt[c])*c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(6*a^(7/4)*Sqrt[a + b*x^2 + c*x^4])","A",5,4,27,0.1481,1,"{1281, 1197, 1103, 1195}"
181,1,98,0,0.086537,"\int \frac{x^7 \left(2+3 x^2\right)}{\sqrt{3+5 x^2+x^4}} \, dx","Int[(x^7*(2 + 3*x^2))/Sqrt[3 + 5*x^2 + x^4],x]","\frac{3}{8} \sqrt{x^4+5 x^2+3} x^6-\frac{89}{48} \sqrt{x^4+5 x^2+3} x^4-\frac{1}{384} \left(24243-3802 x^2\right) \sqrt{x^4+5 x^2+3}+\frac{32801}{256} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)","\frac{3}{8} \sqrt{x^4+5 x^2+3} x^6-\frac{89}{48} \sqrt{x^4+5 x^2+3} x^4-\frac{1}{384} \left(24243-3802 x^2\right) \sqrt{x^4+5 x^2+3}+\frac{32801}{256} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)",1,"(-89*x^4*Sqrt[3 + 5*x^2 + x^4])/48 + (3*x^6*Sqrt[3 + 5*x^2 + x^4])/8 - ((24243 - 3802*x^2)*Sqrt[3 + 5*x^2 + x^4])/384 + (32801*ArcTanh[(5 + 2*x^2)/(2*Sqrt[3 + 5*x^2 + x^4])])/256","A",6,5,25,0.2000,1,"{1251, 832, 779, 621, 206}"
182,1,77,0,0.0662238,"\int \frac{x^5 \left(2+3 x^2\right)}{\sqrt{3+5 x^2+x^4}} \, dx","Int[(x^5*(2 + 3*x^2))/Sqrt[3 + 5*x^2 + x^4],x]","\frac{1}{2} \sqrt{x^4+5 x^2+3} x^4+\frac{3}{16} \left(89-14 x^2\right) \sqrt{x^4+5 x^2+3}-\frac{1083}{32} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)","\frac{1}{2} \sqrt{x^4+5 x^2+3} x^4+\frac{3}{16} \left(89-14 x^2\right) \sqrt{x^4+5 x^2+3}-\frac{1083}{32} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)",1,"(x^4*Sqrt[3 + 5*x^2 + x^4])/2 + (3*(89 - 14*x^2)*Sqrt[3 + 5*x^2 + x^4])/16 - (1083*ArcTanh[(5 + 2*x^2)/(2*Sqrt[3 + 5*x^2 + x^4])])/32","A",5,5,25,0.2000,1,"{1251, 832, 779, 621, 206}"
183,1,56,0,0.0449077,"\int \frac{x^3 \left(2+3 x^2\right)}{\sqrt{3+5 x^2+x^4}} \, dx","Int[(x^3*(2 + 3*x^2))/Sqrt[3 + 5*x^2 + x^4],x]","\frac{149}{16} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)-\frac{1}{8} \left(37-6 x^2\right) \sqrt{x^4+5 x^2+3}","\frac{149}{16} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)-\frac{1}{8} \left(37-6 x^2\right) \sqrt{x^4+5 x^2+3}",1,"-((37 - 6*x^2)*Sqrt[3 + 5*x^2 + x^4])/8 + (149*ArcTanh[(5 + 2*x^2)/(2*Sqrt[3 + 5*x^2 + x^4])])/16","A",4,4,25,0.1600,1,"{1251, 779, 621, 206}"
184,1,49,0,0.0323246,"\int \frac{x \left(2+3 x^2\right)}{\sqrt{3+5 x^2+x^4}} \, dx","Int[(x*(2 + 3*x^2))/Sqrt[3 + 5*x^2 + x^4],x]","\frac{3}{2} \sqrt{x^4+5 x^2+3}-\frac{11}{4} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)","\frac{3}{2} \sqrt{x^4+5 x^2+3}-\frac{11}{4} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)",1,"(3*Sqrt[3 + 5*x^2 + x^4])/2 - (11*ArcTanh[(5 + 2*x^2)/(2*Sqrt[3 + 5*x^2 + x^4])])/4","A",4,4,23,0.1739,1,"{1247, 640, 621, 206}"
185,1,69,0,0.0624769,"\int \frac{2+3 x^2}{x \sqrt{3+5 x^2+x^4}} \, dx","Int[(2 + 3*x^2)/(x*Sqrt[3 + 5*x^2 + x^4]),x]","\frac{3}{2} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)-\frac{\tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{\sqrt{3}}","\frac{3}{2} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)-\frac{\tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{\sqrt{3}}",1,"(3*ArcTanh[(5 + 2*x^2)/(2*Sqrt[3 + 5*x^2 + x^4])])/2 - ArcTanh[(6 + 5*x^2)/(2*Sqrt[3]*Sqrt[3 + 5*x^2 + x^4])]/Sqrt[3]","A",6,5,25,0.2000,1,"{1251, 843, 621, 206, 724}"
186,1,62,0,0.0500117,"\int \frac{2+3 x^2}{x^3 \sqrt{3+5 x^2+x^4}} \, dx","Int[(2 + 3*x^2)/(x^3*Sqrt[3 + 5*x^2 + x^4]),x]","-\frac{\sqrt{x^4+5 x^2+3}}{3 x^2}-\frac{2 \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{3 \sqrt{3}}","-\frac{\sqrt{x^4+5 x^2+3}}{3 x^2}-\frac{2 \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{3 \sqrt{3}}",1,"-Sqrt[3 + 5*x^2 + x^4]/(3*x^2) - (2*ArcTanh[(6 + 5*x^2)/(2*Sqrt[3]*Sqrt[3 + 5*x^2 + x^4])])/(3*Sqrt[3])","A",4,4,25,0.1600,1,"{1251, 806, 724, 206}"
187,1,83,0,0.0699484,"\int \frac{2+3 x^2}{x^5 \sqrt{3+5 x^2+x^4}} \, dx","Int[(2 + 3*x^2)/(x^5*Sqrt[3 + 5*x^2 + x^4]),x]","-\frac{\sqrt{x^4+5 x^2+3}}{12 x^2}-\frac{\sqrt{x^4+5 x^2+3}}{6 x^4}+\frac{1}{8} \sqrt{3} \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)","-\frac{\sqrt{x^4+5 x^2+3}}{12 x^2}-\frac{\sqrt{x^4+5 x^2+3}}{6 x^4}+\frac{1}{8} \sqrt{3} \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)",1,"-Sqrt[3 + 5*x^2 + x^4]/(6*x^4) - Sqrt[3 + 5*x^2 + x^4]/(12*x^2) + (Sqrt[3]*ArcTanh[(6 + 5*x^2)/(2*Sqrt[3]*Sqrt[3 + 5*x^2 + x^4])])/8","A",5,5,25,0.2000,1,"{1251, 834, 806, 724, 206}"
188,1,104,0,0.0881354,"\int \frac{2+3 x^2}{x^7 \sqrt{3+5 x^2+x^4}} \, dx","Int[(2 + 3*x^2)/(x^7*Sqrt[3 + 5*x^2 + x^4]),x]","\frac{13 \sqrt{x^4+5 x^2+3}}{108 x^2}-\frac{\sqrt{x^4+5 x^2+3}}{54 x^4}-\frac{\sqrt{x^4+5 x^2+3}}{9 x^6}-\frac{61 \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{216 \sqrt{3}}","\frac{13 \sqrt{x^4+5 x^2+3}}{108 x^2}-\frac{\sqrt{x^4+5 x^2+3}}{54 x^4}-\frac{\sqrt{x^4+5 x^2+3}}{9 x^6}-\frac{61 \tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{216 \sqrt{3}}",1,"-Sqrt[3 + 5*x^2 + x^4]/(9*x^6) - Sqrt[3 + 5*x^2 + x^4]/(54*x^4) + (13*Sqrt[3 + 5*x^2 + x^4])/(108*x^2) - (61*ArcTanh[(6 + 5*x^2)/(2*Sqrt[3]*Sqrt[3 + 5*x^2 + x^4])])/(216*Sqrt[3])","A",6,5,25,0.2000,1,"{1251, 834, 806, 724, 206}"
189,1,298,0,0.1752858,"\int \frac{x^4 \left(2+3 x^2\right)}{\sqrt{3+5 x^2+x^4}} \, dx","Int[(x^4*(2 + 3*x^2))/Sqrt[3 + 5*x^2 + x^4],x]","\frac{3}{5} \sqrt{x^4+5 x^2+3} x^3-\frac{10}{3} \sqrt{x^4+5 x^2+3} x+\frac{419 \left(2 x^2+\sqrt{13}+5\right) x}{30 \sqrt{x^4+5 x^2+3}}+\frac{5 \sqrt{\frac{2}{3 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{x^4+5 x^2+3}}-\frac{419 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{30 \sqrt{x^4+5 x^2+3}}","\frac{3}{5} \sqrt{x^4+5 x^2+3} x^3-\frac{10}{3} \sqrt{x^4+5 x^2+3} x+\frac{419 \left(2 x^2+\sqrt{13}+5\right) x}{30 \sqrt{x^4+5 x^2+3}}+\frac{5 \sqrt{\frac{2}{3 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{x^4+5 x^2+3}}-\frac{419 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{30 \sqrt{x^4+5 x^2+3}}",1,"(419*x*(5 + Sqrt[13] + 2*x^2))/(30*Sqrt[3 + 5*x^2 + x^4]) - (10*x*Sqrt[3 + 5*x^2 + x^4])/3 + (3*x^3*Sqrt[3 + 5*x^2 + x^4])/5 - (419*Sqrt[(5 + Sqrt[13])/6]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(30*Sqrt[3 + 5*x^2 + x^4]) + (5*Sqrt[2/(3*(5 + Sqrt[13]))]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/Sqrt[3 + 5*x^2 + x^4]","A",5,4,25,0.1600,1,"{1279, 1189, 1099, 1135}"
190,1,270,0,0.1198493,"\int \frac{x^2 \left(2+3 x^2\right)}{\sqrt{3+5 x^2+x^4}} \, dx","Int[(x^2*(2 + 3*x^2))/Sqrt[3 + 5*x^2 + x^4],x]","\sqrt{x^4+5 x^2+3} x-\frac{4 \left(2 x^2+\sqrt{13}+5\right) x}{\sqrt{x^4+5 x^2+3}}-\frac{\sqrt{\frac{3}{2 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{x^4+5 x^2+3}}+\frac{2 \sqrt{\frac{2}{3} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{x^4+5 x^2+3}}","\sqrt{x^4+5 x^2+3} x-\frac{4 \left(2 x^2+\sqrt{13}+5\right) x}{\sqrt{x^4+5 x^2+3}}-\frac{\sqrt{\frac{3}{2 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{x^4+5 x^2+3}}+\frac{2 \sqrt{\frac{2}{3} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{x^4+5 x^2+3}}",1,"(-4*x*(5 + Sqrt[13] + 2*x^2))/Sqrt[3 + 5*x^2 + x^4] + x*Sqrt[3 + 5*x^2 + x^4] + (2*Sqrt[(2*(5 + Sqrt[13]))/3]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/Sqrt[3 + 5*x^2 + x^4] - (Sqrt[3/(2*(5 + Sqrt[13]))]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/Sqrt[3 + 5*x^2 + x^4]","A",4,4,25,0.1600,1,"{1279, 1189, 1099, 1135}"
191,1,257,0,0.0767277,"\int \frac{2+3 x^2}{\sqrt{3+5 x^2+x^4}} \, dx","Int[(2 + 3*x^2)/Sqrt[3 + 5*x^2 + x^4],x]","\frac{3 x \left(2 x^2+\sqrt{13}+5\right)}{2 \sqrt{x^4+5 x^2+3}}+\frac{\sqrt{\frac{2}{3 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{x^4+5 x^2+3}}-\frac{\sqrt{\frac{3}{2} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{2 \sqrt{x^4+5 x^2+3}}","\frac{3 x \left(2 x^2+\sqrt{13}+5\right)}{2 \sqrt{x^4+5 x^2+3}}+\frac{\sqrt{\frac{2}{3 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{x^4+5 x^2+3}}-\frac{\sqrt{\frac{3}{2} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{2 \sqrt{x^4+5 x^2+3}}",1,"(3*x*(5 + Sqrt[13] + 2*x^2))/(2*Sqrt[3 + 5*x^2 + x^4]) - (Sqrt[(3*(5 + Sqrt[13]))/2]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(2*Sqrt[3 + 5*x^2 + x^4]) + (Sqrt[2/(3*(5 + Sqrt[13]))]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/Sqrt[3 + 5*x^2 + x^4]","A",3,3,22,0.1364,1,"{1189, 1099, 1135}"
192,1,278,0,0.1226582,"\int \frac{2+3 x^2}{x^2 \sqrt{3+5 x^2+x^4}} \, dx","Int[(2 + 3*x^2)/(x^2*Sqrt[3 + 5*x^2 + x^4]),x]","\frac{x \left(2 x^2+\sqrt{13}+5\right)}{3 \sqrt{x^4+5 x^2+3}}-\frac{2 \sqrt{x^4+5 x^2+3}}{3 x}+\frac{\sqrt{\frac{3}{2 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{x^4+5 x^2+3}}-\frac{\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{3 \sqrt{x^4+5 x^2+3}}","\frac{x \left(2 x^2+\sqrt{13}+5\right)}{3 \sqrt{x^4+5 x^2+3}}-\frac{2 \sqrt{x^4+5 x^2+3}}{3 x}+\frac{\sqrt{\frac{3}{2 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{\sqrt{x^4+5 x^2+3}}-\frac{\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{3 \sqrt{x^4+5 x^2+3}}",1,"(x*(5 + Sqrt[13] + 2*x^2))/(3*Sqrt[3 + 5*x^2 + x^4]) - (2*Sqrt[3 + 5*x^2 + x^4])/(3*x) - (Sqrt[(5 + Sqrt[13])/6]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(3*Sqrt[3 + 5*x^2 + x^4]) + (Sqrt[3/(2*(5 + Sqrt[13]))]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/Sqrt[3 + 5*x^2 + x^4]","A",4,4,25,0.1600,1,"{1281, 1189, 1099, 1135}"
193,1,302,0,0.1633201,"\int \frac{2+3 x^2}{x^4 \sqrt{3+5 x^2+x^4}} \, dx","Int[(2 + 3*x^2)/(x^4*Sqrt[3 + 5*x^2 + x^4]),x]","\frac{7 x \left(2 x^2+\sqrt{13}+5\right)}{54 \sqrt{x^4+5 x^2+3}}-\frac{7 \sqrt{x^4+5 x^2+3}}{27 x}-\frac{2 \sqrt{x^4+5 x^2+3}}{9 x^3}-\frac{\sqrt{\frac{2}{3 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{9 \sqrt{x^4+5 x^2+3}}-\frac{7 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{54 \sqrt{x^4+5 x^2+3}}","\frac{7 x \left(2 x^2+\sqrt{13}+5\right)}{54 \sqrt{x^4+5 x^2+3}}-\frac{7 \sqrt{x^4+5 x^2+3}}{27 x}-\frac{2 \sqrt{x^4+5 x^2+3}}{9 x^3}-\frac{\sqrt{\frac{2}{3 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{9 \sqrt{x^4+5 x^2+3}}-\frac{7 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{54 \sqrt{x^4+5 x^2+3}}",1,"(7*x*(5 + Sqrt[13] + 2*x^2))/(54*Sqrt[3 + 5*x^2 + x^4]) - (2*Sqrt[3 + 5*x^2 + x^4])/(9*x^3) - (7*Sqrt[3 + 5*x^2 + x^4])/(27*x) - (7*Sqrt[(5 + Sqrt[13])/6]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(54*Sqrt[3 + 5*x^2 + x^4]) - (Sqrt[2/(3*(5 + Sqrt[13]))]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(9*Sqrt[3 + 5*x^2 + x^4])","A",5,4,25,0.1600,1,"{1281, 1189, 1099, 1135}"
194,1,77,0,0.0576965,"\int \frac{x^5 \left(2+3 x^2\right)}{\left(3+5 x^2+x^4\right)^{3/2}} \, dx","Int[(x^5*(2 + 3*x^2))/(3 + 5*x^2 + x^4)^(3/2),x]","-\frac{\left(47 x^2+33\right) x^2}{13 \sqrt{x^4+5 x^2+3}}+\frac{133}{26} \sqrt{x^4+5 x^2+3}-\frac{41}{4} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)","-\frac{\left(47 x^2+33\right) x^2}{13 \sqrt{x^4+5 x^2+3}}+\frac{133}{26} \sqrt{x^4+5 x^2+3}-\frac{41}{4} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)",1,"-(x^2*(33 + 47*x^2))/(13*Sqrt[3 + 5*x^2 + x^4]) + (133*Sqrt[3 + 5*x^2 + x^4])/26 - (41*ArcTanh[(5 + 2*x^2)/(2*Sqrt[3 + 5*x^2 + x^4])])/4","A",5,5,25,0.2000,1,"{1251, 818, 640, 621, 206}"
195,1,56,0,0.0434781,"\int \frac{x^3 \left(2+3 x^2\right)}{\left(3+5 x^2+x^4\right)^{3/2}} \, dx","Int[(x^3*(2 + 3*x^2))/(3 + 5*x^2 + x^4)^(3/2),x]","\frac{3}{2} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)-\frac{47 x^2+33}{13 \sqrt{x^4+5 x^2+3}}","\frac{3}{2} \tanh ^{-1}\left(\frac{2 x^2+5}{2 \sqrt{x^4+5 x^2+3}}\right)-\frac{47 x^2+33}{13 \sqrt{x^4+5 x^2+3}}",1,"-(33 + 47*x^2)/(13*Sqrt[3 + 5*x^2 + x^4]) + (3*ArcTanh[(5 + 2*x^2)/(2*Sqrt[3 + 5*x^2 + x^4])])/2","A",4,4,25,0.1600,1,"{1251, 777, 621, 206}"
196,1,25,0,0.0191952,"\int \frac{x \left(2+3 x^2\right)}{\left(3+5 x^2+x^4\right)^{3/2}} \, dx","Int[(x*(2 + 3*x^2))/(3 + 5*x^2 + x^4)^(3/2),x]","\frac{11 x^2+8}{13 \sqrt{x^4+5 x^2+3}}","\frac{11 x^2+8}{13 \sqrt{x^4+5 x^2+3}}",1,"(8 + 11*x^2)/(13*Sqrt[3 + 5*x^2 + x^4])","A",2,2,23,0.08696,1,"{1247, 636}"
197,1,66,0,0.0570446,"\int \frac{2+3 x^2}{x \left(3+5 x^2+x^4\right)^{3/2}} \, dx","Int[(2 + 3*x^2)/(x*(3 + 5*x^2 + x^4)^(3/2)),x]","-\frac{8 x^2+7}{39 \sqrt{x^4+5 x^2+3}}-\frac{\tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{3 \sqrt{3}}","-\frac{8 x^2+7}{39 \sqrt{x^4+5 x^2+3}}-\frac{\tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{3 \sqrt{3}}",1,"-(7 + 8*x^2)/(39*Sqrt[3 + 5*x^2 + x^4]) - ArcTanh[(6 + 5*x^2)/(2*Sqrt[3]*Sqrt[3 + 5*x^2 + x^4])]/(3*Sqrt[3])","A",5,5,25,0.2000,1,"{1251, 822, 12, 724, 206}"
198,1,90,0,0.0707172,"\int \frac{2+3 x^2}{x^3 \left(3+5 x^2+x^4\right)^{3/2}} \, dx","Int[(2 + 3*x^2)/(x^3*(3 + 5*x^2 + x^4)^(3/2)),x]","-\frac{8 x^2+7}{39 x^2 \sqrt{x^4+5 x^2+3}}-\frac{2 \sqrt{x^4+5 x^2+3}}{39 x^2}+\frac{\tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{3 \sqrt{3}}","-\frac{8 x^2+7}{39 x^2 \sqrt{x^4+5 x^2+3}}-\frac{2 \sqrt{x^4+5 x^2+3}}{39 x^2}+\frac{\tanh ^{-1}\left(\frac{5 x^2+6}{2 \sqrt{3} \sqrt{x^4+5 x^2+3}}\right)}{3 \sqrt{3}}",1,"-(7 + 8*x^2)/(39*x^2*Sqrt[3 + 5*x^2 + x^4]) - (2*Sqrt[3 + 5*x^2 + x^4])/(39*x^2) + ArcTanh[(6 + 5*x^2)/(2*Sqrt[3]*Sqrt[3 + 5*x^2 + x^4])]/(3*Sqrt[3])","A",5,5,25,0.2000,1,"{1251, 822, 806, 724, 206}"
199,1,307,0,0.1632816,"\int \frac{x^4 \left(2+3 x^2\right)}{\left(3+5 x^2+x^4\right)^{3/2}} \, dx","Int[(x^4*(2 + 3*x^2))/(3 + 5*x^2 + x^4)^(3/2),x]","\frac{\left(11 x^2+8\right) x^3}{13 \sqrt{x^4+5 x^2+3}}-\frac{11}{13} \sqrt{x^4+5 x^2+3} x+\frac{43 \left(2 x^2+\sqrt{13}+5\right) x}{13 \sqrt{x^4+5 x^2+3}}+\frac{11 \sqrt{\frac{3}{2 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{13 \sqrt{x^4+5 x^2+3}}-\frac{43 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{13 \sqrt{x^4+5 x^2+3}}","\frac{\left(11 x^2+8\right) x^3}{13 \sqrt{x^4+5 x^2+3}}-\frac{11}{13} \sqrt{x^4+5 x^2+3} x+\frac{43 \left(2 x^2+\sqrt{13}+5\right) x}{13 \sqrt{x^4+5 x^2+3}}+\frac{11 \sqrt{\frac{3}{2 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{13 \sqrt{x^4+5 x^2+3}}-\frac{43 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{13 \sqrt{x^4+5 x^2+3}}",1,"(43*x*(5 + Sqrt[13] + 2*x^2))/(13*Sqrt[3 + 5*x^2 + x^4]) + (x^3*(8 + 11*x^2))/(13*Sqrt[3 + 5*x^2 + x^4]) - (11*x*Sqrt[3 + 5*x^2 + x^4])/13 - (43*Sqrt[(5 + Sqrt[13])/6]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(13*Sqrt[3 + 5*x^2 + x^4]) + (11*Sqrt[3/(2*(5 + Sqrt[13]))]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(13*Sqrt[3 + 5*x^2 + x^4])","A",5,5,25,0.2000,1,"{1275, 1279, 1189, 1099, 1135}"
200,1,286,0,0.1227317,"\int \frac{x^2 \left(2+3 x^2\right)}{\left(3+5 x^2+x^4\right)^{3/2}} \, dx","Int[(x^2*(2 + 3*x^2))/(3 + 5*x^2 + x^4)^(3/2),x]","-\frac{11 x \left(2 x^2+\sqrt{13}+5\right)}{26 \sqrt{x^4+5 x^2+3}}+\frac{x \left(11 x^2+8\right)}{13 \sqrt{x^4+5 x^2+3}}-\frac{4 \sqrt{\frac{2}{3 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{13 \sqrt{x^4+5 x^2+3}}+\frac{11 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{26 \sqrt{x^4+5 x^2+3}}","-\frac{11 x \left(2 x^2+\sqrt{13}+5\right)}{26 \sqrt{x^4+5 x^2+3}}+\frac{x \left(11 x^2+8\right)}{13 \sqrt{x^4+5 x^2+3}}-\frac{4 \sqrt{\frac{2}{3 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{13 \sqrt{x^4+5 x^2+3}}+\frac{11 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{26 \sqrt{x^4+5 x^2+3}}",1,"(-11*x*(5 + Sqrt[13] + 2*x^2))/(26*Sqrt[3 + 5*x^2 + x^4]) + (x*(8 + 11*x^2))/(13*Sqrt[3 + 5*x^2 + x^4]) + (11*Sqrt[(5 + Sqrt[13])/6]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(26*Sqrt[3 + 5*x^2 + x^4]) - (4*Sqrt[2/(3*(5 + Sqrt[13]))]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(13*Sqrt[3 + 5*x^2 + x^4])","A",4,4,25,0.1600,1,"{1275, 1189, 1099, 1135}"
201,1,282,0,0.1094336,"\int \frac{2+3 x^2}{\left(3+5 x^2+x^4\right)^{3/2}} \, dx","Int[(2 + 3*x^2)/(3 + 5*x^2 + x^4)^(3/2),x]","\frac{4 x \left(2 x^2+\sqrt{13}+5\right)}{39 \sqrt{x^4+5 x^2+3}}-\frac{x \left(8 x^2+7\right)}{39 \sqrt{x^4+5 x^2+3}}+\frac{11 \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{13 \sqrt{6 \left(5+\sqrt{13}\right)} \sqrt{x^4+5 x^2+3}}-\frac{2 \sqrt{\frac{2}{3} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{39 \sqrt{x^4+5 x^2+3}}","\frac{4 x \left(2 x^2+\sqrt{13}+5\right)}{39 \sqrt{x^4+5 x^2+3}}-\frac{x \left(8 x^2+7\right)}{39 \sqrt{x^4+5 x^2+3}}+\frac{11 \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{13 \sqrt{6 \left(5+\sqrt{13}\right)} \sqrt{x^4+5 x^2+3}}-\frac{2 \sqrt{\frac{2}{3} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{39 \sqrt{x^4+5 x^2+3}}",1,"(4*x*(5 + Sqrt[13] + 2*x^2))/(39*Sqrt[3 + 5*x^2 + x^4]) - (x*(7 + 8*x^2))/(39*Sqrt[3 + 5*x^2 + x^4]) - (2*Sqrt[(2*(5 + Sqrt[13]))/3]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(39*Sqrt[3 + 5*x^2 + x^4]) + (11*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(13*Sqrt[6*(5 + Sqrt[13])]*Sqrt[3 + 5*x^2 + x^4])","A",4,4,22,0.1818,1,"{1178, 1189, 1099, 1135}"
202,1,309,0,0.1635575,"\int \frac{2+3 x^2}{x^2 \left(3+5 x^2+x^4\right)^{3/2}} \, dx","Int[(2 + 3*x^2)/(x^2*(3 + 5*x^2 + x^4)^(3/2)),x]","\frac{19 x \left(2 x^2+\sqrt{13}+5\right)}{234 \sqrt{x^4+5 x^2+3}}-\frac{19 \sqrt{x^4+5 x^2+3}}{117 x}-\frac{8 x^2+7}{39 x \sqrt{x^4+5 x^2+3}}-\frac{4 \sqrt{\frac{2}{3 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{39 \sqrt{x^4+5 x^2+3}}-\frac{19 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{234 \sqrt{x^4+5 x^2+3}}","\frac{19 x \left(2 x^2+\sqrt{13}+5\right)}{234 \sqrt{x^4+5 x^2+3}}-\frac{19 \sqrt{x^4+5 x^2+3}}{117 x}-\frac{8 x^2+7}{39 x \sqrt{x^4+5 x^2+3}}-\frac{4 \sqrt{\frac{2}{3 \left(5+\sqrt{13}\right)}} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{39 \sqrt{x^4+5 x^2+3}}-\frac{19 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{234 \sqrt{x^4+5 x^2+3}}",1,"(19*x*(5 + Sqrt[13] + 2*x^2))/(234*Sqrt[3 + 5*x^2 + x^4]) - (7 + 8*x^2)/(39*x*Sqrt[3 + 5*x^2 + x^4]) - (19*Sqrt[3 + 5*x^2 + x^4])/(117*x) - (19*Sqrt[(5 + Sqrt[13])/6]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(234*Sqrt[3 + 5*x^2 + x^4]) - (4*Sqrt[2/(3*(5 + Sqrt[13]))]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(39*Sqrt[3 + 5*x^2 + x^4])","A",5,5,25,0.2000,1,"{1277, 1281, 1189, 1099, 1135}"
203,1,326,0,0.2058359,"\int \frac{2+3 x^2}{x^4 \left(3+5 x^2+x^4\right)^{3/2}} \, dx","Int[(2 + 3*x^2)/(x^4*(3 + 5*x^2 + x^4)^(3/2)),x]","-\frac{133 x \left(2 x^2+\sqrt{13}+5\right)}{1053 \sqrt{x^4+5 x^2+3}}+\frac{266 \sqrt{x^4+5 x^2+3}}{1053 x}-\frac{5 \sqrt{x^4+5 x^2+3}}{351 x^3}-\frac{8 x^2+7}{39 x^3 \sqrt{x^4+5 x^2+3}}-\frac{5 \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{351 \sqrt{6 \left(5+\sqrt{13}\right)} \sqrt{x^4+5 x^2+3}}+\frac{133 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{1053 \sqrt{x^4+5 x^2+3}}","-\frac{133 x \left(2 x^2+\sqrt{13}+5\right)}{1053 \sqrt{x^4+5 x^2+3}}+\frac{266 \sqrt{x^4+5 x^2+3}}{1053 x}-\frac{5 \sqrt{x^4+5 x^2+3}}{351 x^3}-\frac{8 x^2+7}{39 x^3 \sqrt{x^4+5 x^2+3}}-\frac{5 \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) F\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{351 \sqrt{6 \left(5+\sqrt{13}\right)} \sqrt{x^4+5 x^2+3}}+\frac{133 \sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} \sqrt{\frac{\left(5-\sqrt{13}\right) x^2+6}{\left(5+\sqrt{13}\right) x^2+6}} \left(\left(5+\sqrt{13}\right) x^2+6\right) E\left(\tan ^{-1}\left(\sqrt{\frac{1}{6} \left(5+\sqrt{13}\right)} x\right)|\frac{1}{6} \left(-13+5 \sqrt{13}\right)\right)}{1053 \sqrt{x^4+5 x^2+3}}",1,"(-133*x*(5 + Sqrt[13] + 2*x^2))/(1053*Sqrt[3 + 5*x^2 + x^4]) - (7 + 8*x^2)/(39*x^3*Sqrt[3 + 5*x^2 + x^4]) - (5*Sqrt[3 + 5*x^2 + x^4])/(351*x^3) + (266*Sqrt[3 + 5*x^2 + x^4])/(1053*x) + (133*Sqrt[(5 + Sqrt[13])/6]*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticE[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(1053*Sqrt[3 + 5*x^2 + x^4]) - (5*Sqrt[(6 + (5 - Sqrt[13])*x^2)/(6 + (5 + Sqrt[13])*x^2)]*(6 + (5 + Sqrt[13])*x^2)*EllipticF[ArcTan[Sqrt[(5 + Sqrt[13])/6]*x], (-13 + 5*Sqrt[13])/6])/(351*Sqrt[6*(5 + Sqrt[13])]*Sqrt[3 + 5*x^2 + x^4])","A",6,5,25,0.2000,1,"{1277, 1281, 1189, 1099, 1135}"
204,1,297,0,0.3853354,"\int (f x)^{3/2} \left(d+e x^2\right) \sqrt{a+b x^2+c x^4} \, dx","Int[(f*x)^(3/2)*(d + e*x^2)*Sqrt[a + b*x^2 + c*x^4],x]","\frac{2 d (f x)^{5/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{5}{4};-\frac{1}{2},-\frac{1}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 f \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}+\frac{2 e (f x)^{9/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{9}{4};-\frac{1}{2},-\frac{1}{2};\frac{13}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{9 f^3 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}","\frac{2 d (f x)^{5/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{5}{4};-\frac{1}{2},-\frac{1}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 f \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}+\frac{2 e (f x)^{9/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{9}{4};-\frac{1}{2},-\frac{1}{2};\frac{13}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{9 f^3 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}",1,"(2*d*(f*x)^(5/2)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[5/4, -1/2, -1/2, 9/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(5*f*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])]) + (2*e*(f*x)^(9/2)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[9/4, -1/2, -1/2, 13/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(9*f^3*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])","A",6,3,31,0.09677,1,"{1335, 1141, 510}"
205,1,297,0,0.322517,"\int \sqrt{f x} \left(d+e x^2\right) \sqrt{a+b x^2+c x^4} \, dx","Int[Sqrt[f*x]*(d + e*x^2)*Sqrt[a + b*x^2 + c*x^4],x]","\frac{2 d (f x)^{3/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{3}{4};-\frac{1}{2},-\frac{1}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 f \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}+\frac{2 e (f x)^{7/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{7}{4};-\frac{1}{2},-\frac{1}{2};\frac{11}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{7 f^3 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}","\frac{2 d (f x)^{3/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{3}{4};-\frac{1}{2},-\frac{1}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 f \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}+\frac{2 e (f x)^{7/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{7}{4};-\frac{1}{2},-\frac{1}{2};\frac{11}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{7 f^3 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}",1,"(2*d*(f*x)^(3/2)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[3/4, -1/2, -1/2, 7/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(3*f*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])]) + (2*e*(f*x)^(7/2)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[7/4, -1/2, -1/2, 11/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(7*f^3*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])","A",6,3,31,0.09677,1,"{1335, 1141, 510}"
206,1,295,0,0.321355,"\int \frac{\left(d+e x^2\right) \sqrt{a+b x^2+c x^4}}{\sqrt{f x}} \, dx","Int[((d + e*x^2)*Sqrt[a + b*x^2 + c*x^4])/Sqrt[f*x],x]","\frac{2 d \sqrt{f x} \sqrt{a+b x^2+c x^4} F_1\left(\frac{1}{4};-\frac{1}{2},-\frac{1}{2};\frac{5}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}+\frac{2 e (f x)^{5/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{5}{4};-\frac{1}{2},-\frac{1}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 f^3 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}","\frac{2 d \sqrt{f x} \sqrt{a+b x^2+c x^4} F_1\left(\frac{1}{4};-\frac{1}{2},-\frac{1}{2};\frac{5}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}+\frac{2 e (f x)^{5/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{5}{4};-\frac{1}{2},-\frac{1}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 f^3 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}",1,"(2*d*Sqrt[f*x]*Sqrt[a + b*x^2 + c*x^4]*AppellF1[1/4, -1/2, -1/2, 5/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(f*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])]) + (2*e*(f*x)^(5/2)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[5/4, -1/2, -1/2, 9/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(5*f^3*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])","A",6,3,31,0.09677,1,"{1335, 1141, 510}"
207,1,295,0,0.3173377,"\int \frac{\left(d+e x^2\right) \sqrt{a+b x^2+c x^4}}{(f x)^{3/2}} \, dx","Int[((d + e*x^2)*Sqrt[a + b*x^2 + c*x^4])/(f*x)^(3/2),x]","\frac{2 e (f x)^{3/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{3}{4};-\frac{1}{2},-\frac{1}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 f^3 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}-\frac{2 d \sqrt{a+b x^2+c x^4} F_1\left(-\frac{1}{4};-\frac{1}{2},-\frac{1}{2};\frac{3}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f \sqrt{f x} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}","\frac{2 e (f x)^{3/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{3}{4};-\frac{1}{2},-\frac{1}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 f^3 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}-\frac{2 d \sqrt{a+b x^2+c x^4} F_1\left(-\frac{1}{4};-\frac{1}{2},-\frac{1}{2};\frac{3}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f \sqrt{f x} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}",1,"(-2*d*Sqrt[a + b*x^2 + c*x^4]*AppellF1[-1/4, -1/2, -1/2, 3/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(f*Sqrt[f*x]*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]) + (2*e*(f*x)^(3/2)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[3/4, -1/2, -1/2, 7/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(3*f^3*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])","A",6,3,31,0.09677,1,"{1335, 1141, 510}"
208,1,299,0,0.347235,"\int (f x)^{3/2} \left(d+e x^2\right) \left(a+b x^2+c x^4\right)^{3/2} \, dx","Int[(f*x)^(3/2)*(d + e*x^2)*(a + b*x^2 + c*x^4)^(3/2),x]","\frac{2 a d (f x)^{5/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{5}{4};-\frac{3}{2},-\frac{3}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 f \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}+\frac{2 a e (f x)^{9/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{9}{4};-\frac{3}{2},-\frac{3}{2};\frac{13}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{9 f^3 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}","\frac{2 a d (f x)^{5/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{5}{4};-\frac{3}{2},-\frac{3}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 f \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}+\frac{2 a e (f x)^{9/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{9}{4};-\frac{3}{2},-\frac{3}{2};\frac{13}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{9 f^3 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}",1,"(2*a*d*(f*x)^(5/2)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[5/4, -3/2, -3/2, 9/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(5*f*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])]) + (2*a*e*(f*x)^(9/2)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[9/4, -3/2, -3/2, 13/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(9*f^3*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])","A",6,3,31,0.09677,1,"{1335, 1141, 510}"
209,1,299,0,0.3543682,"\int \sqrt{f x} \left(d+e x^2\right) \left(a+b x^2+c x^4\right)^{3/2} \, dx","Int[Sqrt[f*x]*(d + e*x^2)*(a + b*x^2 + c*x^4)^(3/2),x]","\frac{2 a d (f x)^{3/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{3}{4};-\frac{3}{2},-\frac{3}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 f \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}+\frac{2 a e (f x)^{7/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{7}{4};-\frac{3}{2},-\frac{3}{2};\frac{11}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{7 f^3 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}","\frac{2 a d (f x)^{3/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{3}{4};-\frac{3}{2},-\frac{3}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 f \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}+\frac{2 a e (f x)^{7/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{7}{4};-\frac{3}{2},-\frac{3}{2};\frac{11}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{7 f^3 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}",1,"(2*a*d*(f*x)^(3/2)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[3/4, -3/2, -3/2, 7/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(3*f*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])]) + (2*a*e*(f*x)^(7/2)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[7/4, -3/2, -3/2, 11/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(7*f^3*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])","A",6,3,31,0.09677,1,"{1335, 1141, 510}"
210,1,297,0,0.3510795,"\int \frac{\left(d+e x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{\sqrt{f x}} \, dx","Int[((d + e*x^2)*(a + b*x^2 + c*x^4)^(3/2))/Sqrt[f*x],x]","\frac{2 a d \sqrt{f x} \sqrt{a+b x^2+c x^4} F_1\left(\frac{1}{4};-\frac{3}{2},-\frac{3}{2};\frac{5}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}+\frac{2 a e (f x)^{5/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{5}{4};-\frac{3}{2},-\frac{3}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 f^3 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}","\frac{2 a d \sqrt{f x} \sqrt{a+b x^2+c x^4} F_1\left(\frac{1}{4};-\frac{3}{2},-\frac{3}{2};\frac{5}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}+\frac{2 a e (f x)^{5/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{5}{4};-\frac{3}{2},-\frac{3}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 f^3 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}",1,"(2*a*d*Sqrt[f*x]*Sqrt[a + b*x^2 + c*x^4]*AppellF1[1/4, -3/2, -3/2, 5/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(f*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])]) + (2*a*e*(f*x)^(5/2)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[5/4, -3/2, -3/2, 9/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(5*f^3*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])","A",6,3,31,0.09677,1,"{1335, 1141, 510}"
211,1,297,0,0.3479378,"\int \frac{\left(d+e x^2\right) \left(a+b x^2+c x^4\right)^{3/2}}{(f x)^{3/2}} \, dx","Int[((d + e*x^2)*(a + b*x^2 + c*x^4)^(3/2))/(f*x)^(3/2),x]","\frac{2 a e (f x)^{3/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{3}{4};-\frac{3}{2},-\frac{3}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 f^3 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}-\frac{2 a d \sqrt{a+b x^2+c x^4} F_1\left(-\frac{1}{4};-\frac{3}{2},-\frac{3}{2};\frac{3}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f \sqrt{f x} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}","\frac{2 a e (f x)^{3/2} \sqrt{a+b x^2+c x^4} F_1\left(\frac{3}{4};-\frac{3}{2},-\frac{3}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 f^3 \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}-\frac{2 a d \sqrt{a+b x^2+c x^4} F_1\left(-\frac{1}{4};-\frac{3}{2},-\frac{3}{2};\frac{3}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f \sqrt{f x} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}",1,"(-2*a*d*Sqrt[a + b*x^2 + c*x^4]*AppellF1[-1/4, -3/2, -3/2, 3/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(f*Sqrt[f*x]*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]) + (2*a*e*(f*x)^(3/2)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[3/4, -3/2, -3/2, 7/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(3*f^3*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])","A",6,3,31,0.09677,1,"{1335, 1141, 510}"
212,1,297,0,0.3281775,"\int \frac{(f x)^{3/2} \left(d+e x^2\right)}{\sqrt{a+b x^2+c x^4}} \, dx","Int[((f*x)^(3/2)*(d + e*x^2))/Sqrt[a + b*x^2 + c*x^4],x]","\frac{2 d (f x)^{5/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{5}{4};\frac{1}{2},\frac{1}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 f \sqrt{a+b x^2+c x^4}}+\frac{2 e (f x)^{9/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{9}{4};\frac{1}{2},\frac{1}{2};\frac{13}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{9 f^3 \sqrt{a+b x^2+c x^4}}","\frac{2 d (f x)^{5/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{5}{4};\frac{1}{2},\frac{1}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 f \sqrt{a+b x^2+c x^4}}+\frac{2 e (f x)^{9/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{9}{4};\frac{1}{2},\frac{1}{2};\frac{13}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{9 f^3 \sqrt{a+b x^2+c x^4}}",1,"(2*d*(f*x)^(5/2)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[5/4, 1/2, 1/2, 9/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(5*f*Sqrt[a + b*x^2 + c*x^4]) + (2*e*(f*x)^(9/2)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[9/4, 1/2, 1/2, 13/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(9*f^3*Sqrt[a + b*x^2 + c*x^4])","A",6,3,31,0.09677,1,"{1335, 1141, 510}"
213,1,297,0,0.3221149,"\int \frac{\sqrt{f x} \left(d+e x^2\right)}{\sqrt{a+b x^2+c x^4}} \, dx","Int[(Sqrt[f*x]*(d + e*x^2))/Sqrt[a + b*x^2 + c*x^4],x]","\frac{2 d (f x)^{3/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{3}{4};\frac{1}{2},\frac{1}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 f \sqrt{a+b x^2+c x^4}}+\frac{2 e (f x)^{7/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{7}{4};\frac{1}{2},\frac{1}{2};\frac{11}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{7 f^3 \sqrt{a+b x^2+c x^4}}","\frac{2 d (f x)^{3/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{3}{4};\frac{1}{2},\frac{1}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 f \sqrt{a+b x^2+c x^4}}+\frac{2 e (f x)^{7/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{7}{4};\frac{1}{2},\frac{1}{2};\frac{11}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{7 f^3 \sqrt{a+b x^2+c x^4}}",1,"(2*d*(f*x)^(3/2)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[3/4, 1/2, 1/2, 7/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(3*f*Sqrt[a + b*x^2 + c*x^4]) + (2*e*(f*x)^(7/2)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[7/4, 1/2, 1/2, 11/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(7*f^3*Sqrt[a + b*x^2 + c*x^4])","A",6,3,31,0.09677,1,"{1335, 1141, 510}"
214,1,295,0,0.3252687,"\int \frac{d+e x^2}{\sqrt{f x} \sqrt{a+b x^2+c x^4}} \, dx","Int[(d + e*x^2)/(Sqrt[f*x]*Sqrt[a + b*x^2 + c*x^4]),x]","\frac{2 d \sqrt{f x} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{1}{4};\frac{1}{2},\frac{1}{2};\frac{5}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f \sqrt{a+b x^2+c x^4}}+\frac{2 e (f x)^{5/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{5}{4};\frac{1}{2},\frac{1}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 f^3 \sqrt{a+b x^2+c x^4}}","\frac{2 d \sqrt{f x} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{1}{4};\frac{1}{2},\frac{1}{2};\frac{5}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f \sqrt{a+b x^2+c x^4}}+\frac{2 e (f x)^{5/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{5}{4};\frac{1}{2},\frac{1}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 f^3 \sqrt{a+b x^2+c x^4}}",1,"(2*d*Sqrt[f*x]*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[1/4, 1/2, 1/2, 5/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(f*Sqrt[a + b*x^2 + c*x^4]) + (2*e*(f*x)^(5/2)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[5/4, 1/2, 1/2, 9/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(5*f^3*Sqrt[a + b*x^2 + c*x^4])","A",6,3,31,0.09677,1,"{1335, 1141, 510}"
215,1,295,0,0.3248361,"\int \frac{d+e x^2}{(f x)^{3/2} \sqrt{a+b x^2+c x^4}} \, dx","Int[(d + e*x^2)/((f*x)^(3/2)*Sqrt[a + b*x^2 + c*x^4]),x]","\frac{2 e (f x)^{3/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{3}{4};\frac{1}{2},\frac{1}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 f^3 \sqrt{a+b x^2+c x^4}}-\frac{2 d \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{1}{4};\frac{1}{2},\frac{1}{2};\frac{3}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f \sqrt{f x} \sqrt{a+b x^2+c x^4}}","\frac{2 e (f x)^{3/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{3}{4};\frac{1}{2},\frac{1}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 f^3 \sqrt{a+b x^2+c x^4}}-\frac{2 d \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{1}{4};\frac{1}{2},\frac{1}{2};\frac{3}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f \sqrt{f x} \sqrt{a+b x^2+c x^4}}",1,"(-2*d*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[-1/4, 1/2, 1/2, 3/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(f*Sqrt[f*x]*Sqrt[a + b*x^2 + c*x^4]) + (2*e*(f*x)^(3/2)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[3/4, 1/2, 1/2, 7/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(3*f^3*Sqrt[a + b*x^2 + c*x^4])","A",6,3,31,0.09677,1,"{1335, 1141, 510}"
216,1,303,0,0.3441197,"\int \frac{(f x)^{3/2} \left(d+e x^2\right)}{\left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[((f*x)^(3/2)*(d + e*x^2))/(a + b*x^2 + c*x^4)^(3/2),x]","\frac{2 d (f x)^{5/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{5}{4};\frac{3}{2},\frac{3}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 a f \sqrt{a+b x^2+c x^4}}+\frac{2 e (f x)^{9/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{9}{4};\frac{3}{2},\frac{3}{2};\frac{13}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{9 a f^3 \sqrt{a+b x^2+c x^4}}","\frac{2 d (f x)^{5/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{5}{4};\frac{3}{2},\frac{3}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 a f \sqrt{a+b x^2+c x^4}}+\frac{2 e (f x)^{9/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{9}{4};\frac{3}{2},\frac{3}{2};\frac{13}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{9 a f^3 \sqrt{a+b x^2+c x^4}}",1,"(2*d*(f*x)^(5/2)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[5/4, 3/2, 3/2, 9/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(5*a*f*Sqrt[a + b*x^2 + c*x^4]) + (2*e*(f*x)^(9/2)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[9/4, 3/2, 3/2, 13/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(9*a*f^3*Sqrt[a + b*x^2 + c*x^4])","A",6,3,31,0.09677,1,"{1335, 1141, 510}"
217,1,303,0,0.3488419,"\int \frac{\sqrt{f x} \left(d+e x^2\right)}{\left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[(Sqrt[f*x]*(d + e*x^2))/(a + b*x^2 + c*x^4)^(3/2),x]","\frac{2 d (f x)^{3/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{3}{4};\frac{3}{2},\frac{3}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 a f \sqrt{a+b x^2+c x^4}}+\frac{2 e (f x)^{7/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{7}{4};\frac{3}{2},\frac{3}{2};\frac{11}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{7 a f^3 \sqrt{a+b x^2+c x^4}}","\frac{2 d (f x)^{3/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{3}{4};\frac{3}{2},\frac{3}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 a f \sqrt{a+b x^2+c x^4}}+\frac{2 e (f x)^{7/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{7}{4};\frac{3}{2},\frac{3}{2};\frac{11}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{7 a f^3 \sqrt{a+b x^2+c x^4}}",1,"(2*d*(f*x)^(3/2)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[3/4, 3/2, 3/2, 7/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(3*a*f*Sqrt[a + b*x^2 + c*x^4]) + (2*e*(f*x)^(7/2)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[7/4, 3/2, 3/2, 11/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(7*a*f^3*Sqrt[a + b*x^2 + c*x^4])","A",6,3,31,0.09677,1,"{1335, 1141, 510}"
218,1,301,0,0.3498146,"\int \frac{d+e x^2}{\sqrt{f x} \left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[(d + e*x^2)/(Sqrt[f*x]*(a + b*x^2 + c*x^4)^(3/2)),x]","\frac{2 d \sqrt{f x} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{1}{4};\frac{3}{2},\frac{3}{2};\frac{5}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{a f \sqrt{a+b x^2+c x^4}}+\frac{2 e (f x)^{5/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{5}{4};\frac{3}{2},\frac{3}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 a f^3 \sqrt{a+b x^2+c x^4}}","\frac{2 d \sqrt{f x} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{1}{4};\frac{3}{2},\frac{3}{2};\frac{5}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{a f \sqrt{a+b x^2+c x^4}}+\frac{2 e (f x)^{5/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{5}{4};\frac{3}{2},\frac{3}{2};\frac{9}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{5 a f^3 \sqrt{a+b x^2+c x^4}}",1,"(2*d*Sqrt[f*x]*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[1/4, 3/2, 3/2, 5/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(a*f*Sqrt[a + b*x^2 + c*x^4]) + (2*e*(f*x)^(5/2)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[5/4, 3/2, 3/2, 9/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(5*a*f^3*Sqrt[a + b*x^2 + c*x^4])","A",6,3,31,0.09677,1,"{1335, 1141, 510}"
219,1,301,0,0.3512305,"\int \frac{d+e x^2}{(f x)^{3/2} \left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[(d + e*x^2)/((f*x)^(3/2)*(a + b*x^2 + c*x^4)^(3/2)),x]","\frac{2 e (f x)^{3/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{3}{4};\frac{3}{2},\frac{3}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 a f^3 \sqrt{a+b x^2+c x^4}}-\frac{2 d \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{1}{4};\frac{3}{2},\frac{3}{2};\frac{3}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{a f \sqrt{f x} \sqrt{a+b x^2+c x^4}}","\frac{2 e (f x)^{3/2} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{3}{4};\frac{3}{2},\frac{3}{2};\frac{7}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{3 a f^3 \sqrt{a+b x^2+c x^4}}-\frac{2 d \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(-\frac{1}{4};\frac{3}{2},\frac{3}{2};\frac{3}{4};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{a f \sqrt{f x} \sqrt{a+b x^2+c x^4}}",1,"(-2*d*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[-1/4, 3/2, 3/2, 3/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(a*f*Sqrt[f*x]*Sqrt[a + b*x^2 + c*x^4]) + (2*e*(f*x)^(3/2)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[3/4, 3/2, 3/2, 7/4, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(3*a*f^3*Sqrt[a + b*x^2 + c*x^4])","A",6,3,31,0.09677,1,"{1335, 1141, 510}"
220,1,243,0,0.1761173,"\int (f x)^m \left(d+e x^2\right) \left(a+b x^2+c x^4\right)^3 \, dx","Int[(f*x)^m*(d + e*x^2)*(a + b*x^2 + c*x^4)^3,x]","\frac{(f x)^{m+7} \left(3 a^2 c e+3 a b^2 e+6 a b c d+b^3 d\right)}{f^7 (m+7)}+\frac{a^2 (f x)^{m+3} (a e+3 b d)}{f^3 (m+3)}+\frac{a^3 d (f x)^{m+1}}{f (m+1)}+\frac{(f x)^{m+9} \left(6 a b c e+3 a c^2 d+3 b^2 c d+b^3 e\right)}{f^9 (m+9)}+\frac{3 a (f x)^{m+5} \left(a b e+a c d+b^2 d\right)}{f^5 (m+5)}+\frac{3 c (f x)^{m+11} \left(a c e+b^2 e+b c d\right)}{f^{11} (m+11)}+\frac{c^2 (f x)^{m+13} (3 b e+c d)}{f^{13} (m+13)}+\frac{c^3 e (f x)^{m+15}}{f^{15} (m+15)}","\frac{(f x)^{m+7} \left(3 a^2 c e+3 a b^2 e+6 a b c d+b^3 d\right)}{f^7 (m+7)}+\frac{a^2 (f x)^{m+3} (a e+3 b d)}{f^3 (m+3)}+\frac{a^3 d (f x)^{m+1}}{f (m+1)}+\frac{(f x)^{m+9} \left(6 a b c e+3 a c^2 d+3 b^2 c d+b^3 e\right)}{f^9 (m+9)}+\frac{3 a (f x)^{m+5} \left(a b e+a c d+b^2 d\right)}{f^5 (m+5)}+\frac{3 c (f x)^{m+11} \left(a c e+b^2 e+b c d\right)}{f^{11} (m+11)}+\frac{c^2 (f x)^{m+13} (3 b e+c d)}{f^{13} (m+13)}+\frac{c^3 e (f x)^{m+15}}{f^{15} (m+15)}",1,"(a^3*d*(f*x)^(1 + m))/(f*(1 + m)) + (a^2*(3*b*d + a*e)*(f*x)^(3 + m))/(f^3*(3 + m)) + (3*a*(b^2*d + a*c*d + a*b*e)*(f*x)^(5 + m))/(f^5*(5 + m)) + ((b^3*d + 6*a*b*c*d + 3*a*b^2*e + 3*a^2*c*e)*(f*x)^(7 + m))/(f^7*(7 + m)) + ((3*b^2*c*d + 3*a*c^2*d + b^3*e + 6*a*b*c*e)*(f*x)^(9 + m))/(f^9*(9 + m)) + (3*c*(b*c*d + b^2*e + a*c*e)*(f*x)^(11 + m))/(f^11*(11 + m)) + (c^2*(c*d + 3*b*e)*(f*x)^(13 + m))/(f^13*(13 + m)) + (c^3*e*(f*x)^(15 + m))/(f^15*(15 + m))","A",2,1,27,0.03704,1,"{1261}"
221,1,155,0,0.0994351,"\int (f x)^m \left(d+e x^2\right) \left(a+b x^2+c x^4\right)^2 \, dx","Int[(f*x)^m*(d + e*x^2)*(a + b*x^2 + c*x^4)^2,x]","\frac{a^2 d (f x)^{m+1}}{f (m+1)}+\frac{(f x)^{m+5} \left(2 a b e+2 a c d+b^2 d\right)}{f^5 (m+5)}+\frac{(f x)^{m+7} \left(2 a c e+b^2 e+2 b c d\right)}{f^7 (m+7)}+\frac{a (f x)^{m+3} (a e+2 b d)}{f^3 (m+3)}+\frac{c (f x)^{m+9} (2 b e+c d)}{f^9 (m+9)}+\frac{c^2 e (f x)^{m+11}}{f^{11} (m+11)}","\frac{a^2 d (f x)^{m+1}}{f (m+1)}+\frac{(f x)^{m+5} \left(2 a b e+2 a c d+b^2 d\right)}{f^5 (m+5)}+\frac{(f x)^{m+7} \left(2 a c e+b^2 e+2 b c d\right)}{f^7 (m+7)}+\frac{a (f x)^{m+3} (a e+2 b d)}{f^3 (m+3)}+\frac{c (f x)^{m+9} (2 b e+c d)}{f^9 (m+9)}+\frac{c^2 e (f x)^{m+11}}{f^{11} (m+11)}",1,"(a^2*d*(f*x)^(1 + m))/(f*(1 + m)) + (a*(2*b*d + a*e)*(f*x)^(3 + m))/(f^3*(3 + m)) + ((b^2*d + 2*a*c*d + 2*a*b*e)*(f*x)^(5 + m))/(f^5*(5 + m)) + ((2*b*c*d + b^2*e + 2*a*c*e)*(f*x)^(7 + m))/(f^7*(7 + m)) + (c*(c*d + 2*b*e)*(f*x)^(9 + m))/(f^9*(9 + m)) + (c^2*e*(f*x)^(11 + m))/(f^11*(11 + m))","A",2,1,27,0.03704,1,"{1261}"
222,1,83,0,0.0474501,"\int (f x)^m \left(d+e x^2\right) \left(a+b x^2+c x^4\right) \, dx","Int[(f*x)^m*(d + e*x^2)*(a + b*x^2 + c*x^4),x]","\frac{(f x)^{m+3} (a e+b d)}{f^3 (m+3)}+\frac{a d (f x)^{m+1}}{f (m+1)}+\frac{(f x)^{m+5} (b e+c d)}{f^5 (m+5)}+\frac{c e (f x)^{m+7}}{f^7 (m+7)}","\frac{(f x)^{m+3} (a e+b d)}{f^3 (m+3)}+\frac{a d (f x)^{m+1}}{f (m+1)}+\frac{(f x)^{m+5} (b e+c d)}{f^5 (m+5)}+\frac{c e (f x)^{m+7}}{f^7 (m+7)}",1,"(a*d*(f*x)^(1 + m))/(f*(1 + m)) + ((b*d + a*e)*(f*x)^(3 + m))/(f^3*(3 + m)) + ((c*d + b*e)*(f*x)^(5 + m))/(f^5*(5 + m)) + (c*e*(f*x)^(7 + m))/(f^7*(7 + m))","A",2,1,25,0.04000,1,"{1261}"
223,1,194,0,0.2988593,"\int \frac{(f x)^m \left(d+e x^2\right)}{a+b x^2+c x^4} \, dx","Int[((f*x)^m*(d + e*x^2))/(a + b*x^2 + c*x^4),x]","\frac{(f x)^{m+1} \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}\right)}{f (m+1) \left(b-\sqrt{b^2-4 a c}\right)}+\frac{(f x)^{m+1} \left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f (m+1) \left(\sqrt{b^2-4 a c}+b\right)}","\frac{(f x)^{m+1} \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}\right)}{f (m+1) \left(b-\sqrt{b^2-4 a c}\right)}+\frac{(f x)^{m+1} \left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f (m+1) \left(\sqrt{b^2-4 a c}+b\right)}",1,"((e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*(f*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])])/((b - Sqrt[b^2 - 4*a*c])*f*(1 + m)) + ((e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*(f*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/((b + Sqrt[b^2 - 4*a*c])*f*(1 + m))","A",3,2,27,0.07407,1,"{1285, 364}"
224,1,358,0,2.6459999,"\int \frac{(f x)^m \left(d+e x^2\right)}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[((f*x)^m*(d + e*x^2))/(a + b*x^2 + c*x^4)^2,x]","\frac{c (f x)^{m+1} \left((1-m) \sqrt{b^2-4 a c} (b d-2 a e)+4 a b e-4 a c d (3-m)+b^2 (d-d m)\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}\right)}{2 a f (m+1) \left(b^2-4 a c\right)^{3/2} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{c (f x)^{m+1} \left(-(1-m) \sqrt{b^2-4 a c} (b d-2 a e)+4 a b e-4 a c d (3-m)+b^2 (d-d m)\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{2 a f (m+1) \left(b^2-4 a c\right)^{3/2} \left(\sqrt{b^2-4 a c}+b\right)}+\frac{(f x)^{m+1} \left(c x^2 (b d-2 a e)-a b e-2 a c d+b^2 d\right)}{2 a f \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}","\frac{c (f x)^{m+1} \left(b \left(d (1-m) \sqrt{b^2-4 a c}+4 a e\right)-2 a \left(e (1-m) \sqrt{b^2-4 a c}+2 c d (3-m)\right)+b^2 (d-d m)\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}\right)}{2 a f (m+1) \left(b^2-4 a c\right)^{3/2} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{c (f x)^{m+1} \left(b \left(4 a e-d (1-m) \sqrt{b^2-4 a c}\right)+2 a \left(e (1-m) \sqrt{b^2-4 a c}-2 c d (3-m)\right)+b^2 d (1-m)\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{2 a f (m+1) \left(b^2-4 a c\right)^{3/2} \left(\sqrt{b^2-4 a c}+b\right)}+\frac{(f x)^{m+1} \left(c x^2 (b d-2 a e)-a b e-2 a c d+b^2 d\right)}{2 a f \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}",1,"((f*x)^(1 + m)*(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)*f*(a + b*x^2 + c*x^4)) + (c*(4*a*b*e + Sqrt[b^2 - 4*a*c]*(b*d - 2*a*e)*(1 - m) - 4*a*c*d*(3 - m) + b^2*(d - d*m))*(f*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])])/(2*a*(b^2 - 4*a*c)^(3/2)*(b - Sqrt[b^2 - 4*a*c])*f*(1 + m)) - (c*(4*a*b*e - Sqrt[b^2 - 4*a*c]*(b*d - 2*a*e)*(1 - m) - 4*a*c*d*(3 - m) + b^2*(d - d*m))*(f*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(2*a*(b^2 - 4*a*c)^(3/2)*(b + Sqrt[b^2 - 4*a*c])*f*(1 + m))","A",4,3,27,0.1111,1,"{1277, 1285, 364}"
225,1,319,0,0.399319,"\int (f x)^m \left(d+e x^2\right) \left(a+b x^2+c x^4\right)^{3/2} \, dx","Int[(f*x)^m*(d + e*x^2)*(a + b*x^2 + c*x^4)^(3/2),x]","\frac{a d (f x)^{m+1} \sqrt{a+b x^2+c x^4} F_1\left(\frac{m+1}{2};-\frac{3}{2},-\frac{3}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f (m+1) \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}+\frac{a e (f x)^{m+3} \sqrt{a+b x^2+c x^4} F_1\left(\frac{m+3}{2};-\frac{3}{2},-\frac{3}{2};\frac{m+5}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f^3 (m+3) \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}","\frac{a d (f x)^{m+1} \sqrt{a+b x^2+c x^4} F_1\left(\frac{m+1}{2};-\frac{3}{2},-\frac{3}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f (m+1) \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}+\frac{a e (f x)^{m+3} \sqrt{a+b x^2+c x^4} F_1\left(\frac{m+3}{2};-\frac{3}{2},-\frac{3}{2};\frac{m+5}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f^3 (m+3) \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}",1,"(a*d*(f*x)^(1 + m)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[(1 + m)/2, -3/2, -3/2, (3 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(f*(1 + m)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]) + (a*e*(f*x)^(3 + m)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[(3 + m)/2, -3/2, -3/2, (5 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(f^3*(3 + m)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])","A",6,3,29,0.1034,1,"{1335, 1141, 510}"
226,1,317,0,0.3607759,"\int (f x)^m \left(d+e x^2\right) \sqrt{a+b x^2+c x^4} \, dx","Int[(f*x)^m*(d + e*x^2)*Sqrt[a + b*x^2 + c*x^4],x]","\frac{d (f x)^{m+1} \sqrt{a+b x^2+c x^4} F_1\left(\frac{m+1}{2};-\frac{1}{2},-\frac{1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f (m+1) \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}+\frac{e (f x)^{m+3} \sqrt{a+b x^2+c x^4} F_1\left(\frac{m+3}{2};-\frac{1}{2},-\frac{1}{2};\frac{m+5}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f^3 (m+3) \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}","\frac{d (f x)^{m+1} \sqrt{a+b x^2+c x^4} F_1\left(\frac{m+1}{2};-\frac{1}{2},-\frac{1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f (m+1) \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}+\frac{e (f x)^{m+3} \sqrt{a+b x^2+c x^4} F_1\left(\frac{m+3}{2};-\frac{1}{2},-\frac{1}{2};\frac{m+5}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f^3 (m+3) \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1}}",1,"(d*(f*x)^(1 + m)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[(1 + m)/2, -1/2, -1/2, (3 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(f*(1 + m)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]) + (e*(f*x)^(3 + m)*Sqrt[a + b*x^2 + c*x^4]*AppellF1[(3 + m)/2, -1/2, -1/2, (5 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(f^3*(3 + m)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])","A",6,3,29,0.1034,1,"{1335, 1141, 510}"
227,1,317,0,0.3524812,"\int \frac{(f x)^m \left(d+e x^2\right)}{\sqrt{a+b x^2+c x^4}} \, dx","Int[((f*x)^m*(d + e*x^2))/Sqrt[a + b*x^2 + c*x^4],x]","\frac{d (f x)^{m+1} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{m+1}{2};\frac{1}{2},\frac{1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f (m+1) \sqrt{a+b x^2+c x^4}}+\frac{e (f x)^{m+3} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{m+3}{2};\frac{1}{2},\frac{1}{2};\frac{m+5}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f^3 (m+3) \sqrt{a+b x^2+c x^4}}","\frac{d (f x)^{m+1} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{m+1}{2};\frac{1}{2},\frac{1}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f (m+1) \sqrt{a+b x^2+c x^4}}+\frac{e (f x)^{m+3} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{m+3}{2};\frac{1}{2},\frac{1}{2};\frac{m+5}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{f^3 (m+3) \sqrt{a+b x^2+c x^4}}",1,"(d*(f*x)^(1 + m)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[(1 + m)/2, 1/2, 1/2, (3 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(f*(1 + m)*Sqrt[a + b*x^2 + c*x^4]) + (e*(f*x)^(3 + m)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[(3 + m)/2, 1/2, 1/2, (5 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(f^3*(3 + m)*Sqrt[a + b*x^2 + c*x^4])","A",6,3,29,0.1034,1,"{1335, 1141, 510}"
228,1,323,0,0.3880581,"\int \frac{(f x)^m \left(d+e x^2\right)}{\left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[((f*x)^m*(d + e*x^2))/(a + b*x^2 + c*x^4)^(3/2),x]","\frac{d (f x)^{m+1} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{m+1}{2};\frac{3}{2},\frac{3}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{a f (m+1) \sqrt{a+b x^2+c x^4}}+\frac{e (f x)^{m+3} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{m+3}{2};\frac{3}{2},\frac{3}{2};\frac{m+5}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{a f^3 (m+3) \sqrt{a+b x^2+c x^4}}","\frac{d (f x)^{m+1} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{m+1}{2};\frac{3}{2},\frac{3}{2};\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{a f (m+1) \sqrt{a+b x^2+c x^4}}+\frac{e (f x)^{m+3} \sqrt{\frac{2 c x^2}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x^2}{\sqrt{b^2-4 a c}+b}+1} F_1\left(\frac{m+3}{2};\frac{3}{2},\frac{3}{2};\frac{m+5}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}}\right)}{a f^3 (m+3) \sqrt{a+b x^2+c x^4}}",1,"(d*(f*x)^(1 + m)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[(1 + m)/2, 3/2, 3/2, (3 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(a*f*(1 + m)*Sqrt[a + b*x^2 + c*x^4]) + (e*(f*x)^(3 + m)*Sqrt[1 + (2*c*x^2)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[(3 + m)/2, 3/2, 3/2, (5 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c])])/(a*f^3*(3 + m)*Sqrt[a + b*x^2 + c*x^4])","A",6,3,29,0.1034,1,"{1335, 1141, 510}"
229,1,134,0,0.1789271,"\int \frac{x^9}{\left(d+e x^2\right) \left(a+c x^4\right)} \, dx","Int[x^9/((d + e*x^2)*(a + c*x^4)),x]","-\frac{a^2 e \log \left(a+c x^4\right)}{4 c^2 \left(a e^2+c d^2\right)}+\frac{a^{3/2} d \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 c^{3/2} \left(a e^2+c d^2\right)}+\frac{d^4 \log \left(d+e x^2\right)}{2 e^3 \left(a e^2+c d^2\right)}-\frac{d x^2}{2 c e^2}+\frac{x^4}{4 c e}","-\frac{a^2 e \log \left(a+c x^4\right)}{4 c^2 \left(a e^2+c d^2\right)}+\frac{a^{3/2} d \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 c^{3/2} \left(a e^2+c d^2\right)}+\frac{d^4 \log \left(d+e x^2\right)}{2 e^3 \left(a e^2+c d^2\right)}-\frac{d x^2}{2 c e^2}+\frac{x^4}{4 c e}",1,"-(d*x^2)/(2*c*e^2) + x^4/(4*c*e) + (a^(3/2)*d*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*c^(3/2)*(c*d^2 + a*e^2)) + (d^4*Log[d + e*x^2])/(2*e^3*(c*d^2 + a*e^2)) - (a^2*e*Log[a + c*x^4])/(4*c^2*(c*d^2 + a*e^2))","A",6,5,22,0.2273,1,"{1252, 1629, 635, 205, 260}"
230,1,118,0,0.1519508,"\int \frac{x^7}{\left(d+e x^2\right) \left(a+c x^4\right)} \, dx","Int[x^7/((d + e*x^2)*(a + c*x^4)),x]","-\frac{a^{3/2} e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 c^{3/2} \left(a e^2+c d^2\right)}-\frac{d^3 \log \left(d+e x^2\right)}{2 e^2 \left(a e^2+c d^2\right)}-\frac{a d \log \left(a+c x^4\right)}{4 c \left(a e^2+c d^2\right)}+\frac{x^2}{2 c e}","-\frac{a^{3/2} e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 c^{3/2} \left(a e^2+c d^2\right)}-\frac{d^3 \log \left(d+e x^2\right)}{2 e^2 \left(a e^2+c d^2\right)}-\frac{a d \log \left(a+c x^4\right)}{4 c \left(a e^2+c d^2\right)}+\frac{x^2}{2 c e}",1,"x^2/(2*c*e) - (a^(3/2)*e*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*c^(3/2)*(c*d^2 + a*e^2)) - (d^3*Log[d + e*x^2])/(2*e^2*(c*d^2 + a*e^2)) - (a*d*Log[a + c*x^4])/(4*c*(c*d^2 + a*e^2))","A",6,5,22,0.2273,1,"{1252, 1629, 635, 205, 260}"
231,1,105,0,0.1367449,"\int \frac{x^5}{\left(d+e x^2\right) \left(a+c x^4\right)} \, dx","Int[x^5/((d + e*x^2)*(a + c*x^4)),x]","\frac{d^2 \log \left(d+e x^2\right)}{2 e \left(a e^2+c d^2\right)}+\frac{a e \log \left(a+c x^4\right)}{4 c \left(a e^2+c d^2\right)}-\frac{\sqrt{a} d \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 \sqrt{c} \left(a e^2+c d^2\right)}","\frac{d^2 \log \left(d+e x^2\right)}{2 e \left(a e^2+c d^2\right)}+\frac{a e \log \left(a+c x^4\right)}{4 c \left(a e^2+c d^2\right)}-\frac{\sqrt{a} d \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 \sqrt{c} \left(a e^2+c d^2\right)}",1,"-(Sqrt[a]*d*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*Sqrt[c]*(c*d^2 + a*e^2)) + (d^2*Log[d + e*x^2])/(2*e*(c*d^2 + a*e^2)) + (a*e*Log[a + c*x^4])/(4*c*(c*d^2 + a*e^2))","A",6,5,22,0.2273,1,"{1252, 1629, 635, 205, 260}"
232,1,96,0,0.0944008,"\int \frac{x^3}{\left(d+e x^2\right) \left(a+c x^4\right)} \, dx","Int[x^3/((d + e*x^2)*(a + c*x^4)),x]","-\frac{d \log \left(d+e x^2\right)}{2 \left(a e^2+c d^2\right)}+\frac{d \log \left(a+c x^4\right)}{4 \left(a e^2+c d^2\right)}+\frac{\sqrt{a} e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 \sqrt{c} \left(a e^2+c d^2\right)}","-\frac{d \log \left(d+e x^2\right)}{2 \left(a e^2+c d^2\right)}+\frac{d \log \left(a+c x^4\right)}{4 \left(a e^2+c d^2\right)}+\frac{\sqrt{a} e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 \sqrt{c} \left(a e^2+c d^2\right)}",1,"(Sqrt[a]*e*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*Sqrt[c]*(c*d^2 + a*e^2)) - (d*Log[d + e*x^2])/(2*(c*d^2 + a*e^2)) + (d*Log[a + c*x^4])/(4*(c*d^2 + a*e^2))","A",6,5,22,0.2273,1,"{1252, 801, 635, 205, 260}"
233,1,96,0,0.0636733,"\int \frac{x}{\left(d+e x^2\right) \left(a+c x^4\right)} \, dx","Int[x/((d + e*x^2)*(a + c*x^4)),x]","\frac{e \log \left(d+e x^2\right)}{2 \left(a e^2+c d^2\right)}-\frac{e \log \left(a+c x^4\right)}{4 \left(a e^2+c d^2\right)}+\frac{\sqrt{c} d \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \left(a e^2+c d^2\right)}","\frac{e \log \left(d+e x^2\right)}{2 \left(a e^2+c d^2\right)}-\frac{e \log \left(a+c x^4\right)}{4 \left(a e^2+c d^2\right)}+\frac{\sqrt{c} d \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \left(a e^2+c d^2\right)}",1,"(Sqrt[c]*d*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*Sqrt[a]*(c*d^2 + a*e^2)) + (e*Log[d + e*x^2])/(2*(c*d^2 + a*e^2)) - (e*Log[a + c*x^4])/(4*(c*d^2 + a*e^2))","A",6,6,20,0.3000,1,"{1248, 706, 31, 635, 205, 260}"
234,1,114,0,0.1249058,"\int \frac{1}{x \left(d+e x^2\right) \left(a+c x^4\right)} \, dx","Int[1/(x*(d + e*x^2)*(a + c*x^4)),x]","-\frac{e^2 \log \left(d+e x^2\right)}{2 d \left(a e^2+c d^2\right)}-\frac{c d \log \left(a+c x^4\right)}{4 a \left(a e^2+c d^2\right)}-\frac{\sqrt{c} e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \left(a e^2+c d^2\right)}+\frac{\log (x)}{a d}","-\frac{e^2 \log \left(d+e x^2\right)}{2 d \left(a e^2+c d^2\right)}-\frac{c d \log \left(a+c x^4\right)}{4 a \left(a e^2+c d^2\right)}-\frac{\sqrt{c} e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \left(a e^2+c d^2\right)}+\frac{\log (x)}{a d}",1,"-(Sqrt[c]*e*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*Sqrt[a]*(c*d^2 + a*e^2)) + Log[x]/(a*d) - (e^2*Log[d + e*x^2])/(2*d*(c*d^2 + a*e^2)) - (c*d*Log[a + c*x^4])/(4*a*(c*d^2 + a*e^2))","A",6,5,22,0.2273,1,"{1252, 894, 635, 205, 260}"
235,1,129,0,0.1497692,"\int \frac{1}{x^3 \left(d+e x^2\right) \left(a+c x^4\right)} \, dx","Int[1/(x^3*(d + e*x^2)*(a + c*x^4)),x]","-\frac{c^{3/2} d \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 a^{3/2} \left(a e^2+c d^2\right)}+\frac{e^3 \log \left(d+e x^2\right)}{2 d^2 \left(a e^2+c d^2\right)}+\frac{c e \log \left(a+c x^4\right)}{4 a \left(a e^2+c d^2\right)}-\frac{e \log (x)}{a d^2}-\frac{1}{2 a d x^2}","-\frac{c^{3/2} d \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 a^{3/2} \left(a e^2+c d^2\right)}+\frac{e^3 \log \left(d+e x^2\right)}{2 d^2 \left(a e^2+c d^2\right)}+\frac{c e \log \left(a+c x^4\right)}{4 a \left(a e^2+c d^2\right)}-\frac{e \log (x)}{a d^2}-\frac{1}{2 a d x^2}",1,"-1/(2*a*d*x^2) - (c^(3/2)*d*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*a^(3/2)*(c*d^2 + a*e^2)) - (e*Log[x])/(a*d^2) + (e^3*Log[d + e*x^2])/(2*d^2*(c*d^2 + a*e^2)) + (c*e*Log[a + c*x^4])/(4*a*(c*d^2 + a*e^2))","A",6,5,22,0.2273,1,"{1252, 894, 635, 205, 260}"
236,1,156,0,0.183466,"\int \frac{1}{x^5 \left(d+e x^2\right) \left(a+c x^4\right)} \, dx","Int[1/(x^5*(d + e*x^2)*(a + c*x^4)),x]","\frac{c^2 d \log \left(a+c x^4\right)}{4 a^2 \left(a e^2+c d^2\right)}+\frac{c^{3/2} e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 a^{3/2} \left(a e^2+c d^2\right)}-\frac{\log (x) \left(c d^2-a e^2\right)}{a^2 d^3}-\frac{e^4 \log \left(d+e x^2\right)}{2 d^3 \left(a e^2+c d^2\right)}+\frac{e}{2 a d^2 x^2}-\frac{1}{4 a d x^4}","\frac{c^2 d \log \left(a+c x^4\right)}{4 a^2 \left(a e^2+c d^2\right)}+\frac{c^{3/2} e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 a^{3/2} \left(a e^2+c d^2\right)}-\frac{\log (x) \left(c d^2-a e^2\right)}{a^2 d^3}-\frac{e^4 \log \left(d+e x^2\right)}{2 d^3 \left(a e^2+c d^2\right)}+\frac{e}{2 a d^2 x^2}-\frac{1}{4 a d x^4}",1,"-1/(4*a*d*x^4) + e/(2*a*d^2*x^2) + (c^(3/2)*e*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*a^(3/2)*(c*d^2 + a*e^2)) - ((c*d^2 - a*e^2)*Log[x])/(a^2*d^3) - (e^4*Log[d + e*x^2])/(2*d^3*(c*d^2 + a*e^2)) + (c^2*d*Log[a + c*x^4])/(4*a^2*(c*d^2 + a*e^2))","A",6,5,22,0.2273,1,"{1252, 894, 635, 205, 260}"
237,1,359,0,0.3458674,"\int \frac{x^8}{\left(d+e x^2\right) \left(a+c x^4\right)} \, dx","Int[x^8/((d + e*x^2)*(a + c*x^4)),x]","-\frac{a^{5/4} \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} c^{7/4} \left(a e^2+c d^2\right)}+\frac{a^{5/4} \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} c^{7/4} \left(a e^2+c d^2\right)}-\frac{a^{5/4} \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} c^{7/4} \left(a e^2+c d^2\right)}+\frac{a^{5/4} \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} c^{7/4} \left(a e^2+c d^2\right)}+\frac{d^{7/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{e^{5/2} \left(a e^2+c d^2\right)}-\frac{d x}{c e^2}+\frac{x^3}{3 c e}","-\frac{a^{5/4} \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} c^{7/4} \left(a e^2+c d^2\right)}+\frac{a^{5/4} \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} c^{7/4} \left(a e^2+c d^2\right)}-\frac{a^{5/4} \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} c^{7/4} \left(a e^2+c d^2\right)}+\frac{a^{5/4} \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} c^{7/4} \left(a e^2+c d^2\right)}+\frac{d^{7/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{e^{5/2} \left(a e^2+c d^2\right)}-\frac{d x}{c e^2}+\frac{x^3}{3 c e}",1,"-((d*x)/(c*e^2)) + x^3/(3*c*e) + (d^(7/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(e^(5/2)*(c*d^2 + a*e^2)) - (a^(5/4)*(Sqrt[c]*d - Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*c^(7/4)*(c*d^2 + a*e^2)) + (a^(5/4)*(Sqrt[c]*d - Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*c^(7/4)*(c*d^2 + a*e^2)) - (a^(5/4)*(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]*c^(7/4)*(c*d^2 + a*e^2)) + (a^(5/4)*(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]*c^(7/4)*(c*d^2 + a*e^2))","A",12,8,22,0.3636,1,"{1288, 205, 1168, 1162, 617, 204, 1165, 628}"
238,1,345,0,0.3021421,"\int \frac{x^6}{\left(d+e x^2\right) \left(a+c x^4\right)} \, dx","Int[x^6/((d + e*x^2)*(a + c*x^4)),x]","-\frac{a^{3/4} \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} c^{5/4} \left(a e^2+c d^2\right)}+\frac{a^{3/4} \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} c^{5/4} \left(a e^2+c d^2\right)}+\frac{a^{3/4} \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} c^{5/4} \left(a e^2+c d^2\right)}-\frac{a^{3/4} \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} c^{5/4} \left(a e^2+c d^2\right)}-\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{e^{3/2} \left(a e^2+c d^2\right)}+\frac{x}{c e}","-\frac{a^{3/4} \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} c^{5/4} \left(a e^2+c d^2\right)}+\frac{a^{3/4} \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} c^{5/4} \left(a e^2+c d^2\right)}+\frac{a^{3/4} \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} c^{5/4} \left(a e^2+c d^2\right)}-\frac{a^{3/4} \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} c^{5/4} \left(a e^2+c d^2\right)}-\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{e^{3/2} \left(a e^2+c d^2\right)}+\frac{x}{c e}",1,"x/(c*e) - (d^(5/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(e^(3/2)*(c*d^2 + a*e^2)) + (a^(3/4)*(Sqrt[c]*d + Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*c^(5/4)*(c*d^2 + a*e^2)) - (a^(3/4)*(Sqrt[c]*d + Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*c^(5/4)*(c*d^2 + a*e^2)) - (a^(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]*c^(5/4)*(c*d^2 + a*e^2)) + (a^(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]*c^(5/4)*(c*d^2 + a*e^2))","A",12,8,22,0.3636,1,"{1288, 205, 1168, 1162, 617, 204, 1165, 628}"
239,1,336,0,0.274359,"\int \frac{x^4}{\left(d+e x^2\right) \left(a+c x^4\right)} \, dx","Int[x^4/((d + e*x^2)*(a + c*x^4)),x]","\frac{\sqrt[4]{a} \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} c^{3/4} \left(a e^2+c d^2\right)}-\frac{\sqrt[4]{a} \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} c^{3/4} \left(a e^2+c d^2\right)}+\frac{\sqrt[4]{a} \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} c^{3/4} \left(a e^2+c d^2\right)}-\frac{\sqrt[4]{a} \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} c^{3/4} \left(a e^2+c d^2\right)}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e} \left(a e^2+c d^2\right)}","\frac{\sqrt[4]{a} \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} c^{3/4} \left(a e^2+c d^2\right)}-\frac{\sqrt[4]{a} \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} c^{3/4} \left(a e^2+c d^2\right)}+\frac{\sqrt[4]{a} \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} c^{3/4} \left(a e^2+c d^2\right)}-\frac{\sqrt[4]{a} \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} c^{3/4} \left(a e^2+c d^2\right)}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e} \left(a e^2+c d^2\right)}",1,"(d^(3/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[e]*(c*d^2 + a*e^2)) + (a^(1/4)*(Sqrt[c]*d - Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*c^(3/4)*(c*d^2 + a*e^2)) - (a^(1/4)*(Sqrt[c]*d - Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*c^(3/4)*(c*d^2 + a*e^2)) + (a^(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]*c^(3/4)*(c*d^2 + a*e^2)) - (a^(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]*c^(3/4)*(c*d^2 + a*e^2))","A",12,8,22,0.3636,1,"{1288, 205, 1168, 1162, 617, 204, 1165, 628}"
240,1,337,0,0.2671392,"\int \frac{x^2}{\left(d+e x^2\right) \left(a+c x^4\right)} \, dx","Int[x^2/((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} \sqrt[4]{a} \sqrt[4]{c} \left(a e^2+c d^2\right)}-\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} \sqrt[4]{a} \sqrt[4]{c} \left(a e^2+c d^2\right)}-\frac{\sqrt{d} \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{a e^2+c d^2}-\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} \sqrt[4]{a} \sqrt[4]{c} \left(a e^2+c d^2\right)}+\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} \sqrt[4]{a} \sqrt[4]{c} \left(a e^2+c d^2\right)}","\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} \sqrt[4]{a} \sqrt[4]{c} \left(a e^2+c d^2\right)}-\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} \sqrt[4]{a} \sqrt[4]{c} \left(a e^2+c d^2\right)}-\frac{\sqrt{d} \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{a e^2+c d^2}-\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} \sqrt[4]{a} \sqrt[4]{c} \left(a e^2+c d^2\right)}+\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} \sqrt[4]{a} \sqrt[4]{c} \left(a e^2+c d^2\right)}",1,"-((Sqrt[d]*Sqrt[e]*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(c*d^2 + a*e^2)) - ((Sqrt[c]*d + Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(1/4)*c^(1/4)*(c*d^2 + a*e^2)) + ((Sqrt[c]*d + Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(1/4)*c^(1/4)*(c*d^2 + a*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^(1/4)*c^(1/4)*(c*d^2 + a*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^(1/4)*c^(1/4)*(c*d^2 + a*e^2))","A",12,8,22,0.3636,1,"{1288, 205, 1168, 1162, 617, 204, 1165, 628}"
241,1,336,0,0.2729334,"\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}"
242,1,348,0,0.2995379,"\int \frac{1}{x^2 \left(d+e x^2\right) \left(a+c x^4\right)} \, dx","Int[1/(x^2*(d + e*x^2)*(a + c*x^4)),x]","-\frac{c^{3/4} \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^{5/4} \left(a e^2+c d^2\right)}+\frac{c^{3/4} \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^{5/4} \left(a e^2+c d^2\right)}+\frac{c^{3/4} \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^{5/4} \left(a e^2+c d^2\right)}-\frac{c^{3/4} \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^{5/4} \left(a e^2+c d^2\right)}-\frac{e^{5/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{d^{3/2} \left(a e^2+c d^2\right)}-\frac{1}{a d x}","-\frac{c^{3/4} \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^{5/4} \left(a e^2+c d^2\right)}+\frac{c^{3/4} \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^{5/4} \left(a e^2+c d^2\right)}+\frac{c^{3/4} \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^{5/4} \left(a e^2+c d^2\right)}-\frac{c^{3/4} \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^{5/4} \left(a e^2+c d^2\right)}-\frac{e^{5/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{d^{3/2} \left(a e^2+c d^2\right)}-\frac{1}{a d x}",1,"-(1/(a*d*x)) - (e^(5/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(d^(3/2)*(c*d^2 + a*e^2)) + (c^(3/4)*(Sqrt[c]*d + Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(5/4)*(c*d^2 + a*e^2)) - (c^(3/4)*(Sqrt[c]*d + Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(5/4)*(c*d^2 + a*e^2)) - (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^(5/4)*(c*d^2 + a*e^2)) + (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^(5/4)*(c*d^2 + a*e^2))","A",12,8,22,0.3636,1,"{1288, 205, 1168, 1162, 617, 204, 1165, 628}"
243,1,360,0,0.3009987,"\int \frac{1}{x^4 \left(d+e x^2\right) \left(a+c x^4\right)} \, dx","Int[1/(x^4*(d + e*x^2)*(a + c*x^4)),x]","\frac{c^{5/4} \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^{7/4} \left(a e^2+c d^2\right)}-\frac{c^{5/4} \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^{7/4} \left(a e^2+c d^2\right)}+\frac{c^{5/4} \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^{7/4} \left(a e^2+c d^2\right)}-\frac{c^{5/4} \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^{7/4} \left(a e^2+c d^2\right)}+\frac{e^{7/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{d^{5/2} \left(a e^2+c d^2\right)}+\frac{e}{a d^2 x}-\frac{1}{3 a d x^3}","\frac{c^{5/4} \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^{7/4} \left(a e^2+c d^2\right)}-\frac{c^{5/4} \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^{7/4} \left(a e^2+c d^2\right)}+\frac{c^{5/4} \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^{7/4} \left(a e^2+c d^2\right)}-\frac{c^{5/4} \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^{7/4} \left(a e^2+c d^2\right)}+\frac{e^{7/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{d^{5/2} \left(a e^2+c d^2\right)}+\frac{e}{a d^2 x}-\frac{1}{3 a d x^3}",1,"-1/(3*a*d*x^3) + e/(a*d^2*x) + (e^(7/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(d^(5/2)*(c*d^2 + a*e^2)) + (c^(5/4)*(Sqrt[c]*d - Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(7/4)*(c*d^2 + a*e^2)) - (c^(5/4)*(Sqrt[c]*d - Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(7/4)*(c*d^2 + a*e^2)) + (c^(5/4)*(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^(7/4)*(c*d^2 + a*e^2)) - (c^(5/4)*(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^(7/4)*(c*d^2 + a*e^2))","A",12,8,22,0.3636,1,"{1288, 205, 1168, 1162, 617, 204, 1165, 628}"
244,1,169,0,0.3667268,"\int \frac{x^9}{\left(d+e x^2\right) \left(a+c x^4\right)^2} \, dx","Int[x^9/((d + e*x^2)*(a + c*x^4)^2),x]","\frac{a \left(a e+c d x^2\right)}{4 c^2 \left(a+c x^4\right) \left(a e^2+c d^2\right)}+\frac{a e \left(a e^2+2 c d^2\right) \log \left(a+c x^4\right)}{4 c^2 \left(a e^2+c d^2\right)^2}-\frac{\sqrt{a} d \left(a e^2+3 c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 c^{3/2} \left(a e^2+c d^2\right)^2}+\frac{d^4 \log \left(d+e x^2\right)}{2 e \left(a e^2+c d^2\right)^2}","\frac{a \left(a e+c d x^2\right)}{4 c^2 \left(a+c x^4\right) \left(a e^2+c d^2\right)}+\frac{a e \left(a e^2+2 c d^2\right) \log \left(a+c x^4\right)}{4 c^2 \left(a e^2+c d^2\right)^2}-\frac{\sqrt{a} d \left(a e^2+3 c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 c^{3/2} \left(a e^2+c d^2\right)^2}+\frac{d^4 \log \left(d+e x^2\right)}{2 e \left(a e^2+c d^2\right)^2}",1,"(a*(a*e + c*d*x^2))/(4*c^2*(c*d^2 + a*e^2)*(a + c*x^4)) - (Sqrt[a]*d*(3*c*d^2 + a*e^2)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(4*c^(3/2)*(c*d^2 + a*e^2)^2) + (d^4*Log[d + e*x^2])/(2*e*(c*d^2 + a*e^2)^2) + (a*e*(2*c*d^2 + a*e^2)*Log[a + c*x^4])/(4*c^2*(c*d^2 + a*e^2)^2)","A",7,6,22,0.2727,1,"{1252, 1647, 1629, 635, 205, 260}"
245,1,150,0,0.2466748,"\int \frac{x^7}{\left(d+e x^2\right) \left(a+c x^4\right)^2} \, dx","Int[x^7/((d + e*x^2)*(a + c*x^4)^2),x]","\frac{\sqrt{a} e \left(a e^2+3 c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 c^{3/2} \left(a e^2+c d^2\right)^2}+\frac{a \left(d-e x^2\right)}{4 c \left(a+c x^4\right) \left(a e^2+c d^2\right)}-\frac{d^3 \log \left(d+e x^2\right)}{2 \left(a e^2+c d^2\right)^2}+\frac{d^3 \log \left(a+c x^4\right)}{4 \left(a e^2+c d^2\right)^2}","\frac{\sqrt{a} e \left(a e^2+3 c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 c^{3/2} \left(a e^2+c d^2\right)^2}+\frac{a \left(d-e x^2\right)}{4 c \left(a+c x^4\right) \left(a e^2+c d^2\right)}-\frac{d^3 \log \left(d+e x^2\right)}{2 \left(a e^2+c d^2\right)^2}+\frac{d^3 \log \left(a+c x^4\right)}{4 \left(a e^2+c d^2\right)^2}",1,"(a*(d - e*x^2))/(4*c*(c*d^2 + a*e^2)*(a + c*x^4)) + (Sqrt[a]*e*(3*c*d^2 + a*e^2)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(4*c^(3/2)*(c*d^2 + a*e^2)^2) - (d^3*Log[d + e*x^2])/(2*(c*d^2 + a*e^2)^2) + (d^3*Log[a + c*x^4])/(4*(c*d^2 + a*e^2)^2)","A",7,6,22,0.2727,1,"{1252, 1647, 801, 635, 205, 260}"
246,1,153,0,0.2476456,"\int \frac{x^5}{\left(d+e x^2\right) \left(a+c x^4\right)^2} \, dx","Int[x^5/((d + e*x^2)*(a + c*x^4)^2),x]","-\frac{a e+c d x^2}{4 c \left(a+c x^4\right) \left(a e^2+c d^2\right)}+\frac{d^2 e \log \left(d+e x^2\right)}{2 \left(a e^2+c d^2\right)^2}-\frac{d^2 e \log \left(a+c x^4\right)}{4 \left(a e^2+c d^2\right)^2}+\frac{d \left(c d^2-a e^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 \sqrt{a} \sqrt{c} \left(a e^2+c d^2\right)^2}","-\frac{a e+c d x^2}{4 c \left(a+c x^4\right) \left(a e^2+c d^2\right)}+\frac{d^2 e \log \left(d+e x^2\right)}{2 \left(a e^2+c d^2\right)^2}-\frac{d^2 e \log \left(a+c x^4\right)}{4 \left(a e^2+c d^2\right)^2}+\frac{d \left(c d^2-a e^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 \sqrt{a} \sqrt{c} \left(a e^2+c d^2\right)^2}",1,"-(a*e + c*d*x^2)/(4*c*(c*d^2 + a*e^2)*(a + c*x^4)) + (d*(c*d^2 - a*e^2)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(4*Sqrt[a]*Sqrt[c]*(c*d^2 + a*e^2)^2) + (d^2*e*Log[d + e*x^2])/(2*(c*d^2 + a*e^2)^2) - (d^2*e*Log[a + c*x^4])/(4*(c*d^2 + a*e^2)^2)","A",7,6,22,0.2727,1,"{1252, 1647, 801, 635, 205, 260}"
247,1,148,0,0.1868617,"\int \frac{x^3}{\left(d+e x^2\right) \left(a+c x^4\right)^2} \, dx","Int[x^3/((d + e*x^2)*(a + c*x^4)^2),x]","-\frac{d-e x^2}{4 \left(a+c x^4\right) \left(a e^2+c d^2\right)}-\frac{d e^2 \log \left(d+e x^2\right)}{2 \left(a e^2+c d^2\right)^2}+\frac{d e^2 \log \left(a+c x^4\right)}{4 \left(a e^2+c d^2\right)^2}-\frac{e \left(c d^2-a e^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 \sqrt{a} \sqrt{c} \left(a e^2+c d^2\right)^2}","-\frac{d-e x^2}{4 \left(a+c x^4\right) \left(a e^2+c d^2\right)}-\frac{d e^2 \log \left(d+e x^2\right)}{2 \left(a e^2+c d^2\right)^2}+\frac{d e^2 \log \left(a+c x^4\right)}{4 \left(a e^2+c d^2\right)^2}-\frac{e \left(c d^2-a e^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 \sqrt{a} \sqrt{c} \left(a e^2+c d^2\right)^2}",1,"-(d - e*x^2)/(4*(c*d^2 + a*e^2)*(a + c*x^4)) - (e*(c*d^2 - a*e^2)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(4*Sqrt[a]*Sqrt[c]*(c*d^2 + a*e^2)^2) - (d*e^2*Log[d + e*x^2])/(2*(c*d^2 + a*e^2)^2) + (d*e^2*Log[a + c*x^4])/(4*(c*d^2 + a*e^2)^2)","A",7,6,22,0.2727,1,"{1252, 823, 801, 635, 205, 260}"
248,1,151,0,0.1806377,"\int \frac{x}{\left(d+e x^2\right) \left(a+c x^4\right)^2} \, dx","Int[x/((d + e*x^2)*(a + c*x^4)^2),x]","\frac{\sqrt{c} d \left(3 a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \left(a e^2+c d^2\right)^2}+\frac{a e+c d x^2}{4 a \left(a+c x^4\right) \left(a e^2+c d^2\right)}+\frac{e^3 \log \left(d+e x^2\right)}{2 \left(a e^2+c d^2\right)^2}-\frac{e^3 \log \left(a+c x^4\right)}{4 \left(a e^2+c d^2\right)^2}","\frac{\sqrt{c} d \left(3 a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \left(a e^2+c d^2\right)^2}+\frac{a e+c d x^2}{4 a \left(a+c x^4\right) \left(a e^2+c d^2\right)}+\frac{e^3 \log \left(d+e x^2\right)}{2 \left(a e^2+c d^2\right)^2}-\frac{e^3 \log \left(a+c x^4\right)}{4 \left(a e^2+c d^2\right)^2}",1,"(a*e + c*d*x^2)/(4*a*(c*d^2 + a*e^2)*(a + c*x^4)) + (Sqrt[c]*d*(c*d^2 + 3*a*e^2)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(4*a^(3/2)*(c*d^2 + a*e^2)^2) + (e^3*Log[d + e*x^2])/(2*(c*d^2 + a*e^2)^2) - (e^3*Log[a + c*x^4])/(4*(c*d^2 + a*e^2)^2)","A",7,6,20,0.3000,1,"{1248, 741, 801, 635, 205, 260}"
249,1,209,0,0.239187,"\int \frac{1}{x \left(d+e x^2\right) \left(a+c x^4\right)^2} \, dx","Int[1/(x*(d + e*x^2)*(a + c*x^4)^2),x]","-\frac{c d \left(2 a e^2+c d^2\right) \log \left(a+c x^4\right)}{4 a^2 \left(a e^2+c d^2\right)^2}-\frac{\sqrt{c} e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \left(a e^2+c d^2\right)}+\frac{\log (x)}{a^2 d}+\frac{c \left(d-e x^2\right)}{4 a \left(a+c x^4\right) \left(a e^2+c d^2\right)}-\frac{e^4 \log \left(d+e x^2\right)}{2 d \left(a e^2+c d^2\right)^2}-\frac{\sqrt{c} e^3 \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \left(a e^2+c d^2\right)^2}","-\frac{c d \left(2 a e^2+c d^2\right) \log \left(a+c x^4\right)}{4 a^2 \left(a e^2+c d^2\right)^2}-\frac{\sqrt{c} e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 a^{3/2} \left(a e^2+c d^2\right)}+\frac{\log (x)}{a^2 d}+\frac{c \left(d-e x^2\right)}{4 a \left(a+c x^4\right) \left(a e^2+c d^2\right)}-\frac{e^4 \log \left(d+e x^2\right)}{2 d \left(a e^2+c d^2\right)^2}-\frac{\sqrt{c} e^3 \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} \left(a e^2+c d^2\right)^2}",1,"(c*(d - e*x^2))/(4*a*(c*d^2 + a*e^2)*(a + c*x^4)) - (Sqrt[c]*e^3*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*Sqrt[a]*(c*d^2 + a*e^2)^2) - (Sqrt[c]*e*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(4*a^(3/2)*(c*d^2 + a*e^2)) + Log[x]/(a^2*d) - (e^4*Log[d + e*x^2])/(2*d*(c*d^2 + a*e^2)^2) - (c*d*(c*d^2 + 2*a*e^2)*Log[a + c*x^4])/(4*a^2*(c*d^2 + a*e^2)^2)","A",8,6,22,0.2727,1,"{1252, 894, 639, 205, 635, 260}"
250,1,236,0,0.2610943,"\int \frac{1}{x^3 \left(d+e x^2\right) \left(a+c x^4\right)^2} \, dx","Int[1/(x^3*(d + e*x^2)*(a + c*x^4)^2),x]","-\frac{c^{3/2} d \left(2 a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 a^{5/2} \left(a e^2+c d^2\right)^2}-\frac{c^{3/2} d \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 a^{5/2} \left(a e^2+c d^2\right)}-\frac{c \left(a e+c d x^2\right)}{4 a^2 \left(a+c x^4\right) \left(a e^2+c d^2\right)}+\frac{c e \left(2 a e^2+c d^2\right) \log \left(a+c x^4\right)}{4 a^2 \left(a e^2+c d^2\right)^2}-\frac{e \log (x)}{a^2 d^2}-\frac{1}{2 a^2 d x^2}+\frac{e^5 \log \left(d+e x^2\right)}{2 d^2 \left(a e^2+c d^2\right)^2}","-\frac{c^{3/2} d \left(2 a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 a^{5/2} \left(a e^2+c d^2\right)^2}-\frac{c^{3/2} d \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 a^{5/2} \left(a e^2+c d^2\right)}-\frac{c \left(a e+c d x^2\right)}{4 a^2 \left(a+c x^4\right) \left(a e^2+c d^2\right)}+\frac{c e \left(2 a e^2+c d^2\right) \log \left(a+c x^4\right)}{4 a^2 \left(a e^2+c d^2\right)^2}-\frac{e \log (x)}{a^2 d^2}-\frac{1}{2 a^2 d x^2}+\frac{e^5 \log \left(d+e x^2\right)}{2 d^2 \left(a e^2+c d^2\right)^2}",1,"-1/(2*a^2*d*x^2) - (c*(a*e + c*d*x^2))/(4*a^2*(c*d^2 + a*e^2)*(a + c*x^4)) - (c^(3/2)*d*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(4*a^(5/2)*(c*d^2 + a*e^2)) - (c^(3/2)*d*(c*d^2 + 2*a*e^2)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*a^(5/2)*(c*d^2 + a*e^2)^2) - (e*Log[x])/(a^2*d^2) + (e^5*Log[d + e*x^2])/(2*d^2*(c*d^2 + a*e^2)^2) + (c*e*(c*d^2 + 2*a*e^2)*Log[a + c*x^4])/(4*a^2*(c*d^2 + a*e^2)^2)","A",8,6,22,0.2727,1,"{1252, 894, 639, 205, 635, 260}"
251,1,265,0,0.3268111,"\int \frac{1}{x^5 \left(d+e x^2\right) \left(a+c x^4\right)^2} \, dx","Int[1/(x^5*(d + e*x^2)*(a + c*x^4)^2),x]","-\frac{c^2 \left(d-e x^2\right)}{4 a^2 \left(a+c x^4\right) \left(a e^2+c d^2\right)}+\frac{c^2 d \left(3 a e^2+2 c d^2\right) \log \left(a+c x^4\right)}{4 a^3 \left(a e^2+c d^2\right)^2}+\frac{c^{3/2} e \left(2 a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 a^{5/2} \left(a e^2+c d^2\right)^2}+\frac{c^{3/2} e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 a^{5/2} \left(a e^2+c d^2\right)}-\frac{\log (x) \left(2 c d^2-a e^2\right)}{a^3 d^3}+\frac{e}{2 a^2 d^2 x^2}-\frac{1}{4 a^2 d x^4}-\frac{e^6 \log \left(d+e x^2\right)}{2 d^3 \left(a e^2+c d^2\right)^2}","-\frac{c^2 \left(d-e x^2\right)}{4 a^2 \left(a+c x^4\right) \left(a e^2+c d^2\right)}+\frac{c^2 d \left(3 a e^2+2 c d^2\right) \log \left(a+c x^4\right)}{4 a^3 \left(a e^2+c d^2\right)^2}+\frac{c^{3/2} e \left(2 a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{2 a^{5/2} \left(a e^2+c d^2\right)^2}+\frac{c^{3/2} e \tan ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a}}\right)}{4 a^{5/2} \left(a e^2+c d^2\right)}-\frac{\log (x) \left(2 c d^2-a e^2\right)}{a^3 d^3}+\frac{e}{2 a^2 d^2 x^2}-\frac{1}{4 a^2 d x^4}-\frac{e^6 \log \left(d+e x^2\right)}{2 d^3 \left(a e^2+c d^2\right)^2}",1,"-1/(4*a^2*d*x^4) + e/(2*a^2*d^2*x^2) - (c^2*(d - e*x^2))/(4*a^2*(c*d^2 + a*e^2)*(a + c*x^4)) + (c^(3/2)*e*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(4*a^(5/2)*(c*d^2 + a*e^2)) + (c^(3/2)*e*(c*d^2 + 2*a*e^2)*ArcTan[(Sqrt[c]*x^2)/Sqrt[a]])/(2*a^(5/2)*(c*d^2 + a*e^2)^2) - ((2*c*d^2 - a*e^2)*Log[x])/(a^3*d^3) - (e^6*Log[d + e*x^2])/(2*d^3*(c*d^2 + a*e^2)^2) + (c^2*d*(2*c*d^2 + 3*a*e^2)*Log[a + c*x^4])/(4*a^3*(c*d^2 + a*e^2)^2)","A",8,6,22,0.2727,1,"{1252, 894, 639, 205, 635, 260}"
252,1,712,0,0.6706926,"\int \frac{x^8}{\left(d+e x^2\right) \left(a+c x^4\right)^2} \, dx","Int[x^8/((d + e*x^2)*(a + c*x^4)^2),x]","\frac{\sqrt[4]{a} d^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} c^{3/4} \left(a e^2+c d^2\right)^2}-\frac{\sqrt[4]{a} d^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} c^{3/4} \left(a e^2+c d^2\right)^2}+\frac{\sqrt[4]{a} \left(3 \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)}{16 \sqrt{2} c^{7/4} \left(a e^2+c d^2\right)}-\frac{\sqrt[4]{a} \left(3 \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)}{16 \sqrt{2} c^{7/4} \left(a e^2+c d^2\right)}+\frac{\sqrt[4]{a} d^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} c^{3/4} \left(a e^2+c d^2\right)^2}-\frac{\sqrt[4]{a} d^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} c^{3/4} \left(a e^2+c d^2\right)^2}+\frac{\sqrt[4]{a} \left(\sqrt{c} d-3 \sqrt{a} e\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} c^{7/4} \left(a e^2+c d^2\right)}-\frac{\sqrt[4]{a} \left(\sqrt{c} d-3 \sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} c^{7/4} \left(a e^2+c d^2\right)}-\frac{x^3 \left(a e+c d x^2\right)}{4 c \left(a+c x^4\right) \left(a e^2+c d^2\right)}+\frac{d x}{4 c \left(a e^2+c d^2\right)}+\frac{d^{7/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e} \left(a e^2+c d^2\right)^2}","\frac{\sqrt[4]{a} d^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} c^{3/4} \left(a e^2+c d^2\right)^2}-\frac{\sqrt[4]{a} d^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} c^{3/4} \left(a e^2+c d^2\right)^2}+\frac{\sqrt[4]{a} \left(3 \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)}{16 \sqrt{2} c^{7/4} \left(a e^2+c d^2\right)}-\frac{\sqrt[4]{a} \left(3 \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)}{16 \sqrt{2} c^{7/4} \left(a e^2+c d^2\right)}+\frac{\sqrt[4]{a} d^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} c^{3/4} \left(a e^2+c d^2\right)^2}-\frac{\sqrt[4]{a} d^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} c^{3/4} \left(a e^2+c d^2\right)^2}+\frac{\sqrt[4]{a} \left(\sqrt{c} d-3 \sqrt{a} e\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} c^{7/4} \left(a e^2+c d^2\right)}-\frac{\sqrt[4]{a} \left(\sqrt{c} d-3 \sqrt{a} e\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} c^{7/4} \left(a e^2+c d^2\right)}-\frac{x^3 \left(a e+c d x^2\right)}{4 c \left(a+c x^4\right) \left(a e^2+c d^2\right)}+\frac{d x}{4 c \left(a e^2+c d^2\right)}+\frac{d^{7/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e} \left(a e^2+c d^2\right)^2}",1,"(d*x)/(4*c*(c*d^2 + a*e^2)) - (x^3*(a*e + c*d*x^2))/(4*c*(c*d^2 + a*e^2)*(a + c*x^4)) + (d^(7/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[e]*(c*d^2 + a*e^2)^2) + (a^(1/4)*d^2*(Sqrt[c]*d - Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*c^(3/4)*(c*d^2 + a*e^2)^2) + (a^(1/4)*(Sqrt[c]*d - 3*Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*c^(7/4)*(c*d^2 + a*e^2)) - (a^(1/4)*d^2*(Sqrt[c]*d - Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*c^(3/4)*(c*d^2 + a*e^2)^2) - (a^(1/4)*(Sqrt[c]*d - 3*Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*c^(7/4)*(c*d^2 + a*e^2)) + (a^(1/4)*d^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]*c^(3/4)*(c*d^2 + a*e^2)^2) + (a^(1/4)*(Sqrt[c]*d + 3*Sqrt[a]*e)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*c^(7/4)*(c*d^2 + a*e^2)) - (a^(1/4)*d^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]*c^(3/4)*(c*d^2 + a*e^2)^2) - (a^(1/4)*(Sqrt[c]*d + 3*Sqrt[a]*e)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*c^(7/4)*(c*d^2 + a*e^2))","A",24,11,22,0.5000,1,"{1314, 1276, 1280, 1168, 1162, 617, 204, 1165, 628, 1288, 205}"
253,1,687,0,0.6019169,"\int \frac{x^6}{\left(d+e x^2\right) \left(a+c x^4\right)^2} \, dx","Int[x^6/((d + e*x^2)*(a + c*x^4)^2),x]","-\frac{\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)}{16 \sqrt{2} \sqrt[4]{a} c^{5/4} \left(a e^2+c d^2\right)}+\frac{\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)}{16 \sqrt{2} \sqrt[4]{a} c^{5/4} \left(a e^2+c d^2\right)}+\frac{\left(\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} \sqrt[4]{a} c^{5/4} \left(a e^2+c d^2\right)}-\frac{\left(\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} \sqrt[4]{a} c^{5/4} \left(a e^2+c d^2\right)}-\frac{x \left(a e+c d x^2\right)}{4 c \left(a+c x^4\right) \left(a e^2+c d^2\right)}+\frac{d^2 \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} \sqrt[4]{a} \sqrt[4]{c} \left(a e^2+c d^2\right)^2}-\frac{d^2 \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} \sqrt[4]{a} \sqrt[4]{c} \left(a e^2+c d^2\right)^2}-\frac{d^{5/2} \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\left(a e^2+c d^2\right)^2}-\frac{d^2 \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} \sqrt[4]{a} \sqrt[4]{c} \left(a e^2+c d^2\right)^2}+\frac{d^2 \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} \sqrt[4]{a} \sqrt[4]{c} \left(a e^2+c d^2\right)^2}","-\frac{\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)}{16 \sqrt{2} \sqrt[4]{a} c^{5/4} \left(a e^2+c d^2\right)}+\frac{\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)}{16 \sqrt{2} \sqrt[4]{a} c^{5/4} \left(a e^2+c d^2\right)}+\frac{\left(\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} \sqrt[4]{a} c^{5/4} \left(a e^2+c d^2\right)}-\frac{\left(\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} \sqrt[4]{a} c^{5/4} \left(a e^2+c d^2\right)}-\frac{x \left(a e+c d x^2\right)}{4 c \left(a+c x^4\right) \left(a e^2+c d^2\right)}+\frac{d^2 \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} \sqrt[4]{a} \sqrt[4]{c} \left(a e^2+c d^2\right)^2}-\frac{d^2 \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} \sqrt[4]{a} \sqrt[4]{c} \left(a e^2+c d^2\right)^2}-\frac{d^{5/2} \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\left(a e^2+c d^2\right)^2}-\frac{d^2 \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} \sqrt[4]{a} \sqrt[4]{c} \left(a e^2+c d^2\right)^2}+\frac{d^2 \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} \sqrt[4]{a} \sqrt[4]{c} \left(a e^2+c d^2\right)^2}",1,"-(x*(a*e + c*d*x^2))/(4*c*(c*d^2 + a*e^2)*(a + c*x^4)) - (d^(5/2)*Sqrt[e]*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(c*d^2 + a*e^2)^2 - (d^2*(Sqrt[c]*d + Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(1/4)*c^(1/4)*(c*d^2 + a*e^2)^2) + ((Sqrt[c]*d - Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(1/4)*c^(5/4)*(c*d^2 + a*e^2)) + (d^2*(Sqrt[c]*d + Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(1/4)*c^(1/4)*(c*d^2 + a*e^2)^2) - ((Sqrt[c]*d - Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(1/4)*c^(5/4)*(c*d^2 + a*e^2)) + (d^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^(1/4)*c^(1/4)*(c*d^2 + a*e^2)^2) - ((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^(1/4)*c^(5/4)*(c*d^2 + a*e^2)) - (d^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^(1/4)*c^(1/4)*(c*d^2 + a*e^2)^2) + ((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^(1/4)*c^(5/4)*(c*d^2 + a*e^2))","A",23,10,22,0.4545,1,"{1314, 1276, 1168, 1162, 617, 204, 1165, 628, 1288, 205}"
254,1,685,0,0.6094038,"\int \frac{x^4}{\left(d+e x^2\right) \left(a+c x^4\right)^2} \, dx","Int[x^4/((d + e*x^2)*(a + c*x^4)^2),x]","\frac{\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^{3/4} c^{3/4} \left(a e^2+c d^2\right)}-\frac{\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^{3/4} c^{3/4} \left(a e^2+c d^2\right)}+\frac{\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^{3/4} c^{3/4} \left(a e^2+c d^2\right)}-\frac{\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^{3/4} c^{3/4} \left(a e^2+c d^2\right)}-\frac{\sqrt[4]{c} d^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} d^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} d^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} d^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{x \left(d-e x^2\right)}{4 \left(a+c x^4\right) \left(a e^2+c d^2\right)}+\frac{d^{3/2} e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\left(a e^2+c d^2\right)^2}","\frac{\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^{3/4} c^{3/4} \left(a e^2+c d^2\right)}-\frac{\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^{3/4} c^{3/4} \left(a e^2+c d^2\right)}+\frac{\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^{3/4} c^{3/4} \left(a e^2+c d^2\right)}-\frac{\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^{3/4} c^{3/4} \left(a e^2+c d^2\right)}-\frac{\sqrt[4]{c} d^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} d^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} d^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} d^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{x \left(d-e x^2\right)}{4 \left(a+c x^4\right) \left(a e^2+c d^2\right)}+\frac{d^{3/2} e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\left(a e^2+c d^2\right)^2}",1,"-(x*(d - e*x^2))/(4*(c*d^2 + a*e^2)*(a + c*x^4)) + (d^(3/2)*e^(3/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(c*d^2 + a*e^2)^2 - (c^(1/4)*d^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) + ((3*Sqrt[c]*d - Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(3/4)*c^(3/4)*(c*d^2 + a*e^2)) + (c^(1/4)*d^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) - ((3*Sqrt[c]*d - Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(3/4)*c^(3/4)*(c*d^2 + a*e^2)) - (c^(1/4)*d^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) + ((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^(3/4)*c^(3/4)*(c*d^2 + a*e^2)) + (c^(1/4)*d^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) - ((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^(3/4)*c^(3/4)*(c*d^2 + a*e^2))","A",23,10,22,0.4545,1,"{1314, 1179, 1168, 1162, 617, 204, 1165, 628, 1171, 205}"
255,1,685,0,0.5604473,"\int \frac{x^2}{\left(d+e x^2\right) \left(a+c x^4\right)^2} \, dx","Int[x^2/((d + e*x^2)*(a + c*x^4)^2),x]","\frac{\sqrt[4]{c} d e \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} d e \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{\left(\sqrt{c} d-3 \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^{5/4} \sqrt[4]{c} \left(a e^2+c d^2\right)}-\frac{\left(\sqrt{c} d-3 \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^{5/4} \sqrt[4]{c} \left(a e^2+c d^2\right)}+\frac{\sqrt[4]{c} d e \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} d e \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{\left(3 \sqrt{a} e+\sqrt{c} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{5/4} \sqrt[4]{c} \left(a e^2+c d^2\right)}+\frac{\left(3 \sqrt{a} e+\sqrt{c} d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{5/4} \sqrt[4]{c} \left(a e^2+c d^2\right)}+\frac{x \left(a e+c d x^2\right)}{4 a \left(a+c x^4\right) \left(a e^2+c d^2\right)}-\frac{\sqrt{d} e^{5/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\left(a e^2+c d^2\right)^2}","\frac{\sqrt[4]{c} d e \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} d e \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{\left(\sqrt{c} d-3 \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^{5/4} \sqrt[4]{c} \left(a e^2+c d^2\right)}-\frac{\left(\sqrt{c} d-3 \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^{5/4} \sqrt[4]{c} \left(a e^2+c d^2\right)}+\frac{\sqrt[4]{c} d e \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} d e \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{\left(3 \sqrt{a} e+\sqrt{c} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{5/4} \sqrt[4]{c} \left(a e^2+c d^2\right)}+\frac{\left(3 \sqrt{a} e+\sqrt{c} d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{5/4} \sqrt[4]{c} \left(a e^2+c d^2\right)}+\frac{x \left(a e+c d x^2\right)}{4 a \left(a+c x^4\right) \left(a e^2+c d^2\right)}-\frac{\sqrt{d} e^{5/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\left(a e^2+c d^2\right)^2}",1,"(x*(a*e + c*d*x^2))/(4*a*(c*d^2 + a*e^2)*(a + c*x^4)) - (Sqrt[d]*e^(5/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(c*d^2 + a*e^2)^2 + (c^(1/4)*d*e*(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) - ((Sqrt[c]*d + 3*Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(5/4)*c^(1/4)*(c*d^2 + a*e^2)) - (c^(1/4)*d*e*(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) + ((Sqrt[c]*d + 3*Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(5/4)*c^(1/4)*(c*d^2 + a*e^2)) + (c^(1/4)*d*e*(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) + ((Sqrt[c]*d - 3*Sqrt[a]*e)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(5/4)*c^(1/4)*(c*d^2 + a*e^2)) - (c^(1/4)*d*e*(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) - ((Sqrt[c]*d - 3*Sqrt[a]*e)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(5/4)*c^(1/4)*(c*d^2 + a*e^2))","A",23,10,22,0.4545,1,"{1316, 1179, 1168, 1162, 617, 204, 1165, 628, 1171, 205}"
256,1,689,0,0.6006291,"\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}"
257,1,745,0,0.772443,"\int \frac{1}{x^2 \left(d+e x^2\right) \left(a+c x^4\right)^2} \, dx","Int[1/(x^2*(d + e*x^2)*(a + c*x^4)^2),x]","\frac{c^{3/4} \left(a^{3/2} e^3-\sqrt{c} d \left(2 a e^2+c d^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^{9/4} \left(a e^2+c d^2\right)^2}-\frac{c^{3/4} \left(\sqrt{c} d-3 \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^{9/4} \left(a e^2+c d^2\right)}-\frac{c^{3/4} \left(a^{3/2} e^3-\sqrt{c} d \left(2 a e^2+c d^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^{9/4} \left(a e^2+c d^2\right)^2}+\frac{c^{3/4} \left(\sqrt{c} d-3 \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^{9/4} \left(a e^2+c d^2\right)}+\frac{c^{3/4} \left(a^{3/2} e^3+\sqrt{c} d \left(2 a e^2+c d^2\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{9/4} \left(a e^2+c d^2\right)^2}+\frac{c^{3/4} \left(3 \sqrt{a} e+\sqrt{c} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{9/4} \left(a e^2+c d^2\right)}-\frac{c^{3/4} \left(a^{3/2} e^3+\sqrt{c} d \left(2 a e^2+c d^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{9/4} \left(a e^2+c d^2\right)^2}-\frac{c^{3/4} \left(3 \sqrt{a} e+\sqrt{c} d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{9/4} \left(a e^2+c d^2\right)}-\frac{c x \left(a e+c d x^2\right)}{4 a^2 \left(a+c x^4\right) \left(a e^2+c d^2\right)}-\frac{1}{a^2 d x}-\frac{e^{9/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{d^{3/2} \left(a e^2+c d^2\right)^2}","\frac{c^{3/4} \left(a^{3/2} e^3-\sqrt{c} d \left(2 a e^2+c d^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^{9/4} \left(a e^2+c d^2\right)^2}-\frac{c^{3/4} \left(\sqrt{c} d-3 \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^{9/4} \left(a e^2+c d^2\right)}-\frac{c^{3/4} \left(a^{3/2} e^3-\sqrt{c} d \left(2 a e^2+c d^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^{9/4} \left(a e^2+c d^2\right)^2}+\frac{c^{3/4} \left(\sqrt{c} d-3 \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^{9/4} \left(a e^2+c d^2\right)}+\frac{c^{3/4} \left(a^{3/2} e^3+\sqrt{c} d \left(2 a e^2+c d^2\right)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{9/4} \left(a e^2+c d^2\right)^2}+\frac{c^{3/4} \left(3 \sqrt{a} e+\sqrt{c} d\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}\right)}{8 \sqrt{2} a^{9/4} \left(a e^2+c d^2\right)}-\frac{c^{3/4} \left(a^{3/2} e^3+\sqrt{c} d \left(2 a e^2+c d^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{9/4} \left(a e^2+c d^2\right)^2}-\frac{c^{3/4} \left(3 \sqrt{a} e+\sqrt{c} d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} x}{\sqrt[4]{a}}+1\right)}{8 \sqrt{2} a^{9/4} \left(a e^2+c d^2\right)}-\frac{c x \left(a e+c d x^2\right)}{4 a^2 \left(a+c x^4\right) \left(a e^2+c d^2\right)}-\frac{1}{a^2 d x}-\frac{e^{9/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{d^{3/2} \left(a e^2+c d^2\right)^2}",1,"-(1/(a^2*d*x)) - (c*x*(a*e + c*d*x^2))/(4*a^2*(c*d^2 + a*e^2)*(a + c*x^4)) - (e^(9/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(d^(3/2)*(c*d^2 + a*e^2)^2) + (c^(3/4)*(Sqrt[c]*d + 3*Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(9/4)*(c*d^2 + a*e^2)) + (c^(3/4)*(a^(3/2)*e^3 + Sqrt[c]*d*(c*d^2 + 2*a*e^2))*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(9/4)*(c*d^2 + a*e^2)^2) - (c^(3/4)*(Sqrt[c]*d + 3*Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(9/4)*(c*d^2 + a*e^2)) - (c^(3/4)*(a^(3/2)*e^3 + Sqrt[c]*d*(c*d^2 + 2*a*e^2))*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(9/4)*(c*d^2 + a*e^2)^2) - (c^(3/4)*(Sqrt[c]*d - 3*Sqrt[a]*e)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(9/4)*(c*d^2 + a*e^2)) + (c^(3/4)*(a^(3/2)*e^3 - Sqrt[c]*d*(c*d^2 + 2*a*e^2))*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(9/4)*(c*d^2 + a*e^2)^2) + (c^(3/4)*(Sqrt[c]*d - 3*Sqrt[a]*e)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(16*Sqrt[2]*a^(9/4)*(c*d^2 + a*e^2)) - (c^(3/4)*(a^(3/2)*e^3 - Sqrt[c]*d*(c*d^2 + 2*a*e^2))*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(9/4)*(c*d^2 + a*e^2)^2)","A",22,9,22,0.4091,1,"{1336, 205, 1179, 1168, 1162, 617, 204, 1165, 628}"
258,1,751,0,0.6861089,"\int \frac{1}{x^4 \left(d+e x^2\right) \left(a+c x^4\right)^2} \, dx","Int[1/(x^4*(d + e*x^2)*(a + c*x^4)^2),x]","-\frac{c^2 x \left(d-e x^2\right)}{4 a^2 \left(a+c x^4\right) \left(a e^2+c d^2\right)}+\frac{c^{5/4} \left(\sqrt{a} e+\sqrt{c} d\right) \left(2 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^{11/4} \left(a e^2+c d^2\right)^2}+\frac{c^{5/4} \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^{11/4} \left(a e^2+c d^2\right)}-\frac{c^{5/4} \left(\sqrt{a} e+\sqrt{c} d\right) \left(2 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^{11/4} \left(a e^2+c d^2\right)^2}-\frac{c^{5/4} \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^{11/4} \left(a e^2+c d^2\right)}+\frac{c^{5/4} \left(\sqrt{c} d-\sqrt{a} e\right) \left(2 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^{11/4} \left(a e^2+c d^2\right)^2}+\frac{c^{5/4} \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^{11/4} \left(a e^2+c d^2\right)}-\frac{c^{5/4} \left(\sqrt{c} d-\sqrt{a} e\right) \left(2 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^{11/4} \left(a e^2+c d^2\right)^2}-\frac{c^{5/4} \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^{11/4} \left(a e^2+c d^2\right)}+\frac{e}{a^2 d^2 x}-\frac{1}{3 a^2 d x^3}+\frac{e^{11/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{d^{5/2} \left(a e^2+c d^2\right)^2}","-\frac{c^2 x \left(d-e x^2\right)}{4 a^2 \left(a+c x^4\right) \left(a e^2+c d^2\right)}+\frac{c^{5/4} \left(\sqrt{a} e+\sqrt{c} d\right) \left(2 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^{11/4} \left(a e^2+c d^2\right)^2}+\frac{c^{5/4} \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^{11/4} \left(a e^2+c d^2\right)}-\frac{c^{5/4} \left(\sqrt{a} e+\sqrt{c} d\right) \left(2 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^{11/4} \left(a e^2+c d^2\right)^2}-\frac{c^{5/4} \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^{11/4} \left(a e^2+c d^2\right)}+\frac{c^{5/4} \left(\sqrt{c} d-\sqrt{a} e\right) \left(2 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^{11/4} \left(a e^2+c d^2\right)^2}+\frac{c^{5/4} \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^{11/4} \left(a e^2+c d^2\right)}-\frac{c^{5/4} \left(\sqrt{c} d-\sqrt{a} e\right) \left(2 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^{11/4} \left(a e^2+c d^2\right)^2}-\frac{c^{5/4} \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^{11/4} \left(a e^2+c d^2\right)}+\frac{e}{a^2 d^2 x}-\frac{1}{3 a^2 d x^3}+\frac{e^{11/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{d^{5/2} \left(a e^2+c d^2\right)^2}",1,"-1/(3*a^2*d*x^3) + e/(a^2*d^2*x) - (c^2*x*(d - e*x^2))/(4*a^2*(c*d^2 + a*e^2)*(a + c*x^4)) + (e^(11/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(d^(5/2)*(c*d^2 + a*e^2)^2) + (c^(5/4)*(3*Sqrt[c]*d - Sqrt[a]*e)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(11/4)*(c*d^2 + a*e^2)) + (c^(5/4)*(Sqrt[c]*d - Sqrt[a]*e)*(c*d^2 + 2*a*e^2)*ArcTan[1 - (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(11/4)*(c*d^2 + a*e^2)^2) - (c^(5/4)*(3*Sqrt[c]*d - Sqrt[a]*e)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(8*Sqrt[2]*a^(11/4)*(c*d^2 + a*e^2)) - (c^(5/4)*(Sqrt[c]*d - Sqrt[a]*e)*(c*d^2 + 2*a*e^2)*ArcTan[1 + (Sqrt[2]*c^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(11/4)*(c*d^2 + a*e^2)^2) + (c^(5/4)*(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^(11/4)*(c*d^2 + a*e^2)) + (c^(5/4)*(Sqrt[c]*d + Sqrt[a]*e)*(c*d^2 + 2*a*e^2)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(11/4)*(c*d^2 + a*e^2)^2) - (c^(5/4)*(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^(11/4)*(c*d^2 + a*e^2)) - (c^(5/4)*(Sqrt[c]*d + Sqrt[a]*e)*(c*d^2 + 2*a*e^2)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*x + Sqrt[c]*x^2])/(4*Sqrt[2]*a^(11/4)*(c*d^2 + a*e^2)^2)","A",22,9,22,0.4091,1,"{1336, 205, 1179, 1168, 1162, 617, 204, 1165, 628}"
259,1,70,0,0.0594416,"\int \frac{x^2}{\left(1+x^2\right) \sqrt{1+x^4}} \, dx","Int[x^2/((1 + x^2)*Sqrt[1 + x^4]),x]","\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+1}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{2 \sqrt{2}}","\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+1}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{2 \sqrt{2}}",1,"-ArcTan[(Sqrt[2]*x)/Sqrt[1 + x^4]]/(2*Sqrt[2]) + ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(4*Sqrt[1 + x^4])","A",4,4,20,0.2000,1,"{1318, 220, 1699, 203}"
260,1,70,0,0.0607269,"\int \frac{x^2}{\left(1-x^2\right) \sqrt{1+x^4}} \, dx","Int[x^2/((1 - x^2)*Sqrt[1 + x^4]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{2 \sqrt{2}}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+1}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^4+1}}\right)}{2 \sqrt{2}}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{x^4+1}}",1,"ArcTanh[(Sqrt[2]*x)/Sqrt[1 + x^4]]/(2*Sqrt[2]) - ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(4*Sqrt[1 + x^4])","A",4,4,22,0.1818,1,"{1318, 220, 1699, 206}"
261,1,99,0,0.0548223,"\int \frac{x^2}{\left(1+x^2\right) \sqrt{1-x^4}} \, dx","Int[x^2/((1 + x^2)*Sqrt[1 - x^4]),x]","-\frac{x \left(1-x^2\right)}{2 \sqrt{1-x^4}}+\frac{\sqrt{x^2+1} \sqrt{1-x^2} F\left(\left.\sin ^{-1}(x)\right|-1\right)}{\sqrt{1-x^4}}-\frac{\sqrt{x^2+1} \sqrt{1-x^2} E\left(\left.\sin ^{-1}(x)\right|-1\right)}{2 \sqrt{1-x^4}}","-\frac{x \left(1-x^2\right)}{2 \sqrt{1-x^4}}+\frac{\sqrt{x^2+1} \sqrt{1-x^2} F\left(\left.\sin ^{-1}(x)\right|-1\right)}{\sqrt{1-x^4}}-\frac{\sqrt{x^2+1} \sqrt{1-x^2} E\left(\left.\sin ^{-1}(x)\right|-1\right)}{2 \sqrt{1-x^4}}",1,"-(x*(1 - x^2))/(2*Sqrt[1 - x^4]) - (Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticE[ArcSin[x], -1])/(2*Sqrt[1 - x^4]) + (Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[x], -1])/Sqrt[1 - x^4]","A",6,6,22,0.2727,1,"{1256, 471, 423, 424, 248, 221}"
262,1,61,0,0.0406191,"\int \frac{x^2}{\left(1-x^2\right) \sqrt{1-x^4}} \, dx","Int[x^2/((1 - x^2)*Sqrt[1 - x^4]),x]","\frac{x \left(x^2+1\right)}{2 \sqrt{1-x^4}}-\frac{\sqrt{1-x^2} \sqrt{x^2+1} E\left(\left.\sin ^{-1}(x)\right|-1\right)}{2 \sqrt{1-x^4}}","\frac{x \left(x^2+1\right)}{2 \sqrt{1-x^4}}-\frac{\sqrt{1-x^2} \sqrt{x^2+1} E\left(\left.\sin ^{-1}(x)\right|-1\right)}{2 \sqrt{1-x^4}}",1,"(x*(1 + x^2))/(2*Sqrt[1 - x^4]) - (Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticE[ArcSin[x], -1])/(2*Sqrt[1 - x^4])","A",3,3,24,0.1250,1,"{1256, 471, 424}"
263,1,113,0,0.0647771,"\int \frac{x^2}{\left(1+x^2\right) \sqrt{-1+x^4}} \, dx","Int[x^2/((1 + x^2)*Sqrt[-1 + x^4]),x]","-\frac{x \left(1-x^2\right)}{2 \sqrt{x^4-1}}+\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4-1}}-\frac{\sqrt{x^2+1} \sqrt{1-x^2} E\left(\left.\sin ^{-1}(x)\right|-1\right)}{2 \sqrt{x^4-1}}","-\frac{x \left(1-x^2\right)}{2 \sqrt{x^4-1}}+\frac{\sqrt{x^2-1} \sqrt{x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{x^2-1}}\right)|\frac{1}{2}\right)}{\sqrt{2} \sqrt{x^4-1}}-\frac{\sqrt{x^2+1} \sqrt{1-x^2} E\left(\left.\sin ^{-1}(x)\right|-1\right)}{2 \sqrt{x^4-1}}",1,"-(x*(1 - x^2))/(2*Sqrt[-1 + x^4]) - (Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticE[ArcSin[x], -1])/(2*Sqrt[-1 + x^4]) + (Sqrt[-1 + x^2]*Sqrt[1 + x^2]*EllipticF[ArcSin[(Sqrt[2]*x)/Sqrt[-1 + x^2]], 1/2])/(Sqrt[2]*Sqrt[-1 + x^4])","A",7,7,20,0.3500,1,"{1256, 471, 423, 427, 424, 253, 222}"
264,1,57,0,0.053107,"\int \frac{x^2}{\left(1-x^2\right) \sqrt{-1+x^4}} \, dx","Int[x^2/((1 - x^2)*Sqrt[-1 + x^4]),x]","\frac{x \left(x^2+1\right)}{2 \sqrt{x^4-1}}-\frac{\sqrt{1-x^2} \sqrt{x^2+1} E\left(\left.\sin ^{-1}(x)\right|-1\right)}{2 \sqrt{x^4-1}}","\frac{x \left(x^2+1\right)}{2 \sqrt{x^4-1}}-\frac{\sqrt{1-x^2} \sqrt{x^2+1} E\left(\left.\sin ^{-1}(x)\right|-1\right)}{2 \sqrt{x^4-1}}",1,"(x*(1 + x^2))/(2*Sqrt[-1 + x^4]) - (Sqrt[1 - x^2]*Sqrt[1 + x^2]*EllipticE[ArcSin[x], -1])/(2*Sqrt[-1 + x^4])","A",4,4,22,0.1818,1,"{1256, 471, 426, 424}"
265,1,74,0,0.0635063,"\int \frac{x^2}{\left(1+x^2\right) \sqrt{-1-x^4}} \, dx","Int[x^2/((1 + x^2)*Sqrt[-1 - x^4]),x]","\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{-x^4-1}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{-x^4-1}}\right)}{2 \sqrt{2}}","\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{-x^4-1}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{-x^4-1}}\right)}{2 \sqrt{2}}",1,"-ArcTanh[(Sqrt[2]*x)/Sqrt[-1 - x^4]]/(2*Sqrt[2]) + ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(4*Sqrt[-1 - x^4])","A",4,4,22,0.1818,1,"{1318, 220, 1699, 206}"
266,1,74,0,0.0647003,"\int \frac{x^2}{\left(1-x^2\right) \sqrt{-1-x^4}} \, dx","Int[x^2/((1 - x^2)*Sqrt[-1 - x^4]),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{-x^4-1}}\right)}{2 \sqrt{2}}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{-x^4-1}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{-x^4-1}}\right)}{2 \sqrt{2}}-\frac{\left(x^2+1\right) \sqrt{\frac{x^4+1}{\left(x^2+1\right)^2}} F\left(2 \tan ^{-1}(x)|\frac{1}{2}\right)}{4 \sqrt{-x^4-1}}",1,"ArcTan[(Sqrt[2]*x)/Sqrt[-1 - x^4]]/(2*Sqrt[2]) - ((1 + x^2)*Sqrt[(1 + x^4)/(1 + x^2)^2]*EllipticF[2*ArcTan[x], 1/2])/(4*Sqrt[-1 - x^4])","A",4,4,24,0.1667,1,"{1318, 220, 1699, 203}"
267,1,243,0,0.1300776,"\int x^2 \sqrt{c+d x^2} \sqrt{a^2+2 a b x^2+b^2 x^4} \, dx","Int[x^2*Sqrt[c + d*x^2]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{c^2 \sqrt{a^2+2 a b x^2+b^2 x^4} (b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{16 d^{5/2} \left(a+b x^2\right)}-\frac{c x \sqrt{a^2+2 a b x^2+b^2 x^4} \sqrt{c+d x^2} (b c-2 a d)}{16 d^2 \left(a+b x^2\right)}+\frac{b x^3 \sqrt{a^2+2 a b x^2+b^2 x^4} \left(c+d x^2\right)^{3/2}}{6 d \left(a+b x^2\right)}-\frac{x^3 \sqrt{a^2+2 a b x^2+b^2 x^4} \sqrt{c+d x^2} (b c-2 a d)}{8 d \left(a+b x^2\right)}","\frac{c^2 \sqrt{a^2+2 a b x^2+b^2 x^4} (b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{16 d^{5/2} \left(a+b x^2\right)}-\frac{c x \sqrt{a^2+2 a b x^2+b^2 x^4} \sqrt{c+d x^2} (b c-2 a d)}{16 d^2 \left(a+b x^2\right)}+\frac{b x^3 \sqrt{a^2+2 a b x^2+b^2 x^4} \left(c+d x^2\right)^{3/2}}{6 d \left(a+b x^2\right)}-\frac{x^3 \sqrt{a^2+2 a b x^2+b^2 x^4} \sqrt{c+d x^2} (b c-2 a d)}{8 d \left(a+b x^2\right)}",1,"-(c*(b*c - 2*a*d)*x*Sqrt[c + d*x^2]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(16*d^2*(a + b*x^2)) - ((b*c - 2*a*d)*x^3*Sqrt[c + d*x^2]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(8*d*(a + b*x^2)) + (b*x^3*(c + d*x^2)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(6*d*(a + b*x^2)) + (c^2*(b*c - 2*a*d)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(16*d^(5/2)*(a + b*x^2))","A",6,6,37,0.1622,1,"{1250, 459, 279, 321, 217, 206}"
268,1,108,0,0.1010928,"\int x \sqrt{c+d x^2} \sqrt{a^2+2 a b x^2+b^2 x^4} \, dx","Int[x*Sqrt[c + d*x^2]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","\frac{b \sqrt{a^2+2 a b x^2+b^2 x^4} \left(c+d x^2\right)^{5/2}}{5 d^2 \left(a+b x^2\right)}-\frac{\sqrt{a^2+2 a b x^2+b^2 x^4} \left(c+d x^2\right)^{3/2} (b c-a d)}{3 d^2 \left(a+b x^2\right)}","\frac{b \sqrt{a^2+2 a b x^2+b^2 x^4} \left(c+d x^2\right)^{5/2}}{5 d^2 \left(a+b x^2\right)}-\frac{\sqrt{a^2+2 a b x^2+b^2 x^4} \left(c+d x^2\right)^{3/2} (b c-a d)}{3 d^2 \left(a+b x^2\right)}",1,"-((b*c - a*d)*(c + d*x^2)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*d^2*(a + b*x^2)) + (b*(c + d*x^2)^(5/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(5*d^2*(a + b*x^2))","A",4,3,35,0.08571,1,"{1247, 646, 43}"
269,1,178,0,0.0762214,"\int \sqrt{c+d x^2} \sqrt{a^2+2 a b x^2+b^2 x^4} \, dx","Int[Sqrt[c + d*x^2]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4],x]","-\frac{c \sqrt{a^2+2 a b x^2+b^2 x^4} (b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 d^{3/2} \left(a+b x^2\right)}+\frac{b x \sqrt{a^2+2 a b x^2+b^2 x^4} \left(c+d x^2\right)^{3/2}}{4 d \left(a+b x^2\right)}-\frac{x \sqrt{a^2+2 a b x^2+b^2 x^4} \sqrt{c+d x^2} (b c-4 a d)}{8 d \left(a+b x^2\right)}","-\frac{c \sqrt{a^2+2 a b x^2+b^2 x^4} (b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 d^{3/2} \left(a+b x^2\right)}+\frac{b x \sqrt{a^2+2 a b x^2+b^2 x^4} \left(c+d x^2\right)^{3/2}}{4 d \left(a+b x^2\right)}-\frac{x \sqrt{a^2+2 a b x^2+b^2 x^4} \sqrt{c+d x^2} (b c-4 a d)}{8 d \left(a+b x^2\right)}",1,"-((b*c - 4*a*d)*x*Sqrt[c + d*x^2]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(8*d*(a + b*x^2)) + (b*x*(c + d*x^2)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(4*d*(a + b*x^2)) - (c*(b*c - 4*a*d)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(8*d^(3/2)*(a + b*x^2))","A",5,5,34,0.1471,1,"{1148, 388, 195, 217, 206}"
270,1,152,0,0.0948647,"\int \frac{\sqrt{c+d x^2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{x} \, dx","Int[(Sqrt[c + d*x^2]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/x,x]","\frac{b \sqrt{a^2+2 a b x^2+b^2 x^4} \left(c+d x^2\right)^{3/2}}{3 d \left(a+b x^2\right)}+\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4} \sqrt{c+d x^2}}{a+b x^2}-\frac{a \sqrt{c} \sqrt{a^2+2 a b x^2+b^2 x^4} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a+b x^2}","\frac{b \sqrt{a^2+2 a b x^2+b^2 x^4} \left(c+d x^2\right)^{3/2}}{3 d \left(a+b x^2\right)}+\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4} \sqrt{c+d x^2}}{a+b x^2}-\frac{a \sqrt{c} \sqrt{a^2+2 a b x^2+b^2 x^4} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a+b x^2}",1,"(a*Sqrt[c + d*x^2]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(a + b*x^2) + (b*(c + d*x^2)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(3*d*(a + b*x^2)) - (a*Sqrt[c]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(a + b*x^2)","A",6,6,37,0.1622,1,"{1250, 446, 80, 50, 63, 208}"
271,1,177,0,0.0912602,"\int \frac{\sqrt{c+d x^2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{x^2} \, dx","Int[(Sqrt[c + d*x^2]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/x^2,x]","-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4} \left(c+d x^2\right)^{3/2}}{c x \left(a+b x^2\right)}+\frac{x \sqrt{a^2+2 a b x^2+b^2 x^4} \sqrt{c+d x^2} (2 a d+b c)}{2 c \left(a+b x^2\right)}+\frac{\sqrt{a^2+2 a b x^2+b^2 x^4} (2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 \sqrt{d} \left(a+b x^2\right)}","-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4} \left(c+d x^2\right)^{3/2}}{c x \left(a+b x^2\right)}+\frac{x \sqrt{a^2+2 a b x^2+b^2 x^4} \sqrt{c+d x^2} (2 a d+b c)}{2 c \left(a+b x^2\right)}+\frac{\sqrt{a^2+2 a b x^2+b^2 x^4} (2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 \sqrt{d} \left(a+b x^2\right)}",1,"((b*c + 2*a*d)*x*Sqrt[c + d*x^2]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*c*(a + b*x^2)) - (a*(c + d*x^2)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(c*x*(a + b*x^2)) + ((b*c + 2*a*d)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(2*Sqrt[d]*(a + b*x^2))","A",5,5,37,0.1351,1,"{1250, 453, 195, 217, 206}"
272,1,177,0,0.118521,"\int \frac{\sqrt{c+d x^2} \sqrt{a^2+2 a b x^2+b^2 x^4}}{x^3} \, dx","Int[(Sqrt[c + d*x^2]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/x^3,x]","-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4} \left(c+d x^2\right)^{3/2}}{2 c x^2 \left(a+b x^2\right)}+\frac{\sqrt{a^2+2 a b x^2+b^2 x^4} \sqrt{c+d x^2} (a d+2 b c)}{2 c \left(a+b x^2\right)}-\frac{\sqrt{a^2+2 a b x^2+b^2 x^4} (a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 \sqrt{c} \left(a+b x^2\right)}","-\frac{a \sqrt{a^2+2 a b x^2+b^2 x^4} \left(c+d x^2\right)^{3/2}}{2 c x^2 \left(a+b x^2\right)}+\frac{\sqrt{a^2+2 a b x^2+b^2 x^4} \sqrt{c+d x^2} (a d+2 b c)}{2 c \left(a+b x^2\right)}-\frac{\sqrt{a^2+2 a b x^2+b^2 x^4} (a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 \sqrt{c} \left(a+b x^2\right)}",1,"((2*b*c + a*d)*Sqrt[c + d*x^2]*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*c*(a + b*x^2)) - (a*(c + d*x^2)^(3/2)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4])/(2*c*x^2*(a + b*x^2)) - ((2*b*c + a*d)*Sqrt[a^2 + 2*a*b*x^2 + b^2*x^4]*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(2*Sqrt[c]*(a + b*x^2))","A",6,6,37,0.1622,1,"{1250, 446, 78, 50, 63, 208}"
273,1,78,0,0.1345398,"\int x^3 \left(d+e x^2\right)^2 \left(a+b x^2+c x^4\right) \, dx","Int[x^3*(d + e*x^2)^2*(a + b*x^2 + c*x^4),x]","\frac{1}{8} x^8 \left(e (a e+2 b d)+c d^2\right)+\frac{1}{6} d x^6 (2 a e+b d)+\frac{1}{4} a d^2 x^4+\frac{1}{10} e x^{10} (b e+2 c d)+\frac{1}{12} c e^2 x^{12}","\frac{1}{8} x^8 \left(e (a e+2 b d)+c d^2\right)+\frac{1}{6} d x^6 (2 a e+b d)+\frac{1}{4} a d^2 x^4+\frac{1}{10} e x^{10} (b e+2 c d)+\frac{1}{12} c e^2 x^{12}",1,"(a*d^2*x^4)/4 + (d*(b*d + 2*a*e)*x^6)/6 + ((c*d^2 + e*(2*b*d + a*e))*x^8)/8 + (e*(2*c*d + b*e)*x^10)/10 + (c*e^2*x^12)/12","A",3,2,25,0.08000,1,"{1251, 771}"
274,1,78,0,0.0637748,"\int x^2 \left(d+e x^2\right)^2 \left(a+b x^2+c x^4\right) \, dx","Int[x^2*(d + e*x^2)^2*(a + b*x^2 + c*x^4),x]","\frac{1}{7} x^7 \left(e (a e+2 b d)+c d^2\right)+\frac{1}{5} d x^5 (2 a e+b d)+\frac{1}{3} a d^2 x^3+\frac{1}{9} e x^9 (b e+2 c d)+\frac{1}{11} c e^2 x^{11}","\frac{1}{7} x^7 \left(e (a e+2 b d)+c d^2\right)+\frac{1}{5} d x^5 (2 a e+b d)+\frac{1}{3} a d^2 x^3+\frac{1}{9} e x^9 (b e+2 c d)+\frac{1}{11} c e^2 x^{11}",1,"(a*d^2*x^3)/3 + (d*(b*d + 2*a*e)*x^5)/5 + ((c*d^2 + e*(2*b*d + a*e))*x^7)/7 + (e*(2*c*d + b*e)*x^9)/9 + (c*e^2*x^11)/11","A",2,1,25,0.04000,1,"{1261}"
275,1,75,0,0.1312033,"\int x \left(d+e x^2\right)^2 \left(a+b x^2+c x^4\right) \, dx","Int[x*(d + e*x^2)^2*(a + b*x^2 + c*x^4),x]","\frac{\left(d+e x^2\right)^3 \left(a e^2-b d e+c d^2\right)}{6 e^3}-\frac{\left(d+e x^2\right)^4 (2 c d-b e)}{8 e^3}+\frac{c \left(d+e x^2\right)^5}{10 e^3}","\frac{\left(d+e x^2\right)^3 \left(a e^2-b d e+c d^2\right)}{6 e^3}-\frac{\left(d+e x^2\right)^4 (2 c d-b e)}{8 e^3}+\frac{c \left(d+e x^2\right)^5}{10 e^3}",1,"((c*d^2 - b*d*e + a*e^2)*(d + e*x^2)^3)/(6*e^3) - ((2*c*d - b*e)*(d + e*x^2)^4)/(8*e^3) + (c*(d + e*x^2)^5)/(10*e^3)","A",3,2,23,0.08696,1,"{1247, 698}"
276,1,73,0,0.044485,"\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}"
277,1,74,0,0.0901146,"\int \frac{\left(d+e x^2\right)^2 \left(a+b x^2+c x^4\right)}{x} \, dx","Int[((d + e*x^2)^2*(a + b*x^2 + c*x^4))/x,x]","\frac{1}{4} x^4 \left(e (a e+2 b d)+c d^2\right)+\frac{1}{2} d x^2 (2 a e+b d)+a d^2 \log (x)+\frac{1}{6} e x^6 (b e+2 c d)+\frac{1}{8} c e^2 x^8","\frac{1}{4} x^4 \left(e (a e+2 b d)+c d^2\right)+\frac{1}{2} d x^2 (2 a e+b d)+a d^2 \log (x)+\frac{1}{6} e x^6 (b e+2 c d)+\frac{1}{8} c e^2 x^8",1,"(d*(b*d + 2*a*e)*x^2)/2 + ((c*d^2 + e*(2*b*d + a*e))*x^4)/4 + (e*(2*c*d + b*e)*x^6)/6 + (c*e^2*x^8)/8 + a*d^2*Log[x]","A",3,2,25,0.08000,1,"{1251, 893}"
278,1,71,0,0.0483196,"\int \frac{\left(d+e x^2\right)^2 \left(a+b x^2+c x^4\right)}{x^2} \, dx","Int[((d + e*x^2)^2*(a + b*x^2 + c*x^4))/x^2,x]","\frac{1}{3} x^3 \left(e (a e+2 b d)+c d^2\right)+d x (2 a e+b d)-\frac{a d^2}{x}+\frac{1}{5} e x^5 (b e+2 c d)+\frac{1}{7} c e^2 x^7","\frac{1}{3} x^3 \left(e (a e+2 b d)+c d^2\right)+d x (2 a e+b d)-\frac{a d^2}{x}+\frac{1}{5} e x^5 (b e+2 c d)+\frac{1}{7} c e^2 x^7",1,"-((a*d^2)/x) + d*(b*d + 2*a*e)*x + ((c*d^2 + e*(2*b*d + a*e))*x^3)/3 + (e*(2*c*d + b*e)*x^5)/5 + (c*e^2*x^7)/7","A",2,1,25,0.04000,1,"{1261}"
279,1,74,0,0.0957302,"\int \frac{\left(d+e x^2\right)^2 \left(a+b x^2+c x^4\right)}{x^3} \, dx","Int[((d + e*x^2)^2*(a + b*x^2 + c*x^4))/x^3,x]","\frac{1}{2} x^2 \left(e (a e+2 b d)+c d^2\right)+d \log (x) (2 a e+b d)-\frac{a d^2}{2 x^2}+\frac{1}{4} e x^4 (b e+2 c d)+\frac{1}{6} c e^2 x^6","\frac{1}{2} x^2 \left(e (a e+2 b d)+c d^2\right)+d \log (x) (2 a e+b d)-\frac{a d^2}{2 x^2}+\frac{1}{4} e x^4 (b e+2 c d)+\frac{1}{6} c e^2 x^6",1,"-(a*d^2)/(2*x^2) + ((c*d^2 + e*(2*b*d + a*e))*x^2)/2 + (e*(2*c*d + b*e)*x^4)/4 + (c*e^2*x^6)/6 + d*(b*d + 2*a*e)*Log[x]","A",3,2,25,0.08000,1,"{1251, 893}"
280,1,168,0,0.234486,"\int \frac{x^6 \left(a+b x^2+c x^4\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^6*(a + b*x^2 + c*x^4))/(d + e*x^2)^2,x]","\frac{x^3 \left(3 c d^2-e (2 b d-a e)\right)}{3 e^4}-\frac{d^2 x \left(a e^2-b d e+c d^2\right)}{2 e^5 \left(d+e x^2\right)}-\frac{d x \left(4 c d^2-e (3 b d-2 a e)\right)}{e^5}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(9 c d^2-e (7 b d-5 a e)\right)}{2 e^{11/2}}-\frac{x^5 (2 c d-b e)}{5 e^3}+\frac{c x^7}{7 e^2}","\frac{x^3 \left(3 c d^2-e (2 b d-a e)\right)}{3 e^4}-\frac{d^2 x \left(a e^2-b d e+c d^2\right)}{2 e^5 \left(d+e x^2\right)}-\frac{d x \left(4 c d^2-e (3 b d-2 a e)\right)}{e^5}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(9 c d^2-e (7 b d-5 a e)\right)}{2 e^{11/2}}-\frac{x^5 (2 c d-b e)}{5 e^3}+\frac{c x^7}{7 e^2}",1,"-((d*(4*c*d^2 - e*(3*b*d - 2*a*e))*x)/e^5) + ((3*c*d^2 - e*(2*b*d - a*e))*x^3)/(3*e^4) - ((2*c*d - b*e)*x^5)/(5*e^3) + (c*x^7)/(7*e^2) - (d^2*(c*d^2 - b*d*e + a*e^2)*x)/(2*e^5*(d + e*x^2)) + (d^(3/2)*(9*c*d^2 - e*(7*b*d - 5*a*e))*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*e^(11/2))","A",4,3,25,0.1200,1,"{1257, 1810, 205}"
281,1,135,0,0.1590709,"\int \frac{x^4 \left(a+b x^2+c x^4\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^4*(a + b*x^2 + c*x^4))/(d + e*x^2)^2,x]","\frac{d x \left(a e^2-b d e+c d^2\right)}{2 e^4 \left(d+e x^2\right)}+\frac{x \left(3 c d^2-e (2 b d-a e)\right)}{e^4}-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(7 c d^2-e (5 b d-3 a e)\right)}{2 e^{9/2}}-\frac{x^3 (2 c d-b e)}{3 e^3}+\frac{c x^5}{5 e^2}","\frac{d x \left(a e^2-b d e+c d^2\right)}{2 e^4 \left(d+e x^2\right)}+\frac{x \left(3 c d^2-e (2 b d-a e)\right)}{e^4}-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(7 c d^2-e (5 b d-3 a e)\right)}{2 e^{9/2}}-\frac{x^3 (2 c d-b e)}{3 e^3}+\frac{c x^5}{5 e^2}",1,"((3*c*d^2 - e*(2*b*d - a*e))*x)/e^4 - ((2*c*d - b*e)*x^3)/(3*e^3) + (c*x^5)/(5*e^2) + (d*(c*d^2 - b*d*e + a*e^2)*x)/(2*e^4*(d + e*x^2)) - (Sqrt[d]*(7*c*d^2 - e*(5*b*d - 3*a*e))*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*e^(9/2))","A",4,3,25,0.1200,1,"{1257, 1810, 205}"
282,1,106,0,0.1059086,"\int \frac{x^2 \left(a+b x^2+c x^4\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^2*(a + b*x^2 + c*x^4))/(d + e*x^2)^2,x]","-\frac{x \left(a e^2-b d e+c d^2\right)}{2 e^3 \left(d+e x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(5 c d^2-e (3 b d-a e)\right)}{2 \sqrt{d} e^{7/2}}-\frac{x (2 c d-b e)}{e^3}+\frac{c x^3}{3 e^2}","-\frac{x \left(a e^2-b d e+c d^2\right)}{2 e^3 \left(d+e x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(5 c d^2-e (3 b d-a e)\right)}{2 \sqrt{d} e^{7/2}}-\frac{x (2 c d-b e)}{e^3}+\frac{c x^3}{3 e^2}",1,"-(((2*c*d - b*e)*x)/e^3) + (c*x^3)/(3*e^2) - ((c*d^2 - b*d*e + a*e^2)*x)/(2*e^3*(d + e*x^2)) + ((5*c*d^2 - e*(3*b*d - a*e))*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*Sqrt[d]*e^(7/2))","A",4,3,25,0.1200,1,"{1257, 1153, 205}"
283,1,83,0,0.0929843,"\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}"
284,1,86,0,0.1184522,"\int \frac{a+b x^2+c x^4}{x^2 \left(d+e x^2\right)^2} \, dx","Int[(a + b*x^2 + c*x^4)/(x^2*(d + e*x^2)^2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(e (b d-3 a e)+c d^2\right)}{2 d^{5/2} e^{3/2}}-\frac{x \left(\frac{c}{e}-\frac{b d-a e}{d^2}\right)}{2 \left(d+e x^2\right)}-\frac{a}{d^2 x}","-\frac{x \left(a e^2-b d e+c d^2\right)}{2 d^2 e \left(d+e x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(e (b d-3 a e)+c d^2\right)}{2 d^{5/2} e^{3/2}}-\frac{a}{d^2 x}",1,"-(a/(d^2*x)) - ((c/e - (b*d - a*e)/d^2)*x)/(2*(d + e*x^2)) + ((c*d^2 + e*(b*d - 3*a*e))*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*d^(5/2)*e^(3/2))","A",3,3,25,0.1200,1,"{1259, 453, 205}"
285,1,106,0,0.1373952,"\int \frac{a+b x^2+c x^4}{x^4 \left(d+e x^2\right)^2} \, dx","Int[(a + b*x^2 + c*x^4)/(x^4*(d + e*x^2)^2),x]","\frac{x \left(a e^2-b d e+c d^2\right)}{2 d^3 \left(d+e x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(c d^2-e (3 b d-5 a e)\right)}{2 d^{7/2} \sqrt{e}}-\frac{b d-2 a e}{d^3 x}-\frac{a}{3 d^2 x^3}","\frac{x \left(a e^2-b d e+c d^2\right)}{2 d^3 \left(d+e x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(c d^2-e (3 b d-5 a e)\right)}{2 d^{7/2} \sqrt{e}}-\frac{b d-2 a e}{d^3 x}-\frac{a}{3 d^2 x^3}",1,"-a/(3*d^2*x^3) - (b*d - 2*a*e)/(d^3*x) + ((c*d^2 - b*d*e + a*e^2)*x)/(2*d^3*(d + e*x^2)) + ((c*d^2 - e*(3*b*d - 5*a*e))*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*d^(7/2)*Sqrt[e])","A",4,3,25,0.1200,1,"{1259, 1261, 205}"
286,1,136,0,0.2522716,"\int \frac{a+b x^2+c x^4}{x^6 \left(d+e x^2\right)^2} \, dx","Int[(a + b*x^2 + c*x^4)/(x^6*(d + e*x^2)^2),x]","-\frac{e x \left(a e^2-b d e+c d^2\right)}{2 d^4 \left(d+e x^2\right)}-\frac{c d^2-e (2 b d-3 a e)}{d^4 x}-\frac{\sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(3 c d^2-e (5 b d-7 a e)\right)}{2 d^{9/2}}-\frac{b d-2 a e}{3 d^3 x^3}-\frac{a}{5 d^2 x^5}","-\frac{e x \left(a e^2-b d e+c d^2\right)}{2 d^4 \left(d+e x^2\right)}-\frac{c d^2-e (2 b d-3 a e)}{d^4 x}-\frac{\sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(3 c d^2-e (5 b d-7 a e)\right)}{2 d^{9/2}}-\frac{b d-2 a e}{3 d^3 x^3}-\frac{a}{5 d^2 x^5}",1,"-a/(5*d^2*x^5) - (b*d - 2*a*e)/(3*d^3*x^3) - (c*d^2 - e*(2*b*d - 3*a*e))/(d^4*x) - (e*(c*d^2 - b*d*e + a*e^2)*x)/(2*d^4*(d + e*x^2)) - (Sqrt[e]*(3*c*d^2 - e*(5*b*d - 7*a*e))*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*d^(9/2))","A",4,3,25,0.1200,1,"{1259, 1802, 205}"
287,1,167,0,0.3302101,"\int \frac{a+b x^2+c x^4}{x^8 \left(d+e x^2\right)^2} \, dx","Int[(a + b*x^2 + c*x^4)/(x^8*(d + e*x^2)^2),x]","\frac{e^2 x \left(a e^2-b d e+c d^2\right)}{2 d^5 \left(d+e x^2\right)}+\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(5 c d^2-e (7 b d-9 a e)\right)}{2 d^{11/2}}-\frac{c d^2-e (2 b d-3 a e)}{3 d^4 x^3}+\frac{e \left(2 c d^2-e (3 b d-4 a e)\right)}{d^5 x}-\frac{b d-2 a e}{5 d^3 x^5}-\frac{a}{7 d^2 x^7}","\frac{e^2 x \left(a e^2-b d e+c d^2\right)}{2 d^5 \left(d+e x^2\right)}+\frac{e^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(5 c d^2-e (7 b d-9 a e)\right)}{2 d^{11/2}}-\frac{c d^2-e (2 b d-3 a e)}{3 d^4 x^3}+\frac{e \left(2 c d^2-e (3 b d-4 a e)\right)}{d^5 x}-\frac{b d-2 a e}{5 d^3 x^5}-\frac{a}{7 d^2 x^7}",1,"-a/(7*d^2*x^7) - (b*d - 2*a*e)/(5*d^3*x^5) - (c*d^2 - e*(2*b*d - 3*a*e))/(3*d^4*x^3) + (e*(2*c*d^2 - e*(3*b*d - 4*a*e)))/(d^5*x) + (e^2*(c*d^2 - b*d*e + a*e^2)*x)/(2*d^5*(d + e*x^2)) + (e^(3/2)*(5*c*d^2 - e*(7*b*d - 9*a*e))*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(2*d^(11/2))","A",4,3,25,0.1200,1,"{1259, 1802, 205}"
288,1,173,0,0.3212157,"\int \frac{x^6 \left(a+b x^2+c x^4\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^6*(a + b*x^2 + c*x^4))/(d + e*x^2)^3,x]","\frac{d x \left(17 c d^2-e (13 b d-9 a e)\right)}{8 e^5 \left(d+e x^2\right)}-\frac{d^2 x \left(a e^2-b d e+c d^2\right)}{4 e^5 \left(d+e x^2\right)^2}+\frac{x \left(6 c d^2-e (3 b d-a e)\right)}{e^5}-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(15 a e^2-35 b d e+63 c d^2\right)}{8 e^{11/2}}-\frac{x^3 (3 c d-b e)}{3 e^4}+\frac{c x^5}{5 e^3}","\frac{d x \left(17 c d^2-e (13 b d-9 a e)\right)}{8 e^5 \left(d+e x^2\right)}-\frac{d^2 x \left(a e^2-b d e+c d^2\right)}{4 e^5 \left(d+e x^2\right)^2}+\frac{x \left(6 c d^2-e (3 b d-a e)\right)}{e^5}-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(15 a e^2-35 b d e+63 c d^2\right)}{8 e^{11/2}}-\frac{x^3 (3 c d-b e)}{3 e^4}+\frac{c x^5}{5 e^3}",1,"((6*c*d^2 - e*(3*b*d - a*e))*x)/e^5 - ((3*c*d - b*e)*x^3)/(3*e^4) + (c*x^5)/(5*e^3) - (d^2*(c*d^2 - b*d*e + a*e^2)*x)/(4*e^5*(d + e*x^2)^2) + (d*(17*c*d^2 - e*(13*b*d - 9*a*e))*x)/(8*e^5*(d + e*x^2)) - (Sqrt[d]*(63*c*d^2 - 35*b*d*e + 15*a*e^2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(8*e^(11/2))","A",5,4,25,0.1600,1,"{1257, 1814, 1810, 205}"
289,1,143,0,0.2101999,"\int \frac{x^4 \left(a+b x^2+c x^4\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^4*(a + b*x^2 + c*x^4))/(d + e*x^2)^3,x]","-\frac{x \left(13 c d^2-e (9 b d-5 a e)\right)}{8 e^4 \left(d+e x^2\right)}+\frac{d x \left(a e^2-b d e+c d^2\right)}{4 e^4 \left(d+e x^2\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(35 c d^2-3 e (5 b d-a e)\right)}{8 \sqrt{d} e^{9/2}}-\frac{x (3 c d-b e)}{e^4}+\frac{c x^3}{3 e^3}","-\frac{x \left(13 c d^2-e (9 b d-5 a e)\right)}{8 e^4 \left(d+e x^2\right)}+\frac{d x \left(a e^2-b d e+c d^2\right)}{4 e^4 \left(d+e x^2\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(35 c d^2-3 e (5 b d-a e)\right)}{8 \sqrt{d} e^{9/2}}-\frac{x (3 c d-b e)}{e^4}+\frac{c x^3}{3 e^3}",1,"-(((3*c*d - b*e)*x)/e^4) + (c*x^3)/(3*e^3) + (d*(c*d^2 - b*d*e + a*e^2)*x)/(4*e^4*(d + e*x^2)^2) - ((13*c*d^2 - e*(9*b*d - 5*a*e))*x)/(8*e^4*(d + e*x^2)) + ((35*c*d^2 - 3*e*(5*b*d - a*e))*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(8*Sqrt[d]*e^(9/2))","A",5,4,25,0.1600,1,"{1257, 1814, 1153, 205}"
290,1,124,0,0.1379039,"\int \frac{x^2 \left(a+b x^2+c x^4\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^2*(a + b*x^2 + c*x^4))/(d + e*x^2)^3,x]","\frac{x \left(9 c d^2-e (5 b d-a e)\right)}{8 d e^3 \left(d+e x^2\right)}-\frac{x \left(a e^2-b d e+c d^2\right)}{4 e^3 \left(d+e x^2\right)^2}-\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(15 c d^2-e (a e+3 b d)\right)}{8 d^{3/2} e^{7/2}}+\frac{c x}{e^3}","\frac{x \left(9 c d^2-e (5 b d-a e)\right)}{8 d e^3 \left(d+e x^2\right)}-\frac{x \left(a e^2-b d e+c d^2\right)}{4 e^3 \left(d+e x^2\right)^2}-\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(15 c d^2-e (a e+3 b d)\right)}{8 d^{3/2} e^{7/2}}+\frac{c x}{e^3}",1,"(c*x)/e^3 - ((c*d^2 - b*d*e + a*e^2)*x)/(4*e^3*(d + e*x^2)^2) + ((9*c*d^2 - e*(5*b*d - a*e))*x)/(8*d*e^3*(d + e*x^2)) - ((15*c*d^2 - e*(3*b*d + a*e))*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(8*d^(3/2)*e^(7/2))","A",4,4,25,0.1600,1,"{1257, 1157, 388, 205}"
291,1,115,0,0.116052,"\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}"
292,1,124,0,0.2040634,"\int \frac{a+b x^2+c x^4}{x^2 \left(d+e x^2\right)^3} \, dx","Int[(a + b*x^2 + c*x^4)/(x^2*(d + e*x^2)^3),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(3 e (b d-5 a e)+c d^2\right)}{8 d^{7/2} e^{3/2}}+\frac{x \left(e (3 b d-7 a e)+c d^2\right)}{8 d^3 e \left(d+e x^2\right)}-\frac{x \left(\frac{c}{e}-\frac{b d-a e}{d^2}\right)}{4 \left(d+e x^2\right)^2}-\frac{a}{d^3 x}","-\frac{x \left(a e^2-b d e+c d^2\right)}{4 d^2 e \left(d+e x^2\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(3 e (b d-5 a e)+c d^2\right)}{8 d^{7/2} e^{3/2}}+\frac{x \left(e (3 b d-7 a e)+c d^2\right)}{8 d^3 e \left(d+e x^2\right)}-\frac{a}{d^3 x}",1,"-(a/(d^3*x)) - ((c/e - (b*d - a*e)/d^2)*x)/(4*(d + e*x^2)^2) + ((c*d^2 + e*(3*b*d - 7*a*e))*x)/(8*d^3*e*(d + e*x^2)) + ((c*d^2 + 3*e*(b*d - 5*a*e))*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(8*d^(7/2)*e^(3/2))","A",4,4,25,0.1600,1,"{1259, 456, 453, 205}"
293,1,142,0,0.2174121,"\int \frac{a+b x^2+c x^4}{x^4 \left(d+e x^2\right)^3} \, dx","Int[(a + b*x^2 + c*x^4)/(x^4*(d + e*x^2)^3),x]","\frac{x \left(a e^2-b d e+c d^2\right)}{4 d^3 \left(d+e x^2\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(35 a e^2-15 b d e+3 c d^2\right)}{8 d^{9/2} \sqrt{e}}+\frac{x \left(3 c d^2-e (7 b d-11 a e)\right)}{8 d^4 \left(d+e x^2\right)}-\frac{b d-3 a e}{d^4 x}-\frac{a}{3 d^3 x^3}","\frac{x \left(a e^2-b d e+c d^2\right)}{4 d^3 \left(d+e x^2\right)^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(35 a e^2-15 b d e+3 c d^2\right)}{8 d^{9/2} \sqrt{e}}+\frac{x \left(3 c d^2-e (7 b d-11 a e)\right)}{8 d^4 \left(d+e x^2\right)}-\frac{b d-3 a e}{d^4 x}-\frac{a}{3 d^3 x^3}",1,"-a/(3*d^3*x^3) - (b*d - 3*a*e)/(d^4*x) + ((c*d^2 - b*d*e + a*e^2)*x)/(4*d^3*(d + e*x^2)^2) + ((3*c*d^2 - e*(7*b*d - 11*a*e))*x)/(8*d^4*(d + e*x^2)) + ((3*c*d^2 - 15*b*d*e + 35*a*e^2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(8*d^(9/2)*Sqrt[e])","A",5,3,25,0.1200,1,"{1259, 1261, 205}"
294,1,171,0,0.373194,"\int \frac{a+b x^2+c x^4}{x^6 \left(d+e x^2\right)^3} \, dx","Int[(a + b*x^2 + c*x^4)/(x^6*(d + e*x^2)^3),x]","-\frac{e x \left(a e^2-b d e+c d^2\right)}{4 d^4 \left(d+e x^2\right)^2}-\frac{6 a e^2-3 b d e+c d^2}{d^5 x}-\frac{\sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(63 a e^2-35 b d e+15 c d^2\right)}{8 d^{11/2}}-\frac{e x \left(7 c d^2-e (11 b d-15 a e)\right)}{8 d^5 \left(d+e x^2\right)}-\frac{b d-3 a e}{3 d^4 x^3}-\frac{a}{5 d^3 x^5}","-\frac{e x \left(a e^2-b d e+c d^2\right)}{4 d^4 \left(d+e x^2\right)^2}-\frac{6 a e^2-3 b d e+c d^2}{d^5 x}-\frac{\sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(63 a e^2-35 b d e+15 c d^2\right)}{8 d^{11/2}}-\frac{e x \left(7 c d^2-e (11 b d-15 a e)\right)}{8 d^5 \left(d+e x^2\right)}-\frac{b d-3 a e}{3 d^4 x^3}-\frac{a}{5 d^3 x^5}",1,"-a/(5*d^3*x^5) - (b*d - 3*a*e)/(3*d^4*x^3) - (c*d^2 - 3*b*d*e + 6*a*e^2)/(d^5*x) - (e*(c*d^2 - b*d*e + a*e^2)*x)/(4*d^4*(d + e*x^2)^2) - (e*(7*c*d^2 - e*(11*b*d - 15*a*e))*x)/(8*d^5*(d + e*x^2)) - (Sqrt[e]*(15*c*d^2 - 35*b*d*e + 63*a*e^2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(8*d^(11/2))","A",5,4,25,0.1600,1,"{1259, 1805, 1802, 205}"
295,1,230,0,0.4874824,"\int \frac{x^9}{\left(d+e x^2\right) \left(a+b x^2+c x^4\right)} \, dx","Int[x^9/((d + e*x^2)*(a + b*x^2 + c*x^4)),x]","-\frac{\left(a^2 c e-a b^2 e-2 a b c d+b^3 d\right) \log \left(a+b x^2+c x^4\right)}{4 c^3 \left(a e^2-b d e+c d^2\right)}-\frac{\left(3 a^2 b c e+2 a^2 c^2 d-4 a b^2 c d-a b^3 e+b^4 d\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^3 \sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}+\frac{d^4 \log \left(d+e x^2\right)}{2 e^3 \left(a e^2-b d e+c d^2\right)}-\frac{x^2 (b e+c d)}{2 c^2 e^2}+\frac{x^4}{4 c e}","-\frac{\left(a^2 c e-a b^2 e-2 a b c d+b^3 d\right) \log \left(a+b x^2+c x^4\right)}{4 c^3 \left(a e^2-b d e+c d^2\right)}-\frac{\left(3 a^2 b c e+2 a^2 c^2 d-4 a b^2 c d-a b^3 e+b^4 d\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^3 \sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}+\frac{d^4 \log \left(d+e x^2\right)}{2 e^3 \left(a e^2-b d e+c d^2\right)}-\frac{x^2 (b e+c d)}{2 c^2 e^2}+\frac{x^4}{4 c e}",1,"-((c*d + b*e)*x^2)/(2*c^2*e^2) + x^4/(4*c*e) - ((b^4*d - 4*a*b^2*c*d + 2*a^2*c^2*d - a*b^3*e + 3*a^2*b*c*e)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^3*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)) + (d^4*Log[d + e*x^2])/(2*e^3*(c*d^2 - b*d*e + a*e^2)) - ((b^3*d - 2*a*b*c*d - a*b^2*e + a^2*c*e)*Log[a + b*x^2 + c*x^4])/(4*c^3*(c*d^2 - b*d*e + a*e^2))","A",7,6,27,0.2222,1,"{1251, 1628, 634, 618, 206, 628}"
296,1,189,0,0.3290827,"\int \frac{x^7}{\left(d+e x^2\right) \left(a+b x^2+c x^4\right)} \, dx","Int[x^7/((d + e*x^2)*(a + b*x^2 + c*x^4)),x]","\frac{\left(2 a^2 c e-a b^2 e-3 a b c d+b^3 d\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^2 \sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}+\frac{\left(-a b e-a c d+b^2 d\right) \log \left(a+b x^2+c x^4\right)}{4 c^2 \left(a e^2-b d e+c d^2\right)}-\frac{d^3 \log \left(d+e x^2\right)}{2 e^2 \left(a e^2-b d e+c d^2\right)}+\frac{x^2}{2 c e}","\frac{\left(2 a^2 c e-a b^2 e-3 a b c d+b^3 d\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c^2 \sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}+\frac{\left(-a b e-a c d+b^2 d\right) \log \left(a+b x^2+c x^4\right)}{4 c^2 \left(a e^2-b d e+c d^2\right)}-\frac{d^3 \log \left(d+e x^2\right)}{2 e^2 \left(a e^2-b d e+c d^2\right)}+\frac{x^2}{2 c e}",1,"x^2/(2*c*e) + ((b^3*d - 3*a*b*c*d - a*b^2*e + 2*a^2*c*e)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^2*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)) - (d^3*Log[d + e*x^2])/(2*e^2*(c*d^2 - b*d*e + a*e^2)) + ((b^2*d - a*c*d - a*b*e)*Log[a + b*x^2 + c*x^4])/(4*c^2*(c*d^2 - b*d*e + a*e^2))","A",7,6,27,0.2222,1,"{1251, 1628, 634, 618, 206, 628}"
297,1,158,0,0.2606002,"\int \frac{x^5}{\left(d+e x^2\right) \left(a+b x^2+c x^4\right)} \, dx","Int[x^5/((d + e*x^2)*(a + b*x^2 + c*x^4)),x]","-\frac{\left(-a b e-2 a c d+b^2 d\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c \sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}+\frac{d^2 \log \left(d+e x^2\right)}{2 e \left(a e^2-b d e+c d^2\right)}-\frac{(b d-a e) \log \left(a+b x^2+c x^4\right)}{4 c \left(a e^2-b d e+c d^2\right)}","-\frac{\left(-a b e-2 a c d+b^2 d\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 c \sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}+\frac{d^2 \log \left(d+e x^2\right)}{2 e \left(a e^2-b d e+c d^2\right)}-\frac{(b d-a e) \log \left(a+b x^2+c x^4\right)}{4 c \left(a e^2-b d e+c d^2\right)}",1,"-((b^2*d - 2*a*c*d - a*b*e)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)) + (d^2*Log[d + e*x^2])/(2*e*(c*d^2 - b*d*e + a*e^2)) - ((b*d - a*e)*Log[a + b*x^2 + c*x^4])/(4*c*(c*d^2 - b*d*e + a*e^2))","A",7,6,27,0.2222,1,"{1251, 1628, 634, 618, 206, 628}"
298,1,132,0,0.1570509,"\int \frac{x^3}{\left(d+e x^2\right) \left(a+b x^2+c x^4\right)} \, dx","Int[x^3/((d + e*x^2)*(a + b*x^2 + c*x^4)),x]","\frac{(b d-2 a e) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 \sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}-\frac{d \log \left(d+e x^2\right)}{2 \left(a e^2-b d e+c d^2\right)}+\frac{d \log \left(a+b x^2+c x^4\right)}{4 \left(a e^2-b d e+c d^2\right)}","\frac{(b d-2 a e) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 \sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}-\frac{d \log \left(d+e x^2\right)}{2 \left(a e^2-b d e+c d^2\right)}+\frac{d \log \left(a+b x^2+c x^4\right)}{4 \left(a e^2-b d e+c d^2\right)}",1,"((b*d - 2*a*e)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)) - (d*Log[d + e*x^2])/(2*(c*d^2 - b*d*e + a*e^2)) + (d*Log[a + b*x^2 + c*x^4])/(4*(c*d^2 - b*d*e + a*e^2))","A",7,6,27,0.2222,1,"{1251, 800, 634, 618, 206, 628}"
299,1,133,0,0.1233145,"\int \frac{x}{\left(d+e x^2\right) \left(a+b x^2+c x^4\right)} \, dx","Int[x/((d + e*x^2)*(a + b*x^2 + c*x^4)),x]","-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 \sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}+\frac{e \log \left(d+e x^2\right)}{2 \left(a e^2-b d e+c d^2\right)}-\frac{e \log \left(a+b x^2+c x^4\right)}{4 \left(a e^2-b d e+c d^2\right)}","-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 \sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}+\frac{e \log \left(d+e x^2\right)}{2 \left(a e^2-b d e+c d^2\right)}-\frac{e \log \left(a+b x^2+c x^4\right)}{4 \left(a e^2-b d e+c d^2\right)}",1,"-((2*c*d - b*e)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)) + (e*Log[d + e*x^2])/(2*(c*d^2 - b*d*e + a*e^2)) - (e*Log[a + b*x^2 + c*x^4])/(4*(c*d^2 - b*d*e + a*e^2))","A",7,7,25,0.2800,1,"{1247, 705, 31, 634, 618, 206, 628}"
300,1,167,0,0.3057967,"\int \frac{1}{x \left(d+e x^2\right) \left(a+b x^2+c x^4\right)} \, dx","Int[1/(x*(d + e*x^2)*(a + b*x^2 + c*x^4)),x]","\frac{\left(2 a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a \sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}-\frac{e^2 \log \left(d+e x^2\right)}{2 d \left(a e^2-b d e+c d^2\right)}-\frac{(c d-b e) \log \left(a+b x^2+c x^4\right)}{4 a \left(a e^2-b d e+c d^2\right)}+\frac{\log (x)}{a d}","\frac{\left(2 a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a \sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}-\frac{e^2 \log \left(d+e x^2\right)}{2 d \left(a e^2-b d e+c d^2\right)}-\frac{(c d-b e) \log \left(a+b x^2+c x^4\right)}{4 a \left(a e^2-b d e+c d^2\right)}+\frac{\log (x)}{a d}",1,"((b*c*d - b^2*e + 2*a*c*e)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)) + Log[x]/(a*d) - (e^2*Log[d + e*x^2])/(2*d*(c*d^2 - b*d*e + a*e^2)) - ((c*d - b*e)*Log[a + b*x^2 + c*x^4])/(4*a*(c*d^2 - b*d*e + a*e^2))","A",7,6,27,0.2222,1,"{1251, 893, 634, 618, 206, 628}"
301,1,205,0,0.4704967,"\int \frac{1}{x^3 \left(d+e x^2\right) \left(a+b x^2+c x^4\right)} \, dx","Int[1/(x^3*(d + e*x^2)*(a + b*x^2 + c*x^4)),x]","-\frac{\left(3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}+\frac{\left(a c e+b^2 (-e)+b c d\right) \log \left(a+b x^2+c x^4\right)}{4 a^2 \left(a e^2-b d e+c d^2\right)}-\frac{\log (x) (a e+b d)}{a^2 d^2}+\frac{e^3 \log \left(d+e x^2\right)}{2 d^2 \left(a e^2-b d e+c d^2\right)}-\frac{1}{2 a d x^2}","-\frac{\left(3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^2 \sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}+\frac{\left(a c e+b^2 (-e)+b c d\right) \log \left(a+b x^2+c x^4\right)}{4 a^2 \left(a e^2-b d e+c d^2\right)}-\frac{\log (x) (a e+b d)}{a^2 d^2}+\frac{e^3 \log \left(d+e x^2\right)}{2 d^2 \left(a e^2-b d e+c d^2\right)}-\frac{1}{2 a d x^2}",1,"-1/(2*a*d*x^2) - ((b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^2*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)) - ((b*d + a*e)*Log[x])/(a^2*d^2) + (e^3*Log[d + e*x^2])/(2*d^2*(c*d^2 - b*d*e + a*e^2)) + ((b*c*d - b^2*e + a*c*e)*Log[a + b*x^2 + c*x^4])/(4*a^2*(c*d^2 - b*d*e + a*e^2))","A",7,6,27,0.2222,1,"{1251, 893, 634, 618, 206, 628}"
302,1,268,0,0.5968829,"\int \frac{1}{x^5 \left(d+e x^2\right) \left(a+b x^2+c x^4\right)} \, dx","Int[1/(x^5*(d + e*x^2)*(a + b*x^2 + c*x^4)),x]","-\frac{\left(2 a b c e-a c^2 d+b^2 c d+b^3 (-e)\right) \log \left(a+b x^2+c x^4\right)}{4 a^3 \left(a e^2-b d e+c d^2\right)}+\frac{\left(-2 a^2 c^2 e+4 a b^2 c e-3 a b c^2 d+b^3 c d+b^4 (-e)\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^3 \sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}+\frac{\log (x) \left(a b d e-a \left(c d^2-a e^2\right)+b^2 d^2\right)}{a^3 d^3}+\frac{a e+b d}{2 a^2 d^2 x^2}-\frac{e^4 \log \left(d+e x^2\right)}{2 d^3 \left(a e^2-b d e+c d^2\right)}-\frac{1}{4 a d x^4}","-\frac{\left(2 a b c e-a c^2 d+b^2 c d+b^3 (-e)\right) \log \left(a+b x^2+c x^4\right)}{4 a^3 \left(a e^2-b d e+c d^2\right)}+\frac{\left(-2 a^2 c^2 e+4 a b^2 c e-3 a b c^2 d+b^3 c d+b^4 (-e)\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{2 a^3 \sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}+\frac{\log (x) \left(a b d e-a \left(c d^2-a e^2\right)+b^2 d^2\right)}{a^3 d^3}+\frac{a e+b d}{2 a^2 d^2 x^2}-\frac{e^4 \log \left(d+e x^2\right)}{2 d^3 \left(a e^2-b d e+c d^2\right)}-\frac{1}{4 a d x^4}",1,"-1/(4*a*d*x^4) + (b*d + a*e)/(2*a^2*d^2*x^2) + ((b^3*c*d - 3*a*b*c^2*d - b^4*e + 4*a*b^2*c*e - 2*a^2*c^2*e)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*a^3*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)) + ((b^2*d^2 + a*b*d*e - a*(c*d^2 - a*e^2))*Log[x])/(a^3*d^3) - (e^4*Log[d + e*x^2])/(2*d^3*(c*d^2 - b*d*e + a*e^2)) - ((b^2*c*d - a*c^2*d - b^3*e + 2*a*b*c*e)*Log[a + b*x^2 + c*x^4])/(4*a^3*(c*d^2 - b*d*e + a*e^2))","A",7,6,27,0.2222,1,"{1251, 893, 634, 618, 206, 628}"
303,1,387,0,4.0316631,"\int \frac{x^8}{\left(d+e x^2\right) \left(a+b x^2+c x^4\right)} \, dx","Int[x^8/((d + e*x^2)*(a + b*x^2 + c*x^4)),x]","-\frac{\left(-\frac{3 a^2 b c e+2 a^2 c^2 d-4 a b^2 c d-a b^3 e+b^4 d}{\sqrt{b^2-4 a c}}+a^2 c e-a b^2 e-2 a b c d+b^3 d\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}} \left(a e^2-b d e+c d^2\right)}-\frac{\left(\frac{3 a^2 b c e+2 a^2 c^2 d-4 a b^2 c d-a b^3 e+b^4 d}{\sqrt{b^2-4 a c}}+a^2 c e-a b^2 e-2 a b c d+b^3 d\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} \left(a e^2-b d e+c d^2\right)}+\frac{d^{7/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{e^{5/2} \left(a e^2-b d e+c d^2\right)}-\frac{x (b e+c d)}{c^2 e^2}+\frac{x^3}{3 c e}","-\frac{\left(-\frac{3 a^2 b c e+2 a^2 c^2 d-4 a b^2 c d-a b^3 e+b^4 d}{\sqrt{b^2-4 a c}}+a^2 c e-a b^2 e-2 a b c d+b^3 d\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}} \left(a e^2-b d e+c d^2\right)}-\frac{\left(\frac{3 a^2 b c e+2 a^2 c^2 d-4 a b^2 c d-a b^3 e+b^4 d}{\sqrt{b^2-4 a c}}+a^2 c e-a b^2 e-2 a b c d+b^3 d\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} \left(a e^2-b d e+c d^2\right)}+\frac{d^{7/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{e^{5/2} \left(a e^2-b d e+c d^2\right)}-\frac{x (b e+c d)}{c^2 e^2}+\frac{x^3}{3 c e}",1,"-(((c*d + b*e)*x)/(c^2*e^2)) + x^3/(3*c*e) - ((b^3*d - 2*a*b*c*d - a*b^2*e + a^2*c*e - (b^4*d - 4*a*b^2*c*d + 2*a^2*c^2*d - a*b^3*e + 3*a^2*b*c*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]]*(c*d^2 - b*d*e + a*e^2)) - ((b^3*d - 2*a*b*c*d - a*b^2*e + a^2*c*e + (b^4*d - 4*a*b^2*c*d + 2*a^2*c^2*d - a*b^3*e + 3*a^2*b*c*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]]*(c*d^2 - b*d*e + a*e^2)) + (d^(7/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(e^(5/2)*(c*d^2 - b*d*e + a*e^2))","A",6,3,27,0.1111,1,"{1287, 205, 1166}"
304,1,323,0,1.3663893,"\int \frac{x^6}{\left(d+e x^2\right) \left(a+b x^2+c x^4\right)} \, dx","Int[x^6/((d + e*x^2)*(a + b*x^2 + c*x^4)),x]","\frac{\left(-\frac{2 a^2 c e-a b^2 e-3 a b c d+b^3 d}{\sqrt{b^2-4 a c}}-a b e-a c d+b^2 d\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}} \left(a e^2-b d e+c d^2\right)}+\frac{\left(\frac{2 a^2 c e-a b^2 e-3 a b c d+b^3 d}{\sqrt{b^2-4 a c}}-a b e-a c d+b^2 d\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} \left(a e^2-b d e+c d^2\right)}-\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{e^{3/2} \left(a e^2-b d e+c d^2\right)}+\frac{x}{c e}","\frac{\left(-\frac{2 a^2 c e-a b^2 e-3 a b c d+b^3 d}{\sqrt{b^2-4 a c}}-a b e-a c d+b^2 d\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}} \left(a e^2-b d e+c d^2\right)}+\frac{\left(\frac{2 a^2 c e-a b^2 e-3 a b c d+b^3 d}{\sqrt{b^2-4 a c}}-a b e-a c d+b^2 d\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} \left(a e^2-b d e+c d^2\right)}-\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{e^{3/2} \left(a e^2-b d e+c d^2\right)}+\frac{x}{c e}",1,"x/(c*e) + ((b^2*d - a*c*d - a*b*e - (b^3*d - 3*a*b*c*d - a*b^2*e + 2*a^2*c*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]]*(c*d^2 - b*d*e + a*e^2)) + ((b^2*d - a*c*d - a*b*e + (b^3*d - 3*a*b*c*d - a*b^2*e + 2*a^2*c*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]]*(c*d^2 - b*d*e + a*e^2)) - (d^(5/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(e^(3/2)*(c*d^2 - b*d*e + a*e^2))","A",6,3,27,0.1111,1,"{1287, 205, 1166}"
305,1,280,0,0.8944491,"\int \frac{x^4}{\left(d+e x^2\right) \left(a+b x^2+c x^4\right)} \, dx","Int[x^4/((d + e*x^2)*(a + b*x^2 + c*x^4)),x]","-\frac{\left(-\frac{-a b e-2 a c d+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\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}} \left(a e^2-b d e+c d^2\right)}-\frac{\left(\frac{-a b e-2 a c d+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\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} \left(a e^2-b d e+c d^2\right)}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e} \left(a e^2-b d e+c d^2\right)}","-\frac{\left(-\frac{-a b e-2 a c d+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\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}} \left(a e^2-b d e+c d^2\right)}-\frac{\left(\frac{-a b e-2 a c d+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\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} \left(a e^2-b d e+c d^2\right)}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e} \left(a e^2-b d e+c d^2\right)}",1,"-(((b*d - a*e - (b^2*d - 2*a*c*d - a*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]]*(c*d^2 - b*d*e + a*e^2))) - ((b*d - a*e + (b^2*d - 2*a*c*d - a*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]]*(c*d^2 - b*d*e + a*e^2)) + (d^(3/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[e]*(c*d^2 - b*d*e + a*e^2))","A",6,3,27,0.1111,1,"{1287, 205, 1166}"
306,1,251,0,0.4511038,"\int \frac{x^2}{\left(d+e x^2\right) \left(a+b x^2+c x^4\right)} \, dx","Int[x^2/((d + e*x^2)*(a + b*x^2 + c*x^4)),x]","\frac{\sqrt{c} \left(d-\frac{b d-2 a 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{b d-2 a e}{\sqrt{b^2-4 a c}}+d\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{\sqrt{d} \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{a e^2-b d e+c d^2}","\frac{\sqrt{c} \left(d-\frac{b d-2 a 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{b d-2 a e}{\sqrt{b^2-4 a c}}+d\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{\sqrt{d} \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{a e^2-b d e+c d^2}",1,"(Sqrt[c]*(d - (b*d - 2*a*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]*(d + (b*d - 2*a*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[d]*Sqrt[e]*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(c*d^2 - b*d*e + a*e^2)","A",6,3,27,0.1111,1,"{1287, 205, 1166}"
307,1,254,0,0.519666,"\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}"
308,1,298,0,0.9602952,"\int \frac{1}{x^2 \left(d+e x^2\right) \left(a+b x^2+c x^4\right)} \, dx","Int[1/(x^2*(d + e*x^2)*(a + b*x^2 + c*x^4)),x]","-\frac{\sqrt{c} \left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a \sqrt{b-\sqrt{b^2-4 a c}} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{c} \left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a \sqrt{\sqrt{b^2-4 a c}+b} \left(a e^2-b d e+c d^2\right)}-\frac{e^{5/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{d^{3/2} \left(a e^2-b d e+c d^2\right)}-\frac{1}{a d x}","-\frac{\sqrt{c} \left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a \sqrt{b-\sqrt{b^2-4 a c}} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{c} \left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a \sqrt{\sqrt{b^2-4 a c}+b} \left(a e^2-b d e+c d^2\right)}-\frac{e^{5/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{d^{3/2} \left(a e^2-b d e+c d^2\right)}-\frac{1}{a d x}",1,"-(1/(a*d*x)) - (Sqrt[c]*(c*d - b*e + (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[b - Sqrt[b^2 - 4*a*c]]*(c*d^2 - b*d*e + a*e^2)) - (Sqrt[c]*(c*d - b*e - (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[b + Sqrt[b^2 - 4*a*c]]*(c*d^2 - b*d*e + a*e^2)) - (e^(5/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(d^(3/2)*(c*d^2 - b*d*e + a*e^2))","A",6,3,27,0.1111,1,"{1287, 205, 1166}"
309,1,348,0,1.5494032,"\int \frac{1}{x^4 \left(d+e x^2\right) \left(a+b x^2+c x^4\right)} \, dx","Int[1/(x^4*(d + e*x^2)*(a + b*x^2 + c*x^4)),x]","\frac{\sqrt{c} \left(\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+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)}{\sqrt{2} a^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{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+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)}{\sqrt{2} a^2 \sqrt{\sqrt{b^2-4 a c}+b} \left(a e^2-b d e+c d^2\right)}+\frac{a e+b d}{a^2 d^2 x}+\frac{e^{7/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{d^{5/2} \left(a e^2-b d e+c d^2\right)}-\frac{1}{3 a d x^3}","\frac{\sqrt{c} \left(\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+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)}{\sqrt{2} a^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{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+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)}{\sqrt{2} a^2 \sqrt{\sqrt{b^2-4 a c}+b} \left(a e^2-b d e+c d^2\right)}+\frac{a e+b d}{a^2 d^2 x}+\frac{e^{7/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{d^{5/2} \left(a e^2-b d e+c d^2\right)}-\frac{1}{3 a d x^3}",1,"-1/(3*a*d*x^3) + (b*d + a*e)/(a^2*d^2*x) + (Sqrt[c]*(b*c*d - b^2*e + a*c*e + (b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]*(c*d^2 - b*d*e + a*e^2)) + (Sqrt[c]*(b*c*d - b^2*e + a*c*e - (b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^2*Sqrt[b + Sqrt[b^2 - 4*a*c]]*(c*d^2 - b*d*e + a*e^2)) + (e^(7/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(d^(5/2)*(c*d^2 - b*d*e + a*e^2))","A",6,3,27,0.1111,1,"{1287, 205, 1166}"
310,1,866,0,2.5085768,"\int \frac{1}{\sqrt{f x} \left(d+e x^2\right) \left(a+b x^2+c x^4\right)} \, dx","Int[1/(Sqrt[f*x]*(d + e*x^2)*(a + b*x^2 + c*x^4)),x]","-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{f x}}{\sqrt[4]{d} \sqrt{f}}\right) e^{7/4}}{\sqrt{2} d^{3/4} \left(c d^2-b e d+a e^2\right) \sqrt{f}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{f x}}{\sqrt[4]{d} \sqrt{f}}+1\right) e^{7/4}}{\sqrt{2} d^{3/4} \left(c d^2-b e d+a e^2\right) \sqrt{f}}-\frac{\log \left(\sqrt{e} \sqrt{f} x+\sqrt{d} \sqrt{f}-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{f x}\right) e^{7/4}}{2 \sqrt{2} d^{3/4} \left(c d^2-b e d+a e^2\right) \sqrt{f}}+\frac{\log \left(\sqrt{e} \sqrt{f} x+\sqrt{d} \sqrt{f}+\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{f x}\right) e^{7/4}}{2 \sqrt{2} d^{3/4} \left(c d^2-b e d+a e^2\right) \sqrt{f}}+\frac{c^{3/4} \left(2 c d-\left(b-\sqrt{b^2-4 a c}\right) e\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{f x}}{\sqrt[4]{-b-\sqrt{b^2-4 a c}} \sqrt{f}}\right)}{\sqrt[4]{2} \sqrt{b^2-4 a c} \left(-b-\sqrt{b^2-4 a c}\right)^{3/4} \left(c d^2-b e d+a e^2\right) \sqrt{f}}-\frac{c^{3/4} \left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{f x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b} \sqrt{f}}\right)}{\sqrt[4]{2} \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}-b\right)^{3/4} \left(c d^2-b e d+a e^2\right) \sqrt{f}}+\frac{c^{3/4} \left(2 c d-\left(b-\sqrt{b^2-4 a c}\right) e\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{f x}}{\sqrt[4]{-b-\sqrt{b^2-4 a c}} \sqrt{f}}\right)}{\sqrt[4]{2} \sqrt{b^2-4 a c} \left(-b-\sqrt{b^2-4 a c}\right)^{3/4} \left(c d^2-b e d+a e^2\right) \sqrt{f}}-\frac{c^{3/4} \left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{f x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b} \sqrt{f}}\right)}{\sqrt[4]{2} \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}-b\right)^{3/4} \left(c d^2-b e d+a e^2\right) \sqrt{f}}","-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{f x}}{\sqrt[4]{d} \sqrt{f}}\right) e^{7/4}}{\sqrt{2} d^{3/4} \left(c d^2-b e d+a e^2\right) \sqrt{f}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{f x}}{\sqrt[4]{d} \sqrt{f}}+1\right) e^{7/4}}{\sqrt{2} d^{3/4} \left(c d^2-b e d+a e^2\right) \sqrt{f}}-\frac{\log \left(\sqrt{e} \sqrt{f} x+\sqrt{d} \sqrt{f}-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{f x}\right) e^{7/4}}{2 \sqrt{2} d^{3/4} \left(c d^2-b e d+a e^2\right) \sqrt{f}}+\frac{\log \left(\sqrt{e} \sqrt{f} x+\sqrt{d} \sqrt{f}+\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{f x}\right) e^{7/4}}{2 \sqrt{2} d^{3/4} \left(c d^2-b e d+a e^2\right) \sqrt{f}}+\frac{c^{3/4} \left(2 c d-\left(b-\sqrt{b^2-4 a c}\right) e\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{f x}}{\sqrt[4]{-b-\sqrt{b^2-4 a c}} \sqrt{f}}\right)}{\sqrt[4]{2} \sqrt{b^2-4 a c} \left(-b-\sqrt{b^2-4 a c}\right)^{3/4} \left(c d^2-b e d+a e^2\right) \sqrt{f}}-\frac{c^{3/4} \left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \tan ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{f x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b} \sqrt{f}}\right)}{\sqrt[4]{2} \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}-b\right)^{3/4} \left(c d^2-b e d+a e^2\right) \sqrt{f}}+\frac{c^{3/4} \left(2 c d-\left(b-\sqrt{b^2-4 a c}\right) e\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{f x}}{\sqrt[4]{-b-\sqrt{b^2-4 a c}} \sqrt{f}}\right)}{\sqrt[4]{2} \sqrt{b^2-4 a c} \left(-b-\sqrt{b^2-4 a c}\right)^{3/4} \left(c d^2-b e d+a e^2\right) \sqrt{f}}-\frac{c^{3/4} \left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt[4]{c} \sqrt{f x}}{\sqrt[4]{\sqrt{b^2-4 a c}-b} \sqrt{f}}\right)}{\sqrt[4]{2} \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}-b\right)^{3/4} \left(c d^2-b e d+a e^2\right) \sqrt{f}}",1,"(c^(3/4)*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[f*x])/((-b - Sqrt[b^2 - 4*a*c])^(1/4)*Sqrt[f])])/(2^(1/4)*Sqrt[b^2 - 4*a*c]*(-b - Sqrt[b^2 - 4*a*c])^(3/4)*(c*d^2 - b*d*e + a*e^2)*Sqrt[f]) - (c^(3/4)*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*ArcTan[(2^(1/4)*c^(1/4)*Sqrt[f*x])/((-b + Sqrt[b^2 - 4*a*c])^(1/4)*Sqrt[f])])/(2^(1/4)*Sqrt[b^2 - 4*a*c]*(-b + Sqrt[b^2 - 4*a*c])^(3/4)*(c*d^2 - b*d*e + a*e^2)*Sqrt[f]) - (e^(7/4)*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[f*x])/(d^(1/4)*Sqrt[f])])/(Sqrt[2]*d^(3/4)*(c*d^2 - b*d*e + a*e^2)*Sqrt[f]) + (e^(7/4)*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[f*x])/(d^(1/4)*Sqrt[f])])/(Sqrt[2]*d^(3/4)*(c*d^2 - b*d*e + a*e^2)*Sqrt[f]) + (c^(3/4)*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[f*x])/((-b - Sqrt[b^2 - 4*a*c])^(1/4)*Sqrt[f])])/(2^(1/4)*Sqrt[b^2 - 4*a*c]*(-b - Sqrt[b^2 - 4*a*c])^(3/4)*(c*d^2 - b*d*e + a*e^2)*Sqrt[f]) - (c^(3/4)*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*ArcTanh[(2^(1/4)*c^(1/4)*Sqrt[f*x])/((-b + Sqrt[b^2 - 4*a*c])^(1/4)*Sqrt[f])])/(2^(1/4)*Sqrt[b^2 - 4*a*c]*(-b + Sqrt[b^2 - 4*a*c])^(3/4)*(c*d^2 - b*d*e + a*e^2)*Sqrt[f]) - (e^(7/4)*Log[Sqrt[d]*Sqrt[f] + Sqrt[e]*Sqrt[f]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[f*x]])/(2*Sqrt[2]*d^(3/4)*(c*d^2 - b*d*e + a*e^2)*Sqrt[f]) + (e^(7/4)*Log[Sqrt[d]*Sqrt[f] + Sqrt[e]*Sqrt[f]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[f*x]])/(2*Sqrt[2]*d^(3/4)*(c*d^2 - b*d*e + a*e^2)*Sqrt[f])","A",19,12,31,0.3871,1,"{1269, 1424, 211, 1165, 628, 1162, 617, 204, 1422, 212, 208, 205}"
311,1,272,0,0.573454,"\int \frac{x^5 \sqrt{a+b x^2+c x^4}}{d+e x^2} \, dx","Int[(x^5*Sqrt[a + b*x^2 + c*x^4])/(d + e*x^2),x]","-\frac{\left(-8 c^2 d e (b d-a e)-2 b c e^2 (b d-2 a e)-b^3 e^3+16 c^3 d^3\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{32 c^{5/2} e^4}+\frac{\sqrt{a+b x^2+c x^4} \left((2 c d-b e) (b e+4 c d)-2 c e x^2 (b e+2 c d)\right)}{16 c^2 e^3}+\frac{d^2 \sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e^4}+\frac{\left(a+b x^2+c x^4\right)^{3/2}}{6 c e}","-\frac{\left(-8 c^2 d e (b d-a e)-2 b c e^2 (b d-2 a e)-b^3 e^3+16 c^3 d^3\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{32 c^{5/2} e^4}+\frac{\sqrt{a+b x^2+c x^4} \left((2 c d-b e) (b e+4 c d)-2 c e x^2 (b e+2 c d)\right)}{16 c^2 e^3}+\frac{d^2 \sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e^4}+\frac{\left(a+b x^2+c x^4\right)^{3/2}}{6 c e}",1,"(((2*c*d - b*e)*(4*c*d + b*e) - 2*c*e*(2*c*d + b*e)*x^2)*Sqrt[a + b*x^2 + c*x^4])/(16*c^2*e^3) + (a + b*x^2 + c*x^4)^(3/2)/(6*c*e) - ((16*c^3*d^3 - b^3*e^3 - 2*b*c*e^2*(b*d - 2*a*e) - 8*c^2*d*e*(b*d - a*e))*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(32*c^(5/2)*e^4) + (d^2*Sqrt[c*d^2 - b*d*e + a*e^2]*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])])/(2*e^4)","A",8,7,29,0.2414,1,"{1251, 1653, 814, 843, 621, 206, 724}"
312,1,208,0,0.314967,"\int \frac{x^3 \sqrt{a+b x^2+c x^4}}{d+e x^2} \, dx","Int[(x^3*Sqrt[a + b*x^2 + c*x^4])/(d + e*x^2),x]","\frac{\left(-4 c e (b d-a e)-b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{16 c^{3/2} e^3}-\frac{d \sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e^3}-\frac{\sqrt{a+b x^2+c x^4} \left(-b e+4 c d-2 c e x^2\right)}{8 c e^2}","\frac{\left(-4 c e (b d-a e)-b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{16 c^{3/2} e^3}-\frac{d \sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e^3}-\frac{\sqrt{a+b x^2+c x^4} \left(-b e+4 c d-2 c e x^2\right)}{8 c e^2}",1,"-((4*c*d - b*e - 2*c*e*x^2)*Sqrt[a + b*x^2 + c*x^4])/(8*c*e^2) + ((8*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - a*e))*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(16*c^(3/2)*e^3) - (d*Sqrt[c*d^2 - b*d*e + a*e^2]*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])])/(2*e^3)","A",7,6,29,0.2069,1,"{1251, 814, 843, 621, 206, 724}"
313,1,168,0,0.2168957,"\int \frac{x \sqrt{a+b x^2+c x^4}}{d+e x^2} \, dx","Int[(x*Sqrt[a + b*x^2 + c*x^4])/(d + e*x^2),x]","\frac{\sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e^2}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 \sqrt{c} e^2}+\frac{\sqrt{a+b x^2+c x^4}}{2 e}","\frac{\sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e^2}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 \sqrt{c} e^2}+\frac{\sqrt{a+b x^2+c x^4}}{2 e}",1,"Sqrt[a + b*x^2 + c*x^4]/(2*e) - ((2*c*d - b*e)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(4*Sqrt[c]*e^2) + (Sqrt[c*d^2 - b*d*e + a*e^2]*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])])/(2*e^2)","A",7,6,27,0.2222,1,"{1247, 734, 843, 621, 206, 724}"
314,1,186,0,0.255888,"\int \frac{\sqrt{a+b x^2+c x^4}}{x \left(d+e x^2\right)} \, dx","Int[Sqrt[a + b*x^2 + c*x^4]/(x*(d + e*x^2)),x]","-\frac{\sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 d e}-\frac{\sqrt{a} \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 d}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{2 e}","-\frac{\sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 d e}-\frac{\sqrt{a} \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 d}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{2 e}",1,"-(Sqrt[a]*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(2*d) + (Sqrt[c]*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(2*e) - (Sqrt[c*d^2 - b*d*e + a*e^2]*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])])/(2*d*e)","A",9,6,29,0.2069,1,"{1251, 895, 724, 206, 843, 621}"
315,1,361,0,0.5091547,"\int \frac{\sqrt{a+b x^2+c x^4}}{x^3 \left(d+e x^2\right)} \, dx","Int[Sqrt[a + b*x^2 + c*x^4]/(x^3*(d + e*x^2)),x]","\frac{\sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 d^2}+\frac{\sqrt{a} e \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 d^2}-\frac{b e \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 \sqrt{c} d^2}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 \sqrt{c} d^2}-\frac{\sqrt{a+b x^2+c x^4}}{2 d x^2}-\frac{b \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{4 \sqrt{a} d}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{2 d}","\frac{\sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 d^2}+\frac{\sqrt{a} e \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 d^2}-\frac{b e \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 \sqrt{c} d^2}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 \sqrt{c} d^2}-\frac{\sqrt{a+b x^2+c x^4}}{2 d x^2}-\frac{b \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{4 \sqrt{a} d}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{2 d}",1,"-Sqrt[a + b*x^2 + c*x^4]/(2*d*x^2) - (b*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(4*Sqrt[a]*d) + (Sqrt[a]*e*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(2*d^2) + (Sqrt[c]*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(2*d) - (b*e*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(4*Sqrt[c]*d^2) - ((2*c*d - b*e)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(4*Sqrt[c]*d^2) + (Sqrt[c*d^2 - b*d*e + a*e^2]*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])])/(2*d^2)","A",21,8,29,0.2759,1,"{1251, 960, 732, 843, 621, 206, 724, 734}"
316,1,619,0,0.5610119,"\int \frac{x^4 \sqrt{1+2 x^2+2 x^4}}{3+2 x^2} \, dx","Int[(x^4*Sqrt[1 + 2*x^2 + 2*x^4])/(3 + 2*x^2),x]","\frac{1}{30} \left(3 x^2+1\right) \sqrt{2 x^4+2 x^2+1} x+\frac{109 \sqrt{2 x^4+2 x^2+1} x}{60 \sqrt{2} \left(\sqrt{2} x^2+1\right)}-\frac{1}{4} \sqrt{2 x^4+2 x^2+1} x+\frac{3}{16} \sqrt{15} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)+\frac{45 \left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{112 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}-\frac{\left(1+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{4\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{139 \left(1-\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{240 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}-\frac{109 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{60\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{15 \left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{224 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}","-\frac{1}{60} \left(13-6 x^2\right) \sqrt{2 x^4+2 x^2+1} x+\frac{109 \sqrt{2 x^4+2 x^2+1} x}{60 \sqrt{2} \left(\sqrt{2} x^2+1\right)}+\frac{3}{16} \sqrt{15} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)+\frac{\left(263 \sqrt{2}-70\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{60\ 2^{3/4} \left(3 \sqrt{2}-2\right) \sqrt{2 x^4+2 x^2+1}}-\frac{109 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{60\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}+\frac{15 \left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{16\ 2^{3/4} \left(2-3 \sqrt{2}\right) \sqrt{2 x^4+2 x^2+1}}",1,"-(x*Sqrt[1 + 2*x^2 + 2*x^4])/4 + (x*(1 + 3*x^2)*Sqrt[1 + 2*x^2 + 2*x^4])/30 + (109*x*Sqrt[1 + 2*x^2 + 2*x^4])/(60*Sqrt[2]*(1 + Sqrt[2]*x^2)) + (3*Sqrt[15]*ArcTan[(Sqrt[5/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]])/16 - (109*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(60*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - (139*(1 - Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(240*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - ((1 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(4*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + (45*(3 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(112*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - (15*(3 + Sqrt[2])^2*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 - 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(224*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4])","A",17,9,29,0.3103,1,"{1335, 1091, 1197, 1103, 1195, 1116, 1208, 1216, 1706}"
317,1,591,0,0.409872,"\int \frac{x^2 \sqrt{1+2 x^2+2 x^4}}{3+2 x^2} \, dx","Int[(x^2*Sqrt[1 + 2*x^2 + 2*x^4])/(3 + 2*x^2),x]","-\frac{7 \sqrt{2 x^4+2 x^2+1} x}{6 \sqrt{2} \left(\sqrt{2} x^2+1\right)}+\frac{1}{6} \sqrt{2 x^4+2 x^2+1} x-\frac{1}{8} \sqrt{15} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)-\frac{15 \left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{56 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}+\frac{\left(1+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{6\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}+\frac{3 \left(1-\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{8 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}+\frac{7 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{6\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}+\frac{5 \left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{112 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}","-\frac{7 \sqrt{2 x^4+2 x^2+1} x}{6 \sqrt{2} \left(\sqrt{2} x^2+1\right)}+\frac{1}{6} \sqrt{2 x^4+2 x^2+1} x-\frac{1}{8} \sqrt{15} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)-\frac{\left(17 \sqrt{2}-4\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{6\ 2^{3/4} \left(3 \sqrt{2}-2\right) \sqrt{2 x^4+2 x^2+1}}+\frac{7 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{6\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{5 \left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{8\ 2^{3/4} \left(2-3 \sqrt{2}\right) \sqrt{2 x^4+2 x^2+1}}",1,"(x*Sqrt[1 + 2*x^2 + 2*x^4])/6 - (7*x*Sqrt[1 + 2*x^2 + 2*x^4])/(6*Sqrt[2]*(1 + Sqrt[2]*x^2)) - (Sqrt[15]*ArcTan[(Sqrt[5/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]])/8 + (7*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(6*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + (3*(1 - Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(8*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + ((1 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(6*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - (15*(3 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(56*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + (5*(3 + Sqrt[2])^2*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 - 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(112*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4])","A",13,8,29,0.2759,1,"{1335, 1091, 1197, 1103, 1195, 1208, 1216, 1706}"
318,1,470,0,0.2023874,"\int \frac{\sqrt{1+2 x^2+2 x^4}}{3+2 x^2} \, dx","Int[Sqrt[1 + 2*x^2 + 2*x^4]/(3 + 2*x^2),x]","\frac{\sqrt{2 x^4+2 x^2+1} x}{\sqrt{2} \left(\sqrt{2} x^2+1\right)}+\frac{1}{4} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)+\frac{5 \left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{28 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}-\frac{\left(1-\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{4 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}-\frac{\left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{5 \left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{168 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}","\frac{\sqrt{2 x^4+2 x^2+1} x}{\sqrt{2} \left(\sqrt{2} x^2+1\right)}+\frac{1}{4} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)+\frac{2^{3/4} \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{\left(3 \sqrt{2}-2\right) \sqrt{2 x^4+2 x^2+1}}-\frac{\left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{2^{3/4} \sqrt{2 x^4+2 x^2+1}}+\frac{5 \left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{12\ 2^{3/4} \left(2-3 \sqrt{2}\right) \sqrt{2 x^4+2 x^2+1}}",1,"(x*Sqrt[1 + 2*x^2 + 2*x^4])/(Sqrt[2]*(1 + Sqrt[2]*x^2)) + (Sqrt[5/3]*ArcTan[(Sqrt[5/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]])/4 - ((1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - ((1 - Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(4*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + (5*(3 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(28*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - (5*(3 + Sqrt[2])^2*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 - 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(168*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4])","A",7,6,26,0.2308,1,"{1208, 1197, 1103, 1195, 1216, 1706}"
319,1,399,0,0.2421024,"\int \frac{\sqrt{1+2 x^2+2 x^4}}{x^2 \left(3+2 x^2\right)} \, dx","Int[Sqrt[1 + 2*x^2 + 2*x^4]/(x^2*(3 + 2*x^2)),x]","\frac{\sqrt{2} \sqrt{2 x^4+2 x^2+1} x}{3 \left(\sqrt{2} x^2+1\right)}-\frac{\sqrt{2 x^4+2 x^2+1}}{3 x}-\frac{1}{6} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)+\frac{\left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{21 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}-\frac{\sqrt[4]{2} \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{3 \sqrt{2 x^4+2 x^2+1}}+\frac{5 \left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{252 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}","\frac{\sqrt{2} \sqrt{2 x^4+2 x^2+1} x}{3 \left(\sqrt{2} x^2+1\right)}-\frac{\sqrt{2 x^4+2 x^2+1}}{3 x}-\frac{1}{6} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)+\frac{\left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{21 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}-\frac{\sqrt[4]{2} \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{3 \sqrt{2 x^4+2 x^2+1}}+\frac{5 \left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{252 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}",1,"-Sqrt[1 + 2*x^2 + 2*x^4]/(3*x) + (Sqrt[2]*x*Sqrt[1 + 2*x^2 + 2*x^4])/(3*(1 + Sqrt[2]*x^2)) - (Sqrt[5/3]*ArcTan[(Sqrt[5/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]])/6 - (2^(1/4)*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(3*Sqrt[1 + 2*x^2 + 2*x^4]) + ((3 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(21*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + (5*(3 + Sqrt[2])^2*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 - 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(252*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4])","A",8,7,29,0.2414,1,"{1311, 1281, 1197, 1103, 1195, 1216, 1706}"
320,1,360,0,0.1941825,"\int \frac{\sqrt{1+2 x^2+2 x^4}}{x^4 \left(3+2 x^2\right)} \, dx","Int[Sqrt[1 + 2*x^2 + 2*x^4]/(x^4*(3 + 2*x^2)),x]","-\frac{\sqrt{2 x^4+2 x^2+1}}{9 x^3}+\frac{1}{9} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)+\frac{5 \left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{63 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}-\frac{\left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{9 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}-\frac{5 \left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{378 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}","-\frac{\sqrt{2 x^4+2 x^2+1}}{9 x^3}+\frac{1}{9} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)+\frac{5 \left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{63 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}-\frac{\left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{9 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}-\frac{5 \left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{378 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}",1,"-Sqrt[1 + 2*x^2 + 2*x^4]/(9*x^3) + (Sqrt[5/3]*ArcTan[(Sqrt[5/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]])/9 - ((1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(9*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + (5*(3 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(63*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - (5*(3 + Sqrt[2])^2*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 - 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(378*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4])","A",7,6,29,0.2069,1,"{1309, 1281, 12, 1103, 1216, 1706}"
321,1,546,0,0.5435527,"\int \frac{\sqrt{1+2 x^2+2 x^4}}{x^6 \left(3+2 x^2\right)} \, dx","Int[Sqrt[1 + 2*x^2 + 2*x^4]/(x^6*(3 + 2*x^2)),x]","\frac{4 \sqrt{2} \sqrt{2 x^4+2 x^2+1} x}{45 \left(\sqrt{2} x^2+1\right)}-\frac{4 \sqrt{2 x^4+2 x^2+1}}{45 x}+\frac{4 \sqrt{2 x^4+2 x^2+1}}{135 x^3}-\frac{\sqrt{2 x^4+2 x^2+1}}{15 x^5}-\frac{2}{27} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)-\frac{\sqrt[4]{2} \left(19-2 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{135 \sqrt{2 x^4+2 x^2+1}}+\frac{5 \sqrt[4]{2} \left(5-3 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{189 \sqrt{2 x^4+2 x^2+1}}-\frac{4 \sqrt[4]{2} \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{45 \sqrt{2 x^4+2 x^2+1}}+\frac{5 \left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{567 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}","\frac{4 \sqrt{2} \sqrt{2 x^4+2 x^2+1} x}{45 \left(\sqrt{2} x^2+1\right)}-\frac{4 \sqrt{2 x^4+2 x^2+1}}{45 x}+\frac{4 \sqrt{2 x^4+2 x^2+1}}{135 x^3}-\frac{\sqrt{2 x^4+2 x^2+1}}{15 x^5}-\frac{2}{27} \sqrt{\frac{5}{3}} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)-\frac{\sqrt[4]{2} \left(19-2 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{135 \sqrt{2 x^4+2 x^2+1}}+\frac{5 \sqrt[4]{2} \left(5-3 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{189 \sqrt{2 x^4+2 x^2+1}}-\frac{4 \sqrt[4]{2} \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{45 \sqrt{2 x^4+2 x^2+1}}+\frac{5 \left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{567 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}",1,"-Sqrt[1 + 2*x^2 + 2*x^4]/(15*x^5) + (4*Sqrt[1 + 2*x^2 + 2*x^4])/(135*x^3) - (4*Sqrt[1 + 2*x^2 + 2*x^4])/(45*x) + (4*Sqrt[2]*x*Sqrt[1 + 2*x^2 + 2*x^4])/(45*(1 + Sqrt[2]*x^2)) - (2*Sqrt[5/3]*ArcTan[(Sqrt[5/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]])/27 - (4*2^(1/4)*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(45*Sqrt[1 + 2*x^2 + 2*x^4]) + (5*2^(1/4)*(5 - 3*Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(189*Sqrt[1 + 2*x^2 + 2*x^4]) - (2^(1/4)*(19 - 2*Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(135*Sqrt[1 + 2*x^2 + 2*x^4]) + (5*(3 + Sqrt[2])^2*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 - 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(567*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4])","A",13,9,29,0.3103,1,"{1309, 1281, 1197, 1103, 1195, 1329, 1714, 1708, 1706}"
322,1,482,0,1.1029285,"\int \frac{x^5 \left(a+b x^2+c x^4\right)^{3/2}}{d+e x^2} \, dx","Int[(x^5*(a + b*x^2 + c*x^4)^(3/2))/(d + e*x^2),x]","-\frac{\left(16 b c^2 e^3 \left(3 a^2 e^2-3 a b d e+b^2 d^2\right)+6 b^3 c e^4 (b d-4 a e)-384 c^4 d^3 e (b d-a e)+96 c^3 d e^2 (b d-a e)^2+3 b^5 e^5+256 c^5 d^5\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{512 c^{7/2} e^6}+\frac{\left(a+b x^2+c x^4\right)^{3/2} \left(-3 b^2 e^2-6 c e x^2 (b e+2 c d)-6 b c d e+16 c^2 d^2\right)}{96 c^2 e^3}+\frac{\sqrt{a+b x^2+c x^4} \left(-2 c e x^2 \left(-8 c^2 d e (2 b d-3 a e)-6 b c e^2 (b d-2 a e)-3 b^3 e^3+32 c^3 d^3\right)+6 b^2 c e^3 (b d-2 a e)-32 c^3 d^2 e (5 b d-4 a e)+8 b c^2 d e^2 (2 b d-3 a e)+3 b^4 e^4+128 c^4 d^4\right)}{256 c^3 e^5}+\frac{d^2 \left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e^6}+\frac{\left(a+b x^2+c x^4\right)^{5/2}}{10 c e}","-\frac{\left(16 b c^2 e^3 \left(3 a^2 e^2-3 a b d e+b^2 d^2\right)+6 b^3 c e^4 (b d-4 a e)-384 c^4 d^3 e (b d-a e)+96 c^3 d e^2 (b d-a e)^2+3 b^5 e^5+256 c^5 d^5\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{512 c^{7/2} e^6}+\frac{\left(a+b x^2+c x^4\right)^{3/2} \left(-3 b^2 e^2-6 c e x^2 (b e+2 c d)-6 b c d e+16 c^2 d^2\right)}{96 c^2 e^3}+\frac{\sqrt{a+b x^2+c x^4} \left(-2 c e x^2 \left(-8 c^2 d e (2 b d-3 a e)-6 b c e^2 (b d-2 a e)-3 b^3 e^3+32 c^3 d^3\right)+6 b^2 c e^3 (b d-2 a e)-32 c^3 d^2 e (5 b d-4 a e)+8 b c^2 d e^2 (2 b d-3 a e)+3 b^4 e^4+128 c^4 d^4\right)}{256 c^3 e^5}+\frac{d^2 \left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e^6}+\frac{\left(a+b x^2+c x^4\right)^{5/2}}{10 c e}",1,"((128*c^4*d^4 + 3*b^4*e^4 - 32*c^3*d^2*e*(5*b*d - 4*a*e) + 8*b*c^2*d*e^2*(2*b*d - 3*a*e) + 6*b^2*c*e^3*(b*d - 2*a*e) - 2*c*e*(32*c^3*d^3 - 3*b^3*e^3 - 8*c^2*d*e*(2*b*d - 3*a*e) - 6*b*c*e^2*(b*d - 2*a*e))*x^2)*Sqrt[a + b*x^2 + c*x^4])/(256*c^3*e^5) + ((16*c^2*d^2 - 6*b*c*d*e - 3*b^2*e^2 - 6*c*e*(2*c*d + b*e)*x^2)*(a + b*x^2 + c*x^4)^(3/2))/(96*c^2*e^3) + (a + b*x^2 + c*x^4)^(5/2)/(10*c*e) - ((256*c^5*d^5 + 3*b^5*e^5 + 6*b^3*c*e^4*(b*d - 4*a*e) - 384*c^4*d^3*e*(b*d - a*e) + 96*c^3*d*e^2*(b*d - a*e)^2 + 16*b*c^2*e^3*(b^2*d^2 - 3*a*b*d*e + 3*a^2*e^2))*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(512*c^(7/2)*e^6) + (d^2*(c*d^2 - b*d*e + a*e^2)^(3/2)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])])/(2*e^6)","A",9,7,29,0.2414,1,"{1251, 1653, 814, 843, 621, 206, 724}"
323,1,360,0,0.6967598,"\int \frac{x^3 \left(a+b x^2+c x^4\right)^{3/2}}{d+e x^2} \, dx","Int[(x^3*(a + b*x^2 + c*x^4)^(3/2))/(d + e*x^2),x]","-\frac{\sqrt{a+b x^2+c x^4} \left(-2 c e x^2 \left(-4 c e (2 b d-3 a e)-3 b^2 e^2+16 c^2 d^2\right)-16 c^2 d e (5 b d-4 a e)+4 b c e^2 (2 b d-3 a e)+3 b^3 e^3+64 c^3 d^3\right)}{128 c^2 e^4}+\frac{\left(8 b^2 c e^3 (b d-3 a e)-192 c^3 d^2 e (b d-a e)+48 c^2 e^2 (b d-a e)^2+3 b^4 e^4+128 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{256 c^{5/2} e^5}-\frac{d \left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e^5}-\frac{\left(a+b x^2+c x^4\right)^{3/2} \left(-3 b e+8 c d-6 c e x^2\right)}{48 c e^2}","-\frac{\sqrt{a+b x^2+c x^4} \left(-2 c e x^2 \left(-4 c e (2 b d-3 a e)-3 b^2 e^2+16 c^2 d^2\right)-16 c^2 d e (5 b d-4 a e)+4 b c e^2 (2 b d-3 a e)+3 b^3 e^3+64 c^3 d^3\right)}{128 c^2 e^4}+\frac{\left(8 b^2 c e^3 (b d-3 a e)-192 c^3 d^2 e (b d-a e)+48 c^2 e^2 (b d-a e)^2+3 b^4 e^4+128 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{256 c^{5/2} e^5}-\frac{d \left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e^5}-\frac{\left(a+b x^2+c x^4\right)^{3/2} \left(-3 b e+8 c d-6 c e x^2\right)}{48 c e^2}",1,"-((64*c^3*d^3 + 3*b^3*e^3 - 16*c^2*d*e*(5*b*d - 4*a*e) + 4*b*c*e^2*(2*b*d - 3*a*e) - 2*c*e*(16*c^2*d^2 - 3*b^2*e^2 - 4*c*e*(2*b*d - 3*a*e))*x^2)*Sqrt[a + b*x^2 + c*x^4])/(128*c^2*e^4) - ((8*c*d - 3*b*e - 6*c*e*x^2)*(a + b*x^2 + c*x^4)^(3/2))/(48*c*e^2) + ((128*c^4*d^4 + 3*b^4*e^4 + 8*b^2*c*e^3*(b*d - 3*a*e) - 192*c^3*d^2*e*(b*d - a*e) + 48*c^2*e^2*(b*d - a*e)^2)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(256*c^(5/2)*e^5) - (d*(c*d^2 - b*d*e + a*e^2)^(3/2)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])])/(2*e^5)","A",8,6,29,0.2069,1,"{1251, 814, 843, 621, 206, 724}"
324,1,269,0,0.4555488,"\int \frac{x \left(a+b x^2+c x^4\right)^{3/2}}{d+e x^2} \, dx","Int[(x*(a + b*x^2 + c*x^4)^(3/2))/(d + e*x^2),x]","\frac{\sqrt{a+b x^2+c x^4} \left(-2 c e (5 b d-4 a e)+b^2 e^2-2 c e x^2 (2 c d-b e)+8 c^2 d^2\right)}{16 c e^3}-\frac{(2 c d-b e) \left(-4 c e (2 b d-3 a e)-b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{32 c^{3/2} e^4}+\frac{\left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e^4}+\frac{\left(a+b x^2+c x^4\right)^{3/2}}{6 e}","\frac{\sqrt{a+b x^2+c x^4} \left(-2 c e (5 b d-4 a e)+b^2 e^2-2 c e x^2 (2 c d-b e)+8 c^2 d^2\right)}{16 c e^3}-\frac{(2 c d-b e) \left(-4 c e (2 b d-3 a e)-b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{32 c^{3/2} e^4}+\frac{\left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e^4}+\frac{\left(a+b x^2+c x^4\right)^{3/2}}{6 e}",1,"((8*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 4*a*e) - 2*c*e*(2*c*d - b*e)*x^2)*Sqrt[a + b*x^2 + c*x^4])/(16*c*e^3) + (a + b*x^2 + c*x^4)^(3/2)/(6*e) - ((2*c*d - b*e)*(8*c^2*d^2 - b^2*e^2 - 4*c*e*(2*b*d - 3*a*e))*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(32*c^(3/2)*e^4) + ((c*d^2 - b*d*e + a*e^2)^(3/2)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])])/(2*e^4)","A",8,7,27,0.2593,1,"{1247, 734, 814, 843, 621, 206, 724}"
325,1,350,0,0.5732229,"\int \frac{\left(a+b x^2+c x^4\right)^{3/2}}{x \left(d+e x^2\right)} \, dx","Int[(a + b*x^2 + c*x^4)^(3/2)/(x*(d + e*x^2)),x]","-\frac{a^{3/2} \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 d}+\frac{\left(-12 c d e (b d-a e)+b e^2 (3 b d-4 a e)+8 c^2 d^3\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{16 \sqrt{c} d e^3}-\frac{\sqrt{a+b x^2+c x^4} \left(-e (5 b d-4 a e)+4 c d^2-2 c d e x^2\right)}{8 d e^2}-\frac{\left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 d e^3}+\frac{a \sqrt{a+b x^2+c x^4}}{2 d}+\frac{a b \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 \sqrt{c} d}","-\frac{a^{3/2} \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 d}+\frac{\left(-12 c d e (b d-a e)+b e^2 (3 b d-4 a e)+8 c^2 d^3\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{16 \sqrt{c} d e^3}-\frac{\sqrt{a+b x^2+c x^4} \left(-e (5 b d-4 a e)+4 c d^2-2 c d e x^2\right)}{8 d e^2}-\frac{\left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 d e^3}+\frac{a \sqrt{a+b x^2+c x^4}}{2 d}+\frac{a b \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 \sqrt{c} d}",1,"(a*Sqrt[a + b*x^2 + c*x^4])/(2*d) - ((4*c*d^2 - e*(5*b*d - 4*a*e) - 2*c*d*e*x^2)*Sqrt[a + b*x^2 + c*x^4])/(8*d*e^2) - (a^(3/2)*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(2*d) + (a*b*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(4*Sqrt[c]*d) + ((8*c^2*d^3 + b*e^2*(3*b*d - 4*a*e) - 12*c*d*e*(b*d - a*e))*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(16*Sqrt[c]*d*e^3) - ((c*d^2 - b*d*e + a*e^2)^(3/2)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])])/(2*d*e^3)","A",14,8,29,0.2759,1,"{1251, 895, 734, 843, 621, 206, 724, 814}"
326,1,562,0,0.9239261,"\int \frac{\left(a+b x^2+c x^4\right)^{3/2}}{x^3 \left(d+e x^2\right)} \, dx","Int[(a + b*x^2 + c*x^4)^(3/2)/(x^3*(d + e*x^2)),x]","\frac{a^{3/2} e \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 d^2}+\frac{\sqrt{a+b x^2+c x^4} \left(-2 c e (5 b d-4 a e)+b^2 e^2-2 c e x^2 (2 c d-b e)+8 c^2 d^2\right)}{16 c d^2 e}-\frac{(2 c d-b e) \left(-4 c e (2 b d-3 a e)-b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{32 c^{3/2} d^2 e^2}+\frac{b e \left(b^2-12 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{32 c^{3/2} d^2}-\frac{e \left(8 a c+b^2+2 b c x^2\right) \sqrt{a+b x^2+c x^4}}{16 c d^2}+\frac{3 \left(4 a c+b^2\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{16 \sqrt{c} d}+\frac{\left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 d^2 e^2}-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{2 d x^2}+\frac{3 \left(3 b+2 c x^2\right) \sqrt{a+b x^2+c x^4}}{8 d}-\frac{3 \sqrt{a} b \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{4 d}","\frac{a^{3/2} e \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 d^2}+\frac{\sqrt{a+b x^2+c x^4} \left(-2 c e (5 b d-4 a e)+b^2 e^2-2 c e x^2 (2 c d-b e)+8 c^2 d^2\right)}{16 c d^2 e}-\frac{(2 c d-b e) \left(-4 c e (2 b d-3 a e)-b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{32 c^{3/2} d^2 e^2}+\frac{b e \left(b^2-12 a c\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{32 c^{3/2} d^2}-\frac{e \left(8 a c+b^2+2 b c x^2\right) \sqrt{a+b x^2+c x^4}}{16 c d^2}+\frac{3 \left(4 a c+b^2\right) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{16 \sqrt{c} d}+\frac{\left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 d^2 e^2}-\frac{\left(a+b x^2+c x^4\right)^{3/2}}{2 d x^2}+\frac{3 \left(3 b+2 c x^2\right) \sqrt{a+b x^2+c x^4}}{8 d}-\frac{3 \sqrt{a} b \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{4 d}",1,"(3*(3*b + 2*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(8*d) - (e*(b^2 + 8*a*c + 2*b*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(16*c*d^2) + ((8*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 4*a*e) - 2*c*e*(2*c*d - b*e)*x^2)*Sqrt[a + b*x^2 + c*x^4])/(16*c*d^2*e) - (a + b*x^2 + c*x^4)^(3/2)/(2*d*x^2) - (3*Sqrt[a]*b*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(4*d) + (a^(3/2)*e*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(2*d^2) + (3*(b^2 + 4*a*c)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(16*Sqrt[c]*d) + (b*(b^2 - 12*a*c)*e*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(32*c^(3/2)*d^2) - ((2*c*d - b*e)*(8*c^2*d^2 - b^2*e^2 - 4*c*e*(2*b*d - 3*a*e))*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(32*c^(3/2)*d^2*e^2) + ((c*d^2 - b*d*e + a*e^2)^(3/2)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])])/(2*d^2*e^2)","A",24,9,29,0.3103,1,"{1251, 960, 732, 814, 843, 621, 206, 724, 734}"
327,1,875,0,0.6718205,"\int \frac{x^2 \left(1+2 x^2+2 x^4\right)^{3/2}}{3-2 x^2} \, dx","Int[(x^2*(1 + 2*x^2 + 2*x^4)^(3/2))/(3 - 2*x^2),x]","-\frac{1}{14} x \left(2 x^4+2 x^2+1\right)^{3/2}-\frac{3}{35} x \left(x^2+2\right) \sqrt{2 x^4+2 x^2+1}-\frac{3}{20} x \left(2 x^2+9\right) \sqrt{2 x^4+2 x^2+1}-\frac{6 \sqrt{2} x \sqrt{2 x^4+2 x^2+1}}{35 \left(\sqrt{2} x^2+1\right)}-\frac{309 x \sqrt{2 x^4+2 x^2+1}}{20 \sqrt{2} \left(\sqrt{2} x^2+1\right)}+\frac{17}{16} \sqrt{51} \tanh ^{-1}\left(\frac{\sqrt{\frac{17}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)+\frac{6 \sqrt[4]{2} \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{35 \sqrt{2 x^4+2 x^2+1}}+\frac{309 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{20\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{3 \left(9+8 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{20\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{3 \left(3+2 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{70 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}-\frac{51 \left(5+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{16 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}+\frac{867 \left(3-\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{112 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}-\frac{289 \left(11-6 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12+11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{224 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}","-\frac{27}{70} \sqrt{2 x^4+2 x^2+1} x^3-\frac{1}{14} \left(2 x^4+2 x^2+1\right)^{3/2} x-\frac{2211 \sqrt{2 x^4+2 x^2+1} x}{140 \sqrt{2} \left(\sqrt{2} x^2+1\right)}-\frac{213}{140} \sqrt{2 x^4+2 x^2+1} x+\frac{17}{16} \sqrt{51} \tanh ^{-1}\left(\frac{\sqrt{\frac{17}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)-\frac{3 \left(514+2717 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{140\ 2^{3/4} \left(2+3 \sqrt{2}\right) \sqrt{2 x^4+2 x^2+1}}+\frac{2211 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{140\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{289 \left(3-\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12+11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{16\ 2^{3/4} \left(2+3 \sqrt{2}\right) \sqrt{2 x^4+2 x^2+1}}",1,"(-3*x*(2 + x^2)*Sqrt[1 + 2*x^2 + 2*x^4])/35 - (3*x*(9 + 2*x^2)*Sqrt[1 + 2*x^2 + 2*x^4])/20 - (309*x*Sqrt[1 + 2*x^2 + 2*x^4])/(20*Sqrt[2]*(1 + Sqrt[2]*x^2)) - (6*Sqrt[2]*x*Sqrt[1 + 2*x^2 + 2*x^4])/(35*(1 + Sqrt[2]*x^2)) - (x*(1 + 2*x^2 + 2*x^4)^(3/2))/14 + (17*Sqrt[51]*ArcTanh[(Sqrt[17/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]])/16 + (309*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(20*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + (6*2^(1/4)*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(35*Sqrt[1 + 2*x^2 + 2*x^4]) + (867*(3 - Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(112*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - (51*(5 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(16*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - (3*(3 + 2*Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(70*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - (3*(9 + 8*Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(20*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - (289*(11 - 6*Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 + 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(224*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4])","A",19,9,29,0.3103,1,"{1335, 1091, 1176, 1197, 1103, 1195, 1208, 1216, 1706}"
328,1,602,0,0.3489607,"\int \frac{\left(1+2 x^2+2 x^4\right)^{3/2}}{3-2 x^2} \, dx","Int[(1 + 2*x^2 + 2*x^4)^(3/2)/(3 - 2*x^2),x]","-\frac{1}{10} \left(2 x^2+9\right) \sqrt{2 x^4+2 x^2+1} x-\frac{103 \sqrt{2 x^4+2 x^2+1} x}{10 \sqrt{2} \left(\sqrt{2} x^2+1\right)}+\frac{17}{8} \sqrt{\frac{17}{3}} \tanh ^{-1}\left(\frac{\sqrt{\frac{17}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)-\frac{\left(9+8 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{10\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{17 \left(5+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{8 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}+\frac{289 \left(3-\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{56 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}+\frac{103 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{10\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{289 \left(11-6 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12+11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{336 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}","-\frac{1}{10} \left(2 x^2+9\right) \sqrt{2 x^4+2 x^2+1} x-\frac{103 \sqrt{2 x^4+2 x^2+1} x}{10 \sqrt{2} \left(\sqrt{2} x^2+1\right)}+\frac{17}{8} \sqrt{\frac{17}{3}} \tanh ^{-1}\left(\frac{\sqrt{\frac{17}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)-\frac{\left(66+383 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{10\ 2^{3/4} \left(2+3 \sqrt{2}\right) \sqrt{2 x^4+2 x^2+1}}+\frac{103 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{10\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{289 \left(3-\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12+11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{24\ 2^{3/4} \left(2+3 \sqrt{2}\right) \sqrt{2 x^4+2 x^2+1}}",1,"-(x*(9 + 2*x^2)*Sqrt[1 + 2*x^2 + 2*x^4])/10 - (103*x*Sqrt[1 + 2*x^2 + 2*x^4])/(10*Sqrt[2]*(1 + Sqrt[2]*x^2)) + (17*Sqrt[17/3]*ArcTanh[(Sqrt[17/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]])/8 + (103*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(10*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + (289*(3 - Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(56*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - (17*(5 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(8*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - ((9 + 8*Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(10*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - (289*(11 - 6*Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 + 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(336*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4])","A",12,7,26,0.2692,1,"{1208, 1176, 1197, 1103, 1195, 1216, 1706}"
329,1,722,0,0.3684268,"\int \frac{\left(1+2 x^2+2 x^4\right)^{3/2}}{x^2 \left(3-2 x^2\right)} \, dx","Int[(1 + 2*x^2 + 2*x^4)^(3/2)/(x^2*(3 - 2*x^2)),x]","\frac{\sqrt{2} \sqrt{2 x^4+2 x^2+1} x}{3 \left(\sqrt{2} x^2+1\right)}-\frac{17 \sqrt{2 x^4+2 x^2+1} x}{3 \sqrt{2} \left(\sqrt{2} x^2+1\right)}-\frac{\left(x^2+1\right) \sqrt{2 x^4+2 x^2+1}}{3 x}+\frac{17}{12} \sqrt{\frac{17}{3}} \tanh ^{-1}\left(\frac{\sqrt{\frac{17}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)-\frac{17 \left(5+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{12 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}+\frac{289 \left(3-\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{84 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}+\frac{\left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{3\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{\sqrt[4]{2} \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{3 \sqrt{2 x^4+2 x^2+1}}+\frac{17 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{3\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{289 \left(11-6 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12+11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{504 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}","\frac{\sqrt{2} \sqrt{2 x^4+2 x^2+1} x}{3 \left(\sqrt{2} x^2+1\right)}-\frac{17 \sqrt{2 x^4+2 x^2+1} x}{3 \sqrt{2} \left(\sqrt{2} x^2+1\right)}-\frac{\left(x^2+1\right) \sqrt{2 x^4+2 x^2+1}}{3 x}+\frac{17}{12} \sqrt{\frac{17}{3}} \tanh ^{-1}\left(\frac{\sqrt{\frac{17}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)-\frac{17 \left(5+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{12 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}+\frac{289 \left(3-\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{84 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}+\frac{\left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{3\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{\sqrt[4]{2} \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{3 \sqrt{2 x^4+2 x^2+1}}+\frac{17 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{3\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{289 \left(11-6 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12+11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{504 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}",1,"-((1 + x^2)*Sqrt[1 + 2*x^2 + 2*x^4])/(3*x) - (17*x*Sqrt[1 + 2*x^2 + 2*x^4])/(3*Sqrt[2]*(1 + Sqrt[2]*x^2)) + (Sqrt[2]*x*Sqrt[1 + 2*x^2 + 2*x^4])/(3*(1 + Sqrt[2]*x^2)) + (17*Sqrt[17/3]*ArcTanh[(Sqrt[17/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]])/12 + (17*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(3*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - (2^(1/4)*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(3*Sqrt[1 + 2*x^2 + 2*x^4]) + ((1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(3*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + (289*(3 - Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(84*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - (17*(5 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(12*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - (289*(11 - 6*Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 + 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(504*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4])","A",13,10,29,0.3448,1,"{1311, 1271, 12, 1139, 1103, 1195, 1208, 1197, 1216, 1706}"
330,1,625,0,0.366185,"\int \frac{\left(1+2 x^2+2 x^4\right)^{3/2}}{x^4 \left(3-2 x^2\right)} \, dx","Int[(1 + 2*x^2 + 2*x^4)^(3/2)/(x^4*(3 - 2*x^2)),x]","\frac{\sqrt{2} \sqrt{2 x^4+2 x^2+1} x}{9 \left(\sqrt{2} x^2+1\right)}-\frac{2 \sqrt{2 x^4+2 x^2+1}}{x}-\frac{\left(1-8 x^2\right) \sqrt{2 x^4+2 x^2+1}}{9 x^3}+\frac{17}{18} \sqrt{\frac{17}{3}} \tanh ^{-1}\left(\frac{\sqrt{\frac{17}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)+\frac{\sqrt[4]{2} \left(9+5 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{9 \sqrt{2 x^4+2 x^2+1}}-\frac{17 \left(5+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{18 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}+\frac{289 \left(3-\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{126 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}-\frac{\sqrt[4]{2} \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{9 \sqrt{2 x^4+2 x^2+1}}-\frac{289 \left(11-6 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12+11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{756 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}","\frac{\sqrt{2} \sqrt{2 x^4+2 x^2+1} x}{9 \left(\sqrt{2} x^2+1\right)}-\frac{2 \sqrt{2 x^4+2 x^2+1}}{x}-\frac{\left(1-8 x^2\right) \sqrt{2 x^4+2 x^2+1}}{9 x^3}+\frac{17}{18} \sqrt{\frac{17}{3}} \tanh ^{-1}\left(\frac{\sqrt{\frac{17}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)+\frac{\sqrt[4]{2} \left(9+5 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{9 \sqrt{2 x^4+2 x^2+1}}-\frac{17 \left(5+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{18 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}+\frac{289 \left(3-\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{126 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}-\frac{\sqrt[4]{2} \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{9 \sqrt{2 x^4+2 x^2+1}}-\frac{289 \left(11-6 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12+11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{756 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}",1,"(-2*Sqrt[1 + 2*x^2 + 2*x^4])/x - ((1 - 8*x^2)*Sqrt[1 + 2*x^2 + 2*x^4])/(9*x^3) + (Sqrt[2]*x*Sqrt[1 + 2*x^2 + 2*x^4])/(9*(1 + Sqrt[2]*x^2)) + (17*Sqrt[17/3]*ArcTanh[(Sqrt[17/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]])/18 - (2^(1/4)*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(9*Sqrt[1 + 2*x^2 + 2*x^4]) + (289*(3 - Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(126*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - (17*(5 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(18*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + (2^(1/4)*(9 + 5*Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(9*Sqrt[1 + 2*x^2 + 2*x^4]) - (289*(11 - 6*Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 + 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(756*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4])","A",13,9,29,0.3103,1,"{1309, 1271, 1281, 1197, 1103, 1195, 1208, 1216, 1706}"
331,1,553,0,0.4877373,"\int \frac{\left(1+2 x^2+2 x^4\right)^{3/2}}{x^6 \left(3-2 x^2\right)} \, dx","Int[(1 + 2*x^2 + 2*x^4)^(3/2)/(x^6*(3 - 2*x^2)),x]","\frac{262 \sqrt{2} \sqrt{2 x^4+2 x^2+1} x}{135 \left(\sqrt{2} x^2+1\right)}-\frac{262 \sqrt{2 x^4+2 x^2+1}}{135 x}+\frac{74 \sqrt{2 x^4+2 x^2+1}}{135 x^3}-\frac{\left(40 x^2+3\right) \sqrt{2 x^4+2 x^2+1}}{45 x^5}+\frac{17}{27} \sqrt{\frac{17}{3}} \tanh ^{-1}\left(\frac{\sqrt{\frac{17}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)+\frac{2^{3/4} \left(37+23 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{135 \sqrt{2 x^4+2 x^2+1}}+\frac{85\ 2^{3/4} \left(3-\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{189 \sqrt{2 x^4+2 x^2+1}}-\frac{262 \sqrt[4]{2} \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{135 \sqrt{2 x^4+2 x^2+1}}-\frac{289 \left(11-6 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12+11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{1134 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}","\frac{262 \sqrt{2} \sqrt{2 x^4+2 x^2+1} x}{135 \left(\sqrt{2} x^2+1\right)}-\frac{262 \sqrt{2 x^4+2 x^2+1}}{135 x}+\frac{74 \sqrt{2 x^4+2 x^2+1}}{135 x^3}-\frac{\left(40 x^2+3\right) \sqrt{2 x^4+2 x^2+1}}{45 x^5}+\frac{17}{27} \sqrt{\frac{17}{3}} \tanh ^{-1}\left(\frac{\sqrt{\frac{17}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)+\frac{2^{3/4} \left(37+23 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{135 \sqrt{2 x^4+2 x^2+1}}+\frac{85\ 2^{3/4} \left(3-\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{189 \sqrt{2 x^4+2 x^2+1}}-\frac{262 \sqrt[4]{2} \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{135 \sqrt{2 x^4+2 x^2+1}}-\frac{289 \left(11-6 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12+11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{1134 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}",1,"(74*Sqrt[1 + 2*x^2 + 2*x^4])/(135*x^3) - (262*Sqrt[1 + 2*x^2 + 2*x^4])/(135*x) - ((3 + 40*x^2)*Sqrt[1 + 2*x^2 + 2*x^4])/(45*x^5) + (262*Sqrt[2]*x*Sqrt[1 + 2*x^2 + 2*x^4])/(135*(1 + Sqrt[2]*x^2)) + (17*Sqrt[17/3]*ArcTanh[(Sqrt[17/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]])/27 - (262*2^(1/4)*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(135*Sqrt[1 + 2*x^2 + 2*x^4]) + (85*2^(3/4)*(3 - Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(189*Sqrt[1 + 2*x^2 + 2*x^4]) + (2^(3/4)*(37 + 23*Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(135*Sqrt[1 + 2*x^2 + 2*x^4]) - (289*(11 - 6*Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 + 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(1134*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4])","A",15,9,29,0.3103,1,"{1309, 1271, 1281, 1197, 1103, 1195, 1311, 1216, 1706}"
332,1,173,0,0.3137395,"\int \frac{x^5}{\left(d+e x^2\right) \sqrt{a+b x^2+c x^4}} \, dx","Int[x^5/((d + e*x^2)*Sqrt[a + b*x^2 + c*x^4]),x]","-\frac{(b e+2 c d) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 c^{3/2} e^2}+\frac{d^2 \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e^2 \sqrt{a e^2-b d e+c d^2}}+\frac{\sqrt{a+b x^2+c x^4}}{2 c e}","-\frac{(b e+2 c d) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 c^{3/2} e^2}+\frac{d^2 \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e^2 \sqrt{a e^2-b d e+c d^2}}+\frac{\sqrt{a+b x^2+c x^4}}{2 c e}",1,"Sqrt[a + b*x^2 + c*x^4]/(2*c*e) - ((2*c*d + b*e)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(4*c^(3/2)*e^2) + (d^2*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])])/(2*e^2*Sqrt[c*d^2 - b*d*e + a*e^2])","A",7,6,29,0.2069,1,"{1251, 1653, 843, 621, 206, 724}"
333,1,137,0,0.157354,"\int \frac{x^3}{\left(d+e x^2\right) \sqrt{a+b x^2+c x^4}} \, dx","Int[x^3/((d + e*x^2)*Sqrt[a + b*x^2 + c*x^4]),x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{c} e}-\frac{d \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e \sqrt{a e^2-b d e+c d^2}}","\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{c} e}-\frac{d \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e \sqrt{a e^2-b d e+c d^2}}",1,"ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])]/(2*Sqrt[c]*e) - (d*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])])/(2*e*Sqrt[c*d^2 - b*d*e + a*e^2])","A",6,5,29,0.1724,1,"{1251, 843, 621, 206, 724}"
334,1,86,0,0.0836072,"\int \frac{x}{\left(d+e x^2\right) \sqrt{a+b x^2+c x^4}} \, dx","Int[x/((d + e*x^2)*Sqrt[a + b*x^2 + c*x^4]),x]","\frac{\tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 \sqrt{a e^2-b d e+c d^2}}","\frac{\tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 \sqrt{a e^2-b d e+c d^2}}",1,"ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])]/(2*Sqrt[c*d^2 - b*d*e + a*e^2])","A",3,3,27,0.1111,1,"{1247, 724, 206}"
335,1,138,0,0.1947223,"\int \frac{1}{x \left(d+e x^2\right) \sqrt{a+b x^2+c x^4}} \, dx","Int[1/(x*(d + e*x^2)*Sqrt[a + b*x^2 + c*x^4]),x]","-\frac{e \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 d \sqrt{a e^2-b d e+c d^2}}-\frac{\tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{a} d}","-\frac{e \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 d \sqrt{a e^2-b d e+c d^2}}-\frac{\tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{a} d}",1,"-ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])]/(2*Sqrt[a]*d) - (e*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])])/(2*d*Sqrt[c*d^2 - b*d*e + a*e^2])","A",7,4,29,0.1379,1,"{1251, 960, 724, 206}"
336,1,218,0,0.2660958,"\int \frac{1}{x^3 \left(d+e x^2\right) \sqrt{a+b x^2+c x^4}} \, dx","Int[1/(x^3*(d + e*x^2)*Sqrt[a + b*x^2 + c*x^4]),x]","\frac{b \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{4 a^{3/2} d}+\frac{e^2 \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 d^2 \sqrt{a e^2-b d e+c d^2}}+\frac{e \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{a} d^2}-\frac{\sqrt{a+b x^2+c x^4}}{2 a d x^2}","\frac{b \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{4 a^{3/2} d}+\frac{e^2 \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 d^2 \sqrt{a e^2-b d e+c d^2}}+\frac{e \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 \sqrt{a} d^2}-\frac{\sqrt{a+b x^2+c x^4}}{2 a d x^2}",1,"-Sqrt[a + b*x^2 + c*x^4]/(2*a*d*x^2) + (b*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(4*a^(3/2)*d) + (e*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(2*Sqrt[a]*d^2) + (e^2*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])])/(2*d^2*Sqrt[c*d^2 - b*d*e + a*e^2])","A",10,5,29,0.1724,1,"{1251, 960, 730, 724, 206}"
337,1,418,0,0.1842037,"\int \frac{x^4}{\left(3+2 x^2\right) \sqrt{1+2 x^2+2 x^4}} \, dx","Int[x^4/((3 + 2*x^2)*Sqrt[1 + 2*x^2 + 2*x^4]),x]","\frac{\sqrt{2 x^4+2 x^2+1} x}{2 \sqrt{2} \left(\sqrt{2} x^2+1\right)}-\frac{3 \sqrt{\frac{3}{10}} \left(3-\sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)}{4 \left(2-3 \sqrt{2}\right)}+\frac{\left(1-3 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{2\ 2^{3/4} \left(2-3 \sqrt{2}\right) \sqrt{2 x^4+2 x^2+1}}-\frac{\left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{2\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}+\frac{3 \left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{8\ 2^{3/4} \left(2-3 \sqrt{2}\right) \sqrt{2 x^4+2 x^2+1}}","\frac{\sqrt{2 x^4+2 x^2+1} x}{2 \sqrt{2} \left(\sqrt{2} x^2+1\right)}-\frac{3 \sqrt{\frac{3}{10}} \left(3-\sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)}{4 \left(2-3 \sqrt{2}\right)}+\frac{\left(1-3 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{2\ 2^{3/4} \left(2-3 \sqrt{2}\right) \sqrt{2 x^4+2 x^2+1}}-\frac{\left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{2\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}+\frac{3 \left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{8\ 2^{3/4} \left(2-3 \sqrt{2}\right) \sqrt{2 x^4+2 x^2+1}}",1,"(x*Sqrt[1 + 2*x^2 + 2*x^4])/(2*Sqrt[2]*(1 + Sqrt[2]*x^2)) - (3*Sqrt[3/10]*(3 - Sqrt[2])*ArcTan[(Sqrt[5/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]])/(4*(2 - 3*Sqrt[2])) - ((1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(2*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + ((1 - 3*Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(2*2^(3/4)*(2 - 3*Sqrt[2])*Sqrt[1 + 2*x^2 + 2*x^4]) + (3*(3 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 - 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(8*2^(3/4)*(2 - 3*Sqrt[2])*Sqrt[1 + 2*x^2 + 2*x^4])","A",4,4,29,0.1379,1,"{1325, 1103, 1195, 1706}"
338,1,247,0,0.1258263,"\int \frac{x^2}{\left(3+2 x^2\right) \sqrt{1+2 x^2+2 x^4}} \, dx","Int[x^2/((3 + 2*x^2)*Sqrt[1 + 2*x^2 + 2*x^4]),x]","-\frac{1}{4} \sqrt{\frac{3}{5}} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)-\frac{\left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{14\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}+\frac{\left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{56 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}","-\frac{1}{4} \sqrt{\frac{3}{5}} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)-\frac{\left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{14\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}+\frac{\left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{56 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}",1,"-(Sqrt[3/5]*ArcTan[(Sqrt[5/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]])/4 - ((3 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(14*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + ((3 + Sqrt[2])^2*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 - 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(56*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4])","A",3,3,29,0.1034,1,"{1319, 1103, 1706}"
339,1,245,0,0.1105875,"\int \frac{1}{\left(3+2 x^2\right) \sqrt{1+2 x^2+2 x^4}} \, dx","Int[1/((3 + 2*x^2)*Sqrt[1 + 2*x^2 + 2*x^4]),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)}{2 \sqrt{15}}+\frac{\left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{14 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}-\frac{\left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{84 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}","\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)}{2 \sqrt{15}}+\frac{\left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{14 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}-\frac{\left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{84 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}",1,"ArcTan[(Sqrt[5/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]]/(2*Sqrt[15]) + ((3 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(14*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - ((3 + Sqrt[2])^2*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 - 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(84*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4])","A",3,3,26,0.1154,1,"{1216, 1103, 1706}"
340,1,399,0,0.3471788,"\int \frac{1}{x^2 \left(3+2 x^2\right) \sqrt{1+2 x^2+2 x^4}} \, dx","Int[1/(x^2*(3 + 2*x^2)*Sqrt[1 + 2*x^2 + 2*x^4]),x]","\frac{\sqrt{2} \sqrt{2 x^4+2 x^2+1} x}{3 \left(\sqrt{2} x^2+1\right)}-\frac{\sqrt{2 x^4+2 x^2+1}}{3 x}-\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)}{3 \sqrt{15}}+\frac{\left(5-3 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{21\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{\sqrt[4]{2} \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{3 \sqrt{2 x^4+2 x^2+1}}+\frac{\left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{126 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}","\frac{\sqrt{2} \sqrt{2 x^4+2 x^2+1} x}{3 \left(\sqrt{2} x^2+1\right)}-\frac{\sqrt{2 x^4+2 x^2+1}}{3 x}-\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)}{3 \sqrt{15}}+\frac{\left(5-3 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{21\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{\sqrt[4]{2} \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{3 \sqrt{2 x^4+2 x^2+1}}+\frac{\left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{126 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}",1,"-Sqrt[1 + 2*x^2 + 2*x^4]/(3*x) + (Sqrt[2]*x*Sqrt[1 + 2*x^2 + 2*x^4])/(3*(1 + Sqrt[2]*x^2)) - ArcTan[(Sqrt[5/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]]/(3*Sqrt[15]) - (2^(1/4)*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(3*Sqrt[1 + 2*x^2 + 2*x^4]) + ((5 - 3*Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(21*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + ((3 + Sqrt[2])^2*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 - 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(126*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4])","A",6,6,29,0.2069,1,"{1329, 1714, 1195, 1708, 1103, 1706}"
341,1,422,0,0.5170978,"\int \frac{1}{x^4 \left(3+2 x^2\right) \sqrt{1+2 x^2+2 x^4}} \, dx","Int[1/(x^4*(3 + 2*x^2)*Sqrt[1 + 2*x^2 + 2*x^4]),x]","-\frac{2 \sqrt{2} \sqrt{2 x^4+2 x^2+1} x}{3 \left(\sqrt{2} x^2+1\right)}+\frac{2 \sqrt{2 x^4+2 x^2+1}}{3 x}-\frac{\sqrt{2 x^4+2 x^2+1}}{9 x^3}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)}{9 \sqrt{15}}-\frac{\left(1+19 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{63 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}+\frac{2 \sqrt[4]{2} \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{3 \sqrt{2 x^4+2 x^2+1}}-\frac{\left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{189 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}","-\frac{2 \sqrt{2} \sqrt{2 x^4+2 x^2+1} x}{3 \left(\sqrt{2} x^2+1\right)}+\frac{2 \sqrt{2 x^4+2 x^2+1}}{3 x}-\frac{\sqrt{2 x^4+2 x^2+1}}{9 x^3}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)}{9 \sqrt{15}}-\frac{\left(1+19 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{63 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}+\frac{2 \sqrt[4]{2} \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{3 \sqrt{2 x^4+2 x^2+1}}-\frac{\left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{189 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}",1,"-Sqrt[1 + 2*x^2 + 2*x^4]/(9*x^3) + (2*Sqrt[1 + 2*x^2 + 2*x^4])/(3*x) - (2*Sqrt[2]*x*Sqrt[1 + 2*x^2 + 2*x^4])/(3*(1 + Sqrt[2]*x^2)) + (2*ArcTan[(Sqrt[5/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]])/(9*Sqrt[15]) + (2*2^(1/4)*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(3*Sqrt[1 + 2*x^2 + 2*x^4]) - ((1 + 19*Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(63*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - ((3 + Sqrt[2])^2*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 - 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(189*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4])","A",7,7,29,0.2414,1,"{1329, 1683, 1714, 1195, 1708, 1103, 1706}"
342,1,236,0,0.4736713,"\int \frac{x^7}{\left(d+e x^2\right) \left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[x^7/((d + e*x^2)*(a + b*x^2 + c*x^4)^(3/2)),x]","\frac{x^2 \left(2 a^2 c e-a b^2 e-3 a b c d+b^3 d\right)+a \left(-a b e-2 a c d+b^2 d\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4} \left(a e^2-b d e+c d^2\right)}+\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{2 c^{3/2} e}-\frac{d^3 \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e \left(a e^2-b d e+c d^2\right)^{3/2}}","\frac{x^2 \left(2 a^2 c e-a b^2 e-3 a b c d+b^3 d\right)+a \left(-a b e-2 a c d+b^2 d\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4} \left(a e^2-b d e+c d^2\right)}+\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{2 c^{3/2} e}-\frac{d^3 \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e \left(a e^2-b d e+c d^2\right)^{3/2}}",1,"(a*(b^2*d - 2*a*c*d - a*b*e) + (b^3*d - 3*a*b*c*d - a*b^2*e + 2*a^2*c*e)*x^2)/(c*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x^2 + c*x^4]) + ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])]/(2*c^(3/2)*e) - (d^3*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])])/(2*e*(c*d^2 - b*d*e + a*e^2)^(3/2))","A",7,6,29,0.2069,1,"{1251, 1646, 843, 621, 206, 724}"
343,1,167,0,0.294319,"\int \frac{x^5}{\left(d+e x^2\right) \left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[x^5/((d + e*x^2)*(a + b*x^2 + c*x^4)^(3/2)),x]","\frac{d^2 \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 \left(a e^2-b d e+c d^2\right)^{3/2}}-\frac{x^2 \left(-a b e-2 a c d+b^2 d\right)+a (b d-2 a e)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4} \left(a e^2-b d e+c d^2\right)}","\frac{d^2 \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 \left(a e^2-b d e+c d^2\right)^{3/2}}-\frac{x^2 \left(-a b e-2 a c d+b^2 d\right)+a (b d-2 a e)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4} \left(a e^2-b d e+c d^2\right)}",1,"-((a*(b*d - 2*a*e) + (b^2*d - 2*a*c*d - a*b*e)*x^2)/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x^2 + c*x^4])) + (d^2*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])])/(2*(c*d^2 - b*d*e + a*e^2)^(3/2))","A",5,5,29,0.1724,1,"{1251, 1646, 12, 724, 206}"
344,1,159,0,0.1911057,"\int \frac{x^3}{\left(d+e x^2\right) \left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[x^3/((d + e*x^2)*(a + b*x^2 + c*x^4)^(3/2)),x]","\frac{c x^2 (b d-2 a e)+a (2 c d-b e)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4} \left(a e^2-b d e+c d^2\right)}-\frac{d e \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 \left(a e^2-b d e+c d^2\right)^{3/2}}","\frac{c x^2 (b d-2 a e)+a (2 c d-b e)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4} \left(a e^2-b d e+c d^2\right)}-\frac{d e \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 \left(a e^2-b d e+c d^2\right)^{3/2}}",1,"(a*(2*c*d - b*e) + c*(b*d - 2*a*e)*x^2)/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x^2 + c*x^4]) - (d*e*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])])/(2*(c*d^2 - b*d*e + a*e^2)^(3/2))","A",5,5,29,0.1724,1,"{1251, 822, 12, 724, 206}"
345,1,166,0,0.1707198,"\int \frac{x}{\left(d+e x^2\right) \left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[x/((d + e*x^2)*(a + b*x^2 + c*x^4)^(3/2)),x]","\frac{e^2 \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 \left(a e^2-b d e+c d^2\right)^{3/2}}-\frac{2 a c e+b^2 (-e)+c x^2 (2 c d-b e)+b c d}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4} \left(a e^2-b d e+c d^2\right)}","\frac{e^2 \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 \left(a e^2-b d e+c d^2\right)^{3/2}}-\frac{2 a c e+b^2 (-e)+c x^2 (2 c d-b e)+b c d}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4} \left(a e^2-b d e+c d^2\right)}",1,"-((b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x^2)/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x^2 + c*x^4])) + (e^2*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])])/(2*(c*d^2 - b*d*e + a*e^2)^(3/2))","A",5,5,27,0.1852,1,"{1247, 740, 12, 724, 206}"
346,1,266,0,0.3880853,"\int \frac{1}{x \left(d+e x^2\right) \left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[1/(x*(d + e*x^2)*(a + b*x^2 + c*x^4)^(3/2)),x]","-\frac{\tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 a^{3/2} d}+\frac{e \left(2 a c e+b^2 (-e)+c x^2 (2 c d-b e)+b c d\right)}{d \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4} \left(a e^2-b d e+c d^2\right)}+\frac{-2 a c+b^2+b c x^2}{a d \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{e^3 \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 d \left(a e^2-b d e+c d^2\right)^{3/2}}","-\frac{\tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 a^{3/2} d}+\frac{e \left(2 a c e+b^2 (-e)+c x^2 (2 c d-b e)+b c d\right)}{d \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4} \left(a e^2-b d e+c d^2\right)}+\frac{-2 a c+b^2+b c x^2}{a d \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{e^3 \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 d \left(a e^2-b d e+c d^2\right)^{3/2}}",1,"(b^2 - 2*a*c + b*c*x^2)/(a*(b^2 - 4*a*c)*d*Sqrt[a + b*x^2 + c*x^4]) + (e*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x^2))/((b^2 - 4*a*c)*d*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x^2 + c*x^4]) - ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])]/(2*a^(3/2)*d) - (e^3*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])])/(2*d*(c*d^2 - b*d*e + a*e^2)^(3/2))","A",11,6,29,0.2069,1,"{1251, 960, 740, 12, 724, 206}"
347,1,419,0,0.5643163,"\int \frac{1}{x^3 \left(d+e x^2\right) \left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[1/(x^3*(d + e*x^2)*(a + b*x^2 + c*x^4)^(3/2)),x]","-\frac{\left(3 b^2-8 a c\right) \sqrt{a+b x^2+c x^4}}{2 a^2 d x^2 \left(b^2-4 a c\right)}+\frac{e \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 a^{3/2} d^2}+\frac{3 b \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{4 a^{5/2} d}-\frac{e^2 \left(2 a c e+b^2 (-e)+c x^2 (2 c d-b e)+b c d\right)}{d^2 \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4} \left(a e^2-b d e+c d^2\right)}-\frac{e \left(-2 a c+b^2+b c x^2\right)}{a d^2 \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}+\frac{-2 a c+b^2+b c x^2}{a d x^2 \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}+\frac{e^4 \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 d^2 \left(a e^2-b d e+c d^2\right)^{3/2}}","-\frac{\left(3 b^2-8 a c\right) \sqrt{a+b x^2+c x^4}}{2 a^2 d x^2 \left(b^2-4 a c\right)}+\frac{e \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{2 a^{3/2} d^2}+\frac{3 b \tanh ^{-1}\left(\frac{2 a+b x^2}{2 \sqrt{a} \sqrt{a+b x^2+c x^4}}\right)}{4 a^{5/2} d}-\frac{e^2 \left(2 a c e+b^2 (-e)+c x^2 (2 c d-b e)+b c d\right)}{d^2 \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4} \left(a e^2-b d e+c d^2\right)}-\frac{e \left(-2 a c+b^2+b c x^2\right)}{a d^2 \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}+\frac{-2 a c+b^2+b c x^2}{a d x^2 \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}+\frac{e^4 \tanh ^{-1}\left(\frac{-2 a e+x^2 (2 c d-b e)+b d}{2 \sqrt{a+b x^2+c x^4} \sqrt{a e^2-b d e+c d^2}}\right)}{2 d^2 \left(a e^2-b d e+c d^2\right)^{3/2}}",1,"-((e*(b^2 - 2*a*c + b*c*x^2))/(a*(b^2 - 4*a*c)*d^2*Sqrt[a + b*x^2 + c*x^4])) + (b^2 - 2*a*c + b*c*x^2)/(a*(b^2 - 4*a*c)*d*x^2*Sqrt[a + b*x^2 + c*x^4]) - (e^2*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x^2))/((b^2 - 4*a*c)*d^2*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x^2 + c*x^4]) - ((3*b^2 - 8*a*c)*Sqrt[a + b*x^2 + c*x^4])/(2*a^2*(b^2 - 4*a*c)*d*x^2) + (3*b*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(4*a^(5/2)*d) + (e*ArcTanh[(2*a + b*x^2)/(2*Sqrt[a]*Sqrt[a + b*x^2 + c*x^4])])/(2*a^(3/2)*d^2) + (e^4*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x^2)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x^2 + c*x^4])])/(2*d^2*(c*d^2 - b*d*e + a*e^2)^(3/2))","A",15,7,29,0.2414,1,"{1251, 960, 740, 806, 724, 206, 12}"
348,1,566,0,0.3474273,"\int \frac{x^8}{\left(3+2 x^2\right) \left(1+2 x^2+2 x^4\right)^{3/2}} \, dx","Int[x^8/((3 + 2*x^2)*(1 + 2*x^2 + 2*x^4)^(3/2)),x]","\frac{\left(1-2 x^2\right) x^3}{20 \sqrt{2 x^4+2 x^2+1}}+\frac{\sqrt{2 x^4+2 x^2+1} x}{10 \sqrt{2} \left(\sqrt{2} x^2+1\right)}+\frac{1}{20} \sqrt{2 x^4+2 x^2+1} x-\frac{27 \sqrt{\frac{3}{10}} \left(3-\sqrt{2}\right) \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)}{40 \left(2-3 \sqrt{2}\right)}-\frac{\left(7+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{40\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}+\frac{9 \left(1-3 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{20\ 2^{3/4} \left(2-3 \sqrt{2}\right) \sqrt{2 x^4+2 x^2+1}}-\frac{\left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{10\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}+\frac{27 \left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{80\ 2^{3/4} \left(2-3 \sqrt{2}\right) \sqrt{2 x^4+2 x^2+1}}","\frac{\left(1-2 x^2\right) x^3}{20 \sqrt{2 x^4+2 x^2+1}}+\frac{\sqrt{2 x^4+2 x^2+1} x}{10 \sqrt{2} \left(\sqrt{2} x^2+1\right)}+\frac{1}{20} \sqrt{2 x^4+2 x^2+1} x+\frac{27}{80} \sqrt{\frac{3}{5}} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)+\frac{\left(7 \sqrt{2}-2\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{8\ 2^{3/4} \left(3 \sqrt{2}-2\right) \sqrt{2 x^4+2 x^2+1}}-\frac{\left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{10\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}+\frac{27 \left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{80\ 2^{3/4} \left(2-3 \sqrt{2}\right) \sqrt{2 x^4+2 x^2+1}}",1,"(x^3*(1 - 2*x^2))/(20*Sqrt[1 + 2*x^2 + 2*x^4]) + (x*Sqrt[1 + 2*x^2 + 2*x^4])/20 + (x*Sqrt[1 + 2*x^2 + 2*x^4])/(10*Sqrt[2]*(1 + Sqrt[2]*x^2)) - (27*Sqrt[3/10]*(3 - Sqrt[2])*ArcTan[(Sqrt[5/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]])/(40*(2 - 3*Sqrt[2])) - ((1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(10*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + (9*(1 - 3*Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(20*2^(3/4)*(2 - 3*Sqrt[2])*Sqrt[1 + 2*x^2 + 2*x^4]) - ((7 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(40*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + (27*(3 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 - 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(80*2^(3/4)*(2 - 3*Sqrt[2])*Sqrt[1 + 2*x^2 + 2*x^4])","A",10,8,29,0.2759,1,"{1313, 1275, 1279, 1197, 1103, 1195, 1325, 1706}"
349,1,503,0,0.2564845,"\int \frac{x^6}{\left(3+2 x^2\right) \left(1+2 x^2+2 x^4\right)^{3/2}} \, dx","Int[x^6/((3 + 2*x^2)*(1 + 2*x^2 + 2*x^4)^(3/2)),x]","\frac{\sqrt{2 x^4+2 x^2+1} x}{10 \sqrt{2} \left(\sqrt{2} x^2+1\right)}+\frac{\left(1-2 x^2\right) x}{20 \sqrt{2 x^4+2 x^2+1}}-\frac{9}{40} \sqrt{\frac{3}{5}} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)-\frac{9 \left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{140\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{\left(1-\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{40 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}-\frac{\left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{10\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}+\frac{9 \left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{560 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}","\frac{\sqrt{2 x^4+2 x^2+1} x}{10 \sqrt{2} \left(\sqrt{2} x^2+1\right)}+\frac{\left(1-2 x^2\right) x}{20 \sqrt{2 x^4+2 x^2+1}}-\frac{9}{40} \sqrt{\frac{3}{5}} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)-\frac{\left(\sqrt[4]{2}+2^{3/4}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{8 \left(3 \sqrt{2}-2\right) \sqrt{2 x^4+2 x^2+1}}-\frac{\left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{10\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{9 \left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{40\ 2^{3/4} \left(2-3 \sqrt{2}\right) \sqrt{2 x^4+2 x^2+1}}",1,"(x*(1 - 2*x^2))/(20*Sqrt[1 + 2*x^2 + 2*x^4]) + (x*Sqrt[1 + 2*x^2 + 2*x^4])/(10*Sqrt[2]*(1 + Sqrt[2]*x^2)) - (9*Sqrt[3/5]*ArcTan[(Sqrt[5/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]])/40 - ((1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(10*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - ((1 - Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(40*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - (9*(3 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(140*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + (9*(3 + Sqrt[2])^2*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 - 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(560*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4])","A",8,7,29,0.2414,1,"{1313, 1275, 1197, 1103, 1195, 1319, 1706}"
350,1,501,0,0.2401803,"\int \frac{x^4}{\left(3+2 x^2\right) \left(1+2 x^2+2 x^4\right)^{3/2}} \, dx","Int[x^4/((3 + 2*x^2)*(1 + 2*x^2 + 2*x^4)^(3/2)),x]","\frac{\sqrt{2 x^4+2 x^2+1} x}{10 \sqrt{2} \left(\sqrt{2} x^2+1\right)}-\frac{\left(x^2+2\right) x}{10 \sqrt{2 x^4+2 x^2+1}}+\frac{3}{20} \sqrt{\frac{3}{5}} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)+\frac{9 \left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{140 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}+\frac{\left(1-\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{20\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{\left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{10\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{3 \left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{280 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}","\frac{\sqrt{2 x^4+2 x^2+1} x}{10 \sqrt{2} \left(\sqrt{2} x^2+1\right)}-\frac{\left(x^2+2\right) x}{10 \sqrt{2 x^4+2 x^2+1}}+\frac{3}{20} \sqrt{\frac{3}{5}} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)+\frac{\left(2+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{4\ 2^{3/4} \left(3 \sqrt{2}-2\right) \sqrt{2 x^4+2 x^2+1}}-\frac{\left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{10\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}+\frac{3 \left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{20\ 2^{3/4} \left(2-3 \sqrt{2}\right) \sqrt{2 x^4+2 x^2+1}}",1,"-(x*(2 + x^2))/(10*Sqrt[1 + 2*x^2 + 2*x^4]) + (x*Sqrt[1 + 2*x^2 + 2*x^4])/(10*Sqrt[2]*(1 + Sqrt[2]*x^2)) + (3*Sqrt[3/5]*ArcTan[(Sqrt[5/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]])/20 - ((1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(10*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + ((1 - Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(20*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + (9*(3 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(140*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - (3*(3 + Sqrt[2])^2*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 - 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(280*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4])","A",8,7,29,0.2414,1,"{1313, 1178, 1197, 1103, 1195, 1216, 1706}"
351,1,503,0,0.2416754,"\int \frac{x^2}{\left(3+2 x^2\right) \left(1+2 x^2+2 x^4\right)^{3/2}} \, dx","Int[x^2/((3 + 2*x^2)*(1 + 2*x^2 + 2*x^4)^(3/2)),x]","-\frac{\sqrt{2} \sqrt{2 x^4+2 x^2+1} x}{5 \left(\sqrt{2} x^2+1\right)}+\frac{\left(4 x^2+3\right) x}{10 \sqrt{2 x^4+2 x^2+1}}-\frac{1}{10} \sqrt{\frac{3}{5}} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)-\frac{\left(1+2 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{20 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}-\frac{3 \left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{70 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}+\frac{\sqrt[4]{2} \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{5 \sqrt{2 x^4+2 x^2+1}}+\frac{\left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{140 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}","-\frac{\sqrt{2} \sqrt{2 x^4+2 x^2+1} x}{5 \left(\sqrt{2} x^2+1\right)}+\frac{\left(4 x^2+3\right) x}{10 \sqrt{2 x^4+2 x^2+1}}-\frac{1}{10} \sqrt{\frac{3}{5}} \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)-\frac{\left(\sqrt[4]{2}+2^{3/4}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{4 \left(3 \sqrt{2}-2\right) \sqrt{2 x^4+2 x^2+1}}+\frac{\sqrt[4]{2} \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{5 \sqrt{2 x^4+2 x^2+1}}-\frac{\left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{10\ 2^{3/4} \left(2-3 \sqrt{2}\right) \sqrt{2 x^4+2 x^2+1}}",1,"(x*(3 + 4*x^2))/(10*Sqrt[1 + 2*x^2 + 2*x^4]) - (Sqrt[2]*x*Sqrt[1 + 2*x^2 + 2*x^4])/(5*(1 + Sqrt[2]*x^2)) - (Sqrt[3/5]*ArcTan[(Sqrt[5/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]])/10 + (2^(1/4)*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(5*Sqrt[1 + 2*x^2 + 2*x^4]) - (3*(3 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(70*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - ((1 + 2*Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(20*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + ((3 + Sqrt[2])^2*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 - 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(140*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4])","A",8,7,29,0.2414,1,"{1315, 1178, 1197, 1103, 1195, 1216, 1706}"
352,1,501,0,0.2262692,"\int \frac{1}{\left(3+2 x^2\right) \left(1+2 x^2+2 x^4\right)^{3/2}} \, dx","Int[1/((3 + 2*x^2)*(1 + 2*x^2 + 2*x^4)^(3/2)),x]","\frac{3 \sqrt{2 x^4+2 x^2+1} x}{5 \sqrt{2} \left(\sqrt{2} x^2+1\right)}-\frac{\left(3 x^2+1\right) x}{5 \sqrt{2 x^4+2 x^2+1}}+\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)}{5 \sqrt{15}}+\frac{\left(3+2 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{10\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}+\frac{\left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{35 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}-\frac{3 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{5\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{\left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{210 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}","\frac{3 \sqrt{2 x^4+2 x^2+1} x}{5 \sqrt{2} \left(\sqrt{2} x^2+1\right)}-\frac{\left(3 x^2+1\right) x}{5 \sqrt{2 x^4+2 x^2+1}}+\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)}{5 \sqrt{15}}+\frac{\left(2+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{2\ 2^{3/4} \left(3 \sqrt{2}-2\right) \sqrt{2 x^4+2 x^2+1}}-\frac{3 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{5\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}+\frac{\left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{15\ 2^{3/4} \left(2-3 \sqrt{2}\right) \sqrt{2 x^4+2 x^2+1}}",1,"-(x*(1 + 3*x^2))/(5*Sqrt[1 + 2*x^2 + 2*x^4]) + (3*x*Sqrt[1 + 2*x^2 + 2*x^4])/(5*Sqrt[2]*(1 + Sqrt[2]*x^2)) + ArcTan[(Sqrt[5/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]]/(5*Sqrt[15]) - (3*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(5*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + ((3 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(35*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + ((3 + 2*Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(10*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - ((3 + Sqrt[2])^2*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 - 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(210*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4])","A",8,7,26,0.2692,1,"{1221, 1178, 1197, 1103, 1195, 1216, 1706}"
353,1,644,0,0.4454633,"\int \frac{1}{x^2 \left(3+2 x^2\right) \left(1+2 x^2+2 x^4\right)^{3/2}} \, dx","Int[1/(x^2*(3 + 2*x^2)*(1 + 2*x^2 + 2*x^4)^(3/2)),x]","\frac{2 \sqrt{2} \sqrt{2 x^4+2 x^2+1} x}{15 \left(\sqrt{2} x^2+1\right)}+\frac{2 \left(3 x^2+1\right) x}{15 \sqrt{2 x^4+2 x^2+1}}-\frac{x}{3 \sqrt{2 x^4+2 x^2+1}}-\frac{\sqrt{2 x^4+2 x^2+1}}{3 x}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)}{15 \sqrt{15}}-\frac{\left(3+2 \sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{15\ 2^{3/4} \sqrt{2 x^4+2 x^2+1}}-\frac{2^{3/4} \left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{105 \sqrt{2 x^4+2 x^2+1}}-\frac{\left(1-\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{6 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}-\frac{2 \sqrt[4]{2} \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{15 \sqrt{2 x^4+2 x^2+1}}+\frac{\left(3+\sqrt{2}\right)^2 \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{315 \sqrt[4]{2} \sqrt{2 x^4+2 x^2+1}}","\frac{2 \sqrt{2} \sqrt{2 x^4+2 x^2+1} x}{15 \left(\sqrt{2} x^2+1\right)}+\frac{2 \left(3 x^2+1\right) x}{15 \sqrt{2 x^4+2 x^2+1}}-\frac{x}{3 \sqrt{2 x^4+2 x^2+1}}-\frac{\sqrt{2 x^4+2 x^2+1}}{3 x}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{\frac{5}{3}} x}{\sqrt{2 x^4+2 x^2+1}}\right)}{15 \sqrt{15}}+\frac{\left(3 \sqrt{2}-7\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{3\ 2^{3/4} \left(3 \sqrt{2}-2\right) \sqrt{2 x^4+2 x^2+1}}-\frac{2 \sqrt[4]{2} \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{15 \sqrt{2 x^4+2 x^2+1}}-\frac{\sqrt[4]{2} \left(3+\sqrt{2}\right) \left(\sqrt{2} x^2+1\right) \sqrt{\frac{2 x^4+2 x^2+1}{\left(\sqrt{2} x^2+1\right)^2}} \Pi \left(\frac{1}{24} \left(12-11 \sqrt{2}\right);2 \tan ^{-1}\left(\sqrt[4]{2} x\right)|\frac{1}{4} \left(2-\sqrt{2}\right)\right)}{45 \left(2-3 \sqrt{2}\right) \sqrt{2 x^4+2 x^2+1}}",1,"-x/(3*Sqrt[1 + 2*x^2 + 2*x^4]) + (2*x*(1 + 3*x^2))/(15*Sqrt[1 + 2*x^2 + 2*x^4]) - Sqrt[1 + 2*x^2 + 2*x^4]/(3*x) + (2*Sqrt[2]*x*Sqrt[1 + 2*x^2 + 2*x^4])/(15*(1 + Sqrt[2]*x^2)) - (2*ArcTan[(Sqrt[5/3]*x)/Sqrt[1 + 2*x^2 + 2*x^4]])/(15*Sqrt[15]) - (2*2^(1/4)*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticE[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(15*Sqrt[1 + 2*x^2 + 2*x^4]) - ((1 - Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(6*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4]) - (2^(3/4)*(3 + Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(105*Sqrt[1 + 2*x^2 + 2*x^4]) - ((3 + 2*Sqrt[2])*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticF[2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(15*2^(3/4)*Sqrt[1 + 2*x^2 + 2*x^4]) + ((3 + Sqrt[2])^2*(1 + Sqrt[2]*x^2)*Sqrt[(1 + 2*x^2 + 2*x^4)/(1 + Sqrt[2]*x^2)^2]*EllipticPi[(12 - 11*Sqrt[2])/24, 2*ArcTan[2^(1/4)*x], (2 - Sqrt[2])/4])/(315*2^(1/4)*Sqrt[1 + 2*x^2 + 2*x^4])","A",15,10,29,0.3448,1,"{1335, 1121, 1281, 1197, 1103, 1195, 1221, 1178, 1216, 1706}"
354,1,406,0,8.5929932,"\int \frac{x^7 \sqrt{d+e x^2}}{a+b x^2+c x^4} \, dx","Int[(x^7*Sqrt[d + e*x^2])/(a + b*x^2 + c*x^4),x]","-\frac{\left(-\frac{-2 a^2 c^2 e+4 a b^2 c e-3 a b c^2 d+b^3 c d+b^4 (-e)}{\sqrt{b^2-4 a c}}+2 a b c e-a c^2 d+b^2 c d+b^3 (-e)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} c^{7/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\left(\frac{-2 a^2 c^2 e+4 a b^2 c e-3 a b c^2 d+b^3 c d+b^4 (-e)}{\sqrt{b^2-4 a c}}+2 a b c e-a c^2 d+b^2 c d+b^3 (-e)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} c^{7/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{\left(b^2-a c\right) \sqrt{d+e x^2}}{c^3}-\frac{\left(d+e x^2\right)^{3/2} (b e+c d)}{3 c^2 e^2}+\frac{\left(d+e x^2\right)^{5/2}}{5 c e^2}","-\frac{\left(-\frac{-2 a^2 c^2 e+4 a b^2 c e-3 a b c^2 d+b^3 c d+b^4 (-e)}{\sqrt{b^2-4 a c}}+2 a b c e-a c^2 d+b^2 c d+b^3 (-e)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} c^{7/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\left(\frac{-2 a^2 c^2 e+4 a b^2 c e-3 a b c^2 d+b^3 c d+b^4 (-e)}{\sqrt{b^2-4 a c}}+2 a b c e-a c^2 d+b^2 c d+b^3 (-e)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} c^{7/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{\left(b^2-a c\right) \sqrt{d+e x^2}}{c^3}-\frac{\left(d+e x^2\right)^{3/2} (b e+c d)}{3 c^2 e^2}+\frac{\left(d+e x^2\right)^{5/2}}{5 c e^2}",1,"((b^2 - a*c)*Sqrt[d + e*x^2])/c^3 - ((c*d + b*e)*(d + e*x^2)^(3/2))/(3*c^2*e^2) + (d + e*x^2)^(5/2)/(5*c*e^2) - ((b^2*c*d - a*c^2*d - b^3*e + 2*a*b*c*e - (b^3*c*d - 3*a*b*c^2*d - b^4*e + 4*a*b^2*c*e - 2*a^2*c^2*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*c^(7/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - ((b^2*c*d - a*c^2*d - b^3*e + 2*a*b*c*e + (b^3*c*d - 3*a*b*c^2*d - b^4*e + 4*a*b^2*c*e - 2*a^2*c^2*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*c^(7/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",7,5,29,0.1724,1,"{1251, 897, 1287, 1166, 208}"
355,1,324,0,3.5286566,"\int \frac{x^5 \sqrt{d+e x^2}}{a+b x^2+c x^4} \, dx","Int[(x^5*Sqrt[d + e*x^2])/(a + b*x^2 + c*x^4),x]","\frac{\left(-\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} c^{5/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\left(\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} c^{5/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{b \sqrt{d+e x^2}}{c^2}+\frac{\left(d+e x^2\right)^{3/2}}{3 c e}","\frac{\left(-\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} c^{5/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\left(\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} c^{5/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{b \sqrt{d+e x^2}}{c^2}+\frac{\left(d+e x^2\right)^{3/2}}{3 c e}",1,"-((b*Sqrt[d + e*x^2])/c^2) + (d + e*x^2)^(3/2)/(3*c*e) + ((b*c*d - b^2*e + a*c*e - (b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*c^(5/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + ((b*c*d - b^2*e + a*c*e + (b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*c^(5/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",7,5,29,0.1724,1,"{1251, 897, 1287, 1166, 208}"
356,1,292,0,3.5996494,"\int \frac{x^3 \sqrt{d+e x^2}}{a+b x^2+c x^4} \, dx","Int[(x^3*Sqrt[d + e*x^2])/(a + b*x^2 + c*x^4),x]","\frac{\left(-\sqrt{b^2-4 a c} (c d-b e)+2 a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\left(\sqrt{b^2-4 a c} (c d-b e)+2 a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{\sqrt{d+e x^2}}{c}","\frac{\left(-\sqrt{b^2-4 a c} (c d-b e)+2 a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\left(\sqrt{b^2-4 a c} (c d-b e)+2 a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{\sqrt{d+e x^2}}{c}",1,"Sqrt[d + e*x^2]/c + ((b*c*d - b^2*e + 2*a*c*e - Sqrt[b^2 - 4*a*c]*(c*d - b*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*c^(3/2)*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - ((b*c*d - b^2*e + 2*a*c*e + Sqrt[b^2 - 4*a*c]*(c*d - b*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*c^(3/2)*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",6,5,29,0.1724,1,"{1251, 824, 826, 1166, 208}"
357,1,202,0,0.3626907,"\int \frac{x \sqrt{d+e x^2}}{a+b x^2+c x^4} \, dx","Int[(x*Sqrt[d + e*x^2])/(a + b*x^2 + c*x^4),x]","\frac{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}-\frac{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}","\frac{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}-\frac{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}",1,"-((Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c])) + (Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c])","A",5,4,27,0.1481,1,"{1247, 699, 1130, 208}"
358,1,281,0,1.3501671,"\int \frac{\sqrt{d+e x^2}}{x \left(a+b x^2+c x^4\right)} \, dx","Int[Sqrt[d + e*x^2]/(x*(a + b*x^2 + c*x^4)),x]","\frac{\sqrt{c} \left(d \sqrt{b^2-4 a c}-2 a e+b d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} a \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{c} \left(-d \sqrt{b^2-4 a c}-2 a e+b d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} a \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{a}","\frac{\sqrt{c} \left(d \sqrt{b^2-4 a c}-2 a e+b d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} a \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{c} \left(-d \sqrt{b^2-4 a c}-2 a e+b d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} a \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{a}",1,"-((Sqrt[d]*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/a) + (Sqrt[c]*(b*d + Sqrt[b^2 - 4*a*c]*d - 2*a*e)*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*a*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - (Sqrt[c]*(b*d - Sqrt[b^2 - 4*a*c]*d - 2*a*e)*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*a*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",8,6,29,0.2069,1,"{1251, 897, 1287, 206, 1166, 208}"
359,1,370,0,4.133796,"\int \frac{\sqrt{d+e x^2}}{x^3 \left(a+b x^2+c x^4\right)} \, dx","Int[Sqrt[d + e*x^2]/(x^3*(a + b*x^2 + c*x^4)),x]","-\frac{\sqrt{c} \left(\sqrt{b^2-4 a c} (b d-a e)-a b e-2 a c d+b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} a^2 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{c} \left(-\sqrt{b^2-4 a c} (b d-a e)-a b e-2 a c d+b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} a^2 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{(b d-a e) \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{a^2 \sqrt{d}}-\frac{\sqrt{d+e x^2}}{2 a x^2}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{2 a \sqrt{d}}","-\frac{\sqrt{c} \left(\sqrt{b^2-4 a c} (b d-a e)-a b e-2 a c d+b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} a^2 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{c} \left(-b \left(d \sqrt{b^2-4 a c}+a e\right)-a \left(2 c d-e \sqrt{b^2-4 a c}\right)+b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} a^2 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{(b d-a e) \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{a^2 \sqrt{d}}-\frac{\sqrt{d+e x^2}}{2 a x^2}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{2 a \sqrt{d}}",1,"-Sqrt[d + e*x^2]/(2*a*x^2) + (e*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(2*a*Sqrt[d]) + ((b*d - a*e)*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(a^2*Sqrt[d]) - (Sqrt[c]*(b^2*d - 2*a*c*d - a*b*e + Sqrt[b^2 - 4*a*c]*(b*d - a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*a^2*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + (Sqrt[c]*(b^2*d - 2*a*c*d - a*b*e - Sqrt[b^2 - 4*a*c]*(b*d - a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*a^2*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",10,7,29,0.2414,1,"{1251, 897, 1287, 199, 206, 1166, 208}"
360,1,552,0,4.2438862,"\int \frac{\sqrt{d+e x^2}}{x^5 \left(a+b x^2+c x^4\right)} \, dx","Int[Sqrt[d + e*x^2]/(x^5*(a + b*x^2 + c*x^4)),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right) \left(-a b e-a c d+b^2 d\right)}{a^3 \sqrt{d}}+\frac{\sqrt{c} \left(b^2 \left(d \sqrt{b^2-4 a c}-a e\right)-a b \left(e \sqrt{b^2-4 a c}+3 c d\right)-a c \left(d \sqrt{b^2-4 a c}-2 a e\right)+b^3 d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} a^3 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{c} \left(-b^2 \left(d \sqrt{b^2-4 a c}+a e\right)-a b \left(3 c d-e \sqrt{b^2-4 a c}\right)+a c \left(d \sqrt{b^2-4 a c}+2 a e\right)+b^3 d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} a^3 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{e (b d-a e) \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{2 a^2 d^{3/2}}+\frac{\sqrt{d+e x^2} (b d-a e)}{2 a^2 d x^2}-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{8 a d^{3/2}}+\frac{3 e \sqrt{d+e x^2}}{8 a d x^2}-\frac{\sqrt{d+e x^2}}{4 a x^4}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right) \left(-a b e-a c d+b^2 d\right)}{a^3 \sqrt{d}}+\frac{\sqrt{c} \left(b^2 \left(d \sqrt{b^2-4 a c}-a e\right)-a b \left(e \sqrt{b^2-4 a c}+3 c d\right)-a c \left(d \sqrt{b^2-4 a c}-2 a e\right)+b^3 d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} a^3 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{c} \left(-b^2 \left(d \sqrt{b^2-4 a c}+a e\right)-a b \left(3 c d-e \sqrt{b^2-4 a c}\right)+a c \left(d \sqrt{b^2-4 a c}+2 a e\right)+b^3 d\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} a^3 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{e (b d-a e) \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{2 a^2 d^{3/2}}+\frac{\sqrt{d+e x^2} (b d-a e)}{2 a^2 d x^2}-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{8 a d^{3/2}}+\frac{3 e \sqrt{d+e x^2}}{8 a d x^2}-\frac{\sqrt{d+e x^2}}{4 a x^4}",1,"-Sqrt[d + e*x^2]/(4*a*x^4) + (3*e*Sqrt[d + e*x^2])/(8*a*d*x^2) + ((b*d - a*e)*Sqrt[d + e*x^2])/(2*a^2*d*x^2) - (3*e^2*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(8*a*d^(3/2)) - (e*(b*d - a*e)*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(2*a^2*d^(3/2)) - ((b^2*d - a*c*d - a*b*e)*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(a^3*Sqrt[d]) + (Sqrt[c]*(b^3*d - a*c*(Sqrt[b^2 - 4*a*c]*d - 2*a*e) + b^2*(Sqrt[b^2 - 4*a*c]*d - a*e) - a*b*(3*c*d + Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*a^3*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - (Sqrt[c]*(b^3*d - b^2*(Sqrt[b^2 - 4*a*c]*d + a*e) + a*c*(Sqrt[b^2 - 4*a*c]*d + 2*a*e) - a*b*(3*c*d - Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*a^3*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",13,7,29,0.2414,1,"{1251, 897, 1287, 199, 206, 1166, 208}"
361,1,390,0,2.9194882,"\int \frac{x^4 \sqrt{d+e x^2}}{a+b x^2+c x^4} \, dx","Int[(x^4*Sqrt[d + e*x^2])/(a + b*x^2 + c*x^4),x]","-\frac{\left(-\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{c^2 \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\left(\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{c^2 \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{(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{\left(-\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{c^2 \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\left(\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{c^2 \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{(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) - ((b*c*d - b^2*e + a*c*e - (b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(c^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - ((b*c*d - b^2*e + a*c*e + (b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(c^2*Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]) + ((c*d - 2*b*e)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(2*c^2*Sqrt[e])","A",10,7,29,0.2414,1,"{1291, 388, 217, 206, 1692, 377, 205}"
362,1,324,0,1.5168419,"\int \frac{x^2 \sqrt{d+e x^2}}{a+b x^2+c x^4} \, dx","Int[(x^2*Sqrt[d + e*x^2])/(a + b*x^2 + c*x^4),x]","\frac{\left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{c \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{c \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{c}","\frac{\left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{c \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{c \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{c}",1,"((c*d - b*e - (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(c*Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + ((c*d - b*e + (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(c*Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]) + (Sqrt[e]*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/c","A",9,6,29,0.2069,1,"{1293, 217, 206, 1692, 377, 205}"
363,1,240,0,0.3184618,"\int \frac{\sqrt{d+e x^2}}{a+b x^2+c x^4} \, dx","Int[Sqrt[d + e*x^2]/(a + b*x^2 + c*x^4),x]","\frac{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(Sqrt[b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",11,6,26,0.2308,1,"{1174, 402, 217, 206, 377, 205}"
364,1,291,0,0.670755,"\int \frac{\sqrt{d+e x^2}}{x^2 \left(a+b x^2+c x^4\right)} \, dx","Int[Sqrt[d + e*x^2]/(x^2*(a + b*x^2 + c*x^4)),x]","-\frac{c \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{a \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{c \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{a \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{\sqrt{d+e x^2}}{a x}","-\frac{c \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{a \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{c \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{a \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{\sqrt{d+e x^2}}{a x}",1,"-(Sqrt[d + e*x^2]/(a*x)) - (c*(d + (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(a*Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - (c*(d - (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(a*Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",8,5,29,0.1724,1,"{1295, 264, 1692, 377, 205}"
365,1,373,0,2.5271098,"\int \frac{\sqrt{d+e x^2}}{x^4 \left(a+b x^2+c x^4\right)} \, dx","Int[Sqrt[d + e*x^2]/(x^4*(a + b*x^2 + c*x^4)),x]","\frac{c \left(\frac{-a b e-2 a c d+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{a^2 \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{c \left(-\frac{-a b e-2 a c d+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{a^2 \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{\sqrt{d+e x^2} (b d-a e)}{a^2 d x}+\frac{2 e \sqrt{d+e x^2}}{3 a d x}-\frac{\sqrt{d+e x^2}}{3 a x^3}","\frac{c \left(\frac{-a b e-2 a c d+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{a^2 \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{c \left(-\frac{-a b e-2 a c d+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{a^2 \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{\sqrt{d+e x^2} (b d-a e)}{a^2 d x}+\frac{2 e \sqrt{d+e x^2}}{3 a d x}-\frac{\sqrt{d+e x^2}}{3 a x^3}",1,"-Sqrt[d + e*x^2]/(3*a*x^3) + (2*e*Sqrt[d + e*x^2])/(3*a*d*x) + ((b*d - a*e)*Sqrt[d + e*x^2])/(a^2*d*x) + (c*(b*d - a*e + (b^2*d - 2*a*c*d - a*b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(a^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + (c*(b*d - a*e - (b^2*d - 2*a*c*d - a*b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(a^2*Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",12,7,29,0.2414,1,"{1295, 271, 264, 6728, 1692, 377, 205}"
366,1,512,0,4.9425336,"\int \frac{\sqrt{d+e x^2}}{x^6 \left(a+b x^2+c x^4\right)} \, dx","Int[Sqrt[d + e*x^2]/(x^6*(a + b*x^2 + c*x^4)),x]","-\frac{\sqrt{d+e x^2} \left(-a b e-a c d+b^2 d\right)}{a^3 d x}-\frac{c \left(\frac{2 a^2 c e-a b^2 e-3 a b c d+b^3 d}{\sqrt{b^2-4 a c}}-a b e-a c d+b^2 d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{a^3 \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{c \left(-\frac{2 a^2 c e-a b^2 e-3 a b c d+b^3 d}{\sqrt{b^2-4 a c}}-a b e-a c d+b^2 d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{a^3 \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{2 e \sqrt{d+e x^2} (b d-a e)}{3 a^2 d^2 x}+\frac{\sqrt{d+e x^2} (b d-a e)}{3 a^2 d x^3}-\frac{8 e^2 \sqrt{d+e x^2}}{15 a d^2 x}+\frac{4 e \sqrt{d+e x^2}}{15 a d x^3}-\frac{\sqrt{d+e x^2}}{5 a x^5}","-\frac{\sqrt{d+e x^2} \left(-a b e-a c d+b^2 d\right)}{a^3 d x}-\frac{c \left(\frac{2 a^2 c e-a b^2 e-3 a b c d+b^3 d}{\sqrt{b^2-4 a c}}-a b e-a c d+b^2 d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{a^3 \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{c \left(-\frac{2 a^2 c e-a b^2 e-3 a b c d+b^3 d}{\sqrt{b^2-4 a c}}-a b e-a c d+b^2 d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{a^3 \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{2 e \sqrt{d+e x^2} (b d-a e)}{3 a^2 d^2 x}+\frac{\sqrt{d+e x^2} (b d-a e)}{3 a^2 d x^3}-\frac{8 e^2 \sqrt{d+e x^2}}{15 a d^2 x}+\frac{4 e \sqrt{d+e x^2}}{15 a d x^3}-\frac{\sqrt{d+e x^2}}{5 a x^5}",1,"-Sqrt[d + e*x^2]/(5*a*x^5) + (4*e*Sqrt[d + e*x^2])/(15*a*d*x^3) + ((b*d - a*e)*Sqrt[d + e*x^2])/(3*a^2*d*x^3) - (8*e^2*Sqrt[d + e*x^2])/(15*a*d^2*x) - (2*e*(b*d - a*e)*Sqrt[d + e*x^2])/(3*a^2*d^2*x) - ((b^2*d - a*c*d - a*b*e)*Sqrt[d + e*x^2])/(a^3*d*x) - (c*(b^2*d - a*c*d - a*b*e + (b^3*d - 3*a*b*c*d - a*b^2*e + 2*a^2*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(a^3*Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - (c*(b^2*d - a*c*d - a*b*e - (b^3*d - 3*a*b*c*d - a*b^2*e + 2*a^2*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(a^3*Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",15,7,29,0.2414,1,"{1295, 271, 264, 6728, 1692, 377, 205}"
367,1,460,0,5.0844395,"\int \frac{x^3 \left(d+e x^2\right)^{3/2}}{a+b x^2+c x^4} \, dx","Int[(x^3*(d + e*x^2)^(3/2))/(a + b*x^2 + c*x^4),x]","\frac{\left(b c \left(e \left(2 d \sqrt{b^2-4 a c}-3 a e\right)+c d^2\right)+c \left(a e^2 \sqrt{b^2-4 a c}-c d \left(d \sqrt{b^2-4 a c}-4 a e\right)\right)-b^2 e \left(e \sqrt{b^2-4 a c}+2 c d\right)+b^3 e^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} c^{5/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\left(b c \left(c d^2-e \left(2 d \sqrt{b^2-4 a c}+3 a e\right)\right)-c \left(a e^2 \sqrt{b^2-4 a c}-c d \left(d \sqrt{b^2-4 a c}+4 a e\right)\right)-b^2 e \left(2 c d-e \sqrt{b^2-4 a c}\right)+b^3 e^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} c^{5/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{\sqrt{d+e x^2} (c d-b e)}{c^2}+\frac{\left(d+e x^2\right)^{3/2}}{3 c}","\frac{\left(b c \left(e \left(2 d \sqrt{b^2-4 a c}-3 a e\right)+c d^2\right)+c \left(a e^2 \sqrt{b^2-4 a c}-c d \left(d \sqrt{b^2-4 a c}-4 a e\right)\right)-b^2 e \left(e \sqrt{b^2-4 a c}+2 c d\right)+b^3 e^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} c^{5/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\left(b c \left(c d^2-e \left(2 d \sqrt{b^2-4 a c}+3 a e\right)\right)-c \left(a e^2 \sqrt{b^2-4 a c}-c d \left(d \sqrt{b^2-4 a c}+4 a e\right)\right)-b^2 e \left(2 c d-e \sqrt{b^2-4 a c}\right)+b^3 e^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} c^{5/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{\sqrt{d+e x^2} (c d-b e)}{c^2}+\frac{\left(d+e x^2\right)^{3/2}}{3 c}",1,"((c*d - b*e)*Sqrt[d + e*x^2])/c^2 + (d + e*x^2)^(3/2)/(3*c) + ((b^3*e^2 - b^2*e*(2*c*d + Sqrt[b^2 - 4*a*c]*e) + c*(a*Sqrt[b^2 - 4*a*c]*e^2 - c*d*(Sqrt[b^2 - 4*a*c]*d - 4*a*e)) + b*c*(c*d^2 + e*(2*Sqrt[b^2 - 4*a*c]*d - 3*a*e)))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*c^(5/2)*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - ((b^3*e^2 - b^2*e*(2*c*d - Sqrt[b^2 - 4*a*c]*e) + b*c*(c*d^2 - e*(2*Sqrt[b^2 - 4*a*c]*d + 3*a*e)) - c*(a*Sqrt[b^2 - 4*a*c]*e^2 - c*d*(Sqrt[b^2 - 4*a*c]*d + 4*a*e)))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*c^(5/2)*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",7,5,29,0.1724,1,"{1251, 824, 826, 1166, 208}"
368,1,327,0,1.4563246,"\int \frac{x \left(d+e x^2\right)^{3/2}}{a+b x^2+c x^4} \, dx","Int[(x*(d + e*x^2)^(3/2))/(a + b*x^2 + c*x^4),x]","-\frac{\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) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\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) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{e \sqrt{d+e x^2}}{c}","-\frac{\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) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\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) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{e \sqrt{d+e x^2}}{c}",1,"(e*Sqrt[d + e*x^2])/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))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*c^(3/2)*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + ((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))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*c^(3/2)*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",6,5,27,0.1852,1,"{1247, 703, 826, 1166, 208}"
369,1,346,0,1.7437845,"\int \frac{\left(d+e x^2\right)^{3/2}}{x \left(a+b x^2+c x^4\right)} \, dx","Int[(d + e*x^2)^(3/2)/(x*(a + b*x^2 + c*x^4)),x]","-\frac{\left(-c d \left(d \sqrt{b^2-4 a c}-4 a e\right)+a e^2 \sqrt{b^2-4 a c}-b \left(a e^2+c d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} a \sqrt{c} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\left(-c d \left(d \sqrt{b^2-4 a c}+4 a e\right)+a e^2 \sqrt{b^2-4 a c}+b \left(a e^2+c d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} a \sqrt{c} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{a}","-\frac{\left(-c d \left(d \sqrt{b^2-4 a c}-4 a e\right)+a e^2 \sqrt{b^2-4 a c}-b \left(a e^2+c d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} a \sqrt{c} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\left(-c d \left(d \sqrt{b^2-4 a c}+4 a e\right)+a e^2 \sqrt{b^2-4 a c}+b \left(a e^2+c d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} a \sqrt{c} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{a}",1,"-((d^(3/2)*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/a) - ((a*Sqrt[b^2 - 4*a*c]*e^2 - c*d*(Sqrt[b^2 - 4*a*c]*d - 4*a*e) - b*(c*d^2 + a*e^2))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*a*Sqrt[c]*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - ((a*Sqrt[b^2 - 4*a*c]*e^2 - c*d*(Sqrt[b^2 - 4*a*c]*d + 4*a*e) + b*(c*d^2 + a*e^2))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*a*Sqrt[c]*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",8,6,29,0.2069,1,"{1251, 897, 1287, 206, 1166, 208}"
370,1,416,0,3.2426534,"\int \frac{\left(d+e x^2\right)^{3/2}}{x^3 \left(a+b x^2+c x^4\right)} \, dx","Int[(d + e*x^2)^(3/2)/(x^3*(a + b*x^2 + c*x^4)),x]","-\frac{\sqrt{c} \left(b d \left(d \sqrt{b^2-4 a c}-2 a e\right)-2 a e \left(d \sqrt{b^2-4 a c}-a e\right)-2 a c d^2+b^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} a^2 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{c} \left(-b d \left(d \sqrt{b^2-4 a c}+2 a e\right)+2 a e \left(d \sqrt{b^2-4 a c}+a e\right)-2 a c d^2+b^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} a^2 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{\sqrt{d} (b d-2 a e) \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{a^2}-\frac{d \sqrt{d+e x^2}}{2 a x^2}+\frac{\sqrt{d} e \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{2 a}","-\frac{\sqrt{c} \left(-2 a \left(e \left(d \sqrt{b^2-4 a c}-a e\right)+c d^2\right)+b d \left(d \sqrt{b^2-4 a c}-2 a e\right)+b^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} a^2 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{c} \left(-2 a \left(c d^2-e \left(d \sqrt{b^2-4 a c}+a e\right)\right)-b d \left(d \sqrt{b^2-4 a c}+2 a e\right)+b^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x^2}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} a^2 \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{\sqrt{d} (b d-2 a e) \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{a^2}-\frac{d \sqrt{d+e x^2}}{2 a x^2}+\frac{\sqrt{d} e \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{2 a}",1,"-(d*Sqrt[d + e*x^2])/(2*a*x^2) + (Sqrt[d]*e*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(2*a) + (Sqrt[d]*(b*d - 2*a*e)*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/a^2 - (Sqrt[c]*(b^2*d^2 - 2*a*c*d^2 + b*d*(Sqrt[b^2 - 4*a*c]*d - 2*a*e) - 2*a*e*(Sqrt[b^2 - 4*a*c]*d - a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*a^2*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + (Sqrt[c]*(b^2*d^2 - 2*a*c*d^2 + 2*a*e*(Sqrt[b^2 - 4*a*c]*d + a*e) - b*d*(Sqrt[b^2 - 4*a*c]*d + 2*a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x^2])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*a^2*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",10,7,29,0.2414,1,"{1251, 897, 1287, 199, 206, 1166, 208}"
371,1,595,0,3.2846234,"\int \frac{x^4 \left(d+e x^2\right)^{3/2}}{a+b x^2+c x^4} \, dx","Int[(x^4*(d + e*x^2)^(3/2))/(a + b*x^2 + c*x^4),x]","-\frac{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(-\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{2 c^3 \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{2 c^3 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(-\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right)}{2 c^3}-\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right)}{2 c^3}+\frac{x \sqrt{d+e x^2} (3 c d-4 b e)}{8 c^2}+\frac{d (3 c d-4 b e) \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{8 c^2 \sqrt{e}}+\frac{x \left(d+e x^2\right)^{3/2}}{4 c}","-\frac{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(-\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{2 c^3 \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{2 c^3 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(-\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right)}{2 c^3}-\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right)}{2 c^3}+\frac{x \sqrt{d+e x^2} (3 c d-4 b e)}{8 c^2}+\frac{d (3 c d-4 b e) \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{8 c^2 \sqrt{e}}+\frac{x \left(d+e x^2\right)^{3/2}}{4 c}",1,"((3*c*d - 4*b*e)*x*Sqrt[d + e*x^2])/(8*c^2) + (x*(d + e*x^2)^(3/2))/(4*c) - (Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(b*c*d - b^2*e + a*c*e - (b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(2*c^3*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(b*c*d - b^2*e + a*c*e + (b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(2*c^3*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + (d*(3*c*d - 4*b*e)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(8*c^2*Sqrt[e]) - (Sqrt[e]*(b*c*d - b^2*e + a*c*e - (b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(2*c^3) - (Sqrt[e]*(b*c*d - b^2*e + a*c*e + (b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(2*c^3)","A",17,9,29,0.3103,1,"{1291, 388, 195, 217, 206, 1692, 402, 377, 205}"
372,1,491,0,1.802191,"\int \frac{x^2 \left(d+e x^2\right)^{3/2}}{a+b x^2+c x^4} \, dx","Int[(x^2*(d + e*x^2)^(3/2))/(a + b*x^2 + c*x^4),x]","\frac{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{2 c^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{2 c^2 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right)}{2 c^2}+\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right)}{2 c^2}+\frac{e x \sqrt{d+e x^2}}{2 c}+\frac{d \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{2 c}","\frac{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{2 c^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{2 c^2 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right)}{2 c^2}+\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right)}{2 c^2}+\frac{e x \sqrt{d+e x^2}}{2 c}+\frac{d \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{2 c}",1,"(e*x*Sqrt[d + e*x^2])/(2*c) + (Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(c*d - b*e - (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(2*c^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(c*d - b*e + (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(2*c^2*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + (d*Sqrt[e]*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(2*c) + (Sqrt[e]*(c*d - b*e - (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(2*c^2) + (Sqrt[e]*(c*d - b*e + (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(2*c^2)","A",16,8,29,0.2759,1,"{1293, 195, 217, 206, 1692, 402, 377, 205}"
373,1,487,0,1.5721678,"\int \frac{\left(d+e x^2\right)^{3/2}}{a+b x^2+c x^4} \, dx","Int[(d + e*x^2)^(3/2)/(a + b*x^2 + c*x^4),x]","\frac{\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{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{c \sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\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{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{c \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(3 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}{2 c \sqrt{b^2-4 a c}}-\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(3 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}{2 c \sqrt{b^2-4 a c}}","\frac{\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{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{c \sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\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{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{c \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(3 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}{2 c \sqrt{b^2-4 a c}}-\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(3 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}{2 c \sqrt{b^2-4 a c}}",1,"((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*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(c*Sqrt[b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - ((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*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(c*Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]) + (Sqrt[e]*(3*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(2*c*Sqrt[b^2 - 4*a*c]) - (Sqrt[e]*(3*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(2*c*Sqrt[b^2 - 4*a*c])","A",13,7,26,0.2692,1,"{1174, 416, 523, 217, 206, 377, 205}"
374,1,432,0,0.8549726,"\int \frac{\left(d+e x^2\right)^{3/2}}{x^2 \left(a+b x^2+c x^4\right)} \, dx","Int[(d + e*x^2)^(3/2)/(x^2*(a + b*x^2 + c*x^4)),x]","-\frac{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{2 a \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{2 a \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right)}{2 a}-\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right)}{2 a}-\frac{d \sqrt{d+e x^2}}{a x}+\frac{d \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{a}","-\frac{\left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)^{3/2} \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{\sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)^{3/2}}+\frac{\left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)^{3/2} \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{\sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)^{3/2}}-\frac{d \sqrt{d+e x^2}}{a x}",1,"-((d*Sqrt[d + e*x^2])/(a*x)) - (Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(d + (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(2*a*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(d - (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(2*a*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + (d*Sqrt[e]*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/a - (Sqrt[e]*(d - (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(2*a) - (Sqrt[e]*(d + (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(2*a)","A",16,8,29,0.2759,1,"{1295, 277, 217, 206, 1692, 402, 377, 205}"
375,1,523,0,2.617447,"\int \frac{\left(d+e x^2\right)^{3/2}}{x^4 \left(a+b x^2+c x^4\right)} \, dx","Int[(d + e*x^2)^(3/2)/(x^4*(a + b*x^2 + c*x^4)),x]","\frac{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(\frac{-a b e-2 a c d+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{2 a^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(-\frac{-a b e-2 a c d+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{2 a^2 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(-\frac{-a b e-2 a c d+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\right)}{2 a^2}+\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(\frac{-a b e-2 a c d+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\right)}{2 a^2}+\frac{\sqrt{d+e x^2} (b d-a e)}{a^2 x}-\frac{\sqrt{e} (b d-a e) \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{a^2}-\frac{\left(d+e x^2\right)^{3/2}}{3 a x^3}","\frac{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(\frac{-a b e-2 a c d+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{2 a^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(-\frac{-a b e-2 a c d+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{2 a^2 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(-\frac{-a b e-2 a c d+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\right)}{2 a^2}+\frac{\sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \left(\frac{-a b e-2 a c d+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\right)}{2 a^2}+\frac{\sqrt{d+e x^2} (b d-a e)}{a^2 x}-\frac{\sqrt{e} (b d-a e) \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{a^2}-\frac{\left(d+e x^2\right)^{3/2}}{3 a x^3}",1,"((b*d - a*e)*Sqrt[d + e*x^2])/(a^2*x) - (d + e*x^2)^(3/2)/(3*a*x^3) + (Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(b*d - a*e + (b^2*d - 2*a*c*d - a*b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(2*a^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(b*d - a*e - (b^2*d - 2*a*c*d - a*b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(2*a^2*Sqrt[b + Sqrt[b^2 - 4*a*c]]) - (Sqrt[e]*(b*d - a*e)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/a^2 + (Sqrt[e]*(b*d - a*e - (b^2*d - 2*a*c*d - a*b*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(2*a^2) + (Sqrt[e]*(b*d - a*e + (b^2*d - 2*a*c*d - a*b*e)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(2*a^2)","A",19,10,29,0.3448,1,"{1295, 264, 6728, 277, 217, 206, 1692, 402, 377, 205}"
376,1,281,0,7.3356144,"\int \frac{x^5 \sqrt{1-x^2}}{a+b x^2+c x^4} \, dx","Int[(x^5*Sqrt[1 - x^2])/(a + b*x^2 + c*x^4),x]","\frac{\left(-\frac{-3 a b c-2 a c^2+b^2 c+b^3}{\sqrt{b^2-4 a c}}-a c+b^2+b c\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{1-x^2}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{2} c^{5/2} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}+\frac{\left(\frac{-3 a b c-2 a c^2+b^2 c+b^3}{\sqrt{b^2-4 a c}}-a c+b^2+b c\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{1-x^2}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{2} c^{5/2} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}-\frac{b \sqrt{1-x^2}}{c^2}-\frac{\left(1-x^2\right)^{3/2}}{3 c}","\frac{\left(-\frac{-3 a b c-2 a c^2+b^2 c+b^3}{\sqrt{b^2-4 a c}}-a c+b^2+b c\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{1-x^2}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{2} c^{5/2} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}+\frac{\left(\frac{-3 a b c-2 a c^2+b^2 c+b^3}{\sqrt{b^2-4 a c}}-a c+b^2+b c\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{1-x^2}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{2} c^{5/2} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}-\frac{b \sqrt{1-x^2}}{c^2}-\frac{\left(1-x^2\right)^{3/2}}{3 c}",1,"-((b*Sqrt[1 - x^2])/c^2) - (1 - x^2)^(3/2)/(3*c) + ((b^2 - a*c + b*c - (b^3 - 3*a*b*c + b^2*c - 2*a*c^2)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[1 - x^2])/Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(5/2)*Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]) + ((b^2 - a*c + b*c + (b^3 - 3*a*b*c + b^2*c - 2*a*c^2)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[1 - x^2])/Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(5/2)*Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]])","A",7,5,29,0.1724,1,"{1251, 897, 1287, 1166, 208}"
377,1,229,0,1.7511119,"\int \frac{x^3 \sqrt{1-x^2}}{a+b x^2+c x^4} \, dx","Int[(x^3*Sqrt[1 - x^2])/(a + b*x^2 + c*x^4),x]","-\frac{\left(-\frac{-2 a c+b^2+b c}{\sqrt{b^2-4 a c}}+b+c\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{1-x^2}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{2} c^{3/2} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{\left(\frac{-2 a c+b^2+b c}{\sqrt{b^2-4 a c}}+b+c\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{1-x^2}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}+\frac{\sqrt{1-x^2}}{c}","-\frac{\left(-\frac{-2 a c+b^2+b c}{\sqrt{b^2-4 a c}}+b+c\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{1-x^2}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{2} c^{3/2} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{\left(\frac{-2 a c+b^2+b c}{\sqrt{b^2-4 a c}}+b+c\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{1-x^2}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}+\frac{\sqrt{1-x^2}}{c}",1,"Sqrt[1 - x^2]/c - ((b + c - (b^2 - 2*a*c + b*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[1 - x^2])/Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]) - ((b + c + (b^2 - 2*a*c + b*c)/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[1 - x^2])/Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]])","A",6,5,29,0.1724,1,"{1251, 824, 826, 1166, 208}"
378,1,182,0,0.2679613,"\int \frac{x \sqrt{1-x^2}}{a+b x^2+c x^4} \, dx","Int[(x*Sqrt[1 - x^2])/(a + b*x^2 + c*x^4),x]","\frac{\sqrt{\sqrt{b^2-4 a c}+b+2 c} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{1-x^2}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}-\frac{\sqrt{-\sqrt{b^2-4 a c}+b+2 c} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{1-x^2}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}","\frac{\sqrt{\sqrt{b^2-4 a c}+b+2 c} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{1-x^2}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}-\frac{\sqrt{-\sqrt{b^2-4 a c}+b+2 c} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{1-x^2}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}",1,"-((Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[1 - x^2])/Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c])) + (Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[1 - x^2])/Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c])","A",5,4,27,0.1481,1,"{1247, 699, 1130, 208}"
379,1,241,0,1.6454326,"\int \frac{\sqrt{1-x^2}}{x \left(a+b x^2+c x^4\right)} \, dx","Int[Sqrt[1 - x^2]/(x*(a + b*x^2 + c*x^4)),x]","\frac{\sqrt{c} \left(\sqrt{b^2-4 a c}+2 a+b\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{1-x^2}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{2} a \sqrt{b^2-4 a c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{\sqrt{c} \left(-\sqrt{b^2-4 a c}+2 a+b\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{1-x^2}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{2} a \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}-\frac{\tanh ^{-1}\left(\sqrt{1-x^2}\right)}{a}","\frac{\sqrt{c} \left(\sqrt{b^2-4 a c}+2 a+b\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{1-x^2}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{2} a \sqrt{b^2-4 a c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{\sqrt{c} \left(-\sqrt{b^2-4 a c}+2 a+b\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{1-x^2}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{2} a \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}-\frac{\tanh ^{-1}\left(\sqrt{1-x^2}\right)}{a}",1,"-(ArcTanh[Sqrt[1 - x^2]]/a) + (Sqrt[c]*(2*a + b + Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[1 - x^2])/Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[b^2 - 4*a*c]*Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(2*a + b - Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[1 - x^2])/Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*Sqrt[b^2 - 4*a*c]*Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]])","A",8,6,29,0.2069,1,"{1251, 897, 1287, 207, 1166, 208}"
380,1,290,0,2.3622272,"\int \frac{\sqrt{1-x^2}}{x^3 \left(a+b x^2+c x^4\right)} \, dx","Int[Sqrt[1 - x^2]/(x^3*(a + b*x^2 + c*x^4)),x]","-\frac{\sqrt{c} \left(\frac{a (b-2 c)+b^2}{\sqrt{b^2-4 a c}}+a+b\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{1-x^2}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{2} a^2 \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{\sqrt{c} \left(-\frac{a (b-2 c)+b^2}{\sqrt{b^2-4 a c}}+a+b\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{1-x^2}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{2} a^2 \sqrt{\sqrt{b^2-4 a c}+b+2 c}}+\frac{(a+2 b) \tanh ^{-1}\left(\sqrt{1-x^2}\right)}{2 a^2}-\frac{1}{4 a \left(1-\sqrt{1-x^2}\right)}+\frac{1}{4 a \left(\sqrt{1-x^2}+1\right)}","-\frac{\sqrt{c} \left(\frac{a (b-2 c)+b^2}{\sqrt{b^2-4 a c}}+a+b\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{1-x^2}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{2} a^2 \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{\sqrt{c} \left(-\frac{a (b-2 c)+b^2}{\sqrt{b^2-4 a c}}+a+b\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{1-x^2}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{2} a^2 \sqrt{\sqrt{b^2-4 a c}+b+2 c}}+\frac{(a+2 b) \tanh ^{-1}\left(\sqrt{1-x^2}\right)}{2 a^2}-\frac{1}{4 a \left(1-\sqrt{1-x^2}\right)}+\frac{1}{4 a \left(\sqrt{1-x^2}+1\right)}",1,"-1/(4*a*(1 - Sqrt[1 - x^2])) + 1/(4*a*(1 + Sqrt[1 - x^2])) + ((a + 2*b)*ArcTanh[Sqrt[1 - x^2]])/(2*a^2) - (Sqrt[c]*(a + b + (b^2 + a*(b - 2*c))/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[1 - x^2])/Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^2*Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(a + b - (b^2 + a*(b - 2*c))/Sqrt[b^2 - 4*a*c])*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[1 - x^2])/Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^2*Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]])","A",8,6,29,0.2069,1,"{1251, 897, 1287, 207, 1166, 208}"
381,1,325,0,5.3906408,"\int \frac{x^4 \sqrt{1-x^2}}{a+b x^2+c x^4} \, dx","Int[(x^4*Sqrt[1 - x^2])/(a + b*x^2 + c*x^4),x]","-\frac{\left(-\frac{-3 a b c-2 a c^2+b^2 c+b^3}{\sqrt{b^2-4 a c}}-a c+b^2+b c\right) \tan ^{-1}\left(\frac{x \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}{\sqrt{1-x^2} \sqrt{b-\sqrt{b^2-4 a c}}}\right)}{c^2 \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{\left(\frac{-3 a b c-2 a c^2+b^2 c+b^3}{\sqrt{b^2-4 a c}}-a c+b^2+b c\right) \tan ^{-1}\left(\frac{x \sqrt{\sqrt{b^2-4 a c}+b+2 c}}{\sqrt{1-x^2} \sqrt{\sqrt{b^2-4 a c}+b}}\right)}{c^2 \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}+\frac{(2 b+c) \sin ^{-1}(x)}{2 c^2}+\frac{\sqrt{1-x^2} x}{2 c}","-\frac{\left(-\frac{-3 a b c-2 a c^2+b^2 c+b^3}{\sqrt{b^2-4 a c}}-a c+b^2+b c\right) \tan ^{-1}\left(\frac{x \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}{\sqrt{1-x^2} \sqrt{b-\sqrt{b^2-4 a c}}}\right)}{c^2 \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{\left(\frac{-3 a b c-2 a c^2+b^2 c+b^3}{\sqrt{b^2-4 a c}}-a c+b^2+b c\right) \tan ^{-1}\left(\frac{x \sqrt{\sqrt{b^2-4 a c}+b+2 c}}{\sqrt{1-x^2} \sqrt{\sqrt{b^2-4 a c}+b}}\right)}{c^2 \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}+\frac{(2 b+c) \sin ^{-1}(x)}{2 c^2}+\frac{\sqrt{1-x^2} x}{2 c}",1,"(x*Sqrt[1 - x^2])/(2*c) + ((2*b + c)*ArcSin[x])/(2*c^2) - ((b^2 - a*c + b*c - (b^3 - 3*a*b*c + b^2*c - 2*a*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[1 - x^2])])/(c^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]) - ((b^2 - a*c + b*c + (b^3 - 3*a*b*c + b^2*c - 2*a*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[1 - x^2])])/(c^2*Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]])","A",9,6,29,0.2069,1,"{1291, 388, 216, 1692, 377, 205}"
382,1,263,0,2.1348225,"\int \frac{x^2 \sqrt{1-x^2}}{a+b x^2+c x^4} \, dx","Int[(x^2*Sqrt[1 - x^2])/(a + b*x^2 + c*x^4),x]","\frac{\left(-\frac{-2 a c+b^2+b c}{\sqrt{b^2-4 a c}}+b+c\right) \tan ^{-1}\left(\frac{x \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}{\sqrt{1-x^2} \sqrt{b-\sqrt{b^2-4 a c}}}\right)}{c \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}+\frac{\left(\frac{-2 a c+b^2+b c}{\sqrt{b^2-4 a c}}+b+c\right) \tan ^{-1}\left(\frac{x \sqrt{\sqrt{b^2-4 a c}+b+2 c}}{\sqrt{1-x^2} \sqrt{\sqrt{b^2-4 a c}+b}}\right)}{c \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}-\frac{\sin ^{-1}(x)}{c}","\frac{\left(-\frac{-2 a c+b^2+b c}{\sqrt{b^2-4 a c}}+b+c\right) \tan ^{-1}\left(\frac{x \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}{\sqrt{1-x^2} \sqrt{b-\sqrt{b^2-4 a c}}}\right)}{c \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}+\frac{\left(\frac{-2 a c+b^2+b c}{\sqrt{b^2-4 a c}}+b+c\right) \tan ^{-1}\left(\frac{x \sqrt{\sqrt{b^2-4 a c}+b+2 c}}{\sqrt{1-x^2} \sqrt{\sqrt{b^2-4 a c}+b}}\right)}{c \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}-\frac{\sin ^{-1}(x)}{c}",1,"-(ArcSin[x]/c) + ((b + c - (b^2 - 2*a*c + b*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[1 - x^2])])/(c*Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]) + ((b + c + (b^2 - 2*a*c + b*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[1 - x^2])])/(c*Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]])","A",8,5,29,0.1724,1,"{1293, 216, 1692, 377, 205}"
383,1,220,0,0.294096,"\int \frac{\sqrt{1-x^2}}{a+b x^2+c x^4} \, dx","Int[Sqrt[1 - x^2]/(a + b*x^2 + c*x^4),x]","\frac{\sqrt{-\sqrt{b^2-4 a c}+b+2 c} \tan ^{-1}\left(\frac{x \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}{\sqrt{1-x^2} \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{\sqrt{b^2-4 a c}+b+2 c} \tan ^{-1}\left(\frac{x \sqrt{\sqrt{b^2-4 a c}+b+2 c}}{\sqrt{1-x^2} \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{-\sqrt{b^2-4 a c}+b+2 c} \tan ^{-1}\left(\frac{x \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}{\sqrt{1-x^2} \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{\sqrt{b^2-4 a c}+b+2 c} \tan ^{-1}\left(\frac{x \sqrt{\sqrt{b^2-4 a c}+b+2 c}}{\sqrt{1-x^2} \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[b + 2*c - Sqrt[b^2 - 4*a*c]]*ArcTan[(Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[1 - x^2])])/(Sqrt[b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]*ArcTan[(Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[1 - x^2])])/(Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",9,5,26,0.1923,1,"{1174, 402, 216, 377, 205}"
384,1,265,0,0.7795617,"\int \frac{\sqrt{1-x^2}}{x^2 \left(a+b x^2+c x^4\right)} \, dx","Int[Sqrt[1 - x^2]/(x^2*(a + b*x^2 + c*x^4)),x]","-\frac{c \left(\frac{2 a+b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{x \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}{\sqrt{1-x^2} \sqrt{b-\sqrt{b^2-4 a c}}}\right)}{a \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{c \left(1-\frac{2 a+b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{x \sqrt{\sqrt{b^2-4 a c}+b+2 c}}{\sqrt{1-x^2} \sqrt{\sqrt{b^2-4 a c}+b}}\right)}{a \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}-\frac{\sqrt{1-x^2}}{a x}","-\frac{c \left(\frac{2 a+b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{x \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}{\sqrt{1-x^2} \sqrt{b-\sqrt{b^2-4 a c}}}\right)}{a \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{c \left(1-\frac{2 a+b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{x \sqrt{\sqrt{b^2-4 a c}+b+2 c}}{\sqrt{1-x^2} \sqrt{\sqrt{b^2-4 a c}+b}}\right)}{a \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}-\frac{\sqrt{1-x^2}}{a x}",1,"-(Sqrt[1 - x^2]/(a*x)) - (c*(1 + (2*a + b)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[1 - x^2])])/(a*Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]) - (c*(1 - (2*a + b)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[1 - x^2])])/(a*Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]])","A",8,5,29,0.1724,1,"{1295, 264, 1692, 377, 205}"
385,1,96,0,0.2003986,"\int \frac{x^2 \sqrt{1-x^2}}{-1+x^2+x^4} \, dx","Int[(x^2*Sqrt[1 - x^2])/(-1 + x^2 + x^4),x]","\sqrt{\frac{1}{5} \left(2+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)} x}{\sqrt{1-x^2}}\right)-\sqrt{\frac{1}{5} \left(\sqrt{5}-2\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{2} \left(\sqrt{5}-1\right)} x}{\sqrt{1-x^2}}\right)-\sin ^{-1}(x)","\sqrt{\frac{1}{5} \left(2+\sqrt{5}\right)} \tan ^{-1}\left(\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)} x}{\sqrt{1-x^2}}\right)-\sqrt{\frac{1}{5} \left(\sqrt{5}-2\right)} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{2} \left(\sqrt{5}-1\right)} x}{\sqrt{1-x^2}}\right)-\sin ^{-1}(x)",1,"-ArcSin[x] + Sqrt[(2 + Sqrt[5])/5]*ArcTan[(Sqrt[(1 + Sqrt[5])/2]*x)/Sqrt[1 - x^2]] - Sqrt[(-2 + Sqrt[5])/5]*ArcTanh[(Sqrt[(-1 + Sqrt[5])/2]*x)/Sqrt[1 - x^2]]","A",8,6,25,0.2400,1,"{1293, 216, 1692, 377, 207, 203}"
386,1,479,0,1.8582092,"\int \frac{x^8}{\sqrt{d+e x^2} \left(a+b x^2+c x^4\right)} \, dx","Int[x^8/(Sqrt[d + e*x^2]*(a + b*x^2 + c*x^4)),x]","-\frac{\left(-\frac{2 a^2 c^2-4 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-2 a b c+b^3\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{c^3 \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\left(\frac{2 a^2 c^2-4 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-2 a b c+b^3\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{c^3 \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{\left(b^2-a c\right) \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{c^3 \sqrt{e}}+\frac{b d \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{2 c^2 e^{3/2}}-\frac{b x \sqrt{d+e x^2}}{2 c^2 e}+\frac{3 d^2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{8 c e^{5/2}}-\frac{3 d x \sqrt{d+e x^2}}{8 c e^2}+\frac{x^3 \sqrt{d+e x^2}}{4 c e}","-\frac{\left(-\frac{2 a^2 c^2-4 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-2 a b c+b^3\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{c^3 \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\left(\frac{2 a^2 c^2-4 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-2 a b c+b^3\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{c^3 \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{\left(b^2-a c\right) \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{c^3 \sqrt{e}}+\frac{b d \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{2 c^2 e^{3/2}}-\frac{b x \sqrt{d+e x^2}}{2 c^2 e}+\frac{3 d^2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{8 c e^{5/2}}-\frac{3 d x \sqrt{d+e x^2}}{8 c e^2}+\frac{x^3 \sqrt{d+e x^2}}{4 c e}",1,"(-3*d*x*Sqrt[d + e*x^2])/(8*c*e^2) - (b*x*Sqrt[d + e*x^2])/(2*c^2*e) + (x^3*Sqrt[d + e*x^2])/(4*c*e) - ((b^3 - 2*a*b*c - (b^4 - 4*a*b^2*c + 2*a^2*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(c^3*Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - ((b^3 - 2*a*b*c + (b^4 - 4*a*b^2*c + 2*a^2*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(c^3*Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]) + (3*d^2*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(8*c*e^(5/2)) + (b*d*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(2*c^2*e^(3/2)) + ((b^2 - a*c)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(c^3*Sqrt[e])","A",17,7,29,0.2414,1,"{1303, 217, 206, 321, 1692, 377, 205}"
387,1,366,0,1.1727002,"\int \frac{x^6}{\sqrt{d+e x^2} \left(a+b x^2+c x^4\right)} \, dx","Int[x^6/(Sqrt[d + e*x^2]*(a + b*x^2 + c*x^4)),x]","\frac{\left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{c^2 \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{c^2 \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{c^2 \sqrt{e}}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{2 c e^{3/2}}+\frac{x \sqrt{d+e x^2}}{2 c e}","\frac{\left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{c^2 \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{c^2 \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{c^2 \sqrt{e}}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{2 c e^{3/2}}+\frac{x \sqrt{d+e x^2}}{2 c e}",1,"(x*Sqrt[d + e*x^2])/(2*c*e) + ((b^2 - a*c - (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(c^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + ((b^2 - a*c + (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(c^2*Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]) - (d*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(2*c*e^(3/2)) - (b*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(c^2*Sqrt[e])","A",13,7,29,0.2414,1,"{1303, 217, 206, 321, 1692, 377, 205}"
388,1,298,0,0.723755,"\int \frac{x^4}{\sqrt{d+e x^2} \left(a+b x^2+c x^4\right)} \, dx","Int[x^4/(Sqrt[d + e*x^2]*(a + b*x^2 + c*x^4)),x]","-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{c \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{c \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{c \sqrt{e}}","-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{c \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{c \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{c \sqrt{e}}",1,"-(((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(c*Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e])) - ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(c*Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]) + ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/(c*Sqrt[e])","A",10,6,29,0.2069,1,"{1303, 217, 206, 1692, 377, 205}"
389,1,240,0,0.3042579,"\int \frac{x^2}{\sqrt{d+e x^2} \left(a+b x^2+c x^4\right)} \, dx","Int[x^2/(Sqrt[d + e*x^2]*(a + b*x^2 + c*x^4)),x]","\frac{\sqrt{\sqrt{b^2-4 a c}+b} \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{\sqrt{b-\sqrt{b^2-4 a c}} \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}","\frac{\sqrt{\sqrt{b^2-4 a c}+b} \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{\sqrt{b-\sqrt{b^2-4 a c}} \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}",1,"-((Sqrt[b - Sqrt[b^2 - 4*a*c]]*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e])) + (Sqrt[b + Sqrt[b^2 - 4*a*c]]*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",6,3,29,0.1034,1,"{1303, 377, 205}"
390,1,243,0,0.1782827,"\int \frac{1}{\sqrt{d+e x^2} \left(a+b x^2+c x^4\right)} \, dx","Int[1/(Sqrt[d + e*x^2]*(a + b*x^2 + c*x^4)),x]","\frac{2 c \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{2 c \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}","\frac{2 c \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{2 c \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{\sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}",1,"(2*c*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(Sqrt[b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - (2*c*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",5,3,26,0.1154,1,"{1174, 377, 205}"
391,1,280,0,0.602196,"\int \frac{1}{x^2 \sqrt{d+e x^2} \left(a+b x^2+c x^4\right)} \, dx","Int[1/(x^2*Sqrt[d + e*x^2]*(a + b*x^2 + c*x^4)),x]","-\frac{c \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{a \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{c \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{a \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{\sqrt{d+e x^2}}{a d x}","-\frac{c \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{a \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{c \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{a \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{\sqrt{d+e x^2}}{a d x}",1,"-(Sqrt[d + e*x^2]/(a*d*x)) - (c*(1 + b/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(a*Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - (c*(1 - b/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(a*Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",9,5,29,0.1724,1,"{1303, 264, 1692, 377, 205}"
392,1,341,0,0.7413856,"\int \frac{1}{x^4 \sqrt{d+e x^2} \left(a+b x^2+c x^4\right)} \, dx","Int[1/(x^4*Sqrt[d + e*x^2]*(a + b*x^2 + c*x^4)),x]","\frac{c \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{a^2 \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{c \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{a^2 \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{b \sqrt{d+e x^2}}{a^2 d x}+\frac{2 e \sqrt{d+e x^2}}{3 a d^2 x}-\frac{\sqrt{d+e x^2}}{3 a d x^3}","\frac{c \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{a^2 \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{c \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{a^2 \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{b \sqrt{d+e x^2}}{a^2 d x}+\frac{2 e \sqrt{d+e x^2}}{3 a d^2 x}-\frac{\sqrt{d+e x^2}}{3 a d x^3}",1,"-Sqrt[d + e*x^2]/(3*a*d*x^3) + (b*Sqrt[d + e*x^2])/(a^2*d*x) + (2*e*Sqrt[d + e*x^2])/(3*a*d^2*x) + (c*(b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(a^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + (c*(b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(a^2*Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",11,6,29,0.2069,1,"{1303, 271, 264, 1692, 377, 205}"
393,1,443,0,1.4320154,"\int \frac{1}{x^6 \sqrt{d+e x^2} \left(a+b x^2+c x^4\right)} \, dx","Int[1/(x^6*Sqrt[d + e*x^2]*(a + b*x^2 + c*x^4)),x]","-\frac{\left(b^2-a c\right) \sqrt{d+e x^2}}{a^3 d x}-\frac{c \left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{a^3 \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{c \left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{a^3 \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{2 b e \sqrt{d+e x^2}}{3 a^2 d^2 x}+\frac{b \sqrt{d+e x^2}}{3 a^2 d x^3}-\frac{8 e^2 \sqrt{d+e x^2}}{15 a d^3 x}+\frac{4 e \sqrt{d+e x^2}}{15 a d^2 x^3}-\frac{\sqrt{d+e x^2}}{5 a d x^5}","-\frac{\left(b^2-a c\right) \sqrt{d+e x^2}}{a^3 d x}-\frac{c \left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{a^3 \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{c \left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{a^3 \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{2 b e \sqrt{d+e x^2}}{3 a^2 d^2 x}+\frac{b \sqrt{d+e x^2}}{3 a^2 d x^3}-\frac{8 e^2 \sqrt{d+e x^2}}{15 a d^3 x}+\frac{4 e \sqrt{d+e x^2}}{15 a d^2 x^3}-\frac{\sqrt{d+e x^2}}{5 a d x^5}",1,"-Sqrt[d + e*x^2]/(5*a*d*x^5) + (b*Sqrt[d + e*x^2])/(3*a^2*d*x^3) + (4*e*Sqrt[d + e*x^2])/(15*a*d^2*x^3) - ((b^2 - a*c)*Sqrt[d + e*x^2])/(a^3*d*x) - (2*b*e*Sqrt[d + e*x^2])/(3*a^2*d^2*x) - (8*e^2*Sqrt[d + e*x^2])/(15*a*d^3*x) - (c*(b^2 - a*c + (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(a^3*Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - (c*(b^2 - a*c - (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(a^3*Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",14,6,29,0.2069,1,"{1303, 271, 264, 1692, 377, 205}"
394,1,507,0,4.3278009,"\int \frac{x^6}{\left(d+e x^2\right)^{3/2} \left(a+b x^2+c x^4\right)} \, dx","Int[x^6/((d + e*x^2)^(3/2)*(a + b*x^2 + c*x^4)),x]","\frac{\left(-\frac{2 a^2 c e-a b^2 e-3 a b c d+b^3 d}{\sqrt{b^2-4 a c}}-a b e-a c d+b^2 d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{c \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}+\frac{\left(\frac{2 a^2 c e-a b^2 e-3 a b c d+b^3 d}{\sqrt{b^2-4 a c}}-a b e-a c d+b^2 d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{c \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}-\frac{d^2 x}{e \sqrt{d+e x^2} \left(a e^2-b d e+c d^2\right)}+\frac{d^2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{e^{3/2} \left(a e^2-b d e+c d^2\right)}-\frac{(b d-a e) \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{c \sqrt{e} \left(a e^2-b d e+c d^2\right)}","\frac{2 \left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{c \sqrt{b-\sqrt{b^2-4 a c}} \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)^{3/2}}+\frac{2 \left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{c \sqrt{\sqrt{b^2-4 a c}+b} \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)^{3/2}}-\frac{d^2 x}{e \sqrt{d+e x^2} \left(a e^2-b d e+c d^2\right)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{c e^{3/2}}",1,"-((d^2*x)/(e*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x^2])) + ((b^2*d - a*c*d - a*b*e - (b^3*d - 3*a*b*c*d - a*b^2*e + 2*a^2*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(c*Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)) + ((b^2*d - a*c*d - a*b*e + (b^3*d - 3*a*b*c*d - a*b^2*e + 2*a^2*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(c*Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)) + (d^2*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(e^(3/2)*(c*d^2 - b*d*e + a*e^2)) - ((b*d - a*e)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(c*Sqrt[e]*(c*d^2 - b*d*e + a*e^2))","A",14,7,29,0.2414,1,"{1297, 288, 217, 206, 1692, 377, 205}"
395,1,360,0,1.2670619,"\int \frac{x^4}{\left(d+e x^2\right)^{3/2} \left(a+b x^2+c x^4\right)} \, dx","Int[x^4/((d + e*x^2)^(3/2)*(a + b*x^2 + c*x^4)),x]","-\frac{\left(-\frac{-a b e-2 a c d+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}-\frac{\left(\frac{-a b e-2 a c d+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}+\frac{d x}{\sqrt{d+e x^2} \left(a e^2-b d e+c d^2\right)}","-\frac{\left(-\frac{-a b e-2 a c d+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}-\frac{\left(\frac{-a b e-2 a c d+b^2 d}{\sqrt{b^2-4 a c}}-a e+b d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}+\frac{d x}{\sqrt{d+e x^2} \left(a e^2-b d e+c d^2\right)}",1,"(d*x)/((c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x^2]) - ((b*d - a*e - (b^2*d - 2*a*c*d - a*b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)) - ((b*d - a*e + (b^2*d - 2*a*c*d - a*b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2))","A",8,5,29,0.1724,1,"{1297, 191, 1692, 377, 205}"
396,1,333,0,0.6578202,"\int \frac{x^2}{\left(d+e x^2\right)^{3/2} \left(a+b x^2+c x^4\right)} \, dx","Int[x^2/((d + e*x^2)^(3/2)*(a + b*x^2 + c*x^4)),x]","\frac{c \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}+\frac{c \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}-\frac{e x}{\sqrt{d+e x^2} \left(a e^2-b d e+c d^2\right)}","\frac{c \left(d-\frac{b d-2 a e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}+\frac{c \left(\frac{b d-2 a e}{\sqrt{b^2-4 a c}}+d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}-\frac{e x}{\sqrt{d+e x^2} \left(a e^2-b d e+c d^2\right)}",1,"-((e*x)/((c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x^2])) + (c*(d - (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)) + (c*(d + (b*d - 2*a*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2))","A",8,5,29,0.1724,1,"{1299, 191, 1692, 377, 205}"
397,1,341,0,0.7738412,"\int \frac{1}{\left(d+e x^2\right)^{3/2} \left(a+b x^2+c x^4\right)} \, dx","Int[1/((d + e*x^2)^(3/2)*(a + b*x^2 + c*x^4)),x]","-\frac{c \left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}-\frac{c \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}+\frac{e^2 x}{d \sqrt{d+e x^2} \left(a e^2-b d e+c d^2\right)}","-\frac{c \left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}-\frac{c \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}+\frac{e^2 x}{d \sqrt{d+e x^2} \left(a e^2-b d e+c d^2\right)}",1,"(e^2*x)/(d*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x^2]) - (c*(e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)) - (c*(e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2))","A",8,5,26,0.1923,1,"{1172, 191, 1692, 377, 205}"
398,1,462,0,2.836659,"\int \frac{1}{x^2 \left(d+e x^2\right)^{3/2} \left(a+b x^2+c x^4\right)} \, dx","Int[1/(x^2*(d + e*x^2)^(3/2)*(a + b*x^2 + c*x^4)),x]","-\frac{c \left(\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{a \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}-\frac{c \left(-\frac{2 a c e+b^2 (-e)+b c d}{\sqrt{b^2-4 a c}}-b e+c d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{a \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}-\frac{2 e^3 x}{d^2 \sqrt{d+e x^2} \left(a e^2-b d e+c d^2\right)}-\frac{e^2}{d x \sqrt{d+e x^2} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{d+e x^2} (c d-b e)}{a d x \left(a e^2-b d e+c d^2\right)}","-\frac{2 c^2 \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{a \sqrt{b-\sqrt{b^2-4 a c}} \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)^{3/2}}-\frac{2 c^2 \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{a \sqrt{\sqrt{b^2-4 a c}+b} \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)^{3/2}}+\frac{e x (c d-b e)}{a d \sqrt{d+e x^2} \left(e (a e-b d)+c d^2\right)}+\frac{-d-2 e x^2}{a d^2 x \sqrt{d+e x^2}}",1,"-(e^2/(d*(c*d^2 - b*d*e + a*e^2)*x*Sqrt[d + e*x^2])) - (2*e^3*x)/(d^2*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x^2]) - ((c*d - b*e)*Sqrt[d + e*x^2])/(a*d*(c*d^2 - b*d*e + a*e^2)*x) - (c*(c*d - b*e + (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(a*Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)) - (c*(c*d - b*e - (b*c*d - b^2*e + 2*a*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(a*Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2))","A",12,8,29,0.2759,1,"{1301, 271, 191, 6728, 264, 1692, 377, 205}"
399,1,647,0,5.5664071,"\int \frac{1}{x^4 \left(d+e x^2\right)^{3/2} \left(a+b x^2+c x^4\right)} \, dx","Int[1/(x^4*(d + e*x^2)^(3/2)*(a + b*x^2 + c*x^4)),x]","\frac{c \left(\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{a^2 \sqrt{b-\sqrt{b^2-4 a c}} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}+\frac{c \left(-\frac{3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)}{\sqrt{b^2-4 a c}}+a c e+b^2 (-e)+b c d\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{a^2 \sqrt{\sqrt{b^2-4 a c}+b} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{d+e x^2} \left(a c e+b^2 (-e)+b c d\right)}{a^2 d x \left(a e^2-b d e+c d^2\right)}+\frac{8 e^4 x}{3 d^3 \sqrt{d+e x^2} \left(a e^2-b d e+c d^2\right)}+\frac{4 e^3}{3 d^2 x \sqrt{d+e x^2} \left(a e^2-b d e+c d^2\right)}-\frac{e^2}{3 d x^3 \sqrt{d+e x^2} \left(a e^2-b d e+c d^2\right)}+\frac{2 e \sqrt{d+e x^2} (c d-b e)}{3 a d^2 x \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{d+e x^2} (c d-b e)}{3 a d x^3 \left(a e^2-b d e+c d^2\right)}","\frac{2 c^2 \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}{\sqrt{b-\sqrt{b^2-4 a c}} \sqrt{d+e x^2}}\right)}{a^2 \sqrt{b-\sqrt{b^2-4 a c}} \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)^{3/2}}+\frac{2 c^2 \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{x \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}{\sqrt{\sqrt{b^2-4 a c}+b} \sqrt{d+e x^2}}\right)}{a^2 \sqrt{\sqrt{b^2-4 a c}+b} \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)^{3/2}}-\frac{e x \left(a c e+b^2 (-e)+b c d\right)}{a^2 d \sqrt{d+e x^2} \left(e (a e-b d)+c d^2\right)}+\frac{2 e x (4 a e+3 b d)}{3 a^2 d^3 \sqrt{d+e x^2}}+\frac{4 a e+3 b d}{3 a^2 d^2 x \sqrt{d+e x^2}}-\frac{1}{3 a d x^3 \sqrt{d+e x^2}}",1,"-e^2/(3*d*(c*d^2 - b*d*e + a*e^2)*x^3*Sqrt[d + e*x^2]) + (4*e^3)/(3*d^2*(c*d^2 - b*d*e + a*e^2)*x*Sqrt[d + e*x^2]) + (8*e^4*x)/(3*d^3*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x^2]) - ((c*d - b*e)*Sqrt[d + e*x^2])/(3*a*d*(c*d^2 - b*d*e + a*e^2)*x^3) + (2*e*(c*d - b*e)*Sqrt[d + e*x^2])/(3*a*d^2*(c*d^2 - b*d*e + a*e^2)*x) + ((b*c*d - b^2*e + a*c*e)*Sqrt[d + e*x^2])/(a^2*d*(c*d^2 - b*d*e + a*e^2)*x) + (c*(b*c*d - b^2*e + a*c*e + (b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(a^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)) + (c*(b*c*d - b^2*e + a*c*e - (b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*x)/(Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[d + e*x^2])])/(a^2*Sqrt[b + Sqrt[b^2 - 4*a*c]]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2))","A",15,8,29,0.2759,1,"{1301, 271, 191, 6728, 264, 1692, 377, 205}"
400,1,243,0,0.649722,"\int \frac{(f x)^m \left(d+e x^2\right)^q}{a+b x^2+c x^4} \, dx","Int[((f*x)^m*(d + e*x^2)^q)/(a + b*x^2 + c*x^4),x]","\frac{2 c (f x)^{m+1} \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{m+1}{2};1,-q;\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{f (m+1) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{2 c (f x)^{m+1} \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{m+1}{2};1,-q;\frac{m+3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{f (m+1) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}","\frac{2 c (f x)^{m+1} \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{m+1}{2};1,-q;\frac{m+3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{f (m+1) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{2 c (f x)^{m+1} \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{m+1}{2};1,-q;\frac{m+3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{f (m+1) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}",1,"(2*c*(f*x)^(1 + m)*(d + e*x^2)^q*AppellF1[(1 + m)/2, 1, -q, (3 + m)/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), -((e*x^2)/d)])/(Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])*f*(1 + m)*(1 + (e*x^2)/d)^q) - (2*c*(f*x)^(1 + m)*(d + e*x^2)^q*AppellF1[(1 + m)/2, 1, -q, (3 + m)/2, (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c]), -((e*x^2)/d)])/(Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])*f*(1 + m)*(1 + (e*x^2)/d)^q)","A",6,3,29,0.1034,1,"{1305, 511, 510}"
401,1,313,0,0.9388957,"\int \frac{x^7 \left(d+e x^2\right)^q}{a+b x^2+c x^4} \, dx","Int[(x^7*(d + e*x^2)^q)/(a + b*x^2 + c*x^4),x]","\frac{\left(\frac{b \left(b^2-3 a c\right)}{c \sqrt{b^2-4 a c}}+a-\frac{b^2}{c}\right) \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{2 c (q+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}+\frac{\left(-\frac{b \left(b^2-3 a c\right)}{c \sqrt{b^2-4 a c}}+a-\frac{b^2}{c}\right) \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{2 c (q+1) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}-\frac{(b e+c d) \left(d+e x^2\right)^{q+1}}{2 c^2 e^2 (q+1)}+\frac{\left(d+e x^2\right)^{q+2}}{2 c e^2 (q+2)}","\frac{\left(\frac{b \left(b^2-3 a c\right)}{c \sqrt{b^2-4 a c}}+a-\frac{b^2}{c}\right) \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{2 c (q+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}+\frac{\left(-\frac{b \left(b^2-3 a c\right)}{c \sqrt{b^2-4 a c}}+a-\frac{b^2}{c}\right) \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{2 c (q+1) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}-\frac{(b e+c d) \left(d+e x^2\right)^{q+1}}{2 c^2 e^2 (q+1)}+\frac{\left(d+e x^2\right)^{q+2}}{2 c e^2 (q+2)}",1,"-((c*d + b*e)*(d + e*x^2)^(1 + q))/(2*c^2*e^2*(1 + q)) + (d + e*x^2)^(2 + q)/(2*c*e^2*(2 + q)) + ((a - b^2/c + (b*(b^2 - 3*a*c))/(c*Sqrt[b^2 - 4*a*c]))*(d + e*x^2)^(1 + q)*Hypergeometric2F1[1, 1 + q, 2 + q, (2*c*(d + e*x^2))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)])/(2*c*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(1 + q)) + ((a - b^2/c - (b*(b^2 - 3*a*c))/(c*Sqrt[b^2 - 4*a*c]))*(d + e*x^2)^(1 + q)*Hypergeometric2F1[1, 1 + q, 2 + q, (2*c*(d + e*x^2))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(2*c*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(1 + q))","A",5,3,27,0.1111,1,"{1251, 1628, 68}"
402,1,256,0,0.5416684,"\int \frac{x^5 \left(d+e x^2\right)^q}{a+b x^2+c x^4} \, dx","Int[(x^5*(d + e*x^2)^q)/(a + b*x^2 + c*x^4),x]","\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{2 c (q+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{2 c (q+1) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}+\frac{\left(d+e x^2\right)^{q+1}}{2 c e (q+1)}","\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{2 c (q+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}+\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{2 c (q+1) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}+\frac{\left(d+e x^2\right)^{q+1}}{2 c e (q+1)}",1,"(d + e*x^2)^(1 + q)/(2*c*e*(1 + q)) + ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*(d + e*x^2)^(1 + q)*Hypergeometric2F1[1, 1 + q, 2 + q, (2*c*(d + e*x^2))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)])/(2*c*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(1 + q)) + ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*(d + e*x^2)^(1 + q)*Hypergeometric2F1[1, 1 + q, 2 + q, (2*c*(d + e*x^2))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(2*c*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(1 + q))","A",5,3,27,0.1111,1,"{1251, 1628, 68}"
403,1,210,0,0.3288819,"\int \frac{x^3 \left(d+e x^2\right)^q}{a+b x^2+c x^4} \, dx","Int[(x^3*(d + e*x^2)^q)/(a + b*x^2 + c*x^4),x]","-\frac{\left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{2 (q+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}-\frac{\left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{2 (q+1) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}","-\frac{\left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{2 (q+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}-\frac{\left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{2 (q+1) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}",1,"-((1 - b/Sqrt[b^2 - 4*a*c])*(d + e*x^2)^(1 + q)*Hypergeometric2F1[1, 1 + q, 2 + q, (2*c*(d + e*x^2))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)])/(2*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(1 + q)) - ((1 + b/Sqrt[b^2 - 4*a*c])*(d + e*x^2)^(1 + q)*Hypergeometric2F1[1, 1 + q, 2 + q, (2*c*(d + e*x^2))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(2*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(1 + q))","A",5,3,27,0.1111,1,"{1251, 830, 68}"
404,1,198,0,0.357378,"\int \frac{x \left(d+e x^2\right)^q}{a+b x^2+c x^4} \, dx","Int[(x*(d + e*x^2)^q)/(a + b*x^2 + c*x^4),x]","\frac{c \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{(q+1) \sqrt{b^2-4 a c} \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}-\frac{c \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{(q+1) \sqrt{b^2-4 a c} \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}","\frac{c \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{(q+1) \sqrt{b^2-4 a c} \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}-\frac{c \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{(q+1) \sqrt{b^2-4 a c} \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}",1,"-((c*(d + e*x^2)^(1 + q)*Hypergeometric2F1[1, 1 + q, 2 + q, (2*c*(d + e*x^2))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)])/(Sqrt[b^2 - 4*a*c]*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(1 + q))) + (c*(d + e*x^2)^(1 + q)*Hypergeometric2F1[1, 1 + q, 2 + q, (2*c*(d + e*x^2))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(Sqrt[b^2 - 4*a*c]*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(1 + q))","A",5,3,25,0.1200,1,"{1247, 711, 68}"
405,1,262,0,0.5021021,"\int \frac{\left(d+e x^2\right)^q}{x \left(a+b x^2+c x^4\right)} \, dx","Int[(d + e*x^2)^q/(x*(a + b*x^2 + c*x^4)),x]","\frac{c \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{2 a (q+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}+\frac{c \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{2 a (q+1) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}-\frac{\left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{e x^2}{d}+1\right)}{2 a d (q+1)}","\frac{c \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{2 a (q+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}+\frac{c \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{2 a (q+1) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}-\frac{\left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{e x^2}{d}+1\right)}{2 a d (q+1)}",1,"(c*(1 + b/Sqrt[b^2 - 4*a*c])*(d + e*x^2)^(1 + q)*Hypergeometric2F1[1, 1 + q, 2 + q, (2*c*(d + e*x^2))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)])/(2*a*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(1 + q)) + (c*(1 - b/Sqrt[b^2 - 4*a*c])*(d + e*x^2)^(1 + q)*Hypergeometric2F1[1, 1 + q, 2 + q, (2*c*(d + e*x^2))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(2*a*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(1 + q)) - ((d + e*x^2)^(1 + q)*Hypergeometric2F1[1, 1 + q, 2 + q, 1 + (e*x^2)/d])/(2*a*d*(1 + q))","A",8,5,27,0.1852,1,"{1251, 960, 65, 830, 68}"
406,1,322,0,0.66344,"\int \frac{\left(d+e x^2\right)^q}{x^3 \left(a+b x^2+c x^4\right)} \, dx","Int[(d + e*x^2)^q/(x^3*(a + b*x^2 + c*x^4)),x]","-\frac{c \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{2 a^2 (q+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}-\frac{c \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{2 a^2 (q+1) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}+\frac{b \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{e x^2}{d}+1\right)}{2 a^2 d (q+1)}+\frac{e \left(d+e x^2\right)^{q+1} \, _2F_1\left(2,q+1;q+2;\frac{e x^2}{d}+1\right)}{2 a d^2 (q+1)}","-\frac{c \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{2 a^2 (q+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}-\frac{c \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{2 c \left(e x^2+d\right)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{2 a^2 (q+1) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}+\frac{b \left(d+e x^2\right)^{q+1} \, _2F_1\left(1,q+1;q+2;\frac{e x^2}{d}+1\right)}{2 a^2 d (q+1)}+\frac{e \left(d+e x^2\right)^{q+1} \, _2F_1\left(2,q+1;q+2;\frac{e x^2}{d}+1\right)}{2 a d^2 (q+1)}",1,"-(c*(b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*(d + e*x^2)^(1 + q)*Hypergeometric2F1[1, 1 + q, 2 + q, (2*c*(d + e*x^2))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)])/(2*a^2*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(1 + q)) - (c*(b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*(d + e*x^2)^(1 + q)*Hypergeometric2F1[1, 1 + q, 2 + q, (2*c*(d + e*x^2))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(2*a^2*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(1 + q)) + (b*(d + e*x^2)^(1 + q)*Hypergeometric2F1[1, 1 + q, 2 + q, 1 + (e*x^2)/d])/(2*a^2*d*(1 + q)) + (e*(d + e*x^2)^(1 + q)*Hypergeometric2F1[2, 1 + q, 2 + q, 1 + (e*x^2)/d])/(2*a*d^2*(1 + q))","A",9,5,27,0.1852,1,"{1251, 960, 65, 830, 68}"
407,1,339,0,0.6281952,"\int \frac{x^6 \left(d+e x^2\right)^q}{a+b x^2+c x^4} \, dx","Int[(x^6*(d + e*x^2)^q)/(a + b*x^2 + c*x^4),x]","\frac{x \left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{c^2 \left(b-\sqrt{b^2-4 a c}\right)}+\frac{x \left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{c^2 \left(\sqrt{b^2-4 a c}+b\right)}-\frac{b x \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} \, _2F_1\left(\frac{1}{2},-q;\frac{3}{2};-\frac{e x^2}{d}\right)}{c^2}+\frac{x^3 \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} \, _2F_1\left(\frac{3}{2},-q;\frac{5}{2};-\frac{e x^2}{d}\right)}{3 c}","\frac{x \left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{c^2 \left(b-\sqrt{b^2-4 a c}\right)}+\frac{x \left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{c^2 \left(\sqrt{b^2-4 a c}+b\right)}-\frac{b x \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} \, _2F_1\left(\frac{1}{2},-q;\frac{3}{2};-\frac{e x^2}{d}\right)}{c^2}+\frac{x^3 \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} \, _2F_1\left(\frac{3}{2},-q;\frac{5}{2};-\frac{e x^2}{d}\right)}{3 c}",1,"((b^2 - a*c - (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*c])*x*(d + e*x^2)^q*AppellF1[1/2, 1, -q, 3/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), -((e*x^2)/d)])/(c^2*(b - Sqrt[b^2 - 4*a*c])*(1 + (e*x^2)/d)^q) + ((b^2 - a*c + (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*c])*x*(d + e*x^2)^q*AppellF1[1/2, 1, -q, 3/2, (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c]), -((e*x^2)/d)])/(c^2*(b + Sqrt[b^2 - 4*a*c])*(1 + (e*x^2)/d)^q) - (b*x*(d + e*x^2)^q*Hypergeometric2F1[1/2, -q, 3/2, -((e*x^2)/d)])/(c^2*(1 + (e*x^2)/d)^q) + (x^3*(d + e*x^2)^q*Hypergeometric2F1[3/2, -q, 5/2, -((e*x^2)/d)])/(3*c*(1 + (e*x^2)/d)^q)","A",12,8,27,0.2963,1,"{1303, 246, 245, 365, 364, 1692, 430, 429}"
408,1,273,0,0.5306396,"\int \frac{x^4 \left(d+e x^2\right)^q}{a+b x^2+c x^4} \, dx","Int[(x^4*(d + e*x^2)^q)/(a + b*x^2 + c*x^4),x]","-\frac{x \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{c \left(b-\sqrt{b^2-4 a c}\right)}-\frac{x \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{c \left(\sqrt{b^2-4 a c}+b\right)}+\frac{x \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} \, _2F_1\left(\frac{1}{2},-q;\frac{3}{2};-\frac{e x^2}{d}\right)}{c}","-\frac{x \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{c \left(b-\sqrt{b^2-4 a c}\right)}-\frac{x \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{c \left(\sqrt{b^2-4 a c}+b\right)}+\frac{x \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} \, _2F_1\left(\frac{1}{2},-q;\frac{3}{2};-\frac{e x^2}{d}\right)}{c}",1,"-(((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*x*(d + e*x^2)^q*AppellF1[1/2, 1, -q, 3/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), -((e*x^2)/d)])/(c*(b - Sqrt[b^2 - 4*a*c])*(1 + (e*x^2)/d)^q)) - ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*x*(d + e*x^2)^q*AppellF1[1/2, 1, -q, 3/2, (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c]), -((e*x^2)/d)])/(c*(b + Sqrt[b^2 - 4*a*c])*(1 + (e*x^2)/d)^q) + (x*(d + e*x^2)^q*Hypergeometric2F1[1/2, -q, 3/2, -((e*x^2)/d)])/(c*(1 + (e*x^2)/d)^q)","A",10,6,27,0.2222,1,"{1303, 246, 245, 1692, 430, 429}"
409,1,162,0,0.3135522,"\int \frac{x^2 \left(d+e x^2\right)^q}{a+b x^2+c x^4} \, dx","Int[(x^2*(d + e*x^2)^q)/(a + b*x^2 + c*x^4),x]","\frac{x \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{\sqrt{b^2-4 a c}}-\frac{x \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{\sqrt{b^2-4 a c}}","\frac{x \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{\sqrt{b^2-4 a c}}-\frac{x \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{\sqrt{b^2-4 a c}}",1,"-((x*(d + e*x^2)^q*AppellF1[1/2, 1, -q, 3/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), -((e*x^2)/d)])/(Sqrt[b^2 - 4*a*c]*(1 + (e*x^2)/d)^q)) + (x*(d + e*x^2)^q*AppellF1[1/2, 1, -q, 3/2, (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c]), -((e*x^2)/d)])/(Sqrt[b^2 - 4*a*c]*(1 + (e*x^2)/d)^q)","A",6,3,27,0.1111,1,"{1303, 430, 429}"
410,1,190,0,0.2938365,"\int \frac{\left(d+e x^2\right)^q}{a+b x^2+c x^4} \, dx","Int[(d + e*x^2)^q/(a + b*x^2 + c*x^4),x]","-\frac{2 c x \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{-b \sqrt{b^2-4 a c}-4 a c+b^2}-\frac{2 c x \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{b \sqrt{b^2-4 a c}-4 a c+b^2}","-\frac{2 c x \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{-b \sqrt{b^2-4 a c}-4 a c+b^2}-\frac{2 c x \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{b \sqrt{b^2-4 a c}-4 a c+b^2}",1,"(-2*c*x*(d + e*x^2)^q*AppellF1[1/2, 1, -q, 3/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), -((e*x^2)/d)])/((b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c])*(1 + (e*x^2)/d)^q) - (2*c*x*(d + e*x^2)^q*AppellF1[1/2, 1, -q, 3/2, (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c]), -((e*x^2)/d)])/((b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c])*(1 + (e*x^2)/d)^q)","A",5,3,24,0.1250,1,"{1174, 430, 429}"
411,1,264,0,0.5529015,"\int \frac{\left(d+e x^2\right)^q}{x^2 \left(a+b x^2+c x^4\right)} \, dx","Int[(d + e*x^2)^q/(x^2*(a + b*x^2 + c*x^4)),x]","-\frac{c x \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{a \left(b-\sqrt{b^2-4 a c}\right)}-\frac{c x \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{a \left(\sqrt{b^2-4 a c}+b\right)}-\frac{\left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} \, _2F_1\left(-\frac{1}{2},-q;\frac{1}{2};-\frac{e x^2}{d}\right)}{a x}","-\frac{c x \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{a \left(b-\sqrt{b^2-4 a c}\right)}-\frac{c x \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{a \left(\sqrt{b^2-4 a c}+b\right)}-\frac{\left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} \, _2F_1\left(-\frac{1}{2},-q;\frac{1}{2};-\frac{e x^2}{d}\right)}{a x}",1,"-((c*(1 + b/Sqrt[b^2 - 4*a*c])*x*(d + e*x^2)^q*AppellF1[1/2, 1, -q, 3/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), -((e*x^2)/d)])/(a*(b - Sqrt[b^2 - 4*a*c])*(1 + (e*x^2)/d)^q)) - (c*(1 - b/Sqrt[b^2 - 4*a*c])*x*(d + e*x^2)^q*AppellF1[1/2, 1, -q, 3/2, (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c]), -((e*x^2)/d)])/(a*(b + Sqrt[b^2 - 4*a*c])*(1 + (e*x^2)/d)^q) - ((d + e*x^2)^q*Hypergeometric2F1[-1/2, -q, 1/2, -((e*x^2)/d)])/(a*x*(1 + (e*x^2)/d)^q)","A",10,6,27,0.2222,1,"{1303, 365, 364, 1692, 430, 429}"
412,1,328,0,0.6204631,"\int \frac{\left(d+e x^2\right)^q}{x^4 \left(a+b x^2+c x^4\right)} \, dx","Int[(d + e*x^2)^q/(x^4*(a + b*x^2 + c*x^4)),x]","\frac{c x \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{a^2 \left(b-\sqrt{b^2-4 a c}\right)}+\frac{c x \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{a^2 \left(\sqrt{b^2-4 a c}+b\right)}+\frac{b \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} \, _2F_1\left(-\frac{1}{2},-q;\frac{1}{2};-\frac{e x^2}{d}\right)}{a^2 x}-\frac{\left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} \, _2F_1\left(-\frac{3}{2},-q;-\frac{1}{2};-\frac{e x^2}{d}\right)}{3 a x^3}","\frac{c x \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b-\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{a^2 \left(b-\sqrt{b^2-4 a c}\right)}+\frac{c x \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} F_1\left(\frac{1}{2};1,-q;\frac{3}{2};-\frac{2 c x^2}{b+\sqrt{b^2-4 a c}},-\frac{e x^2}{d}\right)}{a^2 \left(\sqrt{b^2-4 a c}+b\right)}+\frac{b \left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} \, _2F_1\left(-\frac{1}{2},-q;\frac{1}{2};-\frac{e x^2}{d}\right)}{a^2 x}-\frac{\left(d+e x^2\right)^q \left(\frac{e x^2}{d}+1\right)^{-q} \, _2F_1\left(-\frac{3}{2},-q;-\frac{1}{2};-\frac{e x^2}{d}\right)}{3 a x^3}",1,"(c*(b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*x*(d + e*x^2)^q*AppellF1[1/2, 1, -q, 3/2, (-2*c*x^2)/(b - Sqrt[b^2 - 4*a*c]), -((e*x^2)/d)])/(a^2*(b - Sqrt[b^2 - 4*a*c])*(1 + (e*x^2)/d)^q) + (c*(b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*x*(d + e*x^2)^q*AppellF1[1/2, 1, -q, 3/2, (-2*c*x^2)/(b + Sqrt[b^2 - 4*a*c]), -((e*x^2)/d)])/(a^2*(b + Sqrt[b^2 - 4*a*c])*(1 + (e*x^2)/d)^q) - ((d + e*x^2)^q*Hypergeometric2F1[-3/2, -q, -1/2, -((e*x^2)/d)])/(3*a*x^3*(1 + (e*x^2)/d)^q) + (b*(d + e*x^2)^q*Hypergeometric2F1[-1/2, -q, 1/2, -((e*x^2)/d)])/(a^2*x*(1 + (e*x^2)/d)^q)","A",12,6,27,0.2222,1,"{1303, 365, 364, 1692, 430, 429}"
413,1,44,0,0.0722516,"\int \frac{\sqrt{1+\frac{1}{c^2 x^2}}}{\sqrt{1-c^4 x^4}} \, dx","Int[Sqrt[1 + 1/(c^2*x^2)]/Sqrt[1 - c^4*x^4],x]","-\frac{x \sqrt{\frac{1}{c^2 x^2}+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{\sqrt{c^2 x^2+1}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{1-c^4 x^4}}{c x \sqrt{\frac{1}{c^2 x^2}+1}}\right)}{c}",1,"-((Sqrt[1 + 1/(c^2*x^2)]*x*ArcTanh[Sqrt[1 - c^2*x^2]])/Sqrt[1 + c^2*x^2])","A",5,5,28,0.1786,1,"{1448, 1252, 848, 63, 208}"