1,1,40,0,1.248955," ","integrate((e*x+d)*(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{1}{6} \, c e x^{6} + \frac{1}{5} \, c d x^{5} + \frac{1}{4} \, b e x^{4} + \frac{1}{3} \, b d x^{3} + \frac{1}{2} \, a e x^{2} + a d x"," ",0,"1/6*c*e*x^6 + 1/5*c*d*x^5 + 1/4*b*e*x^4 + 1/3*b*d*x^3 + 1/2*a*e*x^2 + a*d*x","A",0
2,1,57,0,1.207310," ","integrate((f*x^2+e*x+d)*(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{1}{7} \, c f x^{7} + \frac{1}{6} \, c e x^{6} + \frac{1}{4} \, b e x^{4} + \frac{1}{5} \, {\left(c d + b f\right)} x^{5} + \frac{1}{2} \, a e x^{2} + \frac{1}{3} \, {\left(b d + a f\right)} x^{3} + a d x"," ",0,"1/7*c*f*x^7 + 1/6*c*e*x^6 + 1/4*b*e*x^4 + 1/5*(c*d + b*f)*x^5 + 1/2*a*e*x^2 + 1/3*(b*d + a*f)*x^3 + a*d*x","A",0
3,1,74,0,1.559055," ","integrate((g*x^3+f*x^2+e*x+d)*(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{1}{8} \, c g x^{8} + \frac{1}{7} \, c f x^{7} + \frac{1}{6} \, {\left(c e + b g\right)} x^{6} + \frac{1}{5} \, {\left(c d + b f\right)} x^{5} + \frac{1}{4} \, {\left(b e + a g\right)} x^{4} + \frac{1}{2} \, a e x^{2} + \frac{1}{3} \, {\left(b d + a f\right)} x^{3} + a d x"," ",0,"1/8*c*g*x^8 + 1/7*c*f*x^7 + 1/6*(c*e + b*g)*x^6 + 1/5*(c*d + b*f)*x^5 + 1/4*(b*e + a*g)*x^4 + 1/2*a*e*x^2 + 1/3*(b*d + a*f)*x^3 + a*d*x","A",0
4,1,89,0,1.643425," ","integrate((c*x^4+b*x^2+a)*(h*x^4+g*x^3+f*x^2+e*x+d),x, algorithm=""maxima"")","\frac{1}{9} \, c h x^{9} + \frac{1}{8} \, c g x^{8} + \frac{1}{7} \, {\left(c f + b h\right)} x^{7} + \frac{1}{6} \, {\left(c e + b g\right)} x^{6} + \frac{1}{5} \, {\left(c d + b f + a h\right)} x^{5} + \frac{1}{4} \, {\left(b e + a g\right)} x^{4} + \frac{1}{2} \, a e x^{2} + \frac{1}{3} \, {\left(b d + a f\right)} x^{3} + a d x"," ",0,"1/9*c*h*x^9 + 1/8*c*g*x^8 + 1/7*(c*f + b*h)*x^7 + 1/6*(c*e + b*g)*x^6 + 1/5*(c*d + b*f + a*h)*x^5 + 1/4*(b*e + a*g)*x^4 + 1/2*a*e*x^2 + 1/3*(b*d + a*f)*x^3 + a*d*x","A",0
5,1,104,0,1.173621," ","integrate((c*x^4+b*x^2+a)*(i*x^5+h*x^4+g*x^3+f*x^2+e*x+d),x, algorithm=""maxima"")","\frac{1}{10} \, c i x^{10} + \frac{1}{9} \, c h x^{9} + \frac{1}{8} \, {\left(c g + b i\right)} x^{8} + \frac{1}{7} \, {\left(c f + b h\right)} x^{7} + \frac{1}{6} \, {\left(c e + b g + a i\right)} x^{6} + \frac{1}{5} \, {\left(c d + b f + a h\right)} x^{5} + \frac{1}{4} \, {\left(b e + a g\right)} x^{4} + \frac{1}{2} \, a e x^{2} + \frac{1}{3} \, {\left(b d + a f\right)} x^{3} + a d x"," ",0,"1/10*c*i*x^10 + 1/9*c*h*x^9 + 1/8*(c*g + b*i)*x^8 + 1/7*(c*f + b*h)*x^7 + 1/6*(c*e + b*g + a*i)*x^6 + 1/5*(c*d + b*f + a*h)*x^5 + 1/4*(b*e + a*g)*x^4 + 1/2*a*e*x^2 + 1/3*(b*d + a*f)*x^3 + a*d*x","A",0
6,1,94,0,1.059645," ","integrate((e*x+d)*(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{1}{10} \, c^{2} e x^{10} + \frac{1}{9} \, c^{2} d x^{9} + \frac{1}{4} \, b c e x^{8} + \frac{2}{7} \, b c d x^{7} + \frac{1}{6} \, {\left(b^{2} + 2 \, a c\right)} e x^{6} + \frac{1}{2} \, a b e x^{4} + \frac{1}{5} \, {\left(b^{2} + 2 \, a c\right)} d x^{5} + \frac{2}{3} \, a b d x^{3} + \frac{1}{2} \, a^{2} e x^{2} + a^{2} d x"," ",0,"1/10*c^2*e*x^10 + 1/9*c^2*d*x^9 + 1/4*b*c*e*x^8 + 2/7*b*c*d*x^7 + 1/6*(b^2 + 2*a*c)*e*x^6 + 1/2*a*b*e*x^4 + 1/5*(b^2 + 2*a*c)*d*x^5 + 2/3*a*b*d*x^3 + 1/2*a^2*e*x^2 + a^2*d*x","A",0
7,1,138,0,1.027424," ","integrate((f*x^2+e*x+d)*(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{1}{11} \, c^{2} f x^{11} + \frac{1}{10} \, c^{2} e x^{10} + \frac{1}{4} \, b c e x^{8} + \frac{1}{9} \, {\left(c^{2} d + 2 \, b c f\right)} x^{9} + \frac{1}{6} \, {\left(b^{2} + 2 \, a c\right)} e x^{6} + \frac{1}{7} \, {\left(2 \, b c d + {\left(b^{2} + 2 \, a c\right)} f\right)} x^{7} + \frac{1}{2} \, a b e x^{4} + \frac{1}{5} \, {\left(2 \, a b f + {\left(b^{2} + 2 \, a c\right)} d\right)} x^{5} + \frac{1}{2} \, a^{2} e x^{2} + a^{2} d x + \frac{1}{3} \, {\left(2 \, a b d + a^{2} f\right)} x^{3}"," ",0,"1/11*c^2*f*x^11 + 1/10*c^2*e*x^10 + 1/4*b*c*e*x^8 + 1/9*(c^2*d + 2*b*c*f)*x^9 + 1/6*(b^2 + 2*a*c)*e*x^6 + 1/7*(2*b*c*d + (b^2 + 2*a*c)*f)*x^7 + 1/2*a*b*e*x^4 + 1/5*(2*a*b*f + (b^2 + 2*a*c)*d)*x^5 + 1/2*a^2*e*x^2 + a^2*d*x + 1/3*(2*a*b*d + a^2*f)*x^3","A",0
8,1,182,0,1.399691," ","integrate((g*x^3+f*x^2+e*x+d)*(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{1}{12} \, c^{2} g x^{12} + \frac{1}{11} \, c^{2} f x^{11} + \frac{1}{10} \, {\left(c^{2} e + 2 \, b c g\right)} x^{10} + \frac{1}{9} \, {\left(c^{2} d + 2 \, b c f\right)} x^{9} + \frac{1}{8} \, {\left(2 \, b c e + {\left(b^{2} + 2 \, a c\right)} g\right)} x^{8} + \frac{1}{7} \, {\left(2 \, b c d + {\left(b^{2} + 2 \, a c\right)} f\right)} x^{7} + \frac{1}{6} \, {\left(2 \, a b g + {\left(b^{2} + 2 \, a c\right)} e\right)} x^{6} + \frac{1}{5} \, {\left(2 \, a b f + {\left(b^{2} + 2 \, a c\right)} d\right)} x^{5} + \frac{1}{2} \, a^{2} e x^{2} + \frac{1}{4} \, {\left(2 \, a b e + a^{2} g\right)} x^{4} + a^{2} d x + \frac{1}{3} \, {\left(2 \, a b d + a^{2} f\right)} x^{3}"," ",0,"1/12*c^2*g*x^12 + 1/11*c^2*f*x^11 + 1/10*(c^2*e + 2*b*c*g)*x^10 + 1/9*(c^2*d + 2*b*c*f)*x^9 + 1/8*(2*b*c*e + (b^2 + 2*a*c)*g)*x^8 + 1/7*(2*b*c*d + (b^2 + 2*a*c)*f)*x^7 + 1/6*(2*a*b*g + (b^2 + 2*a*c)*e)*x^6 + 1/5*(2*a*b*f + (b^2 + 2*a*c)*d)*x^5 + 1/2*a^2*e*x^2 + 1/4*(2*a*b*e + a^2*g)*x^4 + a^2*d*x + 1/3*(2*a*b*d + a^2*f)*x^3","A",0
9,1,218,0,1.137970," ","integrate((c*x^4+b*x^2+a)^2*(h*x^4+g*x^3+f*x^2+e*x+d),x, algorithm=""maxima"")","\frac{1}{13} \, c^{2} h x^{13} + \frac{1}{12} \, c^{2} g x^{12} + \frac{1}{11} \, {\left(c^{2} f + 2 \, b c h\right)} x^{11} + \frac{1}{10} \, {\left(c^{2} e + 2 \, b c g\right)} x^{10} + \frac{1}{9} \, {\left(c^{2} d + 2 \, b c f + {\left(b^{2} + 2 \, a c\right)} h\right)} x^{9} + \frac{1}{8} \, {\left(2 \, b c e + {\left(b^{2} + 2 \, a c\right)} g\right)} x^{8} + \frac{1}{7} \, {\left(2 \, b c d + 2 \, a b h + {\left(b^{2} + 2 \, a c\right)} f\right)} x^{7} + \frac{1}{6} \, {\left(2 \, a b g + {\left(b^{2} + 2 \, a c\right)} e\right)} x^{6} + \frac{1}{5} \, {\left(2 \, a b f + a^{2} h + {\left(b^{2} + 2 \, a c\right)} d\right)} x^{5} + \frac{1}{2} \, a^{2} e x^{2} + \frac{1}{4} \, {\left(2 \, a b e + a^{2} g\right)} x^{4} + a^{2} d x + \frac{1}{3} \, {\left(2 \, a b d + a^{2} f\right)} x^{3}"," ",0,"1/13*c^2*h*x^13 + 1/12*c^2*g*x^12 + 1/11*(c^2*f + 2*b*c*h)*x^11 + 1/10*(c^2*e + 2*b*c*g)*x^10 + 1/9*(c^2*d + 2*b*c*f + (b^2 + 2*a*c)*h)*x^9 + 1/8*(2*b*c*e + (b^2 + 2*a*c)*g)*x^8 + 1/7*(2*b*c*d + 2*a*b*h + (b^2 + 2*a*c)*f)*x^7 + 1/6*(2*a*b*g + (b^2 + 2*a*c)*e)*x^6 + 1/5*(2*a*b*f + a^2*h + (b^2 + 2*a*c)*d)*x^5 + 1/2*a^2*e*x^2 + 1/4*(2*a*b*e + a^2*g)*x^4 + a^2*d*x + 1/3*(2*a*b*d + a^2*f)*x^3","A",0
10,1,43,0,1.125052," ","integrate((e*x+d)/(x^4-5*x^2+4),x, algorithm=""maxima"")","-\frac{1}{12} \, {\left(d - 2 \, e\right)} \log\left(x + 2\right) + \frac{1}{6} \, {\left(d - e\right)} \log\left(x + 1\right) - \frac{1}{6} \, {\left(d + e\right)} \log\left(x - 1\right) + \frac{1}{12} \, {\left(d + 2 \, e\right)} \log\left(x - 2\right)"," ",0,"-1/12*(d - 2*e)*log(x + 2) + 1/6*(d - e)*log(x + 1) - 1/6*(d + e)*log(x - 1) + 1/12*(d + 2*e)*log(x - 2)","A",0
11,1,51,0,1.121967," ","integrate((f*x^2+e*x+d)/(x^4-5*x^2+4),x, algorithm=""maxima"")","-\frac{1}{12} \, {\left(d - 2 \, e + 4 \, f\right)} \log\left(x + 2\right) + \frac{1}{6} \, {\left(d - e + f\right)} \log\left(x + 1\right) - \frac{1}{6} \, {\left(d + e + f\right)} \log\left(x - 1\right) + \frac{1}{12} \, {\left(d + 2 \, e + 4 \, f\right)} \log\left(x - 2\right)"," ",0,"-1/12*(d - 2*e + 4*f)*log(x + 2) + 1/6*(d - e + f)*log(x + 1) - 1/6*(d + e + f)*log(x - 1) + 1/12*(d + 2*e + 4*f)*log(x - 2)","A",0
12,1,61,0,1.354713," ","integrate((g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4),x, algorithm=""maxima"")","-\frac{1}{12} \, {\left(d - 2 \, e + 4 \, f - 8 \, g\right)} \log\left(x + 2\right) + \frac{1}{6} \, {\left(d - e + f - g\right)} \log\left(x + 1\right) - \frac{1}{6} \, {\left(d + e + f + g\right)} \log\left(x - 1\right) + \frac{1}{12} \, {\left(d + 2 \, e + 4 \, f + 8 \, g\right)} \log\left(x - 2\right)"," ",0,"-1/12*(d - 2*e + 4*f - 8*g)*log(x + 2) + 1/6*(d - e + f - g)*log(x + 1) - 1/6*(d + e + f + g)*log(x - 1) + 1/12*(d + 2*e + 4*f + 8*g)*log(x - 2)","A",0
13,1,72,0,1.238212," ","integrate((h*x^4+g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4),x, algorithm=""maxima"")","h x - \frac{1}{12} \, {\left(d - 2 \, e + 4 \, f - 8 \, g + 16 \, h\right)} \log\left(x + 2\right) + \frac{1}{6} \, {\left(d - e + f - g + h\right)} \log\left(x + 1\right) - \frac{1}{6} \, {\left(d + e + f + g + h\right)} \log\left(x - 1\right) + \frac{1}{12} \, {\left(d + 2 \, e + 4 \, f + 8 \, g + 16 \, h\right)} \log\left(x - 2\right)"," ",0,"h*x - 1/12*(d - 2*e + 4*f - 8*g + 16*h)*log(x + 2) + 1/6*(d - e + f - g + h)*log(x + 1) - 1/6*(d + e + f + g + h)*log(x - 1) + 1/12*(d + 2*e + 4*f + 8*g + 16*h)*log(x - 2)","A",0
14,1,88,0,1.245099," ","integrate((i*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4),x, algorithm=""maxima"")","\frac{1}{2} \, i x^{2} + h x - \frac{1}{12} \, {\left(d - 2 \, e + 4 \, f - 8 \, g + 16 \, h - 32 \, i\right)} \log\left(x + 2\right) + \frac{1}{6} \, {\left(d - e + f - g + h - i\right)} \log\left(x + 1\right) - \frac{1}{6} \, {\left(d + e + f + g + h + i\right)} \log\left(x - 1\right) + \frac{1}{12} \, {\left(d + 2 \, e + 4 \, f + 8 \, g + 16 \, h + 32 \, i\right)} \log\left(x - 2\right)"," ",0,"1/2*i*x^2 + h*x - 1/12*(d - 2*e + 4*f - 8*g + 16*h - 32*i)*log(x + 2) + 1/6*(d - e + f - g + h - i)*log(x + 1) - 1/6*(d + e + f + g + h + i)*log(x - 1) + 1/12*(d + 2*e + 4*f + 8*g + 16*h + 32*i)*log(x - 2)","A",0
15,1,65,0,2.208714," ","integrate((e*x+d)/(x^4+x^2+1),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{3} {\left(d - 2 \, e\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{6} \, \sqrt{3} {\left(d + 2 \, e\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{4} \, d \log\left(x^{2} + x + 1\right) - \frac{1}{4} \, d \log\left(x^{2} - x + 1\right)"," ",0,"1/6*sqrt(3)*(d - 2*e)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/6*sqrt(3)*(d + 2*e)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/4*d*log(x^2 + x + 1) - 1/4*d*log(x^2 - x + 1)","A",0
16,1,75,0,2.578674," ","integrate((f*x^2+e*x+d)/(x^4+x^2+1),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{3} {\left(d - 2 \, e + f\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{6} \, \sqrt{3} {\left(d + 2 \, e + f\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{4} \, {\left(d - f\right)} \log\left(x^{2} + x + 1\right) - \frac{1}{4} \, {\left(d - f\right)} \log\left(x^{2} - x + 1\right)"," ",0,"1/6*sqrt(3)*(d - 2*e + f)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/6*sqrt(3)*(d + 2*e + f)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/4*(d - f)*log(x^2 + x + 1) - 1/4*(d - f)*log(x^2 - x + 1)","A",0
17,1,83,0,2.385057," ","integrate((g*x^3+f*x^2+e*x+d)/(x^4+x^2+1),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{3} {\left(d - 2 \, e + f + g\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{6} \, \sqrt{3} {\left(d + 2 \, e + f - g\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{4} \, {\left(d - f + g\right)} \log\left(x^{2} + x + 1\right) - \frac{1}{4} \, {\left(d - f - g\right)} \log\left(x^{2} - x + 1\right)"," ",0,"1/6*sqrt(3)*(d - 2*e + f + g)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/6*sqrt(3)*(d + 2*e + f - g)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/4*(d - f + g)*log(x^2 + x + 1) - 1/4*(d - f - g)*log(x^2 - x + 1)","A",0
18,1,92,0,2.618165," ","integrate((h*x^4+g*x^3+f*x^2+e*x+d)/(x^4+x^2+1),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{3} {\left(d - 2 \, e + f + g - 2 \, h\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{6} \, \sqrt{3} {\left(d + 2 \, e + f - g - 2 \, h\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + h x + \frac{1}{4} \, {\left(d - f + g\right)} \log\left(x^{2} + x + 1\right) - \frac{1}{4} \, {\left(d - f - g\right)} \log\left(x^{2} - x + 1\right)"," ",0,"1/6*sqrt(3)*(d - 2*e + f + g - 2*h)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/6*sqrt(3)*(d + 2*e + f - g - 2*h)*arctan(1/3*sqrt(3)*(2*x - 1)) + h*x + 1/4*(d - f + g)*log(x^2 + x + 1) - 1/4*(d - f - g)*log(x^2 - x + 1)","A",0
19,1,106,0,2.367098," ","integrate((i*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(x^4+x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, i x^{2} + \frac{1}{6} \, \sqrt{3} {\left(d - 2 \, e + f + g - 2 \, h + i\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{6} \, \sqrt{3} {\left(d + 2 \, e + f - g - 2 \, h - i\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + h x + \frac{1}{4} \, {\left(d - f + g - i\right)} \log\left(x^{2} + x + 1\right) - \frac{1}{4} \, {\left(d - f - g + i\right)} \log\left(x^{2} - x + 1\right)"," ",0,"1/2*i*x^2 + 1/6*sqrt(3)*(d - 2*e + f + g - 2*h + i)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/6*sqrt(3)*(d + 2*e + f - g - 2*h - i)*arctan(1/3*sqrt(3)*(2*x - 1)) + h*x + 1/4*(d - f + g - i)*log(x^2 + x + 1) - 1/4*(d - f - g + i)*log(x^2 - x + 1)","A",0
20,0,0,0,0.000000," ","integrate((e*x+d)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\int \frac{e x + d}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate((e*x + d)/(c*x^4 + b*x^2 + a), x)","F",0
21,0,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\int \frac{f x^{2} + e x + d}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate((f*x^2 + e*x + d)/(c*x^4 + b*x^2 + a), x)","F",0
22,0,0,0,0.000000," ","integrate((g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\int \frac{g x^{3} + f x^{2} + e x + d}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate((g*x^3 + f*x^2 + e*x + d)/(c*x^4 + b*x^2 + a), x)","F",0
23,0,0,0,0.000000," ","integrate((h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{h x}{c} + \frac{\frac{1}{4} \, g \log\left({\left| c x^{4} + b x^{2} + a \right|}\right) + \frac{{\left({\left(2 \, b^{4} c^{3} - 16 \, a b^{2} c^{4} + 32 \, a^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} c^{2} f - {\left(2 \, b^{5} c^{2} - 16 \, a b^{3} c^{3} + 32 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} c^{2} h + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 2 \, b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} - 16 \, a b^{2} c^{5} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{6} + 32 \, a^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{5}\right)} c d - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, a b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 16 \, a^{2} b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 32 \, a^{3} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} c h + 2 \, {\left(2 \, b^{3} c^{6} - 8 \, a b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{6}\right)} d - {\left(2 \, b^{4} c^{5} - 8 \, a b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{5}\right)} f + {\left(2 \, b^{5} c^{4} - 12 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5}\right)} h\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} c x}{\sqrt{b c + \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}\right)}{8 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} - 2 \, a b^{3} c^{3} + 16 \, a^{3} c^{4} + 8 \, a^{2} b c^{4} + a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} c^{2}} - \frac{{\left({\left(2 \, b^{4} c^{3} - 16 \, a b^{2} c^{4} + 32 \, a^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} c^{2} f - {\left(2 \, b^{5} c^{2} - 16 \, a b^{3} c^{3} + 32 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} c^{2} h - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} - 2 \, b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} + 16 \, a b^{2} c^{5} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{6} - 32 \, a^{2} c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{5}\right)} c d + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 2 \, a b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 16 \, a^{2} b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 32 \, a^{3} c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} c h + 2 \, {\left(2 \, b^{3} c^{6} - 8 \, a b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{6}\right)} d - {\left(2 \, b^{4} c^{5} - 8 \, a b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{5}\right)} f + {\left(2 \, b^{5} c^{4} - 12 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5}\right)} h\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} c x}{\sqrt{b c - \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}\right)}{8 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} - 2 \, a b^{3} c^{3} + 16 \, a^{3} c^{4} + 8 \, a^{2} b c^{4} + a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} c^{2}} - \frac{{\left({\left(b^{6} c - 8 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} + 16 \, a^{2} b^{2} c^{3} + 8 \, a b^{3} c^{3} + b^{4} c^{3} - 4 \, a b^{2} c^{4} - {\left(b^{5} c - 8 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + 16 \, a^{2} b c^{3} + 8 \, a b^{2} c^{3} + b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} c g - 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} - 2 \, b^{4} c^{3} + 16 \, a^{2} b c^{4} + 8 \, a b^{2} c^{4} + b^{3} c^{4} - 4 \, a b c^{5} - {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} - 2 \, b^{3} c^{3} + 16 \, a^{2} c^{4} + 8 \, a b c^{4} + b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} c e + {\left(b^{6} c^{2} - 8 \, a b^{4} c^{3} - 2 \, b^{5} c^{3} + 16 \, a^{2} b^{2} c^{4} + 8 \, a b^{3} c^{4} + b^{4} c^{4} - 4 \, a b^{2} c^{5} + {\left(b^{5} c^{2} - 4 \, a b^{3} c^{3} - 2 \, b^{4} c^{3} + b^{3} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} g - 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} - 2 \, b^{4} c^{4} + 16 \, a^{2} b c^{5} + 8 \, a b^{2} c^{5} + b^{3} c^{5} - 4 \, a b c^{6} - {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4} - 2 \, b^{3} c^{4} + b^{2} c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} e\right)} \log\left(x^{2} + \frac{b c + \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{2 \, c^{2}}\right)}{16 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c^{3}} - \frac{{\left({\left(b^{6} c - 8 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} + 16 \, a^{2} b^{2} c^{3} + 8 \, a b^{3} c^{3} + b^{4} c^{3} - 4 \, a b^{2} c^{4} + {\left(b^{5} c - 8 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + 16 \, a^{2} b c^{3} + 8 \, a b^{2} c^{3} + b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} c g - 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} - 2 \, b^{4} c^{3} + 16 \, a^{2} b c^{4} + 8 \, a b^{2} c^{4} + b^{3} c^{4} - 4 \, a b c^{5} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} - 2 \, b^{3} c^{3} + 16 \, a^{2} c^{4} + 8 \, a b c^{4} + b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} c e + {\left(b^{6} c^{2} - 8 \, a b^{4} c^{3} - 2 \, b^{5} c^{3} + 16 \, a^{2} b^{2} c^{4} + 8 \, a b^{3} c^{4} + b^{4} c^{4} - 4 \, a b^{2} c^{5} + {\left(b^{5} c^{2} - 4 \, a b^{3} c^{3} - 2 \, b^{4} c^{3} + b^{3} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} g - 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} - 2 \, b^{4} c^{4} + 16 \, a^{2} b c^{5} + 8 \, a b^{2} c^{5} + b^{3} c^{5} - 4 \, a b c^{6} + {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4} - 2 \, b^{3} c^{4} + b^{2} c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} e\right)} \log\left(x^{2} + \frac{b c - \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{2 \, c^{2}}\right)}{16 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c^{3}}}{c}"," ",0,"h*x/c + integrate((c*g*x^3 + c*e*x + (c*f - b*h)*x^2 + c*d - a*h)/(c*x^4 + b*x^2 + a), x)/c","F",0
24,0,0,0,0.000000," ","integrate((i*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{i x^{2} + 2 \, h x}{2 \, c} - \frac{-\int \frac{{\left(c g - b i\right)} x^{3} + {\left(c f - b h\right)} x^{2} + c d - a h + {\left(c e - a i\right)} x}{c x^{4} + b x^{2} + a}\,{d x}}{c}"," ",0,"1/2*(i*x^2 + 2*h*x)/c - integrate(-((c*g - b*i)*x^3 + (c*f - b*h)*x^2 + c*d - a*h + (c*e - a*i)*x)/(c*x^4 + b*x^2 + a), x)/c","F",0
25,0,0,0,0.000000," ","integrate((m*x^8+l*x^7+k*x^6+j*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{12 \, c^{2} m x^{5} + 15 \, c^{2} l x^{4} + 20 \, {\left(c^{2} k - b c m\right)} x^{3} + 30 \, {\left(c^{2} j - b c l\right)} x^{2} + 60 \, {\left(c^{2} h - b c k + {\left(b^{2} - a c\right)} m\right)} x}{60 \, c^{3}} - \frac{-\int \frac{c^{3} d - a c^{2} h + a b c k + {\left(c^{3} g - b c^{2} j + {\left(b^{2} c - a c^{2}\right)} l\right)} x^{3} + {\left(c^{3} f - b c^{2} h + {\left(b^{2} c - a c^{2}\right)} k - {\left(b^{3} - 2 \, a b c\right)} m\right)} x^{2} - {\left(a b^{2} - a^{2} c\right)} m + {\left(c^{3} e - a c^{2} j + a b c l\right)} x}{c x^{4} + b x^{2} + a}\,{d x}}{c^{3}}"," ",0,"1/60*(12*c^2*m*x^5 + 15*c^2*l*x^4 + 20*(c^2*k - b*c*m)*x^3 + 30*(c^2*j - b*c*l)*x^2 + 60*(c^2*h - b*c*k + (b^2 - a*c)*m)*x)/c^3 - integrate(-(c^3*d - a*c^2*h + a*b*c*k + (c^3*g - b*c^2*j + (b^2*c - a*c^2)*l)*x^3 + (c^3*f - b*c^2*h + (b^2*c - a*c^2)*k - (b^3 - 2*a*b*c)*m)*x^2 - (a*b^2 - a^2*c)*m + (c^3*e - a*c^2*j + a*b*c*l)*x)/(c*x^4 + b*x^2 + a), x)/c^3","F",0
26,1,83,0,1.676604," ","integrate((e*x+d)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","\frac{1}{864} \, {\left(19 \, d - 32 \, e\right)} \log\left(x + 2\right) - \frac{1}{108} \, {\left(d - 4 \, e\right)} \log\left(x + 1\right) + \frac{1}{108} \, {\left(d + 4 \, e\right)} \log\left(x - 1\right) - \frac{1}{864} \, {\left(19 \, d + 32 \, e\right)} \log\left(x - 2\right) - \frac{5 \, d x^{3} + 8 \, e x^{2} - 17 \, d x - 20 \, e}{72 \, {\left(x^{4} - 5 \, x^{2} + 4\right)}}"," ",0,"1/864*(19*d - 32*e)*log(x + 2) - 1/108*(d - 4*e)*log(x + 1) + 1/108*(d + 4*e)*log(x - 1) - 1/864*(19*d + 32*e)*log(x - 2) - 1/72*(5*d*x^3 + 8*e*x^2 - 17*d*x - 20*e)/(x^4 - 5*x^2 + 4)","A",0
27,1,106,0,1.068035," ","integrate((f*x^2+e*x+d)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","\frac{1}{864} \, {\left(19 \, d - 32 \, e + 52 \, f\right)} \log\left(x + 2\right) - \frac{1}{108} \, {\left(d - 4 \, e + 7 \, f\right)} \log\left(x + 1\right) + \frac{1}{108} \, {\left(d + 4 \, e + 7 \, f\right)} \log\left(x - 1\right) - \frac{1}{864} \, {\left(19 \, d + 32 \, e + 52 \, f\right)} \log\left(x - 2\right) - \frac{{\left(5 \, d + 8 \, f\right)} x^{3} + 8 \, e x^{2} - {\left(17 \, d + 20 \, f\right)} x - 20 \, e}{72 \, {\left(x^{4} - 5 \, x^{2} + 4\right)}}"," ",0,"1/864*(19*d - 32*e + 52*f)*log(x + 2) - 1/108*(d - 4*e + 7*f)*log(x + 1) + 1/108*(d + 4*e + 7*f)*log(x - 1) - 1/864*(19*d + 32*e + 52*f)*log(x - 2) - 1/72*((5*d + 8*f)*x^3 + 8*e*x^2 - (17*d + 20*f)*x - 20*e)/(x^4 - 5*x^2 + 4)","A",0
28,1,127,0,0.970717," ","integrate((g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","\frac{1}{864} \, {\left(19 \, d - 32 \, e + 52 \, f - 80 \, g\right)} \log\left(x + 2\right) - \frac{1}{108} \, {\left(d - 4 \, e + 7 \, f - 10 \, g\right)} \log\left(x + 1\right) + \frac{1}{108} \, {\left(d + 4 \, e + 7 \, f + 10 \, g\right)} \log\left(x - 1\right) - \frac{1}{864} \, {\left(19 \, d + 32 \, e + 52 \, f + 80 \, g\right)} \log\left(x - 2\right) - \frac{{\left(5 \, d + 8 \, f\right)} x^{3} + 4 \, {\left(2 \, e + 5 \, g\right)} x^{2} - {\left(17 \, d + 20 \, f\right)} x - 20 \, e - 32 \, g}{72 \, {\left(x^{4} - 5 \, x^{2} + 4\right)}}"," ",0,"1/864*(19*d - 32*e + 52*f - 80*g)*log(x + 2) - 1/108*(d - 4*e + 7*f - 10*g)*log(x + 1) + 1/108*(d + 4*e + 7*f + 10*g)*log(x - 1) - 1/864*(19*d + 32*e + 52*f + 80*g)*log(x - 2) - 1/72*((5*d + 8*f)*x^3 + 4*(2*e + 5*g)*x^2 - (17*d + 20*f)*x - 20*e - 32*g)/(x^4 - 5*x^2 + 4)","A",0
29,1,145,0,1.182972," ","integrate((h*x^4+g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","\frac{1}{864} \, {\left(19 \, d - 32 \, e + 52 \, f - 80 \, g + 112 \, h\right)} \log\left(x + 2\right) - \frac{1}{108} \, {\left(d - 4 \, e + 7 \, f - 10 \, g + 13 \, h\right)} \log\left(x + 1\right) + \frac{1}{108} \, {\left(d + 4 \, e + 7 \, f + 10 \, g + 13 \, h\right)} \log\left(x - 1\right) - \frac{1}{864} \, {\left(19 \, d + 32 \, e + 52 \, f + 80 \, g + 112 \, h\right)} \log\left(x - 2\right) - \frac{{\left(5 \, d + 8 \, f + 20 \, h\right)} x^{3} + 4 \, {\left(2 \, e + 5 \, g\right)} x^{2} - {\left(17 \, d + 20 \, f + 32 \, h\right)} x - 20 \, e - 32 \, g}{72 \, {\left(x^{4} - 5 \, x^{2} + 4\right)}}"," ",0,"1/864*(19*d - 32*e + 52*f - 80*g + 112*h)*log(x + 2) - 1/108*(d - 4*e + 7*f - 10*g + 13*h)*log(x + 1) + 1/108*(d + 4*e + 7*f + 10*g + 13*h)*log(x - 1) - 1/864*(19*d + 32*e + 52*f + 80*g + 112*h)*log(x - 2) - 1/72*((5*d + 8*f + 20*h)*x^3 + 4*(2*e + 5*g)*x^2 - (17*d + 20*f + 32*h)*x - 20*e - 32*g)/(x^4 - 5*x^2 + 4)","A",0
30,1,163,0,1.349223," ","integrate((i*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","\frac{1}{864} \, {\left(19 \, d - 32 \, e + 52 \, f - 80 \, g + 112 \, h - 128 \, i\right)} \log\left(x + 2\right) - \frac{1}{108} \, {\left(d - 4 \, e + 7 \, f - 10 \, g + 13 \, h - 16 \, i\right)} \log\left(x + 1\right) + \frac{1}{108} \, {\left(d + 4 \, e + 7 \, f + 10 \, g + 13 \, h + 16 \, i\right)} \log\left(x - 1\right) - \frac{1}{864} \, {\left(19 \, d + 32 \, e + 52 \, f + 80 \, g + 112 \, h + 128 \, i\right)} \log\left(x - 2\right) - \frac{{\left(5 \, d + 8 \, f + 20 \, h\right)} x^{3} + 4 \, {\left(2 \, e + 5 \, g + 17 \, i\right)} x^{2} - {\left(17 \, d + 20 \, f + 32 \, h\right)} x - 20 \, e - 32 \, g - 80 \, i}{72 \, {\left(x^{4} - 5 \, x^{2} + 4\right)}}"," ",0,"1/864*(19*d - 32*e + 52*f - 80*g + 112*h - 128*i)*log(x + 2) - 1/108*(d - 4*e + 7*f - 10*g + 13*h - 16*i)*log(x + 1) + 1/108*(d + 4*e + 7*f + 10*g + 13*h + 16*i)*log(x - 1) - 1/864*(19*d + 32*e + 52*f + 80*g + 112*h + 128*i)*log(x - 2) - 1/72*((5*d + 8*f + 20*h)*x^3 + 4*(2*e + 5*g + 17*i)*x^2 - (17*d + 20*f + 32*h)*x - 20*e - 32*g - 80*i)/(x^4 - 5*x^2 + 4)","A",0
31,1,96,0,2.416965," ","integrate((e*x+d)/(x^4+x^2+1)^2,x, algorithm=""maxima"")","\frac{1}{9} \, \sqrt{3} {\left(d - 2 \, e\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{9} \, \sqrt{3} {\left(d + 2 \, e\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\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 x^{3} - 2 \, e x^{2} - d x - e}{6 \, {\left(x^{4} + x^{2} + 1\right)}}"," ",0,"1/9*sqrt(3)*(d - 2*e)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/9*sqrt(3)*(d + 2*e)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/4*d*log(x^2 + x + 1) - 1/4*d*log(x^2 - x + 1) - 1/6*(d*x^3 - 2*e*x^2 - d*x - e)/(x^4 + x^2 + 1)","A",0
32,1,120,0,2.390994," ","integrate((f*x^2+e*x+d)/(x^4+x^2+1)^2,x, algorithm=""maxima"")","\frac{1}{36} \, \sqrt{3} {\left(4 \, d - 8 \, e + f\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{36} \, \sqrt{3} {\left(4 \, d + 8 \, e + f\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{8} \, {\left(2 \, d - f\right)} \log\left(x^{2} + x + 1\right) - \frac{1}{8} \, {\left(2 \, d - f\right)} \log\left(x^{2} - x + 1\right) - \frac{{\left(d - 2 \, f\right)} x^{3} - 2 \, e x^{2} - {\left(d + f\right)} x - e}{6 \, {\left(x^{4} + x^{2} + 1\right)}}"," ",0,"1/36*sqrt(3)*(4*d - 8*e + f)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/36*sqrt(3)*(4*d + 8*e + f)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/8*(2*d - f)*log(x^2 + x + 1) - 1/8*(2*d - f)*log(x^2 - x + 1) - 1/6*((d - 2*f)*x^3 - 2*e*x^2 - (d + f)*x - e)/(x^4 + x^2 + 1)","A",0
33,1,135,0,2.581228," ","integrate((g*x^3+f*x^2+e*x+d)/(x^4+x^2+1)^2,x, algorithm=""maxima"")","\frac{1}{36} \, \sqrt{3} {\left(4 \, d - 8 \, e + f + 4 \, g\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{36} \, \sqrt{3} {\left(4 \, d + 8 \, e + f - 4 \, g\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{8} \, {\left(2 \, d - f\right)} \log\left(x^{2} + x + 1\right) - \frac{1}{8} \, {\left(2 \, d - f\right)} \log\left(x^{2} - x + 1\right) - \frac{{\left(d - 2 \, f\right)} x^{3} - {\left(2 \, e - g\right)} x^{2} - {\left(d + f\right)} x - e + 2 \, g}{6 \, {\left(x^{4} + x^{2} + 1\right)}}"," ",0,"1/36*sqrt(3)*(4*d - 8*e + f + 4*g)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/36*sqrt(3)*(4*d + 8*e + f - 4*g)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/8*(2*d - f)*log(x^2 + x + 1) - 1/8*(2*d - f)*log(x^2 - x + 1) - 1/6*((d - 2*f)*x^3 - (2*e - g)*x^2 - (d + f)*x - e + 2*g)/(x^4 + x^2 + 1)","A",0
34,1,143,0,2.951420," ","integrate((h*x^4+g*x^3+f*x^2+e*x+d)/(x^4+x^2+1)^2,x, algorithm=""maxima"")","\frac{1}{36} \, \sqrt{3} {\left(4 \, d - 8 \, e + f + 4 \, g + h\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{36} \, \sqrt{3} {\left(4 \, d + 8 \, e + f - 4 \, g + h\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{8} \, {\left(2 \, d - f + h\right)} \log\left(x^{2} + x + 1\right) - \frac{1}{8} \, {\left(2 \, d - f + h\right)} \log\left(x^{2} - x + 1\right) - \frac{{\left(d - 2 \, f + h\right)} x^{3} - {\left(2 \, e - g\right)} x^{2} - {\left(d + f - 2 \, h\right)} x - e + 2 \, g}{6 \, {\left(x^{4} + x^{2} + 1\right)}}"," ",0,"1/36*sqrt(3)*(4*d - 8*e + f + 4*g + h)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/36*sqrt(3)*(4*d + 8*e + f - 4*g + h)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/8*(2*d - f + h)*log(x^2 + x + 1) - 1/8*(2*d - f + h)*log(x^2 - x + 1) - 1/6*((d - 2*f + h)*x^3 - (2*e - g)*x^2 - (d + f - 2*h)*x - e + 2*g)/(x^4 + x^2 + 1)","A",0
35,1,155,0,2.627777," ","integrate((i*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(x^4+x^2+1)^2,x, algorithm=""maxima"")","\frac{1}{36} \, \sqrt{3} {\left(4 \, d - 8 \, e + f + 4 \, g + h - 8 \, i\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{36} \, \sqrt{3} {\left(4 \, d + 8 \, e + f - 4 \, g + h + 8 \, i\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{8} \, {\left(2 \, d - f + h\right)} \log\left(x^{2} + x + 1\right) - \frac{1}{8} \, {\left(2 \, d - f + h\right)} \log\left(x^{2} - x + 1\right) - \frac{{\left(d - 2 \, f + h\right)} x^{3} - {\left(2 \, e - g - i\right)} x^{2} - {\left(d + f - 2 \, h\right)} x - e + 2 \, g - i}{6 \, {\left(x^{4} + x^{2} + 1\right)}}"," ",0,"1/36*sqrt(3)*(4*d - 8*e + f + 4*g + h - 8*i)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/36*sqrt(3)*(4*d + 8*e + f - 4*g + h + 8*i)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/8*(2*d - f + h)*log(x^2 + x + 1) - 1/8*(2*d - f + h)*log(x^2 - x + 1) - 1/6*((d - 2*f + h)*x^3 - (2*e - g - i)*x^2 - (d + f - 2*h)*x - e + 2*g - i)/(x^4 + x^2 + 1)","A",0
36,0,0,0,0.000000," ","integrate((e*x+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{b c d x^{3} - 2 \, a c e x^{2} - a b e + {\left(b^{2} - 2 \, a c\right)} d x}{2 \, {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)}} + \frac{\frac{{\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 2 \, b^{6} c + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 28 \, a b^{4} c^{2} + 2 \, b^{5} c^{2} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 128 \, a^{2} b^{2} c^{3} - 24 \, a b^{3} c^{3} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 192 \, a^{3} c^{4} + 64 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c - 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} + 16 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} d \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c} + \frac{{\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 2 \, b^{6} c + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 28 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 128 \, a^{2} b^{2} c^{3} + 24 \, a b^{3} c^{3} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 192 \, a^{3} c^{4} - 64 \, a^{2} b c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c + 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} - 16 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} d \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c} + \frac{2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} - 2 \, a b c^{4} + a c^{5}\right)} \sqrt{b^{2} - 4 \, a c} e \log\left(x^{2} + \frac{b + \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} - \frac{2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} - 2 \, a b c^{4} + a c^{5}\right)} \sqrt{b^{2} - 4 \, a c} e \log\left(x^{2} + \frac{b - \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}}}{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}"," ",0,"1/2*(b*c*d*x^3 - 2*a*c*e*x^2 - a*b*e + (b^2 - 2*a*c)*d*x)/((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2) + 1/2*integrate((b*c*d*x^2 - 4*a*c*e*x + (b^2 - 6*a*c)*d)/(c*x^4 + b*x^2 + a), x)/(a*b^2 - 4*a^2*c)","F",0
37,0,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{2 \, a c e x^{2} - {\left(b c d - 2 \, a c f\right)} x^{3} + a b e + {\left(a b f - {\left(b^{2} - 2 \, a c\right)} d\right)} x}{2 \, {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)}} - \frac{-\frac{2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} - 2 \, a b c^{4} + a c^{5}\right)} \sqrt{b^{2} - 4 \, a c} e \log\left(x^{2} + \frac{b + \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} + \frac{2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} - 2 \, a b c^{4} + a c^{5}\right)} \sqrt{b^{2} - 4 \, a c} e \log\left(x^{2} + \frac{b - \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} - \frac{{\left({\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 2 \, b^{6} c + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 28 \, a b^{4} c^{2} + 2 \, b^{5} c^{2} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 128 \, a^{2} b^{2} c^{3} - 24 \, a b^{3} c^{3} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 192 \, a^{3} c^{4} + 64 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c - 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} + 16 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} d + {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, a b^{5} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 16 \, a^{2} b^{3} c^{2} + 2 \, a b^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 32 \, a^{3} b c^{3} - 32 \, a^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} f\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c} - \frac{{\left({\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 2 \, b^{6} c + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 28 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 128 \, a^{2} b^{2} c^{3} + 24 \, a b^{3} c^{3} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 192 \, a^{3} c^{4} - 64 \, a^{2} b c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c + 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} - 16 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} d + {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, a b^{5} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 16 \, a^{2} b^{3} c^{2} - 2 \, a b^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 32 \, a^{3} b c^{3} + 32 \, a^{3} c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} f\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c}}{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}"," ",0,"-1/2*(2*a*c*e*x^2 - (b*c*d - 2*a*c*f)*x^3 + a*b*e + (a*b*f - (b^2 - 2*a*c)*d)*x)/((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2) - 1/2*integrate((4*a*c*e*x - a*b*f - (b*c*d - 2*a*c*f)*x^2 - (b^2 - 6*a*c)*d)/(c*x^4 + b*x^2 + a), x)/(a*b^2 - 4*a^2*c)","F",0
38,0,0,0,0.000000," ","integrate((g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(b c d - 2 \, a c f\right)} x^{3} - a b e + 2 \, a^{2} g - {\left(2 \, a c e - a b g\right)} x^{2} - {\left(a b f - {\left(b^{2} - 2 \, a c\right)} d\right)} x}{2 \, {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)}} - \frac{-\int \frac{a b f + {\left(b c d - 2 \, a c f\right)} x^{2} + {\left(b^{2} - 6 \, a c\right)} d - 2 \, {\left(2 \, a c e - a b g\right)} x}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}"," ",0,"1/2*((b*c*d - 2*a*c*f)*x^3 - a*b*e + 2*a^2*g - (2*a*c*e - a*b*g)*x^2 - (a*b*f - (b^2 - 2*a*c)*d)*x)/((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2) - 1/2*integrate(-(a*b*f + (b*c*d - 2*a*c*f)*x^2 + (b^2 - 6*a*c)*d - 2*(2*a*c*e - a*b*g)*x)/(c*x^4 + b*x^2 + a), x)/(a*b^2 - 4*a^2*c)","F",0
39,0,0,0,0.000000," ","integrate((h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(b c d - 2 \, a c f + a b h\right)} x^{3} - a b e + 2 \, a^{2} g - {\left(2 \, a c e - a b g\right)} x^{2} - {\left(a b f - 2 \, a^{2} h - {\left(b^{2} - 2 \, a c\right)} d\right)} x}{2 \, {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)}} + \frac{\frac{{\left({\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 2 \, b^{6} c + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 28 \, a b^{4} c^{2} + 2 \, b^{5} c^{2} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 128 \, a^{2} b^{2} c^{3} - 24 \, a b^{3} c^{3} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 192 \, a^{3} c^{4} + 64 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c - 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} + 16 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} d + {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, a b^{5} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 16 \, a^{2} b^{3} c^{2} + 2 \, a b^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 32 \, a^{3} b c^{3} - 32 \, a^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} f - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, a^{2} b^{4} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 16 \, a^{3} b^{2} c^{2} + 4 \, a^{2} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 32 \, a^{4} c^{3} - 16 \, a^{3} b c^{3} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{2} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2}\right)} h\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c} + \frac{{\left({\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 2 \, b^{6} c + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 28 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 128 \, a^{2} b^{2} c^{3} + 24 \, a b^{3} c^{3} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 192 \, a^{3} c^{4} - 64 \, a^{2} b c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c + 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} - 16 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} d + {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, a b^{5} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 16 \, a^{2} b^{3} c^{2} - 2 \, a b^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 32 \, a^{3} b c^{3} + 32 \, a^{3} c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} f - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c + 2 \, a^{2} b^{4} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 16 \, a^{3} b^{2} c^{2} - 4 \, a^{2} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 32 \, a^{4} c^{3} + 16 \, a^{3} b c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2}\right)} h\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c} - \frac{{\left({\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3} - 2 \, a b^{2} c^{3} + a b c^{4}\right)} \sqrt{b^{2} - 4 \, a c} g - 2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} - 2 \, a b c^{4} + a c^{5}\right)} \sqrt{b^{2} - 4 \, a c} e\right)} \log\left(x^{2} + \frac{b + \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} + \frac{{\left({\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3} - 2 \, a b^{2} c^{3} + a b c^{4}\right)} \sqrt{b^{2} - 4 \, a c} g - 2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} - 2 \, a b c^{4} + a c^{5}\right)} \sqrt{b^{2} - 4 \, a c} e\right)} \log\left(x^{2} + \frac{b - \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}}}{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}"," ",0,"1/2*((b*c*d - 2*a*c*f + a*b*h)*x^3 - a*b*e + 2*a^2*g - (2*a*c*e - a*b*g)*x^2 - (a*b*f - 2*a^2*h - (b^2 - 2*a*c)*d)*x)/((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2) + 1/2*integrate((a*b*f - 2*a^2*h + (b*c*d - 2*a*c*f + a*b*h)*x^2 + (b^2 - 6*a*c)*d - 2*(2*a*c*e - a*b*g)*x)/(c*x^4 + b*x^2 + a), x)/(a*b^2 - 4*a^2*c)","F",0
40,0,0,0,0.000000," ","integrate((i*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{a b c e - 2 \, a^{2} c g + a^{2} b i - {\left(b c^{2} d - 2 \, a c^{2} f + a b c h\right)} x^{3} + {\left(2 \, a c^{2} e - a b c g + {\left(a b^{2} - 2 \, a^{2} c\right)} i\right)} x^{2} + {\left(a b c f - 2 \, a^{2} c h - {\left(b^{2} c - 2 \, a c^{2}\right)} d\right)} x}{2 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} x^{4} + {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} x^{2}\right)}} + \frac{\frac{2 \, {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} - 2 \, a^{2} b c^{3} + a^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c} i \log\left(x^{2} + \frac{b + \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} - \frac{2 \, {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} - 2 \, a^{2} b c^{3} + a^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c} i \log\left(x^{2} + \frac{b - \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} + \frac{{\left({\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 2 \, b^{6} c + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 28 \, a b^{4} c^{2} + 2 \, b^{5} c^{2} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 128 \, a^{2} b^{2} c^{3} - 24 \, a b^{3} c^{3} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 192 \, a^{3} c^{4} + 64 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c - 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} + 16 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} d + {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, a b^{5} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 16 \, a^{2} b^{3} c^{2} + 2 \, a b^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 32 \, a^{3} b c^{3} - 32 \, a^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} f - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, a^{2} b^{4} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 16 \, a^{3} b^{2} c^{2} + 4 \, a^{2} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 32 \, a^{4} c^{3} - 16 \, a^{3} b c^{3} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{2} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2}\right)} h\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c} + \frac{{\left({\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 2 \, b^{6} c + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 28 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 128 \, a^{2} b^{2} c^{3} + 24 \, a b^{3} c^{3} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 192 \, a^{3} c^{4} - 64 \, a^{2} b c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c + 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} - 16 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} d + {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, a b^{5} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 16 \, a^{2} b^{3} c^{2} - 2 \, a b^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 32 \, a^{3} b c^{3} + 32 \, a^{3} c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} f - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c + 2 \, a^{2} b^{4} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 16 \, a^{3} b^{2} c^{2} - 4 \, a^{2} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 32 \, a^{4} c^{3} + 16 \, a^{3} b c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2}\right)} h\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c} - \frac{{\left({\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3} - 2 \, a b^{2} c^{3} + a b c^{4}\right)} \sqrt{b^{2} - 4 \, a c} g - 2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} - 2 \, a b c^{4} + a c^{5}\right)} \sqrt{b^{2} - 4 \, a c} e\right)} \log\left(x^{2} + \frac{b + \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} + \frac{{\left({\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3} - 2 \, a b^{2} c^{3} + a b c^{4}\right)} \sqrt{b^{2} - 4 \, a c} g - 2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} - 2 \, a b c^{4} + a c^{5}\right)} \sqrt{b^{2} - 4 \, a c} e\right)} \log\left(x^{2} + \frac{b - \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}}}{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}"," ",0,"-1/2*(a*b*c*e - 2*a^2*c*g + a^2*b*i - (b*c^2*d - 2*a*c^2*f + a*b*c*h)*x^3 + (2*a*c^2*e - a*b*c*g + (a*b^2 - 2*a^2*c)*i)*x^2 + (a*b*c*f - 2*a^2*c*h - (b^2*c - 2*a*c^2)*d)*x)/(a^2*b^2*c - 4*a^3*c^2 + (a*b^2*c^2 - 4*a^2*c^3)*x^4 + (a*b^3*c - 4*a^2*b*c^2)*x^2) + 1/2*integrate((a*b*f - 2*a^2*h + (b*c*d - 2*a*c*f + a*b*h)*x^2 + (b^2 - 6*a*c)*d - 2*(2*a*c*e - a*b*g + 2*a^2*i)*x)/(c*x^4 + b*x^2 + a), x)/(a*b^2 - 4*a^2*c)","F",0
41,0,0,0,0.000000," ","integrate((m*x^8+l*x^7+k*x^6+j*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{a b c^{2} e - 2 \, a^{2} c^{2} g + a^{2} b c j - {\left(b c^{3} d - 2 \, a c^{3} f + a b c^{2} h - {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} k + {\left(a b^{3} - 3 \, a^{2} b c\right)} m\right)} x^{3} + {\left(2 \, a c^{3} e - a b c^{2} g + {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} j - {\left(a b^{3} - 3 \, a^{2} b c\right)} l\right)} x^{2} - {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} l + {\left(a b c^{2} f - 2 \, a^{2} c^{2} h + a^{2} b c k - {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d - {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} m\right)} x}{2 \, {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} + {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} x^{4} + {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} x^{2}\right)}} + \frac{m x}{c^{2}} - \frac{-\int \frac{a b c^{2} f - 2 \, a^{2} c^{2} h + a^{2} b c k + 2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} l x^{3} + {\left(b c^{3} d - 2 \, a c^{3} f + a b c^{2} h + {\left(a b^{2} c - 6 \, a^{2} c^{2}\right)} k - {\left(3 \, a b^{3} - 13 \, a^{2} b c\right)} m\right)} x^{2} + {\left(b^{2} c^{2} - 6 \, a c^{3}\right)} d - {\left(3 \, a^{2} b^{2} - 10 \, a^{3} c\right)} m - 2 \, {\left(2 \, a c^{3} e - a b c^{2} g + 2 \, a^{2} c^{2} j - a^{2} b c l\right)} x}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)}}"," ",0,"-1/2*(a*b*c^2*e - 2*a^2*c^2*g + a^2*b*c*j - (b*c^3*d - 2*a*c^3*f + a*b*c^2*h - (a*b^2*c - 2*a^2*c^2)*k + (a*b^3 - 3*a^2*b*c)*m)*x^3 + (2*a*c^3*e - a*b*c^2*g + (a*b^2*c - 2*a^2*c^2)*j - (a*b^3 - 3*a^2*b*c)*l)*x^2 - (a^2*b^2 - 2*a^3*c)*l + (a*b*c^2*f - 2*a^2*c^2*h + a^2*b*c*k - (b^2*c^2 - 2*a*c^3)*d - (a^2*b^2 - 2*a^3*c)*m)*x)/(a^2*b^2*c^2 - 4*a^3*c^3 + (a*b^2*c^3 - 4*a^2*c^4)*x^4 + (a*b^3*c^2 - 4*a^2*b*c^3)*x^2) + m*x/c^2 - 1/2*integrate(-(a*b*c^2*f - 2*a^2*c^2*h + a^2*b*c*k + 2*(a*b^2*c - 4*a^2*c^2)*l*x^3 + (b*c^3*d - 2*a*c^3*f + a*b*c^2*h + (a*b^2*c - 6*a^2*c^2)*k - (3*a*b^3 - 13*a^2*b*c)*m)*x^2 + (b^2*c^2 - 6*a*c^3)*d - (3*a^2*b^2 - 10*a^3*c)*m - 2*(2*a*c^3*e - a*b*c^2*g + 2*a^2*c^2*j - a^2*b*c*l)*x)/(c*x^4 + b*x^2 + a), x)/(a*b^2*c^2 - 4*a^2*c^3)","F",0
42,1,121,0,1.061808," ","integrate((e*x+d)/(x^4-5*x^2+4)^3,x, algorithm=""maxima"")","-\frac{1}{41472} \, {\left(313 \, d - 512 \, e\right)} \log\left(x + 2\right) + \frac{1}{1296} \, {\left(13 \, d - 16 \, e\right)} \log\left(x + 1\right) - \frac{1}{1296} \, {\left(13 \, d + 16 \, e\right)} \log\left(x - 1\right) + \frac{1}{41472} \, {\left(313 \, d + 512 \, e\right)} \log\left(x - 2\right) + \frac{35 \, d x^{7} + 128 \, e x^{6} - 234 \, d x^{5} - 960 \, e x^{4} + 315 \, d x^{3} + 1920 \, e x^{2} + 172 \, d x - 800 \, e}{3456 \, {\left(x^{8} - 10 \, x^{6} + 33 \, x^{4} - 40 \, x^{2} + 16\right)}}"," ",0,"-1/41472*(313*d - 512*e)*log(x + 2) + 1/1296*(13*d - 16*e)*log(x + 1) - 1/1296*(13*d + 16*e)*log(x - 1) + 1/41472*(313*d + 512*e)*log(x - 2) + 1/3456*(35*d*x^7 + 128*e*x^6 - 234*d*x^5 - 960*e*x^4 + 315*d*x^3 + 1920*e*x^2 + 172*d*x - 800*e)/(x^8 - 10*x^6 + 33*x^4 - 40*x^2 + 16)","A",0
43,1,155,0,1.098456," ","integrate((f*x^2+e*x+d)/(x^4-5*x^2+4)^3,x, algorithm=""maxima"")","-\frac{1}{41472} \, {\left(313 \, d - 512 \, e + 820 \, f\right)} \log\left(x + 2\right) + \frac{1}{1296} \, {\left(13 \, d - 16 \, e + 25 \, f\right)} \log\left(x + 1\right) - \frac{1}{1296} \, {\left(13 \, d + 16 \, e + 25 \, f\right)} \log\left(x - 1\right) + \frac{1}{41472} \, {\left(313 \, d + 512 \, e + 820 \, f\right)} \log\left(x - 2\right) + \frac{35 \, {\left(d + 4 \, f\right)} x^{7} + 128 \, e x^{6} - 18 \, {\left(13 \, d + 60 \, f\right)} x^{5} - 960 \, e x^{4} + 63 \, {\left(5 \, d + 36 \, f\right)} x^{3} + 1920 \, e x^{2} + 4 \, {\left(43 \, d - 260 \, f\right)} x - 800 \, e}{3456 \, {\left(x^{8} - 10 \, x^{6} + 33 \, x^{4} - 40 \, x^{2} + 16\right)}}"," ",0,"-1/41472*(313*d - 512*e + 820*f)*log(x + 2) + 1/1296*(13*d - 16*e + 25*f)*log(x + 1) - 1/1296*(13*d + 16*e + 25*f)*log(x - 1) + 1/41472*(313*d + 512*e + 820*f)*log(x - 2) + 1/3456*(35*(d + 4*f)*x^7 + 128*e*x^6 - 18*(13*d + 60*f)*x^5 - 960*e*x^4 + 63*(5*d + 36*f)*x^3 + 1920*e*x^2 + 4*(43*d - 260*f)*x - 800*e)/(x^8 - 10*x^6 + 33*x^4 - 40*x^2 + 16)","A",0
44,1,188,0,1.082215," ","integrate((g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4)^3,x, algorithm=""maxima"")","-\frac{1}{41472} \, {\left(313 \, d - 512 \, e + 820 \, f - 1280 \, g\right)} \log\left(x + 2\right) + \frac{1}{1296} \, {\left(13 \, d - 16 \, e + 25 \, f - 40 \, g\right)} \log\left(x + 1\right) - \frac{1}{1296} \, {\left(13 \, d + 16 \, e + 25 \, f + 40 \, g\right)} \log\left(x - 1\right) + \frac{1}{41472} \, {\left(313 \, d + 512 \, e + 820 \, f + 1280 \, g\right)} \log\left(x - 2\right) + \frac{35 \, {\left(d + 4 \, f\right)} x^{7} + 64 \, {\left(2 \, e + 5 \, g\right)} x^{6} - 18 \, {\left(13 \, d + 60 \, f\right)} x^{5} - 480 \, {\left(2 \, e + 5 \, g\right)} x^{4} + 63 \, {\left(5 \, d + 36 \, f\right)} x^{3} + 960 \, {\left(2 \, e + 5 \, g\right)} x^{2} + 4 \, {\left(43 \, d - 260 \, f\right)} x - 800 \, e - 2432 \, g}{3456 \, {\left(x^{8} - 10 \, x^{6} + 33 \, x^{4} - 40 \, x^{2} + 16\right)}}"," ",0,"-1/41472*(313*d - 512*e + 820*f - 1280*g)*log(x + 2) + 1/1296*(13*d - 16*e + 25*f - 40*g)*log(x + 1) - 1/1296*(13*d + 16*e + 25*f + 40*g)*log(x - 1) + 1/41472*(313*d + 512*e + 820*f + 1280*g)*log(x - 2) + 1/3456*(35*(d + 4*f)*x^7 + 64*(2*e + 5*g)*x^6 - 18*(13*d + 60*f)*x^5 - 480*(2*e + 5*g)*x^4 + 63*(5*d + 36*f)*x^3 + 960*(2*e + 5*g)*x^2 + 4*(43*d - 260*f)*x - 800*e - 2432*g)/(x^8 - 10*x^6 + 33*x^4 - 40*x^2 + 16)","A",0
45,1,214,0,1.064709," ","integrate((h*x^4+g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4)^3,x, algorithm=""maxima"")","-\frac{1}{41472} \, {\left(313 \, d - 512 \, e + 820 \, f - 1280 \, g + 1936 \, h\right)} \log\left(x + 2\right) + \frac{1}{1296} \, {\left(13 \, d - 16 \, e + 25 \, f - 40 \, g + 61 \, h\right)} \log\left(x + 1\right) - \frac{1}{1296} \, {\left(13 \, d + 16 \, e + 25 \, f + 40 \, g + 61 \, h\right)} \log\left(x - 1\right) + \frac{1}{41472} \, {\left(313 \, d + 512 \, e + 820 \, f + 1280 \, g + 1936 \, h\right)} \log\left(x - 2\right) + \frac{5 \, {\left(7 \, d + 28 \, f + 64 \, h\right)} x^{7} + 64 \, {\left(2 \, e + 5 \, g\right)} x^{6} - 18 \, {\left(13 \, d + 60 \, f + 136 \, h\right)} x^{5} - 480 \, {\left(2 \, e + 5 \, g\right)} x^{4} + 63 \, {\left(5 \, d + 36 \, f + 80 \, h\right)} x^{3} + 960 \, {\left(2 \, e + 5 \, g\right)} x^{2} + 4 \, {\left(43 \, d - 260 \, f - 656 \, h\right)} x - 800 \, e - 2432 \, g}{3456 \, {\left(x^{8} - 10 \, x^{6} + 33 \, x^{4} - 40 \, x^{2} + 16\right)}}"," ",0,"-1/41472*(313*d - 512*e + 820*f - 1280*g + 1936*h)*log(x + 2) + 1/1296*(13*d - 16*e + 25*f - 40*g + 61*h)*log(x + 1) - 1/1296*(13*d + 16*e + 25*f + 40*g + 61*h)*log(x - 1) + 1/41472*(313*d + 512*e + 820*f + 1280*g + 1936*h)*log(x - 2) + 1/3456*(5*(7*d + 28*f + 64*h)*x^7 + 64*(2*e + 5*g)*x^6 - 18*(13*d + 60*f + 136*h)*x^5 - 480*(2*e + 5*g)*x^4 + 63*(5*d + 36*f + 80*h)*x^3 + 960*(2*e + 5*g)*x^2 + 4*(43*d - 260*f - 656*h)*x - 800*e - 2432*g)/(x^8 - 10*x^6 + 33*x^4 - 40*x^2 + 16)","A",0
46,1,238,0,1.116886," ","integrate((i*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4)^3,x, algorithm=""maxima"")","-\frac{1}{41472} \, {\left(313 \, d - 512 \, e + 820 \, f - 1280 \, g + 1936 \, h - 2816 \, i\right)} \log\left(x + 2\right) + \frac{1}{1296} \, {\left(13 \, d - 16 \, e + 25 \, f - 40 \, g + 61 \, h - 88 \, i\right)} \log\left(x + 1\right) - \frac{1}{1296} \, {\left(13 \, d + 16 \, e + 25 \, f + 40 \, g + 61 \, h + 88 \, i\right)} \log\left(x - 1\right) + \frac{1}{41472} \, {\left(313 \, d + 512 \, e + 820 \, f + 1280 \, g + 1936 \, h + 2816 \, i\right)} \log\left(x - 2\right) + \frac{5 \, {\left(7 \, d + 28 \, f + 64 \, h\right)} x^{7} + 64 \, {\left(2 \, e + 5 \, g + 11 \, i\right)} x^{6} - 18 \, {\left(13 \, d + 60 \, f + 136 \, h\right)} x^{5} - 480 \, {\left(2 \, e + 5 \, g + 11 \, i\right)} x^{4} + 63 \, {\left(5 \, d + 36 \, f + 80 \, h\right)} x^{3} + 192 \, {\left(10 \, e + 25 \, g + 52 \, i\right)} x^{2} + 4 \, {\left(43 \, d - 260 \, f - 656 \, h\right)} x - 800 \, e - 2432 \, g - 5120 \, i}{3456 \, {\left(x^{8} - 10 \, x^{6} + 33 \, x^{4} - 40 \, x^{2} + 16\right)}}"," ",0,"-1/41472*(313*d - 512*e + 820*f - 1280*g + 1936*h - 2816*i)*log(x + 2) + 1/1296*(13*d - 16*e + 25*f - 40*g + 61*h - 88*i)*log(x + 1) - 1/1296*(13*d + 16*e + 25*f + 40*g + 61*h + 88*i)*log(x - 1) + 1/41472*(313*d + 512*e + 820*f + 1280*g + 1936*h + 2816*i)*log(x - 2) + 1/3456*(5*(7*d + 28*f + 64*h)*x^7 + 64*(2*e + 5*g + 11*i)*x^6 - 18*(13*d + 60*f + 136*h)*x^5 - 480*(2*e + 5*g + 11*i)*x^4 + 63*(5*d + 36*f + 80*h)*x^3 + 192*(10*e + 25*g + 52*i)*x^2 + 4*(43*d - 260*f - 656*h)*x - 800*e - 2432*g - 5120*i)/(x^8 - 10*x^6 + 33*x^4 - 40*x^2 + 16)","A",0
47,1,137,0,2.554173," ","integrate((e*x+d)/(x^4+x^2+1)^3,x, algorithm=""maxima"")","\frac{1}{144} \, \sqrt{3} {\left(13 \, d - 32 \, e\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{144} \, \sqrt{3} {\left(13 \, d + 32 \, e\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{9}{32} \, d \log\left(x^{2} + x + 1\right) - \frac{9}{32} \, d \log\left(x^{2} - x + 1\right) - \frac{7 \, d x^{7} - 8 \, e x^{6} + 5 \, d x^{5} - 12 \, e x^{4} + 7 \, d x^{3} - 16 \, e x^{2} - 4 \, d x - 6 \, e}{24 \, {\left(x^{8} + 2 \, x^{6} + 3 \, x^{4} + 2 \, x^{2} + 1\right)}}"," ",0,"1/144*sqrt(3)*(13*d - 32*e)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/144*sqrt(3)*(13*d + 32*e)*arctan(1/3*sqrt(3)*(2*x - 1)) + 9/32*d*log(x^2 + x + 1) - 9/32*d*log(x^2 - x + 1) - 1/24*(7*d*x^7 - 8*e*x^6 + 5*d*x^5 - 12*e*x^4 + 7*d*x^3 - 16*e*x^2 - 4*d*x - 6*e)/(x^8 + 2*x^6 + 3*x^4 + 2*x^2 + 1)","A",0
48,1,173,0,2.568342," ","integrate((f*x^2+e*x+d)/(x^4+x^2+1)^3,x, algorithm=""maxima"")","\frac{1}{144} \, \sqrt{3} {\left(13 \, d - 32 \, e + 2 \, f\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{144} \, \sqrt{3} {\left(13 \, d + 32 \, e + 2 \, f\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{32} \, {\left(9 \, d - 4 \, f\right)} \log\left(x^{2} + x + 1\right) - \frac{1}{32} \, {\left(9 \, d - 4 \, f\right)} \log\left(x^{2} - x + 1\right) - \frac{7 \, {\left(d - f\right)} x^{7} - 8 \, e x^{6} + 5 \, {\left(d - 2 \, f\right)} x^{5} - 12 \, e x^{4} + 7 \, {\left(d - 2 \, f\right)} x^{3} - 16 \, e x^{2} - {\left(4 \, d + 5 \, f\right)} x - 6 \, e}{24 \, {\left(x^{8} + 2 \, x^{6} + 3 \, x^{4} + 2 \, x^{2} + 1\right)}}"," ",0,"1/144*sqrt(3)*(13*d - 32*e + 2*f)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/144*sqrt(3)*(13*d + 32*e + 2*f)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/32*(9*d - 4*f)*log(x^2 + x + 1) - 1/32*(9*d - 4*f)*log(x^2 - x + 1) - 1/24*(7*(d - f)*x^7 - 8*e*x^6 + 5*(d - 2*f)*x^5 - 12*e*x^4 + 7*(d - 2*f)*x^3 - 16*e*x^2 - (4*d + 5*f)*x - 6*e)/(x^8 + 2*x^6 + 3*x^4 + 2*x^2 + 1)","A",0
49,1,200,0,2.606206," ","integrate((g*x^3+f*x^2+e*x+d)/(x^4+x^2+1)^3,x, algorithm=""maxima"")","\frac{1}{144} \, \sqrt{3} {\left(13 \, d - 32 \, e + 2 \, f + 16 \, g\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{144} \, \sqrt{3} {\left(13 \, d + 32 \, e + 2 \, f - 16 \, g\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{32} \, {\left(9 \, d - 4 \, f\right)} \log\left(x^{2} + x + 1\right) - \frac{1}{32} \, {\left(9 \, d - 4 \, f\right)} \log\left(x^{2} - x + 1\right) - \frac{7 \, {\left(d - f\right)} x^{7} - 4 \, {\left(2 \, e - g\right)} x^{6} + 5 \, {\left(d - 2 \, f\right)} x^{5} - 6 \, {\left(2 \, e - g\right)} x^{4} + 7 \, {\left(d - 2 \, f\right)} x^{3} - 8 \, {\left(2 \, e - g\right)} x^{2} - {\left(4 \, d + 5 \, f\right)} x - 6 \, e + 6 \, g}{24 \, {\left(x^{8} + 2 \, x^{6} + 3 \, x^{4} + 2 \, x^{2} + 1\right)}}"," ",0,"1/144*sqrt(3)*(13*d - 32*e + 2*f + 16*g)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/144*sqrt(3)*(13*d + 32*e + 2*f - 16*g)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/32*(9*d - 4*f)*log(x^2 + x + 1) - 1/32*(9*d - 4*f)*log(x^2 - x + 1) - 1/24*(7*(d - f)*x^7 - 4*(2*e - g)*x^6 + 5*(d - 2*f)*x^5 - 6*(2*e - g)*x^4 + 7*(d - 2*f)*x^3 - 8*(2*e - g)*x^2 - (4*d + 5*f)*x - 6*e + 6*g)/(x^8 + 2*x^6 + 3*x^4 + 2*x^2 + 1)","A",0
50,1,217,0,3.146861," ","integrate((h*x^4+g*x^3+f*x^2+e*x+d)/(x^4+x^2+1)^3,x, algorithm=""maxima"")","\frac{1}{144} \, \sqrt{3} {\left(13 \, d - 32 \, e + 2 \, f + 16 \, g + h\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{144} \, \sqrt{3} {\left(13 \, d + 32 \, e + 2 \, f - 16 \, g + h\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{32} \, {\left(9 \, d - 4 \, f + 3 \, h\right)} \log\left(x^{2} + x + 1\right) - \frac{1}{32} \, {\left(9 \, d - 4 \, f + 3 \, h\right)} \log\left(x^{2} - x + 1\right) - \frac{{\left(7 \, d - 7 \, f + 4 \, h\right)} x^{7} - 4 \, {\left(2 \, e - g\right)} x^{6} + 5 \, {\left(d - 2 \, f + h\right)} x^{5} - 6 \, {\left(2 \, e - g\right)} x^{4} + 7 \, {\left(d - 2 \, f + h\right)} x^{3} - 8 \, {\left(2 \, e - g\right)} x^{2} - {\left(4 \, d + 5 \, f - 5 \, h\right)} x - 6 \, e + 6 \, g}{24 \, {\left(x^{8} + 2 \, x^{6} + 3 \, x^{4} + 2 \, x^{2} + 1\right)}}"," ",0,"1/144*sqrt(3)*(13*d - 32*e + 2*f + 16*g + h)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/144*sqrt(3)*(13*d + 32*e + 2*f - 16*g + h)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/32*(9*d - 4*f + 3*h)*log(x^2 + x + 1) - 1/32*(9*d - 4*f + 3*h)*log(x^2 - x + 1) - 1/24*((7*d - 7*f + 4*h)*x^7 - 4*(2*e - g)*x^6 + 5*(d - 2*f + h)*x^5 - 6*(2*e - g)*x^4 + 7*(d - 2*f + h)*x^3 - 8*(2*e - g)*x^2 - (4*d + 5*f - 5*h)*x - 6*e + 6*g)/(x^8 + 2*x^6 + 3*x^4 + 2*x^2 + 1)","A",0
51,1,229,0,2.119941," ","integrate((i*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(x^4+x^2+1)^3,x, algorithm=""maxima"")","\frac{1}{144} \, \sqrt{3} {\left(13 \, d - 32 \, e + 2 \, f + 16 \, g + h - 16 \, i\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{144} \, \sqrt{3} {\left(13 \, d + 32 \, e + 2 \, f - 16 \, g + h + 16 \, i\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{32} \, {\left(9 \, d - 4 \, f + 3 \, h\right)} \log\left(x^{2} + x + 1\right) - \frac{1}{32} \, {\left(9 \, d - 4 \, f + 3 \, h\right)} \log\left(x^{2} - x + 1\right) - \frac{{\left(7 \, d - 7 \, f + 4 \, h\right)} x^{7} - 4 \, {\left(2 \, e - g + i\right)} x^{6} + 5 \, {\left(d - 2 \, f + h\right)} x^{5} - 6 \, {\left(2 \, e - g + i\right)} x^{4} + 7 \, {\left(d - 2 \, f + h\right)} x^{3} - 4 \, {\left(4 \, e - 2 \, g + i\right)} x^{2} - {\left(4 \, d + 5 \, f - 5 \, h\right)} x - 6 \, e + 6 \, g - 4 \, i}{24 \, {\left(x^{8} + 2 \, x^{6} + 3 \, x^{4} + 2 \, x^{2} + 1\right)}}"," ",0,"1/144*sqrt(3)*(13*d - 32*e + 2*f + 16*g + h - 16*i)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/144*sqrt(3)*(13*d + 32*e + 2*f - 16*g + h + 16*i)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/32*(9*d - 4*f + 3*h)*log(x^2 + x + 1) - 1/32*(9*d - 4*f + 3*h)*log(x^2 - x + 1) - 1/24*((7*d - 7*f + 4*h)*x^7 - 4*(2*e - g + i)*x^6 + 5*(d - 2*f + h)*x^5 - 6*(2*e - g + i)*x^4 + 7*(d - 2*f + h)*x^3 - 4*(4*e - 2*g + i)*x^2 - (4*d + 5*f - 5*h)*x - 6*e + 6*g - 4*i)/(x^8 + 2*x^6 + 3*x^4 + 2*x^2 + 1)","A",0
52,0,0,0,0.000000," ","integrate((e*x+d)/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{24 \, a^{2} c^{3} e x^{6} + 36 \, a^{2} b c^{2} e x^{4} + 3 \, {\left(b^{3} c^{2} - 8 \, a b c^{3}\right)} d x^{7} + {\left(6 \, b^{4} c - 49 \, a b^{2} c^{2} + 28 \, a^{2} c^{3}\right)} d x^{5} + {\left(3 \, b^{5} - 20 \, a b^{3} c - 4 \, a^{2} b c^{2}\right)} d x^{3} + 8 \, {\left(a^{2} b^{2} c + 5 \, a^{3} c^{2}\right)} e x^{2} + {\left(5 \, a b^{4} - 37 \, a^{2} b^{2} c + 44 \, a^{3} c^{2}\right)} d x - 2 \, {\left(a^{2} b^{3} - 10 \, a^{3} b c\right)} e}{8 \, {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{8} + a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2}\right)}} - \frac{-3 \, \int \frac{16 \, a^{2} c^{2} e x + {\left(b^{3} c - 8 \, a b c^{2}\right)} d x^{2} + {\left(b^{4} - 9 \, a b^{2} c + 28 \, a^{2} c^{2}\right)} d}{c x^{4} + b x^{2} + a}\,{d x}}{8 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)}}"," ",0,"1/8*(24*a^2*c^3*e*x^6 + 36*a^2*b*c^2*e*x^4 + 3*(b^3*c^2 - 8*a*b*c^3)*d*x^7 + (6*b^4*c - 49*a*b^2*c^2 + 28*a^2*c^3)*d*x^5 + (3*b^5 - 20*a*b^3*c - 4*a^2*b*c^2)*d*x^3 + 8*(a^2*b^2*c + 5*a^3*c^2)*e*x^2 + (5*a*b^4 - 37*a^2*b^2*c + 44*a^3*c^2)*d*x - 2*(a^2*b^3 - 10*a^3*b*c)*e)/((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^8 + a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2) - 3/8*integrate(-(16*a^2*c^2*e*x + (b^3*c - 8*a*b*c^2)*d*x^2 + (b^4 - 9*a*b^2*c + 28*a^2*c^2)*d)/(c*x^4 + b*x^2 + a), x)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)","F",0
53,0,0,0,0.000000," ","integrate((f*x^2+e*x+d)/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{24 \, a^{2} c^{3} e x^{6} + 36 \, a^{2} b c^{2} e x^{4} + {\left(3 \, {\left(b^{3} c^{2} - 8 \, a b c^{3}\right)} d + {\left(a b^{2} c^{2} + 20 \, a^{2} c^{3}\right)} f\right)} x^{7} + {\left({\left(6 \, b^{4} c - 49 \, a b^{2} c^{2} + 28 \, a^{2} c^{3}\right)} d + 2 \, {\left(a b^{3} c + 14 \, a^{2} b c^{2}\right)} f\right)} x^{5} + 8 \, {\left(a^{2} b^{2} c + 5 \, a^{3} c^{2}\right)} e x^{2} + {\left({\left(3 \, b^{5} - 20 \, a b^{3} c - 4 \, a^{2} b c^{2}\right)} d + {\left(a b^{4} + 5 \, a^{2} b^{2} c + 36 \, a^{3} c^{2}\right)} f\right)} x^{3} - 2 \, {\left(a^{2} b^{3} - 10 \, a^{3} b c\right)} e + {\left({\left(5 \, a b^{4} - 37 \, a^{2} b^{2} c + 44 \, a^{3} c^{2}\right)} d - {\left(a^{2} b^{3} - 16 \, a^{3} b c\right)} f\right)} x}{8 \, {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{8} + a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2}\right)}} + \frac{-\frac{24 \, {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5} - 2 \, a^{2} b c^{5} + a^{2} c^{6}\right)} \sqrt{b^{2} - 4 \, a c} e \log\left(x^{2} + \frac{b + \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} + \frac{24 \, {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5} - 2 \, a^{2} b c^{5} + a^{2} c^{6}\right)} \sqrt{b^{2} - 4 \, a c} e \log\left(x^{2} + \frac{b - \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} + \frac{{\left(3 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} - 17 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c - 2 \, b^{8} c + 116 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 26 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 34 \, a b^{6} c^{2} + 2 \, b^{7} c^{2} - 368 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 13 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 232 \, a^{2} b^{4} c^{3} - 30 \, a b^{5} c^{3} + 448 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 224 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 736 \, a^{3} b^{2} c^{4} + 176 \, a^{2} b^{3} c^{4} - 112 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} - 896 \, a^{4} c^{5} - 352 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 15 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c - 26 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} + 22 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 224 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} - 88 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} d + {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, a b^{7} c + 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 40 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 48 \, a^{2} b^{5} c^{2} + 2 \, a b^{6} c^{2} - 256 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 288 \, a^{3} b^{3} c^{3} - 44 \, a^{2} b^{4} c^{3} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 512 \, a^{4} b c^{4} + 64 \, a^{3} b^{2} c^{4} + 320 \, a^{4} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} - 36 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c - 40 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3} + 36 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} + 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} f\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c} + \frac{{\left(3 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} - 17 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c + 2 \, b^{8} c + 116 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 26 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} - 34 \, a b^{6} c^{2} - 2 \, b^{7} c^{2} - 368 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 13 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 232 \, a^{2} b^{4} c^{3} + 30 \, a b^{5} c^{3} + 448 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 224 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 736 \, a^{3} b^{2} c^{4} - 176 \, a^{2} b^{3} c^{4} - 112 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 896 \, a^{4} c^{5} + 352 \, a^{3} b c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} - 15 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c + 26 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 22 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} + 224 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} + 88 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} d + {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c + 2 \, a b^{7} c + 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 40 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 48 \, a^{2} b^{5} c^{2} - 2 \, a b^{6} c^{2} - 256 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 288 \, a^{3} b^{3} c^{3} + 44 \, a^{2} b^{4} c^{3} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 512 \, a^{4} b c^{4} - 64 \, a^{3} b^{2} c^{4} - 320 \, a^{4} c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 36 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c + 40 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3} - 36 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} f\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c}}{8 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)}}"," ",0,"1/8*(24*a^2*c^3*e*x^6 + 36*a^2*b*c^2*e*x^4 + (3*(b^3*c^2 - 8*a*b*c^3)*d + (a*b^2*c^2 + 20*a^2*c^3)*f)*x^7 + ((6*b^4*c - 49*a*b^2*c^2 + 28*a^2*c^3)*d + 2*(a*b^3*c + 14*a^2*b*c^2)*f)*x^5 + 8*(a^2*b^2*c + 5*a^3*c^2)*e*x^2 + ((3*b^5 - 20*a*b^3*c - 4*a^2*b*c^2)*d + (a*b^4 + 5*a^2*b^2*c + 36*a^3*c^2)*f)*x^3 - 2*(a^2*b^3 - 10*a^3*b*c)*e + ((5*a*b^4 - 37*a^2*b^2*c + 44*a^3*c^2)*d - (a^2*b^3 - 16*a^3*b*c)*f)*x)/((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^8 + a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2) + 1/8*integrate((48*a^2*c^2*e*x + (3*(b^3*c - 8*a*b*c^2)*d + (a*b^2*c + 20*a^2*c^2)*f)*x^2 + 3*(b^4 - 9*a*b^2*c + 28*a^2*c^2)*d + (a*b^3 - 16*a^2*b*c)*f)/(c*x^4 + b*x^2 + a), x)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)","F",0
54,0,0,0,0.000000," ","integrate((g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{{\left(3 \, {\left(b^{3} c^{2} - 8 \, a b c^{3}\right)} d + {\left(a b^{2} c^{2} + 20 \, a^{2} c^{3}\right)} f\right)} x^{7} + 12 \, {\left(2 \, a^{2} c^{3} e - a^{2} b c^{2} g\right)} x^{6} + {\left({\left(6 \, b^{4} c - 49 \, a b^{2} c^{2} + 28 \, a^{2} c^{3}\right)} d + 2 \, {\left(a b^{3} c + 14 \, a^{2} b c^{2}\right)} f\right)} x^{5} + 18 \, {\left(2 \, a^{2} b c^{2} e - a^{2} b^{2} c g\right)} x^{4} + {\left({\left(3 \, b^{5} - 20 \, a b^{3} c - 4 \, a^{2} b c^{2}\right)} d + {\left(a b^{4} + 5 \, a^{2} b^{2} c + 36 \, a^{3} c^{2}\right)} f\right)} x^{3} + 4 \, {\left(2 \, {\left(a^{2} b^{2} c + 5 \, a^{3} c^{2}\right)} e - {\left(a^{2} b^{3} + 5 \, a^{3} b c\right)} g\right)} x^{2} - 2 \, {\left(a^{2} b^{3} - 10 \, a^{3} b c\right)} e - 2 \, {\left(a^{3} b^{2} + 8 \, a^{4} c\right)} g + {\left({\left(5 \, a b^{4} - 37 \, a^{2} b^{2} c + 44 \, a^{3} c^{2}\right)} d - {\left(a^{2} b^{3} - 16 \, a^{3} b c\right)} f\right)} x}{8 \, {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{8} + a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2}\right)}} + \frac{\frac{{\left(3 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} - 17 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c - 2 \, b^{8} c + 116 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 26 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 34 \, a b^{6} c^{2} + 2 \, b^{7} c^{2} - 368 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 13 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 232 \, a^{2} b^{4} c^{3} - 30 \, a b^{5} c^{3} + 448 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 224 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 736 \, a^{3} b^{2} c^{4} + 176 \, a^{2} b^{3} c^{4} - 112 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} - 896 \, a^{4} c^{5} - 352 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 15 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c - 26 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} + 22 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 224 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} - 88 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} d + {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, a b^{7} c + 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 40 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 48 \, a^{2} b^{5} c^{2} + 2 \, a b^{6} c^{2} - 256 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 288 \, a^{3} b^{3} c^{3} - 44 \, a^{2} b^{4} c^{3} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 512 \, a^{4} b c^{4} + 64 \, a^{3} b^{2} c^{4} + 320 \, a^{4} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} - 36 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c - 40 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3} + 36 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} + 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} f\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c} + \frac{{\left(3 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} - 17 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c + 2 \, b^{8} c + 116 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 26 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} - 34 \, a b^{6} c^{2} - 2 \, b^{7} c^{2} - 368 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 13 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 232 \, a^{2} b^{4} c^{3} + 30 \, a b^{5} c^{3} + 448 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 224 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 736 \, a^{3} b^{2} c^{4} - 176 \, a^{2} b^{3} c^{4} - 112 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 896 \, a^{4} c^{5} + 352 \, a^{3} b c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} - 15 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c + 26 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 22 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} + 224 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} + 88 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} d + {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c + 2 \, a b^{7} c + 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 40 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 48 \, a^{2} b^{5} c^{2} - 2 \, a b^{6} c^{2} - 256 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 288 \, a^{3} b^{3} c^{3} + 44 \, a^{2} b^{4} c^{3} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 512 \, a^{4} b c^{4} - 64 \, a^{3} b^{2} c^{4} - 320 \, a^{4} c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 36 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c + 40 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3} - 36 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} f\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c} + \frac{12 \, {\left({\left(a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4} - 2 \, a^{2} b^{2} c^{4} + a^{2} b c^{5}\right)} \sqrt{b^{2} - 4 \, a c} g - 2 \, {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5} - 2 \, a^{2} b c^{5} + a^{2} c^{6}\right)} \sqrt{b^{2} - 4 \, a c} e\right)} \log\left(x^{2} + \frac{b + \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} - \frac{12 \, {\left({\left(a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4} - 2 \, a^{2} b^{2} c^{4} + a^{2} b c^{5}\right)} \sqrt{b^{2} - 4 \, a c} g - 2 \, {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5} - 2 \, a^{2} b c^{5} + a^{2} c^{6}\right)} \sqrt{b^{2} - 4 \, a c} e\right)} \log\left(x^{2} + \frac{b - \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}}}{8 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)}}"," ",0,"1/8*((3*(b^3*c^2 - 8*a*b*c^3)*d + (a*b^2*c^2 + 20*a^2*c^3)*f)*x^7 + 12*(2*a^2*c^3*e - a^2*b*c^2*g)*x^6 + ((6*b^4*c - 49*a*b^2*c^2 + 28*a^2*c^3)*d + 2*(a*b^3*c + 14*a^2*b*c^2)*f)*x^5 + 18*(2*a^2*b*c^2*e - a^2*b^2*c*g)*x^4 + ((3*b^5 - 20*a*b^3*c - 4*a^2*b*c^2)*d + (a*b^4 + 5*a^2*b^2*c + 36*a^3*c^2)*f)*x^3 + 4*(2*(a^2*b^2*c + 5*a^3*c^2)*e - (a^2*b^3 + 5*a^3*b*c)*g)*x^2 - 2*(a^2*b^3 - 10*a^3*b*c)*e - 2*(a^3*b^2 + 8*a^4*c)*g + ((5*a*b^4 - 37*a^2*b^2*c + 44*a^3*c^2)*d - (a^2*b^3 - 16*a^3*b*c)*f)*x)/((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^8 + a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2) + 1/8*integrate(((3*(b^3*c - 8*a*b*c^2)*d + (a*b^2*c + 20*a^2*c^2)*f)*x^2 + 3*(b^4 - 9*a*b^2*c + 28*a^2*c^2)*d + (a*b^3 - 16*a^2*b*c)*f + 24*(2*a^2*c^2*e - a^2*b*c*g)*x)/(c*x^4 + b*x^2 + a), x)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)","F",0
55,0,0,0,0.000000," ","integrate((h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{{\left(12 \, a^{2} b c^{2} h - 3 \, {\left(b^{3} c^{2} - 8 \, a b c^{3}\right)} d - {\left(a b^{2} c^{2} + 20 \, a^{2} c^{3}\right)} f\right)} x^{7} - 12 \, {\left(2 \, a^{2} c^{3} e - a^{2} b c^{2} g\right)} x^{6} - {\left({\left(6 \, b^{4} c - 49 \, a b^{2} c^{2} + 28 \, a^{2} c^{3}\right)} d + 2 \, {\left(a b^{3} c + 14 \, a^{2} b c^{2}\right)} f - {\left(19 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} h\right)} x^{5} - 18 \, {\left(2 \, a^{2} b c^{2} e - a^{2} b^{2} c g\right)} x^{4} - {\left({\left(3 \, b^{5} - 20 \, a b^{3} c - 4 \, a^{2} b c^{2}\right)} d + {\left(a b^{4} + 5 \, a^{2} b^{2} c + 36 \, a^{3} c^{2}\right)} f - {\left(5 \, a^{2} b^{3} + 16 \, a^{3} b c\right)} h\right)} x^{3} - 4 \, {\left(2 \, {\left(a^{2} b^{2} c + 5 \, a^{3} c^{2}\right)} e - {\left(a^{2} b^{3} + 5 \, a^{3} b c\right)} g\right)} x^{2} + 2 \, {\left(a^{2} b^{3} - 10 \, a^{3} b c\right)} e + 2 \, {\left(a^{3} b^{2} + 8 \, a^{4} c\right)} g - {\left({\left(5 \, a b^{4} - 37 \, a^{2} b^{2} c + 44 \, a^{3} c^{2}\right)} d - {\left(a^{2} b^{3} - 16 \, a^{3} b c\right)} f - 3 \, {\left(a^{3} b^{2} + 4 \, a^{4} c\right)} h\right)} x}{8 \, {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{8} + a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2}\right)}} - \frac{-\frac{{\left(3 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} - 17 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c - 2 \, b^{8} c + 116 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 26 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 34 \, a b^{6} c^{2} + 2 \, b^{7} c^{2} - 368 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 13 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 232 \, a^{2} b^{4} c^{3} - 30 \, a b^{5} c^{3} + 448 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 224 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 736 \, a^{3} b^{2} c^{4} + 176 \, a^{2} b^{3} c^{4} - 112 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} - 896 \, a^{4} c^{5} - 352 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 15 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c - 26 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} + 22 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 224 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} - 88 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} d + {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, a b^{7} c + 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 40 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 48 \, a^{2} b^{5} c^{2} + 2 \, a b^{6} c^{2} - 256 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 288 \, a^{3} b^{3} c^{3} - 44 \, a^{2} b^{4} c^{3} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 512 \, a^{4} b c^{4} + 64 \, a^{3} b^{2} c^{4} + 320 \, a^{4} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} - 36 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c - 40 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3} + 36 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} + 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} f + 3 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, a^{2} b^{6} c - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 8 \, a^{3} b^{4} c^{2} + 2 \, a^{2} b^{5} c^{2} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{3} + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} + 32 \, a^{4} b^{2} c^{3} + 16 \, a^{3} b^{3} c^{3} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} - 128 \, a^{5} c^{4} - 96 \, a^{4} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c + 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{2} + 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{3} - 24 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3}\right)} h\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c} - \frac{{\left(3 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} - 17 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c + 2 \, b^{8} c + 116 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 26 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} - 34 \, a b^{6} c^{2} - 2 \, b^{7} c^{2} - 368 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 13 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 232 \, a^{2} b^{4} c^{3} + 30 \, a b^{5} c^{3} + 448 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 224 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 736 \, a^{3} b^{2} c^{4} - 176 \, a^{2} b^{3} c^{4} - 112 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 896 \, a^{4} c^{5} + 352 \, a^{3} b c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} - 15 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c + 26 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 22 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} + 224 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} + 88 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} d + {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c + 2 \, a b^{7} c + 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 40 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 48 \, a^{2} b^{5} c^{2} - 2 \, a b^{6} c^{2} - 256 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 288 \, a^{3} b^{3} c^{3} + 44 \, a^{2} b^{4} c^{3} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 512 \, a^{4} b c^{4} - 64 \, a^{3} b^{2} c^{4} - 320 \, a^{4} c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 36 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c + 40 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3} - 36 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} f + 3 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c + 2 \, a^{2} b^{6} c - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} - 8 \, a^{3} b^{4} c^{2} - 2 \, a^{2} b^{5} c^{2} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{3} + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 32 \, a^{4} b^{2} c^{3} - 16 \, a^{3} b^{3} c^{3} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 128 \, a^{5} c^{4} + 96 \, a^{4} b c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{2} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{3} + 24 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3}\right)} h\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c} - \frac{12 \, {\left({\left(a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4} - 2 \, a^{2} b^{2} c^{4} + a^{2} b c^{5}\right)} \sqrt{b^{2} - 4 \, a c} g - 2 \, {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5} - 2 \, a^{2} b c^{5} + a^{2} c^{6}\right)} \sqrt{b^{2} - 4 \, a c} e\right)} \log\left(x^{2} + \frac{b + \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} + \frac{12 \, {\left({\left(a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4} - 2 \, a^{2} b^{2} c^{4} + a^{2} b c^{5}\right)} \sqrt{b^{2} - 4 \, a c} g - 2 \, {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5} - 2 \, a^{2} b c^{5} + a^{2} c^{6}\right)} \sqrt{b^{2} - 4 \, a c} e\right)} \log\left(x^{2} + \frac{b - \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}}}{8 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)}}"," ",0,"-1/8*((12*a^2*b*c^2*h - 3*(b^3*c^2 - 8*a*b*c^3)*d - (a*b^2*c^2 + 20*a^2*c^3)*f)*x^7 - 12*(2*a^2*c^3*e - a^2*b*c^2*g)*x^6 - ((6*b^4*c - 49*a*b^2*c^2 + 28*a^2*c^3)*d + 2*(a*b^3*c + 14*a^2*b*c^2)*f - (19*a^2*b^2*c - 4*a^3*c^2)*h)*x^5 - 18*(2*a^2*b*c^2*e - a^2*b^2*c*g)*x^4 - ((3*b^5 - 20*a*b^3*c - 4*a^2*b*c^2)*d + (a*b^4 + 5*a^2*b^2*c + 36*a^3*c^2)*f - (5*a^2*b^3 + 16*a^3*b*c)*h)*x^3 - 4*(2*(a^2*b^2*c + 5*a^3*c^2)*e - (a^2*b^3 + 5*a^3*b*c)*g)*x^2 + 2*(a^2*b^3 - 10*a^3*b*c)*e + 2*(a^3*b^2 + 8*a^4*c)*g - ((5*a*b^4 - 37*a^2*b^2*c + 44*a^3*c^2)*d - (a^2*b^3 - 16*a^3*b*c)*f - 3*(a^3*b^2 + 4*a^4*c)*h)*x)/((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^8 + a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2) - 1/8*integrate(((12*a^2*b*c*h - 3*(b^3*c - 8*a*b*c^2)*d - (a*b^2*c + 20*a^2*c^2)*f)*x^2 - 3*(b^4 - 9*a*b^2*c + 28*a^2*c^2)*d - (a*b^3 - 16*a^2*b*c)*f - 3*(a^2*b^2 + 4*a^3*c)*h - 24*(2*a^2*c^2*e - a^2*b*c*g)*x)/(c*x^4 + b*x^2 + a), x)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)","F",0
56,0,0,0,0.000000," ","integrate((i*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{{\left(12 \, a^{2} b c^{2} h - 3 \, {\left(b^{3} c^{2} - 8 \, a b c^{3}\right)} d - {\left(a b^{2} c^{2} + 20 \, a^{2} c^{3}\right)} f\right)} x^{7} - 4 \, {\left(6 \, a^{2} c^{3} e - 3 \, a^{2} b c^{2} g + {\left(a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} i\right)} x^{6} - 12 \, a^{4} b i - {\left({\left(6 \, b^{4} c - 49 \, a b^{2} c^{2} + 28 \, a^{2} c^{3}\right)} d + 2 \, {\left(a b^{3} c + 14 \, a^{2} b c^{2}\right)} f - {\left(19 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} h\right)} x^{5} - 6 \, {\left(6 \, a^{2} b c^{2} e - 3 \, a^{2} b^{2} c g + {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} i\right)} x^{4} - {\left({\left(3 \, b^{5} - 20 \, a b^{3} c - 4 \, a^{2} b c^{2}\right)} d + {\left(a b^{4} + 5 \, a^{2} b^{2} c + 36 \, a^{3} c^{2}\right)} f - {\left(5 \, a^{2} b^{3} + 16 \, a^{3} b c\right)} h\right)} x^{3} - 4 \, {\left(2 \, {\left(a^{2} b^{2} c + 5 \, a^{3} c^{2}\right)} e - {\left(a^{2} b^{3} + 5 \, a^{3} b c\right)} g + {\left(5 \, a^{3} b^{2} - 2 \, a^{4} c\right)} i\right)} x^{2} + 2 \, {\left(a^{2} b^{3} - 10 \, a^{3} b c\right)} e + 2 \, {\left(a^{3} b^{2} + 8 \, a^{4} c\right)} g - {\left({\left(5 \, a b^{4} - 37 \, a^{2} b^{2} c + 44 \, a^{3} c^{2}\right)} d - {\left(a^{2} b^{3} - 16 \, a^{3} b c\right)} f - 3 \, {\left(a^{3} b^{2} + 4 \, a^{4} c\right)} h\right)} x}{8 \, {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{8} + a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2}\right)}} - \frac{\frac{4 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{2} c^{3} - 2 \, a^{2} b^{3} c^{3} - 8 \, a^{4} c^{4} - 4 \, a^{3} b c^{4} + a^{2} b^{2} c^{4} + 2 \, a^{3} c^{5}\right)} \sqrt{b^{2} - 4 \, a c} i \log\left(x^{2} + \frac{b + \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} - \frac{4 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{2} c^{3} - 2 \, a^{2} b^{3} c^{3} - 8 \, a^{4} c^{4} - 4 \, a^{3} b c^{4} + a^{2} b^{2} c^{4} + 2 \, a^{3} c^{5}\right)} \sqrt{b^{2} - 4 \, a c} i \log\left(x^{2} + \frac{b - \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} - \frac{{\left(3 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} - 17 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c - 2 \, b^{8} c + 116 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 26 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 34 \, a b^{6} c^{2} - 2 \, b^{7} c^{2} - 368 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 13 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 232 \, a^{2} b^{4} c^{3} + 30 \, a b^{5} c^{3} + 448 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 224 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 736 \, a^{3} b^{2} c^{4} - 176 \, a^{2} b^{3} c^{4} - 112 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} - 896 \, a^{4} c^{5} + 352 \, a^{3} b c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} - 15 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c - 26 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 22 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 224 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} + 88 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} d + {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, a b^{7} c + 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 40 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 48 \, a^{2} b^{5} c^{2} - 2 \, a b^{6} c^{2} - 256 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 288 \, a^{3} b^{3} c^{3} + 44 \, a^{2} b^{4} c^{3} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 512 \, a^{4} b c^{4} - 64 \, a^{3} b^{2} c^{4} - 320 \, a^{4} c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 36 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c - 40 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3} - 36 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} f + 3 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, a^{2} b^{6} c - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 8 \, a^{3} b^{4} c^{2} - 2 \, a^{2} b^{5} c^{2} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{3} + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} + 32 \, a^{4} b^{2} c^{3} - 16 \, a^{3} b^{3} c^{3} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} - 128 \, a^{5} c^{4} + 96 \, a^{4} b c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{2} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{3} + 24 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3}\right)} h\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c} - \frac{{\left(3 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} - 17 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c + 2 \, b^{8} c + 116 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 26 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} - 34 \, a b^{6} c^{2} - 2 \, b^{7} c^{2} - 368 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 13 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 232 \, a^{2} b^{4} c^{3} + 30 \, a b^{5} c^{3} + 448 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 224 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 736 \, a^{3} b^{2} c^{4} - 176 \, a^{2} b^{3} c^{4} - 112 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 896 \, a^{4} c^{5} + 352 \, a^{3} b c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} - 15 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c + 26 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 22 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} + 224 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} + 88 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} d + {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c + 2 \, a b^{7} c + 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 40 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 48 \, a^{2} b^{5} c^{2} - 2 \, a b^{6} c^{2} - 256 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 288 \, a^{3} b^{3} c^{3} + 44 \, a^{2} b^{4} c^{3} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 512 \, a^{4} b c^{4} - 64 \, a^{3} b^{2} c^{4} - 320 \, a^{4} c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 36 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c + 40 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3} - 36 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} f + 3 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c + 2 \, a^{2} b^{6} c - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} - 8 \, a^{3} b^{4} c^{2} - 2 \, a^{2} b^{5} c^{2} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{3} + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 32 \, a^{4} b^{2} c^{3} - 16 \, a^{3} b^{3} c^{3} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 128 \, a^{5} c^{4} + 96 \, a^{4} b c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{2} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{3} + 24 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3}\right)} h\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c} - \frac{12 \, {\left({\left(a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4} - 2 \, a^{2} b^{2} c^{4} + a^{2} b c^{5}\right)} \sqrt{b^{2} - 4 \, a c} g - 2 \, {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5} - 2 \, a^{2} b c^{5} + a^{2} c^{6}\right)} \sqrt{b^{2} - 4 \, a c} e\right)} \log\left(x^{2} + \frac{b + \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} + \frac{12 \, {\left({\left(a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4} - 2 \, a^{2} b^{2} c^{4} + a^{2} b c^{5}\right)} \sqrt{b^{2} - 4 \, a c} g - 2 \, {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5} - 2 \, a^{2} b c^{5} + a^{2} c^{6}\right)} \sqrt{b^{2} - 4 \, a c} e\right)} \log\left(x^{2} + \frac{b - \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}}}{8 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)}}"," ",0,"-1/8*((12*a^2*b*c^2*h - 3*(b^3*c^2 - 8*a*b*c^3)*d - (a*b^2*c^2 + 20*a^2*c^3)*f)*x^7 - 4*(6*a^2*c^3*e - 3*a^2*b*c^2*g + (a^2*b^2*c + 2*a^3*c^2)*i)*x^6 - 12*a^4*b*i - ((6*b^4*c - 49*a*b^2*c^2 + 28*a^2*c^3)*d + 2*(a*b^3*c + 14*a^2*b*c^2)*f - (19*a^2*b^2*c - 4*a^3*c^2)*h)*x^5 - 6*(6*a^2*b*c^2*e - 3*a^2*b^2*c*g + (a^2*b^3 + 2*a^3*b*c)*i)*x^4 - ((3*b^5 - 20*a*b^3*c - 4*a^2*b*c^2)*d + (a*b^4 + 5*a^2*b^2*c + 36*a^3*c^2)*f - (5*a^2*b^3 + 16*a^3*b*c)*h)*x^3 - 4*(2*(a^2*b^2*c + 5*a^3*c^2)*e - (a^2*b^3 + 5*a^3*b*c)*g + (5*a^3*b^2 - 2*a^4*c)*i)*x^2 + 2*(a^2*b^3 - 10*a^3*b*c)*e + 2*(a^3*b^2 + 8*a^4*c)*g - ((5*a*b^4 - 37*a^2*b^2*c + 44*a^3*c^2)*d - (a^2*b^3 - 16*a^3*b*c)*f - 3*(a^3*b^2 + 4*a^4*c)*h)*x)/((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^8 + a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2) - 1/8*integrate(((12*a^2*b*c*h - 3*(b^3*c - 8*a*b*c^2)*d - (a*b^2*c + 20*a^2*c^2)*f)*x^2 - 3*(b^4 - 9*a*b^2*c + 28*a^2*c^2)*d - (a*b^3 - 16*a^2*b*c)*f - 3*(a^2*b^2 + 4*a^3*c)*h - 8*(6*a^2*c^2*e - 3*a^2*b*c*g + (a^2*b^2 + 2*a^3*c)*i)*x)/(c*x^4 + b*x^2 + a), x)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)","F",0
57,0,0,0,0.000000," ","integrate((m*x^8+l*x^7+k*x^6+j*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{{\left(12 \, a^{2} b c^{3} h - 3 \, {\left(b^{3} c^{3} - 8 \, a b c^{4}\right)} d - {\left(a b^{2} c^{3} + 20 \, a^{2} c^{4}\right)} f - 3 \, {\left(a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} k - {\left(a^{2} b^{3} c - 16 \, a^{3} b c^{2}\right)} m\right)} x^{7} - 12 \, a^{4} b c j - 4 \, {\left(6 \, a^{2} c^{4} e - 3 \, a^{2} b c^{3} g - 3 \, a^{3} b c^{2} l + {\left(a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} j\right)} x^{6} - {\left({\left(6 \, b^{4} c^{2} - 49 \, a b^{2} c^{3} + 28 \, a^{2} c^{4}\right)} d + 2 \, {\left(a b^{3} c^{2} + 14 \, a^{2} b c^{3}\right)} f - {\left(19 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} h + {\left(5 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} k - {\left(a^{2} b^{4} + 5 \, a^{3} b^{2} c + 36 \, a^{4} c^{2}\right)} m\right)} x^{5} - 2 \, {\left(18 \, a^{2} b c^{3} e - 9 \, a^{2} b^{2} c^{2} g + 3 \, {\left(a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} j - {\left(a^{2} b^{4} + a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} l\right)} x^{4} - {\left({\left(3 \, b^{5} c - 20 \, a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d + {\left(a b^{4} c + 5 \, a^{2} b^{2} c^{2} + 36 \, a^{3} c^{3}\right)} f - {\left(5 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} h + {\left(19 \, a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} k - 2 \, {\left(a^{3} b^{3} + 14 \, a^{4} b c\right)} m\right)} x^{3} - 4 \, {\left(2 \, {\left(a^{2} b^{2} c^{2} + 5 \, a^{3} c^{3}\right)} e - {\left(a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} g + {\left(5 \, a^{3} b^{2} c - 2 \, a^{4} c^{2}\right)} j - {\left(a^{3} b^{3} + 5 \, a^{4} b c\right)} l\right)} x^{2} + 2 \, {\left(a^{2} b^{3} c - 10 \, a^{3} b c^{2}\right)} e + 2 \, {\left(a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} g + 2 \, {\left(a^{4} b^{2} + 8 \, a^{5} c\right)} l - {\left(12 \, a^{4} b c k + {\left(5 \, a b^{4} c - 37 \, a^{2} b^{2} c^{2} + 44 \, a^{3} c^{3}\right)} d - {\left(a^{2} b^{3} c - 16 \, a^{3} b c^{2}\right)} f - 3 \, {\left(a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} h - {\left(a^{4} b^{2} + 20 \, a^{5} c\right)} m\right)} x}{8 \, {\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} + {\left(a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5}\right)} x^{8} + 2 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} x^{6} + {\left(a^{2} b^{6} c - 6 \, a^{3} b^{4} c^{2} + 32 \, a^{5} c^{4}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} x^{2}\right)}} - \frac{-\frac{{\left(3 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c - 17 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{2} - 2 \, b^{8} c^{2} + 116 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} + 26 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{3} + 34 \, a b^{6} c^{3} + 2 \, b^{7} c^{3} - 368 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 13 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - 232 \, a^{2} b^{4} c^{4} - 30 \, a b^{5} c^{4} + 448 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{5} + 224 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + 736 \, a^{3} b^{2} c^{5} + 176 \, a^{2} b^{3} c^{5} - 112 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} - 896 \, a^{4} c^{6} - 352 \, a^{3} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c + 15 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} - 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} + 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{2} - 26 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{3} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{4} + 22 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{4} - 224 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{5} - 88 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{5}\right)} d + {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c - 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} - 2 \, a b^{7} c^{2} + 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} + 40 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + 48 \, a^{2} b^{5} c^{3} + 2 \, a b^{6} c^{3} - 256 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} - 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 288 \, a^{3} b^{3} c^{4} - 44 \, a^{2} b^{4} c^{4} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 512 \, a^{4} b c^{5} + 64 \, a^{3} b^{2} c^{5} + 320 \, a^{4} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 36 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{2} - 40 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{3} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{4} + 36 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{4} + 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{5}\right)} f + 3 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} - 2 \, a^{2} b^{6} c^{2} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} + 8 \, a^{3} b^{4} c^{3} + 2 \, a^{2} b^{5} c^{3} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{4} + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} + 32 \, a^{4} b^{2} c^{4} + 16 \, a^{3} b^{3} c^{4} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{5} - 128 \, a^{5} c^{5} - 96 \, a^{4} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} + 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{3} - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{4} - 24 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{4}\right)} h - 6 \, {\left(2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - 4 \, a^{3} b^{5} c^{2} + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} + 32 \, a^{4} b^{3} c^{3} + 6 \, a^{3} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 64 \, a^{5} b c^{4} - 16 \, a^{4} b^{2} c^{4} - 32 \, a^{5} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{2} - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{4}\right)} k + {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} + 12 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c - 2 \, a^{3} b^{6} c - 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{2} - 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - 24 \, a^{4} b^{4} c^{2} - 2 \, a^{3} b^{5} c^{2} + 320 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{3} + 160 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + 288 \, a^{5} b^{2} c^{3} + 112 \, a^{4} b^{3} c^{3} - 80 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{4} - 640 \, a^{6} c^{4} - 416 \, a^{5} b c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c + 208 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{2} + 104 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} - 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{2} - 160 \, {\left(b^{2} - 4 \, a c\right)} a^{5} c^{3} - 104 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{3}\right)} m\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c} - \frac{{\left(3 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c - 17 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{2} + 2 \, b^{8} c^{2} + 116 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} + 26 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{3} - 34 \, a b^{6} c^{3} - 2 \, b^{7} c^{3} - 368 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 13 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} + 232 \, a^{2} b^{4} c^{4} + 30 \, a b^{5} c^{4} + 448 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{5} + 224 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} - 736 \, a^{3} b^{2} c^{5} - 176 \, a^{2} b^{3} c^{5} - 112 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} + 896 \, a^{4} c^{6} + 352 \, a^{3} b c^{6} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c - 15 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{2} + 26 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{4} - 22 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{4} + 224 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{5} + 88 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{5}\right)} d + {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c - 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} + 2 \, a b^{7} c^{2} + 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} + 40 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} - 48 \, a^{2} b^{5} c^{3} - 2 \, a b^{6} c^{3} - 256 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} - 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} + 288 \, a^{3} b^{3} c^{4} + 44 \, a^{2} b^{4} c^{4} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} - 512 \, a^{4} b c^{5} - 64 \, a^{3} b^{2} c^{5} - 320 \, a^{4} c^{6} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} + 36 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{2} + 40 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{4} - 36 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{4} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{5}\right)} f + 3 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 2 \, a^{2} b^{6} c^{2} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} - 8 \, a^{3} b^{4} c^{3} - 2 \, a^{2} b^{5} c^{3} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{4} + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 32 \, a^{4} b^{2} c^{4} - 16 \, a^{3} b^{3} c^{4} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{5} + 128 \, a^{5} c^{5} + 96 \, a^{4} b c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{3} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{4} + 24 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{4}\right)} h - 6 \, {\left(2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} + 4 \, a^{3} b^{5} c^{2} + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 32 \, a^{4} b^{3} c^{3} - 6 \, a^{3} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} + 64 \, a^{5} b c^{4} + 16 \, a^{4} b^{2} c^{4} + 32 \, a^{5} c^{5} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{2} + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{3} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{4}\right)} k + {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} + 12 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c + 2 \, a^{3} b^{6} c - 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{2} - 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} + 24 \, a^{4} b^{4} c^{2} + 2 \, a^{3} b^{5} c^{2} + 320 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{3} + 160 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 288 \, a^{5} b^{2} c^{3} - 112 \, a^{4} b^{3} c^{3} - 80 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{4} + 640 \, a^{6} c^{4} + 416 \, a^{5} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} + 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c - 208 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{2} - 104 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{2} + 160 \, {\left(b^{2} - 4 \, a c\right)} a^{5} c^{3} + 104 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{3}\right)} m\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c} - \frac{4 \, {\left(3 \, {\left(a^{2} b^{3} c^{4} - 4 \, a^{3} b c^{5} - 2 \, a^{2} b^{2} c^{5} + a^{2} b c^{6}\right)} \sqrt{b^{2} - 4 \, a c} g - {\left(a^{2} b^{4} c^{3} - 2 \, a^{3} b^{2} c^{4} - 2 \, a^{2} b^{3} c^{4} - 8 \, a^{4} c^{5} - 4 \, a^{3} b c^{5} + a^{2} b^{2} c^{5} + 2 \, a^{3} c^{6}\right)} \sqrt{b^{2} - 4 \, a c} j + 3 \, {\left(a^{3} b^{3} c^{3} - 4 \, a^{4} b c^{4} - 2 \, a^{3} b^{2} c^{4} + a^{3} b c^{5}\right)} \sqrt{b^{2} - 4 \, a c} l - 6 \, {\left(a^{2} b^{2} c^{5} - 4 \, a^{3} c^{6} - 2 \, a^{2} b c^{6} + a^{2} c^{7}\right)} \sqrt{b^{2} - 4 \, a c} e\right)} \log\left(x^{2} + \frac{b + \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} + \frac{4 \, {\left(3 \, {\left(a^{2} b^{3} c^{4} - 4 \, a^{3} b c^{5} - 2 \, a^{2} b^{2} c^{5} + a^{2} b c^{6}\right)} \sqrt{b^{2} - 4 \, a c} g - {\left(a^{2} b^{4} c^{3} - 2 \, a^{3} b^{2} c^{4} - 2 \, a^{2} b^{3} c^{4} - 8 \, a^{4} c^{5} - 4 \, a^{3} b c^{5} + a^{2} b^{2} c^{5} + 2 \, a^{3} c^{6}\right)} \sqrt{b^{2} - 4 \, a c} j + 3 \, {\left(a^{3} b^{3} c^{3} - 4 \, a^{4} b c^{4} - 2 \, a^{3} b^{2} c^{4} + a^{3} b c^{5}\right)} \sqrt{b^{2} - 4 \, a c} l - 6 \, {\left(a^{2} b^{2} c^{5} - 4 \, a^{3} c^{6} - 2 \, a^{2} b c^{6} + a^{2} c^{7}\right)} \sqrt{b^{2} - 4 \, a c} e\right)} \log\left(x^{2} + \frac{b - \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}}}{8 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)}}"," ",0,"-1/8*((12*a^2*b*c^3*h - 3*(b^3*c^3 - 8*a*b*c^4)*d - (a*b^2*c^3 + 20*a^2*c^4)*f - 3*(a^2*b^2*c^2 + 4*a^3*c^3)*k - (a^2*b^3*c - 16*a^3*b*c^2)*m)*x^7 - 12*a^4*b*c*j - 4*(6*a^2*c^4*e - 3*a^2*b*c^3*g - 3*a^3*b*c^2*l + (a^2*b^2*c^2 + 2*a^3*c^3)*j)*x^6 - ((6*b^4*c^2 - 49*a*b^2*c^3 + 28*a^2*c^4)*d + 2*(a*b^3*c^2 + 14*a^2*b*c^3)*f - (19*a^2*b^2*c^2 - 4*a^3*c^3)*h + (5*a^2*b^3*c + 16*a^3*b*c^2)*k - (a^2*b^4 + 5*a^3*b^2*c + 36*a^4*c^2)*m)*x^5 - 2*(18*a^2*b*c^3*e - 9*a^2*b^2*c^2*g + 3*(a^2*b^3*c + 2*a^3*b*c^2)*j - (a^2*b^4 + a^3*b^2*c + 16*a^4*c^2)*l)*x^4 - ((3*b^5*c - 20*a*b^3*c^2 - 4*a^2*b*c^3)*d + (a*b^4*c + 5*a^2*b^2*c^2 + 36*a^3*c^3)*f - (5*a^2*b^3*c + 16*a^3*b*c^2)*h + (19*a^3*b^2*c - 4*a^4*c^2)*k - 2*(a^3*b^3 + 14*a^4*b*c)*m)*x^3 - 4*(2*(a^2*b^2*c^2 + 5*a^3*c^3)*e - (a^2*b^3*c + 5*a^3*b*c^2)*g + (5*a^3*b^2*c - 2*a^4*c^2)*j - (a^3*b^3 + 5*a^4*b*c)*l)*x^2 + 2*(a^2*b^3*c - 10*a^3*b*c^2)*e + 2*(a^3*b^2*c + 8*a^4*c^2)*g + 2*(a^4*b^2 + 8*a^5*c)*l - (12*a^4*b*c*k + (5*a*b^4*c - 37*a^2*b^2*c^2 + 44*a^3*c^3)*d - (a^2*b^3*c - 16*a^3*b*c^2)*f - 3*(a^3*b^2*c + 4*a^4*c^2)*h - (a^4*b^2 + 20*a^5*c)*m)*x)/(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3 + (a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4*c^5)*x^8 + 2*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*x^6 + (a^2*b^6*c - 6*a^3*b^4*c^2 + 32*a^5*c^4)*x^4 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*x^2) - 1/8*integrate((12*a^3*b*c*k + (12*a^2*b*c^2*h - 3*(b^3*c^2 - 8*a*b*c^3)*d - (a*b^2*c^2 + 20*a^2*c^3)*f - 3*(a^2*b^2*c + 4*a^3*c^2)*k - (a^2*b^3 - 16*a^3*b*c)*m)*x^2 - 3*(b^4*c - 9*a*b^2*c^2 + 28*a^2*c^3)*d - (a*b^3*c - 16*a^2*b*c^2)*f - 3*(a^2*b^2*c + 4*a^3*c^2)*h - (a^3*b^2 + 20*a^4*c)*m - 8*(6*a^2*c^3*e - 3*a^2*b*c^2*g - 3*a^3*b*c*l + (a^2*b^2*c + 2*a^3*c^2)*j)*x)/(c*x^4 + b*x^2 + a), x)/(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)","F",0
58,0,0,0,0.000000," ","integrate((k*x^7+j*x^6+i*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{a b c^{2} e - 2 \, a^{2} c^{2} g + a^{2} b c i - {\left(b c^{3} d - 2 \, a c^{3} f + a b c^{2} h - {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} j\right)} x^{3} + {\left(2 \, a c^{3} e - a b c^{2} g + {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} i - {\left(a b^{3} - 3 \, a^{2} b c\right)} k\right)} x^{2} - {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} k + {\left(a b c^{2} f - 2 \, a^{2} c^{2} h + a^{2} b c j - {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d\right)} x}{2 \, {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} + {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} x^{4} + {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} x^{2}\right)}} - \frac{-\int \frac{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} k x^{3} + a b c f - 2 \, a^{2} c h + a^{2} b j + {\left(b c^{2} d - 2 \, a c^{2} f + a b c h + {\left(a b^{2} - 6 \, a^{2} c\right)} j\right)} x^{2} + {\left(b^{2} c - 6 \, a c^{2}\right)} d - 2 \, {\left(2 \, a c^{2} e - a b c g + 2 \, a^{2} c i - a^{2} b k\right)} x}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}}"," ",0,"-1/2*(a*b*c^2*e - 2*a^2*c^2*g + a^2*b*c*i - (b*c^3*d - 2*a*c^3*f + a*b*c^2*h - (a*b^2*c - 2*a^2*c^2)*j)*x^3 + (2*a*c^3*e - a*b*c^2*g + (a*b^2*c - 2*a^2*c^2)*i - (a*b^3 - 3*a^2*b*c)*k)*x^2 - (a^2*b^2 - 2*a^3*c)*k + (a*b*c^2*f - 2*a^2*c^2*h + a^2*b*c*j - (b^2*c^2 - 2*a*c^3)*d)*x)/(a^2*b^2*c^2 - 4*a^3*c^3 + (a*b^2*c^3 - 4*a^2*c^4)*x^4 + (a*b^3*c^2 - 4*a^2*b*c^3)*x^2) - 1/2*integrate(-(2*(a*b^2 - 4*a^2*c)*k*x^3 + a*b*c*f - 2*a^2*c*h + a^2*b*j + (b*c^2*d - 2*a*c^2*f + a*b*c*h + (a*b^2 - 6*a^2*c)*j)*x^2 + (b^2*c - 6*a*c^2)*d - 2*(2*a*c^2*e - a*b*c*g + 2*a^2*c*i - a^2*b*k)*x)/(c*x^4 + b*x^2 + a), x)/(a*b^2*c - 4*a^2*c^2)","F",0
59,0,0,0,0.000000," ","integrate((k*x^11+j*x^8+i*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{12 \, a^{4} b c^{3} i - {\left(12 \, a^{2} b c^{5} h - 3 \, {\left(b^{3} c^{5} - 8 \, a b c^{6}\right)} d - {\left(a b^{2} c^{5} + 20 \, a^{2} c^{6}\right)} f - {\left(a^{2} b^{3} c^{3} - 16 \, a^{3} b c^{4}\right)} j\right)} x^{7} + 4 \, {\left(6 \, a^{2} c^{6} e - 3 \, a^{2} b c^{5} g + {\left(a^{2} b^{2} c^{4} + 2 \, a^{3} c^{5}\right)} i + {\left(2 \, a^{2} b^{5} c - 15 \, a^{3} b^{3} c^{2} + 25 \, a^{4} b c^{3}\right)} k\right)} x^{6} + {\left({\left(6 \, b^{4} c^{4} - 49 \, a b^{2} c^{5} + 28 \, a^{2} c^{6}\right)} d + 2 \, {\left(a b^{3} c^{4} + 14 \, a^{2} b c^{5}\right)} f - {\left(19 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} h - {\left(a^{2} b^{4} c^{2} + 5 \, a^{3} b^{2} c^{3} + 36 \, a^{4} c^{4}\right)} j\right)} x^{5} + 2 \, {\left(18 \, a^{2} b c^{5} e - 9 \, a^{2} b^{2} c^{4} g + 3 \, {\left(a^{2} b^{3} c^{3} + 2 \, a^{3} b c^{4}\right)} i + {\left(3 \, a^{2} b^{6} - 19 \, a^{3} b^{4} c + 11 \, a^{4} b^{2} c^{2} + 32 \, a^{5} c^{3}\right)} k\right)} x^{4} + {\left({\left(3 \, b^{5} c^{3} - 20 \, a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d + {\left(a b^{4} c^{3} + 5 \, a^{2} b^{2} c^{4} + 36 \, a^{3} c^{5}\right)} f - {\left(5 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} h - 2 \, {\left(a^{3} b^{3} c^{2} + 14 \, a^{4} b c^{3}\right)} j\right)} x^{3} + 4 \, {\left(2 \, {\left(a^{2} b^{2} c^{4} + 5 \, a^{3} c^{5}\right)} e - {\left(a^{2} b^{3} c^{3} + 5 \, a^{3} b c^{4}\right)} g + {\left(5 \, a^{3} b^{2} c^{3} - 2 \, a^{4} c^{4}\right)} i + {\left(3 \, a^{3} b^{5} - 22 \, a^{4} b^{3} c + 31 \, a^{5} b c^{2}\right)} k\right)} x^{2} - 2 \, {\left(a^{2} b^{3} c^{3} - 10 \, a^{3} b c^{4}\right)} e - 2 \, {\left(a^{3} b^{2} c^{3} + 8 \, a^{4} c^{4}\right)} g + 6 \, {\left(a^{4} b^{4} - 7 \, a^{5} b^{2} c + 8 \, a^{6} c^{2}\right)} k + {\left({\left(5 \, a b^{4} c^{3} - 37 \, a^{2} b^{2} c^{4} + 44 \, a^{3} c^{5}\right)} d - {\left(a^{2} b^{3} c^{3} - 16 \, a^{3} b c^{4}\right)} f - 3 \, {\left(a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}\right)} h - {\left(a^{4} b^{2} c^{2} + 20 \, a^{5} c^{3}\right)} j\right)} x}{8 \, {\left(a^{4} b^{4} c^{3} - 8 \, a^{5} b^{2} c^{4} + 16 \, a^{6} c^{5} + {\left(a^{2} b^{4} c^{5} - 8 \, a^{3} b^{2} c^{6} + 16 \, a^{4} c^{7}\right)} x^{8} + 2 \, {\left(a^{2} b^{5} c^{4} - 8 \, a^{3} b^{3} c^{5} + 16 \, a^{4} b c^{6}\right)} x^{6} + {\left(a^{2} b^{6} c^{3} - 6 \, a^{3} b^{4} c^{4} + 32 \, a^{5} c^{6}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} c^{3} - 8 \, a^{4} b^{3} c^{4} + 16 \, a^{5} b c^{5}\right)} x^{2}\right)}} + \frac{\frac{2 \, {\left(a^{2} b^{4} k - 8 \, a^{3} b^{2} c k + 16 \, a^{4} c^{2} k\right)} \log\left({\left| c x^{4} + b x^{2} + a \right|}\right)}{c} + \frac{{\left(3 \, {\left(2 \, b^{7} c^{4} - 32 \, a b^{5} c^{5} + 160 \, a^{2} b^{3} c^{6} - 256 \, a^{3} b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{4} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{4} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{5} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{6}\right)} c^{2} d + {\left(2 \, a b^{6} c^{4} + 24 \, a^{2} b^{4} c^{5} - 288 \, a^{3} b^{2} c^{6} + 640 \, a^{4} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + 144 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - 320 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{5} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{4} - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{5} + 160 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{6}\right)} c^{2} f - 12 \, {\left(2 \, a^{2} b^{5} c^{4} - 16 \, a^{3} b^{3} c^{5} + 32 \, a^{4} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{5}\right)} c^{2} h + {\left(2 \, a^{2} b^{7} c^{2} - 48 \, a^{3} b^{5} c^{3} + 288 \, a^{4} b^{3} c^{4} - 512 \, a^{5} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} + 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c - 144 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} + 40 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} c^{2} j + 6 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{3} - 17 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{4} - 2 \, b^{8} c^{4} + 116 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} + 26 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{5} + 34 \, a b^{6} c^{5} - 368 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{6} - 13 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{6} - 232 \, a^{2} b^{4} c^{6} + 448 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{7} + 224 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{7} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{7} + 736 \, a^{3} b^{2} c^{7} - 112 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{8} - 896 \, a^{4} c^{8} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{4} - 26 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{5} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{6} - 224 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{7}\right)} c d + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{3} - 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{4} - 2 \, a b^{7} c^{4} + 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 40 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{5} + 48 \, a^{2} b^{5} c^{5} - 256 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} - 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{6} - 288 \, a^{3} b^{3} c^{6} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{7} + 512 \, a^{4} b c^{7} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{4} - 40 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{5} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{6}\right)} c f + 6 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} - 2 \, a^{2} b^{6} c^{4} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} + 8 \, a^{3} b^{4} c^{5} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{6} + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} + 32 \, a^{4} b^{2} c^{6} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{7} - 128 \, a^{5} c^{7} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{4} - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{6}\right)} c h + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{2} + 12 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{3} - 2 \, a^{3} b^{6} c^{3} - 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{4} - 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{4} - 24 \, a^{4} b^{4} c^{4} + 320 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{5} + 160 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{5} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{5} + 288 \, a^{5} b^{2} c^{5} - 80 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{6} - 640 \, a^{6} c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{3} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{4} - 160 \, {\left(b^{2} - 4 \, a c\right)} a^{5} c^{5}\right)} c j + 3 \, {\left(2 \, b^{7} c^{6} - 28 \, a b^{5} c^{7} + 192 \, a^{2} b^{3} c^{8} - 448 \, a^{3} b c^{9} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{4} + 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{5} - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{6} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{6} + 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{7} + 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{7} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{7} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{6} + 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{7} - 112 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{8}\right)} d + {\left(2 \, a b^{6} c^{6} - 112 \, a^{2} b^{4} c^{7} + 416 \, a^{3} b^{2} c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{4} + 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{5} - 208 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} - 104 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{6} + 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{6} + 104 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{7}\right)} f + 6 \, {\left(6 \, a^{2} b^{5} c^{6} - 16 \, a^{3} b^{3} c^{7} - 32 \, a^{4} b c^{8} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{6} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{7} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{6} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{7}\right)} h - {\left(2 \, a^{2} b^{7} c^{4} - 44 \, a^{3} b^{5} c^{5} + 64 \, a^{4} b^{3} c^{6} + 320 \, a^{5} b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c^{2} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{4} - 36 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{5} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{5} + 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{4} + 36 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{5} + 80 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{6}\right)} j\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} c x}{\sqrt{b c + \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}\right)}{8 \, {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} - 2 \, a b^{3} c^{2} + 16 \, a^{3} c^{3} + 8 \, a^{2} b c^{3} + a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} c^{2}} - \frac{{\left(3 \, {\left(2 \, b^{7} c^{4} - 32 \, a b^{5} c^{5} + 160 \, a^{2} b^{3} c^{6} - 256 \, a^{3} b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{4} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{4} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{5} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{6}\right)} c^{2} d + {\left(2 \, a b^{6} c^{4} + 24 \, a^{2} b^{4} c^{5} - 288 \, a^{3} b^{2} c^{6} + 640 \, a^{4} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + 144 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - 320 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{5} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{4} - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{5} + 160 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{6}\right)} c^{2} f - 12 \, {\left(2 \, a^{2} b^{5} c^{4} - 16 \, a^{3} b^{3} c^{5} + 32 \, a^{4} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{5}\right)} c^{2} h + {\left(2 \, a^{2} b^{7} c^{2} - 48 \, a^{3} b^{5} c^{3} + 288 \, a^{4} b^{3} c^{4} - 512 \, a^{5} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} + 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c - 144 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} + 40 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} c^{2} j - 6 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{3} - 17 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{4} + 2 \, b^{8} c^{4} + 116 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} + 26 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{5} - 34 \, a b^{6} c^{5} - 368 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{6} - 13 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{6} + 232 \, a^{2} b^{4} c^{6} + 448 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{7} + 224 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{7} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{7} - 736 \, a^{3} b^{2} c^{7} - 112 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{8} + 896 \, a^{4} c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{4} + 26 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{5} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{6} + 224 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{7}\right)} c d - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{3} - 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{4} + 2 \, a b^{7} c^{4} + 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 40 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{5} - 48 \, a^{2} b^{5} c^{5} - 256 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} - 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{6} + 288 \, a^{3} b^{3} c^{6} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{7} - 512 \, a^{4} b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{4} + 40 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{5} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{6}\right)} c f - 6 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} + 2 \, a^{2} b^{6} c^{4} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} - 8 \, a^{3} b^{4} c^{5} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{6} + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} - 32 \, a^{4} b^{2} c^{6} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{7} + 128 \, a^{5} c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{4} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{6}\right)} c h - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{2} + 12 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{3} + 2 \, a^{3} b^{6} c^{3} - 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{4} - 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{4} + 24 \, a^{4} b^{4} c^{4} + 320 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{5} + 160 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{5} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{5} - 288 \, a^{5} b^{2} c^{5} - 80 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{6} + 640 \, a^{6} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{3} - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{4} + 160 \, {\left(b^{2} - 4 \, a c\right)} a^{5} c^{5}\right)} c j + 3 \, {\left(2 \, b^{7} c^{6} - 28 \, a b^{5} c^{7} + 192 \, a^{2} b^{3} c^{8} - 448 \, a^{3} b c^{9} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{4} + 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{5} - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{6} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{6} + 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{7} + 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{7} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{7} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{6} + 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{7} - 112 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{8}\right)} d + {\left(2 \, a b^{6} c^{6} - 112 \, a^{2} b^{4} c^{7} + 416 \, a^{3} b^{2} c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{4} + 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{5} - 208 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} - 104 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{6} + 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{6} + 104 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{7}\right)} f + 6 \, {\left(6 \, a^{2} b^{5} c^{6} - 16 \, a^{3} b^{3} c^{7} - 32 \, a^{4} b c^{8} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{6} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{7} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{6} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{7}\right)} h - {\left(2 \, a^{2} b^{7} c^{4} - 44 \, a^{3} b^{5} c^{5} + 64 \, a^{4} b^{3} c^{6} + 320 \, a^{5} b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c^{2} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{4} - 36 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{5} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{5} + 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{4} + 36 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{5} + 80 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{6}\right)} j\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} c x}{\sqrt{b c - \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}\right)}{8 \, {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} - 2 \, a b^{3} c^{2} + 16 \, a^{3} c^{3} + 8 \, a^{2} b c^{3} + a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} c^{2}} - \frac{{\left(a b^{7} c^{4} - 6 \, a^{2} b^{5} c^{5} - 2 \, a b^{6} c^{5} + 4 \, a^{2} b^{4} c^{6} + a b^{5} c^{6} + 32 \, a^{4} b c^{7} + 16 \, a^{3} b^{2} c^{7} - 2 \, a^{2} b^{3} c^{7} - 8 \, a^{3} b c^{8} - {\left(a b^{7} c^{3} - 6 \, a^{2} b^{5} c^{4} - 2 \, a b^{6} c^{4} + 4 \, a^{2} b^{4} c^{5} + a b^{5} c^{5} + 32 \, a^{4} b c^{6} + 16 \, a^{3} b^{2} c^{6} - 2 \, a^{2} b^{3} c^{6} - 8 \, a^{3} b c^{7} + {\left(a b^{6} c^{3} - 6 \, a^{2} b^{4} c^{4} - 2 \, a b^{5} c^{4} + 4 \, a^{2} b^{3} c^{5} + a b^{4} c^{5} + 32 \, a^{4} c^{6} + 16 \, a^{3} b c^{6} - 2 \, a^{2} b^{2} c^{6} - 8 \, a^{3} c^{7}\right)} \sqrt{b^{2} - 4 \, a c}\right)} c + {\left(a b^{6} c^{4} - 2 \, a^{2} b^{4} c^{5} - 2 \, a b^{5} c^{5} - 8 \, a^{3} b^{2} c^{6} - 4 \, a^{2} b^{3} c^{6} + a b^{4} c^{6} + 2 \, a^{2} b^{2} c^{7}\right)} \sqrt{b^{2} - 4 \, a c}\right)} i \log\left(x^{2} + \frac{b c + \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{2 \, c^{2}}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{3}} - \frac{{\left(a b^{7} c^{4} - 6 \, a^{2} b^{5} c^{5} - 2 \, a b^{6} c^{5} + 4 \, a^{2} b^{4} c^{6} + a b^{5} c^{6} + 32 \, a^{4} b c^{7} + 16 \, a^{3} b^{2} c^{7} - 2 \, a^{2} b^{3} c^{7} - 8 \, a^{3} b c^{8} - {\left(a b^{7} c^{3} - 6 \, a^{2} b^{5} c^{4} - 2 \, a b^{6} c^{4} + 4 \, a^{2} b^{4} c^{5} + a b^{5} c^{5} + 32 \, a^{4} b c^{6} + 16 \, a^{3} b^{2} c^{6} - 2 \, a^{2} b^{3} c^{6} - 8 \, a^{3} b c^{7} - {\left(a b^{6} c^{3} - 6 \, a^{2} b^{4} c^{4} - 2 \, a b^{5} c^{4} + 4 \, a^{2} b^{3} c^{5} + a b^{4} c^{5} + 32 \, a^{4} c^{6} + 16 \, a^{3} b c^{6} - 2 \, a^{2} b^{2} c^{6} - 8 \, a^{3} c^{7}\right)} \sqrt{b^{2} - 4 \, a c}\right)} c - {\left(a b^{6} c^{4} - 2 \, a^{2} b^{4} c^{5} - 2 \, a b^{5} c^{5} - 8 \, a^{3} b^{2} c^{6} - 4 \, a^{2} b^{3} c^{6} + a b^{4} c^{6} + 2 \, a^{2} b^{2} c^{7}\right)} \sqrt{b^{2} - 4 \, a c}\right)} i \log\left(x^{2} + \frac{b c - \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{2 \, c^{2}}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{3}} - \frac{{\left(6 \, {\left(a b^{6} c^{4} - 8 \, a^{2} b^{4} c^{5} - 2 \, a b^{5} c^{5} + 16 \, a^{3} b^{2} c^{6} + 8 \, a^{2} b^{3} c^{6} + a b^{4} c^{6} - 4 \, a^{2} b^{2} c^{7} + {\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} - 2 \, a b^{4} c^{5} + 16 \, a^{3} b c^{6} + 8 \, a^{2} b^{2} c^{6} + a b^{3} c^{6} - 4 \, a^{2} b c^{7}\right)} \sqrt{b^{2} - 4 \, a c}\right)} c g + {\left(a b^{10} - 18 \, a^{2} b^{8} c - 2 \, a b^{9} c + 126 \, a^{3} b^{6} c^{2} + 28 \, a^{2} b^{7} c^{2} + a b^{8} c^{2} - 400 \, a^{4} b^{4} c^{3} - 140 \, a^{3} b^{5} c^{3} - 14 \, a^{2} b^{6} c^{3} + 480 \, a^{5} b^{2} c^{4} + 240 \, a^{4} b^{3} c^{4} + 70 \, a^{3} b^{4} c^{4} - 120 \, a^{4} b^{2} c^{5} + {\left(a b^{9} - 18 \, a^{2} b^{7} c - 2 \, a b^{8} c + 126 \, a^{3} b^{5} c^{2} + 28 \, a^{2} b^{6} c^{2} + a b^{7} c^{2} - 400 \, a^{4} b^{3} c^{3} - 140 \, a^{3} b^{4} c^{3} - 14 \, a^{2} b^{5} c^{3} + 480 \, a^{5} b c^{4} + 240 \, a^{4} b^{2} c^{4} + 70 \, a^{3} b^{3} c^{4} - 120 \, a^{4} b c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} c k - 12 \, {\left(a b^{5} c^{5} - 8 \, a^{2} b^{3} c^{6} - 2 \, a b^{4} c^{6} + 16 \, a^{3} b c^{7} + 8 \, a^{2} b^{2} c^{7} + a b^{3} c^{7} - 4 \, a^{2} b c^{8} + {\left(a b^{4} c^{5} - 8 \, a^{2} b^{2} c^{6} - 2 \, a b^{3} c^{6} + 16 \, a^{3} c^{7} + 8 \, a^{2} b c^{7} + a b^{2} c^{7} - 4 \, a^{2} c^{8}\right)} \sqrt{b^{2} - 4 \, a c}\right)} c e - 6 \, {\left(a b^{6} c^{5} - 8 \, a^{2} b^{4} c^{6} - 2 \, a b^{5} c^{6} + 16 \, a^{3} b^{2} c^{7} + 8 \, a^{2} b^{3} c^{7} + a b^{4} c^{7} - 4 \, a^{2} b^{2} c^{8} + {\left(a b^{5} c^{5} - 4 \, a^{2} b^{3} c^{6} - 2 \, a b^{4} c^{6} + a b^{3} c^{7}\right)} \sqrt{b^{2} - 4 \, a c}\right)} g - {\left(a b^{10} c - 18 \, a^{2} b^{8} c^{2} - 2 \, a b^{9} c^{2} + 126 \, a^{3} b^{6} c^{3} + 28 \, a^{2} b^{7} c^{3} + a b^{8} c^{3} - 400 \, a^{4} b^{4} c^{4} - 140 \, a^{3} b^{5} c^{4} - 14 \, a^{2} b^{6} c^{4} + 480 \, a^{5} b^{2} c^{5} + 240 \, a^{4} b^{3} c^{5} + 70 \, a^{3} b^{4} c^{5} - 120 \, a^{4} b^{2} c^{6} + {\left(a b^{9} c - 14 \, a^{2} b^{7} c^{2} - 2 \, a b^{8} c^{2} + 70 \, a^{3} b^{5} c^{3} + 20 \, a^{2} b^{6} c^{3} + a b^{7} c^{3} - 120 \, a^{4} b^{3} c^{4} - 60 \, a^{3} b^{4} c^{4} - 10 \, a^{2} b^{5} c^{4} + 30 \, a^{3} b^{3} c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} k + 12 \, {\left(a b^{5} c^{6} - 8 \, a^{2} b^{3} c^{7} - 2 \, a b^{4} c^{7} + 16 \, a^{3} b c^{8} + 8 \, a^{2} b^{2} c^{8} + a b^{3} c^{8} - 4 \, a^{2} b c^{9} + {\left(a b^{4} c^{6} - 4 \, a^{2} b^{2} c^{7} - 2 \, a b^{3} c^{7} + a b^{2} c^{8}\right)} \sqrt{b^{2} - 4 \, a c}\right)} e\right)} \log\left(x^{2} + \frac{b c + \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{2 \, c^{2}}\right)}{2 \, {\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{3}} - \frac{{\left(6 \, {\left(a b^{6} c^{4} - 8 \, a^{2} b^{4} c^{5} - 2 \, a b^{5} c^{5} + 16 \, a^{3} b^{2} c^{6} + 8 \, a^{2} b^{3} c^{6} + a b^{4} c^{6} - 4 \, a^{2} b^{2} c^{7} - {\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} - 2 \, a b^{4} c^{5} + 16 \, a^{3} b c^{6} + 8 \, a^{2} b^{2} c^{6} + a b^{3} c^{6} - 4 \, a^{2} b c^{7}\right)} \sqrt{b^{2} - 4 \, a c}\right)} c g + {\left(a b^{10} - 18 \, a^{2} b^{8} c - 2 \, a b^{9} c + 126 \, a^{3} b^{6} c^{2} + 28 \, a^{2} b^{7} c^{2} + a b^{8} c^{2} - 400 \, a^{4} b^{4} c^{3} - 140 \, a^{3} b^{5} c^{3} - 14 \, a^{2} b^{6} c^{3} + 480 \, a^{5} b^{2} c^{4} + 240 \, a^{4} b^{3} c^{4} + 70 \, a^{3} b^{4} c^{4} - 120 \, a^{4} b^{2} c^{5} - {\left(a b^{9} - 18 \, a^{2} b^{7} c - 2 \, a b^{8} c + 126 \, a^{3} b^{5} c^{2} + 28 \, a^{2} b^{6} c^{2} + a b^{7} c^{2} - 400 \, a^{4} b^{3} c^{3} - 140 \, a^{3} b^{4} c^{3} - 14 \, a^{2} b^{5} c^{3} + 480 \, a^{5} b c^{4} + 240 \, a^{4} b^{2} c^{4} + 70 \, a^{3} b^{3} c^{4} - 120 \, a^{4} b c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} c k - 12 \, {\left(a b^{5} c^{5} - 8 \, a^{2} b^{3} c^{6} - 2 \, a b^{4} c^{6} + 16 \, a^{3} b c^{7} + 8 \, a^{2} b^{2} c^{7} + a b^{3} c^{7} - 4 \, a^{2} b c^{8} + {\left(a b^{4} c^{5} - 8 \, a^{2} b^{2} c^{6} - 2 \, a b^{3} c^{6} + 16 \, a^{3} c^{7} + 8 \, a^{2} b c^{7} + a b^{2} c^{7} - 4 \, a^{2} c^{8}\right)} \sqrt{b^{2} - 4 \, a c}\right)} c e - 6 \, {\left(a b^{6} c^{5} - 8 \, a^{2} b^{4} c^{6} - 2 \, a b^{5} c^{6} + 16 \, a^{3} b^{2} c^{7} + 8 \, a^{2} b^{3} c^{7} + a b^{4} c^{7} - 4 \, a^{2} b^{2} c^{8} - {\left(a b^{5} c^{5} - 4 \, a^{2} b^{3} c^{6} - 2 \, a b^{4} c^{6} + a b^{3} c^{7}\right)} \sqrt{b^{2} - 4 \, a c}\right)} g - {\left(a b^{10} c - 18 \, a^{2} b^{8} c^{2} - 2 \, a b^{9} c^{2} + 126 \, a^{3} b^{6} c^{3} + 28 \, a^{2} b^{7} c^{3} + a b^{8} c^{3} - 400 \, a^{4} b^{4} c^{4} - 140 \, a^{3} b^{5} c^{4} - 14 \, a^{2} b^{6} c^{4} + 480 \, a^{5} b^{2} c^{5} + 240 \, a^{4} b^{3} c^{5} + 70 \, a^{3} b^{4} c^{5} - 120 \, a^{4} b^{2} c^{6} - {\left(a b^{9} c - 14 \, a^{2} b^{7} c^{2} - 2 \, a b^{8} c^{2} + 70 \, a^{3} b^{5} c^{3} + 20 \, a^{2} b^{6} c^{3} + a b^{7} c^{3} - 120 \, a^{4} b^{3} c^{4} - 60 \, a^{3} b^{4} c^{4} - 10 \, a^{2} b^{5} c^{4} + 30 \, a^{3} b^{3} c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} k + 12 \, {\left(a b^{5} c^{6} - 8 \, a^{2} b^{3} c^{7} - 2 \, a b^{4} c^{7} + 16 \, a^{3} b c^{8} + 8 \, a^{2} b^{2} c^{8} + a b^{3} c^{8} - 4 \, a^{2} b c^{9} - {\left(a b^{4} c^{6} - 4 \, a^{2} b^{2} c^{7} - 2 \, a b^{3} c^{7} + a b^{2} c^{8}\right)} \sqrt{b^{2} - 4 \, a c}\right)} e\right)} \log\left(x^{2} + \frac{b c - \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{2 \, c^{2}}\right)}{2 \, {\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{3}}}{8 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)}}"," ",0,"1/8*(12*a^4*b*c^3*i - (12*a^2*b*c^5*h - 3*(b^3*c^5 - 8*a*b*c^6)*d - (a*b^2*c^5 + 20*a^2*c^6)*f - (a^2*b^3*c^3 - 16*a^3*b*c^4)*j)*x^7 + 4*(6*a^2*c^6*e - 3*a^2*b*c^5*g + (a^2*b^2*c^4 + 2*a^3*c^5)*i + (2*a^2*b^5*c - 15*a^3*b^3*c^2 + 25*a^4*b*c^3)*k)*x^6 + ((6*b^4*c^4 - 49*a*b^2*c^5 + 28*a^2*c^6)*d + 2*(a*b^3*c^4 + 14*a^2*b*c^5)*f - (19*a^2*b^2*c^4 - 4*a^3*c^5)*h - (a^2*b^4*c^2 + 5*a^3*b^2*c^3 + 36*a^4*c^4)*j)*x^5 + 2*(18*a^2*b*c^5*e - 9*a^2*b^2*c^4*g + 3*(a^2*b^3*c^3 + 2*a^3*b*c^4)*i + (3*a^2*b^6 - 19*a^3*b^4*c + 11*a^4*b^2*c^2 + 32*a^5*c^3)*k)*x^4 + ((3*b^5*c^3 - 20*a*b^3*c^4 - 4*a^2*b*c^5)*d + (a*b^4*c^3 + 5*a^2*b^2*c^4 + 36*a^3*c^5)*f - (5*a^2*b^3*c^3 + 16*a^3*b*c^4)*h - 2*(a^3*b^3*c^2 + 14*a^4*b*c^3)*j)*x^3 + 4*(2*(a^2*b^2*c^4 + 5*a^3*c^5)*e - (a^2*b^3*c^3 + 5*a^3*b*c^4)*g + (5*a^3*b^2*c^3 - 2*a^4*c^4)*i + (3*a^3*b^5 - 22*a^4*b^3*c + 31*a^5*b*c^2)*k)*x^2 - 2*(a^2*b^3*c^3 - 10*a^3*b*c^4)*e - 2*(a^3*b^2*c^3 + 8*a^4*c^4)*g + 6*(a^4*b^4 - 7*a^5*b^2*c + 8*a^6*c^2)*k + ((5*a*b^4*c^3 - 37*a^2*b^2*c^4 + 44*a^3*c^5)*d - (a^2*b^3*c^3 - 16*a^3*b*c^4)*f - 3*(a^3*b^2*c^3 + 4*a^4*c^4)*h - (a^4*b^2*c^2 + 20*a^5*c^3)*j)*x)/(a^4*b^4*c^3 - 8*a^5*b^2*c^4 + 16*a^6*c^5 + (a^2*b^4*c^5 - 8*a^3*b^2*c^6 + 16*a^4*c^7)*x^8 + 2*(a^2*b^5*c^4 - 8*a^3*b^3*c^5 + 16*a^4*b*c^6)*x^6 + (a^2*b^6*c^3 - 6*a^3*b^4*c^4 + 32*a^5*c^6)*x^4 + 2*(a^3*b^5*c^3 - 8*a^4*b^3*c^4 + 16*a^5*b*c^5)*x^2) + 1/8*integrate((8*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*k*x^3 - (12*a^2*b*c^3*h - 3*(b^3*c^3 - 8*a*b*c^4)*d - (a*b^2*c^3 + 20*a^2*c^4)*f - (a^2*b^3*c - 16*a^3*b*c^2)*j)*x^2 + 3*(b^4*c^2 - 9*a*b^2*c^3 + 28*a^2*c^4)*d + (a*b^3*c^2 - 16*a^2*b*c^3)*f + 3*(a^2*b^2*c^2 + 4*a^3*c^3)*h + (a^3*b^2*c + 20*a^4*c^2)*j + 8*(6*a^2*c^4*e - 3*a^2*b*c^3*g + (a^2*b^2*c^2 + 2*a^3*c^3)*i + (a^3*b^3 - 7*a^4*b*c)*k)*x)/(c*x^4 + b*x^2 + a), x)/(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)","F",0
60,1,418,0,0.516614," ","integrate((c*x^4+b*x^2+a)^3*(a*d+a*e*x+(a*f+b*d)*x^2+b*e*x^3+(b*f+c*d)*x^4+c*e*x^5+c*f*x^6),x, algorithm=""maxima"")","\frac{1}{19} \, c^{4} f x^{19} + \frac{1}{18} \, c^{4} e x^{18} + \frac{1}{4} \, b c^{3} e x^{16} + \frac{1}{17} \, {\left(c^{4} d + 4 \, b c^{3} f\right)} x^{17} + \frac{1}{7} \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e x^{14} + \frac{2}{15} \, {\left(2 \, b c^{3} d + {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} f\right)} x^{15} + \frac{1}{3} \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e x^{12} + \frac{2}{13} \, {\left({\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d + 2 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} f\right)} x^{13} + \frac{1}{10} \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e x^{10} + \frac{1}{11} \, {\left(4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} f\right)} x^{11} + \frac{1}{2} \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e x^{8} + \frac{1}{9} \, {\left({\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d + 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} f\right)} x^{9} + a^{3} b e x^{4} + \frac{1}{3} \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e x^{6} + \frac{2}{7} \, {\left(2 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} f\right)} x^{7} + \frac{1}{2} \, a^{4} e x^{2} + a^{4} d x + \frac{2}{5} \, {\left(2 \, a^{3} b f + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d\right)} x^{5} + \frac{1}{3} \, {\left(4 \, a^{3} b d + a^{4} f\right)} x^{3}"," ",0,"1/19*c^4*f*x^19 + 1/18*c^4*e*x^18 + 1/4*b*c^3*e*x^16 + 1/17*(c^4*d + 4*b*c^3*f)*x^17 + 1/7*(3*b^2*c^2 + 2*a*c^3)*e*x^14 + 2/15*(2*b*c^3*d + (3*b^2*c^2 + 2*a*c^3)*f)*x^15 + 1/3*(b^3*c + 3*a*b*c^2)*e*x^12 + 2/13*((3*b^2*c^2 + 2*a*c^3)*d + 2*(b^3*c + 3*a*b*c^2)*f)*x^13 + 1/10*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e*x^10 + 1/11*(4*(b^3*c + 3*a*b*c^2)*d + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*f)*x^11 + 1/2*(a*b^3 + 3*a^2*b*c)*e*x^8 + 1/9*((b^4 + 12*a*b^2*c + 6*a^2*c^2)*d + 4*(a*b^3 + 3*a^2*b*c)*f)*x^9 + a^3*b*e*x^4 + 1/3*(3*a^2*b^2 + 2*a^3*c)*e*x^6 + 2/7*(2*(a*b^3 + 3*a^2*b*c)*d + (3*a^2*b^2 + 2*a^3*c)*f)*x^7 + 1/2*a^4*e*x^2 + a^4*d*x + 2/5*(2*a^3*b*f + (3*a^2*b^2 + 2*a^3*c)*d)*x^5 + 1/3*(4*a^3*b*d + a^4*f)*x^3","A",0
61,1,251,0,0.698004," ","integrate((c*x^4+b*x^2+a)^2*(a*d+a*e*x+(a*f+b*d)*x^2+b*e*x^3+(b*f+c*d)*x^4+c*e*x^5+c*f*x^6),x, algorithm=""maxima"")","\frac{1}{15} \, c^{3} f x^{15} + \frac{1}{14} \, c^{3} e x^{14} + \frac{1}{4} \, b c^{2} e x^{12} + \frac{1}{13} \, {\left(c^{3} d + 3 \, b c^{2} f\right)} x^{13} + \frac{3}{10} \, {\left(b^{2} c + a c^{2}\right)} e x^{10} + \frac{3}{11} \, {\left(b c^{2} d + {\left(b^{2} c + a c^{2}\right)} f\right)} x^{11} + \frac{1}{8} \, {\left(b^{3} + 6 \, a b c\right)} e x^{8} + \frac{1}{9} \, {\left(3 \, {\left(b^{2} c + a c^{2}\right)} d + {\left(b^{3} + 6 \, a b c\right)} f\right)} x^{9} + \frac{3}{4} \, a^{2} b e x^{4} + \frac{1}{2} \, {\left(a b^{2} + a^{2} c\right)} e x^{6} + \frac{1}{7} \, {\left({\left(b^{3} + 6 \, a b c\right)} d + 3 \, {\left(a b^{2} + a^{2} c\right)} f\right)} x^{7} + \frac{1}{2} \, a^{3} e x^{2} + \frac{3}{5} \, {\left(a^{2} b f + {\left(a b^{2} + a^{2} c\right)} d\right)} x^{5} + a^{3} d x + \frac{1}{3} \, {\left(3 \, a^{2} b d + a^{3} f\right)} x^{3}"," ",0,"1/15*c^3*f*x^15 + 1/14*c^3*e*x^14 + 1/4*b*c^2*e*x^12 + 1/13*(c^3*d + 3*b*c^2*f)*x^13 + 3/10*(b^2*c + a*c^2)*e*x^10 + 3/11*(b*c^2*d + (b^2*c + a*c^2)*f)*x^11 + 1/8*(b^3 + 6*a*b*c)*e*x^8 + 1/9*(3*(b^2*c + a*c^2)*d + (b^3 + 6*a*b*c)*f)*x^9 + 3/4*a^2*b*e*x^4 + 1/2*(a*b^2 + a^2*c)*e*x^6 + 1/7*((b^3 + 6*a*b*c)*d + 3*(a*b^2 + a^2*c)*f)*x^7 + 1/2*a^3*e*x^2 + 3/5*(a^2*b*f + (a*b^2 + a^2*c)*d)*x^5 + a^3*d*x + 1/3*(3*a^2*b*d + a^3*f)*x^3","A",0
62,1,138,0,0.587992," ","integrate((c*x^4+b*x^2+a)*(a*d+a*e*x+(a*f+b*d)*x^2+b*e*x^3+(b*f+c*d)*x^4+c*e*x^5+c*f*x^6),x, algorithm=""maxima"")","\frac{1}{11} \, c^{2} f x^{11} + \frac{1}{10} \, c^{2} e x^{10} + \frac{1}{4} \, b c e x^{8} + \frac{1}{9} \, {\left(c^{2} d + 2 \, b c f\right)} x^{9} + \frac{1}{6} \, {\left(b^{2} + 2 \, a c\right)} e x^{6} + \frac{1}{7} \, {\left(2 \, b c d + {\left(b^{2} + 2 \, a c\right)} f\right)} x^{7} + \frac{1}{2} \, a b e x^{4} + \frac{1}{5} \, {\left(2 \, a b f + {\left(b^{2} + 2 \, a c\right)} d\right)} x^{5} + \frac{1}{2} \, a^{2} e x^{2} + a^{2} d x + \frac{1}{3} \, {\left(2 \, a b d + a^{2} f\right)} x^{3}"," ",0,"1/11*c^2*f*x^11 + 1/10*c^2*e*x^10 + 1/4*b*c*e*x^8 + 1/9*(c^2*d + 2*b*c*f)*x^9 + 1/6*(b^2 + 2*a*c)*e*x^6 + 1/7*(2*b*c*d + (b^2 + 2*a*c)*f)*x^7 + 1/2*a*b*e*x^4 + 1/5*(2*a*b*f + (b^2 + 2*a*c)*d)*x^5 + 1/2*a^2*e*x^2 + a^2*d*x + 1/3*(2*a*b*d + a^2*f)*x^3","A",0
63,1,16,0,0.616605," ","integrate((a*d+a*e*x+(a*f+b*d)*x^2+b*e*x^3+(b*f+c*d)*x^4+c*e*x^5+c*f*x^6)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{1}{3} \, f x^{3} + \frac{1}{2} \, e x^{2} + d x"," ",0,"1/3*f*x^3 + 1/2*e*x^2 + d*x","A",0
64,0,0,0,0.000000," ","integrate((a*d+a*e*x+(a*f+b*d)*x^2+b*e*x^3+(b*f+c*d)*x^4+c*e*x^5+c*f*x^6)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{c f x^{6} + c e x^{5} + b e x^{3} + {\left(c d + b f\right)} x^{4} + a e x + {\left(b d + a f\right)} x^{2} + a d}{{\left(c x^{4} + b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate((c*f*x^6 + c*e*x^5 + b*e*x^3 + (c*d + b*f)*x^4 + a*e*x + (b*d + a*f)*x^2 + a*d)/(c*x^4 + b*x^2 + a)^2, x)","F",0
65,0,0,0,0.000000," ","integrate((a*d+a*e*x+(a*f+b*d)*x^2+b*e*x^3+(b*f+c*d)*x^4+c*e*x^5+c*f*x^6)/(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{2 \, a c e x^{2} - {\left(b c d - 2 \, a c f\right)} x^{3} + a b e + {\left(a b f - {\left(b^{2} - 2 \, a c\right)} d\right)} x}{2 \, {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)}} - \frac{-\frac{2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} - 2 \, a b c^{4} + a c^{5}\right)} \sqrt{b^{2} - 4 \, a c} e \log\left(x^{2} + \frac{b + \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} + \frac{2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} - 2 \, a b c^{4} + a c^{5}\right)} \sqrt{b^{2} - 4 \, a c} e \log\left(x^{2} + \frac{b - \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} - \frac{{\left({\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 2 \, b^{6} c + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 28 \, a b^{4} c^{2} + 2 \, b^{5} c^{2} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 128 \, a^{2} b^{2} c^{3} - 24 \, a b^{3} c^{3} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 192 \, a^{3} c^{4} + 64 \, a^{2} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c - 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} + 16 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} d + {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, a b^{5} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 16 \, a^{2} b^{3} c^{2} + 2 \, a b^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 32 \, a^{3} b c^{3} - 32 \, a^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} f\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c} - \frac{{\left({\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 2 \, b^{6} c + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 28 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 128 \, a^{2} b^{2} c^{3} + 24 \, a b^{3} c^{3} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 192 \, a^{3} c^{4} - 64 \, a^{2} b c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c + 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} - 16 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} d + {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, a b^{5} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 16 \, a^{2} b^{3} c^{2} - 2 \, a b^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 32 \, a^{3} b c^{3} + 32 \, a^{3} c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} f\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c}}{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}"," ",0,"-1/2*(2*a*c*e*x^2 - (b*c*d - 2*a*c*f)*x^3 + a*b*e + (a*b*f - (b^2 - 2*a*c)*d)*x)/((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2) - 1/2*integrate((4*a*c*e*x - a*b*f - (b*c*d - 2*a*c*f)*x^2 - (b^2 - 6*a*c)*d)/(c*x^4 + b*x^2 + a), x)/(a*b^2 - 4*a^2*c)","F",0
66,0,0,0,0.000000," ","integrate((a*d+a*e*x+(a*f+b*d)*x^2+b*e*x^3+(b*f+c*d)*x^4+c*e*x^5+c*f*x^6)/(c*x^4+b*x^2+a)^4,x, algorithm=""maxima"")","\frac{24 \, a^{2} c^{3} e x^{6} + 36 \, a^{2} b c^{2} e x^{4} + {\left(3 \, {\left(b^{3} c^{2} - 8 \, a b c^{3}\right)} d + {\left(a b^{2} c^{2} + 20 \, a^{2} c^{3}\right)} f\right)} x^{7} + {\left({\left(6 \, b^{4} c - 49 \, a b^{2} c^{2} + 28 \, a^{2} c^{3}\right)} d + 2 \, {\left(a b^{3} c + 14 \, a^{2} b c^{2}\right)} f\right)} x^{5} + 8 \, {\left(a^{2} b^{2} c + 5 \, a^{3} c^{2}\right)} e x^{2} + {\left({\left(3 \, b^{5} - 20 \, a b^{3} c - 4 \, a^{2} b c^{2}\right)} d + {\left(a b^{4} + 5 \, a^{2} b^{2} c + 36 \, a^{3} c^{2}\right)} f\right)} x^{3} - 2 \, {\left(a^{2} b^{3} - 10 \, a^{3} b c\right)} e + {\left({\left(5 \, a b^{4} - 37 \, a^{2} b^{2} c + 44 \, a^{3} c^{2}\right)} d - {\left(a^{2} b^{3} - 16 \, a^{3} b c\right)} f\right)} x}{8 \, {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{8} + a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2}\right)}} + \frac{-\frac{24 \, {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5} - 2 \, a^{2} b c^{5} + a^{2} c^{6}\right)} \sqrt{b^{2} - 4 \, a c} e \log\left(x^{2} + \frac{b + \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} + \frac{24 \, {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5} - 2 \, a^{2} b c^{5} + a^{2} c^{6}\right)} \sqrt{b^{2} - 4 \, a c} e \log\left(x^{2} + \frac{b - \sqrt{b^{2} - 4 \, a c}}{2 \, c}\right)}{{\left(b^{4} - 8 \, a b^{2} c - 2 \, b^{3} c + 16 \, a^{2} c^{2} + 8 \, a b c^{2} + b^{2} c^{2} - 4 \, a c^{3}\right)} c^{2}} + \frac{{\left(3 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} - 17 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c - 2 \, b^{8} c + 116 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 26 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 34 \, a b^{6} c^{2} + 2 \, b^{7} c^{2} - 368 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 13 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 232 \, a^{2} b^{4} c^{3} - 30 \, a b^{5} c^{3} + 448 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 224 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 736 \, a^{3} b^{2} c^{4} + 176 \, a^{2} b^{3} c^{4} - 112 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} - 896 \, a^{4} c^{5} - 352 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 15 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c - 26 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} + 22 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 224 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} - 88 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} d + {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, a b^{7} c + 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 40 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 48 \, a^{2} b^{5} c^{2} + 2 \, a b^{6} c^{2} - 256 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 288 \, a^{3} b^{3} c^{3} - 44 \, a^{2} b^{4} c^{3} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 512 \, a^{4} b c^{4} + 64 \, a^{3} b^{2} c^{4} + 320 \, a^{4} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} - 36 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c - 40 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3} + 36 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} + 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} f\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c} + \frac{{\left(3 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} - 17 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c + 2 \, b^{8} c + 116 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 26 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} - 34 \, a b^{6} c^{2} - 2 \, b^{7} c^{2} - 368 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 13 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 232 \, a^{2} b^{4} c^{3} + 30 \, a b^{5} c^{3} + 448 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 224 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 736 \, a^{3} b^{2} c^{4} - 176 \, a^{2} b^{3} c^{4} - 112 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 896 \, a^{4} c^{5} + 352 \, a^{3} b c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} - 15 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c + 26 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 22 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} + 224 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} + 88 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} d + {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c + 2 \, a b^{7} c + 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 40 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 48 \, a^{2} b^{5} c^{2} - 2 \, a b^{6} c^{2} - 256 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 288 \, a^{3} b^{3} c^{3} + 44 \, a^{2} b^{4} c^{3} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 512 \, a^{4} b c^{4} - 64 \, a^{3} b^{2} c^{4} - 320 \, a^{4} c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 36 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c + 40 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3} - 36 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} f\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c}}{8 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)}}"," ",0,"1/8*(24*a^2*c^3*e*x^6 + 36*a^2*b*c^2*e*x^4 + (3*(b^3*c^2 - 8*a*b*c^3)*d + (a*b^2*c^2 + 20*a^2*c^3)*f)*x^7 + ((6*b^4*c - 49*a*b^2*c^2 + 28*a^2*c^3)*d + 2*(a*b^3*c + 14*a^2*b*c^2)*f)*x^5 + 8*(a^2*b^2*c + 5*a^3*c^2)*e*x^2 + ((3*b^5 - 20*a*b^3*c - 4*a^2*b*c^2)*d + (a*b^4 + 5*a^2*b^2*c + 36*a^3*c^2)*f)*x^3 - 2*(a^2*b^3 - 10*a^3*b*c)*e + ((5*a*b^4 - 37*a^2*b^2*c + 44*a^3*c^2)*d - (a^2*b^3 - 16*a^3*b*c)*f)*x)/((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^8 + a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2) + 1/8*integrate((48*a^2*c^2*e*x + (3*(b^3*c - 8*a*b*c^2)*d + (a*b^2*c + 20*a^2*c^2)*f)*x^2 + 3*(b^4 - 9*a*b^2*c + 28*a^2*c^2)*d + (a*b^3 - 16*a^2*b*c)*f)/(c*x^4 + b*x^2 + a), x)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)","F",0
67,1,4,0,0.429604," ","integrate((x^3-2*x^2-x+2)/(x^4-5*x^2+4),x, algorithm=""maxima"")","\log\left(x + 2\right)"," ",0,"log(x + 2)","A",0
68,1,14,0,0.436095," ","integrate((e*x+d)*(x^3-2*x^2-x+2)/(x^4-5*x^2+4),x, algorithm=""maxima"")","e x + {\left(d - 2 \, e\right)} \log\left(x + 2\right)"," ",0,"e*x + (d - 2*e)*log(x + 2)","A",0
69,1,27,0,0.454560," ","integrate((f*x^2+e*x+d)*(x^3-2*x^2-x+2)/(x^4-5*x^2+4),x, algorithm=""maxima"")","\frac{1}{2} \, f x^{2} + {\left(e - 2 \, f\right)} x + {\left(d - 2 \, e + 4 \, f\right)} \log\left(x + 2\right)"," ",0,"1/2*f*x^2 + (e - 2*f)*x + (d - 2*e + 4*f)*log(x + 2)","A",0
70,1,43,0,0.448340," ","integrate((x^3-2*x^2-x+2)*(g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4),x, algorithm=""maxima"")","\frac{1}{3} \, g x^{3} + \frac{1}{2} \, {\left(f - 2 \, g\right)} x^{2} + {\left(e - 2 \, f + 4 \, g\right)} x + {\left(d - 2 \, e + 4 \, f - 8 \, g\right)} \log\left(x + 2\right)"," ",0,"1/3*g*x^3 + 1/2*(f - 2*g)*x^2 + (e - 2*f + 4*g)*x + (d - 2*e + 4*f - 8*g)*log(x + 2)","A",0
71,1,62,0,0.436497," ","integrate((x^3-2*x^2-x+2)*(h*x^4+g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4),x, algorithm=""maxima"")","\frac{1}{4} \, h x^{4} + \frac{1}{3} \, {\left(g - 2 \, h\right)} x^{3} + \frac{1}{2} \, {\left(f - 2 \, g + 4 \, h\right)} x^{2} + {\left(e - 2 \, f + 4 \, g - 8 \, h\right)} x + {\left(d - 2 \, e + 4 \, f - 8 \, g + 16 \, h\right)} \log\left(x + 2\right)"," ",0,"1/4*h*x^4 + 1/3*(g - 2*h)*x^3 + 1/2*(f - 2*g + 4*h)*x^2 + (e - 2*f + 4*g - 8*h)*x + (d - 2*e + 4*f - 8*g + 16*h)*log(x + 2)","A",0
72,1,84,0,0.462532," ","integrate((x^3-2*x^2-x+2)*(i*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4),x, algorithm=""maxima"")","\frac{1}{5} \, i x^{5} + \frac{1}{4} \, {\left(h - 2 \, i\right)} x^{4} + \frac{1}{3} \, {\left(g - 2 \, h + 4 \, i\right)} x^{3} + \frac{1}{2} \, {\left(f - 2 \, g + 4 \, h - 8 \, i\right)} x^{2} + {\left(e - 2 \, f + 4 \, g - 8 \, h + 16 \, i\right)} x + {\left(d - 2 \, e + 4 \, f - 8 \, g + 16 \, h - 32 \, i\right)} \log\left(x + 2\right)"," ",0,"1/5*i*x^5 + 1/4*(h - 2*i)*x^4 + 1/3*(g - 2*h + 4*i)*x^3 + 1/2*(f - 2*g + 4*h - 8*i)*x^2 + (e - 2*f + 4*g - 8*h + 16*i)*x + (d - 2*e + 4*f - 8*g + 16*h - 32*i)*log(x + 2)","A",0
73,1,11,0,0.428659," ","integrate((x^2-3*x+2)/(x^4-5*x^2+4),x, algorithm=""maxima"")","-\log\left(x + 2\right) + \log\left(x + 1\right)"," ",0,"-log(x + 2) + log(x + 1)","A",0
74,1,22,0,0.436797," ","integrate((e*x+d)*(x^2-3*x+2)/(x^4-5*x^2+4),x, algorithm=""maxima"")","-{\left(d - 2 \, e\right)} \log\left(x + 2\right) + {\left(d - e\right)} \log\left(x + 1\right)"," ",0,"-(d - 2*e)*log(x + 2) + (d - e)*log(x + 1)","A",0
75,1,29,0,0.434259," ","integrate((x^2-3*x+2)*(f*x^2+e*x+d)/(x^4-5*x^2+4),x, algorithm=""maxima"")","f x - {\left(d - 2 \, e + 4 \, f\right)} \log\left(x + 2\right) + {\left(d - e + f\right)} \log\left(x + 1\right)"," ",0,"f*x - (d - 2*e + 4*f)*log(x + 2) + (d - e + f)*log(x + 1)","A",0
76,1,45,0,0.448403," ","integrate((x^2-3*x+2)*(g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4),x, algorithm=""maxima"")","\frac{1}{2} \, g x^{2} + {\left(f - 3 \, g\right)} x - {\left(d - 2 \, e + 4 \, f - 8 \, g\right)} \log\left(x + 2\right) + {\left(d - e + f - g\right)} \log\left(x + 1\right)"," ",0,"1/2*g*x^2 + (f - 3*g)*x - (d - 2*e + 4*f - 8*g)*log(x + 2) + (d - e + f - g)*log(x + 1)","A",0
77,1,62,0,0.444031," ","integrate((x^2-3*x+2)*(h*x^4+g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4),x, algorithm=""maxima"")","\frac{1}{3} \, h x^{3} + \frac{1}{2} \, {\left(g - 3 \, h\right)} x^{2} + {\left(f - 3 \, g + 7 \, h\right)} x - {\left(d - 2 \, e + 4 \, f - 8 \, g + 16 \, h\right)} \log\left(x + 2\right) + {\left(d - e + f - g + h\right)} \log\left(x + 1\right)"," ",0,"1/3*h*x^3 + 1/2*(g - 3*h)*x^2 + (f - 3*g + 7*h)*x - (d - 2*e + 4*f - 8*g + 16*h)*log(x + 2) + (d - e + f - g + h)*log(x + 1)","A",0
78,1,84,0,0.440544," ","integrate((x^2-3*x+2)*(i*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4),x, algorithm=""maxima"")","\frac{1}{4} \, i x^{4} + \frac{1}{3} \, {\left(h - 3 \, i\right)} x^{3} + \frac{1}{2} \, {\left(g - 3 \, h + 7 \, i\right)} x^{2} + {\left(f - 3 \, g + 7 \, h - 15 \, i\right)} x - {\left(d - 2 \, e + 4 \, f - 8 \, g + 16 \, h - 32 \, i\right)} \log\left(x + 2\right) + {\left(d - e + f - g + h - i\right)} \log\left(x + 1\right)"," ",0,"1/4*i*x^4 + 1/3*(h - 3*i)*x^3 + 1/2*(g - 3*h + 7*i)*x^2 + (f - 3*g + 7*h - 15*i)*x - (d - 2*e + 4*f - 8*g + 16*h - 32*i)*log(x + 2) + (d - e + f - g + h - i)*log(x + 1)","A",0
79,1,19,0,0.438895," ","integrate((2+x)/(x^4-5*x^2+4),x, algorithm=""maxima"")","\frac{1}{6} \, \log\left(x + 1\right) - \frac{1}{2} \, \log\left(x - 1\right) + \frac{1}{3} \, \log\left(x - 2\right)"," ",0,"1/6*log(x + 1) - 1/2*log(x - 1) + 1/3*log(x - 2)","A",0
80,1,32,0,0.443991," ","integrate((2+x)*(e*x+d)/(x^4-5*x^2+4),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(d - e\right)} \log\left(x + 1\right) - \frac{1}{2} \, {\left(d + e\right)} \log\left(x - 1\right) + \frac{1}{3} \, {\left(d + 2 \, e\right)} \log\left(x - 2\right)"," ",0,"1/6*(d - e)*log(x + 1) - 1/2*(d + e)*log(x - 1) + 1/3*(d + 2*e)*log(x - 2)","A",0
81,1,37,0,0.436383," ","integrate((2+x)*(f*x^2+e*x+d)/(x^4-5*x^2+4),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(d - e + f\right)} \log\left(x + 1\right) - \frac{1}{2} \, {\left(d + e + f\right)} \log\left(x - 1\right) + \frac{1}{3} \, {\left(d + 2 \, e + 4 \, f\right)} \log\left(x - 2\right)"," ",0,"1/6*(d - e + f)*log(x + 1) - 1/2*(d + e + f)*log(x - 1) + 1/3*(d + 2*e + 4*f)*log(x - 2)","A",0
82,1,47,0,0.437688," ","integrate((2+x)*(g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4),x, algorithm=""maxima"")","g x + \frac{1}{6} \, {\left(d - e + f - g\right)} \log\left(x + 1\right) - \frac{1}{2} \, {\left(d + e + f + g\right)} \log\left(x - 1\right) + \frac{1}{3} \, {\left(d + 2 \, e + 4 \, f + 8 \, g\right)} \log\left(x - 2\right)"," ",0,"g*x + 1/6*(d - e + f - g)*log(x + 1) - 1/2*(d + e + f + g)*log(x - 1) + 1/3*(d + 2*e + 4*f + 8*g)*log(x - 2)","A",0
83,1,62,0,0.449795," ","integrate((2+x)*(h*x^4+g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4),x, algorithm=""maxima"")","\frac{1}{2} \, h x^{2} + {\left(g + 2 \, h\right)} x + \frac{1}{6} \, {\left(d - e + f - g + h\right)} \log\left(x + 1\right) - \frac{1}{2} \, {\left(d + e + f + g + h\right)} \log\left(x - 1\right) + \frac{1}{3} \, {\left(d + 2 \, e + 4 \, f + 8 \, g + 16 \, h\right)} \log\left(x - 2\right)"," ",0,"1/2*h*x^2 + (g + 2*h)*x + 1/6*(d - e + f - g + h)*log(x + 1) - 1/2*(d + e + f + g + h)*log(x - 1) + 1/3*(d + 2*e + 4*f + 8*g + 16*h)*log(x - 2)","A",0
84,1,82,0,0.449044," ","integrate((2+x)*(i*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4),x, algorithm=""maxima"")","\frac{1}{3} \, i x^{3} + \frac{1}{2} \, {\left(h + 2 \, i\right)} x^{2} + {\left(g + 2 \, h + 5 \, i\right)} x + \frac{1}{6} \, {\left(d - e + f - g + h - i\right)} \log\left(x + 1\right) - \frac{1}{2} \, {\left(d + e + f + g + h + i\right)} \log\left(x - 1\right) + \frac{1}{3} \, {\left(d + 2 \, e + 4 \, f + 8 \, g + 16 \, h + 32 \, i\right)} \log\left(x - 2\right)"," ",0,"1/3*i*x^3 + 1/2*(h + 2*i)*x^2 + (g + 2*h + 5*i)*x + 1/6*(d - e + f - g + h - i)*log(x + 1) - 1/2*(d + e + f + g + h + i)*log(x - 1) + 1/3*(d + 2*e + 4*f + 8*g + 16*h + 32*i)*log(x - 2)","A",0
85,1,32,0,0.436102," ","integrate((x^3-2*x^2-x+2)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","\frac{1}{12 \, {\left(x + 2\right)}} - \frac{19}{144} \, \log\left(x + 2\right) + \frac{1}{6} \, \log\left(x + 1\right) - \frac{1}{18} \, \log\left(x - 1\right) + \frac{1}{48} \, \log\left(x - 2\right)"," ",0,"1/12/(x + 2) - 19/144*log(x + 2) + 1/6*log(x + 1) - 1/18*log(x - 1) + 1/48*log(x - 2)","A",0
86,1,57,0,0.438694," ","integrate((e*x+d)*(x^3-2*x^2-x+2)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","-\frac{1}{144} \, {\left(19 \, d - 26 \, e\right)} \log\left(x + 2\right) + \frac{1}{6} \, {\left(d - e\right)} \log\left(x + 1\right) - \frac{1}{18} \, {\left(d + e\right)} \log\left(x - 1\right) + \frac{1}{48} \, {\left(d + 2 \, e\right)} \log\left(x - 2\right) + \frac{d - 2 \, e}{12 \, {\left(x + 2\right)}}"," ",0,"-1/144*(19*d - 26*e)*log(x + 2) + 1/6*(d - e)*log(x + 1) - 1/18*(d + e)*log(x - 1) + 1/48*(d + 2*e)*log(x - 2) + 1/12*(d - 2*e)/(x + 2)","A",0
87,1,68,0,0.461144," ","integrate((f*x^2+e*x+d)*(x^3-2*x^2-x+2)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","-\frac{1}{144} \, {\left(19 \, d - 26 \, e + 28 \, f\right)} \log\left(x + 2\right) + \frac{1}{6} \, {\left(d - e + f\right)} \log\left(x + 1\right) - \frac{1}{18} \, {\left(d + e + f\right)} \log\left(x - 1\right) + \frac{1}{48} \, {\left(d + 2 \, e + 4 \, f\right)} \log\left(x - 2\right) + \frac{d - 2 \, e + 4 \, f}{12 \, {\left(x + 2\right)}}"," ",0,"-1/144*(19*d - 26*e + 28*f)*log(x + 2) + 1/6*(d - e + f)*log(x + 1) - 1/18*(d + e + f)*log(x - 1) + 1/48*(d + 2*e + 4*f)*log(x - 2) + 1/12*(d - 2*e + 4*f)/(x + 2)","A",0
88,1,81,0,0.443661," ","integrate((x^3-2*x^2-x+2)*(g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","-\frac{1}{144} \, {\left(19 \, d - 26 \, e + 28 \, f - 8 \, g\right)} \log\left(x + 2\right) + \frac{1}{6} \, {\left(d - e + f - g\right)} \log\left(x + 1\right) - \frac{1}{18} \, {\left(d + e + f + g\right)} \log\left(x - 1\right) + \frac{1}{48} \, {\left(d + 2 \, e + 4 \, f + 8 \, g\right)} \log\left(x - 2\right) + \frac{d - 2 \, e + 4 \, f - 8 \, g}{12 \, {\left(x + 2\right)}}"," ",0,"-1/144*(19*d - 26*e + 28*f - 8*g)*log(x + 2) + 1/6*(d - e + f - g)*log(x + 1) - 1/18*(d + e + f + g)*log(x - 1) + 1/48*(d + 2*e + 4*f + 8*g)*log(x - 2) + 1/12*(d - 2*e + 4*f - 8*g)/(x + 2)","A",0
89,1,92,0,0.441734," ","integrate((x^3-2*x^2-x+2)*(h*x^4+g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","-\frac{1}{144} \, {\left(19 \, d - 26 \, e + 28 \, f - 8 \, g - 80 \, h\right)} \log\left(x + 2\right) + \frac{1}{6} \, {\left(d - e + f - g + h\right)} \log\left(x + 1\right) - \frac{1}{18} \, {\left(d + e + f + g + h\right)} \log\left(x - 1\right) + \frac{1}{48} \, {\left(d + 2 \, e + 4 \, f + 8 \, g + 16 \, h\right)} \log\left(x - 2\right) + \frac{d - 2 \, e + 4 \, f - 8 \, g + 16 \, h}{12 \, {\left(x + 2\right)}}"," ",0,"-1/144*(19*d - 26*e + 28*f - 8*g - 80*h)*log(x + 2) + 1/6*(d - e + f - g + h)*log(x + 1) - 1/18*(d + e + f + g + h)*log(x - 1) + 1/48*(d + 2*e + 4*f + 8*g + 16*h)*log(x - 2) + 1/12*(d - 2*e + 4*f - 8*g + 16*h)/(x + 2)","A",0
90,1,108,0,0.450028," ","integrate((x^3-2*x^2-x+2)*(i*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","i x - \frac{1}{144} \, {\left(19 \, d - 26 \, e + 28 \, f - 8 \, g - 80 \, h + 352 \, i\right)} \log\left(x + 2\right) + \frac{1}{6} \, {\left(d - e + f - g + h - i\right)} \log\left(x + 1\right) - \frac{1}{18} \, {\left(d + e + f + g + h + i\right)} \log\left(x - 1\right) + \frac{1}{48} \, {\left(d + 2 \, e + 4 \, f + 8 \, g + 16 \, h + 32 \, i\right)} \log\left(x - 2\right) + \frac{d - 2 \, e + 4 \, f - 8 \, g + 16 \, h - 32 \, i}{12 \, {\left(x + 2\right)}}"," ",0,"i*x - 1/144*(19*d - 26*e + 28*f - 8*g - 80*h + 352*i)*log(x + 2) + 1/6*(d - e + f - g + h - i)*log(x + 1) - 1/18*(d + e + f + g + h + i)*log(x - 1) + 1/48*(d + 2*e + 4*f + 8*g + 16*h + 32*i)*log(x - 2) + 1/12*(d - 2*e + 4*f - 8*g + 16*h - 32*i)/(x + 2)","A",0
91,1,42,0,0.433410," ","integrate((x^2-3*x+2)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","-\frac{3 \, x + 5}{12 \, {\left(x^{2} + 3 \, x + 2\right)}} + \frac{31}{144} \, \log\left(x + 2\right) - \frac{7}{36} \, \log\left(x + 1\right) - \frac{1}{36} \, \log\left(x - 1\right) + \frac{1}{144} \, \log\left(x - 2\right)"," ",0,"-1/12*(3*x + 5)/(x^2 + 3*x + 2) + 31/144*log(x + 2) - 7/36*log(x + 1) - 1/36*log(x - 1) + 1/144*log(x - 2)","A",0
92,1,75,0,0.454076," ","integrate((e*x+d)*(x^2-3*x+2)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","\frac{1}{144} \, {\left(31 \, d - 50 \, e\right)} \log\left(x + 2\right) - \frac{1}{36} \, {\left(7 \, d - 13 \, e\right)} \log\left(x + 1\right) - \frac{1}{36} \, {\left(d + e\right)} \log\left(x - 1\right) + \frac{1}{144} \, {\left(d + 2 \, e\right)} \log\left(x - 2\right) - \frac{{\left(3 \, d - 4 \, e\right)} x + 5 \, d - 6 \, e}{12 \, {\left(x^{2} + 3 \, x + 2\right)}}"," ",0,"1/144*(31*d - 50*e)*log(x + 2) - 1/36*(7*d - 13*e)*log(x + 1) - 1/36*(d + e)*log(x - 1) + 1/144*(d + 2*e)*log(x - 2) - 1/12*((3*d - 4*e)*x + 5*d - 6*e)/(x^2 + 3*x + 2)","A",0
93,1,91,0,0.442097," ","integrate((x^2-3*x+2)*(f*x^2+e*x+d)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","\frac{1}{144} \, {\left(31 \, d - 50 \, e + 76 \, f\right)} \log\left(x + 2\right) - \frac{1}{36} \, {\left(7 \, d - 13 \, e + 19 \, f\right)} \log\left(x + 1\right) - \frac{1}{36} \, {\left(d + e + f\right)} \log\left(x - 1\right) + \frac{1}{144} \, {\left(d + 2 \, e + 4 \, f\right)} \log\left(x - 2\right) - \frac{{\left(3 \, d - 4 \, e + 6 \, f\right)} x + 5 \, d - 6 \, e + 8 \, f}{12 \, {\left(x^{2} + 3 \, x + 2\right)}}"," ",0,"1/144*(31*d - 50*e + 76*f)*log(x + 2) - 1/36*(7*d - 13*e + 19*f)*log(x + 1) - 1/36*(d + e + f)*log(x - 1) + 1/144*(d + 2*e + 4*f)*log(x - 2) - 1/12*((3*d - 4*e + 6*f)*x + 5*d - 6*e + 8*f)/(x^2 + 3*x + 2)","A",0
94,1,107,0,0.440191," ","integrate((x^2-3*x+2)*(g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","\frac{1}{144} \, {\left(31 \, d - 50 \, e + 76 \, f - 104 \, g\right)} \log\left(x + 2\right) - \frac{1}{36} \, {\left(7 \, d - 13 \, e + 19 \, f - 25 \, g\right)} \log\left(x + 1\right) - \frac{1}{36} \, {\left(d + e + f + g\right)} \log\left(x - 1\right) + \frac{1}{144} \, {\left(d + 2 \, e + 4 \, f + 8 \, g\right)} \log\left(x - 2\right) - \frac{{\left(3 \, d - 4 \, e + 6 \, f - 10 \, g\right)} x + 5 \, d - 6 \, e + 8 \, f - 12 \, g}{12 \, {\left(x^{2} + 3 \, x + 2\right)}}"," ",0,"1/144*(31*d - 50*e + 76*f - 104*g)*log(x + 2) - 1/36*(7*d - 13*e + 19*f - 25*g)*log(x + 1) - 1/36*(d + e + f + g)*log(x - 1) + 1/144*(d + 2*e + 4*f + 8*g)*log(x - 2) - 1/12*((3*d - 4*e + 6*f - 10*g)*x + 5*d - 6*e + 8*f - 12*g)/(x^2 + 3*x + 2)","A",0
95,1,123,0,0.454293," ","integrate((x^2-3*x+2)*(h*x^4+g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","\frac{1}{144} \, {\left(31 \, d - 50 \, e + 76 \, f - 104 \, g + 112 \, h\right)} \log\left(x + 2\right) - \frac{1}{36} \, {\left(7 \, d - 13 \, e + 19 \, f - 25 \, g + 31 \, h\right)} \log\left(x + 1\right) - \frac{1}{36} \, {\left(d + e + f + g + h\right)} \log\left(x - 1\right) + \frac{1}{144} \, {\left(d + 2 \, e + 4 \, f + 8 \, g + 16 \, h\right)} \log\left(x - 2\right) - \frac{{\left(3 \, d - 4 \, e + 6 \, f - 10 \, g + 18 \, h\right)} x + 5 \, d - 6 \, e + 8 \, f - 12 \, g + 20 \, h}{12 \, {\left(x^{2} + 3 \, x + 2\right)}}"," ",0,"1/144*(31*d - 50*e + 76*f - 104*g + 112*h)*log(x + 2) - 1/36*(7*d - 13*e + 19*f - 25*g + 31*h)*log(x + 1) - 1/36*(d + e + f + g + h)*log(x - 1) + 1/144*(d + 2*e + 4*f + 8*g + 16*h)*log(x - 2) - 1/12*((3*d - 4*e + 6*f - 10*g + 18*h)*x + 5*d - 6*e + 8*f - 12*g + 20*h)/(x^2 + 3*x + 2)","A",0
96,1,139,0,0.451908," ","integrate((x^2-3*x+2)*(i*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","\frac{1}{144} \, {\left(31 \, d - 50 \, e + 76 \, f - 104 \, g + 112 \, h - 32 \, i\right)} \log\left(x + 2\right) - \frac{1}{36} \, {\left(7 \, d - 13 \, e + 19 \, f - 25 \, g + 31 \, h - 37 \, i\right)} \log\left(x + 1\right) - \frac{1}{36} \, {\left(d + e + f + g + h + i\right)} \log\left(x - 1\right) + \frac{1}{144} \, {\left(d + 2 \, e + 4 \, f + 8 \, g + 16 \, h + 32 \, i\right)} \log\left(x - 2\right) - \frac{{\left(3 \, d - 4 \, e + 6 \, f - 10 \, g + 18 \, h - 34 \, i\right)} x + 5 \, d - 6 \, e + 8 \, f - 12 \, g + 20 \, h - 36 \, i}{12 \, {\left(x^{2} + 3 \, x + 2\right)}}"," ",0,"1/144*(31*d - 50*e + 76*f - 104*g + 112*h - 32*i)*log(x + 2) - 1/36*(7*d - 13*e + 19*f - 25*g + 31*h - 37*i)*log(x + 1) - 1/36*(d + e + f + g + h + i)*log(x - 1) + 1/144*(d + 2*e + 4*f + 8*g + 16*h + 32*i)*log(x - 2) - 1/12*((3*d - 4*e + 6*f - 10*g + 18*h - 34*i)*x + 5*d - 6*e + 8*f - 12*g + 20*h - 36*i)/(x^2 + 3*x + 2)","A",0
97,1,52,0,0.441669," ","integrate((2+x)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","-\frac{5 \, x^{2} - 6 \, x - 5}{36 \, {\left(x^{3} - 2 \, x^{2} - x + 2\right)}} + \frac{1}{144} \, \log\left(x + 2\right) + \frac{1}{54} \, \log\left(x + 1\right) + \frac{1}{18} \, \log\left(x - 1\right) - \frac{35}{432} \, \log\left(x - 2\right)"," ",0,"-1/36*(5*x^2 - 6*x - 5)/(x^3 - 2*x^2 - x + 2) + 1/144*log(x + 2) + 1/54*log(x + 1) + 1/18*log(x - 1) - 35/432*log(x - 2)","A",0
98,1,88,0,0.441061," ","integrate((2+x)*(e*x+d)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","\frac{1}{144} \, {\left(d - 2 \, e\right)} \log\left(x + 2\right) + \frac{1}{108} \, {\left(2 \, d + e\right)} \log\left(x + 1\right) + \frac{1}{36} \, {\left(2 \, d + 5 \, e\right)} \log\left(x - 1\right) - \frac{1}{432} \, {\left(35 \, d + 58 \, e\right)} \log\left(x - 2\right) - \frac{{\left(5 \, d + 4 \, e\right)} x^{2} - 6 \, d x - 5 \, d - 10 \, e}{36 \, {\left(x^{3} - 2 \, x^{2} - x + 2\right)}}"," ",0,"1/144*(d - 2*e)*log(x + 2) + 1/108*(2*d + e)*log(x + 1) + 1/36*(2*d + 5*e)*log(x - 1) - 1/432*(35*d + 58*e)*log(x - 2) - 1/36*((5*d + 4*e)*x^2 - 6*d*x - 5*d - 10*e)/(x^3 - 2*x^2 - x + 2)","A",0
99,1,108,0,0.442287," ","integrate((2+x)*(f*x^2+e*x+d)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","\frac{1}{144} \, {\left(d - 2 \, e + 4 \, f\right)} \log\left(x + 2\right) + \frac{1}{108} \, {\left(2 \, d + e - 4 \, f\right)} \log\left(x + 1\right) + \frac{1}{36} \, {\left(2 \, d + 5 \, e + 8 \, f\right)} \log\left(x - 1\right) - \frac{1}{432} \, {\left(35 \, d + 58 \, e + 92 \, f\right)} \log\left(x - 2\right) - \frac{{\left(5 \, d + 4 \, e + 8 \, f\right)} x^{2} - 6 \, {\left(d + f\right)} x - 5 \, d - 10 \, e - 8 \, f}{36 \, {\left(x^{3} - 2 \, x^{2} - x + 2\right)}}"," ",0,"1/144*(d - 2*e + 4*f)*log(x + 2) + 1/108*(2*d + e - 4*f)*log(x + 1) + 1/36*(2*d + 5*e + 8*f)*log(x - 1) - 1/432*(35*d + 58*e + 92*f)*log(x - 2) - 1/36*((5*d + 4*e + 8*f)*x^2 - 6*(d + f)*x - 5*d - 10*e - 8*f)/(x^3 - 2*x^2 - x + 2)","A",0
100,1,126,0,0.447032," ","integrate((2+x)*(g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","\frac{1}{144} \, {\left(d - 2 \, e + 4 \, f - 8 \, g\right)} \log\left(x + 2\right) + \frac{1}{108} \, {\left(2 \, d + e - 4 \, f + 7 \, g\right)} \log\left(x + 1\right) + \frac{1}{36} \, {\left(2 \, d + 5 \, e + 8 \, f + 11 \, g\right)} \log\left(x - 1\right) - \frac{1}{432} \, {\left(35 \, d + 58 \, e + 92 \, f + 136 \, g\right)} \log\left(x - 2\right) - \frac{{\left(5 \, d + 4 \, e + 8 \, f + 10 \, g\right)} x^{2} - 6 \, {\left(d + f\right)} x - 5 \, d - 10 \, e - 8 \, f - 16 \, g}{36 \, {\left(x^{3} - 2 \, x^{2} - x + 2\right)}}"," ",0,"1/144*(d - 2*e + 4*f - 8*g)*log(x + 2) + 1/108*(2*d + e - 4*f + 7*g)*log(x + 1) + 1/36*(2*d + 5*e + 8*f + 11*g)*log(x - 1) - 1/432*(35*d + 58*e + 92*f + 136*g)*log(x - 2) - 1/36*((5*d + 4*e + 8*f + 10*g)*x^2 - 6*(d + f)*x - 5*d - 10*e - 8*f - 16*g)/(x^3 - 2*x^2 - x + 2)","A",0
101,1,145,0,0.449610," ","integrate((2+x)*(h*x^4+g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","\frac{1}{144} \, {\left(d - 2 \, e + 4 \, f - 8 \, g + 16 \, h\right)} \log\left(x + 2\right) + \frac{1}{108} \, {\left(2 \, d + e - 4 \, f + 7 \, g - 10 \, h\right)} \log\left(x + 1\right) + \frac{1}{36} \, {\left(2 \, d + 5 \, e + 8 \, f + 11 \, g + 14 \, h\right)} \log\left(x - 1\right) - \frac{1}{432} \, {\left(35 \, d + 58 \, e + 92 \, f + 136 \, g + 176 \, h\right)} \log\left(x - 2\right) - \frac{{\left(5 \, d + 4 \, e + 8 \, f + 10 \, g + 20 \, h\right)} x^{2} - 6 \, {\left(d + f + h\right)} x - 5 \, d - 10 \, e - 8 \, f - 16 \, g - 20 \, h}{36 \, {\left(x^{3} - 2 \, x^{2} - x + 2\right)}}"," ",0,"1/144*(d - 2*e + 4*f - 8*g + 16*h)*log(x + 2) + 1/108*(2*d + e - 4*f + 7*g - 10*h)*log(x + 1) + 1/36*(2*d + 5*e + 8*f + 11*g + 14*h)*log(x - 1) - 1/432*(35*d + 58*e + 92*f + 136*g + 176*h)*log(x - 2) - 1/36*((5*d + 4*e + 8*f + 10*g + 20*h)*x^2 - 6*(d + f + h)*x - 5*d - 10*e - 8*f - 16*g - 20*h)/(x^3 - 2*x^2 - x + 2)","A",0
102,1,163,0,0.461774," ","integrate((2+x)*(i*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(x^4-5*x^2+4)^2,x, algorithm=""maxima"")","\frac{1}{144} \, {\left(d - 2 \, e + 4 \, f - 8 \, g + 16 \, h - 32 \, i\right)} \log\left(x + 2\right) + \frac{1}{108} \, {\left(2 \, d + e - 4 \, f + 7 \, g - 10 \, h + 13 \, i\right)} \log\left(x + 1\right) + \frac{1}{36} \, {\left(2 \, d + 5 \, e + 8 \, f + 11 \, g + 14 \, h + 17 \, i\right)} \log\left(x - 1\right) - \frac{1}{432} \, {\left(35 \, d + 58 \, e + 92 \, f + 136 \, g + 176 \, h + 160 \, i\right)} \log\left(x - 2\right) - \frac{{\left(5 \, d + 4 \, e + 8 \, f + 10 \, g + 20 \, h + 34 \, i\right)} x^{2} - 6 \, {\left(d + f + h\right)} x - 5 \, d - 10 \, e - 8 \, f - 16 \, g - 20 \, h - 40 \, i}{36 \, {\left(x^{3} - 2 \, x^{2} - x + 2\right)}}"," ",0,"1/144*(d - 2*e + 4*f - 8*g + 16*h - 32*i)*log(x + 2) + 1/108*(2*d + e - 4*f + 7*g - 10*h + 13*i)*log(x + 1) + 1/36*(2*d + 5*e + 8*f + 11*g + 14*h + 17*i)*log(x - 1) - 1/432*(35*d + 58*e + 92*f + 136*g + 176*h + 160*i)*log(x - 2) - 1/36*((5*d + 4*e + 8*f + 10*g + 20*h + 34*i)*x^2 - 6*(d + f + h)*x - 5*d - 10*e - 8*f - 16*g - 20*h - 40*i)/(x^3 - 2*x^2 - x + 2)","A",0
103,0,0,0,0.000000," ","integrate((g*x^3+f*x^2+e*x+d)*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""maxima"")","\int {\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}} {\left(g x^{3} + f x^{2} + e x + d\right)}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^(3/2)*(g*x^3 + f*x^2 + e*x + d), x)","F",0
104,0,0,0,0.000000," ","integrate((g*x^3+f*x^2+e*x+d)*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","\int \sqrt{c x^{4} + b x^{2} + a} {\left(g x^{3} + f x^{2} + e x + d\right)}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2 + a)*(g*x^3 + f*x^2 + e*x + d), x)","F",0
105,0,0,0,0.000000," ","integrate((g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""maxima"")","\int \frac{g x^{3} + f x^{2} + e x + d}{\sqrt{c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate((g*x^3 + f*x^2 + e*x + d)/sqrt(c*x^4 + b*x^2 + a), x)","F",0
106,0,0,0,0.000000," ","integrate((g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""maxima"")","\int \frac{g x^{3} + f x^{2} + e x + d}{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*x^3 + f*x^2 + e*x + d)/(c*x^4 + b*x^2 + a)^(3/2), x)","F",0
107,0,0,0,0.000000," ","integrate((g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a)^(5/2),x, algorithm=""maxima"")","\int \frac{g x^{3} + f x^{2} + e x + d}{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*x^3 + f*x^2 + e*x + d)/(c*x^4 + b*x^2 + a)^(5/2), x)","F",0
108,1,17,0,0.633240," ","integrate((-c*g*x^4+a*g)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{g x}{\sqrt{c x^{4} + b x^{2} + a}}"," ",0,"g*x/sqrt(c*x^4 + b*x^2 + a)","A",0
109,1,51,0,0.638089," ","integrate((-c*g*x^4+a*g+e*x)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, c e x^{2} + b e - {\left(b^{2} g - 4 \, a c g\right)} x}{\sqrt{c x^{4} + b x^{2} + a} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"-(2*c*e*x^2 + b*e - (b^2*g - 4*a*c*g)*x)/(sqrt(c*x^4 + b*x^2 + a)*(b^2 - 4*a*c))","A",0
110,1,49,0,0.629953," ","integrate((-c*g*x^4+f*x^3+a*g)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{b f x^{2} + 2 \, a f + {\left(b^{2} g - 4 \, a c g\right)} x}{\sqrt{c x^{4} + b x^{2} + a} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"(b*f*x^2 + 2*a*f + (b^2*g - 4*a*c*g)*x)/(sqrt(c*x^4 + b*x^2 + a)*(b^2 - 4*a*c))","A",0
111,1,94,0,0.678497," ","integrate((-c*g*x^4+f*x^3+a*g+e*x)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""maxima"")","-\frac{\sqrt{c x^{4} + b x^{2} + a} {\left({\left(2 \, c e - b f\right)} x^{2} + b e - 2 \, a f - {\left(b^{2} g - 4 \, a c g\right)} x\right)}}{{\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}}"," ",0,"-sqrt(c*x^4 + b*x^2 + a)*((2*c*e - b*f)*x^2 + b*e - 2*a*f - (b^2*g - 4*a*c*g)*x)/((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2)","A",0
