1,1,50,0,0.0412663,"\int (d+e x) \left(a+b x^2+c x^4\right) \, dx","Int[(d + e*x)*(a + b*x^2 + c*x^4),x]","a d x+\frac{1}{2} a e x^2+\frac{1}{3} b d x^3+\frac{1}{4} b e x^4+\frac{1}{5} c d x^5+\frac{1}{6} c e x^6","a d x+\frac{1}{2} a e x^2+\frac{1}{3} b d x^3+\frac{1}{4} b e x^4+\frac{1}{5} c d x^5+\frac{1}{6} c e x^6",1,"a*d*x + (a*e*x^2)/2 + (b*d*x^3)/3 + (b*e*x^4)/4 + (c*d*x^5)/5 + (c*e*x^6)/6","A",2,1,18,0.05556,1,"{1671}"
2,1,69,0,0.0446495,"\int \left(d+e x+f x^2\right) \left(a+b x^2+c x^4\right) \, dx","Int[(d + e*x + f*x^2)*(a + b*x^2 + c*x^4),x]","\frac{1}{3} x^3 (a f+b d)+a d x+\frac{1}{2} a e x^2+\frac{1}{5} x^5 (b f+c d)+\frac{1}{4} b e x^4+\frac{1}{6} c e x^6+\frac{1}{7} c f x^7","\frac{1}{3} x^3 (a f+b d)+a d x+\frac{1}{2} a e x^2+\frac{1}{5} x^5 (b f+c d)+\frac{1}{4} b e x^4+\frac{1}{6} c e x^6+\frac{1}{7} c f x^7",1,"a*d*x + (a*e*x^2)/2 + ((b*d + a*f)*x^3)/3 + (b*e*x^4)/4 + ((c*d + b*f)*x^5)/5 + (c*e*x^6)/6 + (c*f*x^7)/7","A",2,1,23,0.04348,1,"{1657}"
3,1,88,0,0.0733669,"\int \left(d+e x+f x^2+g x^3\right) \left(a+b x^2+c x^4\right) \, dx","Int[(d + e*x + f*x^2 + g*x^3)*(a + b*x^2 + c*x^4),x]","\frac{1}{3} x^3 (a f+b d)+\frac{1}{4} x^4 (a g+b e)+a d x+\frac{1}{2} a e x^2+\frac{1}{5} x^5 (b f+c d)+\frac{1}{6} x^6 (b g+c e)+\frac{1}{7} c f x^7+\frac{1}{8} c g x^8","\frac{1}{3} x^3 (a f+b d)+\frac{1}{4} x^4 (a g+b e)+a d x+\frac{1}{2} a e x^2+\frac{1}{5} x^5 (b f+c d)+\frac{1}{6} x^6 (b g+c e)+\frac{1}{7} c f x^7+\frac{1}{8} c g x^8",1,"a*d*x + (a*e*x^2)/2 + ((b*d + a*f)*x^3)/3 + ((b*e + a*g)*x^4)/4 + ((c*d + b*f)*x^5)/5 + ((c*e + b*g)*x^6)/6 + (c*f*x^7)/7 + (c*g*x^8)/8","A",2,1,28,0.03571,1,"{1671}"
4,1,105,0,0.0948779,"\int \left(a+b x^2+c x^4\right) \left(d+e x+f x^2+g x^3+h x^4\right) \, dx","Int[(a + b*x^2 + c*x^4)*(d + e*x + f*x^2 + g*x^3 + h*x^4),x]","\frac{1}{5} x^5 (a h+b f+c d)+\frac{1}{3} x^3 (a f+b d)+\frac{1}{4} x^4 (a g+b e)+a d x+\frac{1}{2} a e x^2+\frac{1}{6} x^6 (b g+c e)+\frac{1}{7} x^7 (b h+c f)+\frac{1}{8} c g x^8+\frac{1}{9} c h x^9","\frac{1}{5} x^5 (a h+b f+c d)+\frac{1}{3} x^3 (a f+b d)+\frac{1}{4} x^4 (a g+b e)+a d x+\frac{1}{2} a e x^2+\frac{1}{6} x^6 (b g+c e)+\frac{1}{7} x^7 (b h+c f)+\frac{1}{8} c g x^8+\frac{1}{9} c h x^9",1,"a*d*x + (a*e*x^2)/2 + ((b*d + a*f)*x^3)/3 + ((b*e + a*g)*x^4)/4 + ((c*d + b*f + a*h)*x^5)/5 + ((c*e + b*g)*x^6)/6 + ((c*f + b*h)*x^7)/7 + (c*g*x^8)/8 + (c*h*x^9)/9","A",2,1,33,0.03030,1,"{1671}"
5,1,122,0,0.1113155,"\int \left(a+b x^2+c x^4\right) \left(d+e x+f x^2+g x^3+h x^4+i x^5\right) \, dx","Int[(a + b*x^2 + c*x^4)*(d + e*x + f*x^2 + g*x^3 + h*x^4 + i*x^5),x]","\frac{1}{5} x^5 (a h+b f+c d)+\frac{1}{6} x^6 (a i+b g+c e)+\frac{1}{3} x^3 (a f+b d)+\frac{1}{4} x^4 (a g+b e)+a d x+\frac{1}{2} a e x^2+\frac{1}{7} x^7 (b h+c f)+\frac{1}{8} x^8 (b i+c g)+\frac{1}{9} c h x^9+\frac{1}{10} c i x^{10}","\frac{1}{5} x^5 (a h+b f+c d)+\frac{1}{6} x^6 (a i+b g+c e)+\frac{1}{3} x^3 (a f+b d)+\frac{1}{4} x^4 (a g+b e)+a d x+\frac{1}{2} a e x^2+\frac{1}{7} x^7 (b h+c f)+\frac{1}{8} x^8 (b i+c g)+\frac{1}{9} c h x^9+\frac{1}{10} c i x^{10}",1,"a*d*x + (a*e*x^2)/2 + ((b*d + a*f)*x^3)/3 + ((b*e + a*g)*x^4)/4 + ((c*d + b*f + a*h)*x^5)/5 + ((c*e + b*g + a*i)*x^6)/6 + ((c*f + b*h)*x^7)/7 + ((c*g + b*i)*x^8)/8 + (c*h*x^9)/9 + (c*i*x^10)/10","A",2,1,38,0.02632,1,"{1671}"
6,1,112,0,0.1257783,"\int (d+e x) \left(a+b x^2+c x^4\right)^2 \, dx","Int[(d + e*x)*(a + b*x^2 + c*x^4)^2,x]","a^2 d x+\frac{1}{2} a^2 e x^2+\frac{1}{5} d x^5 \left(2 a c+b^2\right)+\frac{1}{6} e x^6 \left(2 a c+b^2\right)+\frac{2}{3} a b d x^3+\frac{1}{2} a b e x^4+\frac{2}{7} b c d x^7+\frac{1}{4} b c e x^8+\frac{1}{9} c^2 d x^9+\frac{1}{10} c^2 e x^{10}","a^2 d x+\frac{1}{2} a^2 e x^2+\frac{1}{5} d x^5 \left(2 a c+b^2\right)+\frac{1}{6} e x^6 \left(2 a c+b^2\right)+\frac{2}{3} a b d x^3+\frac{1}{2} a b e x^4+\frac{2}{7} b c d x^7+\frac{1}{4} b c e x^8+\frac{1}{9} c^2 d x^9+\frac{1}{10} c^2 e x^{10}",1,"a^2*d*x + (a^2*e*x^2)/2 + (2*a*b*d*x^3)/3 + (a*b*e*x^4)/2 + ((b^2 + 2*a*c)*d*x^5)/5 + ((b^2 + 2*a*c)*e*x^6)/6 + (2*b*c*d*x^7)/7 + (b*c*e*x^8)/4 + (c^2*d*x^9)/9 + (c^2*e*x^10)/10","A",2,1,20,0.05000,1,"{1671}"
7,1,154,0,0.1303521,"\int \left(d+e x+f x^2\right) \left(a+b x^2+c x^4\right)^2 \, dx","Int[(d + e*x + f*x^2)*(a + b*x^2 + c*x^4)^2,x]","a^2 d x+\frac{1}{2} a^2 e x^2+\frac{1}{7} x^7 \left(2 a c f+b^2 f+2 b c d\right)+\frac{1}{5} x^5 \left(2 a b f+2 a c d+b^2 d\right)+\frac{1}{6} e x^6 \left(2 a c+b^2\right)+\frac{1}{3} a x^3 (a f+2 b d)+\frac{1}{2} a b e x^4+\frac{1}{9} c x^9 (2 b f+c d)+\frac{1}{4} b c e x^8+\frac{1}{10} c^2 e x^{10}+\frac{1}{11} c^2 f x^{11}","a^2 d x+\frac{1}{2} a^2 e x^2+\frac{1}{7} x^7 \left(2 a c f+b^2 f+2 b c d\right)+\frac{1}{5} x^5 \left(2 a b f+2 a c d+b^2 d\right)+\frac{1}{6} e x^6 \left(2 a c+b^2\right)+\frac{1}{3} a x^3 (a f+2 b d)+\frac{1}{2} a b e x^4+\frac{1}{9} c x^9 (2 b f+c d)+\frac{1}{4} b c e x^8+\frac{1}{10} c^2 e x^{10}+\frac{1}{11} c^2 f x^{11}",1,"a^2*d*x + (a^2*e*x^2)/2 + (a*(2*b*d + a*f)*x^3)/3 + (a*b*e*x^4)/2 + ((b^2*d + 2*a*c*d + 2*a*b*f)*x^5)/5 + ((b^2 + 2*a*c)*e*x^6)/6 + ((2*b*c*d + b^2*f + 2*a*c*f)*x^7)/7 + (b*c*e*x^8)/4 + (c*(c*d + 2*b*f)*x^9)/9 + (c^2*e*x^10)/10 + (c^2*f*x^11)/11","A",2,1,25,0.04000,1,"{1657}"
8,1,196,0,0.1675122,"\int \left(d+e x+f x^2+g x^3\right) \left(a+b x^2+c x^4\right)^2 \, dx","Int[(d + e*x + f*x^2 + g*x^3)*(a + b*x^2 + c*x^4)^2,x]","a^2 d x+\frac{1}{2} a^2 e x^2+\frac{1}{7} x^7 \left(2 a c f+b^2 f+2 b c d\right)+\frac{1}{5} x^5 \left(2 a b f+2 a c d+b^2 d\right)+\frac{1}{8} x^8 \left(2 a c g+b^2 g+2 b c e\right)+\frac{1}{6} x^6 \left(2 a b g+2 a c e+b^2 e\right)+\frac{1}{3} a x^3 (a f+2 b d)+\frac{1}{4} a x^4 (a g+2 b e)+\frac{1}{9} c x^9 (2 b f+c d)+\frac{1}{10} c x^{10} (2 b g+c e)+\frac{1}{11} c^2 f x^{11}+\frac{1}{12} c^2 g x^{12}","a^2 d x+\frac{1}{2} a^2 e x^2+\frac{1}{7} x^7 \left(2 a c f+b^2 f+2 b c d\right)+\frac{1}{5} x^5 \left(2 a b f+2 a c d+b^2 d\right)+\frac{1}{8} x^8 \left(2 a c g+b^2 g+2 b c e\right)+\frac{1}{6} x^6 \left(2 a b g+2 a c e+b^2 e\right)+\frac{1}{3} a x^3 (a f+2 b d)+\frac{1}{4} a x^4 (a g+2 b e)+\frac{1}{9} c x^9 (2 b f+c d)+\frac{1}{10} c x^{10} (2 b g+c e)+\frac{1}{11} c^2 f x^{11}+\frac{1}{12} c^2 g x^{12}",1,"a^2*d*x + (a^2*e*x^2)/2 + (a*(2*b*d + a*f)*x^3)/3 + (a*(2*b*e + a*g)*x^4)/4 + ((b^2*d + 2*a*c*d + 2*a*b*f)*x^5)/5 + ((b^2*e + 2*a*c*e + 2*a*b*g)*x^6)/6 + ((2*b*c*d + b^2*f + 2*a*c*f)*x^7)/7 + ((2*b*c*e + b^2*g + 2*a*c*g)*x^8)/8 + (c*(c*d + 2*b*f)*x^9)/9 + (c*(c*e + 2*b*g)*x^10)/10 + (c^2*f*x^11)/11 + (c^2*g*x^12)/12","A",2,1,30,0.03333,1,"{1671}"
9,1,234,0,0.2380953,"\int \left(a+b x^2+c x^4\right)^2 \left(d+e x+f x^2+g x^3+h x^4\right) \, dx","Int[(a + b*x^2 + c*x^4)^2*(d + e*x + f*x^2 + g*x^3 + h*x^4),x]","a^2 d x+\frac{1}{2} a^2 e x^2+\frac{1}{9} x^9 \left(2 c (a h+b f)+b^2 h+c^2 d\right)+\frac{1}{7} x^7 \left(2 b (a h+c d)+2 a c f+b^2 f\right)+\frac{1}{5} x^5 \left(2 a b f+a (a h+2 c d)+b^2 d\right)+\frac{1}{8} x^8 \left(2 a c g+b^2 g+2 b c e\right)+\frac{1}{6} x^6 \left(2 a b g+2 a c e+b^2 e\right)+\frac{1}{3} a x^3 (a f+2 b d)+\frac{1}{4} a x^4 (a g+2 b e)+\frac{1}{10} c x^{10} (2 b g+c e)+\frac{1}{11} c x^{11} (2 b h+c f)+\frac{1}{12} c^2 g x^{12}+\frac{1}{13} c^2 h x^{13}","a^2 d x+\frac{1}{2} a^2 e x^2+\frac{1}{9} x^9 \left(2 c (a h+b f)+b^2 h+c^2 d\right)+\frac{1}{7} x^7 \left(2 b (a h+c d)+2 a c f+b^2 f\right)+\frac{1}{5} x^5 \left(2 a b f+a (a h+2 c d)+b^2 d\right)+\frac{1}{8} x^8 \left(2 a c g+b^2 g+2 b c e\right)+\frac{1}{6} x^6 \left(2 a b g+2 a c e+b^2 e\right)+\frac{1}{3} a x^3 (a f+2 b d)+\frac{1}{4} a x^4 (a g+2 b e)+\frac{1}{10} c x^{10} (2 b g+c e)+\frac{1}{11} c x^{11} (2 b h+c f)+\frac{1}{12} c^2 g x^{12}+\frac{1}{13} c^2 h x^{13}",1,"a^2*d*x + (a^2*e*x^2)/2 + (a*(2*b*d + a*f)*x^3)/3 + (a*(2*b*e + a*g)*x^4)/4 + ((b^2*d + 2*a*b*f + a*(2*c*d + a*h))*x^5)/5 + ((b^2*e + 2*a*c*e + 2*a*b*g)*x^6)/6 + ((b^2*f + 2*a*c*f + 2*b*(c*d + a*h))*x^7)/7 + ((2*b*c*e + b^2*g + 2*a*c*g)*x^8)/8 + ((c^2*d + b^2*h + 2*c*(b*f + a*h))*x^9)/9 + (c*(c*e + 2*b*g)*x^10)/10 + (c*(c*f + 2*b*h)*x^11)/11 + (c^2*g*x^12)/12 + (c^2*h*x^13)/13","A",2,1,35,0.02857,1,"{1671}"
10,1,45,0,0.0324412,"\int \frac{d+e x}{4-5 x^2+x^4} \, dx","Int[(d + e*x)/(4 - 5*x^2 + x^4),x]","-\frac{1}{6} d \tanh ^{-1}\left(\frac{x}{2}\right)+\frac{1}{3} d \tanh ^{-1}(x)-\frac{1}{6} e \log \left(1-x^2\right)+\frac{1}{6} e \log \left(4-x^2\right)","-\frac{1}{6} d \tanh ^{-1}\left(\frac{x}{2}\right)+\frac{1}{3} d \tanh ^{-1}(x)-\frac{1}{6} e \log \left(1-x^2\right)+\frac{1}{6} e \log \left(4-x^2\right)",1,"-(d*ArcTanh[x/2])/6 + (d*ArcTanh[x])/3 - (e*Log[1 - x^2])/6 + (e*Log[4 - x^2])/6","A",10,7,18,0.3889,1,"{1673, 12, 1093, 207, 1107, 616, 31}"
11,1,51,0,0.0566029,"\int \frac{d+e x+f x^2}{4-5 x^2+x^4} \, dx","Int[(d + e*x + f*x^2)/(4 - 5*x^2 + x^4),x]","-\frac{1}{6} (d+4 f) \tanh ^{-1}\left(\frac{x}{2}\right)+\frac{1}{3} (d+f) \tanh ^{-1}(x)-\frac{1}{6} e \log \left(1-x^2\right)+\frac{1}{6} e \log \left(4-x^2\right)","-\frac{1}{6} (d+4 f) \tanh ^{-1}\left(\frac{x}{2}\right)+\frac{1}{3} (d+f) \tanh ^{-1}(x)-\frac{1}{6} e \log \left(1-x^2\right)+\frac{1}{6} e \log \left(4-x^2\right)",1,"-((d + 4*f)*ArcTanh[x/2])/6 + ((d + f)*ArcTanh[x])/3 - (e*Log[1 - x^2])/6 + (e*Log[4 - x^2])/6","A",9,7,23,0.3043,1,"{1673, 1166, 207, 12, 1107, 616, 31}"
12,1,57,0,0.0722953,"\int \frac{d+e x+f x^2+g x^3}{4-5 x^2+x^4} \, dx","Int[(d + e*x + f*x^2 + g*x^3)/(4 - 5*x^2 + x^4),x]","-\frac{1}{6} (d+4 f) \tanh ^{-1}\left(\frac{x}{2}\right)+\frac{1}{3} (d+f) \tanh ^{-1}(x)-\frac{1}{6} (e+g) \log \left(1-x^2\right)+\frac{1}{6} (e+4 g) \log \left(4-x^2\right)","-\frac{1}{6} (d+4 f) \tanh ^{-1}\left(\frac{x}{2}\right)+\frac{1}{3} (d+f) \tanh ^{-1}(x)-\frac{1}{6} (e+g) \log \left(1-x^2\right)+\frac{1}{6} (e+4 g) \log \left(4-x^2\right)",1,"-((d + 4*f)*ArcTanh[x/2])/6 + ((d + f)*ArcTanh[x])/3 - ((e + g)*Log[1 - x^2])/6 + ((e + 4*g)*Log[4 - x^2])/6","A",8,6,28,0.2143,1,"{1673, 1166, 207, 1247, 632, 31}"
13,1,64,0,0.1470376,"\int \frac{d+e x+f x^2+g x^3+h x^4}{4-5 x^2+x^4} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4)/(4 - 5*x^2 + x^4),x]","-\frac{1}{6} \tanh ^{-1}\left(\frac{x}{2}\right) (d+4 f+16 h)+\frac{1}{3} \tanh ^{-1}(x) (d+f+h)-\frac{1}{6} (e+g) \log \left(1-x^2\right)+\frac{1}{6} (e+4 g) \log \left(4-x^2\right)+h x","-\frac{1}{6} \tanh ^{-1}\left(\frac{x}{2}\right) (d+4 f+16 h)+\frac{1}{3} \tanh ^{-1}(x) (d+f+h)-\frac{1}{6} (e+g) \log \left(1-x^2\right)+\frac{1}{6} (e+4 g) \log \left(4-x^2\right)+h x",1,"h*x - ((d + 4*f + 16*h)*ArcTanh[x/2])/6 + ((d + f + h)*ArcTanh[x])/3 - ((e + g)*Log[1 - x^2])/6 + ((e + 4*g)*Log[4 - x^2])/6","A",10,7,33,0.2121,1,"{1673, 1676, 1166, 207, 1247, 632, 31}"
14,1,76,0,0.1915228,"\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5}{4-5 x^2+x^4} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4 + i*x^5)/(4 - 5*x^2 + x^4),x]","-\frac{1}{6} \tanh ^{-1}\left(\frac{x}{2}\right) (d+4 f+16 h)+\frac{1}{3} \tanh ^{-1}(x) (d+f+h)-\frac{1}{6} \log \left(1-x^2\right) (e+g+i)+\frac{1}{6} \log \left(4-x^2\right) (e+4 g+16 i)+h x+\frac{i x^2}{2}","-\frac{1}{6} \tanh ^{-1}\left(\frac{x}{2}\right) (d+4 f+16 h)+\frac{1}{3} \tanh ^{-1}(x) (d+f+h)-\frac{1}{6} \log \left(1-x^2\right) (e+g+i)+\frac{1}{6} \log \left(4-x^2\right) (e+4 g+16 i)+h x+\frac{i x^2}{2}",1,"h*x + (i*x^2)/2 - ((d + 4*f + 16*h)*ArcTanh[x/2])/6 + ((d + f + h)*ArcTanh[x])/3 - ((e + g + i)*Log[1 - x^2])/6 + ((e + 4*g + 16*i)*Log[4 - x^2])/6","A",12,8,38,0.2105,1,"{1673, 1676, 1166, 207, 1663, 1657, 632, 31}"
15,1,92,0,0.0768899,"\int \frac{d+e x}{1+x^2+x^4} \, dx","Int[(d + e*x)/(1 + x^2 + x^4),x]","-\frac{1}{4} d \log \left(x^2-x+1\right)+\frac{1}{4} d \log \left(x^2+x+1\right)-\frac{d \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{d \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{e \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{1}{4} d \log \left(x^2-x+1\right)+\frac{1}{4} d \log \left(x^2+x+1\right)-\frac{d \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{d \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{e \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(d*ArcTan[(1 - 2*x)/Sqrt[3]])/(2*Sqrt[3]) + (d*ArcTan[(1 + 2*x)/Sqrt[3]])/(2*Sqrt[3]) + (e*ArcTan[(1 + 2*x^2)/Sqrt[3]])/Sqrt[3] - (d*Log[1 - x + x^2])/4 + (d*Log[1 + x + x^2])/4","A",15,8,16,0.5000,1,"{1673, 12, 1094, 634, 618, 204, 628, 1107}"
16,1,104,0,0.0848895,"\int \frac{d+e x+f x^2}{1+x^2+x^4} \, dx","Int[(d + e*x + f*x^2)/(1 + x^2 + x^4),x]","-\frac{1}{4} (d-f) \log \left(x^2-x+1\right)+\frac{1}{4} (d-f) \log \left(x^2+x+1\right)-\frac{(d+f) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{(d+f) \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{e \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{1}{4} (d-f) \log \left(x^2-x+1\right)+\frac{1}{4} (d-f) \log \left(x^2+x+1\right)-\frac{(d+f) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{(d+f) \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{e \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-((d + f)*ArcTan[(1 - 2*x)/Sqrt[3]])/(2*Sqrt[3]) + ((d + f)*ArcTan[(1 + 2*x)/Sqrt[3]])/(2*Sqrt[3]) + (e*ArcTan[(1 + 2*x^2)/Sqrt[3]])/Sqrt[3] - ((d - f)*Log[1 - x + x^2])/4 + ((d - f)*Log[1 + x + x^2])/4","A",14,8,21,0.3810,1,"{1673, 1169, 634, 618, 204, 628, 12, 1107}"
17,1,127,0,0.1010506,"\int \frac{d+e x+f x^2+g x^3}{1+x^2+x^4} \, dx","Int[(d + e*x + f*x^2 + g*x^3)/(1 + x^2 + x^4),x]","-\frac{1}{4} (d-f) \log \left(x^2-x+1\right)+\frac{1}{4} (d-f) \log \left(x^2+x+1\right)-\frac{(d+f) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{(d+f) \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{(2 e-g) \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{4} g \log \left(x^4+x^2+1\right)","-\frac{1}{4} (d-f) \log \left(x^2-x+1\right)+\frac{1}{4} (d-f) \log \left(x^2+x+1\right)-\frac{(d+f) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{(d+f) \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{(2 e-g) \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{4} g \log \left(x^4+x^2+1\right)",1,"-((d + f)*ArcTan[(1 - 2*x)/Sqrt[3]])/(2*Sqrt[3]) + ((d + f)*ArcTan[(1 + 2*x)/Sqrt[3]])/(2*Sqrt[3]) + ((2*e - g)*ArcTan[(1 + 2*x^2)/Sqrt[3]])/(2*Sqrt[3]) - ((d - f)*Log[1 - x + x^2])/4 + ((d - f)*Log[1 + x + x^2])/4 + (g*Log[1 + x^2 + x^4])/4","A",15,7,26,0.2692,1,"{1673, 1169, 634, 618, 204, 628, 1247}"
18,1,136,0,0.1399866,"\int \frac{d+e x+f x^2+g x^3+h x^4}{1+x^2+x^4} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4)/(1 + x^2 + x^4),x]","-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right) (d+f-2 h)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right) (d+f-2 h)}{2 \sqrt{3}}-\frac{1}{4} (d-f) \log \left(x^2-x+1\right)+\frac{1}{4} (d-f) \log \left(x^2+x+1\right)+\frac{(2 e-g) \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{4} g \log \left(x^4+x^2+1\right)+h x","-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right) (d+f-2 h)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right) (d+f-2 h)}{2 \sqrt{3}}-\frac{1}{4} (d-f) \log \left(x^2-x+1\right)+\frac{1}{4} (d-f) \log \left(x^2+x+1\right)+\frac{(2 e-g) \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{2 \sqrt{3}}+\frac{1}{4} g \log \left(x^4+x^2+1\right)+h x",1,"h*x - ((d + f - 2*h)*ArcTan[(1 - 2*x)/Sqrt[3]])/(2*Sqrt[3]) + ((d + f - 2*h)*ArcTan[(1 + 2*x)/Sqrt[3]])/(2*Sqrt[3]) + ((2*e - g)*ArcTan[(1 + 2*x^2)/Sqrt[3]])/(2*Sqrt[3]) - ((d - f)*Log[1 - x + x^2])/4 + ((d - f)*Log[1 + x + x^2])/4 + (g*Log[1 + x^2 + x^4])/4","A",17,8,31,0.2581,1,"{1673, 1676, 1169, 634, 618, 204, 628, 1247}"
19,1,151,0,0.1760349,"\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5}{1+x^2+x^4} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4 + i*x^5)/(1 + x^2 + x^4),x]","-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right) (d+f-2 h)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right) (d+f-2 h)}{2 \sqrt{3}}-\frac{1}{4} (d-f) \log \left(x^2-x+1\right)+\frac{1}{4} (d-f) \log \left(x^2+x+1\right)+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right) (2 e-g-i)}{2 \sqrt{3}}+\frac{1}{4} (g-i) \log \left(x^4+x^2+1\right)+h x+\frac{i x^2}{2}","-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right) (d+f-2 h)}{2 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right) (d+f-2 h)}{2 \sqrt{3}}-\frac{1}{4} (d-f) \log \left(x^2-x+1\right)+\frac{1}{4} (d-f) \log \left(x^2+x+1\right)+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right) (2 e-g-i)}{2 \sqrt{3}}+\frac{1}{4} (g-i) \log \left(x^4+x^2+1\right)+h x+\frac{i x^2}{2}",1,"h*x + (i*x^2)/2 - ((d + f - 2*h)*ArcTan[(1 - 2*x)/Sqrt[3]])/(2*Sqrt[3]) + ((d + f - 2*h)*ArcTan[(1 + 2*x)/Sqrt[3]])/(2*Sqrt[3]) + ((2*e - g - i)*ArcTan[(1 + 2*x^2)/Sqrt[3]])/(2*Sqrt[3]) - ((d - f)*Log[1 - x + x^2])/4 + ((d - f)*Log[1 + x + x^2])/4 + ((g - i)*Log[1 + x^2 + x^4])/4","A",19,9,36,0.2500,1,"{1673, 1676, 1169, 634, 618, 204, 628, 1663, 1657}"
20,1,189,0,0.2108487,"\int \frac{d+e x}{a+b x^2+c x^4} \, dx","Int[(d + e*x)/(a + b*x^2 + c*x^4),x]","\frac{\sqrt{2} \sqrt{c} d \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \sqrt{c} d \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{e \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}","\frac{\sqrt{2} \sqrt{c} d \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \sqrt{c} d \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{e \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}",1,"(Sqrt[2]*Sqrt[c]*d*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[2]*Sqrt[c]*d*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]]) - (e*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/Sqrt[b^2 - 4*a*c]","A",9,7,20,0.3500,1,"{1673, 12, 1093, 205, 1107, 618, 206}"
21,1,211,0,0.2399783,"\int \frac{d+e x+f x^2}{a+b x^2+c x^4} \, dx","Int[(d + e*x + f*x^2)/(a + b*x^2 + c*x^4),x]","\frac{\left(\frac{2 c d-b f}{\sqrt{b^2-4 a c}}+f\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(f-\frac{2 c d-b f}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{e \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}","\frac{\left(\frac{2 c d-b f}{\sqrt{b^2-4 a c}}+f\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(f-\frac{2 c d-b f}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{e \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}",1,"((f + (2*c*d - b*f)/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]]) + ((f - (2*c*d - b*f)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b + Sqrt[b^2 - 4*a*c]]) - (e*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/Sqrt[b^2 - 4*a*c]","A",8,7,25,0.2800,1,"{1673, 1166, 205, 12, 1107, 618, 206}"
22,1,245,0,0.1591762,"\int \frac{d+e x+f x^2+g x^3}{a+b x^2+c x^4} \, dx","Int[(d + e*x + f*x^2 + g*x^3)/(a + b*x^2 + c*x^4),x]","\frac{\left(\frac{2 c d-b f}{\sqrt{b^2-4 a c}}+f\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(f-\frac{2 c d-b f}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{(2 c e-b g) \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{g \log \left(a+b x^2+c x^4\right)}{4 c}","\frac{\left(\frac{2 c d-b f}{\sqrt{b^2-4 a c}}+f\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(f-\frac{2 c d-b f}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{(2 c e-b g) \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{g \log \left(a+b x^2+c x^4\right)}{4 c}",1,"((f + (2*c*d - b*f)/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]]) + ((f - (2*c*d - b*f)/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]]) - ((2*c*e - b*g)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c*Sqrt[b^2 - 4*a*c]) + (g*Log[a + b*x^2 + c*x^4])/(4*c)","A",9,8,30,0.2667,1,"{1673, 1166, 205, 1247, 634, 618, 206, 628}"
23,1,290,0,0.7252547,"\int \frac{d+e x+f x^2+g x^3+h x^4}{a+b x^2+c x^4} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4)/(a + b*x^2 + c*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{-c (2 a h+b f)+b^2 h+2 c^2 d}{\sqrt{b^2-4 a c}}-b h+c f\right)}{\sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{-2 a c h+b^2 h-b c f+2 c^2 d}{\sqrt{b^2-4 a c}}-b h+c f\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{(2 c e-b g) \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{g \log \left(a+b x^2+c x^4\right)}{4 c}+\frac{h x}{c}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{-c (2 a h+b f)+b^2 h+2 c^2 d}{\sqrt{b^2-4 a c}}-b h+c f\right)}{\sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{-2 a c h+b^2 h-b c f+2 c^2 d}{\sqrt{b^2-4 a c}}-b h+c f\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{(2 c e-b g) \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{g \log \left(a+b x^2+c x^4\right)}{4 c}+\frac{h x}{c}",1,"(h*x)/c + ((c*f - b*h + (2*c^2*d + b^2*h - c*(b*f + 2*a*h))/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*f - b*h - (2*c^2*d - b*c*f + b^2*h - 2*a*c*h)/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]]) - ((2*c*e - b*g)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c*Sqrt[b^2 - 4*a*c]) + (g*Log[a + b*x^2 + c*x^4])/(4*c)","A",11,9,35,0.2571,1,"{1673, 1676, 1166, 205, 1247, 634, 618, 206, 628}"
24,1,321,0,0.5339425,"\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5}{a+b x^2+c x^4} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4 + i*x^5)/(a + b*x^2 + c*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{-c (2 a h+b f)+b^2 h+2 c^2 d}{\sqrt{b^2-4 a c}}-b h+c f\right)}{\sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{-2 a c h+b^2 h-b c f+2 c^2 d}{\sqrt{b^2-4 a c}}-b h+c f\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(-2 a c i+b^2 i-b c g+2 c^2 e\right)}{2 c^2 \sqrt{b^2-4 a c}}+\frac{(c g-b i) \log \left(a+b x^2+c x^4\right)}{4 c^2}+\frac{h x}{c}+\frac{i x^2}{2 c}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{-c (2 a h+b f)+b^2 h+2 c^2 d}{\sqrt{b^2-4 a c}}-b h+c f\right)}{\sqrt{2} c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{-2 a c h+b^2 h-b c f+2 c^2 d}{\sqrt{b^2-4 a c}}-b h+c f\right)}{\sqrt{2} c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(-2 a c i+b^2 i-b c g+2 c^2 e\right)}{2 c^2 \sqrt{b^2-4 a c}}+\frac{(c g-b i) \log \left(a+b x^2+c x^4\right)}{4 c^2}+\frac{h x}{c}+\frac{i x^2}{2 c}",1,"(h*x)/c + (i*x^2)/(2*c) + ((c*f - b*h + (2*c^2*d + b^2*h - c*(b*f + 2*a*h))/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*f - b*h - (2*c^2*d - b*c*f + b^2*h - 2*a*c*h)/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]]) - ((2*c^2*e - b*c*g + b^2*i - 2*a*c*i)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^2*Sqrt[b^2 - 4*a*c]) + ((c*g - b*i)*Log[a + b*x^2 + c*x^4])/(4*c^2)","A",13,10,40,0.2500,1,"{1673, 1676, 1166, 205, 1663, 1657, 634, 618, 206, 628}"
25,1,545,0,4.2132796,"\int \frac{d+e x+f x^2+g x^3+h x^4+j x^5+k x^6+l x^7+m x^8}{a+b x^2+c x^4} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4 + j*x^5 + k*x^6 + l*x^7 + m*x^8)/(a + b*x^2 + c*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{c^2 \left(2 a^2 m+3 a b k+b^2 h\right)-b^2 c (4 a m+b k)-c^3 (2 a h+b f)+b^4 m+2 c^4 d}{\sqrt{b^2-4 a c}}-c^2 (a k+b h)+b c (2 a m+b k)+b^3 (-m)+c^3 f\right)}{\sqrt{2} c^{7/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{c^2 \left(2 a^2 m+3 a b k+b^2 h\right)-b^2 c (4 a m+b k)-c^3 (2 a h+b f)+b^4 m+2 c^4 d}{\sqrt{b^2-4 a c}}-c^2 (a k+b h)+b c (2 a m+b k)+b^3 (-m)+c^3 f\right)}{\sqrt{2} c^{7/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(-c^2 (2 a j+b g)+b c (3 a l+b j)+b^3 (-l)+2 c^3 e\right)}{2 c^3 \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x^2+c x^4\right) \left(-c (a l+b j)+b^2 l+c^2 g\right)}{4 c^3}+\frac{x \left(-c (a m+b k)+b^2 m+c^2 h\right)}{c^3}+\frac{x^2 (c j-b l)}{2 c^2}+\frac{x^3 (c k-b m)}{3 c^2}+\frac{l x^4}{4 c}+\frac{m x^5}{5 c}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{c^2 \left(2 a^2 m+3 a b k+b^2 h\right)-b^2 c (4 a m+b k)-c^3 (2 a h+b f)+b^4 m+2 c^4 d}{\sqrt{b^2-4 a c}}-c^2 (a k+b h)+b c (2 a m+b k)+b^3 (-m)+c^3 f\right)}{\sqrt{2} c^{7/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{c^2 \left(2 a^2 m+3 a b k+b^2 h\right)-b^2 c (4 a m+b k)-c^3 (2 a h+b f)+b^4 m+2 c^4 d}{\sqrt{b^2-4 a c}}-c^2 (a k+b h)+b c (2 a m+b k)+b^3 (-m)+c^3 f\right)}{\sqrt{2} c^{7/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(-c^2 (2 a j+b g)+b c (3 a l+b j)+b^3 (-l)+2 c^3 e\right)}{2 c^3 \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x^2+c x^4\right) \left(-c (a l+b j)+b^2 l+c^2 g\right)}{4 c^3}+\frac{x \left(-c (a m+b k)+b^2 m+c^2 h\right)}{c^3}+\frac{x^2 (c j-b l)}{2 c^2}+\frac{x^3 (c k-b m)}{3 c^2}+\frac{l x^4}{4 c}+\frac{m x^5}{5 c}",1,"((c^2*h + b^2*m - c*(b*k + a*m))*x)/c^3 + ((c*j - b*l)*x^2)/(2*c^2) + ((c*k - b*m)*x^3)/(3*c^2) + (l*x^4)/(4*c) + (m*x^5)/(5*c) + ((c^3*f - c^2*(b*h + a*k) - b^3*m + b*c*(b*k + 2*a*m) + (2*c^4*d - c^3*(b*f + 2*a*h) + b^4*m - b^2*c*(b*k + 4*a*m) + c^2*(b^2*h + 3*a*b*k + 2*a^2*m))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(7/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((c^3*f - c^2*(b*h + a*k) - b^3*m + b*c*(b*k + 2*a*m) - (2*c^4*d - c^3*(b*f + 2*a*h) + b^4*m - b^2*c*(b*k + 4*a*m) + c^2*(b^2*h + 3*a*b*k + 2*a^2*m))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(7/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) - ((2*c^3*e - c^2*(b*g + 2*a*j) - b^3*l + b*c*(b*j + 3*a*l))*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^3*Sqrt[b^2 - 4*a*c]) + ((c^2*g + b^2*l - c*(b*j + a*l))*Log[a + b*x^2 + c*x^4])/(4*c^3)","A",13,10,55,0.1818,1,"{1673, 1676, 1166, 205, 1663, 1657, 634, 618, 206, 628}"
26,1,94,0,0.0518091,"\int \frac{d+e x}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[(d + e*x)/(4 - 5*x^2 + x^4)^2,x]","\frac{d x \left(17-5 x^2\right)}{72 \left(x^4-5 x^2+4\right)}+\frac{19}{432} d \tanh ^{-1}\left(\frac{x}{2}\right)-\frac{1}{54} d \tanh ^{-1}(x)+\frac{e \left(5-2 x^2\right)}{18 \left(x^4-5 x^2+4\right)}+\frac{1}{27} e \log \left(1-x^2\right)-\frac{1}{27} e \log \left(4-x^2\right)","\frac{d x \left(17-5 x^2\right)}{72 \left(x^4-5 x^2+4\right)}+\frac{19}{432} d \tanh ^{-1}\left(\frac{x}{2}\right)-\frac{1}{54} d \tanh ^{-1}(x)+\frac{e \left(5-2 x^2\right)}{18 \left(x^4-5 x^2+4\right)}+\frac{1}{27} e \log \left(1-x^2\right)-\frac{1}{27} e \log \left(4-x^2\right)",1,"(d*x*(17 - 5*x^2))/(72*(4 - 5*x^2 + x^4)) + (e*(5 - 2*x^2))/(18*(4 - 5*x^2 + x^4)) + (19*d*ArcTanh[x/2])/432 - (d*ArcTanh[x])/54 + (e*Log[1 - x^2])/27 - (e*Log[4 - x^2])/27","A",12,9,18,0.5000,1,"{1673, 12, 1092, 1166, 207, 1107, 614, 616, 31}"
27,1,115,0,0.1401149,"\int \frac{d+e x+f x^2}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[(d + e*x + f*x^2)/(4 - 5*x^2 + x^4)^2,x]","\frac{x \left(x^2 (-(5 d+8 f))+17 d+20 f\right)}{72 \left(x^4-5 x^2+4\right)}+\frac{1}{432} (19 d+52 f) \tanh ^{-1}\left(\frac{x}{2}\right)-\frac{1}{54} (d+7 f) \tanh ^{-1}(x)+\frac{e \left(5-2 x^2\right)}{18 \left(x^4-5 x^2+4\right)}+\frac{1}{27} e \log \left(1-x^2\right)-\frac{1}{27} e \log \left(4-x^2\right)","\frac{x \left(x^2 (-(5 d+8 f))+17 d+20 f\right)}{72 \left(x^4-5 x^2+4\right)}+\frac{1}{432} (19 d+52 f) \tanh ^{-1}\left(\frac{x}{2}\right)-\frac{1}{54} (d+7 f) \tanh ^{-1}(x)+\frac{e \left(5-2 x^2\right)}{18 \left(x^4-5 x^2+4\right)}+\frac{1}{27} e \log \left(1-x^2\right)-\frac{1}{27} e \log \left(4-x^2\right)",1,"(e*(5 - 2*x^2))/(18*(4 - 5*x^2 + x^4)) + (x*(17*d + 20*f - (5*d + 8*f)*x^2))/(72*(4 - 5*x^2 + x^4)) + ((19*d + 52*f)*ArcTanh[x/2])/432 - ((d + 7*f)*ArcTanh[x])/54 + (e*Log[1 - x^2])/27 - (e*Log[4 - x^2])/27","A",11,9,23,0.3913,1,"{1673, 1178, 1166, 207, 12, 1107, 614, 616, 31}"
28,1,138,0,0.153883,"\int \frac{d+e x+f x^2+g x^3}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[(d + e*x + f*x^2 + g*x^3)/(4 - 5*x^2 + x^4)^2,x]","\frac{x \left(x^2 (-(5 d+8 f))+17 d+20 f\right)}{72 \left(x^4-5 x^2+4\right)}+\frac{1}{432} (19 d+52 f) \tanh ^{-1}\left(\frac{x}{2}\right)-\frac{1}{54} (d+7 f) \tanh ^{-1}(x)+\frac{x^2 (-(2 e+5 g))+5 e+8 g}{18 \left(x^4-5 x^2+4\right)}+\frac{1}{54} (2 e+5 g) \log \left(1-x^2\right)-\frac{1}{54} (2 e+5 g) \log \left(4-x^2\right)","\frac{x \left(x^2 (-(5 d+8 f))+17 d+20 f\right)}{72 \left(x^4-5 x^2+4\right)}+\frac{1}{432} (19 d+52 f) \tanh ^{-1}\left(\frac{x}{2}\right)-\frac{1}{54} (d+7 f) \tanh ^{-1}(x)+\frac{x^2 (-(2 e+5 g))+5 e+8 g}{18 \left(x^4-5 x^2+4\right)}+\frac{1}{54} (2 e+5 g) \log \left(1-x^2\right)-\frac{1}{54} (2 e+5 g) \log \left(4-x^2\right)",1,"(x*(17*d + 20*f - (5*d + 8*f)*x^2))/(72*(4 - 5*x^2 + x^4)) + (5*e + 8*g - (2*e + 5*g)*x^2)/(18*(4 - 5*x^2 + x^4)) + ((19*d + 52*f)*ArcTanh[x/2])/432 - ((d + 7*f)*ArcTanh[x])/54 + ((2*e + 5*g)*Log[1 - x^2])/54 - ((2*e + 5*g)*Log[4 - x^2])/54","A",10,8,28,0.2857,1,"{1673, 1178, 1166, 207, 1247, 638, 616, 31}"
29,1,150,0,0.2142965,"\int \frac{d+e x+f x^2+g x^3+h x^4}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4)/(4 - 5*x^2 + x^4)^2,x]","\frac{x \left(x^2 (-(5 d+8 f+20 h))+17 d+20 f+32 h\right)}{72 \left(x^4-5 x^2+4\right)}+\frac{1}{432} \tanh ^{-1}\left(\frac{x}{2}\right) (19 d+52 f+112 h)-\frac{1}{54} \tanh ^{-1}(x) (d+7 f+13 h)+\frac{x^2 (-(2 e+5 g))+5 e+8 g}{18 \left(x^4-5 x^2+4\right)}+\frac{1}{54} (2 e+5 g) \log \left(1-x^2\right)-\frac{1}{54} (2 e+5 g) \log \left(4-x^2\right)","\frac{x \left(x^2 (-(5 d+8 f+20 h))+17 d+20 f+32 h\right)}{72 \left(x^4-5 x^2+4\right)}+\frac{1}{432} \tanh ^{-1}\left(\frac{x}{2}\right) (19 d+52 f+112 h)-\frac{1}{54} \tanh ^{-1}(x) (d+7 f+13 h)+\frac{x^2 (-(2 e+5 g))+5 e+8 g}{18 \left(x^4-5 x^2+4\right)}+\frac{1}{54} (2 e+5 g) \log \left(1-x^2\right)-\frac{1}{54} (2 e+5 g) \log \left(4-x^2\right)",1,"(5*e + 8*g - (2*e + 5*g)*x^2)/(18*(4 - 5*x^2 + x^4)) + (x*(17*d + 20*f + 32*h - (5*d + 8*f + 20*h)*x^2))/(72*(4 - 5*x^2 + x^4)) + ((19*d + 52*f + 112*h)*ArcTanh[x/2])/432 - ((d + 7*f + 13*h)*ArcTanh[x])/54 + ((2*e + 5*g)*Log[1 - x^2])/54 - ((2*e + 5*g)*Log[4 - x^2])/54","A",10,8,33,0.2424,1,"{1673, 1678, 1166, 207, 1247, 638, 616, 31}"
30,1,162,0,0.2318373,"\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4 + i*x^5)/(4 - 5*x^2 + x^4)^2,x]","\frac{x \left(x^2 (-(5 d+8 f+20 h))+17 d+20 f+32 h\right)}{72 \left(x^4-5 x^2+4\right)}+\frac{1}{432} \tanh ^{-1}\left(\frac{x}{2}\right) (19 d+52 f+112 h)-\frac{1}{54} \tanh ^{-1}(x) (d+7 f+13 h)+\frac{x^2 (-(2 e+5 g+17 i))+5 e+8 g+20 i}{18 \left(x^4-5 x^2+4\right)}+\frac{1}{54} \log \left(1-x^2\right) (2 e+5 g+8 i)-\frac{1}{54} \log \left(4-x^2\right) (2 e+5 g+8 i)","\frac{x \left(x^2 (-(5 d+8 f+20 h))+17 d+20 f+32 h\right)}{72 \left(x^4-5 x^2+4\right)}+\frac{1}{432} \tanh ^{-1}\left(\frac{x}{2}\right) (19 d+52 f+112 h)-\frac{1}{54} \tanh ^{-1}(x) (d+7 f+13 h)+\frac{x^2 (-(2 e+5 g+17 i))+5 e+8 g+20 i}{18 \left(x^4-5 x^2+4\right)}+\frac{1}{54} \log \left(1-x^2\right) (2 e+5 g+8 i)-\frac{1}{54} \log \left(4-x^2\right) (2 e+5 g+8 i)",1,"(x*(17*d + 20*f + 32*h - (5*d + 8*f + 20*h)*x^2))/(72*(4 - 5*x^2 + x^4)) + (5*e + 8*g + 20*i - (2*e + 5*g + 17*i)*x^2)/(18*(4 - 5*x^2 + x^4)) + ((19*d + 52*f + 112*h)*ArcTanh[x/2])/432 - ((d + 7*f + 13*h)*ArcTanh[x])/54 + ((2*e + 5*g + 8*i)*Log[1 - x^2])/54 - ((2*e + 5*g + 8*i)*Log[4 - x^2])/54","A",11,9,38,0.2368,1,"{1673, 1678, 1166, 207, 1663, 1660, 12, 616, 31}"
31,1,140,0,0.09779,"\int \frac{d+e x}{\left(1+x^2+x^4\right)^2} \, dx","Int[(d + e*x)/(1 + x^2 + x^4)^2,x]","\frac{d x \left(1-x^2\right)}{6 \left(x^4+x^2+1\right)}-\frac{1}{4} d \log \left(x^2-x+1\right)+\frac{1}{4} d \log \left(x^2+x+1\right)-\frac{d \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{d \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{e \left(2 x^2+1\right)}{6 \left(x^4+x^2+1\right)}+\frac{2 e \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{d x \left(1-x^2\right)}{6 \left(x^4+x^2+1\right)}-\frac{1}{4} d \log \left(x^2-x+1\right)+\frac{1}{4} d \log \left(x^2+x+1\right)-\frac{d \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{d \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{e \left(2 x^2+1\right)}{6 \left(x^4+x^2+1\right)}+\frac{2 e \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(d*x*(1 - x^2))/(6*(1 + x^2 + x^4)) + (e*(1 + 2*x^2))/(6*(1 + x^2 + x^4)) - (d*ArcTan[(1 - 2*x)/Sqrt[3]])/(3*Sqrt[3]) + (d*ArcTan[(1 + 2*x)/Sqrt[3]])/(3*Sqrt[3]) + (2*e*ArcTan[(1 + 2*x^2)/Sqrt[3]])/(3*Sqrt[3]) - (d*Log[1 - x + x^2])/4 + (d*Log[1 + x + x^2])/4","A",17,10,16,0.6250,1,"{1673, 12, 1092, 1169, 634, 618, 204, 628, 1107, 614}"
32,1,165,0,0.1291924,"\int \frac{d+e x+f x^2}{\left(1+x^2+x^4\right)^2} \, dx","Int[(d + e*x + f*x^2)/(1 + x^2 + x^4)^2,x]","\frac{x \left(x^2 (-(d-2 f))+d+f\right)}{6 \left(x^4+x^2+1\right)}-\frac{1}{8} (2 d-f) \log \left(x^2-x+1\right)+\frac{1}{8} (2 d-f) \log \left(x^2+x+1\right)-\frac{(4 d+f) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{12 \sqrt{3}}+\frac{(4 d+f) \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{12 \sqrt{3}}+\frac{e \left(2 x^2+1\right)}{6 \left(x^4+x^2+1\right)}+\frac{2 e \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{x \left(x^2 (-(d-2 f))+d+f\right)}{6 \left(x^4+x^2+1\right)}-\frac{1}{8} (2 d-f) \log \left(x^2-x+1\right)+\frac{1}{8} (2 d-f) \log \left(x^2+x+1\right)-\frac{(4 d+f) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{12 \sqrt{3}}+\frac{(4 d+f) \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{12 \sqrt{3}}+\frac{e \left(2 x^2+1\right)}{6 \left(x^4+x^2+1\right)}+\frac{2 e \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(e*(1 + 2*x^2))/(6*(1 + x^2 + x^4)) + (x*(d + f - (d - 2*f)*x^2))/(6*(1 + x^2 + x^4)) - ((4*d + f)*ArcTan[(1 - 2*x)/Sqrt[3]])/(12*Sqrt[3]) + ((4*d + f)*ArcTan[(1 + 2*x)/Sqrt[3]])/(12*Sqrt[3]) + (2*e*ArcTan[(1 + 2*x^2)/Sqrt[3]])/(3*Sqrt[3]) - ((2*d - f)*Log[1 - x + x^2])/8 + ((2*d - f)*Log[1 + x + x^2])/8","A",16,10,21,0.4762,1,"{1673, 1178, 1169, 634, 618, 204, 628, 12, 1107, 614}"
33,1,179,0,0.1410119,"\int \frac{d+e x+f x^2+g x^3}{\left(1+x^2+x^4\right)^2} \, dx","Int[(d + e*x + f*x^2 + g*x^3)/(1 + x^2 + x^4)^2,x]","\frac{x \left(x^2 (-(d-2 f))+d+f\right)}{6 \left(x^4+x^2+1\right)}-\frac{1}{8} (2 d-f) \log \left(x^2-x+1\right)+\frac{1}{8} (2 d-f) \log \left(x^2+x+1\right)-\frac{(4 d+f) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{12 \sqrt{3}}+\frac{(4 d+f) \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{12 \sqrt{3}}+\frac{x^2 (2 e-g)+e-2 g}{6 \left(x^4+x^2+1\right)}+\frac{(2 e-g) \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{x \left(x^2 (-(d-2 f))+d+f\right)}{6 \left(x^4+x^2+1\right)}-\frac{1}{8} (2 d-f) \log \left(x^2-x+1\right)+\frac{1}{8} (2 d-f) \log \left(x^2+x+1\right)-\frac{(4 d+f) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{12 \sqrt{3}}+\frac{(4 d+f) \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{12 \sqrt{3}}+\frac{x^2 (2 e-g)+e-2 g}{6 \left(x^4+x^2+1\right)}+\frac{(2 e-g) \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(x*(d + f - (d - 2*f)*x^2))/(6*(1 + x^2 + x^4)) + (e - 2*g + (2*e - g)*x^2)/(6*(1 + x^2 + x^4)) - ((4*d + f)*ArcTan[(1 - 2*x)/Sqrt[3]])/(12*Sqrt[3]) + ((4*d + f)*ArcTan[(1 + 2*x)/Sqrt[3]])/(12*Sqrt[3]) + ((2*e - g)*ArcTan[(1 + 2*x^2)/Sqrt[3]])/(3*Sqrt[3]) - ((2*d - f)*Log[1 - x + x^2])/8 + ((2*d - f)*Log[1 + x + x^2])/8","A",15,9,26,0.3462,1,"{1673, 1178, 1169, 634, 618, 204, 628, 1247, 638}"
34,1,187,0,0.1670954,"\int \frac{d+e x+f x^2+g x^3+h x^4}{\left(1+x^2+x^4\right)^2} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4)/(1 + x^2 + x^4)^2,x]","\frac{x \left(x^2 (-(d-2 f+h))+d+f-2 h\right)}{6 \left(x^4+x^2+1\right)}-\frac{1}{8} \log \left(x^2-x+1\right) (2 d-f+h)+\frac{1}{8} \log \left(x^2+x+1\right) (2 d-f+h)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right) (4 d+f+h)}{12 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right) (4 d+f+h)}{12 \sqrt{3}}+\frac{x^2 (2 e-g)+e-2 g}{6 \left(x^4+x^2+1\right)}+\frac{(2 e-g) \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{x \left(x^2 (-(d-2 f+h))+d+f-2 h\right)}{6 \left(x^4+x^2+1\right)}-\frac{1}{8} \log \left(x^2-x+1\right) (2 d-f+h)+\frac{1}{8} \log \left(x^2+x+1\right) (2 d-f+h)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right) (4 d+f+h)}{12 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right) (4 d+f+h)}{12 \sqrt{3}}+\frac{x^2 (2 e-g)+e-2 g}{6 \left(x^4+x^2+1\right)}+\frac{(2 e-g) \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(e - 2*g + (2*e - g)*x^2)/(6*(1 + x^2 + x^4)) + (x*(d + f - 2*h - (d - 2*f + h)*x^2))/(6*(1 + x^2 + x^4)) - ((4*d + f + h)*ArcTan[(1 - 2*x)/Sqrt[3]])/(12*Sqrt[3]) + ((4*d + f + h)*ArcTan[(1 + 2*x)/Sqrt[3]])/(12*Sqrt[3]) + ((2*e - g)*ArcTan[(1 + 2*x^2)/Sqrt[3]])/(3*Sqrt[3]) - ((2*d - f + h)*Log[1 - x + x^2])/8 + ((2*d - f + h)*Log[1 + x + x^2])/8","A",15,9,31,0.2903,1,"{1673, 1678, 1169, 634, 618, 204, 628, 1247, 638}"
35,1,194,0,0.1973273,"\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5}{\left(1+x^2+x^4\right)^2} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4 + i*x^5)/(1 + x^2 + x^4)^2,x]","\frac{x \left(x^2 (-(d-2 f+h))+d+f-2 h\right)}{6 \left(x^4+x^2+1\right)}-\frac{1}{8} \log \left(x^2-x+1\right) (2 d-f+h)+\frac{1}{8} \log \left(x^2+x+1\right) (2 d-f+h)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right) (4 d+f+h)}{12 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right) (4 d+f+h)}{12 \sqrt{3}}+\frac{x^2 (2 e-g-i)+e-2 g+i}{6 \left(x^4+x^2+1\right)}+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right) (2 e-g+2 i)}{3 \sqrt{3}}","\frac{x \left(x^2 (-(d-2 f+h))+d+f-2 h\right)}{6 \left(x^4+x^2+1\right)}-\frac{1}{8} \log \left(x^2-x+1\right) (2 d-f+h)+\frac{1}{8} \log \left(x^2+x+1\right) (2 d-f+h)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right) (4 d+f+h)}{12 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right) (4 d+f+h)}{12 \sqrt{3}}+\frac{x^2 (2 e-g-i)+e-2 g+i}{6 \left(x^4+x^2+1\right)}+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right) (2 e-g+2 i)}{3 \sqrt{3}}",1,"(x*(d + f - 2*h - (d - 2*f + h)*x^2))/(6*(1 + x^2 + x^4)) + (e - 2*g + i + (2*e - g - i)*x^2)/(6*(1 + x^2 + x^4)) - ((4*d + f + h)*ArcTan[(1 - 2*x)/Sqrt[3]])/(12*Sqrt[3]) + ((4*d + f + h)*ArcTan[(1 + 2*x)/Sqrt[3]])/(12*Sqrt[3]) + ((2*e - g + 2*i)*ArcTan[(1 + 2*x^2)/Sqrt[3]])/(3*Sqrt[3]) - ((2*d - f + h)*Log[1 - x + x^2])/8 + ((2*d - f + h)*Log[1 + x + x^2])/8","A",16,10,36,0.2778,1,"{1673, 1678, 1169, 634, 618, 204, 628, 1663, 1660, 12}"
36,1,330,0,0.7447289,"\int \frac{d+e x}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(d + e*x)/(a + b*x^2 + c*x^4)^2,x]","\frac{d x \left(-2 a c+b^2+b c x^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} d \left(b \sqrt{b^2-4 a c}-12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} d \left(-b \sqrt{b^2-4 a c}-12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{e \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{2 c e \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{d x \left(-2 a c+b^2+b c x^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} d \left(b \sqrt{b^2-4 a c}-12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} d \left(-b \sqrt{b^2-4 a c}-12 a c+b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{e \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{2 c e \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,"-(e*(b + 2*c*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (d*x*(b^2 - 2*a*c + b*c*x^2))/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(b^2 - 12*a*c + b*Sqrt[b^2 - 4*a*c])*d*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(b^2 - 12*a*c - b*Sqrt[b^2 - 4*a*c])*d*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + (2*c*e*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",11,9,20,0.4500,1,"{1673, 12, 1092, 1166, 205, 1107, 614, 618, 206}"
37,1,368,0,0.8704216,"\int \frac{d+e x+f x^2}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(d + e*x + f*x^2)/(a + b*x^2 + c*x^4)^2,x]","\frac{x \left(c x^2 (b d-2 a f)-a b f-2 a c d+b^2 d\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(\frac{4 a b f-12 a c d+b^2 d}{\sqrt{b^2-4 a c}}-2 a f+b d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\frac{4 a b f-12 a c d+b^2 d}{\sqrt{b^2-4 a c}}-2 a f+b d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{e \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{2 c e \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 \left(c x^2 (b d-2 a f)-a b f-2 a c d+b^2 d\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(\frac{4 a b f-12 a c d+b^2 d}{\sqrt{b^2-4 a c}}-2 a f+b d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\frac{4 a b f-12 a c d+b^2 d}{\sqrt{b^2-4 a c}}-2 a f+b d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{e \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{2 c e \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,"-(e*(b + 2*c*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (x*(b^2*d - 2*a*c*d - a*b*f + c*(b*d - 2*a*f)*x^2))/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(b*d - 2*a*f + (b^2*d - 12*a*c*d + 4*a*b*f)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(b*d - 2*a*f - (b^2*d - 12*a*c*d + 4*a*b*f)/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]]) + (2*c*e*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",10,9,25,0.3600,1,"{1673, 1178, 1166, 205, 12, 1107, 614, 618, 206}"
38,1,386,0,0.4899714,"\int \frac{d+e x+f x^2+g x^3}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(d + e*x + f*x^2 + g*x^3)/(a + b*x^2 + c*x^4)^2,x]","\frac{x \left(c x^2 (b d-2 a f)-a b f-2 a c d+b^2 d\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(\frac{4 a b f-12 a c d+b^2 d}{\sqrt{b^2-4 a c}}-2 a f+b d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\frac{4 a b f-12 a c d+b^2 d}{\sqrt{b^2-4 a c}}-2 a f+b d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{-2 a g+x^2 (2 c e-b g)+b e}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{(2 c e-b g) \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 \left(c x^2 (b d-2 a f)-a b f-2 a c d+b^2 d\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(\frac{4 a b f-12 a c d+b^2 d}{\sqrt{b^2-4 a c}}-2 a f+b d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\frac{4 a b f-12 a c d+b^2 d}{\sqrt{b^2-4 a c}}-2 a f+b d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{-2 a g+x^2 (2 c e-b g)+b e}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{(2 c e-b g) \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}",1,"(x*(b^2*d - 2*a*c*d - a*b*f + c*(b*d - 2*a*f)*x^2))/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - (b*e - 2*a*g + (2*c*e - b*g)*x^2)/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(b*d - 2*a*f + (b^2*d - 12*a*c*d + 4*a*b*f)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(b*d - 2*a*f - (b^2*d - 12*a*c*d + 4*a*b*f)/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]]) + ((2*c*e - b*g)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",9,8,30,0.2667,1,"{1673, 1178, 1166, 205, 1247, 638, 618, 206}"
39,1,439,0,1.8943817,"\int \frac{d+e x+f x^2+g x^3+h x^4}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4)/(a + b*x^2 + c*x^4)^2,x]","\frac{x \left(x^2 (a b h-2 a c f+b c d)-a b f-2 a (c d-a h)+b^2 d\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{b^2 (c d-a h)+4 a b c f-4 a c (a h+3 c d)}{\sqrt{b^2-4 a c}}+a b h-2 a c f+b c d\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{b^2 (c d-a h)+4 a b c f-4 a c (a h+3 c d)}{\sqrt{b^2-4 a c}}+a b h-2 a c f+b c d\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{-2 a g+x^2 (2 c e-b g)+b e}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{(2 c e-b g) \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 \left(x^2 (a b h-2 a c f+b c d)-a b f-2 a (c d-a h)+b^2 d\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{b^2 (c d-a h)+4 a b c f-4 a c (a h+3 c d)}{\sqrt{b^2-4 a c}}+a b h-2 a c f+b c d\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{b^2 (c d-a h)+4 a b c f-4 a c (a h+3 c d)}{\sqrt{b^2-4 a c}}+a b h-2 a c f+b c d\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{-2 a g+x^2 (2 c e-b g)+b e}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{(2 c e-b g) \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,"-(b*e - 2*a*g + (2*c*e - b*g)*x^2)/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (x*(b^2*d - a*b*f - 2*a*(c*d - a*h) + (b*c*d - 2*a*c*f + a*b*h)*x^2))/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((b*c*d - 2*a*c*f + a*b*h + (4*a*b*c*f + b^2*(c*d - a*h) - 4*a*c*(3*c*d + a*h))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b*c*d - 2*a*c*f + a*b*h - (4*a*b*c*f + b^2*(c*d - a*h) - 4*a*c*(3*c*d + a*h))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + ((2*c*e - b*g)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",9,8,35,0.2286,1,"{1673, 1678, 1166, 205, 1247, 638, 618, 206}"
40,1,468,0,1.1176499,"\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4 + i*x^5)/(a + b*x^2 + c*x^4)^2,x]","\frac{x^2 \left(-\left(-2 a c i+b^2 i-b c g+2 c^2 e\right)\right)-b (a i+c e)+2 a c g}{2 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{x \left(x^2 (a b h-2 a c f+b c d)-a b f-2 a (c d-a h)+b^2 d\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{b^2 (c d-a h)+4 a b c f-4 a c (a h+3 c d)}{\sqrt{b^2-4 a c}}+a b h-2 a c f+b c d\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{b^2 (c d-a h)+4 a b c f-4 a c (a h+3 c d)}{\sqrt{b^2-4 a c}}+a b h-2 a c f+b c d\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) (2 a i-b g+2 c e)}{\left(b^2-4 a c\right)^{3/2}}","\frac{x^2 \left(-\left(-2 a c i+b^2 i-b c g+2 c^2 e\right)\right)-b (a i+c e)+2 a c g}{2 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{x \left(x^2 (a b h-2 a c f+b c d)-a b f-2 a (c d-a h)+b^2 d\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{b^2 (c d-a h)+4 a b c f-4 a c (a h+3 c d)}{\sqrt{b^2-4 a c}}+a b h-2 a c f+b c d\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{b^2 (c d-a h)+4 a b c f-4 a c (a h+3 c d)}{\sqrt{b^2-4 a c}}+a b h-2 a c f+b c d\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) (2 a i-b g+2 c e)}{\left(b^2-4 a c\right)^{3/2}}",1,"(x*(b^2*d - a*b*f - 2*a*(c*d - a*h) + (b*c*d - 2*a*c*f + a*b*h)*x^2))/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (2*a*c*g - b*(c*e + a*i) - (2*c^2*e - b*c*g + b^2*i - 2*a*c*i)*x^2)/(2*c*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((b*c*d - 2*a*c*f + a*b*h + (4*a*b*c*f + b^2*(c*d - a*h) - 4*a*c*(3*c*d + a*h))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b*c*d - 2*a*c*f + a*b*h - (4*a*b*c*f + b^2*(c*d - a*h) - 4*a*c*(3*c*d + a*h))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + ((2*c*e - b*g + 2*a*i)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",10,9,40,0.2250,1,"{1673, 1678, 1166, 205, 1663, 1660, 12, 618, 206}"
41,1,770,0,7.8347152,"\int \frac{d+e x+f x^2+g x^3+h x^4+j x^5+k x^6+l x^7+m x^8}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4 + j*x^5 + k*x^6 + l*x^7 + m*x^8)/(a + b*x^2 + c*x^4)^2,x]","-\frac{x \left(x^2 \left(-b c \left(-3 a^2 m+a c h+c^2 d\right)+a b^2 c k-a b^3 m+2 a c^2 (c f-a k)\right)+b^2 \left(-\left(a^2 m+c^2 d\right)\right)+2 a c \left(a^2 m-a c h+c^2 d\right)+a b c (a k+c f)\right)}{2 a c^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(-\frac{-b^2 c \left(-19 a^2 m-a c h+c^2 d\right)+4 a c^2 \left(-5 a^2 m+a c h+3 c^2 d\right)+a b^3 c k-3 a b^4 m-4 a b c^2 (2 a k+c f)}{\sqrt{b^2-4 a c}}+b c \left(13 a^2 m+a c h+c^2 d\right)+a b^2 c k-3 a b^3 m-2 a c^2 (3 a k+c f)\right)}{2 \sqrt{2} a c^{5/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(\frac{-b^2 c \left(-19 a^2 m-a c h+c^2 d\right)+4 a c^2 \left(-5 a^2 m+a c h+3 c^2 d\right)+a b^3 c k-3 a b^4 m-4 a b c^2 (2 a k+c f)}{\sqrt{b^2-4 a c}}+b c \left(13 a^2 m+a c h+c^2 d\right)+a b^2 c k-3 a b^3 m-2 a c^2 (3 a k+c f)\right)}{2 \sqrt{2} a c^{5/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{x^2 \left(-c^2 (2 a j+b g)+b c (3 a l+b j)+b^3 (-l)+2 c^3 e\right)-a b^2 l+b c (a j+c e)-2 a c (c g-a l)}{2 c^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(-c^2 (2 b g-4 a j)-6 a b c l+b^3 l+4 c^3 e\right)}{2 c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{l \log \left(a+b x^2+c x^4\right)}{4 c^2}+\frac{m x}{c^2}","-\frac{x \left(x^2 \left(-b c \left(-3 a^2 m+a c h+c^2 d\right)+a b^2 c k-a b^3 m+2 a c^2 (c f-a k)\right)+b^2 \left(-\left(a^2 m+c^2 d\right)\right)+2 a c \left(a^2 m-a c h+c^2 d\right)+a b c (a k+c f)\right)}{2 a c^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(-\frac{-b^2 c \left(-19 a^2 m-a c h+c^2 d\right)+4 a c^2 \left(-5 a^2 m+a c h+3 c^2 d\right)+a b^3 c k-3 a b^4 m-4 a b c^2 (2 a k+c f)}{\sqrt{b^2-4 a c}}+b c \left(13 a^2 m+a c h+c^2 d\right)+a b^2 c k-3 a b^3 m-2 a c^2 (3 a k+c f)\right)}{2 \sqrt{2} a c^{5/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(\frac{-b^2 c \left(-19 a^2 m-a c h+c^2 d\right)+4 a c^2 \left(-5 a^2 m+a c h+3 c^2 d\right)+a b^3 c k-3 a b^4 m-4 a b c^2 (2 a k+c f)}{\sqrt{b^2-4 a c}}+b c \left(13 a^2 m+a c h+c^2 d\right)+a b^2 c k-3 a b^3 m-2 a c^2 (3 a k+c f)\right)}{2 \sqrt{2} a c^{5/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{x^2 \left(-c^2 (2 a j+b g)+b c (3 a l+b j)+b^3 (-l)+2 c^3 e\right)-a b^2 l+b c (a j+c e)-2 a c (c g-a l)}{2 c^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(-c^2 (2 b g-4 a j)-6 a b c l+b^3 l+4 c^3 e\right)}{2 c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{l \log \left(a+b x^2+c x^4\right)}{4 c^2}+\frac{m x}{c^2}",1,"(m*x)/c^2 - (b*c*(c*e + a*j) - a*b^2*l - 2*a*c*(c*g - a*l) + (2*c^3*e - c^2*(b*g + 2*a*j) - b^3*l + b*c*(b*j + 3*a*l))*x^2)/(2*c^2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - (x*(a*b*c*(c*f + a*k) - b^2*(c^2*d + a^2*m) + 2*a*c*(c^2*d - a*c*h + a^2*m) + (a*b^2*c*k + 2*a*c^2*(c*f - a*k) - a*b^3*m - b*c*(c^2*d + a*c*h - 3*a^2*m))*x^2))/(2*a*c^2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((a*b^2*c*k - 2*a*c^2*(c*f + 3*a*k) - 3*a*b^3*m + b*c*(c^2*d + a*c*h + 13*a^2*m) - (a*b^3*c*k - 4*a*b*c^2*(c*f + 2*a*k) - 3*a*b^4*m - b^2*c*(c^2*d - a*c*h - 19*a^2*m) + 4*a*c^2*(3*c^2*d + a*c*h - 5*a^2*m))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*c^(5/2)*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((a*b^2*c*k - 2*a*c^2*(c*f + 3*a*k) - 3*a*b^3*m + b*c*(c^2*d + a*c*h + 13*a^2*m) + (a*b^3*c*k - 4*a*b*c^2*(c*f + 2*a*k) - 3*a*b^4*m - b^2*c*(c^2*d - a*c*h - 19*a^2*m) + 4*a*c^2*(3*c^2*d + a*c*h - 5*a^2*m))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*c^(5/2)*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + ((4*c^3*e - c^2*(2*b*g - 4*a*j) + b^3*l - 6*a*b*c*l)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^2*(b^2 - 4*a*c)^(3/2)) + (l*Log[a + b*x^2 + c*x^4])/(4*c^2)","A",13,11,55,0.2000,1,"{1673, 1678, 1676, 1166, 205, 1663, 1660, 634, 618, 206, 628}"
42,1,143,0,0.0758338,"\int \frac{d+e x}{\left(4-5 x^2+x^4\right)^3} \, dx","Int[(d + e*x)/(4 - 5*x^2 + x^4)^3,x]","-\frac{d x \left(59-35 x^2\right)}{3456 \left(x^4-5 x^2+4\right)}+\frac{d x \left(17-5 x^2\right)}{144 \left(x^4-5 x^2+4\right)^2}-\frac{313 d \tanh ^{-1}\left(\frac{x}{2}\right)}{20736}+\frac{13}{648} d \tanh ^{-1}(x)-\frac{e \left(5-2 x^2\right)}{54 \left(x^4-5 x^2+4\right)}+\frac{e \left(5-2 x^2\right)}{36 \left(x^4-5 x^2+4\right)^2}-\frac{1}{81} e \log \left(1-x^2\right)+\frac{1}{81} e \log \left(4-x^2\right)","-\frac{d x \left(59-35 x^2\right)}{3456 \left(x^4-5 x^2+4\right)}+\frac{d x \left(17-5 x^2\right)}{144 \left(x^4-5 x^2+4\right)^2}-\frac{313 d \tanh ^{-1}\left(\frac{x}{2}\right)}{20736}+\frac{13}{648} d \tanh ^{-1}(x)-\frac{e \left(5-2 x^2\right)}{54 \left(x^4-5 x^2+4\right)}+\frac{e \left(5-2 x^2\right)}{36 \left(x^4-5 x^2+4\right)^2}-\frac{1}{81} e \log \left(1-x^2\right)+\frac{1}{81} e \log \left(4-x^2\right)",1,"(d*x*(17 - 5*x^2))/(144*(4 - 5*x^2 + x^4)^2) + (e*(5 - 2*x^2))/(36*(4 - 5*x^2 + x^4)^2) - (d*x*(59 - 35*x^2))/(3456*(4 - 5*x^2 + x^4)) - (e*(5 - 2*x^2))/(54*(4 - 5*x^2 + x^4)) - (313*d*ArcTanh[x/2])/20736 + (13*d*ArcTanh[x])/648 - (e*Log[1 - x^2])/81 + (e*Log[4 - x^2])/81","A",14,10,18,0.5556,1,"{1673, 12, 1092, 1178, 1166, 207, 1107, 614, 616, 31}"
43,1,175,0,0.2238853,"\int \frac{d+e x+f x^2}{\left(4-5 x^2+x^4\right)^3} \, dx","Int[(d + e*x + f*x^2)/(4 - 5*x^2 + x^4)^3,x]","-\frac{x \left(-35 x^2 (d+4 f)+59 d+380 f\right)}{3456 \left(x^4-5 x^2+4\right)}+\frac{x \left(x^2 (-(5 d+8 f))+17 d+20 f\right)}{144 \left(x^4-5 x^2+4\right)^2}-\frac{(313 d+820 f) \tanh ^{-1}\left(\frac{x}{2}\right)}{20736}+\frac{1}{648} (13 d+25 f) \tanh ^{-1}(x)-\frac{e \left(5-2 x^2\right)}{54 \left(x^4-5 x^2+4\right)}+\frac{e \left(5-2 x^2\right)}{36 \left(x^4-5 x^2+4\right)^2}-\frac{1}{81} e \log \left(1-x^2\right)+\frac{1}{81} e \log \left(4-x^2\right)","-\frac{x \left(-35 x^2 (d+4 f)+59 d+380 f\right)}{3456 \left(x^4-5 x^2+4\right)}+\frac{x \left(x^2 (-(5 d+8 f))+17 d+20 f\right)}{144 \left(x^4-5 x^2+4\right)^2}-\frac{(313 d+820 f) \tanh ^{-1}\left(\frac{x}{2}\right)}{20736}+\frac{1}{648} (13 d+25 f) \tanh ^{-1}(x)-\frac{e \left(5-2 x^2\right)}{54 \left(x^4-5 x^2+4\right)}+\frac{e \left(5-2 x^2\right)}{36 \left(x^4-5 x^2+4\right)^2}-\frac{1}{81} e \log \left(1-x^2\right)+\frac{1}{81} e \log \left(4-x^2\right)",1,"(e*(5 - 2*x^2))/(36*(4 - 5*x^2 + x^4)^2) + (x*(17*d + 20*f - (5*d + 8*f)*x^2))/(144*(4 - 5*x^2 + x^4)^2) - (e*(5 - 2*x^2))/(54*(4 - 5*x^2 + x^4)) - (x*(59*d + 380*f - 35*(d + 4*f)*x^2))/(3456*(4 - 5*x^2 + x^4)) - ((313*d + 820*f)*ArcTanh[x/2])/20736 + ((13*d + 25*f)*ArcTanh[x])/648 - (e*Log[1 - x^2])/81 + (e*Log[4 - x^2])/81","A",13,9,23,0.3913,1,"{1673, 1178, 1166, 207, 12, 1107, 614, 616, 31}"
44,1,204,0,0.2519457,"\int \frac{d+e x+f x^2+g x^3}{\left(4-5 x^2+x^4\right)^3} \, dx","Int[(d + e*x + f*x^2 + g*x^3)/(4 - 5*x^2 + x^4)^3,x]","-\frac{x \left(-35 x^2 (d+4 f)+59 d+380 f\right)}{3456 \left(x^4-5 x^2+4\right)}+\frac{x \left(x^2 (-(5 d+8 f))+17 d+20 f\right)}{144 \left(x^4-5 x^2+4\right)^2}-\frac{(313 d+820 f) \tanh ^{-1}\left(\frac{x}{2}\right)}{20736}+\frac{1}{648} (13 d+25 f) \tanh ^{-1}(x)-\frac{\left(5-2 x^2\right) (2 e+5 g)}{108 \left(x^4-5 x^2+4\right)}+\frac{x^2 (-(2 e+5 g))+5 e+8 g}{36 \left(x^4-5 x^2+4\right)^2}-\frac{1}{162} (2 e+5 g) \log \left(1-x^2\right)+\frac{1}{162} (2 e+5 g) \log \left(4-x^2\right)","-\frac{x \left(-35 x^2 (d+4 f)+59 d+380 f\right)}{3456 \left(x^4-5 x^2+4\right)}+\frac{x \left(x^2 (-(5 d+8 f))+17 d+20 f\right)}{144 \left(x^4-5 x^2+4\right)^2}-\frac{(313 d+820 f) \tanh ^{-1}\left(\frac{x}{2}\right)}{20736}+\frac{1}{648} (13 d+25 f) \tanh ^{-1}(x)-\frac{\left(5-2 x^2\right) (2 e+5 g)}{108 \left(x^4-5 x^2+4\right)}+\frac{x^2 (-(2 e+5 g))+5 e+8 g}{36 \left(x^4-5 x^2+4\right)^2}-\frac{1}{162} (2 e+5 g) \log \left(1-x^2\right)+\frac{1}{162} (2 e+5 g) \log \left(4-x^2\right)",1,"(x*(17*d + 20*f - (5*d + 8*f)*x^2))/(144*(4 - 5*x^2 + x^4)^2) + (5*e + 8*g - (2*e + 5*g)*x^2)/(36*(4 - 5*x^2 + x^4)^2) - ((2*e + 5*g)*(5 - 2*x^2))/(108*(4 - 5*x^2 + x^4)) - (x*(59*d + 380*f - 35*(d + 4*f)*x^2))/(3456*(4 - 5*x^2 + x^4)) - ((313*d + 820*f)*ArcTanh[x/2])/20736 + ((13*d + 25*f)*ArcTanh[x])/648 - ((2*e + 5*g)*Log[1 - x^2])/162 + ((2*e + 5*g)*Log[4 - x^2])/162","A",12,9,28,0.3214,1,"{1673, 1178, 1166, 207, 1247, 638, 614, 616, 31}"
45,1,224,0,0.3068314,"\int \frac{d+e x+f x^2+g x^3+h x^4}{\left(4-5 x^2+x^4\right)^3} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4)/(4 - 5*x^2 + x^4)^3,x]","-\frac{x \left(-5 x^2 (7 d+28 f+64 h)+59 d+380 f+848 h\right)}{3456 \left(x^4-5 x^2+4\right)}+\frac{x \left(x^2 (-(5 d+8 f+20 h))+17 d+20 f+32 h\right)}{144 \left(x^4-5 x^2+4\right)^2}-\frac{\tanh ^{-1}\left(\frac{x}{2}\right) (313 d+820 f+1936 h)}{20736}+\frac{1}{648} \tanh ^{-1}(x) (13 d+25 f+61 h)-\frac{\left(5-2 x^2\right) (2 e+5 g)}{108 \left(x^4-5 x^2+4\right)}+\frac{x^2 (-(2 e+5 g))+5 e+8 g}{36 \left(x^4-5 x^2+4\right)^2}-\frac{1}{162} (2 e+5 g) \log \left(1-x^2\right)+\frac{1}{162} (2 e+5 g) \log \left(4-x^2\right)","-\frac{x \left(-5 x^2 (7 d+28 f+64 h)+59 d+380 f+848 h\right)}{3456 \left(x^4-5 x^2+4\right)}+\frac{x \left(x^2 (-(5 d+8 f+20 h))+17 d+20 f+32 h\right)}{144 \left(x^4-5 x^2+4\right)^2}-\frac{\tanh ^{-1}\left(\frac{x}{2}\right) (313 d+820 f+1936 h)}{20736}+\frac{1}{648} \tanh ^{-1}(x) (13 d+25 f+61 h)-\frac{\left(5-2 x^2\right) (2 e+5 g)}{108 \left(x^4-5 x^2+4\right)}+\frac{x^2 (-(2 e+5 g))+5 e+8 g}{36 \left(x^4-5 x^2+4\right)^2}-\frac{1}{162} (2 e+5 g) \log \left(1-x^2\right)+\frac{1}{162} (2 e+5 g) \log \left(4-x^2\right)",1,"(5*e + 8*g - (2*e + 5*g)*x^2)/(36*(4 - 5*x^2 + x^4)^2) + (x*(17*d + 20*f + 32*h - (5*d + 8*f + 20*h)*x^2))/(144*(4 - 5*x^2 + x^4)^2) - ((2*e + 5*g)*(5 - 2*x^2))/(108*(4 - 5*x^2 + x^4)) - (x*(59*d + 380*f + 848*h - 5*(7*d + 28*f + 64*h)*x^2))/(3456*(4 - 5*x^2 + x^4)) - ((313*d + 820*f + 1936*h)*ArcTanh[x/2])/20736 + ((13*d + 25*f + 61*h)*ArcTanh[x])/648 - ((2*e + 5*g)*Log[1 - x^2])/162 + ((2*e + 5*g)*Log[4 - x^2])/162","A",12,10,33,0.3030,1,"{1673, 1678, 1178, 1166, 207, 1247, 638, 614, 616, 31}"
46,1,239,0,0.344993,"\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5}{\left(4-5 x^2+x^4\right)^3} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4 + i*x^5)/(4 - 5*x^2 + x^4)^3,x]","-\frac{x \left(-5 x^2 (7 d+28 f+64 h)+59 d+380 f+848 h\right)}{3456 \left(x^4-5 x^2+4\right)}+\frac{x \left(x^2 (-(5 d+8 f+20 h))+17 d+20 f+32 h\right)}{144 \left(x^4-5 x^2+4\right)^2}-\frac{\tanh ^{-1}\left(\frac{x}{2}\right) (313 d+820 f+1936 h)}{20736}+\frac{1}{648} \tanh ^{-1}(x) (13 d+25 f+61 h)-\frac{\left(5-2 x^2\right) (2 e+5 g+11 i)}{108 \left(x^4-5 x^2+4\right)}+\frac{x^2 (-(2 e+5 g+17 i))+5 e+8 g+20 i}{36 \left(x^4-5 x^2+4\right)^2}-\frac{1}{162} \log \left(1-x^2\right) (2 e+5 g+11 i)+\frac{1}{162} \log \left(4-x^2\right) (2 e+5 g+11 i)","-\frac{x \left(-5 x^2 (7 d+28 f+64 h)+59 d+380 f+848 h\right)}{3456 \left(x^4-5 x^2+4\right)}+\frac{x \left(x^2 (-(5 d+8 f+20 h))+17 d+20 f+32 h\right)}{144 \left(x^4-5 x^2+4\right)^2}-\frac{\tanh ^{-1}\left(\frac{x}{2}\right) (313 d+820 f+1936 h)}{20736}+\frac{1}{648} \tanh ^{-1}(x) (13 d+25 f+61 h)-\frac{\left(5-2 x^2\right) (2 e+5 g+11 i)}{108 \left(x^4-5 x^2+4\right)}+\frac{x^2 (-(2 e+5 g+17 i))+5 e+8 g+20 i}{36 \left(x^4-5 x^2+4\right)^2}-\frac{1}{162} \log \left(1-x^2\right) (2 e+5 g+11 i)+\frac{1}{162} \log \left(4-x^2\right) (2 e+5 g+11 i)",1,"(x*(17*d + 20*f + 32*h - (5*d + 8*f + 20*h)*x^2))/(144*(4 - 5*x^2 + x^4)^2) + (5*e + 8*g + 20*i - (2*e + 5*g + 17*i)*x^2)/(36*(4 - 5*x^2 + x^4)^2) - ((2*e + 5*g + 11*i)*(5 - 2*x^2))/(108*(4 - 5*x^2 + x^4)) - (x*(59*d + 380*f + 848*h - 5*(7*d + 28*f + 64*h)*x^2))/(3456*(4 - 5*x^2 + x^4)) - ((313*d + 820*f + 1936*h)*ArcTanh[x/2])/20736 + ((13*d + 25*f + 61*h)*ArcTanh[x])/648 - ((2*e + 5*g + 11*i)*Log[1 - x^2])/162 + ((2*e + 5*g + 11*i)*Log[4 - x^2])/162","A",13,11,38,0.2895,1,"{1673, 1678, 1178, 1166, 207, 1663, 1660, 12, 614, 616, 31}"
47,1,185,0,0.1172983,"\int \frac{d+e x}{\left(1+x^2+x^4\right)^3} \, dx","Int[(d + e*x)/(1 + x^2 + x^4)^3,x]","\frac{d x \left(2-7 x^2\right)}{24 \left(x^4+x^2+1\right)}+\frac{d x \left(1-x^2\right)}{12 \left(x^4+x^2+1\right)^2}-\frac{9}{32} d \log \left(x^2-x+1\right)+\frac{9}{32} d \log \left(x^2+x+1\right)-\frac{13 d \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{48 \sqrt{3}}+\frac{13 d \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{48 \sqrt{3}}+\frac{e \left(2 x^2+1\right)}{6 \left(x^4+x^2+1\right)}+\frac{e \left(2 x^2+1\right)}{12 \left(x^4+x^2+1\right)^2}+\frac{2 e \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{d x \left(2-7 x^2\right)}{24 \left(x^4+x^2+1\right)}+\frac{d x \left(1-x^2\right)}{12 \left(x^4+x^2+1\right)^2}-\frac{9}{32} d \log \left(x^2-x+1\right)+\frac{9}{32} d \log \left(x^2+x+1\right)-\frac{13 d \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{48 \sqrt{3}}+\frac{13 d \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{48 \sqrt{3}}+\frac{e \left(2 x^2+1\right)}{6 \left(x^4+x^2+1\right)}+\frac{e \left(2 x^2+1\right)}{12 \left(x^4+x^2+1\right)^2}+\frac{2 e \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(d*x*(1 - x^2))/(12*(1 + x^2 + x^4)^2) + (e*(1 + 2*x^2))/(12*(1 + x^2 + x^4)^2) + (d*x*(2 - 7*x^2))/(24*(1 + x^2 + x^4)) + (e*(1 + 2*x^2))/(6*(1 + x^2 + x^4)) - (13*d*ArcTan[(1 - 2*x)/Sqrt[3]])/(48*Sqrt[3]) + (13*d*ArcTan[(1 + 2*x)/Sqrt[3]])/(48*Sqrt[3]) + (2*e*ArcTan[(1 + 2*x^2)/Sqrt[3]])/(3*Sqrt[3]) - (9*d*Log[1 - x + x^2])/32 + (9*d*Log[1 + x + x^2])/32","A",19,11,16,0.6875,1,"{1673, 12, 1092, 1178, 1169, 634, 618, 204, 628, 1107, 614}"
48,1,223,0,0.2149409,"\int \frac{d+e x+f x^2}{\left(1+x^2+x^4\right)^3} \, dx","Int[(d + e*x + f*x^2)/(1 + x^2 + x^4)^3,x]","\frac{x \left(-7 x^2 (d-f)+2 d+3 f\right)}{24 \left(x^4+x^2+1\right)}+\frac{x \left(x^2 (-(d-2 f))+d+f\right)}{12 \left(x^4+x^2+1\right)^2}-\frac{1}{32} (9 d-4 f) \log \left(x^2-x+1\right)+\frac{1}{32} (9 d-4 f) \log \left(x^2+x+1\right)-\frac{(13 d+2 f) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{48 \sqrt{3}}+\frac{(13 d+2 f) \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{48 \sqrt{3}}+\frac{e \left(2 x^2+1\right)}{6 \left(x^4+x^2+1\right)}+\frac{e \left(2 x^2+1\right)}{12 \left(x^4+x^2+1\right)^2}+\frac{2 e \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{x \left(-7 x^2 (d-f)+2 d+3 f\right)}{24 \left(x^4+x^2+1\right)}+\frac{x \left(x^2 (-(d-2 f))+d+f\right)}{12 \left(x^4+x^2+1\right)^2}-\frac{1}{32} (9 d-4 f) \log \left(x^2-x+1\right)+\frac{1}{32} (9 d-4 f) \log \left(x^2+x+1\right)-\frac{(13 d+2 f) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{48 \sqrt{3}}+\frac{(13 d+2 f) \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{48 \sqrt{3}}+\frac{e \left(2 x^2+1\right)}{6 \left(x^4+x^2+1\right)}+\frac{e \left(2 x^2+1\right)}{12 \left(x^4+x^2+1\right)^2}+\frac{2 e \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(e*(1 + 2*x^2))/(12*(1 + x^2 + x^4)^2) + (x*(d + f - (d - 2*f)*x^2))/(12*(1 + x^2 + x^4)^2) + (e*(1 + 2*x^2))/(6*(1 + x^2 + x^4)) + (x*(2*d + 3*f - 7*(d - f)*x^2))/(24*(1 + x^2 + x^4)) - ((13*d + 2*f)*ArcTan[(1 - 2*x)/Sqrt[3]])/(48*Sqrt[3]) + ((13*d + 2*f)*ArcTan[(1 + 2*x)/Sqrt[3]])/(48*Sqrt[3]) + (2*e*ArcTan[(1 + 2*x^2)/Sqrt[3]])/(3*Sqrt[3]) - ((9*d - 4*f)*Log[1 - x + x^2])/32 + ((9*d - 4*f)*Log[1 + x + x^2])/32","A",18,10,21,0.4762,1,"{1673, 1178, 1169, 634, 618, 204, 628, 12, 1107, 614}"
49,1,243,0,0.2270324,"\int \frac{d+e x+f x^2+g x^3}{\left(1+x^2+x^4\right)^3} \, dx","Int[(d + e*x + f*x^2 + g*x^3)/(1 + x^2 + x^4)^3,x]","\frac{x \left(-7 x^2 (d-f)+2 d+3 f\right)}{24 \left(x^4+x^2+1\right)}+\frac{x \left(x^2 (-(d-2 f))+d+f\right)}{12 \left(x^4+x^2+1\right)^2}-\frac{1}{32} (9 d-4 f) \log \left(x^2-x+1\right)+\frac{1}{32} (9 d-4 f) \log \left(x^2+x+1\right)-\frac{(13 d+2 f) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{48 \sqrt{3}}+\frac{(13 d+2 f) \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{48 \sqrt{3}}+\frac{\left(2 x^2+1\right) (2 e-g)}{12 \left(x^4+x^2+1\right)}+\frac{x^2 (2 e-g)+e-2 g}{12 \left(x^4+x^2+1\right)^2}+\frac{(2 e-g) \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{x \left(-7 x^2 (d-f)+2 d+3 f\right)}{24 \left(x^4+x^2+1\right)}+\frac{x \left(x^2 (-(d-2 f))+d+f\right)}{12 \left(x^4+x^2+1\right)^2}-\frac{1}{32} (9 d-4 f) \log \left(x^2-x+1\right)+\frac{1}{32} (9 d-4 f) \log \left(x^2+x+1\right)-\frac{(13 d+2 f) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{48 \sqrt{3}}+\frac{(13 d+2 f) \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{48 \sqrt{3}}+\frac{\left(2 x^2+1\right) (2 e-g)}{12 \left(x^4+x^2+1\right)}+\frac{x^2 (2 e-g)+e-2 g}{12 \left(x^4+x^2+1\right)^2}+\frac{(2 e-g) \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(x*(d + f - (d - 2*f)*x^2))/(12*(1 + x^2 + x^4)^2) + (e - 2*g + (2*e - g)*x^2)/(12*(1 + x^2 + x^4)^2) + ((2*e - g)*(1 + 2*x^2))/(12*(1 + x^2 + x^4)) + (x*(2*d + 3*f - 7*(d - f)*x^2))/(24*(1 + x^2 + x^4)) - ((13*d + 2*f)*ArcTan[(1 - 2*x)/Sqrt[3]])/(48*Sqrt[3]) + ((13*d + 2*f)*ArcTan[(1 + 2*x)/Sqrt[3]])/(48*Sqrt[3]) + ((2*e - g)*ArcTan[(1 + 2*x^2)/Sqrt[3]])/(3*Sqrt[3]) - ((9*d - 4*f)*Log[1 - x + x^2])/32 + ((9*d - 4*f)*Log[1 + x + x^2])/32","A",17,10,26,0.3846,1,"{1673, 1178, 1169, 634, 618, 204, 628, 1247, 638, 614}"
50,1,263,0,0.262926,"\int \frac{d+e x+f x^2+g x^3+h x^4}{\left(1+x^2+x^4\right)^3} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4)/(1 + x^2 + x^4)^3,x]","\frac{x \left(x^2 (-(7 d-7 f+4 h))+2 d+3 f-h\right)}{24 \left(x^4+x^2+1\right)}+\frac{x \left(x^2 (-(d-2 f+h))+d+f-2 h\right)}{12 \left(x^4+x^2+1\right)^2}-\frac{1}{32} \log \left(x^2-x+1\right) (9 d-4 f+3 h)+\frac{1}{32} \log \left(x^2+x+1\right) (9 d-4 f+3 h)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right) (13 d+2 f+h)}{48 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right) (13 d+2 f+h)}{48 \sqrt{3}}+\frac{\left(2 x^2+1\right) (2 e-g)}{12 \left(x^4+x^2+1\right)}+\frac{x^2 (2 e-g)+e-2 g}{12 \left(x^4+x^2+1\right)^2}+\frac{(2 e-g) \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{x \left(x^2 (-(7 d-7 f+4 h))+2 d+3 f-h\right)}{24 \left(x^4+x^2+1\right)}+\frac{x \left(x^2 (-(d-2 f+h))+d+f-2 h\right)}{12 \left(x^4+x^2+1\right)^2}-\frac{1}{32} \log \left(x^2-x+1\right) (9 d-4 f+3 h)+\frac{1}{32} \log \left(x^2+x+1\right) (9 d-4 f+3 h)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right) (13 d+2 f+h)}{48 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right) (13 d+2 f+h)}{48 \sqrt{3}}+\frac{\left(2 x^2+1\right) (2 e-g)}{12 \left(x^4+x^2+1\right)}+\frac{x^2 (2 e-g)+e-2 g}{12 \left(x^4+x^2+1\right)^2}+\frac{(2 e-g) \tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(e - 2*g + (2*e - g)*x^2)/(12*(1 + x^2 + x^4)^2) + (x*(d + f - 2*h - (d - 2*f + h)*x^2))/(12*(1 + x^2 + x^4)^2) + ((2*e - g)*(1 + 2*x^2))/(12*(1 + x^2 + x^4)) + (x*(2*d + 3*f - h - (7*d - 7*f + 4*h)*x^2))/(24*(1 + x^2 + x^4)) - ((13*d + 2*f + h)*ArcTan[(1 - 2*x)/Sqrt[3]])/(48*Sqrt[3]) + ((13*d + 2*f + h)*ArcTan[(1 + 2*x)/Sqrt[3]])/(48*Sqrt[3]) + ((2*e - g)*ArcTan[(1 + 2*x^2)/Sqrt[3]])/(3*Sqrt[3]) - ((9*d - 4*f + 3*h)*Log[1 - x + x^2])/32 + ((9*d - 4*f + 3*h)*Log[1 + x + x^2])/32","A",17,11,31,0.3548,1,"{1673, 1678, 1178, 1169, 634, 618, 204, 628, 1247, 638, 614}"
51,1,269,0,0.2864726,"\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5}{\left(1+x^2+x^4\right)^3} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4 + i*x^5)/(1 + x^2 + x^4)^3,x]","\frac{x \left(x^2 (-(7 d-7 f+4 h))+2 d+3 f-h\right)}{24 \left(x^4+x^2+1\right)}+\frac{x \left(x^2 (-(d-2 f+h))+d+f-2 h\right)}{12 \left(x^4+x^2+1\right)^2}-\frac{1}{32} \log \left(x^2-x+1\right) (9 d-4 f+3 h)+\frac{1}{32} \log \left(x^2+x+1\right) (9 d-4 f+3 h)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right) (13 d+2 f+h)}{48 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right) (13 d+2 f+h)}{48 \sqrt{3}}+\frac{\left(2 x^2+1\right) (2 e-g+i)}{12 \left(x^4+x^2+1\right)}+\frac{x^2 (2 e-g-i)+e-2 g+i}{12 \left(x^4+x^2+1\right)^2}+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right) (2 e-g+i)}{3 \sqrt{3}}","\frac{x \left(x^2 (-(7 d-7 f+4 h))+2 d+3 f-h\right)}{24 \left(x^4+x^2+1\right)}+\frac{x \left(x^2 (-(d-2 f+h))+d+f-2 h\right)}{12 \left(x^4+x^2+1\right)^2}-\frac{1}{32} \log \left(x^2-x+1\right) (9 d-4 f+3 h)+\frac{1}{32} \log \left(x^2+x+1\right) (9 d-4 f+3 h)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right) (13 d+2 f+h)}{48 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right) (13 d+2 f+h)}{48 \sqrt{3}}+\frac{\left(2 x^2+1\right) (2 e-g+i)}{12 \left(x^4+x^2+1\right)}+\frac{x^2 (2 e-g-i)+e-2 g+i}{12 \left(x^4+x^2+1\right)^2}+\frac{\tan ^{-1}\left(\frac{2 x^2+1}{\sqrt{3}}\right) (2 e-g+i)}{3 \sqrt{3}}",1,"(x*(d + f - 2*h - (d - 2*f + h)*x^2))/(12*(1 + x^2 + x^4)^2) + (e - 2*g + i + (2*e - g - i)*x^2)/(12*(1 + x^2 + x^4)^2) + ((2*e - g + i)*(1 + 2*x^2))/(12*(1 + x^2 + x^4)) + (x*(2*d + 3*f - h - (7*d - 7*f + 4*h)*x^2))/(24*(1 + x^2 + x^4)) - ((13*d + 2*f + h)*ArcTan[(1 - 2*x)/Sqrt[3]])/(48*Sqrt[3]) + ((13*d + 2*f + h)*ArcTan[(1 + 2*x)/Sqrt[3]])/(48*Sqrt[3]) + ((2*e - g + i)*ArcTan[(1 + 2*x^2)/Sqrt[3]])/(3*Sqrt[3]) - ((9*d - 4*f + 3*h)*Log[1 - x + x^2])/32 + ((9*d - 4*f + 3*h)*Log[1 + x + x^2])/32","A",18,12,36,0.3333,1,"{1673, 1678, 1178, 1169, 634, 618, 204, 628, 1663, 1660, 12, 614}"
52,1,474,0,2.1934491,"\int \frac{d+e x}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[(d + e*x)/(a + b*x^2 + c*x^4)^3,x]","\frac{3 \sqrt{c} d \left(56 a^2 c^2-10 a b^2 c+b \left(b^2-8 a c\right) \sqrt{b^2-4 a c}+b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^2 \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{3 \sqrt{c} d \left(-\frac{56 a^2 c^2-10 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-8 a b c+b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a^2 \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{d x \left(3 b c x^2 \left(b^2-8 a c\right)+\left(b^2-7 a c\right) \left(3 b^2-4 a c\right)\right)}{8 a^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{6 c^2 e \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{d x \left(-2 a c+b^2+b c x^2\right)}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 c e \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{e \left(b+2 c x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}","\frac{3 \sqrt{c} d \left(56 a^2 c^2-10 a b^2 c+b \left(b^2-8 a c\right) \sqrt{b^2-4 a c}+b^4\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^2 \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{3 \sqrt{c} d \left(-\frac{56 a^2 c^2-10 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-8 a b c+b^3\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{8 \sqrt{2} a^2 \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{d x \left(3 b c x^2 \left(b^2-8 a c\right)+\left(b^2-7 a c\right) \left(3 b^2-4 a c\right)\right)}{8 a^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{6 c^2 e \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{d x \left(-2 a c+b^2+b c x^2\right)}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 c e \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{e \left(b+2 c x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}",1,"-(e*(b + 2*c*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (d*x*(b^2 - 2*a*c + b*c*x^2))/(4*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (3*c*e*(b + 2*c*x^2))/(2*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (d*x*((b^2 - 7*a*c)*(3*b^2 - 4*a*c) + 3*b*c*(b^2 - 8*a*c)*x^2))/(8*a^2*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (3*Sqrt[c]*(b^4 - 10*a*b^2*c + 56*a^2*c^2 + b*(b^2 - 8*a*c)*Sqrt[b^2 - 4*a*c])*d*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^2*(b^2 - 4*a*c)^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (3*Sqrt[c]*(b^3 - 8*a*b*c - (b^4 - 10*a*b^2*c + 56*a^2*c^2)/Sqrt[b^2 - 4*a*c])*d*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]]) - (6*c^2*e*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",13,10,20,0.5000,1,"{1673, 12, 1092, 1178, 1166, 205, 1107, 614, 618, 206}"
53,1,621,0,4.5119252,"\int \frac{d+e x+f x^2}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[(d + e*x + f*x^2)/(a + b*x^2 + c*x^4)^3,x]","\frac{x \left(c x^2 \left(20 a^2 c f+a b^2 f-24 a b c d+3 b^3 d\right)+8 a^2 b c f+28 a^2 c^2 d-25 a b^2 c d+a b^3 f+3 b^4 d\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{-52 a^2 b c f+168 a^2 c^2 d-30 a b^2 c d+a b^3 f+3 b^4 d}{\sqrt{b^2-4 a c}}+20 a^2 c f+a b^2 f-24 a b c d+3 b^3 d\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{\sqrt{c} \left(4 a^2 c \left(5 f \sqrt{b^2-4 a c}+42 c d\right)+b^3 \left(3 d \sqrt{b^2-4 a c}+a f\right)-a b^2 \left(30 c d-f \sqrt{b^2-4 a c}\right)-4 a b c \left(6 d \sqrt{b^2-4 a c}+13 a f\right)+3 b^4 d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^2 \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{6 c^2 e \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 \left(c x^2 (b d-2 a f)-a b f-2 a c d+b^2 d\right)}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 c e \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{e \left(b+2 c x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}","\frac{x \left(c x^2 \left(20 a^2 c f+a b^2 f-24 a b c d+3 b^3 d\right)+8 a^2 b c f+28 a^2 c^2 d-25 a b^2 c d+a b^3 f+3 b^4 d\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{-52 a^2 b c f+168 a^2 c^2 d-30 a b^2 c d+a b^3 f+3 b^4 d}{\sqrt{b^2-4 a c}}+20 a^2 c f+a b^2 f-24 a b c d+3 b^3 d\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{\sqrt{c} \left(4 a^2 c \left(5 f \sqrt{b^2-4 a c}+42 c d\right)+b^3 \left(3 d \sqrt{b^2-4 a c}+a f\right)-a b^2 \left(30 c d-f \sqrt{b^2-4 a c}\right)-4 a b c \left(6 d \sqrt{b^2-4 a c}+13 a f\right)+3 b^4 d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^2 \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{6 c^2 e \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 \left(c x^2 (b d-2 a f)-a b f-2 a c d+b^2 d\right)}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 c e \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{e \left(b+2 c x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}",1,"-(e*(b + 2*c*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (x*(b^2*d - 2*a*c*d - a*b*f + c*(b*d - 2*a*f)*x^2))/(4*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (3*c*e*(b + 2*c*x^2))/(2*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (x*(3*b^4*d - 25*a*b^2*c*d + 28*a^2*c^2*d + a*b^3*f + 8*a^2*b*c*f + c*(3*b^3*d - 24*a*b*c*d + a*b^2*f + 20*a^2*c*f)*x^2))/(8*a^2*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(3*b^4*d + b^3*(3*Sqrt[b^2 - 4*a*c]*d + a*f) - 4*a*b*c*(6*Sqrt[b^2 - 4*a*c]*d + 13*a*f) - a*b^2*(30*c*d - Sqrt[b^2 - 4*a*c]*f) + 4*a^2*c*(42*c*d + 5*Sqrt[b^2 - 4*a*c]*f))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^2*(b^2 - 4*a*c)^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(3*b^3*d - 24*a*b*c*d + a*b^2*f + 20*a^2*c*f - (3*b^4*d - 30*a*b^2*c*d + 168*a^2*c^2*d + a*b^3*f - 52*a^2*b*c*f)/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]]) - (6*c^2*e*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",12,9,25,0.3600,1,"{1673, 1178, 1166, 205, 12, 1107, 614, 618, 206}"
54,1,646,0,3.2994823,"\int \frac{d+e x+f x^2+g x^3}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[(d + e*x + f*x^2 + g*x^3)/(a + b*x^2 + c*x^4)^3,x]","\frac{x \left(c x^2 \left(20 a^2 c f+a b^2 f-24 a b c d+3 b^3 d\right)+8 a^2 b c f+28 a^2 c^2 d-25 a b^2 c d+a b^3 f+3 b^4 d\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{-52 a^2 b c f+168 a^2 c^2 d-30 a b^2 c d+a b^3 f+3 b^4 d}{\sqrt{b^2-4 a c}}+20 a^2 c f+a b^2 f-24 a b c d+3 b^3 d\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{\sqrt{c} \left(4 a^2 c \left(5 f \sqrt{b^2-4 a c}+42 c d\right)+b^3 \left(3 d \sqrt{b^2-4 a c}+a f\right)-a b^2 \left(30 c d-f \sqrt{b^2-4 a c}\right)-4 a b c \left(6 d \sqrt{b^2-4 a c}+13 a f\right)+3 b^4 d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^2 \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{x \left(c x^2 (b d-2 a f)-a b f-2 a c d+b^2 d\right)}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 \left(b+2 c x^2\right) (2 c e-b g)}{4 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{-2 a g+x^2 (2 c e-b g)+b e}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{3 c (2 c e-b g) \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 \left(c x^2 \left(20 a^2 c f+a b^2 f-24 a b c d+3 b^3 d\right)+8 a^2 b c f+28 a^2 c^2 d-25 a b^2 c d+a b^3 f+3 b^4 d\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{-52 a^2 b c f+168 a^2 c^2 d-30 a b^2 c d+a b^3 f+3 b^4 d}{\sqrt{b^2-4 a c}}+20 a^2 c f+a b^2 f-24 a b c d+3 b^3 d\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{\sqrt{c} \left(4 a^2 c \left(5 f \sqrt{b^2-4 a c}+42 c d\right)+b^3 \left(3 d \sqrt{b^2-4 a c}+a f\right)-a b^2 \left(30 c d-f \sqrt{b^2-4 a c}\right)-4 a b c \left(6 d \sqrt{b^2-4 a c}+13 a f\right)+3 b^4 d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^2 \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{x \left(c x^2 (b d-2 a f)-a b f-2 a c d+b^2 d\right)}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 \left(b+2 c x^2\right) (2 c e-b g)}{4 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{-2 a g+x^2 (2 c e-b g)+b e}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{3 c (2 c e-b g) \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*(b^2*d - 2*a*c*d - a*b*f + c*(b*d - 2*a*f)*x^2))/(4*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) - (b*e - 2*a*g + (2*c*e - b*g)*x^2)/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (3*(2*c*e - b*g)*(b + 2*c*x^2))/(4*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (x*(3*b^4*d - 25*a*b^2*c*d + 28*a^2*c^2*d + a*b^3*f + 8*a^2*b*c*f + c*(3*b^3*d - 24*a*b*c*d + a*b^2*f + 20*a^2*c*f)*x^2))/(8*a^2*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(3*b^4*d + b^3*(3*Sqrt[b^2 - 4*a*c]*d + a*f) - 4*a*b*c*(6*Sqrt[b^2 - 4*a*c]*d + 13*a*f) - a*b^2*(30*c*d - Sqrt[b^2 - 4*a*c]*f) + 4*a^2*c*(42*c*d + 5*Sqrt[b^2 - 4*a*c]*f))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^2*(b^2 - 4*a*c)^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(3*b^3*d - 24*a*b*c*d + a*b^2*f + 20*a^2*c*f - (3*b^4*d - 30*a*b^2*c*d + 168*a^2*c^2*d + a*b^3*f - 52*a^2*b*c*f)/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]]) - (3*c*(2*c*e - b*g)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",11,9,30,0.3000,1,"{1673, 1178, 1166, 205, 1247, 638, 614, 618, 206}"
55,1,679,0,4.1821633,"\int \frac{d+e x+f x^2+g x^3+h x^4}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4)/(a + b*x^2 + c*x^4)^3,x]","\frac{x \left(c x^2 \left(20 a^2 c f+a b^2 f-12 a b (a h+2 c d)+3 b^3 d\right)+8 a^2 b c f+4 a^2 c (a h+7 c d)-a b^2 (7 a h+25 c d)+a b^3 f+3 b^4 d\right)}{8 a^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{-52 a^2 b c f+24 a^2 c (a h+7 c d)-6 a b^2 (5 c d-3 a h)+a b^3 f+3 b^4 d}{\sqrt{b^2-4 a c}}+20 a^2 c f+a b^2 f-12 a b (a h+2 c d)+3 b^3 d\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} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{-52 a^2 b c f+24 a^2 c (a h+7 c d)-6 a b^2 (5 c d-3 a h)+a b^3 f+3 b^4 d}{\sqrt{b^2-4 a c}}+20 a^2 c f+a b^2 f-12 a b (a h+2 c d)+3 b^3 d\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(x^2 (a b h-2 a c f+b c d)-a b f-2 a (c d-a h)+b^2 d\right)}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 \left(b+2 c x^2\right) (2 c e-b g)}{4 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{-2 a g+x^2 (2 c e-b g)+b e}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{3 c (2 c e-b g) \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 \left(c x^2 \left(20 a^2 c f+a b^2 f-12 a b (a h+2 c d)+3 b^3 d\right)+8 a^2 b c f+4 a^2 c (a h+7 c d)-a b^2 (7 a h+25 c d)+a b^3 f+3 b^4 d\right)}{8 a^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{-52 a^2 b c f+24 a^2 c (a h+7 c d)-6 a b^2 (5 c d-3 a h)+a b^3 f+3 b^4 d}{\sqrt{b^2-4 a c}}+20 a^2 c f+a b^2 f-12 a b (a h+2 c d)+3 b^3 d\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} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{-52 a^2 b c f+24 a^2 c (a h+7 c d)-6 a b^2 (5 c d-3 a h)+a b^3 f+3 b^4 d}{\sqrt{b^2-4 a c}}+20 a^2 c f+a b^2 f-12 a b (a h+2 c d)+3 b^3 d\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(x^2 (a b h-2 a c f+b c d)-a b f-2 a (c d-a h)+b^2 d\right)}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 \left(b+2 c x^2\right) (2 c e-b g)}{4 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{-2 a g+x^2 (2 c e-b g)+b e}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{3 c (2 c e-b g) \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,"-(b*e - 2*a*g + (2*c*e - b*g)*x^2)/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (x*(b^2*d - a*b*f - 2*a*(c*d - a*h) + (b*c*d - 2*a*c*f + a*b*h)*x^2))/(4*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (3*(2*c*e - b*g)*(b + 2*c*x^2))/(4*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (x*(3*b^4*d + a*b^3*f + 8*a^2*b*c*f + 4*a^2*c*(7*c*d + a*h) - a*b^2*(25*c*d + 7*a*h) + c*(3*b^3*d + a*b^2*f + 20*a^2*c*f - 12*a*b*(2*c*d + a*h))*x^2))/(8*a^2*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(3*b^3*d + a*b^2*f + 20*a^2*c*f - 12*a*b*(2*c*d + a*h) + (3*b^4*d + a*b^3*f - 52*a^2*b*c*f - 6*a*b^2*(5*c*d - 3*a*h) + 24*a^2*c*(7*c*d + a*h))/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]*(3*b^3*d + a*b^2*f + 20*a^2*c*f - 12*a*b*(2*c*d + a*h) - (3*b^4*d + a*b^3*f - 52*a^2*b*c*f - 6*a*b^2*(5*c*d - 3*a*h) + 24*a^2*c*(7*c*d + a*h))/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]]) - (3*c*(2*c*e - b*g)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",11,10,35,0.2857,1,"{1673, 1678, 1178, 1166, 205, 1247, 638, 614, 618, 206}"
56,1,728,0,2.7327649,"\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4 + i*x^5)/(a + b*x^2 + c*x^4)^3,x]","\frac{x \left(c x^2 \left(20 a^2 c f+a b^2 f-12 a b (a h+2 c d)+3 b^3 d\right)+8 a^2 b c f+4 a^2 c (a h+7 c d)-a b^2 (7 a h+25 c d)+a b^3 f+3 b^4 d\right)}{8 a^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{-52 a^2 b c f+24 a^2 c (a h+7 c d)-6 a b^2 (5 c d-3 a h)+a b^3 f+3 b^4 d}{\sqrt{b^2-4 a c}}+20 a^2 c f+a b^2 f-12 a b (a h+2 c d)+3 b^3 d\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} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{-52 a^2 b c f+24 a^2 c (a h+7 c d)-6 a b^2 (5 c d-3 a h)+a b^3 f+3 b^4 d}{\sqrt{b^2-4 a c}}+20 a^2 c f+a b^2 f-12 a b (a h+2 c d)+3 b^3 d\right)}{8 \sqrt{2} a^2 \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x^2 \left(-\left(-2 a c i+b^2 i-b c g+2 c^2 e\right)\right)-b (a i+c e)+2 a c g}{4 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(2 a c i+b^2 i-3 b c g+6 c^2 e\right)}{\left(b^2-4 a c\right)^{5/2}}+\frac{x \left(x^2 (a b h-2 a c f+b c d)-a b f-2 a (c d-a h)+b^2 d\right)}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{\left(b+2 c x^2\right) \left(2 a i+\frac{b^2 i}{c}-3 b g+6 c e\right)}{4 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}","\frac{x \left(c x^2 \left(20 a^2 c f+a b^2 f-12 a b (a h+2 c d)+3 b^3 d\right)+8 a^2 b c f+4 a^2 c (a h+7 c d)-a b^2 (7 a h+25 c d)+a b^3 f+3 b^4 d\right)}{8 a^2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{-52 a^2 b c f+24 a^2 c (a h+7 c d)-6 a b^2 (5 c d-3 a h)+a b^3 f+3 b^4 d}{\sqrt{b^2-4 a c}}+20 a^2 c f+a b^2 f-12 a b (a h+2 c d)+3 b^3 d\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} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{-52 a^2 b c f+24 a^2 c (a h+7 c d)-6 a b^2 (5 c d-3 a h)+a b^3 f+3 b^4 d}{\sqrt{b^2-4 a c}}+20 a^2 c f+a b^2 f-12 a b (a h+2 c d)+3 b^3 d\right)}{8 \sqrt{2} a^2 \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{x^2 \left(-\left(-2 a c i+b^2 i-b c g+2 c^2 e\right)\right)-b (a i+c e)+2 a c g}{4 c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}-\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(2 a c i+b^2 i-3 b c g+6 c^2 e\right)}{\left(b^2-4 a c\right)^{5/2}}+\frac{x \left(x^2 (a b h-2 a c f+b c d)-a b f-2 a (c d-a h)+b^2 d\right)}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{\left(b+2 c x^2\right) \left(2 a i+\frac{b^2 i}{c}-3 b g+6 c e\right)}{4 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}",1,"(x*(b^2*d - a*b*f - 2*a*(c*d - a*h) + (b*c*d - 2*a*c*f + a*b*h)*x^2))/(4*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (2*a*c*g - b*(c*e + a*i) - (2*c^2*e - b*c*g + b^2*i - 2*a*c*i)*x^2)/(4*c*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + ((6*c*e - 3*b*g + 2*a*i + (b^2*i)/c)*(b + 2*c*x^2))/(4*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (x*(3*b^4*d + a*b^3*f + 8*a^2*b*c*f + 4*a^2*c*(7*c*d + a*h) - a*b^2*(25*c*d + 7*a*h) + c*(3*b^3*d + a*b^2*f + 20*a^2*c*f - 12*a*b*(2*c*d + a*h))*x^2))/(8*a^2*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(3*b^3*d + a*b^2*f + 20*a^2*c*f - 12*a*b*(2*c*d + a*h) + (3*b^4*d + a*b^3*f - 52*a^2*b*c*f - 6*a*b^2*(5*c*d - 3*a*h) + 24*a^2*c*(7*c*d + a*h))/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]*(3*b^3*d + a*b^2*f + 20*a^2*c*f - 12*a*b*(2*c*d + a*h) - (3*b^4*d + a*b^3*f - 52*a^2*b*c*f - 6*a*b^2*(5*c*d - 3*a*h) + 24*a^2*c*(7*c*d + a*h))/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]]) - ((6*c^2*e - 3*b*c*g + b^2*i + 2*a*c*i)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",12,11,40,0.2750,1,"{1673, 1678, 1178, 1166, 205, 1663, 1660, 12, 614, 618, 206}"
57,1,1144,0,8.1635536,"\int \frac{d+e x+f x^2+g x^3+h x^4+j x^5+k x^6+l x^7+m x^8}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4 + j*x^5 + k*x^6 + l*x^7 + m*x^8)/(a + b*x^2 + c*x^4)^3,x]","\frac{-\frac{l b^4}{c^2}+\frac{j b^3}{c}-\left(3 g-\frac{5 a l}{c}\right) b^2+2 (3 c e+a j) b+2 \left(j b^2-3 c g b-3 a l b+6 c^2 e+2 a c j\right) x^2-16 a^2 l}{4 \left(b^2-4 a c\right)^2 \left(c x^4+b x^2+a\right)}+\frac{\left(\left(\frac{m a^2}{c}+3 c d\right) b^3+a (c f+3 a k) b^2-4 a \left(4 m a^2+3 c h a+6 c^2 d\right) b+4 a^2 c (5 c f+3 a k)+\frac{\left(3 c^2 d-a^2 m\right) b^4+a c (c f-3 a k) b^3-6 a c \left(-3 m a^2-3 c h a+5 c^2 d\right) b^2-4 a^2 c^2 (13 c f+9 a k) b+8 a^2 c^2 \left(5 m a^2+3 c h a+21 c^2 d\right)}{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)}{8 \sqrt{2} a^2 \sqrt{c} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\left(\frac{m a^2}{c}+3 c d\right) b^3+a (c f+3 a k) b^2-4 a \left(4 m a^2+3 c h a+6 c^2 d\right) b+4 a^2 c (5 c f+3 a k)-\frac{\left(3 c^2 d-a^2 m\right) b^4+a c (c f-3 a k) b^3-6 a c \left(-3 m a^2-3 c h a+5 c^2 d\right) b^2-4 a^2 c^2 (13 c f+9 a k) b+8 a^2 c^2 \left(5 m a^2+3 c h a+21 c^2 d\right)}{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)}{8 \sqrt{2} a^2 \sqrt{c} \left(b^2-4 a c\right)^2 \sqrt{b+\sqrt{b^2-4 a c}}}-\frac{\left(j b^2-3 c g b-3 a l b+6 c^2 e+2 a c j\right) \tanh ^{-1}\left(\frac{2 c x^2+b}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}+\frac{x \left(\left(3 c d-\frac{2 a^2 m}{c}\right) b^4+a (c f+2 a k) b^3-a \left(-11 m a^2+7 c h a+25 c^2 d\right) b^2+4 a^2 c (2 c f+a k) b+\left(\left(m a^2+3 c^2 d\right) b^3+a c (c f+3 a k) b^2-4 a c \left(4 m a^2+3 c h a+6 c^2 d\right) b+4 a^2 c^2 (5 c f+3 a k)\right) x^2+4 a^2 c \left(-9 m a^2+c h a+7 c^2 d\right)\right)}{8 a^2 c \left(b^2-4 a c\right)^2 \left(c x^4+b x^2+a\right)}-\frac{-a l b^2+c (c e+a j) b+\left(-l b^3+c (b j+3 a l) b+2 c^3 e-c^2 (b g+2 a j)\right) x^2-2 a c (c g-a l)}{4 c^2 \left(b^2-4 a c\right) \left(c x^4+b x^2+a\right)^2}-\frac{x \left(-\left(m a^2+c^2 d\right) b^2+a c (c f+a k) b+\left(-a m b^3+a c k b^2-c \left(-3 m a^2+c h a+c^2 d\right) b+2 a c^2 (c f-a k)\right) x^2+2 a c \left(m a^2-c h a+c^2 d\right)\right)}{4 a c^2 \left(b^2-4 a c\right) \left(c x^4+b x^2+a\right)^2}","\frac{-\frac{l b^4}{c^2}+\frac{j b^3}{c}-\left(3 g-\frac{5 a l}{c}\right) b^2+2 (3 c e+a j) b+2 \left(j b^2-3 c g b-3 a l b+6 c^2 e+2 a c j\right) x^2-16 a^2 l}{4 \left(b^2-4 a c\right)^2 \left(c x^4+b x^2+a\right)}+\frac{\left(\left(m a^2+3 c^2 d\right) b^3+a c (c f+3 a k) b^2-4 a c \left(4 m a^2+3 c h a+6 c^2 d\right) b+4 a^2 c^2 (5 c f+3 a k)+\frac{\left(3 c^2 d-a^2 m\right) b^4+a c (c f-3 a k) b^3-6 a c \left(-3 m a^2-3 c h a+5 c^2 d\right) b^2-4 a^2 c^2 (13 c f+9 a k) b+8 a^2 c^2 \left(5 m a^2+3 c h a+21 c^2 d\right)}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^2 c^{3/2} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\left(m a^2+3 c^2 d\right) b^3+a c (c f+3 a k) b^2-4 a c \left(4 m a^2+3 c h a+6 c^2 d\right) b+4 a^2 c^2 (5 c f+3 a k)-\frac{\left(3 c^2 d-a^2 m\right) b^4+a c (c f-3 a k) b^3-6 a c \left(-3 m a^2-3 c h a+5 c^2 d\right) b^2-4 a^2 c^2 (13 c f+9 a k) b+8 a^2 c^2 \left(5 m a^2+3 c h a+21 c^2 d\right)}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^2 c^{3/2} \left(b^2-4 a c\right)^2 \sqrt{b+\sqrt{b^2-4 a c}}}-\frac{\left(j b^2-3 c g b-3 a l b+6 c^2 e+2 a c j\right) \tanh ^{-1}\left(\frac{2 c x^2+b}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}+\frac{x \left(\left(3 c^2 d-2 a^2 m\right) b^4+a c (c f+2 a k) b^3-a c \left(-11 m a^2+7 c h a+25 c^2 d\right) b^2+4 a^2 c^2 (2 c f+a k) b+c \left(\left(m a^2+3 c^2 d\right) b^3+a c (c f+3 a k) b^2-4 a c \left(4 m a^2+3 c h a+6 c^2 d\right) b+4 a^2 c^2 (5 c f+3 a k)\right) x^2+4 a^2 c^2 \left(-9 m a^2+c h a+7 c^2 d\right)\right)}{8 a^2 c^2 \left(b^2-4 a c\right)^2 \left(c x^4+b x^2+a\right)}-\frac{-a l b^2+c (c e+a j) b+\left(-l b^3+c (b j+3 a l) b+2 c^3 e-c^2 (b g+2 a j)\right) x^2-2 a c (c g-a l)}{4 c^2 \left(b^2-4 a c\right) \left(c x^4+b x^2+a\right)^2}-\frac{x \left(-\left(m a^2+c^2 d\right) b^2+a c (c f+a k) b+\left(-a m b^3+a c k b^2-c \left(-3 m a^2+c h a+c^2 d\right) b+2 a c^2 (c f-a k)\right) x^2+2 a c \left(m a^2-c h a+c^2 d\right)\right)}{4 a c^2 \left(b^2-4 a c\right) \left(c x^4+b x^2+a\right)^2}",1,"-(b*c*(c*e + a*j) - a*b^2*l - 2*a*c*(c*g - a*l) + (2*c^3*e - c^2*(b*g + 2*a*j) - b^3*l + b*c*(b*j + 3*a*l))*x^2)/(4*c^2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) - (x*(a*b*c*(c*f + a*k) - b^2*(c^2*d + a^2*m) + 2*a*c*(c^2*d - a*c*h + a^2*m) + (a*b^2*c*k + 2*a*c^2*(c*f - a*k) - a*b^3*m - b*c*(c^2*d + a*c*h - 3*a^2*m))*x^2))/(4*a*c^2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + ((b^3*j)/c + 2*b*(3*c*e + a*j) - 16*a^2*l - (b^4*l)/c^2 - b^2*(3*g - (5*a*l)/c) + 2*(6*c^2*e - 3*b*c*g + b^2*j + 2*a*c*j - 3*a*b*l)*x^2)/(4*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (x*(4*a^2*b*c*(2*c*f + a*k) + a*b^3*(c*f + 2*a*k) - a*b^2*(25*c^2*d + 7*a*c*h - 11*a^2*m) + 4*a^2*c*(7*c^2*d + a*c*h - 9*a^2*m) + b^4*(3*c*d - (2*a^2*m)/c) + (a*b^2*c*(c*f + 3*a*k) + 4*a^2*c^2*(5*c*f + 3*a*k) + b^3*(3*c^2*d + a^2*m) - 4*a*b*c*(6*c^2*d + 3*a*c*h + 4*a^2*m))*x^2))/(8*a^2*c*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + ((a*b^2*(c*f + 3*a*k) + 4*a^2*c*(5*c*f + 3*a*k) - 4*a*b*(6*c^2*d + 3*a*c*h + 4*a^2*m) + b^3*(3*c*d + (a^2*m)/c) + (a*b^3*c*(c*f - 3*a*k) - 4*a^2*b*c^2*(13*c*f + 9*a*k) - 6*a*b^2*c*(5*c^2*d - 3*a*c*h - 3*a^2*m) + b^4*(3*c^2*d - a^2*m) + 8*a^2*c^2*(21*c^2*d + 3*a*c*h + 5*a^2*m))/(c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^2*Sqrt[c]*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((a*b^2*(c*f + 3*a*k) + 4*a^2*c*(5*c*f + 3*a*k) - 4*a*b*(6*c^2*d + 3*a*c*h + 4*a^2*m) + b^3*(3*c*d + (a^2*m)/c) - (a*b^3*c*(c*f - 3*a*k) - 4*a^2*b*c^2*(13*c*f + 9*a*k) - 6*a*b^2*c*(5*c^2*d - 3*a*c*h - 3*a^2*m) + b^4*(3*c^2*d - a^2*m) + 8*a^2*c^2*(21*c^2*d + 3*a*c*h + 5*a^2*m))/(c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^2*Sqrt[c]*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]]) - ((6*c^2*e - 3*b*c*g + b^2*j + 2*a*c*j - 3*a*b*l)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",11,9,55,0.1636,1,"{1673, 1678, 1166, 205, 1663, 1660, 638, 618, 206}"
58,1,645,0,3.3666224,"\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5+j x^6+k x^7}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4 + i*x^5 + j*x^6 + k*x^7)/(a + b*x^2 + c*x^4)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{b^2 c (c d-a h)-a b^3 j+4 a b c (2 a j+c f)-4 a c^2 (a h+3 c d)}{c \sqrt{b^2-4 a c}}+\frac{a b^2 j}{c}+b (a h+c d)-2 a (3 a j+c f)\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{b^2 c (c d-a h)-a b^3 j+4 a b c (2 a j+c f)-4 a c^2 (a h+3 c d)}{c \sqrt{b^2-4 a c}}+\frac{a b^2 j}{c}+b (a h+c d)-2 a (3 a j+c f)\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{x^2 \left(-c^2 (2 a i+b g)+b c (3 a k+b i)+b^3 (-k)+2 c^3 e\right)-a b^2 k+b c (a i+c e)-2 a c (c g-a k)}{2 c^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(-c^2 (2 b g-4 a i)-6 a b c k+b^3 k+4 c^3 e\right)}{2 c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{x \left(x^2 \left(-a b^2 j+b c (a h+c d)-2 a c (c f-a j)\right)+c \left(-\frac{a b (a j+c f)}{c}-2 a (c d-a h)+b^2 d\right)\right)}{2 a c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{k \log \left(a+b x^2+c x^4\right)}{4 c^2}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right) \left(\frac{b^2 c (c d-a h)-a b^3 j+4 a b c (2 a j+c f)-4 a c^2 (a h+3 c d)}{c \sqrt{b^2-4 a c}}+\frac{a b^2 j}{c}+b (a h+c d)-2 a (3 a j+c f)\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right) \left(-\frac{b^2 c (c d-a h)-a b^3 j+4 a b c (2 a j+c f)-4 a c^2 (a h+3 c d)}{c \sqrt{b^2-4 a c}}+\frac{a b^2 j}{c}+b (a h+c d)-2 a (3 a j+c f)\right)}{2 \sqrt{2} a \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{x^2 \left(-c^2 (2 a i+b g)+b c (3 a k+b i)+b^3 (-k)+2 c^3 e\right)-a b^2 k+b c (a i+c e)-2 a c (c g-a k)}{2 c^2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right) \left(-c^2 (2 b g-4 a i)-6 a b c k+b^3 k+4 c^3 e\right)}{2 c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{x \left(x^2 \left(-a b^2 j+b c (a h+c d)-2 a c (c f-a j)\right)+c \left(-\frac{a b (a j+c f)}{c}-2 a (c d-a h)+b^2 d\right)\right)}{2 a c \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{k \log \left(a+b x^2+c x^4\right)}{4 c^2}",1,"(x*(c*(b^2*d - 2*a*(c*d - a*h) - (a*b*(c*f + a*j))/c) + (b*c*(c*d + a*h) - a*b^2*j - 2*a*c*(c*f - a*j))*x^2))/(2*a*c*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - (b*c*(c*e + a*i) - a*b^2*k - 2*a*c*(c*g - a*k) + (2*c^3*e - c^2*(b*g + 2*a*i) - b^3*k + b*c*(b*i + 3*a*k))*x^2)/(2*c^2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((b*(c*d + a*h) + (a*b^2*j)/c - 2*a*(c*f + 3*a*j) + (b^2*c*(c*d - a*h) - 4*a*c^2*(3*c*d + a*h) - a*b^3*j + 4*a*b*c*(c*f + 2*a*j))/(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*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b*(c*d + a*h) + (a*b^2*j)/c - 2*a*(c*f + 3*a*j) - (b^2*c*(c*d - a*h) - 4*a*c^2*(3*c*d + a*h) - a*b^3*j + 4*a*b*c*(c*f + 2*a*j))/(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*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + ((4*c^3*e - c^2*(2*b*g - 4*a*i) + b^3*k - 6*a*b*c*k)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^2*(b^2 - 4*a*c)^(3/2)) + (k*Log[a + b*x^2 + c*x^4])/(4*c^2)","A",11,10,50,0.2000,1,"{1673, 1678, 1166, 205, 1663, 1660, 634, 618, 206, 628}"
59,1,1179,0,7.9264758,"\int \frac{d+e x+f x^2+g x^3+h x^4+i x^5+j x^8+k x^{11}}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[(d + e*x + f*x^2 + g*x^3 + h*x^4 + i*x^5 + j*x^8 + k*x^11)/(a + b*x^2 + c*x^4)^3,x]","-\frac{x \left(\left(-\left(\frac{j a^2}{c^2}+d\right) b^2+a f b+2 a \left(\frac{j a^2}{c}-h a+c d\right)\right) c^2+\left(-a j b^3-c \left(-3 j a^2+c h a+c^2 d\right) b+2 a c^3 f\right) x^2\right)}{4 a c^2 \left(b^2-4 a c\right) \left(c x^4+b x^2+a\right)^2}+\frac{\left(\left(\frac{j a^2}{c}+3 c d\right) b^3+a c f b^2-4 a \left(4 j a^2+3 c h a+6 c^2 d\right) b+20 a^2 c^2 f+\frac{\left(3 c^2 d-a^2 j\right) b^4+a c^2 f b^3-6 a c \left(-3 j a^2-3 c h a+5 c^2 d\right) b^2-52 a^2 c^3 f b+8 a^2 c^2 \left(5 j a^2+3 c h a+21 c^2 d\right)}{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)}{8 \sqrt{2} a^2 \sqrt{c} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\left(\frac{j a^2}{c}+3 c d\right) b^3+a c f b^2-4 a \left(4 j a^2+3 c h a+6 c^2 d\right) b+20 a^2 c^2 f-\frac{\left(3 c^2 d-a^2 j\right) b^4+a c^2 f b^3-6 a c \left(-3 j a^2-3 c h a+5 c^2 d\right) b^2-52 a^2 c^3 f b+8 a^2 c^2 \left(5 j a^2+3 c h a+21 c^2 d\right)}{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)}{8 \sqrt{2} a^2 \sqrt{c} \left(b^2-4 a c\right)^2 \sqrt{b+\sqrt{b^2-4 a c}}}-\frac{\left(-k b^5+10 a c k b^3+2 c^3 i b^2-30 a^2 c^2 k b+12 c^5 e-c^4 (6 b g-4 a i)\right) \tanh ^{-1}\left(\frac{2 c x^2+b}{\sqrt{b^2-4 a c}}\right)}{2 c^3 \left(b^2-4 a c\right)^{5/2}}+\frac{k \log \left(c x^4+b x^2+a\right)}{4 c^3}+\frac{x \left(\left(\left(j a^2+3 c^2 d\right) b^3+a c^2 f b^2-4 a c \left(4 j a^2+3 c h a+6 c^2 d\right) b+20 a^2 c^3 f\right) x^2+c \left(\left(3 d-\frac{2 a^2 j}{c^2}\right) b^4+a f b^3-a \left(-\frac{11 j a^2}{c}+7 h a+25 c d\right) b^2+8 a^2 c f b+4 a^2 \left(-9 j a^2+c h a+7 c^2 d\right)\right)\right)}{8 a^2 c \left(b^2-4 a c\right)^2 \left(c x^4+b x^2+a\right)}+\frac{-\frac{k b^6}{c}+11 a k b^4+c^2 i b^3-3 \left(g c^3+13 a^2 k c\right) b^2+2 c^3 (3 c e+a i) b+2 \left(2 k b^5-15 a c k b^3+c^3 i b^2+25 a^2 c^2 k b+6 c^5 e-c^4 (3 b g-2 a i)\right) x^2+32 a^3 c^2 k}{4 c^3 \left(b^2-4 a c\right)^2 \left(c x^4+b x^2+a\right)}-\frac{-a k b^4+4 a^2 c k b^2+c^3 (c e+a i) b+\left(-k b^5+5 a c k b^3+c^3 i b^2-5 a^2 c^2 k b+2 c^5 e-c^4 (b g+2 a i)\right) x^2-2 a c^2 \left(k a^2+c^2 g\right)}{4 c^4 \left(b^2-4 a c\right) \left(c x^4+b x^2+a\right)^2}","-\frac{x \left(\left(-\left(\frac{j a^2}{c^2}+d\right) b^2+a f b+2 a \left(\frac{j a^2}{c}-h a+c d\right)\right) c^2+\left(-a j b^3-c \left(-3 j a^2+c h a+c^2 d\right) b+2 a c^3 f\right) x^2\right)}{4 a c^2 \left(b^2-4 a c\right) \left(c x^4+b x^2+a\right)^2}+\frac{\left(\left(j a^2+3 c^2 d\right) b^3+a c^2 f b^2-4 a c \left(4 j a^2+3 c h a+6 c^2 d\right) b+20 a^2 c^3 f+\frac{\left(3 c^2 d-a^2 j\right) b^4+a c^2 f b^3-6 a c \left(-3 j a^2-3 c h a+5 c^2 d\right) b^2-52 a^2 c^3 f b+8 a^2 c^2 \left(5 j a^2+3 c h a+21 c^2 d\right)}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^2 c^{3/2} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\left(j a^2+3 c^2 d\right) b^3+a c^2 f b^2-4 a c \left(4 j a^2+3 c h a+6 c^2 d\right) b+20 a^2 c^3 f-\frac{\left(3 c^2 d-a^2 j\right) b^4+a c^2 f b^3-6 a c \left(-3 j a^2-3 c h a+5 c^2 d\right) b^2-52 a^2 c^3 f b+8 a^2 c^2 \left(5 j a^2+3 c h a+21 c^2 d\right)}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b+\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^2 c^{3/2} \left(b^2-4 a c\right)^2 \sqrt{b+\sqrt{b^2-4 a c}}}-\frac{\left(-k b^5+10 a c k b^3+2 c^3 i b^2-30 a^2 c^2 k b+12 c^5 e-c^4 (6 b g-4 a i)\right) \tanh ^{-1}\left(\frac{2 c x^2+b}{\sqrt{b^2-4 a c}}\right)}{2 c^3 \left(b^2-4 a c\right)^{5/2}}+\frac{k \log \left(c x^4+b x^2+a\right)}{4 c^3}+\frac{x \left(\left(\left(j a^2+3 c^2 d\right) b^3+a c^2 f b^2-4 a c \left(4 j a^2+3 c h a+6 c^2 d\right) b+20 a^2 c^3 f\right) x^2+c \left(\left(3 d-\frac{2 a^2 j}{c^2}\right) b^4+a f b^3-a \left(-\frac{11 j a^2}{c}+7 h a+25 c d\right) b^2+8 a^2 c f b+4 a^2 \left(-9 j a^2+c h a+7 c^2 d\right)\right)\right)}{8 a^2 c \left(b^2-4 a c\right)^2 \left(c x^4+b x^2+a\right)}+\frac{-\frac{k b^6}{c}+11 a k b^4+c^2 i b^3-3 \left(g c^3+13 a^2 k c\right) b^2+2 c^3 (3 c e+a i) b+2 \left(2 k b^5-15 a c k b^3+c^3 i b^2+25 a^2 c^2 k b+6 c^5 e-c^4 (3 b g-2 a i)\right) x^2+32 a^3 c^2 k}{4 c^3 \left(b^2-4 a c\right)^2 \left(c x^4+b x^2+a\right)}-\frac{-a k b^4+4 a^2 c k b^2+c^3 (c e+a i) b+\left(-k b^5+5 a c k b^3+c^3 i b^2-5 a^2 c^2 k b+2 c^5 e-c^4 (b g+2 a i)\right) x^2-2 a c^2 \left(k a^2+c^2 g\right)}{4 c^4 \left(b^2-4 a c\right) \left(c x^4+b x^2+a\right)^2}",1,"-(x*(c^2*(a*b*f - b^2*(d + (a^2*j)/c^2) + 2*a*(c*d - a*h + (a^2*j)/c)) + (2*a*c^3*f - a*b^3*j - b*c*(c^2*d + a*c*h - 3*a^2*j))*x^2))/(4*a*c^2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) - (b*c^3*(c*e + a*i) - a*b^4*k + 4*a^2*b^2*c*k - 2*a*c^2*(c^2*g + a^2*k) + (2*c^5*e + b^2*c^3*i - c^4*(b*g + 2*a*i) - b^5*k + 5*a*b^3*c*k - 5*a^2*b*c^2*k)*x^2)/(4*c^4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (x*(c*(a*b^3*f + 8*a^2*b*c*f + 4*a^2*(7*c^2*d + a*c*h - 9*a^2*j) + b^4*(3*d - (2*a^2*j)/c^2) - a*b^2*(25*c*d + 7*a*h - (11*a^2*j)/c)) + (a*b^2*c^2*f + 20*a^2*c^3*f + b^3*(3*c^2*d + a^2*j) - 4*a*b*c*(6*c^2*d + 3*a*c*h + 4*a^2*j))*x^2))/(8*a^2*c*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (b^3*c^2*i + 2*b*c^3*(3*c*e + a*i) + 11*a*b^4*k - (b^6*k)/c + 32*a^3*c^2*k - 3*b^2*(c^3*g + 13*a^2*c*k) + 2*(6*c^5*e + b^2*c^3*i - c^4*(3*b*g - 2*a*i) + 2*b^5*k - 15*a*b^3*c*k + 25*a^2*b*c^2*k)*x^2)/(4*c^3*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + ((a*b^2*c*f + 20*a^2*c^2*f - 4*a*b*(6*c^2*d + 3*a*c*h + 4*a^2*j) + b^3*(3*c*d + (a^2*j)/c) + (a*b^3*c^2*f - 52*a^2*b*c^3*f - 6*a*b^2*c*(5*c^2*d - 3*a*c*h - 3*a^2*j) + b^4*(3*c^2*d - a^2*j) + 8*a^2*c^2*(21*c^2*d + 3*a*c*h + 5*a^2*j))/(c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^2*Sqrt[c]*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((a*b^2*c*f + 20*a^2*c^2*f - 4*a*b*(6*c^2*d + 3*a*c*h + 4*a^2*j) + b^3*(3*c*d + (a^2*j)/c) - (a*b^3*c^2*f - 52*a^2*b*c^3*f - 6*a*b^2*c*(5*c^2*d - 3*a*c*h - 3*a^2*j) + b^4*(3*c^2*d - a^2*j) + 8*a^2*c^2*(21*c^2*d + 3*a*c*h + 5*a^2*j))/(c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^2*Sqrt[c]*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]]) - ((12*c^5*e + 2*b^2*c^3*i - c^4*(6*b*g - 4*a*i) - b^5*k + 10*a*b^3*c*k - 30*a^2*b*c^2*k)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^3*(b^2 - 4*a*c)^(5/2)) + (k*Log[a + b*x^2 + c*x^4])/(4*c^3)","A",13,10,50,0.2000,1,"{1673, 1678, 1166, 205, 1663, 1660, 634, 618, 206, 628}"
60,1,416,0,0.6289714,"\int \left(a+b x^2+c x^4\right)^3 \left(a d+a e x+(b d+a f) x^2+b e x^3+(c d+b f) x^4+c e x^5+c f x^6\right) \, dx","Int[(a + b*x^2 + c*x^4)^3*(a*d + a*e*x + (b*d + a*f)*x^2 + b*e*x^3 + (c*d + b*f)*x^4 + c*e*x^5 + c*f*x^6),x]","\frac{1}{11} x^{11} \left(6 a^2 c^2 f+12 a b^2 c f+12 a b c^2 d+4 b^3 c d+b^4 f\right)+\frac{1}{9} x^9 \left(12 a^2 b c f+6 a^2 c^2 d+12 a b^2 c d+4 a b^3 f+b^4 d\right)+\frac{1}{10} e x^{10} \left(6 a^2 c^2+12 a b^2 c+b^4\right)+\frac{2}{7} a x^7 \left(2 a^2 c f+3 a b^2 f+6 a b c d+2 b^3 d\right)+\frac{2}{5} a^2 x^5 \left(2 a b f+2 a c d+3 b^2 d\right)+\frac{1}{3} a^2 e x^6 \left(2 a c+3 b^2\right)+\frac{1}{3} a^3 x^3 (a f+4 b d)+a^3 b e x^4+a^4 d x+\frac{1}{2} a^4 e x^2+\frac{2}{15} c^2 x^{15} \left(2 a c f+3 b^2 f+2 b c d\right)+\frac{2}{13} c x^{13} \left(6 a b c f+2 a c^2 d+3 b^2 c d+2 b^3 f\right)+\frac{1}{7} c^2 e x^{14} \left(2 a c+3 b^2\right)+\frac{1}{3} b c e x^{12} \left(3 a c+b^2\right)+\frac{1}{2} a b e x^8 \left(3 a c+b^2\right)+\frac{1}{17} c^3 x^{17} (4 b f+c d)+\frac{1}{4} b c^3 e x^{16}+\frac{1}{18} c^4 e x^{18}+\frac{1}{19} c^4 f x^{19}","\frac{1}{11} x^{11} \left(6 a^2 c^2 f+12 a b^2 c f+12 a b c^2 d+4 b^3 c d+b^4 f\right)+\frac{1}{9} x^9 \left(12 a^2 b c f+6 a^2 c^2 d+12 a b^2 c d+4 a b^3 f+b^4 d\right)+\frac{1}{10} e x^{10} \left(6 a^2 c^2+12 a b^2 c+b^4\right)+\frac{2}{7} a x^7 \left(2 a^2 c f+3 a b^2 f+6 a b c d+2 b^3 d\right)+\frac{2}{5} a^2 x^5 \left(2 a b f+2 a c d+3 b^2 d\right)+\frac{1}{3} a^2 e x^6 \left(2 a c+3 b^2\right)+\frac{1}{3} a^3 x^3 (a f+4 b d)+a^3 b e x^4+a^4 d x+\frac{1}{2} a^4 e x^2+\frac{2}{15} c^2 x^{15} \left(2 a c f+3 b^2 f+2 b c d\right)+\frac{2}{13} c x^{13} \left(6 a b c f+2 a c^2 d+3 b^2 c d+2 b^3 f\right)+\frac{1}{7} c^2 e x^{14} \left(2 a c+3 b^2\right)+\frac{1}{3} b c e x^{12} \left(3 a c+b^2\right)+\frac{1}{2} a b e x^8 \left(3 a c+b^2\right)+\frac{1}{17} c^3 x^{17} (4 b f+c d)+\frac{1}{4} b c^3 e x^{16}+\frac{1}{18} c^4 e x^{18}+\frac{1}{19} c^4 f x^{19}",1,"a^4*d*x + (a^4*e*x^2)/2 + (a^3*(4*b*d + a*f)*x^3)/3 + a^3*b*e*x^4 + (2*a^2*(3*b^2*d + 2*a*c*d + 2*a*b*f)*x^5)/5 + (a^2*(3*b^2 + 2*a*c)*e*x^6)/3 + (2*a*(2*b^3*d + 6*a*b*c*d + 3*a*b^2*f + 2*a^2*c*f)*x^7)/7 + (a*b*(b^2 + 3*a*c)*e*x^8)/2 + ((b^4*d + 12*a*b^2*c*d + 6*a^2*c^2*d + 4*a*b^3*f + 12*a^2*b*c*f)*x^9)/9 + ((b^4 + 12*a*b^2*c + 6*a^2*c^2)*e*x^10)/10 + ((4*b^3*c*d + 12*a*b*c^2*d + b^4*f + 12*a*b^2*c*f + 6*a^2*c^2*f)*x^11)/11 + (b*c*(b^2 + 3*a*c)*e*x^12)/3 + (2*c*(3*b^2*c*d + 2*a*c^2*d + 2*b^3*f + 6*a*b*c*f)*x^13)/13 + (c^2*(3*b^2 + 2*a*c)*e*x^14)/7 + (2*c^2*(2*b*c*d + 3*b^2*f + 2*a*c*f)*x^15)/15 + (b*c^3*e*x^16)/4 + (c^3*(c*d + 4*b*f)*x^17)/17 + (c^4*e*x^18)/18 + (c^4*f*x^19)/19","A",2,1,63,0.01587,1,"{1671}"
61,1,259,0,0.3323305,"\int \left(a+b x^2+c x^4\right)^2 \left(a d+a e x+(b d+a f) x^2+b e x^3+(c d+b f) x^4+c e x^5+c f x^6\right) \, dx","Int[(a + b*x^2 + c*x^4)^2*(a*d + a*e*x + (b*d + a*f)*x^2 + b*e*x^3 + (c*d + b*f)*x^4 + c*e*x^5 + c*f*x^6),x]","\frac{1}{7} x^7 \left(3 a^2 c f+3 a b^2 f+6 a b c d+b^3 d\right)+\frac{1}{3} a^2 x^3 (a f+3 b d)+\frac{3}{4} a^2 b e x^4+a^3 d x+\frac{1}{2} a^3 e x^2+\frac{1}{9} x^9 \left(6 a b c f+3 a c^2 d+3 b^2 c d+b^3 f\right)+\frac{3}{11} c x^{11} \left(a c f+b^2 f+b c d\right)+\frac{3}{5} a x^5 \left(a b f+a c d+b^2 d\right)+\frac{3}{10} c e x^{10} \left(a c+b^2\right)+\frac{1}{8} b e x^8 \left(6 a c+b^2\right)+\frac{1}{2} a e x^6 \left(a c+b^2\right)+\frac{1}{13} c^2 x^{13} (3 b f+c d)+\frac{1}{4} b c^2 e x^{12}+\frac{1}{14} c^3 e x^{14}+\frac{1}{15} c^3 f x^{15}","\frac{1}{7} x^7 \left(3 a^2 c f+3 a b^2 f+6 a b c d+b^3 d\right)+\frac{1}{3} a^2 x^3 (a f+3 b d)+\frac{3}{4} a^2 b e x^4+a^3 d x+\frac{1}{2} a^3 e x^2+\frac{1}{9} x^9 \left(6 a b c f+3 a c^2 d+3 b^2 c d+b^3 f\right)+\frac{3}{11} c x^{11} \left(a c f+b^2 f+b c d\right)+\frac{3}{5} a x^5 \left(a b f+a c d+b^2 d\right)+\frac{3}{10} c e x^{10} \left(a c+b^2\right)+\frac{1}{8} b e x^8 \left(6 a c+b^2\right)+\frac{1}{2} a e x^6 \left(a c+b^2\right)+\frac{1}{13} c^2 x^{13} (3 b f+c d)+\frac{1}{4} b c^2 e x^{12}+\frac{1}{14} c^3 e x^{14}+\frac{1}{15} c^3 f x^{15}",1,"a^3*d*x + (a^3*e*x^2)/2 + (a^2*(3*b*d + a*f)*x^3)/3 + (3*a^2*b*e*x^4)/4 + (3*a*(b^2*d + a*c*d + a*b*f)*x^5)/5 + (a*(b^2 + a*c)*e*x^6)/2 + ((b^3*d + 6*a*b*c*d + 3*a*b^2*f + 3*a^2*c*f)*x^7)/7 + (b*(b^2 + 6*a*c)*e*x^8)/8 + ((3*b^2*c*d + 3*a*c^2*d + b^3*f + 6*a*b*c*f)*x^9)/9 + (3*c*(b^2 + a*c)*e*x^10)/10 + (3*c*(b*c*d + b^2*f + a*c*f)*x^11)/11 + (b*c^2*e*x^12)/4 + (c^2*(c*d + 3*b*f)*x^13)/13 + (c^3*e*x^14)/14 + (c^3*f*x^15)/15","A",2,1,63,0.01587,1,"{1671}"
62,1,154,0,0.1517173,"\int \left(a+b x^2+c x^4\right) \left(a d+a e x+(b d+a f) x^2+b e x^3+(c d+b f) x^4+c e x^5+c f x^6\right) \, dx","Int[(a + b*x^2 + c*x^4)*(a*d + a*e*x + (b*d + a*f)*x^2 + b*e*x^3 + (c*d + b*f)*x^4 + c*e*x^5 + c*f*x^6),x]","a^2 d x+\frac{1}{2} a^2 e x^2+\frac{1}{7} x^7 \left(2 a c f+b^2 f+2 b c d\right)+\frac{1}{5} x^5 \left(2 a b f+2 a c d+b^2 d\right)+\frac{1}{6} e x^6 \left(2 a c+b^2\right)+\frac{1}{3} a x^3 (a f+2 b d)+\frac{1}{2} a b e x^4+\frac{1}{9} c x^9 (2 b f+c d)+\frac{1}{4} b c e x^8+\frac{1}{10} c^2 e x^{10}+\frac{1}{11} c^2 f x^{11}","a^2 d x+\frac{1}{2} a^2 e x^2+\frac{1}{7} x^7 \left(2 a c f+b^2 f+2 b c d\right)+\frac{1}{5} x^5 \left(2 a b f+2 a c d+b^2 d\right)+\frac{1}{6} e x^6 \left(2 a c+b^2\right)+\frac{1}{3} a x^3 (a f+2 b d)+\frac{1}{2} a b e x^4+\frac{1}{9} c x^9 (2 b f+c d)+\frac{1}{4} b c e x^8+\frac{1}{10} c^2 e x^{10}+\frac{1}{11} c^2 f x^{11}",1,"a^2*d*x + (a^2*e*x^2)/2 + (a*(2*b*d + a*f)*x^3)/3 + (a*b*e*x^4)/2 + ((b^2*d + 2*a*c*d + 2*a*b*f)*x^5)/5 + ((b^2 + 2*a*c)*e*x^6)/6 + ((2*b*c*d + b^2*f + 2*a*c*f)*x^7)/7 + (b*c*e*x^8)/4 + (c*(c*d + 2*b*f)*x^9)/9 + (c^2*e*x^10)/10 + (c^2*f*x^11)/11","A",2,1,61,0.01639,1,"{1671}"
63,1,20,0,0.0331228,"\int \frac{a d+a e x+(b d+a f) x^2+b e x^3+(c d+b f) x^4+c e x^5+c f x^6}{a+b x^2+c x^4} \, dx","Int[(a*d + a*e*x + (b*d + a*f)*x^2 + b*e*x^3 + (c*d + b*f)*x^4 + c*e*x^5 + c*f*x^6)/(a + b*x^2 + c*x^4),x]","d x+\frac{e x^2}{2}+\frac{f x^3}{3}","d x+\frac{e x^2}{2}+\frac{f x^3}{3}",1,"d*x + (e*x^2)/2 + (f*x^3)/3","A",2,1,63,0.01587,1,"{1586}"
64,1,211,0,0.3184549,"\int \frac{a d+a e x+(b d+a f) x^2+b e x^3+(c d+b f) x^4+c e x^5+c f x^6}{\left(a+b x^2+c x^4\right)^2} \, dx","Int[(a*d + a*e*x + (b*d + a*f)*x^2 + b*e*x^3 + (c*d + b*f)*x^4 + c*e*x^5 + c*f*x^6)/(a + b*x^2 + c*x^4)^2,x]","\frac{\left(\frac{2 c d-b f}{\sqrt{b^2-4 a c}}+f\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(f-\frac{2 c d-b f}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{e \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}","\frac{\left(\frac{2 c d-b f}{\sqrt{b^2-4 a c}}+f\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(f-\frac{2 c d-b f}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{e \tanh ^{-1}\left(\frac{b+2 c x^2}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}",1,"((f + (2*c*d - b*f)/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]]) + ((f - (2*c*d - b*f)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*Sqrt[b + Sqrt[b^2 - 4*a*c]]) - (e*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/Sqrt[b^2 - 4*a*c]","A",9,8,63,0.1270,1,"{1586, 1673, 1166, 205, 12, 1107, 618, 206}"
65,1,368,0,0.9228013,"\int \frac{a d+a e x+(b d+a f) x^2+b e x^3+(c d+b f) x^4+c e x^5+c f x^6}{\left(a+b x^2+c x^4\right)^3} \, dx","Int[(a*d + a*e*x + (b*d + a*f)*x^2 + b*e*x^3 + (c*d + b*f)*x^4 + c*e*x^5 + c*f*x^6)/(a + b*x^2 + c*x^4)^3,x]","\frac{x \left(c x^2 (b d-2 a f)-a b f-2 a c d+b^2 d\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(\frac{4 a b f-12 a c d+b^2 d}{\sqrt{b^2-4 a c}}-2 a f+b d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\frac{4 a b f-12 a c d+b^2 d}{\sqrt{b^2-4 a c}}-2 a f+b d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{e \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{2 c e \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 \left(c x^2 (b d-2 a f)-a b f-2 a c d+b^2 d\right)}{2 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{\sqrt{c} \left(\frac{4 a b f-12 a c d+b^2 d}{\sqrt{b^2-4 a c}}-2 a f+b d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\frac{4 a b f-12 a c d+b^2 d}{\sqrt{b^2-4 a c}}-2 a f+b d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{2 \sqrt{2} a \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{e \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)}+\frac{2 c e \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,"-(e*(b + 2*c*x^2))/(2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (x*(b^2*d - 2*a*c*d - a*b*f + c*(b*d - 2*a*f)*x^2))/(2*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(b*d - 2*a*f + (b^2*d - 12*a*c*d + 4*a*b*f)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*Sqrt[2]*a*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(b*d - 2*a*f - (b^2*d - 12*a*c*d + 4*a*b*f)/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]]) + (2*c*e*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",11,10,63,0.1587,1,"{1586, 1673, 1178, 1166, 205, 12, 1107, 614, 618, 206}"
66,1,621,0,4.5943283,"\int \frac{a d+a e x+(b d+a f) x^2+b e x^3+(c d+b f) x^4+c e x^5+c f x^6}{\left(a+b x^2+c x^4\right)^4} \, dx","Int[(a*d + a*e*x + (b*d + a*f)*x^2 + b*e*x^3 + (c*d + b*f)*x^4 + c*e*x^5 + c*f*x^6)/(a + b*x^2 + c*x^4)^4,x]","\frac{x \left(c x^2 \left(20 a^2 c f+a b^2 f-24 a b c d+3 b^3 d\right)+8 a^2 b c f+28 a^2 c^2 d-25 a b^2 c d+a b^3 f+3 b^4 d\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{-52 a^2 b c f+168 a^2 c^2 d-30 a b^2 c d+a b^3 f+3 b^4 d}{\sqrt{b^2-4 a c}}+20 a^2 c f+a b^2 f-24 a b c d+3 b^3 d\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{\sqrt{c} \left(4 a^2 c \left(5 f \sqrt{b^2-4 a c}+42 c d\right)+b^3 \left(3 d \sqrt{b^2-4 a c}+a f\right)-a b^2 \left(30 c d-f \sqrt{b^2-4 a c}\right)-4 a b c \left(6 d \sqrt{b^2-4 a c}+13 a f\right)+3 b^4 d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^2 \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{6 c^2 e \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 \left(c x^2 (b d-2 a f)-a b f-2 a c d+b^2 d\right)}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 c e \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{e \left(b+2 c x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}","\frac{x \left(c x^2 \left(20 a^2 c f+a b^2 f-24 a b c d+3 b^3 d\right)+8 a^2 b c f+28 a^2 c^2 d-25 a b^2 c d+a b^3 f+3 b^4 d\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{-52 a^2 b c f+168 a^2 c^2 d-30 a b^2 c d+a b^3 f+3 b^4 d}{\sqrt{b^2-4 a c}}+20 a^2 c f+a b^2 f-24 a b c d+3 b^3 d\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{\sqrt{c} \left(4 a^2 c \left(5 f \sqrt{b^2-4 a c}+42 c d\right)+b^3 \left(3 d \sqrt{b^2-4 a c}+a f\right)-a b^2 \left(30 c d-f \sqrt{b^2-4 a c}\right)-4 a b c \left(6 d \sqrt{b^2-4 a c}+13 a f\right)+3 b^4 d\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} x}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{8 \sqrt{2} a^2 \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{6 c^2 e \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 \left(c x^2 (b d-2 a f)-a b f-2 a c d+b^2 d\right)}{4 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}+\frac{3 c e \left(b+2 c x^2\right)}{2 \left(b^2-4 a c\right)^2 \left(a+b x^2+c x^4\right)}-\frac{e \left(b+2 c x^2\right)}{4 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^2}",1,"-(e*(b + 2*c*x^2))/(4*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (x*(b^2*d - 2*a*c*d - a*b*f + c*(b*d - 2*a*f)*x^2))/(4*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^2) + (3*c*e*(b + 2*c*x^2))/(2*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (x*(3*b^4*d - 25*a*b^2*c*d + 28*a^2*c^2*d + a*b^3*f + 8*a^2*b*c*f + c*(3*b^3*d - 24*a*b*c*d + a*b^2*f + 20*a^2*c*f)*x^2))/(8*a^2*(b^2 - 4*a*c)^2*(a + b*x^2 + c*x^4)) + (Sqrt[c]*(3*b^4*d + b^3*(3*Sqrt[b^2 - 4*a*c]*d + a*f) - 4*a*b*c*(6*Sqrt[b^2 - 4*a*c]*d + 13*a*f) - a*b^2*(30*c*d - Sqrt[b^2 - 4*a*c]*f) + 4*a^2*c*(42*c*d + 5*Sqrt[b^2 - 4*a*c]*f))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(8*Sqrt[2]*a^2*(b^2 - 4*a*c)^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(3*b^3*d - 24*a*b*c*d + a*b^2*f + 20*a^2*c*f - (3*b^4*d - 30*a*b^2*c*d + 168*a^2*c^2*d + a*b^3*f - 52*a^2*b*c*f)/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]]) - (6*c^2*e*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",13,10,63,0.1587,1,"{1586, 1673, 1178, 1166, 205, 12, 1107, 614, 618, 206}"
67,1,4,0,0.0105952,"\int \frac{2-x-2 x^2+x^3}{4-5 x^2+x^4} \, dx","Int[(2 - x - 2*x^2 + x^3)/(4 - 5*x^2 + x^4),x]","\log (x+2)","\log (x+2)",1,"Log[2 + x]","A",2,2,26,0.07692,1,"{1586, 31}"
68,1,14,0,0.0239435,"\int \frac{(d+e x) \left(2-x-2 x^2+x^3\right)}{4-5 x^2+x^4} \, dx","Int[((d + e*x)*(2 - x - 2*x^2 + x^3))/(4 - 5*x^2 + x^4),x]","(d-2 e) \log (x+2)+e x","(d-2 e) \log (x+2)+e x",1,"e*x + (d - 2*e)*Log[2 + x]","A",3,2,31,0.06452,1,"{1586, 43}"
69,1,31,0,0.0522829,"\int \frac{\left(d+e x+f x^2\right) \left(2-x-2 x^2+x^3\right)}{4-5 x^2+x^4} \, dx","Int[((d + e*x + f*x^2)*(2 - x - 2*x^2 + x^3))/(4 - 5*x^2 + x^4),x]","\log (x+2) (d-2 e+4 f)+x (e-4 f)+\frac{1}{2} f (x+2)^2","\log (x+2) (d-2 e+4 f)+x (e-4 f)+\frac{1}{2} f (x+2)^2",1,"(e - 4*f)*x + (f*(2 + x)^2)/2 + (d - 2*e + 4*f)*Log[2 + x]","A",3,2,36,0.05556,1,"{1586, 698}"
70,1,51,0,0.0847926,"\int \frac{\left(2-x-2 x^2+x^3\right) \left(d+e x+f x^2+g x^3\right)}{4-5 x^2+x^4} \, dx","Int[((2 - x - 2*x^2 + x^3)*(d + e*x + f*x^2 + g*x^3))/(4 - 5*x^2 + x^4),x]","\log (x+2) (d-2 e+4 f-8 g)+x (e-4 f+12 g)+\frac{1}{2} (x+2)^2 (f-6 g)+\frac{1}{3} g (x+2)^3","\log (x+2) (d-2 e+4 f-8 g)+x (e-4 f+12 g)+\frac{1}{2} (x+2)^2 (f-6 g)+\frac{1}{3} g (x+2)^3",1,"(e - 4*f + 12*g)*x + ((f - 6*g)*(2 + x)^2)/2 + (g*(2 + x)^3)/3 + (d - 2*e + 4*f - 8*g)*Log[2 + x]","A",3,2,41,0.04878,1,"{1586, 1850}"
71,1,68,0,0.1174643,"\int \frac{\left(2-x-2 x^2+x^3\right) \left(d+e x+f x^2+g x^3+h x^4\right)}{4-5 x^2+x^4} \, dx","Int[((2 - x - 2*x^2 + x^3)*(d + e*x + f*x^2 + g*x^3 + h*x^4))/(4 - 5*x^2 + x^4),x]","\log (x+2) (d-2 e+4 f-8 g+16 h)+x (e-2 f+4 g-8 h)+\frac{1}{2} x^2 (f-2 g+4 h)+\frac{1}{3} x^3 (g-2 h)+\frac{h x^4}{4}","\log (x+2) (d-2 e+4 f-8 g+16 h)+x (e-2 f+4 g-8 h)+\frac{1}{2} x^2 (f-2 g+4 h)+\frac{1}{3} x^3 (g-2 h)+\frac{h x^4}{4}",1,"(e - 2*f + 4*g - 8*h)*x + ((f - 2*g + 4*h)*x^2)/2 + ((g - 2*h)*x^3)/3 + (h*x^4)/4 + (d - 2*e + 4*f - 8*g + 16*h)*Log[2 + x]","A",3,2,46,0.04348,1,"{1586, 1850}"
72,1,92,0,0.1486303,"\int \frac{\left(2-x-2 x^2+x^3\right) \left(d+e x+f x^2+g x^3+h x^4+i x^5\right)}{4-5 x^2+x^4} \, dx","Int[((2 - x - 2*x^2 + x^3)*(d + e*x + f*x^2 + g*x^3 + h*x^4 + i*x^5))/(4 - 5*x^2 + x^4),x]","\log (x+2) (d-2 e+4 f-8 g+16 h-32 i)+x (e-2 f+4 g-8 h+16 i)+\frac{1}{2} x^2 (f-2 g+4 h-8 i)+\frac{1}{3} x^3 (g-2 h+4 i)+\frac{1}{4} x^4 (h-2 i)+\frac{i x^5}{5}","\log (x+2) (d-2 e+4 f-8 g+16 h-32 i)+x (e-2 f+4 g-8 h+16 i)+\frac{1}{2} x^2 (f-2 g+4 h-8 i)+\frac{1}{3} x^3 (g-2 h+4 i)+\frac{1}{4} x^4 (h-2 i)+\frac{i x^5}{5}",1,"(e - 2*f + 4*g - 8*h + 16*i)*x + ((f - 2*g + 4*h - 8*i)*x^2)/2 + ((g - 2*h + 4*i)*x^3)/3 + ((h - 2*i)*x^4)/4 + (i*x^5)/5 + (d - 2*e + 4*f - 8*g + 16*h - 32*i)*Log[2 + x]","A",3,2,51,0.03922,1,"{1586, 1850}"
73,1,11,0,0.0101318,"\int \frac{2-3 x+x^2}{4-5 x^2+x^4} \, dx","Int[(2 - 3*x + x^2)/(4 - 5*x^2 + x^4),x]","\log (x+1)-\log (x+2)","\log (x+1)-\log (x+2)",1,"Log[1 + x] - Log[2 + x]","A",4,3,21,0.1429,1,"{1586, 616, 31}"
74,1,22,0,0.0206828,"\int \frac{(d+e x) \left(2-3 x+x^2\right)}{4-5 x^2+x^4} \, dx","Int[((d + e*x)*(2 - 3*x + x^2))/(4 - 5*x^2 + x^4),x]","(d-e) \log (x+1)-(d-2 e) \log (x+2)","(d-e) \log (x+1)-(d-2 e) \log (x+2)",1,"(d - e)*Log[1 + x] - (d - 2*e)*Log[2 + x]","A",4,3,26,0.1154,1,"{1586, 632, 31}"
75,1,29,0,0.0500694,"\int \frac{\left(2-3 x+x^2\right) \left(d+e x+f x^2\right)}{4-5 x^2+x^4} \, dx","Int[((2 - 3*x + x^2)*(d + e*x + f*x^2))/(4 - 5*x^2 + x^4),x]","\log (x+1) (d-e+f)-\log (x+2) (d-2 e+4 f)+f x","\log (x+1) (d-e+f)-\log (x+2) (d-2 e+4 f)+f x",1,"f*x + (d - e + f)*Log[1 + x] - (d - 2*e + 4*f)*Log[2 + x]","A",6,4,31,0.1290,1,"{1586, 1657, 632, 31}"
76,1,47,0,0.0677106,"\int \frac{\left(2-3 x+x^2\right) \left(d+e x+f x^2+g x^3\right)}{4-5 x^2+x^4} \, dx","Int[((2 - 3*x + x^2)*(d + e*x + f*x^2 + g*x^3))/(4 - 5*x^2 + x^4),x]","\log (x+1) (d-e+f-g)-\log (x+2) (d-2 e+4 f-8 g)+x (f-3 g)+\frac{g x^2}{2}","\log (x+1) (d-e+f-g)-\log (x+2) (d-2 e+4 f-8 g)+x (f-3 g)+\frac{g x^2}{2}",1,"(f - 3*g)*x + (g*x^2)/2 + (d - e + f - g)*Log[1 + x] - (d - 2*e + 4*f - 8*g)*Log[2 + x]","A",6,4,36,0.1111,1,"{1586, 1657, 632, 31}"
77,1,66,0,0.0853165,"\int \frac{\left(2-3 x+x^2\right) \left(d+e x+f x^2+g x^3+h x^4\right)}{4-5 x^2+x^4} \, dx","Int[((2 - 3*x + x^2)*(d + e*x + f*x^2 + g*x^3 + h*x^4))/(4 - 5*x^2 + x^4),x]","\log (x+1) (d-e+f-g+h)-\log (x+2) (d-2 e+4 f-8 g+16 h)+x (f-3 g+7 h)+\frac{1}{2} x^2 (g-3 h)+\frac{h x^3}{3}","\log (x+1) (d-e+f-g+h)-\log (x+2) (d-2 e+4 f-8 g+16 h)+x (f-3 g+7 h)+\frac{1}{2} x^2 (g-3 h)+\frac{h x^3}{3}",1,"(f - 3*g + 7*h)*x + ((g - 3*h)*x^2)/2 + (h*x^3)/3 + (d - e + f - g + h)*Log[1 + x] - (d - 2*e + 4*f - 8*g + 16*h)*Log[2 + x]","A",6,4,41,0.09756,1,"{1586, 1657, 632, 31}"
78,1,90,0,0.1072765,"\int \frac{\left(2-3 x+x^2\right) \left(d+e x+f x^2+g x^3+h x^4+i x^5\right)}{4-5 x^2+x^4} \, dx","Int[((2 - 3*x + x^2)*(d + e*x + f*x^2 + g*x^3 + h*x^4 + i*x^5))/(4 - 5*x^2 + x^4),x]","\log (x+1) (d-e+f-g+h-i)-\log (x+2) (d-2 e+4 f-8 g+16 h-32 i)+x (f-3 g+7 h-15 i)+\frac{1}{2} x^2 (g-3 h+7 i)+\frac{1}{3} x^3 (h-3 i)+\frac{i x^4}{4}","\log (x+1) (d-e+f-g+h-i)-\log (x+2) (d-2 e+4 f-8 g+16 h-32 i)+x (f-3 g+7 h-15 i)+\frac{1}{2} x^2 (g-3 h+7 i)+\frac{1}{3} x^3 (h-3 i)+\frac{i x^4}{4}",1,"(f - 3*g + 7*h - 15*i)*x + ((g - 3*h + 7*i)*x^2)/2 + ((h - 3*i)*x^3)/3 + (i*x^4)/4 + (d - e + f - g + h - i)*Log[1 + x] - (d - 2*e + 4*f - 8*g + 16*h - 32*i)*Log[2 + x]","A",6,4,46,0.08696,1,"{1586, 1657, 632, 31}"
79,1,29,0,0.0207676,"\int \frac{2+x}{4-5 x^2+x^4} \, dx","Int[(2 + x)/(4 - 5*x^2 + x^4),x]","-\frac{1}{2} \log (1-x)+\frac{1}{3} \log (2-x)+\frac{1}{6} \log (x+1)","-\frac{1}{2} \log (1-x)+\frac{1}{3} \log (2-x)+\frac{1}{6} \log (x+1)",1,"-Log[1 - x]/2 + Log[2 - x]/3 + Log[1 + x]/6","A",3,2,16,0.1250,1,"{1586, 2058}"
80,1,42,0,0.0518755,"\int \frac{(2+x) (d+e x)}{4-5 x^2+x^4} \, dx","Int[((2 + x)*(d + e*x))/(4 - 5*x^2 + x^4),x]","-\frac{1}{2} (d+e) \log (1-x)+\frac{1}{3} (d+2 e) \log (2-x)+\frac{1}{6} (d-e) \log (x+1)","-\frac{1}{2} (d+e) \log (1-x)+\frac{1}{3} (d+2 e) \log (2-x)+\frac{1}{6} (d-e) \log (x+1)",1,"-((d + e)*Log[1 - x])/2 + ((d + 2*e)*Log[2 - x])/3 + ((d - e)*Log[1 + x])/6","A",3,2,21,0.09524,1,"{1586, 2074}"
81,1,47,0,0.0638697,"\int \frac{(2+x) \left(d+e x+f x^2\right)}{4-5 x^2+x^4} \, dx","Int[((2 + x)*(d + e*x + f*x^2))/(4 - 5*x^2 + x^4),x]","-\frac{1}{2} \log (1-x) (d+e+f)+\frac{1}{3} \log (2-x) (d+2 e+4 f)+\frac{1}{6} \log (x+1) (d-e+f)","-\frac{1}{2} \log (1-x) (d+e+f)+\frac{1}{3} \log (2-x) (d+2 e+4 f)+\frac{1}{6} \log (x+1) (d-e+f)",1,"-((d + e + f)*Log[1 - x])/2 + ((d + 2*e + 4*f)*Log[2 - x])/3 + ((d - e + f)*Log[1 + x])/6","A",3,2,26,0.07692,1,"{1586, 2074}"
82,1,57,0,0.0793655,"\int \frac{(2+x) \left(d+e x+f x^2+g x^3\right)}{4-5 x^2+x^4} \, dx","Int[((2 + x)*(d + e*x + f*x^2 + g*x^3))/(4 - 5*x^2 + x^4),x]","-\frac{1}{2} \log (1-x) (d+e+f+g)+\frac{1}{3} \log (2-x) (d+2 e+4 f+8 g)+\frac{1}{6} \log (x+1) (d-e+f-g)+g x","-\frac{1}{2} \log (1-x) (d+e+f+g)+\frac{1}{3} \log (2-x) (d+2 e+4 f+8 g)+\frac{1}{6} \log (x+1) (d-e+f-g)+g x",1,"g*x - ((d + e + f + g)*Log[1 - x])/2 + ((d + 2*e + 4*f + 8*g)*Log[2 - x])/3 + ((d - e + f - g)*Log[1 + x])/6","A",3,2,31,0.06452,1,"{1586, 2074}"
83,1,74,0,0.1069732,"\int \frac{(2+x) \left(d+e x+f x^2+g x^3+h x^4\right)}{4-5 x^2+x^4} \, dx","Int[((2 + x)*(d + e*x + f*x^2 + g*x^3 + h*x^4))/(4 - 5*x^2 + x^4),x]","-\frac{1}{2} \log (1-x) (d+e+f+g+h)+\frac{1}{3} \log (2-x) (d+2 e+4 f+8 g+16 h)+\frac{1}{6} \log (x+1) (d-e+f-g+h)+x (g+2 h)+\frac{h x^2}{2}","-\frac{1}{2} \log (1-x) (d+e+f+g+h)+\frac{1}{3} \log (2-x) (d+2 e+4 f+8 g+16 h)+\frac{1}{6} \log (x+1) (d-e+f-g+h)+x (g+2 h)+\frac{h x^2}{2}",1,"(g + 2*h)*x + (h*x^2)/2 - ((d + e + f + g + h)*Log[1 - x])/2 + ((d + 2*e + 4*f + 8*g + 16*h)*Log[2 - x])/3 + ((d - e + f - g + h)*Log[1 + x])/6","A",3,2,36,0.05556,1,"{1586, 2074}"
84,1,96,0,0.1369055,"\int \frac{(2+x) \left(d+e x+f x^2+g x^3+h x^4+i x^5\right)}{4-5 x^2+x^4} \, dx","Int[((2 + x)*(d + e*x + f*x^2 + g*x^3 + h*x^4 + i*x^5))/(4 - 5*x^2 + x^4),x]","-\frac{1}{2} \log (1-x) (d+e+f+g+h+i)+\frac{1}{3} \log (2-x) (d+2 e+4 f+8 g+16 h+32 i)+\frac{1}{6} \log (x+1) (d-e+f-g+h-i)+x (g+2 h+5 i)+\frac{1}{2} x^2 (h+2 i)+\frac{i x^3}{3}","-\frac{1}{2} \log (1-x) (d+e+f+g+h+i)+\frac{1}{3} \log (2-x) (d+2 e+4 f+8 g+16 h+32 i)+\frac{1}{6} \log (x+1) (d-e+f-g+h-i)+x (g+2 h+5 i)+\frac{1}{2} x^2 (h+2 i)+\frac{i x^3}{3}",1,"(g + 2*h + 5*i)*x + ((h + 2*i)*x^2)/2 + (i*x^3)/3 - ((d + e + f + g + h + i)*Log[1 - x])/2 + ((d + 2*e + 4*f + 8*g + 16*h + 32*i)*Log[2 - x])/3 + ((d - e + f - g + h - i)*Log[1 + x])/6","A",3,2,41,0.04878,1,"{1586, 2074}"
85,1,46,0,0.0508525,"\int \frac{2-x-2 x^2+x^3}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[(2 - x - 2*x^2 + x^3)/(4 - 5*x^2 + x^4)^2,x]","\frac{1}{12 (x+2)}-\frac{1}{18} \log (1-x)+\frac{1}{48} \log (2-x)+\frac{1}{6} \log (x+1)-\frac{19}{144} \log (x+2)","\frac{1}{12 (x+2)}-\frac{1}{18} \log (1-x)+\frac{1}{48} \log (2-x)+\frac{1}{6} \log (x+1)-\frac{19}{144} \log (x+2)",1,"1/(12*(2 + x)) - Log[1 - x]/18 + Log[2 - x]/48 + Log[1 + x]/6 - (19*Log[2 + x])/144","A",3,2,26,0.07692,1,"{1586, 2074}"
86,1,71,0,0.1743836,"\int \frac{(d+e x) \left(2-x-2 x^2+x^3\right)}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[((d + e*x)*(2 - x - 2*x^2 + x^3))/(4 - 5*x^2 + x^4)^2,x]","\frac{d-2 e}{12 (x+2)}-\frac{1}{18} (d+e) \log (1-x)+\frac{1}{48} (d+2 e) \log (2-x)+\frac{1}{6} (d-e) \log (x+1)-\frac{1}{144} (19 d-26 e) \log (x+2)","\frac{d-2 e}{12 (x+2)}-\frac{1}{18} (d+e) \log (1-x)+\frac{1}{48} (d+2 e) \log (2-x)+\frac{1}{6} (d-e) \log (x+1)-\frac{1}{144} (19 d-26 e) \log (x+2)",1,"(d - 2*e)/(12*(2 + x)) - ((d + e)*Log[1 - x])/18 + ((d + 2*e)*Log[2 - x])/48 + ((d - e)*Log[1 + x])/6 - ((19*d - 26*e)*Log[2 + x])/144","A",3,2,31,0.06452,1,"{1586, 6742}"
87,1,82,0,0.1987608,"\int \frac{\left(d+e x+f x^2\right) \left(2-x-2 x^2+x^3\right)}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[((d + e*x + f*x^2)*(2 - x - 2*x^2 + x^3))/(4 - 5*x^2 + x^4)^2,x]","\frac{d-2 e+4 f}{12 (x+2)}-\frac{1}{18} \log (1-x) (d+e+f)+\frac{1}{48} \log (2-x) (d+2 e+4 f)+\frac{1}{6} \log (x+1) (d-e+f)-\frac{1}{144} \log (x+2) (19 d-26 e+28 f)","\frac{d-2 e+4 f}{12 (x+2)}-\frac{1}{18} \log (1-x) (d+e+f)+\frac{1}{48} \log (2-x) (d+2 e+4 f)+\frac{1}{6} \log (x+1) (d-e+f)-\frac{1}{144} \log (x+2) (19 d-26 e+28 f)",1,"(d - 2*e + 4*f)/(12*(2 + x)) - ((d + e + f)*Log[1 - x])/18 + ((d + 2*e + 4*f)*Log[2 - x])/48 + ((d - e + f)*Log[1 + x])/6 - ((19*d - 26*e + 28*f)*Log[2 + x])/144","A",3,2,36,0.05556,1,"{1586, 6742}"
88,1,95,0,0.2213229,"\int \frac{\left(2-x-2 x^2+x^3\right) \left(d+e x+f x^2+g x^3\right)}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[((2 - x - 2*x^2 + x^3)*(d + e*x + f*x^2 + g*x^3))/(4 - 5*x^2 + x^4)^2,x]","\frac{d-2 e+4 f-8 g}{12 (x+2)}-\frac{1}{18} \log (1-x) (d+e+f+g)+\frac{1}{48} \log (2-x) (d+2 e+4 f+8 g)+\frac{1}{6} \log (x+1) (d-e+f-g)-\frac{1}{144} \log (x+2) (19 d-26 e+28 f-8 g)","\frac{d-2 e+4 f-8 g}{12 (x+2)}-\frac{1}{18} \log (1-x) (d+e+f+g)+\frac{1}{48} \log (2-x) (d+2 e+4 f+8 g)+\frac{1}{6} \log (x+1) (d-e+f-g)-\frac{1}{144} \log (x+2) (19 d-26 e+28 f-8 g)",1,"(d - 2*e + 4*f - 8*g)/(12*(2 + x)) - ((d + e + f + g)*Log[1 - x])/18 + ((d + 2*e + 4*f + 8*g)*Log[2 - x])/48 + ((d - e + f - g)*Log[1 + x])/6 - ((19*d - 26*e + 28*f - 8*g)*Log[2 + x])/144","A",3,2,41,0.04878,1,"{1586, 6742}"
89,1,106,0,0.2659964,"\int \frac{\left(2-x-2 x^2+x^3\right) \left(d+e x+f x^2+g x^3+h x^4\right)}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[((2 - x - 2*x^2 + x^3)*(d + e*x + f*x^2 + g*x^3 + h*x^4))/(4 - 5*x^2 + x^4)^2,x]","\frac{d-2 e+4 f-8 g+16 h}{12 (x+2)}-\frac{1}{18} \log (1-x) (d+e+f+g+h)+\frac{1}{48} \log (2-x) (d+2 e+4 f+8 g+16 h)+\frac{1}{6} \log (x+1) (d-e+f-g+h)-\frac{1}{144} \log (x+2) (19 d-26 e+28 f-8 g-80 h)","\frac{d-2 e+4 f-8 g+16 h}{12 (x+2)}-\frac{1}{18} \log (1-x) (d+e+f+g+h)+\frac{1}{48} \log (2-x) (d+2 e+4 f+8 g+16 h)+\frac{1}{6} \log (x+1) (d-e+f-g+h)-\frac{1}{144} \log (x+2) (19 d-26 e+28 f-8 g-80 h)",1,"(d - 2*e + 4*f - 8*g + 16*h)/(12*(2 + x)) - ((d + e + f + g + h)*Log[1 - x])/18 + ((d + 2*e + 4*f + 8*g + 16*h)*Log[2 - x])/48 + ((d - e + f - g + h)*Log[1 + x])/6 - ((19*d - 26*e + 28*f - 8*g - 80*h)*Log[2 + x])/144","A",3,2,46,0.04348,1,"{1586, 6742}"
90,1,122,0,0.3149532,"\int \frac{\left(2-x-2 x^2+x^3\right) \left(d+e x+f x^2+g x^3+h x^4+i x^5\right)}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[((2 - x - 2*x^2 + x^3)*(d + e*x + f*x^2 + g*x^3 + h*x^4 + i*x^5))/(4 - 5*x^2 + x^4)^2,x]","\frac{d-2 e+4 f-8 g+16 h-32 i}{12 (x+2)}-\frac{1}{18} \log (1-x) (d+e+f+g+h+i)+\frac{1}{48} \log (2-x) (d+2 e+4 f+8 g+16 h+32 i)+\frac{1}{6} \log (x+1) (d-e+f-g+h-i)-\frac{1}{144} \log (x+2) (19 d-26 e+28 f-8 g-80 h+352 i)+i x","\frac{d-2 e+4 f-8 g+16 h-32 i}{12 (x+2)}-\frac{1}{18} \log (1-x) (d+e+f+g+h+i)+\frac{1}{48} \log (2-x) (d+2 e+4 f+8 g+16 h+32 i)+\frac{1}{6} \log (x+1) (d-e+f-g+h-i)-\frac{1}{144} \log (x+2) (19 d-26 e+28 f-8 g-80 h+352 i)+i x",1,"i*x + (d - 2*e + 4*f - 8*g + 16*h - 32*i)/(12*(2 + x)) - ((d + e + f + g + h + i)*Log[1 - x])/18 + ((d + 2*e + 4*f + 8*g + 16*h + 32*i)*Log[2 - x])/48 + ((d - e + f - g + h - i)*Log[1 + x])/6 - ((19*d - 26*e + 28*f - 8*g - 80*h + 352*i)*Log[2 + x])/144","A",3,2,51,0.03922,1,"{1586, 6742}"
91,1,56,0,0.0565911,"\int \frac{2-3 x+x^2}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[(2 - 3*x + x^2)/(4 - 5*x^2 + x^4)^2,x]","-\frac{3 x+5}{12 \left(x^2+3 x+2\right)}-\frac{1}{36} \log (1-x)+\frac{1}{144} \log (2-x)-\frac{7}{36} \log (x+1)+\frac{31}{144} \log (x+2)","-\frac{3 x+5}{12 \left(x^2+3 x+2\right)}-\frac{1}{36} \log (1-x)+\frac{1}{144} \log (2-x)-\frac{7}{36} \log (x+1)+\frac{31}{144} \log (x+2)",1,"-(5 + 3*x)/(12*(2 + 3*x + x^2)) - Log[1 - x]/36 + Log[2 - x]/144 - (7*Log[1 + x])/36 + (31*Log[2 + x])/144","A",9,5,21,0.2381,1,"{1586, 974, 1072, 632, 31}"
92,1,89,0,0.2601621,"\int \frac{(d+e x) \left(2-3 x+x^2\right)}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[((d + e*x)*(2 - 3*x + x^2))/(4 - 5*x^2 + x^4)^2,x]","-\frac{x (3 d-4 e)+5 d-6 e}{12 \left(x^2+3 x+2\right)}-\frac{1}{36} (d+e) \log (1-x)+\frac{1}{144} (d+2 e) \log (2-x)-\frac{1}{36} (7 d-13 e) \log (x+1)+\frac{1}{144} (31 d-50 e) \log (x+2)","-\frac{x (3 d-4 e)+5 d-6 e}{12 \left(x^2+3 x+2\right)}-\frac{1}{36} (d+e) \log (1-x)+\frac{1}{144} (d+2 e) \log (2-x)-\frac{1}{36} (7 d-13 e) \log (x+1)+\frac{1}{144} (31 d-50 e) \log (x+2)",1,"-(5*d - 6*e + (3*d - 4*e)*x)/(12*(2 + 3*x + x^2)) - ((d + e)*Log[1 - x])/36 + ((d + 2*e)*Log[2 - x])/144 - ((7*d - 13*e)*Log[1 + x])/36 + ((31*d - 50*e)*Log[2 + x])/144","A",9,5,26,0.1923,1,"{1586, 1016, 1072, 632, 31}"
93,1,105,0,0.3195039,"\int \frac{\left(2-3 x+x^2\right) \left(d+e x+f x^2\right)}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[((2 - 3*x + x^2)*(d + e*x + f*x^2))/(4 - 5*x^2 + x^4)^2,x]","-\frac{x (3 d-4 e+6 f)+5 d-6 e+8 f}{12 \left(x^2+3 x+2\right)}-\frac{1}{36} \log (1-x) (d+e+f)+\frac{1}{144} \log (2-x) (d+2 e+4 f)-\frac{1}{36} \log (x+1) (7 d-13 e+19 f)+\frac{1}{144} \log (x+2) (31 d-50 e+76 f)","-\frac{x (3 d-4 e+6 f)+5 d-6 e+8 f}{12 \left(x^2+3 x+2\right)}-\frac{1}{36} \log (1-x) (d+e+f)+\frac{1}{144} \log (2-x) (d+2 e+4 f)-\frac{1}{36} \log (x+1) (7 d-13 e+19 f)+\frac{1}{144} \log (x+2) (31 d-50 e+76 f)",1,"-(5*d - 6*e + 8*f + (3*d - 4*e + 6*f)*x)/(12*(2 + 3*x + x^2)) - ((d + e + f)*Log[1 - x])/36 + ((d + 2*e + 4*f)*Log[2 - x])/144 - ((7*d - 13*e + 19*f)*Log[1 + x])/36 + ((31*d - 50*e + 76*f)*Log[2 + x])/144","A",9,5,31,0.1613,1,"{1586, 1060, 1072, 632, 31}"
94,1,117,0,0.2457459,"\int \frac{\left(2-3 x+x^2\right) \left(d+e x+f x^2+g x^3\right)}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[((2 - 3*x + x^2)*(d + e*x + f*x^2 + g*x^3))/(4 - 5*x^2 + x^4)^2,x]","-\frac{d-2 e+4 f-8 g}{12 (x+2)}-\frac{d-e+f-g}{6 (x+1)}-\frac{1}{36} \log (1-x) (d+e+f+g)+\frac{1}{144} \log (2-x) (d+2 e+4 f+8 g)-\frac{1}{36} \log (x+1) (7 d-13 e+19 f-25 g)+\frac{1}{144} \log (x+2) (31 d-50 e+76 f-104 g)","-\frac{d-2 e+4 f-8 g}{12 (x+2)}-\frac{d-e+f-g}{6 (x+1)}-\frac{1}{36} \log (1-x) (d+e+f+g)+\frac{1}{144} \log (2-x) (d+2 e+4 f+8 g)-\frac{1}{36} \log (x+1) (7 d-13 e+19 f-25 g)+\frac{1}{144} \log (x+2) (31 d-50 e+76 f-104 g)",1,"-(d - e + f - g)/(6*(1 + x)) - (d - 2*e + 4*f - 8*g)/(12*(2 + x)) - ((d + e + f + g)*Log[1 - x])/36 + ((d + 2*e + 4*f + 8*g)*Log[2 - x])/144 - ((7*d - 13*e + 19*f - 25*g)*Log[1 + x])/36 + ((31*d - 50*e + 76*f - 104*g)*Log[2 + x])/144","A",3,2,36,0.05556,1,"{1586, 6728}"
95,1,131,0,0.2804398,"\int \frac{\left(2-3 x+x^2\right) \left(d+e x+f x^2+g x^3+h x^4\right)}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[((2 - 3*x + x^2)*(d + e*x + f*x^2 + g*x^3 + h*x^4))/(4 - 5*x^2 + x^4)^2,x]","-\frac{d-e+f-g+h}{6 (x+1)}-\frac{d-2 e+4 f-8 g+16 h}{12 (x+2)}-\frac{1}{36} \log (1-x) (d+e+f+g+h)+\frac{1}{144} \log (2-x) (d+2 e+4 f+8 g+16 h)-\frac{1}{36} \log (x+1) (7 d-13 e+19 f-25 g+31 h)+\frac{1}{144} \log (x+2) (31 d-50 e+76 f-104 g+112 h)","-\frac{d-e+f-g+h}{6 (x+1)}-\frac{d-2 e+4 f-8 g+16 h}{12 (x+2)}-\frac{1}{36} \log (1-x) (d+e+f+g+h)+\frac{1}{144} \log (2-x) (d+2 e+4 f+8 g+16 h)-\frac{1}{36} \log (x+1) (7 d-13 e+19 f-25 g+31 h)+\frac{1}{144} \log (x+2) (31 d-50 e+76 f-104 g+112 h)",1,"-(d - e + f - g + h)/(6*(1 + x)) - (d - 2*e + 4*f - 8*g + 16*h)/(12*(2 + x)) - ((d + e + f + g + h)*Log[1 - x])/36 + ((d + 2*e + 4*f + 8*g + 16*h)*Log[2 - x])/144 - ((7*d - 13*e + 19*f - 25*g + 31*h)*Log[1 + x])/36 + ((31*d - 50*e + 76*f - 104*g + 112*h)*Log[2 + x])/144","A",3,2,41,0.04878,1,"{1586, 6728}"
96,1,147,0,0.3295453,"\int \frac{\left(2-3 x+x^2\right) \left(d+e x+f x^2+g x^3+h x^4+i x^5\right)}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[((2 - 3*x + x^2)*(d + e*x + f*x^2 + g*x^3 + h*x^4 + i*x^5))/(4 - 5*x^2 + x^4)^2,x]","-\frac{d-2 e+4 f-8 g+16 h-32 i}{12 (x+2)}-\frac{d-e+f-g+h-i}{6 (x+1)}-\frac{1}{36} \log (1-x) (d+e+f+g+h+i)+\frac{1}{144} \log (2-x) (d+2 e+4 f+8 g+16 h+32 i)-\frac{1}{36} \log (x+1) (7 d-13 e+19 f-25 g+31 h-37 i)+\frac{1}{144} \log (x+2) (31 d-50 e+76 f-104 g+112 h-32 i)","-\frac{d-2 e+4 f-8 g+16 h-32 i}{12 (x+2)}-\frac{d-e+f-g+h-i}{6 (x+1)}-\frac{1}{36} \log (1-x) (d+e+f+g+h+i)+\frac{1}{144} \log (2-x) (d+2 e+4 f+8 g+16 h+32 i)-\frac{1}{36} \log (x+1) (7 d-13 e+19 f-25 g+31 h-37 i)+\frac{1}{144} \log (x+2) (31 d-50 e+76 f-104 g+112 h-32 i)",1,"-(d - e + f - g + h - i)/(6*(1 + x)) - (d - 2*e + 4*f - 8*g + 16*h - 32*i)/(12*(2 + x)) - ((d + e + f + g + h + i)*Log[1 - x])/36 + ((d + 2*e + 4*f + 8*g + 16*h + 32*i)*Log[2 - x])/144 - ((7*d - 13*e + 19*f - 25*g + 31*h - 37*i)*Log[1 + x])/36 + ((31*d - 50*e + 76*f - 104*g + 112*h - 32*i)*Log[2 + x])/144","A",3,2,46,0.04348,1,"{1586, 6728}"
97,1,68,0,0.057872,"\int \frac{2+x}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[(2 + x)/(4 - 5*x^2 + x^4)^2,x]","\frac{1}{12 (1-x)}+\frac{1}{36 (2-x)}-\frac{1}{36 (x+1)}+\frac{1}{18} \log (1-x)-\frac{35}{432} \log (2-x)+\frac{1}{54} \log (x+1)+\frac{1}{144} \log (x+2)","\frac{1}{12 (1-x)}+\frac{1}{36 (2-x)}-\frac{1}{36 (x+1)}+\frac{1}{18} \log (1-x)-\frac{35}{432} \log (2-x)+\frac{1}{54} \log (x+1)+\frac{1}{144} \log (x+2)",1,"1/(12*(1 - x)) + 1/(36*(2 - x)) - 1/(36*(1 + x)) + Log[1 - x]/18 - (35*Log[2 - x])/432 + Log[1 + x]/54 + Log[2 + x]/144","A",3,2,16,0.1250,1,"{1586, 2074}"
98,1,105,0,0.196274,"\int \frac{(2+x) (d+e x)}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[((2 + x)*(d + e*x))/(4 - 5*x^2 + x^4)^2,x]","-\frac{d-e}{36 (x+1)}+\frac{d+e}{12 (1-x)}+\frac{d+2 e}{36 (2-x)}+\frac{1}{36} (2 d+5 e) \log (1-x)-\frac{1}{432} (35 d+58 e) \log (2-x)+\frac{1}{108} (2 d+e) \log (x+1)+\frac{1}{144} (d-2 e) \log (x+2)","-\frac{d-e}{36 (x+1)}+\frac{d+e}{12 (1-x)}+\frac{d+2 e}{36 (2-x)}+\frac{1}{36} (2 d+5 e) \log (1-x)-\frac{1}{432} (35 d+58 e) \log (2-x)+\frac{1}{108} (2 d+e) \log (x+1)+\frac{1}{144} (d-2 e) \log (x+2)",1,"(d + e)/(12*(1 - x)) + (d + 2*e)/(36*(2 - x)) - (d - e)/(36*(1 + x)) + ((2*d + 5*e)*Log[1 - x])/36 - ((35*d + 58*e)*Log[2 - x])/432 + ((2*d + e)*Log[1 + x])/108 + ((d - 2*e)*Log[2 + x])/144","A",3,2,21,0.09524,1,"{1586, 6742}"
99,1,122,0,0.2217162,"\int \frac{(2+x) \left(d+e x+f x^2\right)}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[((2 + x)*(d + e*x + f*x^2))/(4 - 5*x^2 + x^4)^2,x]","-\frac{d-e+f}{36 (x+1)}+\frac{d+e+f}{12 (1-x)}+\frac{d+2 e+4 f}{36 (2-x)}+\frac{1}{36} \log (1-x) (2 d+5 e+8 f)-\frac{1}{432} \log (2-x) (35 d+58 e+92 f)+\frac{1}{108} \log (x+1) (2 d+e-4 f)+\frac{1}{144} \log (x+2) (d-2 e+4 f)","-\frac{d-e+f}{36 (x+1)}+\frac{d+e+f}{12 (1-x)}+\frac{d+2 e+4 f}{36 (2-x)}+\frac{1}{36} \log (1-x) (2 d+5 e+8 f)-\frac{1}{432} \log (2-x) (35 d+58 e+92 f)+\frac{1}{108} \log (x+1) (2 d+e-4 f)+\frac{1}{144} \log (x+2) (d-2 e+4 f)",1,"(d + e + f)/(12*(1 - x)) + (d + 2*e + 4*f)/(36*(2 - x)) - (d - e + f)/(36*(1 + x)) + ((2*d + 5*e + 8*f)*Log[1 - x])/36 - ((35*d + 58*e + 92*f)*Log[2 - x])/432 + ((2*d + e - 4*f)*Log[1 + x])/108 + ((d - 2*e + 4*f)*Log[2 + x])/144","A",3,2,26,0.07692,1,"{1586, 6742}"
100,1,141,0,0.2526811,"\int \frac{(2+x) \left(d+e x+f x^2+g x^3\right)}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[((2 + x)*(d + e*x + f*x^2 + g*x^3))/(4 - 5*x^2 + x^4)^2,x]","-\frac{d-e+f-g}{36 (x+1)}+\frac{d+e+f+g}{12 (1-x)}+\frac{d+2 e+4 f+8 g}{36 (2-x)}+\frac{1}{36} \log (1-x) (2 d+5 e+8 f+11 g)-\frac{1}{432} \log (2-x) (35 d+58 e+92 f+136 g)+\frac{1}{108} \log (x+1) (2 d+e-4 f+7 g)+\frac{1}{144} \log (x+2) (d-2 e+4 f-8 g)","-\frac{d-e+f-g}{36 (x+1)}+\frac{d+e+f+g}{12 (1-x)}+\frac{d+2 e+4 f+8 g}{36 (2-x)}+\frac{1}{36} \log (1-x) (2 d+5 e+8 f+11 g)-\frac{1}{432} \log (2-x) (35 d+58 e+92 f+136 g)+\frac{1}{108} \log (x+1) (2 d+e-4 f+7 g)+\frac{1}{144} \log (x+2) (d-2 e+4 f-8 g)",1,"(d + e + f + g)/(12*(1 - x)) + (d + 2*e + 4*f + 8*g)/(36*(2 - x)) - (d - e + f - g)/(36*(1 + x)) + ((2*d + 5*e + 8*f + 11*g)*Log[1 - x])/36 - ((35*d + 58*e + 92*f + 136*g)*Log[2 - x])/432 + ((2*d + e - 4*f + 7*g)*Log[1 + x])/108 + ((d - 2*e + 4*f - 8*g)*Log[2 + x])/144","A",3,2,31,0.06452,1,"{1586, 6742}"
101,1,158,0,0.2886295,"\int \frac{(2+x) \left(d+e x+f x^2+g x^3+h x^4\right)}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[((2 + x)*(d + e*x + f*x^2 + g*x^3 + h*x^4))/(4 - 5*x^2 + x^4)^2,x]","-\frac{d-e+f-g+h}{36 (x+1)}+\frac{d+e+f+g+h}{12 (1-x)}+\frac{d+2 e+4 f+8 g+16 h}{36 (2-x)}+\frac{1}{36} \log (1-x) (2 d+5 e+8 f+11 g+14 h)-\frac{1}{432} \log (2-x) (35 d+58 e+92 f+136 g+176 h)+\frac{1}{108} \log (x+1) (2 d+e-4 f+7 g-10 h)+\frac{1}{144} \log (x+2) (d-2 e+4 f-8 g+16 h)","-\frac{d-e+f-g+h}{36 (x+1)}+\frac{d+e+f+g+h}{12 (1-x)}+\frac{d+2 e+4 f+8 g+16 h}{36 (2-x)}+\frac{1}{36} \log (1-x) (2 d+5 e+8 f+11 g+14 h)-\frac{1}{432} \log (2-x) (35 d+58 e+92 f+136 g+176 h)+\frac{1}{108} \log (x+1) (2 d+e-4 f+7 g-10 h)+\frac{1}{144} \log (x+2) (d-2 e+4 f-8 g+16 h)",1,"(d + e + f + g + h)/(12*(1 - x)) + (d + 2*e + 4*f + 8*g + 16*h)/(36*(2 - x)) - (d - e + f - g + h)/(36*(1 + x)) + ((2*d + 5*e + 8*f + 11*g + 14*h)*Log[1 - x])/36 - ((35*d + 58*e + 92*f + 136*g + 176*h)*Log[2 - x])/432 + ((2*d + e - 4*f + 7*g - 10*h)*Log[1 + x])/108 + ((d - 2*e + 4*f - 8*g + 16*h)*Log[2 + x])/144","A",3,2,36,0.05556,1,"{1586, 6742}"
102,1,177,0,0.3432353,"\int \frac{(2+x) \left(d+e x+f x^2+g x^3+h x^4+i x^5\right)}{\left(4-5 x^2+x^4\right)^2} \, dx","Int[((2 + x)*(d + e*x + f*x^2 + g*x^3 + h*x^4 + i*x^5))/(4 - 5*x^2 + x^4)^2,x]","-\frac{d-e+f-g+h-i}{36 (x+1)}+\frac{d+e+f+g+h+i}{12 (1-x)}+\frac{d+2 e+4 f+8 g+16 h+32 i}{36 (2-x)}+\frac{1}{36} \log (1-x) (2 d+5 e+8 f+11 g+14 h+17 i)-\frac{1}{432} \log (2-x) (35 d+58 e+92 f+136 g+176 h+160 i)+\frac{1}{108} \log (x+1) (2 d+e-4 f+7 g-10 h+13 i)+\frac{1}{144} \log (x+2) (d-2 e+4 f-8 g+16 h-32 i)","-\frac{d-e+f-g+h-i}{36 (x+1)}+\frac{d+e+f+g+h+i}{12 (1-x)}+\frac{d+2 e+4 f+8 g+16 h+32 i}{36 (2-x)}+\frac{1}{36} \log (1-x) (2 d+5 e+8 f+11 g+14 h+17 i)-\frac{1}{432} \log (2-x) (35 d+58 e+92 f+136 g+176 h+160 i)+\frac{1}{108} \log (x+1) (2 d+e-4 f+7 g-10 h+13 i)+\frac{1}{144} \log (x+2) (d-2 e+4 f-8 g+16 h-32 i)",1,"(d + e + f + g + h + i)/(12*(1 - x)) + (d + 2*e + 4*f + 8*g + 16*h + 32*i)/(36*(2 - x)) - (d - e + f - g + h - i)/(36*(1 + x)) + ((2*d + 5*e + 8*f + 11*g + 14*h + 17*i)*Log[1 - x])/36 - ((35*d + 58*e + 92*f + 136*g + 176*h + 160*i)*Log[2 - x])/432 + ((2*d + e - 4*f + 7*g - 10*h + 13*i)*Log[1 + x])/108 + ((d - 2*e + 4*f - 8*g + 16*h - 32*i)*Log[2 + x])/144","A",3,2,41,0.04878,1,"{1586, 6742}"
103,1,717,0,0.5958276,"\int \left(d+e x+f x^2+g x^3\right) \left(a+b x^2+c x^4\right)^{3/2} \, dx","Int[(d + e*x + f*x^2 + g*x^3)*(a + b*x^2 + c*x^4)^(3/2),x]","-\frac{x \sqrt{a+b x^2+c x^4} \left(-84 a^2 c^2 f+57 a b^2 c f-144 a b c^2 d+18 b^3 c d-8 b^4 f\right)}{315 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(-84 a^2 c^2 f+\sqrt{a} \sqrt{c} \left(24 a b c f-180 a c^2 d+9 b^2 c d-4 b^3 f\right)+57 a b^2 c f-144 a b c^2 d+18 b^3 c d-8 b^4 f\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)}{630 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(-84 a^2 c^2 f+57 a b^2 c f-144 a b c^2 d+18 b^3 c d-8 b^4 f\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)}{315 c^{11/4} \sqrt{a+b x^2+c x^4}}+\frac{x \sqrt{a+b x^2+c x^4} \left(3 c x^2 \left(14 a c f-4 b^2 f+9 b c d\right)+9 a b c f+90 a c^2 d+9 b^2 c d-4 b^3 f\right)}{315 c^2}-\frac{3 \left(b^2-4 a c\right) \left(b+2 c x^2\right) \sqrt{a+b x^2+c x^4} (2 c e-b g)}{256 c^3}+\frac{3 \left(b^2-4 a c\right)^2 (2 c e-b g) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{512 c^{7/2}}+\frac{\left(b+2 c x^2\right) \left(a+b x^2+c x^4\right)^{3/2} (2 c e-b g)}{32 c^2}+\frac{x \left(a+b x^2+c x^4\right)^{3/2} \left(3 (b f+3 c d)+7 c f x^2\right)}{63 c}+\frac{g \left(a+b x^2+c x^4\right)^{5/2}}{10 c}","-\frac{x \sqrt{a+b x^2+c x^4} \left(-84 a^2 c^2 f+57 a b^2 c f-144 a b c^2 d+18 b^3 c d-8 b^4 f\right)}{315 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(-84 a^2 c^2 f+\sqrt{a} \sqrt{c} \left(24 a b c f-180 a c^2 d+9 b^2 c d-4 b^3 f\right)+57 a b^2 c f-144 a b c^2 d+18 b^3 c d-8 b^4 f\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)}{630 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(-84 a^2 c^2 f+57 a b^2 c f-144 a b c^2 d+18 b^3 c d-8 b^4 f\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)}{315 c^{11/4} \sqrt{a+b x^2+c x^4}}+\frac{x \sqrt{a+b x^2+c x^4} \left(3 c x^2 \left(14 a c f-4 b^2 f+9 b c d\right)+9 a b c f+90 a c^2 d+9 b^2 c d-4 b^3 f\right)}{315 c^2}-\frac{3 \left(b^2-4 a c\right) \left(b+2 c x^2\right) \sqrt{a+b x^2+c x^4} (2 c e-b g)}{256 c^3}+\frac{3 \left(b^2-4 a c\right)^2 (2 c e-b g) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{512 c^{7/2}}+\frac{\left(b+2 c x^2\right) \left(a+b x^2+c x^4\right)^{3/2} (2 c e-b g)}{32 c^2}+\frac{x \left(a+b x^2+c x^4\right)^{3/2} \left(3 (b f+3 c d)+7 c f x^2\right)}{63 c}+\frac{g \left(a+b x^2+c x^4\right)^{5/2}}{10 c}",1,"-((18*b^3*c*d - 144*a*b*c^2*d - 8*b^4*f + 57*a*b^2*c*f - 84*a^2*c^2*f)*x*Sqrt[a + b*x^2 + c*x^4])/(315*c^(5/2)*(Sqrt[a] + Sqrt[c]*x^2)) - (3*(b^2 - 4*a*c)*(2*c*e - b*g)*(b + 2*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(256*c^3) + (x*(9*b^2*c*d + 90*a*c^2*d - 4*b^3*f + 9*a*b*c*f + 3*c*(9*b*c*d - 4*b^2*f + 14*a*c*f)*x^2)*Sqrt[a + b*x^2 + c*x^4])/(315*c^2) + ((2*c*e - b*g)*(b + 2*c*x^2)*(a + b*x^2 + c*x^4)^(3/2))/(32*c^2) + (x*(3*(3*c*d + b*f) + 7*c*f*x^2)*(a + b*x^2 + c*x^4)^(3/2))/(63*c) + (g*(a + b*x^2 + c*x^4)^(5/2))/(10*c) + (3*(b^2 - 4*a*c)^2*(2*c*e - b*g)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(512*c^(7/2)) + (a^(1/4)*(18*b^3*c*d - 144*a*b*c^2*d - 8*b^4*f + 57*a*b^2*c*f - 84*a^2*c^2*f)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(315*c^(11/4)*Sqrt[a + b*x^2 + c*x^4]) - (a^(1/4)*(18*b^3*c*d - 144*a*b*c^2*d - 8*b^4*f + 57*a*b^2*c*f - 84*a^2*c^2*f + Sqrt[a]*Sqrt[c]*(9*b^2*c*d - 180*a*c^2*d - 4*b^3*f + 24*a*b*c*f))*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(630*c^(11/4)*Sqrt[a + b*x^2 + c*x^4])","A",12,10,32,0.3125,1,"{1673, 1176, 1197, 1103, 1195, 1247, 640, 612, 621, 206}"
104,1,505,0,0.2785048,"\int \left(d+e x+f x^2+g x^3\right) \sqrt{a+b x^2+c x^4} \, dx","Int[(d + e*x + f*x^2 + g*x^3)*Sqrt[a + b*x^2 + c*x^4],x]","\frac{x \sqrt{a+b x^2+c x^4} \left(6 a c f-2 b^2 f+5 b c d\right)}{15 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(6 a c f-2 b^2 f+5 b c d\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^{7/4} \sqrt{a+b x^2+c x^4}}-\frac{\left(b^2-4 a c\right) (2 c e-b g) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{32 c^{5/2}}+\frac{\sqrt[4]{a} \left(2 \sqrt{a} \sqrt{c}+b\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(3 \sqrt{a} \sqrt{c} f-2 b f+5 c d\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^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{\left(b+2 c x^2\right) \sqrt{a+b x^2+c x^4} (2 c e-b g)}{16 c^2}+\frac{x \sqrt{a+b x^2+c x^4} \left(b f+5 c d+3 c f x^2\right)}{15 c}+\frac{g \left(a+b x^2+c x^4\right)^{3/2}}{6 c}","\frac{x \sqrt{a+b x^2+c x^4} \left(6 a c f-2 b^2 f+5 b c d\right)}{15 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(6 a c f-2 b^2 f+5 b c d\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^{7/4} \sqrt{a+b x^2+c x^4}}-\frac{\left(b^2-4 a c\right) (2 c e-b g) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{32 c^{5/2}}+\frac{\sqrt[4]{a} \left(2 \sqrt{a} \sqrt{c}+b\right) \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(3 \sqrt{a} \sqrt{c} f-2 b f+5 c d\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^{7/4} \sqrt{a+b x^2+c x^4}}+\frac{\left(b+2 c x^2\right) \sqrt{a+b x^2+c x^4} (2 c e-b g)}{16 c^2}+\frac{x \sqrt{a+b x^2+c x^4} \left(b f+5 c d+3 c f x^2\right)}{15 c}+\frac{g \left(a+b x^2+c x^4\right)^{3/2}}{6 c}",1,"((5*b*c*d - 2*b^2*f + 6*a*c*f)*x*Sqrt[a + b*x^2 + c*x^4])/(15*c^(3/2)*(Sqrt[a] + Sqrt[c]*x^2)) + ((2*c*e - b*g)*(b + 2*c*x^2)*Sqrt[a + b*x^2 + c*x^4])/(16*c^2) + (x*(5*c*d + b*f + 3*c*f*x^2)*Sqrt[a + b*x^2 + c*x^4])/(15*c) + (g*(a + b*x^2 + c*x^4)^(3/2))/(6*c) - ((b^2 - 4*a*c)*(2*c*e - b*g)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(32*c^(5/2)) - (a^(1/4)*(5*b*c*d - 2*b^2*f + 6*a*c*f)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(15*c^(7/4)*Sqrt[a + b*x^2 + c*x^4]) + (a^(1/4)*(b + 2*Sqrt[a]*Sqrt[c])*(5*c*d - 2*b*f + 3*Sqrt[a]*Sqrt[c]*f)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(30*c^(7/4)*Sqrt[a + b*x^2 + c*x^4])","A",10,10,32,0.3125,1,"{1673, 1176, 1197, 1103, 1195, 1247, 640, 612, 621, 206}"
105,1,359,0,0.1585579,"\int \frac{d+e x+f x^2+g x^3}{\sqrt{a+b x^2+c x^4}} \, dx","Int[(d + e*x + f*x^2 + g*x^3)/Sqrt[a + b*x^2 + c*x^4],x]","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\frac{\sqrt{c} d}{\sqrt{a}}+f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 c^{3/4} \sqrt{a+b x^2+c x^4}}+\frac{(2 c e-b g) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 c^{3/2}}-\frac{\sqrt[4]{a} f \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{f x \sqrt{a+b x^2+c x^4}}{\sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{g \sqrt{a+b x^2+c x^4}}{2 c}","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\frac{\sqrt{c} d}{\sqrt{a}}+f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 c^{3/4} \sqrt{a+b x^2+c x^4}}+\frac{(2 c e-b g) \tanh ^{-1}\left(\frac{b+2 c x^2}{2 \sqrt{c} \sqrt{a+b x^2+c x^4}}\right)}{4 c^{3/2}}-\frac{\sqrt[4]{a} f \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{f x \sqrt{a+b x^2+c x^4}}{\sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{g \sqrt{a+b x^2+c x^4}}{2 c}",1,"(g*Sqrt[a + b*x^2 + c*x^4])/(2*c) + (f*x*Sqrt[a + b*x^2 + c*x^4])/(Sqrt[c]*(Sqrt[a] + Sqrt[c]*x^2)) + ((2*c*e - b*g)*ArcTanh[(b + 2*c*x^2)/(2*Sqrt[c]*Sqrt[a + b*x^2 + c*x^4])])/(4*c^(3/2)) - (a^(1/4)*f*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(c^(3/4)*Sqrt[a + b*x^2 + c*x^4]) + (a^(1/4)*((Sqrt[c]*d)/Sqrt[a] + f)*(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",8,8,32,0.2500,1,"{1673, 1197, 1103, 1195, 1247, 640, 621, 206}"
106,1,447,0,0.2726208,"\int \frac{d+e x+f x^2+g x^3}{\left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[(d + e*x + f*x^2 + g*x^3)/(a + b*x^2 + c*x^4)^(3/2),x]","\frac{\sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} (b d-2 a f) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{a^{3/4} \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{c} d-\sqrt{a} f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 a^{3/4} \sqrt[4]{c} \left(b-2 \sqrt{a} \sqrt{c}\right) \sqrt{a+b x^2+c x^4}}-\frac{\sqrt{c} x \sqrt{a+b x^2+c x^4} (b d-2 a f)}{a \left(b^2-4 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{x \left(c x^2 (b d-2 a f)-a b f-2 a c d+b^2 d\right)}{a \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{-2 a g+x^2 (2 c e-b g)+b e}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}","\frac{\sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} (b d-2 a f) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{a^{3/4} \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{c} d-\sqrt{a} f\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{2 a^{3/4} \sqrt[4]{c} \left(b-2 \sqrt{a} \sqrt{c}\right) \sqrt{a+b x^2+c x^4}}-\frac{\sqrt{c} x \sqrt{a+b x^2+c x^4} (b d-2 a f)}{a \left(b^2-4 a c\right) \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{x \left(c x^2 (b d-2 a f)-a b f-2 a c d+b^2 d\right)}{a \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}-\frac{-2 a g+x^2 (2 c e-b g)+b e}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}",1,"(x*(b^2*d - 2*a*c*d - a*b*f + c*(b*d - 2*a*f)*x^2))/(a*(b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4]) - (b*e - 2*a*g + (2*c*e - b*g)*x^2)/((b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4]) - (Sqrt[c]*(b*d - 2*a*f)*x*Sqrt[a + b*x^2 + c*x^4])/(a*(b^2 - 4*a*c)*(Sqrt[a] + Sqrt[c]*x^2)) + (c^(1/4)*(b*d - 2*a*f)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(a^(3/4)*(b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4]) - ((Sqrt[c]*d - Sqrt[a]*f)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + b*x^2 + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(2*a^(3/4)*(b - 2*Sqrt[a]*Sqrt[c])*c^(1/4)*Sqrt[a + b*x^2 + c*x^4])","A",7,7,32,0.2188,1,"{1673, 1178, 1197, 1103, 1195, 1247, 636}"
107,1,680,0,0.5148044,"\int \frac{d+e x+f x^2+g x^3}{\left(a+b x^2+c x^4\right)^{5/2}} \, dx","Int[(d + e*x + f*x^2 + g*x^3)/(a + b*x^2 + c*x^4)^(5/2),x]","\frac{x \left(c x^2 \left(12 a^2 c f+a b^2 f-16 a b c d+2 b^3 d\right)+4 a^2 b c f+20 a^2 c^2 d-17 a b^2 c d+a b^3 f+2 b^4 d\right)}{3 a^2 \left(b^2-4 a c\right)^2 \sqrt{a+b x^2+c x^4}}-\frac{\sqrt{c} x \sqrt{a+b x^2+c x^4} \left(12 a^2 c f+a b^2 f-16 a b c d+2 b^3 d\right)}{3 a^2 \left(b^2-4 a c\right)^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(6 a^{3/2} \sqrt{c} f-3 \sqrt{a} b \sqrt{c} d+a b f-10 a c d+2 b^2 d\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} \left(b-2 \sqrt{a} \sqrt{c}\right) \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}+\frac{\sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(12 a^2 c f+a b^2 f-16 a b c d+2 b^3 d\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)}{3 a^{7/4} \left(b^2-4 a c\right)^2 \sqrt{a+b x^2+c x^4}}+\frac{x \left(c x^2 (b d-2 a f)-a b f-2 a c d+b^2 d\right)}{3 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^{3/2}}+\frac{4 \left(b+2 c x^2\right) (2 c e-b g)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x^2+c x^4}}-\frac{-2 a g+x^2 (2 c e-b g)+b e}{3 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^{3/2}}","\frac{x \left(c x^2 \left(12 a^2 c f+a b^2 f-16 a b c d+2 b^3 d\right)+4 a^2 b c f+20 a^2 c^2 d-17 a b^2 c d+a b^3 f+2 b^4 d\right)}{3 a^2 \left(b^2-4 a c\right)^2 \sqrt{a+b x^2+c x^4}}-\frac{\sqrt{c} x \sqrt{a+b x^2+c x^4} \left(12 a^2 c f+a b^2 f-16 a b c d+2 b^3 d\right)}{3 a^2 \left(b^2-4 a c\right)^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(6 a^{3/2} \sqrt{c} f-3 \sqrt{a} b \sqrt{c} d+a b f-10 a c d+2 b^2 d\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} \left(b-2 \sqrt{a} \sqrt{c}\right) \left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}+\frac{\sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+b x^2+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(12 a^2 c f+a b^2 f-16 a b c d+2 b^3 d\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)}{3 a^{7/4} \left(b^2-4 a c\right)^2 \sqrt{a+b x^2+c x^4}}+\frac{x \left(c x^2 (b d-2 a f)-a b f-2 a c d+b^2 d\right)}{3 a \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^{3/2}}+\frac{4 \left(b+2 c x^2\right) (2 c e-b g)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x^2+c x^4}}-\frac{-2 a g+x^2 (2 c e-b g)+b e}{3 \left(b^2-4 a c\right) \left(a+b x^2+c x^4\right)^{3/2}}",1,"(x*(b^2*d - 2*a*c*d - a*b*f + c*(b*d - 2*a*f)*x^2))/(3*a*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^(3/2)) - (b*e - 2*a*g + (2*c*e - b*g)*x^2)/(3*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)^(3/2)) + (4*(2*c*e - b*g)*(b + 2*c*x^2))/(3*(b^2 - 4*a*c)^2*Sqrt[a + b*x^2 + c*x^4]) + (x*(2*b^4*d - 17*a*b^2*c*d + 20*a^2*c^2*d + a*b^3*f + 4*a^2*b*c*f + c*(2*b^3*d - 16*a*b*c*d + a*b^2*f + 12*a^2*c*f)*x^2))/(3*a^2*(b^2 - 4*a*c)^2*Sqrt[a + b*x^2 + c*x^4]) - (Sqrt[c]*(2*b^3*d - 16*a*b*c*d + a*b^2*f + 12*a^2*c*f)*x*Sqrt[a + b*x^2 + c*x^4])/(3*a^2*(b^2 - 4*a*c)^2*(Sqrt[a] + Sqrt[c]*x^2)) + (c^(1/4)*(2*b^3*d - 16*a*b*c*d + a*b^2*f + 12*a^2*c*f)*(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)*(b^2 - 4*a*c)^2*Sqrt[a + b*x^2 + c*x^4]) - (c^(1/4)*(2*b^2*d - 3*Sqrt[a]*b*Sqrt[c]*d - 10*a*c*d + a*b*f + 6*a^(3/2)*Sqrt[c]*f)*(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)*(b - 2*Sqrt[a]*Sqrt[c])*(b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4])","A",9,8,32,0.2500,1,"{1673, 1178, 1197, 1103, 1195, 1247, 638, 613}"
108,1,19,0,0.0181643,"\int \frac{a g-c g x^4}{\left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[(a*g - c*g*x^4)/(a + b*x^2 + c*x^4)^(3/2),x]","\frac{g x}{\sqrt{a+b x^2+c x^4}}","\frac{g x}{\sqrt{a+b x^2+c x^4}}",1,"(g*x)/Sqrt[a + b*x^2 + c*x^4]","A",1,1,28,0.03571,1,"{1588}"
109,1,57,0,0.0666024,"\int \frac{a g+e x-c g x^4}{\left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[(a*g + e*x - c*g*x^4)/(a + b*x^2 + c*x^4)^(3/2),x]","\frac{g x}{\sqrt{a+b x^2+c x^4}}-\frac{e \left(b+2 c x^2\right)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}","\frac{g x}{\sqrt{a+b x^2+c x^4}}-\frac{e \left(b+2 c x^2\right)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}",1,"(g*x)/Sqrt[a + b*x^2 + c*x^4] - (e*(b + 2*c*x^2))/((b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4])","A",5,5,31,0.1613,1,"{1673, 1588, 12, 1107, 613}"
110,1,57,0,0.0795246,"\int \frac{a g+f x^3-c g x^4}{\left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[(a*g + f*x^3 - c*g*x^4)/(a + b*x^2 + c*x^4)^(3/2),x]","\frac{f \left(2 a+b x^2\right)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}+\frac{g x}{\sqrt{a+b x^2+c x^4}}","\frac{f \left(2 a+b x^2\right)}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}+\frac{g x}{\sqrt{a+b x^2+c x^4}}",1,"(g*x)/Sqrt[a + b*x^2 + c*x^4] + (f*(2*a + b*x^2))/((b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4])","A",5,5,33,0.1515,1,"{1673, 1588, 12, 1114, 636}"
111,1,69,0,0.0906941,"\int \frac{a g+e x+f x^3-c g x^4}{\left(a+b x^2+c x^4\right)^{3/2}} \, dx","Int[(a*g + e*x + f*x^3 - c*g*x^4)/(a + b*x^2 + c*x^4)^(3/2),x]","\frac{g x}{\sqrt{a+b x^2+c x^4}}-\frac{-2 a f+x^2 (2 c e-b f)+b e}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}","\frac{g x}{\sqrt{a+b x^2+c x^4}}-\frac{-2 a f+x^2 (2 c e-b f)+b e}{\left(b^2-4 a c\right) \sqrt{a+b x^2+c x^4}}",1,"(g*x)/Sqrt[a + b*x^2 + c*x^4] - (b*e - 2*a*f + (2*c*e - b*f)*x^2)/((b^2 - 4*a*c)*Sqrt[a + b*x^2 + c*x^4])","A",4,4,36,0.1111,1,"{1673, 1588, 1247, 636}"