1,1,60,0,0.452069," ","integrate(x^2*(C*x^2+B*x+A)*(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{1}{9} \, C c x^{9} + \frac{1}{8} \, B c x^{8} + \frac{1}{6} \, B b x^{6} + \frac{1}{7} \, {\left(C b + A c\right)} x^{7} + \frac{1}{4} \, B a x^{4} + \frac{1}{5} \, {\left(C a + A b\right)} x^{5} + \frac{1}{3} \, A a x^{3}"," ",0,"1/9*C*c*x^9 + 1/8*B*c*x^8 + 1/6*B*b*x^6 + 1/7*(C*b + A*c)*x^7 + 1/4*B*a*x^4 + 1/5*(C*a + A*b)*x^5 + 1/3*A*a*x^3","A",0
2,1,60,0,0.465193," ","integrate(x*(C*x^2+B*x+A)*(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{1}{8} \, C c x^{8} + \frac{1}{7} \, B c x^{7} + \frac{1}{5} \, B b x^{5} + \frac{1}{6} \, {\left(C b + A c\right)} x^{6} + \frac{1}{3} \, B a x^{3} + \frac{1}{4} \, {\left(C a + A b\right)} x^{4} + \frac{1}{2} \, A a x^{2}"," ",0,"1/8*C*c*x^8 + 1/7*B*c*x^7 + 1/5*B*b*x^5 + 1/6*(C*b + A*c)*x^6 + 1/3*B*a*x^3 + 1/4*(C*a + A*b)*x^4 + 1/2*A*a*x^2","A",0
3,1,57,0,0.455004," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{1}{7} \, C c x^{7} + \frac{1}{6} \, B c x^{6} + \frac{1}{4} \, B b x^{4} + \frac{1}{5} \, {\left(C b + A c\right)} x^{5} + \frac{1}{2} \, B a x^{2} + \frac{1}{3} \, {\left(C a + A b\right)} x^{3} + A a x"," ",0,"1/7*C*c*x^7 + 1/6*B*c*x^6 + 1/4*B*b*x^4 + 1/5*(C*b + A*c)*x^5 + 1/2*B*a*x^2 + 1/3*(C*a + A*b)*x^3 + A*a*x","A",0
4,1,55,0,0.604094," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x,x, algorithm=""maxima"")","\frac{1}{6} \, C c x^{6} + \frac{1}{5} \, B c x^{5} + \frac{1}{3} \, B b x^{3} + \frac{1}{4} \, {\left(C b + A c\right)} x^{4} + B a x + \frac{1}{2} \, {\left(C a + A b\right)} x^{2} + A a \log\left(x\right)"," ",0,"1/6*C*c*x^6 + 1/5*B*c*x^5 + 1/3*B*b*x^3 + 1/4*(C*b + A*c)*x^4 + B*a*x + 1/2*(C*a + A*b)*x^2 + A*a*log(x)","A",0
5,1,55,0,0.680426," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x^2,x, algorithm=""maxima"")","\frac{1}{5} \, C c x^{5} + \frac{1}{4} \, B c x^{4} + \frac{1}{2} \, B b x^{2} + \frac{1}{3} \, {\left(C b + A c\right)} x^{3} + B a \log\left(x\right) + {\left(C a + A b\right)} x - \frac{A a}{x}"," ",0,"1/5*C*c*x^5 + 1/4*B*c*x^4 + 1/2*B*b*x^2 + 1/3*(C*b + A*c)*x^3 + B*a*log(x) + (C*a + A*b)*x - A*a/x","A",0
6,1,55,0,0.752340," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, C c x^{4} + \frac{1}{3} \, B c x^{3} + B b x + \frac{1}{2} \, {\left(C b + A c\right)} x^{2} + {\left(C a + A b\right)} \log\left(x\right) - \frac{2 \, B a x + A a}{2 \, x^{2}}"," ",0,"1/4*C*c*x^4 + 1/3*B*c*x^3 + B*b*x + 1/2*(C*b + A*c)*x^2 + (C*a + A*b)*log(x) - 1/2*(2*B*a*x + A*a)/x^2","A",0
7,1,56,0,0.658785," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, C c x^{3} + \frac{1}{2} \, B c x^{2} + B b \log\left(x\right) + {\left(C b + A c\right)} x - \frac{3 \, B a x + 6 \, {\left(C a + A b\right)} x^{2} + 2 \, A a}{6 \, x^{3}}"," ",0,"1/3*C*c*x^3 + 1/2*B*c*x^2 + B*b*log(x) + (C*b + A*c)*x - 1/6*(3*B*a*x + 6*(C*a + A*b)*x^2 + 2*A*a)/x^3","A",0
8,1,56,0,0.751806," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x^5,x, algorithm=""maxima"")","\frac{1}{2} \, C c x^{2} + B c x + {\left(C b + A c\right)} \log\left(x\right) - \frac{12 \, B b x^{3} + 4 \, B a x + 6 \, {\left(C a + A b\right)} x^{2} + 3 \, A a}{12 \, x^{4}}"," ",0,"1/2*C*c*x^2 + B*c*x + (C*b + A*c)*log(x) - 1/12*(12*B*b*x^3 + 4*B*a*x + 6*(C*a + A*b)*x^2 + 3*A*a)/x^4","A",0
9,1,56,0,0.738886," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x^6,x, algorithm=""maxima"")","C c x + B c \log\left(x\right) - \frac{30 \, B b x^{3} + 60 \, {\left(C b + A c\right)} x^{4} + 15 \, B a x + 20 \, {\left(C a + A b\right)} x^{2} + 12 \, A a}{60 \, x^{5}}"," ",0,"C*c*x + B*c*log(x) - 1/60*(30*B*b*x^3 + 60*(C*b + A*c)*x^4 + 15*B*a*x + 20*(C*a + A*b)*x^2 + 12*A*a)/x^5","A",0
10,1,59,0,0.874450," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x^7,x, algorithm=""maxima"")","C c \log\left(x\right) - \frac{60 \, B c x^{5} + 20 \, B b x^{3} + 30 \, {\left(C b + A c\right)} x^{4} + 12 \, B a x + 15 \, {\left(C a + A b\right)} x^{2} + 10 \, A a}{60 \, x^{6}}"," ",0,"C*c*log(x) - 1/60*(60*B*c*x^5 + 20*B*b*x^3 + 30*(C*b + A*c)*x^4 + 12*B*a*x + 15*(C*a + A*b)*x^2 + 10*A*a)/x^6","A",0
11,1,143,0,1.134322," ","integrate(x^2*(C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{1}{13} \, C c^{2} x^{13} + \frac{1}{12} \, B c^{2} x^{12} + \frac{1}{5} \, B b c x^{10} + \frac{1}{11} \, {\left(2 \, C b c + A c^{2}\right)} x^{11} + \frac{1}{9} \, {\left(C b^{2} + 2 \, {\left(C a + A b\right)} c\right)} x^{9} + \frac{1}{3} \, B a b x^{6} + \frac{1}{8} \, {\left(B b^{2} + 2 \, B a c\right)} x^{8} + \frac{1}{7} \, {\left(2 \, C a b + A b^{2} + 2 \, A a c\right)} x^{7} + \frac{1}{4} \, B a^{2} x^{4} + \frac{1}{3} \, A a^{2} x^{3} + \frac{1}{5} \, {\left(C a^{2} + 2 \, A a b\right)} x^{5}"," ",0,"1/13*C*c^2*x^13 + 1/12*B*c^2*x^12 + 1/5*B*b*c*x^10 + 1/11*(2*C*b*c + A*c^2)*x^11 + 1/9*(C*b^2 + 2*(C*a + A*b)*c)*x^9 + 1/3*B*a*b*x^6 + 1/8*(B*b^2 + 2*B*a*c)*x^8 + 1/7*(2*C*a*b + A*b^2 + 2*A*a*c)*x^7 + 1/4*B*a^2*x^4 + 1/3*A*a^2*x^3 + 1/5*(C*a^2 + 2*A*a*b)*x^5","A",0
12,1,143,0,1.181904," ","integrate(x*(C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{1}{12} \, C c^{2} x^{12} + \frac{1}{11} \, B c^{2} x^{11} + \frac{2}{9} \, B b c x^{9} + \frac{1}{10} \, {\left(2 \, C b c + A c^{2}\right)} x^{10} + \frac{1}{8} \, {\left(C b^{2} + 2 \, {\left(C a + A b\right)} c\right)} x^{8} + \frac{2}{5} \, B a b x^{5} + \frac{1}{7} \, {\left(B b^{2} + 2 \, B a c\right)} x^{7} + \frac{1}{6} \, {\left(2 \, C a b + A b^{2} + 2 \, A a c\right)} x^{6} + \frac{1}{3} \, B a^{2} x^{3} + \frac{1}{2} \, A a^{2} x^{2} + \frac{1}{4} \, {\left(C a^{2} + 2 \, A a b\right)} x^{4}"," ",0,"1/12*C*c^2*x^12 + 1/11*B*c^2*x^11 + 2/9*B*b*c*x^9 + 1/10*(2*C*b*c + A*c^2)*x^10 + 1/8*(C*b^2 + 2*(C*a + A*b)*c)*x^8 + 2/5*B*a*b*x^5 + 1/7*(B*b^2 + 2*B*a*c)*x^7 + 1/6*(2*C*a*b + A*b^2 + 2*A*a*c)*x^6 + 1/3*B*a^2*x^3 + 1/2*A*a^2*x^2 + 1/4*(C*a^2 + 2*A*a*b)*x^4","A",0
13,1,140,0,0.628960," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{1}{11} \, C c^{2} x^{11} + \frac{1}{10} \, B c^{2} x^{10} + \frac{1}{4} \, B b c x^{8} + \frac{1}{9} \, {\left(2 \, C b c + A c^{2}\right)} x^{9} + \frac{1}{7} \, {\left(C b^{2} + 2 \, {\left(C a + A b\right)} c\right)} x^{7} + \frac{1}{2} \, B a b x^{4} + \frac{1}{6} \, {\left(B b^{2} + 2 \, B a c\right)} x^{6} + \frac{1}{5} \, {\left(2 \, C a b + A b^{2} + 2 \, A a c\right)} x^{5} + \frac{1}{2} \, B a^{2} x^{2} + A a^{2} x + \frac{1}{3} \, {\left(C a^{2} + 2 \, A a b\right)} x^{3}"," ",0,"1/11*C*c^2*x^11 + 1/10*B*c^2*x^10 + 1/4*B*b*c*x^8 + 1/9*(2*C*b*c + A*c^2)*x^9 + 1/7*(C*b^2 + 2*(C*a + A*b)*c)*x^7 + 1/2*B*a*b*x^4 + 1/6*(B*b^2 + 2*B*a*c)*x^6 + 1/5*(2*C*a*b + A*b^2 + 2*A*a*c)*x^5 + 1/2*B*a^2*x^2 + A*a^2*x + 1/3*(C*a^2 + 2*A*a*b)*x^3","A",0
14,1,138,0,0.842997," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x,x, algorithm=""maxima"")","\frac{1}{10} \, C c^{2} x^{10} + \frac{1}{9} \, B c^{2} x^{9} + \frac{2}{7} \, B b c x^{7} + \frac{1}{8} \, {\left(2 \, C b c + A c^{2}\right)} x^{8} + \frac{1}{6} \, {\left(C b^{2} + 2 \, {\left(C a + A b\right)} c\right)} x^{6} + \frac{2}{3} \, B a b x^{3} + \frac{1}{5} \, {\left(B b^{2} + 2 \, B a c\right)} x^{5} + \frac{1}{4} \, {\left(2 \, C a b + A b^{2} + 2 \, A a c\right)} x^{4} + B a^{2} x + A a^{2} \log\left(x\right) + \frac{1}{2} \, {\left(C a^{2} + 2 \, A a b\right)} x^{2}"," ",0,"1/10*C*c^2*x^10 + 1/9*B*c^2*x^9 + 2/7*B*b*c*x^7 + 1/8*(2*C*b*c + A*c^2)*x^8 + 1/6*(C*b^2 + 2*(C*a + A*b)*c)*x^6 + 2/3*B*a*b*x^3 + 1/5*(B*b^2 + 2*B*a*c)*x^5 + 1/4*(2*C*a*b + A*b^2 + 2*A*a*c)*x^4 + B*a^2*x + A*a^2*log(x) + 1/2*(C*a^2 + 2*A*a*b)*x^2","A",0
15,1,137,0,0.733886," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x^2,x, algorithm=""maxima"")","\frac{1}{9} \, C c^{2} x^{9} + \frac{1}{8} \, B c^{2} x^{8} + \frac{1}{3} \, B b c x^{6} + \frac{1}{7} \, {\left(2 \, C b c + A c^{2}\right)} x^{7} + \frac{1}{5} \, {\left(C b^{2} + 2 \, {\left(C a + A b\right)} c\right)} x^{5} + B a b x^{2} + \frac{1}{4} \, {\left(B b^{2} + 2 \, B a c\right)} x^{4} + \frac{1}{3} \, {\left(2 \, C a b + A b^{2} + 2 \, A a c\right)} x^{3} + B a^{2} \log\left(x\right) - \frac{A a^{2}}{x} + {\left(C a^{2} + 2 \, A a b\right)} x"," ",0,"1/9*C*c^2*x^9 + 1/8*B*c^2*x^8 + 1/3*B*b*c*x^6 + 1/7*(2*C*b*c + A*c^2)*x^7 + 1/5*(C*b^2 + 2*(C*a + A*b)*c)*x^5 + B*a*b*x^2 + 1/4*(B*b^2 + 2*B*a*c)*x^4 + 1/3*(2*C*a*b + A*b^2 + 2*A*a*c)*x^3 + B*a^2*log(x) - A*a^2/x + (C*a^2 + 2*A*a*b)*x","A",0
16,1,139,0,0.621742," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x^3,x, algorithm=""maxima"")","\frac{1}{8} \, C c^{2} x^{8} + \frac{1}{7} \, B c^{2} x^{7} + \frac{2}{5} \, B b c x^{5} + \frac{1}{6} \, {\left(2 \, C b c + A c^{2}\right)} x^{6} + \frac{1}{4} \, {\left(C b^{2} + 2 \, {\left(C a + A b\right)} c\right)} x^{4} + 2 \, B a b x + \frac{1}{3} \, {\left(B b^{2} + 2 \, B a c\right)} x^{3} + \frac{1}{2} \, {\left(2 \, C a b + A b^{2} + 2 \, A a c\right)} x^{2} + {\left(C a^{2} + 2 \, A a b\right)} \log\left(x\right) - \frac{2 \, B a^{2} x + A a^{2}}{2 \, x^{2}}"," ",0,"1/8*C*c^2*x^8 + 1/7*B*c^2*x^7 + 2/5*B*b*c*x^5 + 1/6*(2*C*b*c + A*c^2)*x^6 + 1/4*(C*b^2 + 2*(C*a + A*b)*c)*x^4 + 2*B*a*b*x + 1/3*(B*b^2 + 2*B*a*c)*x^3 + 1/2*(2*C*a*b + A*b^2 + 2*A*a*c)*x^2 + (C*a^2 + 2*A*a*b)*log(x) - 1/2*(2*B*a^2*x + A*a^2)/x^2","A",0
17,1,140,0,0.681144," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x^4,x, algorithm=""maxima"")","\frac{1}{7} \, C c^{2} x^{7} + \frac{1}{6} \, B c^{2} x^{6} + \frac{1}{2} \, B b c x^{4} + \frac{1}{5} \, {\left(2 \, C b c + A c^{2}\right)} x^{5} + \frac{1}{3} \, {\left(C b^{2} + 2 \, {\left(C a + A b\right)} c\right)} x^{3} + 2 \, B a b \log\left(x\right) + \frac{1}{2} \, {\left(B b^{2} + 2 \, B a c\right)} x^{2} + {\left(2 \, C a b + A b^{2} + 2 \, A a c\right)} x - \frac{3 \, B a^{2} x + 2 \, A a^{2} + 6 \, {\left(C a^{2} + 2 \, A a b\right)} x^{2}}{6 \, x^{3}}"," ",0,"1/7*C*c^2*x^7 + 1/6*B*c^2*x^6 + 1/2*B*b*c*x^4 + 1/5*(2*C*b*c + A*c^2)*x^5 + 1/3*(C*b^2 + 2*(C*a + A*b)*c)*x^3 + 2*B*a*b*log(x) + 1/2*(B*b^2 + 2*B*a*c)*x^2 + (2*C*a*b + A*b^2 + 2*A*a*c)*x - 1/6*(3*B*a^2*x + 2*A*a^2 + 6*(C*a^2 + 2*A*a*b)*x^2)/x^3","A",0
18,1,139,0,0.624444," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x^5,x, algorithm=""maxima"")","\frac{1}{6} \, C c^{2} x^{6} + \frac{1}{5} \, B c^{2} x^{5} + \frac{2}{3} \, B b c x^{3} + \frac{1}{4} \, {\left(2 \, C b c + A c^{2}\right)} x^{4} + \frac{1}{2} \, {\left(C b^{2} + 2 \, {\left(C a + A b\right)} c\right)} x^{2} + {\left(B b^{2} + 2 \, B a c\right)} x + {\left(2 \, C a b + A b^{2} + 2 \, A a c\right)} \log\left(x\right) - \frac{24 \, B a b x^{3} + 4 \, B a^{2} x + 3 \, A a^{2} + 6 \, {\left(C a^{2} + 2 \, A a b\right)} x^{2}}{12 \, x^{4}}"," ",0,"1/6*C*c^2*x^6 + 1/5*B*c^2*x^5 + 2/3*B*b*c*x^3 + 1/4*(2*C*b*c + A*c^2)*x^4 + 1/2*(C*b^2 + 2*(C*a + A*b)*c)*x^2 + (B*b^2 + 2*B*a*c)*x + (2*C*a*b + A*b^2 + 2*A*a*c)*log(x) - 1/12*(24*B*a*b*x^3 + 4*B*a^2*x + 3*A*a^2 + 6*(C*a^2 + 2*A*a*b)*x^2)/x^4","A",0
19,1,138,0,0.612073," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x^6,x, algorithm=""maxima"")","\frac{1}{5} \, C c^{2} x^{5} + \frac{1}{4} \, B c^{2} x^{4} + B b c x^{2} + \frac{1}{3} \, {\left(2 \, C b c + A c^{2}\right)} x^{3} + {\left(C b^{2} + 2 \, {\left(C a + A b\right)} c\right)} x + {\left(B b^{2} + 2 \, B a c\right)} \log\left(x\right) - \frac{60 \, B a b x^{3} + 60 \, {\left(2 \, C a b + A b^{2} + 2 \, A a c\right)} x^{4} + 15 \, B a^{2} x + 12 \, A a^{2} + 20 \, {\left(C a^{2} + 2 \, A a b\right)} x^{2}}{60 \, x^{5}}"," ",0,"1/5*C*c^2*x^5 + 1/4*B*c^2*x^4 + B*b*c*x^2 + 1/3*(2*C*b*c + A*c^2)*x^3 + (C*b^2 + 2*(C*a + A*b)*c)*x + (B*b^2 + 2*B*a*c)*log(x) - 1/60*(60*B*a*b*x^3 + 60*(2*C*a*b + A*b^2 + 2*A*a*c)*x^4 + 15*B*a^2*x + 12*A*a^2 + 20*(C*a^2 + 2*A*a*b)*x^2)/x^5","A",0
20,1,140,0,0.688441," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x^7,x, algorithm=""maxima"")","\frac{1}{4} \, C c^{2} x^{4} + \frac{1}{3} \, B c^{2} x^{3} + 2 \, B b c x + \frac{1}{2} \, {\left(2 \, C b c + A c^{2}\right)} x^{2} + {\left(C b^{2} + 2 \, {\left(C a + A b\right)} c\right)} \log\left(x\right) - \frac{40 \, B a b x^{3} + 60 \, {\left(B b^{2} + 2 \, B a c\right)} x^{5} + 30 \, {\left(2 \, C a b + A b^{2} + 2 \, A a c\right)} x^{4} + 12 \, B a^{2} x + 10 \, A a^{2} + 15 \, {\left(C a^{2} + 2 \, A a b\right)} x^{2}}{60 \, x^{6}}"," ",0,"1/4*C*c^2*x^4 + 1/3*B*c^2*x^3 + 2*B*b*c*x + 1/2*(2*C*b*c + A*c^2)*x^2 + (C*b^2 + 2*(C*a + A*b)*c)*log(x) - 1/60*(40*B*a*b*x^3 + 60*(B*b^2 + 2*B*a*c)*x^5 + 30*(2*C*a*b + A*b^2 + 2*A*a*c)*x^4 + 12*B*a^2*x + 10*A*a^2 + 15*(C*a^2 + 2*A*a*b)*x^2)/x^6","A",0
21,0,0,0,0.000000," ","integrate(x^4*(C*x^2+B*x+A)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{2 \, C c x^{3} + 3 \, B c x^{2} - 6 \, {\left(C b - A c\right)} x}{6 \, c^{2}} - \frac{\frac{1}{4} \, B b \log\left({\left| c x^{4} + b x^{2} + a \right|}\right) - \frac{{\left({\left(2 \, b^{5} c^{3} - 16 \, a b^{3} c^{4} + 32 \, a^{2} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} A c^{2} - {\left(2 \, b^{6} c^{2} - 18 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 32 \, a^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} + 9 \, \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 - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 10 \, \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^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} 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^{3} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 10 \, {\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 c^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 2 \, a b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} + 16 \, a^{2} b^{2} c^{5} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{6} - 32 \, a^{3} c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{5}\right)} A c + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 2 \, a b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 16 \, a^{2} b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} - 32 \, a^{3} b c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} C c - {\left(2 \, b^{5} c^{5} - 12 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{5} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{6}\right)} A + {\left(2 \, b^{6} c^{4} - 14 \, a b^{4} c^{5} + 24 \, a^{2} b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{4} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5}\right)} C\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^{5} c^{3} - 16 \, a b^{3} c^{4} + 32 \, a^{2} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} A c^{2} - {\left(2 \, b^{6} c^{2} - 18 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 32 \, a^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} + 9 \, \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 - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 10 \, \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^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} 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^{3} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 10 \, {\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 c^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 2 \, a b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 16 \, a^{2} b^{2} c^{5} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{6} + 32 \, a^{3} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{5}\right)} A c + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 2 \, a b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 16 \, a^{2} b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + 32 \, a^{3} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} C c - {\left(2 \, b^{5} c^{5} - 12 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{5} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{6}\right)} A + {\left(2 \, b^{6} c^{4} - 14 \, a b^{4} c^{5} + 24 \, a^{2} b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{4} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5}\right)} C\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^{7} c - 10 \, a b^{5} c^{2} - 2 \, b^{6} c^{2} + 32 \, a^{2} b^{3} c^{3} + 12 \, a b^{4} c^{3} + b^{5} c^{3} - 32 \, a^{3} b c^{4} - 16 \, a^{2} b^{2} c^{4} - 6 \, a b^{3} c^{4} + 8 \, a^{2} b c^{5} + {\left(b^{6} c - 10 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} + 32 \, a^{2} b^{2} c^{3} + 12 \, a b^{3} c^{3} + b^{4} c^{3} - 32 \, a^{3} c^{4} - 16 \, a^{2} b c^{4} - 6 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B c - {\left(b^{7} c^{2} - 10 \, a b^{5} c^{3} - 2 \, b^{6} c^{3} + 32 \, a^{2} b^{3} c^{4} + 12 \, a b^{4} c^{4} + b^{5} c^{4} - 32 \, a^{3} b c^{5} - 16 \, a^{2} b^{2} c^{5} - 6 \, a b^{3} c^{5} + 8 \, a^{2} b c^{6} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} - 2 \, b^{5} c^{3} + 8 \, a^{2} b^{2} c^{4} + 4 \, a b^{3} c^{4} + b^{4} c^{4} - 2 \, a b^{2} c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\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^{7} c - 10 \, a b^{5} c^{2} - 2 \, b^{6} c^{2} + 32 \, a^{2} b^{3} c^{3} + 12 \, a b^{4} c^{3} + b^{5} c^{3} - 32 \, a^{3} b c^{4} - 16 \, a^{2} b^{2} c^{4} - 6 \, a b^{3} c^{4} + 8 \, a^{2} b c^{5} - {\left(b^{6} c - 10 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} + 32 \, a^{2} b^{2} c^{3} + 12 \, a b^{3} c^{3} + b^{4} c^{3} - 32 \, a^{3} c^{4} - 16 \, a^{2} b c^{4} - 6 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B c - {\left(b^{7} c^{2} - 10 \, a b^{5} c^{3} - 2 \, b^{6} c^{3} + 32 \, a^{2} b^{3} c^{4} + 12 \, a b^{4} c^{4} + b^{5} c^{4} - 32 \, a^{3} b c^{5} - 16 \, a^{2} b^{2} c^{5} - 6 \, a b^{3} c^{5} + 8 \, a^{2} b c^{6} - {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} - 2 \, b^{5} c^{3} + 8 \, a^{2} b^{2} c^{4} + 4 \, a b^{3} c^{4} + b^{4} c^{4} - 2 \, a b^{2} c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\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^{2}}"," ",0,"1/6*(2*C*c*x^3 + 3*B*c*x^2 - 6*(C*b - A*c)*x)/c^2 - integrate((B*b*c*x^3 + B*a*c*x - C*a*b + A*a*c - (C*b^2 - (C*a + A*b)*c)*x^2)/(c*x^4 + b*x^2 + a), x)/c^2","F",0
22,0,0,0,0.000000," ","integrate(x^3*(C*x^2+B*x+A)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{C x^{2} + 2 \, B x}{2 \, c} + \frac{-\int \frac{B b x^{2} + {\left(C b - A c\right)} x^{3} + C a x + B a}{c x^{4} + b x^{2} + a}\,{d x}}{c}"," ",0,"1/2*(C*x^2 + 2*B*x)/c + integrate(-(B*b*x^2 + (C*b - A*c)*x^3 + C*a*x + B*a)/(c*x^4 + b*x^2 + a), x)/c","F",0
23,0,0,0,0.000000," ","integrate(x^2*(C*x^2+B*x+A)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{C x}{c} + \frac{\frac{1}{4} \, B \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)} A c^{2} - {\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 c^{2} - 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 c - {\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)} A + {\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)} C\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)} A c^{2} - {\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 c^{2} + 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 c - {\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)} A + {\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)} C\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)} B c + {\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)} B\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)} B c + {\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)} B\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,"C*x/c + integrate((B*c*x^3 - (C*b - A*c)*x^2 - C*a)/(c*x^4 + b*x^2 + a), x)/c","F",0
24,0,0,0,0.000000," ","integrate(x*(C*x^2+B*x+A)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\int \frac{{\left(C x^{2} + B x + A\right)} x}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*x/(c*x^4 + b*x^2 + a), x)","F",0
25,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\int \frac{C x^{2} + B x + A}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)/(c*x^4 + b*x^2 + a), x)","F",0
26,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)/x/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{A \log\left(x\right)}{a} - \frac{\frac{1}{4} \, A \log\left({\left| c x^{4} + b x^{2} + a \right|}\right) - \frac{{\left({\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - 16 \, a b^{2} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} + 32 \, a^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2}\right)} B c + {\left(2 \, b^{3} c^{3} - 8 \, a b c^{4} - \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} a b c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{3}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} c x}{\sqrt{b c + \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}\right)}{4 \, {\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^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 16 \, a b^{2} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 32 \, a^{2} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2}\right)} B c - {\left(2 \, b^{3} c^{3} - 8 \, a b c^{4} - \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} a b c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{3}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} c x}{\sqrt{b c - \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}\right)}{4 \, {\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(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)} A c - 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} - 2 \, a b^{4} c^{2} + 16 \, a^{3} b c^{3} + 8 \, a^{2} b^{2} c^{3} + a b^{3} c^{3} - 4 \, a^{2} b c^{4} - {\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)} \sqrt{b^{2} - 4 \, a c}\right)} C c + {\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)} A - 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} - 2 \, a b^{4} c^{3} + 16 \, a^{3} b c^{4} + 8 \, a^{2} b^{2} c^{4} + a b^{3} c^{4} - 4 \, a^{2} b c^{5} - {\left(a b^{4} c^{2} - 4 \, a^{2} b^{2} c^{3} - 2 \, a b^{3} c^{3} + a b^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C\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)} A c - 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} - 2 \, a b^{4} c^{2} + 16 \, a^{3} b c^{3} + 8 \, a^{2} b^{2} c^{3} + a b^{3} c^{3} - 4 \, a^{2} b c^{4} + {\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)} \sqrt{b^{2} - 4 \, a c}\right)} C c + {\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)} A - 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} - 2 \, a b^{4} c^{3} + 16 \, a^{3} b c^{4} + 8 \, a^{2} b^{2} c^{4} + a b^{3} c^{4} - 4 \, a^{2} b c^{5} + {\left(a b^{4} c^{2} - 4 \, a^{2} b^{2} c^{3} - 2 \, a b^{3} c^{3} + a b^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C\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}}}{a}"," ",0,"A*log(x)/a - integrate((A*c*x^3 - B*a - (C*a - A*b)*x)/(c*x^4 + b*x^2 + a), x)/a","F",0
27,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)/x^2/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{B \log\left(x\right)}{a} - \frac{\frac{1}{4} \, B \log\left({\left| c x^{4} + b x^{2} + a \right|}\right) + \frac{{\left({\left(2 \, b^{4} c^{2} - 16 \, a b^{2} c^{3} + 32 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} + 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 - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} A c^{2} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 2 \, b^{5} c^{2} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} - 16 \, a b^{3} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{4} + 32 \, a^{2} b c^{4} - 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)} A c - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 2 \, a b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 16 \, a^{2} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 32 \, a^{3} c^{4} - 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)} C c + {\left(2 \, b^{4} c^{4} - 8 \, a b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{4}\right)} A - 2 \, {\left(2 \, a b^{3} c^{4} - 8 \, a^{2} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} C\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({\left(2 \, b^{4} c^{2} - 16 \, a b^{2} c^{3} + 32 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} + 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 - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} A c^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 2 \, b^{5} c^{2} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} + 16 \, a b^{3} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - 32 \, a^{2} b c^{4} + 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)} A c + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 2 \, a b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 16 \, a^{2} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 32 \, a^{3} c^{4} + 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)} C c + {\left(2 \, b^{4} c^{4} - 8 \, a b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{4}\right)} A - 2 \, {\left(2 \, a b^{3} c^{4} - 8 \, a^{2} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} C\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({\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)} B c + {\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)} B\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)} B c + {\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)} B\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}}}{a} - \frac{A}{a x}"," ",0,"B*log(x)/a - integrate((B*c*x^3 + A*c*x^2 + B*b*x - C*a + A*b)/(c*x^4 + b*x^2 + a), x)/a - A/(a*x)","F",0
28,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)/x^3/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{{\left(C a - A b\right)} \log\left(x\right)}{a^{2}} + \frac{-\int \frac{B a c x^{2} + {\left(C a - A b\right)} c x^{3} + B a b + {\left(C a b - A b^{2} + A a c\right)} x}{c x^{4} + b x^{2} + a}\,{d x}}{a^{2}} - \frac{2 \, B x + A}{2 \, a x^{2}}"," ",0,"(C*a - A*b)*log(x)/a^2 + integrate(-(B*a*c*x^2 + (C*a - A*b)*c*x^3 + B*a*b + (C*a*b - A*b^2 + A*a*c)*x)/(c*x^4 + b*x^2 + a), x)/a^2 - 1/2*(2*B*x + A)/(a*x^2)","F",0
29,0,0,0,0.000000," ","integrate(x^4*(C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(C b^{2} - {\left(2 \, C a + A b\right)} c\right)} x^{3} + B a b + {\left(B b^{2} - 2 \, B a c\right)} x^{2} + {\left(C a b - 2 \, A a c\right)} x}{2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2}\right)}} + \frac{-\int \frac{4 \, B a c x - C a b + 2 \, A a c - {\left(C b^{2} - {\left(6 \, C a - A b\right)} c\right)} x^{2}}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}"," ",0,"-1/2*((C*b^2 - (2*C*a + A*b)*c)*x^3 + B*a*b + (B*b^2 - 2*B*a*c)*x^2 + (C*a*b - 2*A*a*c)*x)/((b^2*c^2 - 4*a*c^3)*x^4 + a*b^2*c - 4*a^2*c^2 + (b^3*c - 4*a*b*c^2)*x^2) + 1/2*integrate(-(4*B*a*c*x - C*a*b + 2*A*a*c - (C*b^2 - (6*C*a - A*b)*c)*x^2)/(c*x^4 + b*x^2 + a), x)/(b^2*c - 4*a*c^2)","F",0
30,0,0,0,0.000000," ","integrate(x^3*(C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{B b c x^{3} + 2 \, B a c x - C a b + 2 \, A a c - {\left(C b^{2} - {\left(2 \, C a + A b\right)} c\right)} x^{2}}{2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2}\right)}} + \frac{-\frac{{\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 16 \, a b^{2} c^{2} + 4 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 32 \, a^{2} c^{3} - 16 \, a b c^{3} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} - 4 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} B \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\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} - \frac{{\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 2 \, b^{4} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - 16 \, a b^{2} c^{2} - 4 \, b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} + 32 \, a^{2} c^{3} + 16 \, a b c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} B \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\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} - \frac{{\left({\left(b^{3} c^{2} - 4 \, a b c^{3} - 2 \, b^{2} c^{3} + b c^{4}\right)} \sqrt{b^{2} - 4 \, a c} A - 2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} - 2 \, a b c^{3} + a c^{4}\right)} \sqrt{b^{2} - 4 \, a c} C\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(b^{3} c^{2} - 4 \, a b c^{3} - 2 \, b^{2} c^{3} + b c^{4}\right)} \sqrt{b^{2} - 4 \, a c} A - 2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} - 2 \, a b c^{3} + a c^{4}\right)} \sqrt{b^{2} - 4 \, a c} C\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(b^{2} - 4 \, a c\right)}}"," ",0,"1/2*(B*b*c*x^3 + 2*B*a*c*x - C*a*b + 2*A*a*c - (C*b^2 - (2*C*a + A*b)*c)*x^2)/((b^2*c^2 - 4*a*c^3)*x^4 + a*b^2*c - 4*a^2*c^2 + (b^3*c - 4*a*b*c^2)*x^2) + 1/2*integrate((B*b*x^2 - 2*B*a - 2*(2*C*a - A*b)*x)/(c*x^4 + b*x^2 + a), x)/(b^2 - 4*a*c)","F",0
31,0,0,0,0.000000," ","integrate(x^2*(C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{B b x^{2} + {\left(C b - 2 \, A c\right)} x^{3} + 2 \, B a + {\left(2 \, C a - A b\right)} x}{2 \, {\left({\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}\right)}} - \frac{-\int \frac{2 \, B b x + {\left(C b - 2 \, A c\right)} x^{2} - 2 \, C a + A b}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left(b^{2} - 4 \, a c\right)}}"," ",0,"1/2*(B*b*x^2 + (C*b - 2*A*c)*x^3 + 2*B*a + (2*C*a - A*b)*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) - 1/2*integrate(-(2*B*b*x + (C*b - 2*A*c)*x^2 - 2*C*a + A*b)/(c*x^4 + b*x^2 + a), x)/(b^2 - 4*a*c)","F",0
32,0,0,0,0.000000," ","integrate(x*(C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{2 \, B c x^{3} + B b x - {\left(C b - 2 \, A c\right)} x^{2} - 2 \, C a + A b}{2 \, {\left({\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}\right)}} - \frac{-\frac{{\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} - 8 \, \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 \, b^{5} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 16 \, a b^{3} c^{2} + 2 \, b^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 32 \, a^{2} b c^{3} - 32 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} B \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^{5} - 8 \, \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 \, b^{5} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 16 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + 32 \, a^{2} b c^{3} + 32 \, a^{2} c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} B \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(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4} - 2 \, b c^{4} + c^{5}\right)} \sqrt{b^{2} - 4 \, a c} A - {\left(b^{3} c^{2} - 4 \, a b c^{3} - 2 \, b^{2} c^{3} + b c^{4}\right)} \sqrt{b^{2} - 4 \, a c} C\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(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4} - 2 \, b c^{4} + c^{5}\right)} \sqrt{b^{2} - 4 \, a c} A - {\left(b^{3} c^{2} - 4 \, a b c^{3} - 2 \, b^{2} c^{3} + b c^{4}\right)} \sqrt{b^{2} - 4 \, a c} C\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(b^{2} - 4 \, a c\right)}}"," ",0,"-1/2*(2*B*c*x^3 + B*b*x - (C*b - 2*A*c)*x^2 - 2*C*a + A*b)/((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2) - 1/2*integrate((2*B*c*x^2 - B*b - 2*(C*b - 2*A*c)*x)/(c*x^4 + b*x^2 + a), x)/(b^2 - 4*a*c)","F",0
33,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{2 \, B a c x^{2} + {\left(2 \, C a - A b\right)} c x^{3} + B a b + {\left(C a b - A b^{2} + 2 \, A a c\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{4 \, B a c x + {\left(2 \, C a - A b\right)} c x^{2} - C a b - A b^{2} + 6 \, A a c}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}"," ",0,"-1/2*(2*B*a*c*x^2 + (2*C*a - A*b)*c*x^3 + B*a*b + (C*a*b - A*b^2 + 2*A*a*c)*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*B*a*c*x + (2*C*a - A*b)*c*x^2 - C*a*b - A*b^2 + 6*A*a*c)/(c*x^4 + b*x^2 + a), x)/(a*b^2 - 4*a^2*c)","F",0
34,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)/x/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{B b c x^{3} - {\left(2 \, C a - A b\right)} c x^{2} - C a b + A b^{2} - 2 \, A a c + {\left(B b^{2} - 2 \, B a c\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{1}{2} \, {\left(A b^{2} - 4 \, A a c\right)} \log\left({\left| c x^{4} + b x^{2} + a \right|}\right) + \frac{{\left({\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)} B c^{2} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 2 \, b^{6} c^{2} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 28 \, a b^{4} c^{3} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 128 \, a^{2} b^{2} c^{4} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 192 \, a^{3} c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} - 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} B c + {\left(2 \, b^{5} c^{4} - 32 \, a b^{3} c^{5} + 96 \, 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} + 16 \, \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} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 24 \, \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} + 12 \, \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} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5}\right)} B\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(b^{4} c - 8 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} + 16 \, a^{2} c^{3} + 8 \, a b c^{3} + b^{2} c^{3} - 4 \, a c^{4}\right)} c^{2}} - \frac{{\left({\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)} B c^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 2 \, b^{6} c^{2} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 28 \, a b^{4} c^{3} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 128 \, a^{2} b^{2} c^{4} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 192 \, a^{3} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} B c + {\left(2 \, b^{5} c^{4} - 32 \, a b^{3} c^{5} + 96 \, 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} + 16 \, \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} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 24 \, \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} + 12 \, \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} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5}\right)} B\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(b^{4} c - 8 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} + 16 \, a^{2} c^{3} + 8 \, a b c^{3} + b^{2} c^{3} - 4 \, a c^{4}\right)} c^{2}} - \frac{{\left({\left(b^{8} c - 14 \, a b^{6} c^{2} - 2 \, b^{7} c^{2} + 64 \, a^{2} b^{4} c^{3} + 20 \, a b^{5} c^{3} + b^{6} c^{3} - 96 \, a^{3} b^{2} c^{4} - 48 \, a^{2} b^{3} c^{4} - 10 \, a b^{4} c^{4} + 24 \, a^{2} b^{2} c^{5} + {\left(b^{7} c - 14 \, a b^{5} c^{2} - 2 \, b^{6} c^{2} + 64 \, a^{2} b^{3} c^{3} + 20 \, a b^{4} c^{3} + b^{5} c^{3} - 96 \, a^{3} b c^{4} - 48 \, a^{2} b^{2} c^{4} - 10 \, a b^{3} c^{4} + 24 \, a^{2} b c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A c + 4 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} - 2 \, a^{2} b^{4} c^{3} + 16 \, a^{4} b c^{4} + 8 \, a^{3} b^{2} c^{4} + a^{2} b^{3} c^{4} - 4 \, a^{3} b c^{5} + {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} - 2 \, a^{2} b^{3} c^{3} + 16 \, a^{4} c^{4} + 8 \, a^{3} b c^{4} + a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C c - {\left(b^{8} c^{2} - 14 \, a b^{6} c^{3} - 2 \, b^{7} c^{3} + 64 \, a^{2} b^{4} c^{4} + 20 \, a b^{5} c^{4} + b^{6} c^{4} - 96 \, a^{3} b^{2} c^{5} - 48 \, a^{2} b^{3} c^{5} - 10 \, a b^{4} c^{5} + 24 \, a^{2} b^{2} c^{6} + {\left(b^{7} c^{2} - 10 \, a b^{5} c^{3} - 2 \, b^{6} c^{3} + 24 \, a^{2} b^{3} c^{4} + 12 \, a b^{4} c^{4} + b^{5} c^{4} - 6 \, a b^{3} c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A - 4 \, {\left(a^{2} b^{5} c^{3} - 8 \, a^{3} b^{3} c^{4} - 2 \, a^{2} b^{4} c^{4} + 16 \, a^{4} b c^{5} + 8 \, a^{3} b^{2} c^{5} + a^{2} b^{3} c^{5} - 4 \, a^{3} b c^{6} + {\left(a^{2} b^{4} c^{3} - 4 \, a^{3} b^{2} c^{4} - 2 \, a^{2} b^{3} c^{4} + a^{2} b^{2} c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C\right)} \log\left(x^{2} + \frac{b c + \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{2 \, c^{2}}\right)}{8 \, {\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^{8} c - 14 \, a b^{6} c^{2} - 2 \, b^{7} c^{2} + 64 \, a^{2} b^{4} c^{3} + 20 \, a b^{5} c^{3} + b^{6} c^{3} - 96 \, a^{3} b^{2} c^{4} - 48 \, a^{2} b^{3} c^{4} - 10 \, a b^{4} c^{4} + 24 \, a^{2} b^{2} c^{5} - {\left(b^{7} c - 14 \, a b^{5} c^{2} - 2 \, b^{6} c^{2} + 64 \, a^{2} b^{3} c^{3} + 20 \, a b^{4} c^{3} + b^{5} c^{3} - 96 \, a^{3} b c^{4} - 48 \, a^{2} b^{2} c^{4} - 10 \, a b^{3} c^{4} + 24 \, a^{2} b c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A c + 4 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} - 2 \, a^{2} b^{4} c^{3} + 16 \, a^{4} b c^{4} + 8 \, a^{3} b^{2} c^{4} + a^{2} b^{3} c^{4} - 4 \, a^{3} b c^{5} - {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} - 2 \, a^{2} b^{3} c^{3} + 16 \, a^{4} c^{4} + 8 \, a^{3} b c^{4} + a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C c - {\left(b^{8} c^{2} - 14 \, a b^{6} c^{3} - 2 \, b^{7} c^{3} + 64 \, a^{2} b^{4} c^{4} + 20 \, a b^{5} c^{4} + b^{6} c^{4} - 96 \, a^{3} b^{2} c^{5} - 48 \, a^{2} b^{3} c^{5} - 10 \, a b^{4} c^{5} + 24 \, a^{2} b^{2} c^{6} - {\left(b^{7} c^{2} - 10 \, a b^{5} c^{3} - 2 \, b^{6} c^{3} + 24 \, a^{2} b^{3} c^{4} + 12 \, a b^{4} c^{4} + b^{5} c^{4} - 6 \, a b^{3} c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A - 4 \, {\left(a^{2} b^{5} c^{3} - 8 \, a^{3} b^{3} c^{4} - 2 \, a^{2} b^{4} c^{4} + 16 \, a^{4} b c^{5} + 8 \, a^{3} b^{2} c^{5} + a^{2} b^{3} c^{5} - 4 \, a^{3} b c^{6} - {\left(a^{2} b^{4} c^{3} - 4 \, a^{3} b^{2} c^{4} - 2 \, a^{2} b^{3} c^{4} + a^{2} b^{2} c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C\right)} \log\left(x^{2} + \frac{b c - \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{2 \, c^{2}}\right)}{8 \, {\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}}}{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}} + \frac{A \log\left(x\right)}{a^{2}}"," ",0,"1/2*(B*b*c*x^3 - (2*C*a - A*b)*c*x^2 - C*a*b + A*b^2 - 2*A*a*c + (B*b^2 - 2*B*a*c)*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*a*b*c*x^2 + B*a*b^2 - 6*B*a^2*c - 2*(A*b^2*c - 4*A*a*c^2)*x^3 - 2*(A*b^3 + (2*C*a^2 - 5*A*a*b)*c)*x)/(c*x^4 + b*x^2 + a), x)/(a^2*b^2 - 4*a^3*c) + A*log(x)/a^2","F",0
35,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)/x^2/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{B a b c x^{3} + {\left(10 \, A a c^{2} + {\left(C a b - 3 \, A b^{2}\right)} c\right)} x^{4} - 2 \, A a b^{2} + 8 \, A a^{2} c + {\left(C a b^{2} - 3 \, A b^{3} - {\left(2 \, C a^{2} - 11 \, A a b\right)} c\right)} x^{2} + {\left(B a b^{2} - 2 \, B a^{2} c\right)} x}{2 \, {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)}} + \frac{-\frac{1}{2} \, {\left(B b^{2} - 4 \, B a c\right)} \log\left({\left| c x^{4} + b x^{2} + a \right|}\right) - \frac{{\left({\left(6 \, b^{6} c^{2} - 68 \, a b^{4} c^{3} + 256 \, a^{2} b^{2} c^{4} - 320 \, a^{3} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} + 34 \, \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 - 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 44 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} A c^{2} - {\left(2 \, a b^{5} c^{2} - 16 \, a^{2} b^{3} c^{3} + 32 \, a^{3} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} + 8 \, \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 - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 8 \, \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 b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} C c^{2} + 2 \, {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c - 37 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 6 \, b^{7} c^{2} + 152 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 50 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 74 \, a b^{5} c^{3} - 208 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 104 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 25 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 304 \, a^{2} b^{3} c^{4} + 52 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} - 416 \, a^{3} b c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 50 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 104 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} A c - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 2 \, a b^{6} c^{2} + 64 \, \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} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 28 \, a^{2} b^{4} c^{3} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 128 \, a^{3} b^{2} c^{4} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} - 192 \, a^{4} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} C c + {\left(6 \, b^{6} c^{4} - 56 \, a b^{4} c^{5} + 128 \, a^{2} b^{2} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{4} + 32 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5}\right)} A - {\left(2 \, a b^{5} c^{4} - 32 \, a^{2} b^{3} c^{5} + 96 \, a^{3} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 12 \, \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)} a b^{3} c^{4} + 24 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{5}\right)} C\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({\left(6 \, b^{6} c^{2} - 68 \, a b^{4} c^{3} + 256 \, a^{2} b^{2} c^{4} - 320 \, a^{3} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} + 34 \, \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 - 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 44 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} A c^{2} - {\left(2 \, a b^{5} c^{2} - 16 \, a^{2} b^{3} c^{3} + 32 \, a^{3} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} + 8 \, \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 - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 8 \, \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 b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} C c^{2} - 2 \, {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c - 37 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} - 6 \, b^{7} c^{2} + 152 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 50 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} + 74 \, a b^{5} c^{3} - 208 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 104 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 25 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 304 \, a^{2} b^{3} c^{4} + 52 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + 416 \, a^{3} b c^{5} + 6 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} - 50 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} + 104 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} A c + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 2 \, a b^{6} c^{2} + 64 \, \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} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 28 \, a^{2} b^{4} c^{3} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 128 \, a^{3} b^{2} c^{4} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 192 \, a^{4} c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} C c + {\left(6 \, b^{6} c^{4} - 56 \, a b^{4} c^{5} + 128 \, a^{2} b^{2} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{4} + 32 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5}\right)} A - {\left(2 \, a b^{5} c^{4} - 32 \, a^{2} b^{3} c^{5} + 96 \, a^{3} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 12 \, \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)} a b^{3} c^{4} + 24 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{5}\right)} C\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({\left(b^{8} c - 14 \, a b^{6} c^{2} - 2 \, b^{7} c^{2} + 64 \, a^{2} b^{4} c^{3} + 20 \, a b^{5} c^{3} + b^{6} c^{3} - 96 \, a^{3} b^{2} c^{4} - 48 \, a^{2} b^{3} c^{4} - 10 \, a b^{4} c^{4} + 24 \, a^{2} b^{2} c^{5} - {\left(b^{7} c - 14 \, a b^{5} c^{2} - 2 \, b^{6} c^{2} + 64 \, a^{2} b^{3} c^{3} + 20 \, a b^{4} c^{3} + b^{5} c^{3} - 96 \, a^{3} b c^{4} - 48 \, a^{2} b^{2} c^{4} - 10 \, a b^{3} c^{4} + 24 \, a^{2} b c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B c + {\left(b^{8} c^{2} - 14 \, a b^{6} c^{3} - 2 \, b^{7} c^{3} + 64 \, a^{2} b^{4} c^{4} + 20 \, a b^{5} c^{4} + b^{6} c^{4} - 96 \, a^{3} b^{2} c^{5} - 48 \, a^{2} b^{3} c^{5} - 10 \, a b^{4} c^{5} + 24 \, a^{2} b^{2} c^{6} - {\left(b^{7} c^{2} - 10 \, a b^{5} c^{3} - 2 \, b^{6} c^{3} + 24 \, a^{2} b^{3} c^{4} + 12 \, a b^{4} c^{4} + b^{5} c^{4} - 6 \, a b^{3} c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{b c + \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{2 \, c^{2}}\right)}{8 \, {\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^{8} c - 14 \, a b^{6} c^{2} - 2 \, b^{7} c^{2} + 64 \, a^{2} b^{4} c^{3} + 20 \, a b^{5} c^{3} + b^{6} c^{3} - 96 \, a^{3} b^{2} c^{4} - 48 \, a^{2} b^{3} c^{4} - 10 \, a b^{4} c^{4} + 24 \, a^{2} b^{2} c^{5} + {\left(b^{7} c - 14 \, a b^{5} c^{2} - 2 \, b^{6} c^{2} + 64 \, a^{2} b^{3} c^{3} + 20 \, a b^{4} c^{3} + b^{5} c^{3} - 96 \, a^{3} b c^{4} - 48 \, a^{2} b^{2} c^{4} - 10 \, a b^{3} c^{4} + 24 \, a^{2} b c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B c + {\left(b^{8} c^{2} - 14 \, a b^{6} c^{3} - 2 \, b^{7} c^{3} + 64 \, a^{2} b^{4} c^{4} + 20 \, a b^{5} c^{4} + b^{6} c^{4} - 96 \, a^{3} b^{2} c^{5} - 48 \, a^{2} b^{3} c^{5} - 10 \, a b^{4} c^{5} + 24 \, a^{2} b^{2} c^{6} + {\left(b^{7} c^{2} - 10 \, a b^{5} c^{3} - 2 \, b^{6} c^{3} + 24 \, a^{2} b^{3} c^{4} + 12 \, a b^{4} c^{4} + b^{5} c^{4} - 6 \, a b^{3} c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{b c - \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{2 \, c^{2}}\right)}{8 \, {\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}}}{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}} + \frac{B \log\left(x\right)}{a^{2}}"," ",0,"1/2*(B*a*b*c*x^3 + (10*A*a*c^2 + (C*a*b - 3*A*b^2)*c)*x^4 - 2*A*a*b^2 + 8*A*a^2*c + (C*a*b^2 - 3*A*b^3 - (2*C*a^2 - 11*A*a*b)*c)*x^2 + (B*a*b^2 - 2*B*a^2*c)*x)/((a^2*b^2*c - 4*a^3*c^2)*x^5 + (a^2*b^3 - 4*a^3*b*c)*x^3 + (a^3*b^2 - 4*a^4*c)*x) + 1/2*integrate((C*a*b^2 - 3*A*b^3 - 2*(B*b^2*c - 4*B*a*c^2)*x^3 + (10*A*a*c^2 + (C*a*b - 3*A*b^2)*c)*x^2 - (6*C*a^2 - 13*A*a*b)*c - 2*(B*b^3 - 5*B*a*b*c)*x)/(c*x^4 + b*x^2 + a), x)/(a^2*b^2 - 4*a^3*c) + B*log(x)/a^2","F",0
36,0,0,0,0.000000," ","integrate((C*x^2+B*x+A)/x^3/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(3 \, B b^{2} c - 10 \, B a c^{2}\right)} x^{5} - {\left(6 \, A a c^{2} + {\left(C a b - 2 \, A b^{2}\right)} c\right)} x^{4} + A a b^{2} - 4 \, A a^{2} c + {\left(3 \, B b^{3} - 11 \, B a b c\right)} x^{3} - {\left(C a b^{2} - 2 \, A b^{3} - {\left(2 \, C a^{2} - 7 \, A a b\right)} c\right)} x^{2} + 2 \, {\left(B a b^{2} - 4 \, B a^{2} c\right)} x}{2 \, {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{6} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{4} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x^{2}\right)}} - \frac{\frac{1}{2} \, {\left(C a b^{2} - 2 \, A b^{3} - 4 \, C a^{2} c + 8 \, A a b c\right)} \log\left({\left| c x^{4} + b x^{2} + a \right|}\right) + \frac{{\left({\left(6 \, b^{6} c^{2} - 68 \, a b^{4} c^{3} + 256 \, a^{2} b^{2} c^{4} - 320 \, a^{3} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} + 34 \, \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 - 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 44 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} B c^{2} + 2 \, {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c - 37 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} - 6 \, b^{7} c^{2} + 152 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 50 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} + 74 \, a b^{5} c^{3} - 208 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 104 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 25 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 304 \, a^{2} b^{3} c^{4} + 52 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + 416 \, a^{3} b c^{5} + 6 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} - 50 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} + 104 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} B c + {\left(6 \, b^{6} c^{4} - 56 \, a b^{4} c^{5} + 128 \, a^{2} b^{2} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{4} + 32 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5}\right)} B\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(b^{4} c - 8 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} + 16 \, a^{2} c^{3} + 8 \, a b c^{3} + b^{2} c^{3} - 4 \, a c^{4}\right)} c^{2}} - \frac{{\left({\left(6 \, b^{6} c^{2} - 68 \, a b^{4} c^{3} + 256 \, a^{2} b^{2} c^{4} - 320 \, a^{3} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} + 34 \, \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 - 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 44 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} B c^{2} - 2 \, {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c - 37 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 6 \, b^{7} c^{2} + 152 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 50 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 74 \, a b^{5} c^{3} - 208 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 104 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 25 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 304 \, a^{2} b^{3} c^{4} + 52 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} - 416 \, a^{3} b c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 50 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 104 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} B c + {\left(6 \, b^{6} c^{4} - 56 \, a b^{4} c^{5} + 128 \, a^{2} b^{2} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{4} + 32 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5}\right)} B\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(b^{4} c - 8 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} + 16 \, a^{2} c^{3} + 8 \, a b c^{3} + b^{2} c^{3} - 4 \, a c^{4}\right)} c^{2}} - \frac{{\left(2 \, {\left(b^{9} c - 14 \, a b^{7} c^{2} - 2 \, b^{8} c^{2} + 70 \, a^{2} b^{5} c^{3} + 20 \, a b^{6} c^{3} + b^{7} c^{3} - 144 \, a^{3} b^{3} c^{4} - 60 \, a^{2} b^{4} c^{4} - 10 \, a b^{5} c^{4} + 96 \, a^{4} b c^{5} + 48 \, a^{3} b^{2} c^{5} + 30 \, a^{2} b^{3} c^{5} - 24 \, a^{3} b c^{6} + {\left(b^{8} c - 14 \, a b^{6} c^{2} - 2 \, b^{7} c^{2} + 70 \, a^{2} b^{4} c^{3} + 20 \, a b^{5} c^{3} + b^{6} c^{3} - 144 \, a^{3} b^{2} c^{4} - 60 \, a^{2} b^{3} c^{4} - 10 \, a b^{4} c^{4} + 96 \, a^{4} c^{5} + 48 \, a^{3} b c^{5} + 30 \, a^{2} b^{2} c^{5} - 24 \, a^{3} c^{6}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A c - {\left(a b^{8} c - 14 \, a^{2} b^{6} c^{2} - 2 \, a b^{7} c^{2} + 64 \, a^{3} b^{4} c^{3} + 20 \, a^{2} b^{5} c^{3} + a b^{6} c^{3} - 96 \, a^{4} b^{2} c^{4} - 48 \, a^{3} b^{3} c^{4} - 10 \, a^{2} b^{4} c^{4} + 24 \, a^{3} b^{2} c^{5} + {\left(a b^{7} c - 14 \, a^{2} b^{5} c^{2} - 2 \, a b^{6} c^{2} + 64 \, a^{3} b^{3} c^{3} + 20 \, a^{2} b^{4} c^{3} + a b^{5} c^{3} - 96 \, a^{4} b c^{4} - 48 \, a^{3} b^{2} c^{4} - 10 \, a^{2} b^{3} c^{4} + 24 \, a^{3} b c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C c - 2 \, {\left(b^{9} c^{2} - 14 \, a b^{7} c^{3} - 2 \, b^{8} c^{3} + 70 \, a^{2} b^{5} c^{4} + 20 \, a b^{6} c^{4} + b^{7} c^{4} - 144 \, a^{3} b^{3} c^{5} - 60 \, a^{2} b^{4} c^{5} - 10 \, a b^{5} c^{5} + 96 \, a^{4} b c^{6} + 48 \, a^{3} b^{2} c^{6} + 30 \, a^{2} b^{3} c^{6} - 24 \, a^{3} b c^{7} + {\left(b^{8} c^{2} - 10 \, a b^{6} c^{3} - 2 \, b^{7} c^{3} + 30 \, a^{2} b^{4} c^{4} + 12 \, a b^{5} c^{4} + b^{6} c^{4} - 24 \, a^{3} b^{2} c^{5} - 12 \, a^{2} b^{3} c^{5} - 6 \, a b^{4} c^{5} + 6 \, a^{2} b^{2} c^{6}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A + {\left(a b^{8} c^{2} - 14 \, a^{2} b^{6} c^{3} - 2 \, a b^{7} c^{3} + 64 \, a^{3} b^{4} c^{4} + 20 \, a^{2} b^{5} c^{4} + a b^{6} c^{4} - 96 \, a^{4} b^{2} c^{5} - 48 \, a^{3} b^{3} c^{5} - 10 \, a^{2} b^{4} c^{5} + 24 \, a^{3} b^{2} c^{6} + {\left(a b^{7} c^{2} - 10 \, a^{2} b^{5} c^{3} - 2 \, a b^{6} c^{3} + 24 \, a^{3} b^{3} c^{4} + 12 \, a^{2} b^{4} c^{4} + a b^{5} c^{4} - 6 \, a^{2} b^{3} c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C\right)} \log\left(x^{2} + \frac{b c + \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{2 \, c^{2}}\right)}{8 \, {\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(2 \, {\left(b^{9} c - 14 \, a b^{7} c^{2} - 2 \, b^{8} c^{2} + 70 \, a^{2} b^{5} c^{3} + 20 \, a b^{6} c^{3} + b^{7} c^{3} - 144 \, a^{3} b^{3} c^{4} - 60 \, a^{2} b^{4} c^{4} - 10 \, a b^{5} c^{4} + 96 \, a^{4} b c^{5} + 48 \, a^{3} b^{2} c^{5} + 30 \, a^{2} b^{3} c^{5} - 24 \, a^{3} b c^{6} - {\left(b^{8} c - 14 \, a b^{6} c^{2} - 2 \, b^{7} c^{2} + 70 \, a^{2} b^{4} c^{3} + 20 \, a b^{5} c^{3} + b^{6} c^{3} - 144 \, a^{3} b^{2} c^{4} - 60 \, a^{2} b^{3} c^{4} - 10 \, a b^{4} c^{4} + 96 \, a^{4} c^{5} + 48 \, a^{3} b c^{5} + 30 \, a^{2} b^{2} c^{5} - 24 \, a^{3} c^{6}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A c - {\left(a b^{8} c - 14 \, a^{2} b^{6} c^{2} - 2 \, a b^{7} c^{2} + 64 \, a^{3} b^{4} c^{3} + 20 \, a^{2} b^{5} c^{3} + a b^{6} c^{3} - 96 \, a^{4} b^{2} c^{4} - 48 \, a^{3} b^{3} c^{4} - 10 \, a^{2} b^{4} c^{4} + 24 \, a^{3} b^{2} c^{5} - {\left(a b^{7} c - 14 \, a^{2} b^{5} c^{2} - 2 \, a b^{6} c^{2} + 64 \, a^{3} b^{3} c^{3} + 20 \, a^{2} b^{4} c^{3} + a b^{5} c^{3} - 96 \, a^{4} b c^{4} - 48 \, a^{3} b^{2} c^{4} - 10 \, a^{2} b^{3} c^{4} + 24 \, a^{3} b c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C c - 2 \, {\left(b^{9} c^{2} - 14 \, a b^{7} c^{3} - 2 \, b^{8} c^{3} + 70 \, a^{2} b^{5} c^{4} + 20 \, a b^{6} c^{4} + b^{7} c^{4} - 144 \, a^{3} b^{3} c^{5} - 60 \, a^{2} b^{4} c^{5} - 10 \, a b^{5} c^{5} + 96 \, a^{4} b c^{6} + 48 \, a^{3} b^{2} c^{6} + 30 \, a^{2} b^{3} c^{6} - 24 \, a^{3} b c^{7} - {\left(b^{8} c^{2} - 10 \, a b^{6} c^{3} - 2 \, b^{7} c^{3} + 30 \, a^{2} b^{4} c^{4} + 12 \, a b^{5} c^{4} + b^{6} c^{4} - 24 \, a^{3} b^{2} c^{5} - 12 \, a^{2} b^{3} c^{5} - 6 \, a b^{4} c^{5} + 6 \, a^{2} b^{2} c^{6}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A + {\left(a b^{8} c^{2} - 14 \, a^{2} b^{6} c^{3} - 2 \, a b^{7} c^{3} + 64 \, a^{3} b^{4} c^{4} + 20 \, a^{2} b^{5} c^{4} + a b^{6} c^{4} - 96 \, a^{4} b^{2} c^{5} - 48 \, a^{3} b^{3} c^{5} - 10 \, a^{2} b^{4} c^{5} + 24 \, a^{3} b^{2} c^{6} - {\left(a b^{7} c^{2} - 10 \, a^{2} b^{5} c^{3} - 2 \, a b^{6} c^{3} + 24 \, a^{3} b^{3} c^{4} + 12 \, a^{2} b^{4} c^{4} + a b^{5} c^{4} - 6 \, a^{2} b^{3} c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C\right)} \log\left(x^{2} + \frac{b c - \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{2 \, c^{2}}\right)}{8 \, {\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}}}{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}} + \frac{{\left(C a - 2 \, A b\right)} \log\left(x\right)}{a^{3}}"," ",0,"-1/2*((3*B*b^2*c - 10*B*a*c^2)*x^5 - (6*A*a*c^2 + (C*a*b - 2*A*b^2)*c)*x^4 + A*a*b^2 - 4*A*a^2*c + (3*B*b^3 - 11*B*a*b*c)*x^3 - (C*a*b^2 - 2*A*b^3 - (2*C*a^2 - 7*A*a*b)*c)*x^2 + 2*(B*a*b^2 - 4*B*a^2*c)*x)/((a^2*b^2*c - 4*a^3*c^2)*x^6 + (a^2*b^3 - 4*a^3*b*c)*x^4 + (a^3*b^2 - 4*a^4*c)*x^2) - 1/2*integrate((3*B*a*b^3 - 13*B*a^2*b*c - 2*(4*(C*a^2 - 2*A*a*b)*c^2 - (C*a*b^2 - 2*A*b^3)*c)*x^3 + (3*B*a*b^2*c - 10*B*a^2*c^2)*x^2 + 2*(C*a*b^3 - 2*A*b^4 - 6*A*a^2*c^2 - 5*(C*a^2*b - 2*A*a*b^2)*c)*x)/(c*x^4 + b*x^2 + a), x)/(a^3*b^2 - 4*a^4*c) + (C*a - 2*A*b)*log(x)/a^3","F",0
37,1,611,0,1.706237," ","integrate((d*x)^m*(C*x^2+B*x+A)*(c*x^4+b*x^2+a)^3,x, algorithm=""maxima"")","\frac{C c^{3} d^{m} x^{15} x^{m}}{m + 15} + \frac{B c^{3} d^{m} x^{14} x^{m}}{m + 14} + \frac{3 \, C b c^{2} d^{m} x^{13} x^{m}}{m + 13} + \frac{A c^{3} d^{m} x^{13} x^{m}}{m + 13} + \frac{3 \, B b c^{2} d^{m} x^{12} x^{m}}{m + 12} + \frac{3 \, C b^{2} c d^{m} x^{11} x^{m}}{m + 11} + \frac{3 \, C a c^{2} d^{m} x^{11} x^{m}}{m + 11} + \frac{3 \, A b c^{2} d^{m} x^{11} x^{m}}{m + 11} + \frac{3 \, B b^{2} c d^{m} x^{10} x^{m}}{m + 10} + \frac{3 \, B a c^{2} d^{m} x^{10} x^{m}}{m + 10} + \frac{C b^{3} d^{m} x^{9} x^{m}}{m + 9} + \frac{6 \, C a b c d^{m} x^{9} x^{m}}{m + 9} + \frac{3 \, A b^{2} c d^{m} x^{9} x^{m}}{m + 9} + \frac{3 \, A a c^{2} d^{m} x^{9} x^{m}}{m + 9} + \frac{B b^{3} d^{m} x^{8} x^{m}}{m + 8} + \frac{6 \, B a b c d^{m} x^{8} x^{m}}{m + 8} + \frac{3 \, C a b^{2} d^{m} x^{7} x^{m}}{m + 7} + \frac{A b^{3} d^{m} x^{7} x^{m}}{m + 7} + \frac{3 \, C a^{2} c d^{m} x^{7} x^{m}}{m + 7} + \frac{6 \, A a b c d^{m} x^{7} x^{m}}{m + 7} + \frac{3 \, B a b^{2} d^{m} x^{6} x^{m}}{m + 6} + \frac{3 \, B a^{2} c d^{m} x^{6} x^{m}}{m + 6} + \frac{3 \, C a^{2} b d^{m} x^{5} x^{m}}{m + 5} + \frac{3 \, A a b^{2} d^{m} x^{5} x^{m}}{m + 5} + \frac{3 \, A a^{2} c d^{m} x^{5} x^{m}}{m + 5} + \frac{3 \, B a^{2} b d^{m} x^{4} x^{m}}{m + 4} + \frac{C a^{3} d^{m} x^{3} x^{m}}{m + 3} + \frac{3 \, A a^{2} b d^{m} x^{3} x^{m}}{m + 3} + \frac{B a^{3} d^{m} x^{2} x^{m}}{m + 2} + \frac{\left(d x\right)^{m + 1} A a^{3}}{d {\left(m + 1\right)}}"," ",0,"C*c^3*d^m*x^15*x^m/(m + 15) + B*c^3*d^m*x^14*x^m/(m + 14) + 3*C*b*c^2*d^m*x^13*x^m/(m + 13) + A*c^3*d^m*x^13*x^m/(m + 13) + 3*B*b*c^2*d^m*x^12*x^m/(m + 12) + 3*C*b^2*c*d^m*x^11*x^m/(m + 11) + 3*C*a*c^2*d^m*x^11*x^m/(m + 11) + 3*A*b*c^2*d^m*x^11*x^m/(m + 11) + 3*B*b^2*c*d^m*x^10*x^m/(m + 10) + 3*B*a*c^2*d^m*x^10*x^m/(m + 10) + C*b^3*d^m*x^9*x^m/(m + 9) + 6*C*a*b*c*d^m*x^9*x^m/(m + 9) + 3*A*b^2*c*d^m*x^9*x^m/(m + 9) + 3*A*a*c^2*d^m*x^9*x^m/(m + 9) + B*b^3*d^m*x^8*x^m/(m + 8) + 6*B*a*b*c*d^m*x^8*x^m/(m + 8) + 3*C*a*b^2*d^m*x^7*x^m/(m + 7) + A*b^3*d^m*x^7*x^m/(m + 7) + 3*C*a^2*c*d^m*x^7*x^m/(m + 7) + 6*A*a*b*c*d^m*x^7*x^m/(m + 7) + 3*B*a*b^2*d^m*x^6*x^m/(m + 6) + 3*B*a^2*c*d^m*x^6*x^m/(m + 6) + 3*C*a^2*b*d^m*x^5*x^m/(m + 5) + 3*A*a*b^2*d^m*x^5*x^m/(m + 5) + 3*A*a^2*c*d^m*x^5*x^m/(m + 5) + 3*B*a^2*b*d^m*x^4*x^m/(m + 4) + C*a^3*d^m*x^3*x^m/(m + 3) + 3*A*a^2*b*d^m*x^3*x^m/(m + 3) + B*a^3*d^m*x^2*x^m/(m + 2) + (d*x)^(m + 1)*A*a^3/(d*(m + 1))","A",0
38,1,344,0,1.730762," ","integrate((d*x)^m*(C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{C c^{2} d^{m} x^{11} x^{m}}{m + 11} + \frac{B c^{2} d^{m} x^{10} x^{m}}{m + 10} + \frac{2 \, C b c d^{m} x^{9} x^{m}}{m + 9} + \frac{A c^{2} d^{m} x^{9} x^{m}}{m + 9} + \frac{2 \, B b c d^{m} x^{8} x^{m}}{m + 8} + \frac{C b^{2} d^{m} x^{7} x^{m}}{m + 7} + \frac{2 \, C a c d^{m} x^{7} x^{m}}{m + 7} + \frac{2 \, A b c d^{m} x^{7} x^{m}}{m + 7} + \frac{B b^{2} d^{m} x^{6} x^{m}}{m + 6} + \frac{2 \, B a c d^{m} x^{6} x^{m}}{m + 6} + \frac{2 \, C a b d^{m} x^{5} x^{m}}{m + 5} + \frac{A b^{2} d^{m} x^{5} x^{m}}{m + 5} + \frac{2 \, A a c d^{m} x^{5} x^{m}}{m + 5} + \frac{2 \, B a b d^{m} x^{4} x^{m}}{m + 4} + \frac{C a^{2} d^{m} x^{3} x^{m}}{m + 3} + \frac{2 \, A a b d^{m} x^{3} x^{m}}{m + 3} + \frac{B a^{2} d^{m} x^{2} x^{m}}{m + 2} + \frac{\left(d x\right)^{m + 1} A a^{2}}{d {\left(m + 1\right)}}"," ",0,"C*c^2*d^m*x^11*x^m/(m + 11) + B*c^2*d^m*x^10*x^m/(m + 10) + 2*C*b*c*d^m*x^9*x^m/(m + 9) + A*c^2*d^m*x^9*x^m/(m + 9) + 2*B*b*c*d^m*x^8*x^m/(m + 8) + C*b^2*d^m*x^7*x^m/(m + 7) + 2*C*a*c*d^m*x^7*x^m/(m + 7) + 2*A*b*c*d^m*x^7*x^m/(m + 7) + B*b^2*d^m*x^6*x^m/(m + 6) + 2*B*a*c*d^m*x^6*x^m/(m + 6) + 2*C*a*b*d^m*x^5*x^m/(m + 5) + A*b^2*d^m*x^5*x^m/(m + 5) + 2*A*a*c*d^m*x^5*x^m/(m + 5) + 2*B*a*b*d^m*x^4*x^m/(m + 4) + C*a^2*d^m*x^3*x^m/(m + 3) + 2*A*a*b*d^m*x^3*x^m/(m + 3) + B*a^2*d^m*x^2*x^m/(m + 2) + (d*x)^(m + 1)*A*a^2/(d*(m + 1))","A",0
39,1,155,0,0.815309," ","integrate((d*x)^m*(C*x^2+B*x+A)*(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{C c d^{m} x^{7} x^{m}}{m + 7} + \frac{B c d^{m} x^{6} x^{m}}{m + 6} + \frac{C b d^{m} x^{5} x^{m}}{m + 5} + \frac{A c d^{m} x^{5} x^{m}}{m + 5} + \frac{B b d^{m} x^{4} x^{m}}{m + 4} + \frac{C a d^{m} x^{3} x^{m}}{m + 3} + \frac{A b d^{m} x^{3} x^{m}}{m + 3} + \frac{B a d^{m} x^{2} x^{m}}{m + 2} + \frac{\left(d x\right)^{m + 1} A a}{d {\left(m + 1\right)}}"," ",0,"C*c*d^m*x^7*x^m/(m + 7) + B*c*d^m*x^6*x^m/(m + 6) + C*b*d^m*x^5*x^m/(m + 5) + A*c*d^m*x^5*x^m/(m + 5) + B*b*d^m*x^4*x^m/(m + 4) + C*a*d^m*x^3*x^m/(m + 3) + A*b*d^m*x^3*x^m/(m + 3) + B*a*d^m*x^2*x^m/(m + 2) + (d*x)^(m + 1)*A*a/(d*(m + 1))","A",0
40,0,0,0,0.000000," ","integrate((d*x)^m*(C*x^2+B*x+A)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\int \frac{{\left(C x^{2} + B x + A\right)} \left(d x\right)^{m}}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*(d*x)^m/(c*x^4 + b*x^2 + a), x)","F",0
41,0,0,0,0.000000," ","integrate((d*x)^m*(C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{{\left(C x^{2} + B x + A\right)} \left(d x\right)^{m}}{{\left(c x^{4} + b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate((C*x^2 + B*x + A)*(d*x)^m/(c*x^4 + b*x^2 + a)^2, x)","F",0
42,0,0,0,0.000000," ","integrate(x^2*(C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{B b x^{2} + {\left(C b - 2 \, A c\right)} x^{3} + 2 \, B a + {\left(2 \, C a - A b\right)} x}{2 \, {\left({\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}\right)}} - \frac{-\int \frac{2 \, B b x + {\left(C b - 2 \, A c\right)} x^{2} - 2 \, C a + A b}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left(b^{2} - 4 \, a c\right)}}"," ",0,"1/2*(B*b*x^2 + (C*b - 2*A*c)*x^3 + 2*B*a + (2*C*a - A*b)*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) - 1/2*integrate(-(2*B*b*x + (C*b - 2*A*c)*x^2 - 2*C*a + A*b)/(c*x^4 + b*x^2 + a), x)/(b^2 - 4*a*c)","F",0
43,0,0,0,0.000000," ","integrate(x*(C*x^3+B*x^2+A*x)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{B b x^{2} + {\left(C b - 2 \, A c\right)} x^{3} + 2 \, B a + {\left(2 \, C a - A b\right)} x}{2 \, {\left({\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}\right)}} - \frac{-\int \frac{2 \, B b x + {\left(C b - 2 \, A c\right)} x^{2} - 2 \, C a + A b}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left(b^{2} - 4 \, a c\right)}}"," ",0,"1/2*(B*b*x^2 + (C*b - 2*A*c)*x^3 + 2*B*a + (2*C*a - A*b)*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) - 1/2*integrate(-(2*B*b*x + (C*b - 2*A*c)*x^2 - 2*C*a + A*b)/(c*x^4 + b*x^2 + a), x)/(b^2 - 4*a*c)","F",0
44,0,0,0,0.000000," ","integrate((C*x^4+B*x^3+A*x^2)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{B b x^{2} + {\left(C b - 2 \, A c\right)} x^{3} + 2 \, B a + {\left(2 \, C a - A b\right)} x}{2 \, {\left({\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}\right)}} - \frac{-\int \frac{2 \, B b x + {\left(C b - 2 \, A c\right)} x^{2} - 2 \, C a + A b}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left(b^{2} - 4 \, a c\right)}}"," ",0,"1/2*(B*b*x^2 + (C*b - 2*A*c)*x^3 + 2*B*a + (2*C*a - A*b)*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) - 1/2*integrate(-(2*B*b*x + (C*b - 2*A*c)*x^2 - 2*C*a + A*b)/(c*x^4 + b*x^2 + a), x)/(b^2 - 4*a*c)","F",0
45,0,0,0,0.000000," ","integrate((C*x^5+B*x^4+A*x^3)/x/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{B b x^{2} + {\left(C b - 2 \, A c\right)} x^{3} + 2 \, B a + {\left(2 \, C a - A b\right)} x}{2 \, {\left({\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}\right)}} - \frac{-\int \frac{2 \, B b x + {\left(C b - 2 \, A c\right)} x^{2} - 2 \, C a + A b}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left(b^{2} - 4 \, a c\right)}}"," ",0,"1/2*(B*b*x^2 + (C*b - 2*A*c)*x^3 + 2*B*a + (2*C*a - A*b)*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) - 1/2*integrate(-(2*B*b*x + (C*b - 2*A*c)*x^2 - 2*C*a + A*b)/(c*x^4 + b*x^2 + a), x)/(b^2 - 4*a*c)","F",0
46,0,0,0,0.000000," ","integrate((C*x^6+B*x^5+A*x^4)/x^2/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{B b x^{2} + {\left(C b - 2 \, A c\right)} x^{3} + 2 \, B a + {\left(2 \, C a - A b\right)} x}{2 \, {\left({\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}\right)}} - \frac{-\int \frac{2 \, B b x + {\left(C b - 2 \, A c\right)} x^{2} - 2 \, C a + A b}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left(b^{2} - 4 \, a c\right)}}"," ",0,"1/2*(B*b*x^2 + (C*b - 2*A*c)*x^3 + 2*B*a + (2*C*a - A*b)*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) - 1/2*integrate(-(2*B*b*x + (C*b - 2*A*c)*x^2 - 2*C*a + A*b)/(c*x^4 + b*x^2 + a), x)/(b^2 - 4*a*c)","F",0
47,-2,0,0,0.000000," ","integrate(x^7*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
48,-2,0,0,0.000000," ","integrate(x^5*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
49,-2,0,0,0.000000," ","integrate(x^3*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
50,-2,0,0,0.000000," ","integrate(x*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
51,-2,0,0,0.000000," ","integrate((f*x^4+e*x^2+d)/x/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
52,-2,0,0,0.000000," ","integrate((f*x^4+e*x^2+d)/x^3/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
53,-2,0,0,0.000000," ","integrate((f*x^4+e*x^2+d)/x^5/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
54,-2,0,0,0.000000," ","integrate((f*x^4+e*x^2+d)/x^7/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
55,0,0,0,0.000000," ","integrate(x^4*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{3 \, c^{2} f x^{5} + 5 \, {\left(c^{2} e - b c f\right)} x^{3} + 15 \, {\left(c^{2} d - b c e + {\left(b^{2} - a c\right)} f\right)} x}{15 \, c^{3}} + \frac{-\int \frac{a c^{2} d - a b c e + {\left(b c^{2} d - {\left(b^{2} c - a c^{2}\right)} e + {\left(b^{3} - 2 \, a b c\right)} f\right)} x^{2} + {\left(a b^{2} - a^{2} c\right)} f}{c x^{4} + b x^{2} + a}\,{d x}}{c^{3}}"," ",0,"1/15*(3*c^2*f*x^5 + 5*(c^2*e - b*c*f)*x^3 + 15*(c^2*d - b*c*e + (b^2 - a*c)*f)*x)/c^3 + integrate(-(a*c^2*d - a*b*c*e + (b*c^2*d - (b^2*c - a*c^2)*e + (b^3 - 2*a*b*c)*f)*x^2 + (a*b^2 - a^2*c)*f)/(c*x^4 + b*x^2 + a), x)/c^3","F",0
56,0,0,0,0.000000," ","integrate(x^2*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{c f x^{3} + 3 \, {\left(c e - b f\right)} x}{3 \, c^{2}} - \frac{\frac{{\left(2 \, {\left(2 \, b^{2} c^{4} - 8 \, a c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{4}\right)} d - {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} - 8 \, \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 \, b^{5} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 16 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 32 \, a^{2} b c^{3} + 12 \, a b^{2} c^{3} - 16 \, a^{2} c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} - 6 \, \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 + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} - 4 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} f + {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 2 \, b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} + 16 \, a b^{2} c^{3} - 2 \, b^{3} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{4} - 32 \, a^{2} c^{4} + 8 \, a b c^{4} + \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} a b c^{2} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{3}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\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} - \frac{{\left(2 \, {\left(2 \, b^{2} c^{4} - 8 \, a c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{4}\right)} d + {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} - 8 \, \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 \, b^{5} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 16 \, a b^{3} c^{2} + 2 \, b^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + 32 \, a^{2} b c^{3} - 12 \, a b^{2} c^{3} + 16 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} + 6 \, \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 - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} f - {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 2 \, b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} - 16 \, a b^{2} c^{3} + 2 \, b^{3} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{4} + 32 \, a^{2} c^{4} - 8 \, a b c^{4} - \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} a b c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{3}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\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}}{c^{2}}"," ",0,"1/3*(c*f*x^3 + 3*(c*e - b*f)*x)/c^2 - integrate((a*c*e - a*b*f - (c^2*d - b*c*e + (b^2 - a*c)*f)*x^2)/(c*x^4 + b*x^2 + a), x)/c^2","F",0
57,0,0,0,0.000000," ","integrate((f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{f x}{c} - \frac{-\int \frac{{\left(c e - b f\right)} x^{2} + c d - a f}{c x^{4} + b x^{2} + a}\,{d x}}{c}"," ",0,"f*x/c - integrate(-((c*e - b*f)*x^2 + c*d - a*f)/(c*x^4 + b*x^2 + a), x)/c","F",0
58,0,0,0,0.000000," ","integrate((f*x^4+e*x^2+d)/x^2/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\frac{-\int \frac{{\left(c d - a f\right)} x^{2} + b d - a e}{c x^{4} + b x^{2} + a}\,{d x}}{a} - \frac{d}{a x}"," ",0,"integrate(-((c*d - a*f)*x^2 + b*d - a*e)/(c*x^4 + b*x^2 + a), x)/a - d/(a*x)","F",0
59,0,0,0,0.000000," ","integrate((f*x^4+e*x^2+d)/x^4/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","-\frac{-\frac{{\left({\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} - 9 \, \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 + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 10 \, \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} + 18 \, a b^{4} c^{2} + 2 \, b^{5} c^{2} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 48 \, a^{2} b^{2} c^{3} - 14 \, a b^{3} c^{3} + 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 32 \, a^{3} c^{4} + 24 \, 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} + 7 \, \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 - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 6 \, \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} + 3 \, \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 - 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} + 6 \, {\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^{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} + 2 \, 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} - 8 \, a^{3} b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c - \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} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2}\right)} f - {\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} - 12 \, a^{2} b^{2} c^{3} + 16 \, 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} + 6 \, \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 b^{3} c - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} - 4 \, \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} + 2 \, \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} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} e\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} - 9 \, \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 + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 10 \, \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} - 18 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 48 \, a^{2} b^{2} c^{3} + 14 \, a b^{3} c^{3} + 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 32 \, a^{3} c^{4} - 24 \, 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} - 7 \, \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 + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 6 \, \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} - 3 \, \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 + 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} - 6 \, {\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^{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} - 2 \, 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} + 8 \, a^{3} b c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c + \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} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2}\right)} f - {\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} + 12 \, a^{2} b^{2} c^{3} - 16 \, 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} - 6 \, \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 b^{3} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} + 4 \, \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} - 2 \, \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} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} e\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}}{a^{2}} + \frac{3 \, {\left(b d - a e\right)} x^{2} - a d}{3 \, a^{2} x^{3}}"," ",0,"-integrate((a*b*e - a^2*f - (b*c*d - a*c*e)*x^2 - (b^2 - a*c)*d)/(c*x^4 + b*x^2 + a), x)/a^2 + 1/3*(3*(b*d - a*e)*x^2 - a*d)/(a^2*x^3)","F",0
60,0,0,0,0.000000," ","integrate((f*x^4+e*x^2+d)/x^6/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","-\frac{\frac{{\left({\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} - 10 \, \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 \, b^{7} c + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 12 \, \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} + 20 \, a b^{5} c^{2} + 2 \, b^{6} c^{2} - 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 64 \, a^{2} b^{3} c^{3} - 16 \, a b^{4} c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 64 \, a^{3} b c^{4} + 36 \, a^{2} b^{2} c^{4} - 16 \, a^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} + 8 \, \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 - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 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^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b 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^{3} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c - 12 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} d + {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, a^{2} b^{5} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{2} + 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} + 16 \, a^{3} b^{3} c^{2} + 2 \, a^{2} b^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, a^{4} b c^{3} - 12 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} + 6 \, \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 - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3}\right)} f - {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 9 \, \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 \, a b^{6} c + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 10 \, \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} + 18 \, a^{2} b^{4} c^{2} + 2 \, a b^{5} c^{2} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 48 \, a^{3} b^{2} c^{3} - 14 \, a^{2} b^{3} c^{3} + 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 32 \, a^{4} c^{4} + 24 \, a^{3} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} + 7 \, \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 - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 6 \, \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 b^{3} c^{2} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} e\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^{7} - 10 \, \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 \, b^{7} c + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 12 \, \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} - 20 \, a b^{5} c^{2} - 2 \, b^{6} c^{2} - 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 64 \, a^{2} b^{3} c^{3} + 16 \, a b^{4} c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 64 \, a^{3} b c^{4} - 36 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} - 8 \, \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 + 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 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^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b 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^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c + 12 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} d + {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c + 2 \, a^{2} b^{5} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{2} + 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} - 16 \, a^{3} b^{3} c^{2} - 2 \, a^{2} b^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 32 \, a^{4} b c^{3} + 12 \, a^{3} b^{2} c^{3} - 16 \, a^{4} c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} - 6 \, \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 + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3}\right)} f - {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 9 \, \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 \, a b^{6} c + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 10 \, \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} - 18 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 48 \, a^{3} b^{2} c^{3} + 14 \, a^{2} b^{3} c^{3} + 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 32 \, a^{4} c^{4} - 24 \, a^{3} b c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 7 \, \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 + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 6 \, \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 b^{3} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c + 10 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} e\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}}{a^{3}} + \frac{15 \, {\left(a b e - a^{2} f - {\left(b^{2} - a c\right)} d\right)} x^{4} - 3 \, a^{2} d + 5 \, {\left(a b d - a^{2} e\right)} x^{2}}{15 \, a^{3} x^{5}}"," ",0,"-integrate((a^2*b*f - (a*b*c*e - a^2*c*f - (b^2*c - a*c^2)*d)*x^2 + (b^3 - 2*a*b*c)*d - (a*b^2 - a^2*c)*e)/(c*x^4 + b*x^2 + a), x)/a^3 + 1/15*(15*(a*b*e - a^2*f - (b^2 - a*c)*d)*x^4 - 3*a^2*d + 5*(a*b*d - a^2*e)*x^2)/(a^3*x^5)","F",0
61,-2,0,0,0.000000," ","integrate(x^7*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
62,-2,0,0,0.000000," ","integrate(x^5*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
63,-2,0,0,0.000000," ","integrate(x^3*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
64,-2,0,0,0.000000," ","integrate(x*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
65,-2,0,0,0.000000," ","integrate((f*x^4+e*x^2+d)/x/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
66,-2,0,0,0.000000," ","integrate((f*x^4+e*x^2+d)/x^3/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
67,-2,0,0,0.000000," ","integrate((f*x^4+e*x^2+d)/x^5/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
68,0,0,0,0.000000," ","integrate(x^6*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left({\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d - {\left(b^{3} c - 3 \, a b c^{2}\right)} e + {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} f\right)} x^{3} + {\left(a b c^{2} d - {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} e + {\left(a b^{3} - 3 \, a^{2} b c\right)} f\right)} x}{2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{4} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x^{2}\right)}} + \frac{\frac{{\left({\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 2 \, b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 16 \, a b^{3} c^{4} + 2 \, b^{4} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 32 \, a^{2} b c^{5} - 32 \, a b^{2} c^{5} + 96 \, a^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} 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^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{4} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{4} + 24 \, {\left(b^{2} - 4 \, a c\right)} a c^{5}\right)} d + {\left(5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} - 59 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 10 \, b^{7} c + 232 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 78 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 118 \, a b^{5} c^{2} + 10 \, b^{6} c^{2} - 304 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 152 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 39 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 464 \, a^{2} b^{3} c^{3} - 98 \, a b^{4} c^{3} + 76 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 608 \, a^{3} b c^{4} + 288 \, a^{2} b^{2} c^{4} - 224 \, a^{3} c^{5} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} + 49 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 144 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 58 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 29 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 10 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c - 78 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 152 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} + 58 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 56 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} f - {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 34 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 6 \, b^{6} c^{2} + 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 44 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 68 \, a b^{4} c^{3} + 6 \, b^{5} c^{3} - 160 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 80 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 22 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 256 \, a^{2} b^{2} c^{4} - 56 \, a b^{3} c^{4} + 40 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 320 \, a^{3} c^{5} + 128 \, a^{2} b c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{4} + 6 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} - 44 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} + 80 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4} + 32 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b + \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\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} + \frac{{\left({\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 2 \, b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} - 16 \, a b^{3} c^{4} + 2 \, b^{4} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{5} + 32 \, a^{2} b c^{5} - 32 \, a b^{2} c^{5} + 96 \, a^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} 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^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{4} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{4} + 24 \, {\left(b^{2} - 4 \, a c\right)} a c^{5}\right)} d + {\left(5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} - 59 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 10 \, b^{7} c + 232 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 78 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 118 \, a b^{5} c^{2} + 10 \, b^{6} c^{2} - 304 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 152 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 39 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 464 \, a^{2} b^{3} c^{3} - 98 \, a b^{4} c^{3} + 76 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 608 \, a^{3} b c^{4} + 288 \, a^{2} b^{2} c^{4} - 224 \, a^{3} c^{5} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} + 49 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 144 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 58 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 29 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c + 78 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} - 152 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} + 58 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 56 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} f - {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 34 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 6 \, b^{6} c^{2} + 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 44 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 68 \, a b^{4} c^{3} + 6 \, b^{5} c^{3} - 160 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 80 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 22 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 256 \, a^{2} b^{2} c^{4} - 56 \, a b^{3} c^{4} + 40 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 320 \, a^{3} c^{5} + 128 \, a^{2} b c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 44 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4} + 32 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b - \sqrt{b^{2} - 4 \, a c}}{c}}}\right)}{4 \, {\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 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}} + \frac{c f x^{3} + 3 \, {\left(c e - 2 \, b f\right)} x}{3 \, c^{3}}"," ",0,"-1/2*(((b^2*c^2 - 2*a*c^3)*d - (b^3*c - 3*a*b*c^2)*e + (b^4 - 4*a*b^2*c + 2*a^2*c^2)*f)*x^3 + (a*b*c^2*d - (a*b^2*c - 2*a^2*c^2)*e + (a*b^3 - 3*a^2*b*c)*f)*x)/(a*b^2*c^3 - 4*a^2*c^4 + (b^2*c^4 - 4*a*c^5)*x^4 + (b^3*c^3 - 4*a*b*c^4)*x^2) + 1/2*integrate((a*b*c^2*d + ((b^2*c^2 - 6*a*c^3)*d - (3*b^3*c - 13*a*b*c^2)*e + (5*b^4 - 24*a*b^2*c + 14*a^2*c^2)*f)*x^2 - (3*a*b^2*c - 10*a^2*c^2)*e + (5*a*b^3 - 19*a^2*b*c)*f)/(c*x^4 + b*x^2 + a), x)/(b^2*c^3 - 4*a*c^4) + 1/3*(c*f*x^3 + 3*(c*e - 2*b*f)*x)/c^3","F",0
69,0,0,0,0.000000," ","integrate(x^4*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(b c^{2} d - {\left(b^{2} c - 2 \, a c^{2}\right)} e + {\left(b^{3} - 3 \, a b c\right)} f\right)} x^{3} + {\left(2 \, a c^{2} d - a b c e + {\left(a b^{2} - 2 \, a^{2} c\right)} f\right)} x}{2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{4} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2}\right)}} + \frac{f x}{c^{2}} + \frac{-\int \frac{2 \, a c^{2} d - a b c e - {\left(b c^{2} d + {\left(b^{2} c - 6 \, a c^{2}\right)} e - {\left(3 \, b^{3} - 13 \, a b c\right)} f\right)} x^{2} + {\left(3 \, a b^{2} - 10 \, a^{2} c\right)} f}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}"," ",0,"1/2*((b*c^2*d - (b^2*c - 2*a*c^2)*e + (b^3 - 3*a*b*c)*f)*x^3 + (2*a*c^2*d - a*b*c*e + (a*b^2 - 2*a^2*c)*f)*x)/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^4 + (b^3*c^2 - 4*a*b*c^3)*x^2) + f*x/c^2 + 1/2*integrate(-(2*a*c^2*d - a*b*c*e - (b*c^2*d + (b^2*c - 6*a*c^2)*e - (3*b^3 - 13*a*b*c)*f)*x^2 + (3*a*b^2 - 10*a^2*c)*f)/(c*x^4 + b*x^2 + a), x)/(b^2*c^2 - 4*a*c^3)","F",0
70,0,0,0,0.000000," ","integrate(x^2*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(2 \, c^{2} d - b c e + {\left(b^{2} - 2 \, a c\right)} f\right)} x^{3} + {\left(b c d - 2 \, a c e + a b f\right)} x}{2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2}\right)}} - \frac{-\int \frac{b c d - 2 \, a c e + a b f - {\left(2 \, c^{2} d - b c e - {\left(b^{2} - 6 \, a c\right)} f\right)} x^{2}}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}"," ",0,"-1/2*((2*c^2*d - b*c*e + (b^2 - 2*a*c)*f)*x^3 + (b*c*d - 2*a*c*e + a*b*f)*x)/((b^2*c^2 - 4*a*c^3)*x^4 + a*b^2*c - 4*a^2*c^2 + (b^3*c - 4*a*b*c^2)*x^2) - 1/2*integrate(-(b*c*d - 2*a*c*e + a*b*f - (2*c^2*d - b*c*e - (b^2 - 6*a*c)*f)*x^2)/(c*x^4 + b*x^2 + a), x)/(b^2*c - 4*a*c^2)","F",0
71,0,0,0,0.000000," ","integrate((f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(b c d - 2 \, a c e + a b f\right)} x^{3} - {\left(a b e - 2 \, a^{2} 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{{\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 - 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)} f + {\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)} e\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 - 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)} f + {\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)} e\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*((b*c*d - 2*a*c*e + a*b*f)*x^3 - (a*b*e - 2*a^2*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*e - 2*a^2*f + (b*c*d - 2*a*c*e + a*b*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
72,0,0,0,0.000000," ","integrate((f*x^4+e*x^2+d)/x^2/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(a b c e - 2 \, a^{2} c f - {\left(3 \, b^{2} c - 10 \, a c^{2}\right)} d\right)} x^{4} - {\left(a^{2} b f + {\left(3 \, b^{3} - 11 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e\right)} x^{2} - 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d}{2 \, {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)}} - \frac{-\int \frac{a^{2} b f + {\left(a b c e - 2 \, a^{2} c f - {\left(3 \, b^{2} c - 10 \, a c^{2}\right)} d\right)} x^{2} - {\left(3 \, b^{3} - 13 \, a b c\right)} d + {\left(a b^{2} - 6 \, a^{2} c\right)} e}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}}"," ",0,"1/2*((a*b*c*e - 2*a^2*c*f - (3*b^2*c - 10*a*c^2)*d)*x^4 - (a^2*b*f + (3*b^3 - 11*a*b*c)*d - (a*b^2 - 2*a^2*c)*e)*x^2 - 2*(a*b^2 - 4*a^2*c)*d)/((a^2*b^2*c - 4*a^3*c^2)*x^5 + (a^2*b^3 - 4*a^3*b*c)*x^3 + (a^3*b^2 - 4*a^4*c)*x) - 1/2*integrate(-(a^2*b*f + (a*b*c*e - 2*a^2*c*f - (3*b^2*c - 10*a*c^2)*d)*x^2 - (3*b^3 - 13*a*b*c)*d + (a*b^2 - 6*a^2*c)*e)/(c*x^4 + b*x^2 + a), x)/(a^2*b^2 - 4*a^3*c)","F",0
73,0,0,0,0.000000," ","integrate((f*x^4+e*x^2+d)/x^4/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(a^{2} b c f + {\left(5 \, b^{3} c - 19 \, a b c^{2}\right)} d - {\left(3 \, a b^{2} c - 10 \, a^{2} c^{2}\right)} e\right)} x^{6} + {\left({\left(15 \, b^{4} - 62 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} d - 3 \, {\left(3 \, a b^{3} - 11 \, a^{2} b c\right)} e + 3 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} f\right)} x^{4} + 2 \, {\left(5 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d - 3 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e\right)} x^{2} - 2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d}{6 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}\right)}} + \frac{\frac{{\left({\left(5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} - 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c - 10 \, b^{8} c + 286 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 88 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 128 \, a b^{6} c^{2} + 10 \, b^{7} c^{2} - 496 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 220 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 44 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 572 \, a^{2} b^{4} c^{3} - 108 \, a b^{5} c^{3} + 224 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 112 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 110 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 992 \, a^{3} b^{2} c^{4} + 376 \, a^{2} b^{3} c^{4} - 56 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} - 448 \, a^{4} c^{5} - 416 \, a^{3} b c^{5} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 54 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 188 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 68 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 208 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 104 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 34 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 10 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c - 88 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 220 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} + 68 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 112 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} - 104 \, {\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^{2} b^{6} - 14 \, \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 + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 28 \, a^{3} b^{4} c^{2} + 2 \, a^{2} b^{5} c^{2} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{3} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 128 \, a^{4} b^{2} c^{3} - 24 \, a^{3} b^{3} c^{3} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 192 \, a^{5} c^{4} + 64 \, 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} + 12 \, \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 - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{2} - 16 \, \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} + 8 \, \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 - 20 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{3} + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3}\right)} f - {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 37 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 6 \, a b^{7} c + 152 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 50 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 74 \, a^{2} b^{5} c^{2} + 6 \, a b^{6} c^{2} - 208 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 104 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 25 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 304 \, a^{3} b^{3} c^{3} - 62 \, a^{2} b^{4} c^{3} + 52 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 416 \, a^{4} b c^{4} + 192 \, a^{3} b^{2} c^{4} - 160 \, a^{4} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} + 31 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} - 38 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 19 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} 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} c^{4} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c - 50 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 104 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3} + 38 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 40 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} e\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(5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} - 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c + 10 \, b^{8} c + 286 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 88 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} - 128 \, a b^{6} c^{2} - 10 \, b^{7} c^{2} - 496 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 220 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 44 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 572 \, a^{2} b^{4} c^{3} + 108 \, a b^{5} c^{3} + 224 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 112 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 110 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 992 \, a^{3} b^{2} c^{4} - 376 \, a^{2} b^{3} c^{4} - 56 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 448 \, a^{4} c^{5} + 416 \, a^{3} b c^{5} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} - 54 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 188 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 68 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 208 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 104 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 34 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c + 88 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 10 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} - 220 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 68 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} + 112 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} + 104 \, {\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^{2} b^{6} - 14 \, \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 + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} - 28 \, a^{3} b^{4} c^{2} - 2 \, a^{2} b^{5} c^{2} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{3} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} + 128 \, a^{4} b^{2} c^{3} + 24 \, a^{3} b^{3} c^{3} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} - 192 \, a^{5} c^{4} - 64 \, 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} - 12 \, \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 + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{2} + 16 \, \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} - 8 \, \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 + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{3} - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3}\right)} f - {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 37 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c + 6 \, a b^{7} c + 152 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 50 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 74 \, a^{2} b^{5} c^{2} - 6 \, a b^{6} c^{2} - 208 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 104 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 25 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 304 \, a^{3} b^{3} c^{3} + 62 \, a^{2} b^{4} c^{3} + 52 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 416 \, a^{4} b c^{4} - 192 \, a^{3} b^{2} c^{4} + 160 \, a^{4} c^{5} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 31 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 38 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 19 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} 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} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c + 50 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 104 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3} - 38 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} + 40 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} e\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^{3} b^{2} - 4 \, a^{4} c\right)}}"," ",0,"1/6*(3*(a^2*b*c*f + (5*b^3*c - 19*a*b*c^2)*d - (3*a*b^2*c - 10*a^2*c^2)*e)*x^6 + ((15*b^4 - 62*a*b^2*c + 14*a^2*c^2)*d - 3*(3*a*b^3 - 11*a^2*b*c)*e + 3*(a^2*b^2 - 2*a^3*c)*f)*x^4 + 2*(5*(a*b^3 - 4*a^2*b*c)*d - 3*(a^2*b^2 - 4*a^3*c)*e)*x^2 - 2*(a^2*b^2 - 4*a^3*c)*d)/((a^3*b^2*c - 4*a^4*c^2)*x^7 + (a^3*b^3 - 4*a^4*b*c)*x^5 + (a^4*b^2 - 4*a^5*c)*x^3) + 1/2*integrate(((a^2*b*c*f + (5*b^3*c - 19*a*b*c^2)*d - (3*a*b^2*c - 10*a^2*c^2)*e)*x^2 + (5*b^4 - 24*a*b^2*c + 14*a^2*c^2)*d - (3*a*b^3 - 13*a^2*b*c)*e + (a^2*b^2 - 6*a^3*c)*f)/(c*x^4 + b*x^2 + a), x)/(a^3*b^2 - 4*a^4*c)","F",0
74,1,58,0,0.602493," ","integrate(x^9*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x, algorithm=""maxima"")","\frac{5}{8} \, x^{8} - \frac{9}{2} \, x^{6} + \frac{49}{2} \, x^{4} - \frac{293}{2} \, x^{2} + \frac{415 \, x^{2} + 414}{2 \, {\left(x^{4} + 3 \, x^{2} + 2\right)}} + 392 \, \log\left(x^{2} + 2\right) + 2 \, \log\left(x^{2} + 1\right)"," ",0,"5/8*x^8 - 9/2*x^6 + 49/2*x^4 - 293/2*x^2 + 1/2*(415*x^2 + 414)/(x^4 + 3*x^2 + 2) + 392*log(x^2 + 2) + 2*log(x^2 + 1)","A",0
75,1,53,0,0.719026," ","integrate(x^7*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x, algorithm=""maxima"")","\frac{5}{6} \, x^{6} - \frac{27}{4} \, x^{4} + 49 \, x^{2} - \frac{207 \, x^{2} + 206}{2 \, {\left(x^{4} + 3 \, x^{2} + 2\right)}} - 144 \, \log\left(x^{2} + 2\right) - \frac{5}{2} \, \log\left(x^{2} + 1\right)"," ",0,"5/6*x^6 - 27/4*x^4 + 49*x^2 - 1/2*(207*x^2 + 206)/(x^4 + 3*x^2 + 2) - 144*log(x^2 + 2) - 5/2*log(x^2 + 1)","A",0
76,1,48,0,1.074988," ","integrate(x^5*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x, algorithm=""maxima"")","\frac{5}{4} \, x^{4} - \frac{27}{2} \, x^{2} + \frac{103 \, x^{2} + 102}{2 \, {\left(x^{4} + 3 \, x^{2} + 2\right)}} + 46 \, \log\left(x^{2} + 2\right) + 3 \, \log\left(x^{2} + 1\right)"," ",0,"5/4*x^4 - 27/2*x^2 + 1/2*(103*x^2 + 102)/(x^4 + 3*x^2 + 2) + 46*log(x^2 + 2) + 3*log(x^2 + 1)","A",0
77,1,43,0,0.513634," ","integrate(x^3*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x, algorithm=""maxima"")","\frac{5}{2} \, x^{2} - \frac{51 \, x^{2} + 50}{2 \, {\left(x^{4} + 3 \, x^{2} + 2\right)}} - 10 \, \log\left(x^{2} + 2\right) - \frac{7}{2} \, \log\left(x^{2} + 1\right)"," ",0,"5/2*x^2 - 1/2*(51*x^2 + 50)/(x^4 + 3*x^2 + 2) - 10*log(x^2 + 2) - 7/2*log(x^2 + 1)","A",0
78,1,38,0,0.521819," ","integrate(x*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x, algorithm=""maxima"")","\frac{25 \, x^{2} + 24}{2 \, {\left(x^{4} + 3 \, x^{2} + 2\right)}} - \frac{3}{2} \, \log\left(x^{2} + 2\right) + 4 \, \log\left(x^{2} + 1\right)"," ",0,"1/2*(25*x^2 + 24)/(x^4 + 3*x^2 + 2) - 3/2*log(x^2 + 2) + 4*log(x^2 + 1)","A",0
79,1,44,0,0.723928," ","integrate((5*x^6+3*x^4+x^2+4)/x/(x^4+3*x^2+2)^2,x, algorithm=""maxima"")","-\frac{12 \, x^{2} + 11}{2 \, {\left(x^{4} + 3 \, x^{2} + 2\right)}} + 4 \, \log\left(x^{2} + 2\right) - \frac{9}{2} \, \log\left(x^{2} + 1\right) + \frac{1}{2} \, \log\left(x^{2}\right)"," ",0,"-1/2*(12*x^2 + 11)/(x^4 + 3*x^2 + 2) + 4*log(x^2 + 2) - 9/2*log(x^2 + 1) + 1/2*log(x^2)","A",0
80,1,53,0,0.791988," ","integrate((5*x^6+3*x^4+x^2+4)/x^3/(x^4+3*x^2+2)^2,x, algorithm=""maxima"")","\frac{9 \, x^{4} + 3 \, x^{2} - 4}{4 \, {\left(x^{6} + 3 \, x^{4} + 2 \, x^{2}\right)}} - \frac{29}{8} \, \log\left(x^{2} + 2\right) + 5 \, \log\left(x^{2} + 1\right) - \frac{11}{8} \, \log\left(x^{2}\right)"," ",0,"1/4*(9*x^4 + 3*x^2 - 4)/(x^6 + 3*x^4 + 2*x^2) - 29/8*log(x^2 + 2) + 5*log(x^2 + 1) - 11/8*log(x^2)","A",0
81,1,56,0,0.678712," ","integrate((5*x^6+3*x^4+x^2+4)/x^5/(x^4+3*x^2+2)^2,x, algorithm=""maxima"")","\frac{x^{6} + 13 \, x^{4} + 8 \, x^{2} - 2}{4 \, {\left(x^{8} + 3 \, x^{6} + 2 \, x^{4}\right)}} + \frac{21}{8} \, \log\left(x^{2} + 2\right) - \frac{11}{2} \, \log\left(x^{2} + 1\right) + \frac{23}{8} \, \log\left(x^{2}\right)"," ",0,"1/4*(x^6 + 13*x^4 + 8*x^2 - 2)/(x^8 + 3*x^6 + 2*x^4) + 21/8*log(x^2 + 2) - 11/2*log(x^2 + 1) + 23/8*log(x^2)","A",0
82,1,58,0,1.638589," ","integrate(x^8*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x, algorithm=""maxima"")","\frac{5}{7} \, x^{7} - \frac{27}{5} \, x^{5} + \frac{98}{3} \, x^{3} + 340 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) - 293 \, x - \frac{207 \, x^{3} + 206 \, x}{2 \, {\left(x^{4} + 3 \, x^{2} + 2\right)}} + \frac{9}{2} \, \arctan\left(x\right)"," ",0,"5/7*x^7 - 27/5*x^5 + 98/3*x^3 + 340*sqrt(2)*arctan(1/2*sqrt(2)*x) - 293*x - 1/2*(207*x^3 + 206*x)/(x^4 + 3*x^2 + 2) + 9/2*arctan(x)","A",0
83,1,51,0,1.621392," ","integrate(x^6*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x, algorithm=""maxima"")","x^{5} - 9 \, x^{3} - 118 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) + 98 \, x + \frac{103 \, x^{3} + 102 \, x}{2 \, {\left(x^{4} + 3 \, x^{2} + 2\right)}} - \frac{11}{2} \, \arctan\left(x\right)"," ",0,"x^5 - 9*x^3 - 118*sqrt(2)*arctan(1/2*sqrt(2)*x) + 98*x + 1/2*(103*x^3 + 102*x)/(x^4 + 3*x^2 + 2) - 11/2*arctan(x)","A",0
84,1,48,0,1.635291," ","integrate(x^4*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x, algorithm=""maxima"")","\frac{5}{3} \, x^{3} + 33 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) - 27 \, x - \frac{51 \, x^{3} + 50 \, x}{2 \, {\left(x^{4} + 3 \, x^{2} + 2\right)}} + \frac{13}{2} \, \arctan\left(x\right)"," ",0,"5/3*x^3 + 33*sqrt(2)*arctan(1/2*sqrt(2)*x) - 27*x - 1/2*(51*x^3 + 50*x)/(x^4 + 3*x^2 + 2) + 13/2*arctan(x)","A",0
85,1,43,0,1.633039," ","integrate(x^2*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x, algorithm=""maxima"")","-\frac{7}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) + 5 \, x + \frac{25 \, x^{3} + 24 \, x}{2 \, {\left(x^{4} + 3 \, x^{2} + 2\right)}} - \frac{15}{2} \, \arctan\left(x\right)"," ",0,"-7/2*sqrt(2)*arctan(1/2*sqrt(2)*x) + 5*x + 1/2*(25*x^3 + 24*x)/(x^4 + 3*x^2 + 2) - 15/2*arctan(x)","A",0
86,1,40,0,1.528942," ","integrate((5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x, algorithm=""maxima"")","-\frac{19}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) - \frac{12 \, x^{3} + 11 \, x}{2 \, {\left(x^{4} + 3 \, x^{2} + 2\right)}} + \frac{17}{2} \, \arctan\left(x\right)"," ",0,"-19/4*sqrt(2)*arctan(1/2*sqrt(2)*x) - 1/2*(12*x^3 + 11*x)/(x^4 + 3*x^2 + 2) + 17/2*arctan(x)","A",0
87,1,45,0,1.553733," ","integrate((5*x^6+3*x^4+x^2+4)/x^2/(x^4+3*x^2+2)^2,x, algorithm=""maxima"")","\frac{45}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) + \frac{7 \, x^{4} - 3 \, x^{2} - 8}{4 \, {\left(x^{5} + 3 \, x^{3} + 2 \, x\right)}} - \frac{19}{2} \, \arctan\left(x\right)"," ",0,"45/8*sqrt(2)*arctan(1/2*sqrt(2)*x) + 1/4*(7*x^4 - 3*x^2 - 8)/(x^5 + 3*x^3 + 2*x) - 19/2*arctan(x)","A",0
88,1,52,0,1.597283," ","integrate((5*x^6+3*x^4+x^2+4)/x^4/(x^4+3*x^2+2)^2,x, algorithm=""maxima"")","-\frac{71}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) + \frac{39 \, x^{6} + 175 \, x^{4} + 108 \, x^{2} - 16}{24 \, {\left(x^{7} + 3 \, x^{5} + 2 \, x^{3}\right)}} + \frac{21}{2} \, \arctan\left(x\right)"," ",0,"-71/16*sqrt(2)*arctan(1/2*sqrt(2)*x) + 1/24*(39*x^6 + 175*x^4 + 108*x^2 - 16)/(x^7 + 3*x^5 + 2*x^3) + 21/2*arctan(x)","A",0
89,1,57,0,1.763594," ","integrate((5*x^6+3*x^4+x^2+4)/x^6/(x^4+3*x^2+2)^2,x, algorithm=""maxima"")","\frac{97}{32} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) - \frac{1305 \, x^{8} + 3965 \, x^{6} + 2148 \, x^{4} - 296 \, x^{2} + 96}{240 \, {\left(x^{9} + 3 \, x^{7} + 2 \, x^{5}\right)}} - \frac{23}{2} \, \arctan\left(x\right)"," ",0,"97/32*sqrt(2)*arctan(1/2*sqrt(2)*x) - 1/240*(1305*x^8 + 3965*x^6 + 2148*x^4 - 296*x^2 + 96)/(x^9 + 3*x^7 + 2*x^5) - 23/2*arctan(x)","A",0
90,1,62,0,1.528170," ","integrate((5*x^6+3*x^4+x^2+4)/x^8/(x^4+3*x^2+2)^2,x, algorithm=""maxima"")","-\frac{123}{64} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) + \frac{29085 \, x^{10} + 81865 \, x^{8} + 40068 \, x^{6} - 7816 \, x^{4} + 2256 \, x^{2} - 960}{3360 \, {\left(x^{11} + 3 \, x^{9} + 2 \, x^{7}\right)}} + \frac{25}{2} \, \arctan\left(x\right)"," ",0,"-123/64*sqrt(2)*arctan(1/2*sqrt(2)*x) + 1/3360*(29085*x^10 + 81865*x^8 + 40068*x^6 - 7816*x^4 + 2256*x^2 - 960)/(x^11 + 3*x^9 + 2*x^7) + 25/2*arctan(x)","A",0
91,1,71,0,1.583873," ","integrate(x^10*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^3,x, algorithm=""maxima"")","x^{5} - 14 \, x^{3} - 351 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) + 214 \, x + \frac{1669 \, x^{7} + 5831 \, x^{5} + 6640 \, x^{3} + 2476 \, x}{8 \, {\left(x^{8} + 6 \, x^{6} + 13 \, x^{4} + 12 \, x^{2} + 4\right)}} + \frac{477}{8} \, \arctan\left(x\right)"," ",0,"x^5 - 14*x^3 - 351*sqrt(2)*arctan(1/2*sqrt(2)*x) + 214*x + 1/8*(1669*x^7 + 5831*x^5 + 6640*x^3 + 2476*x)/(x^8 + 6*x^6 + 13*x^4 + 12*x^2 + 4) + 477/8*arctan(x)","A",0
92,1,68,0,1.914323," ","integrate(x^8*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^3,x, algorithm=""maxima"")","\frac{5}{3} \, x^{3} + \frac{219}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) - 42 \, x - \frac{409 \, x^{7} + 1203 \, x^{5} + 1160 \, x^{3} + 364 \, x}{8 \, {\left(x^{8} + 6 \, x^{6} + 13 \, x^{4} + 12 \, x^{2} + 4\right)}} - \frac{449}{8} \, \arctan\left(x\right)"," ",0,"5/3*x^3 + 219/2*sqrt(2)*arctan(1/2*sqrt(2)*x) - 42*x - 1/8*(409*x^7 + 1203*x^5 + 1160*x^3 + 364*x)/(x^8 + 6*x^6 + 13*x^4 + 12*x^2 + 4) - 449/8*arctan(x)","A",0
93,1,63,0,1.849626," ","integrate(x^6*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^3,x, algorithm=""maxima"")","-\frac{191}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) + 5 \, x - \frac{15 \, x^{7} + 289 \, x^{5} + 556 \, x^{3} + 284 \, x}{8 \, {\left(x^{8} + 6 \, x^{6} + 13 \, x^{4} + 12 \, x^{2} + 4\right)}} + \frac{413}{8} \, \arctan\left(x\right)"," ",0,"-191/4*sqrt(2)*arctan(1/2*sqrt(2)*x) + 5*x - 1/8*(15*x^7 + 289*x^5 + 556*x^3 + 284*x)/(x^8 + 6*x^6 + 13*x^4 + 12*x^2 + 4) + 413/8*arctan(x)","A",0
94,1,60,0,1.526612," ","integrate(x^4*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^3,x, algorithm=""maxima"")","\frac{267}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) + \frac{125 \, x^{7} + 629 \, x^{5} + 910 \, x^{3} + 408 \, x}{8 \, {\left(x^{8} + 6 \, x^{6} + 13 \, x^{4} + 12 \, x^{2} + 4\right)}} - \frac{369}{8} \, \arctan\left(x\right)"," ",0,"267/8*sqrt(2)*arctan(1/2*sqrt(2)*x) + 1/8*(125*x^7 + 629*x^5 + 910*x^3 + 408*x)/(x^8 + 6*x^6 + 13*x^4 + 12*x^2 + 4) - 369/8*arctan(x)","A",0
95,1,60,0,1.744174," ","integrate(x^2*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^3,x, algorithm=""maxima"")","-\frac{447}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) - \frac{130 \, x^{7} + 601 \, x^{5} + 843 \, x^{3} + 374 \, x}{8 \, {\left(x^{8} + 6 \, x^{6} + 13 \, x^{4} + 12 \, x^{2} + 4\right)}} + \frac{317}{8} \, \arctan\left(x\right)"," ",0,"-447/16*sqrt(2)*arctan(1/2*sqrt(2)*x) - 1/8*(130*x^7 + 601*x^5 + 843*x^3 + 374*x)/(x^8 + 6*x^6 + 13*x^4 + 12*x^2 + 4) + 317/8*arctan(x)","A",0
96,1,60,0,1.671419," ","integrate((5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^3,x, algorithm=""maxima"")","\frac{731}{32} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) + \frac{217 \, x^{7} + 986 \, x^{5} + 1391 \, x^{3} + 626 \, x}{16 \, {\left(x^{8} + 6 \, x^{6} + 13 \, x^{4} + 12 \, x^{2} + 4\right)}} - \frac{257}{8} \, \arctan\left(x\right)"," ",0,"731/32*sqrt(2)*arctan(1/2*sqrt(2)*x) + 1/16*(217*x^7 + 986*x^5 + 1391*x^3 + 626*x)/(x^8 + 6*x^6 + 13*x^4 + 12*x^2 + 4) - 257/8*arctan(x)","A",0
97,1,65,0,1.797463," ","integrate((5*x^6+3*x^4+x^2+4)/x^2/(x^4+3*x^2+2)^3,x, algorithm=""maxima"")","-\frac{1119}{64} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) - \frac{363 \, x^{8} + 1684 \, x^{6} + 2499 \, x^{4} + 1250 \, x^{2} + 64}{32 \, {\left(x^{9} + 6 \, x^{7} + 13 \, x^{5} + 12 \, x^{3} + 4 \, x\right)}} + \frac{189}{8} \, \arctan\left(x\right)"," ",0,"-1119/64*sqrt(2)*arctan(1/2*sqrt(2)*x) - 1/32*(363*x^8 + 1684*x^6 + 2499*x^4 + 1250*x^2 + 64)/(x^9 + 6*x^7 + 13*x^5 + 12*x^3 + 4*x) + 189/8*arctan(x)","A",0
98,1,72,0,1.526575," ","integrate((5*x^6+3*x^4+x^2+4)/x^4/(x^4+3*x^2+2)^3,x, algorithm=""maxima"")","\frac{1611}{128} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) + \frac{2121 \, x^{10} + 10408 \, x^{8} + 16989 \, x^{6} + 10126 \, x^{4} + 1248 \, x^{2} - 128}{192 \, {\left(x^{11} + 6 \, x^{9} + 13 \, x^{7} + 12 \, x^{5} + 4 \, x^{3}\right)}} - \frac{113}{8} \, \arctan\left(x\right)"," ",0,"1611/128*sqrt(2)*arctan(1/2*sqrt(2)*x) + 1/192*(2121*x^10 + 10408*x^8 + 16989*x^6 + 10126*x^4 + 1248*x^2 - 128)/(x^11 + 6*x^9 + 13*x^7 + 12*x^5 + 4*x^3) - 113/8*arctan(x)","A",0
99,1,77,0,1.736624," ","integrate((5*x^6+3*x^4+x^2+4)/x^6/(x^4+3*x^2+2)^3,x, algorithm=""maxima"")","-\frac{2207}{256} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) - \frac{26145 \, x^{12} + 137120 \, x^{10} + 246477 \, x^{8} + 170702 \, x^{6} + 30816 \, x^{4} - 3136 \, x^{2} + 768}{1920 \, {\left(x^{13} + 6 \, x^{11} + 13 \, x^{9} + 12 \, x^{7} + 4 \, x^{5}\right)}} + \frac{29}{8} \, \arctan\left(x\right)"," ",0,"-2207/256*sqrt(2)*arctan(1/2*sqrt(2)*x) - 1/1920*(26145*x^12 + 137120*x^10 + 246477*x^8 + 170702*x^6 + 30816*x^4 - 3136*x^2 + 768)/(x^13 + 6*x^11 + 13*x^9 + 12*x^7 + 4*x^5) + 29/8*arctan(x)","A",0
100,1,71,0,1.333162," ","integrate(x^9*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x, algorithm=""maxima"")","\frac{5}{8} \, x^{8} - \frac{17}{6} \, x^{6} + \frac{19}{4} \, x^{4} + 19 \, x^{2} + \frac{201}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x^{2} + 1\right)}\right) - \frac{25 \, {\left(7 \, x^{2} + 15\right)}}{8 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}} - \frac{183}{4} \, \log\left(x^{4} + 2 \, x^{2} + 3\right)"," ",0,"5/8*x^8 - 17/6*x^6 + 19/4*x^4 + 19*x^2 + 201/16*sqrt(2)*arctan(1/2*sqrt(2)*(x^2 + 1)) - 25/8*(7*x^2 + 15)/(x^4 + 2*x^2 + 3) - 183/4*log(x^4 + 2*x^2 + 3)","A",0
101,1,66,0,1.824222," ","integrate(x^7*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x, algorithm=""maxima"")","\frac{5}{6} \, x^{6} - \frac{17}{4} \, x^{4} + \frac{19}{2} \, x^{2} - \frac{455}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x^{2} + 1\right)}\right) + \frac{25 \, {\left(5 \, x^{2} + 3\right)}}{8 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}} + \frac{19}{2} \, \log\left(x^{4} + 2 \, x^{2} + 3\right)"," ",0,"5/6*x^6 - 17/4*x^4 + 19/2*x^2 - 455/16*sqrt(2)*arctan(1/2*sqrt(2)*(x^2 + 1)) + 25/8*(5*x^2 + 3)/(x^4 + 2*x^2 + 3) + 19/2*log(x^4 + 2*x^2 + 3)","A",0
102,1,59,0,1.585366," ","integrate(x^5*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x, algorithm=""maxima"")","\frac{5}{4} \, x^{4} - \frac{17}{2} \, x^{2} + \frac{203}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x^{2} + 1\right)}\right) - \frac{25 \, {\left(x^{2} - 3\right)}}{8 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}} + \frac{19}{4} \, \log\left(x^{4} + 2 \, x^{2} + 3\right)"," ",0,"5/4*x^4 - 17/2*x^2 + 203/16*sqrt(2)*arctan(1/2*sqrt(2)*(x^2 + 1)) - 25/8*(x^2 - 3)/(x^4 + 2*x^2 + 3) + 19/4*log(x^4 + 2*x^2 + 3)","A",0
103,1,54,0,1.718163," ","integrate(x^3*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x, algorithm=""maxima"")","\frac{5}{2} \, x^{2} - \frac{17}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x^{2} + 1\right)}\right) - \frac{25 \, {\left(x^{2} + 3\right)}}{8 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}} - \frac{17}{4} \, \log\left(x^{4} + 2 \, x^{2} + 3\right)"," ",0,"5/2*x^2 - 17/16*sqrt(2)*arctan(1/2*sqrt(2)*(x^2 + 1)) - 25/8*(x^2 + 3)/(x^4 + 2*x^2 + 3) - 17/4*log(x^4 + 2*x^2 + 3)","A",0
104,1,49,0,1.406166," ","integrate(x*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x, algorithm=""maxima"")","-\frac{23}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x^{2} + 1\right)}\right) + \frac{25 \, {\left(x^{2} + 1\right)}}{8 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}} + \frac{5}{4} \, \log\left(x^{4} + 2 \, x^{2} + 3\right)"," ",0,"-23/16*sqrt(2)*arctan(1/2*sqrt(2)*(x^2 + 1)) + 25/8*(x^2 + 1)/(x^4 + 2*x^2 + 3) + 5/4*log(x^4 + 2*x^2 + 3)","A",0
105,1,55,0,1.684527," ","integrate((5*x^6+3*x^4+x^2+4)/x/(x^4+2*x^2+3)^2,x, algorithm=""maxima"")","\frac{89}{144} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x^{2} + 1\right)}\right) - \frac{25 \, {\left(x^{2} - 1\right)}}{24 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}} - \frac{1}{9} \, \log\left(x^{4} + 2 \, x^{2} + 3\right) + \frac{2}{9} \, \log\left(x^{2}\right)"," ",0,"89/144*sqrt(2)*arctan(1/2*sqrt(2)*(x^2 + 1)) - 25/24*(x^2 - 1)/(x^4 + 2*x^2 + 3) - 1/9*log(x^4 + 2*x^2 + 3) + 2/9*log(x^2)","A",0
106,1,66,0,1.426656," ","integrate((5*x^6+3*x^4+x^2+4)/x^3/(x^4+2*x^2+3)^2,x, algorithm=""maxima"")","-\frac{71}{432} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x^{2} + 1\right)}\right) - \frac{41 \, x^{4} + 157 \, x^{2} + 48}{72 \, {\left(x^{6} + 2 \, x^{4} + 3 \, x^{2}\right)}} + \frac{13}{108} \, \log\left(x^{4} + 2 \, x^{2} + 3\right) - \frac{13}{54} \, \log\left(x^{2}\right)"," ",0,"-71/432*sqrt(2)*arctan(1/2*sqrt(2)*(x^2 + 1)) - 1/72*(41*x^4 + 157*x^2 + 48)/(x^6 + 2*x^4 + 3*x^2) + 13/108*log(x^4 + 2*x^2 + 3) - 13/54*log(x^2)","A",0
107,1,71,0,2.380535," ","integrate((5*x^6+3*x^4+x^2+4)/x^5/(x^4+2*x^2+3)^2,x, algorithm=""maxima"")","\frac{125}{432} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x^{2} + 1\right)}\right) + \frac{59 \, x^{6} + 85 \, x^{4} + 36 \, x^{2} - 24}{72 \, {\left(x^{8} + 2 \, x^{6} + 3 \, x^{4}\right)}} - \frac{13}{108} \, \log\left(x^{4} + 2 \, x^{2} + 3\right) + \frac{13}{54} \, \log\left(x^{2}\right)"," ",0,"125/432*sqrt(2)*arctan(1/2*sqrt(2)*(x^2 + 1)) + 1/72*(59*x^6 + 85*x^4 + 36*x^2 - 24)/(x^8 + 2*x^6 + 3*x^4) - 13/108*log(x^4 + 2*x^2 + 3) + 13/54*log(x^2)","A",0
108,1,76,0,2.474205," ","integrate((5*x^6+3*x^4+x^2+4)/x^7/(x^4+2*x^2+3)^2,x, algorithm=""maxima"")","-\frac{1237}{3888} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x^{2} + 1\right)}\right) - \frac{331 \, x^{8} + 209 \, x^{6} + 360 \, x^{4} - 138 \, x^{2} + 144}{648 \, {\left(x^{10} + 2 \, x^{8} + 3 \, x^{6}\right)}} - \frac{61}{972} \, \log\left(x^{4} + 2 \, x^{2} + 3\right) + \frac{61}{486} \, \log\left(x^{2}\right)"," ",0,"-1237/3888*sqrt(2)*arctan(1/2*sqrt(2)*(x^2 + 1)) - 1/648*(331*x^8 + 209*x^6 + 360*x^4 - 138*x^2 + 144)/(x^10 + 2*x^8 + 3*x^6) - 61/972*log(x^4 + 2*x^2 + 3) + 61/486*log(x^2)","A",0
109,0,0,0,0.000000," ","integrate(x^8*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x, algorithm=""maxima"")","\frac{5}{7} \, x^{7} - \frac{17}{5} \, x^{5} + \frac{19}{3} \, x^{3} + 38 \, x + \frac{25 \, {\left(5 \, x^{3} + 3 \, x\right)}}{8 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}} - \frac{1}{8} \, \int \frac{1339 \, x^{2} + 987}{x^{4} + 2 \, x^{2} + 3}\,{d x}"," ",0,"5/7*x^7 - 17/5*x^5 + 19/3*x^3 + 38*x + 25/8*(5*x^3 + 3*x)/(x^4 + 2*x^2 + 3) - 1/8*integrate((1339*x^2 + 987)/(x^4 + 2*x^2 + 3), x)","F",0
110,0,0,0,0.000000," ","integrate(x^6*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x, algorithm=""maxima"")","x^{5} - \frac{17}{3} \, x^{3} + 19 \, x - \frac{25 \, {\left(x^{3} - 3 \, x\right)}}{8 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}} + \frac{9}{8} \, \int \frac{31 \, x^{2} - 59}{x^{4} + 2 \, x^{2} + 3}\,{d x}"," ",0,"x^5 - 17/3*x^3 + 19*x - 25/8*(x^3 - 3*x)/(x^4 + 2*x^2 + 3) + 9/8*integrate((31*x^2 - 59)/(x^4 + 2*x^2 + 3), x)","F",0
111,0,0,0,0.000000," ","integrate(x^4*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x, algorithm=""maxima"")","\frac{5}{3} \, x^{3} - 17 \, x - \frac{25 \, {\left(x^{3} + 3 \, x\right)}}{8 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}} + \frac{1}{8} \, \int \frac{127 \, x^{2} + 483}{x^{4} + 2 \, x^{2} + 3}\,{d x}"," ",0,"5/3*x^3 - 17*x - 25/8*(x^3 + 3*x)/(x^4 + 2*x^2 + 3) + 1/8*integrate((127*x^2 + 483)/(x^4 + 2*x^2 + 3), x)","F",0
112,0,0,0,0.000000," ","integrate(x^2*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x, algorithm=""maxima"")","5 \, x + \frac{25 \, {\left(x^{3} + x\right)}}{8 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}} - \frac{1}{8} \, \int \frac{111 \, x^{2} + 145}{x^{4} + 2 \, x^{2} + 3}\,{d x}"," ",0,"5*x + 25/8*(x^3 + x)/(x^4 + 2*x^2 + 3) - 1/8*integrate((111*x^2 + 145)/(x^4 + 2*x^2 + 3), x)","F",0
113,0,0,0,0.000000," ","integrate((5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x, algorithm=""maxima"")","-\frac{25 \, {\left(x^{3} - x\right)}}{24 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}} + \frac{1}{24} \, \int \frac{95 \, x^{2} + 7}{x^{4} + 2 \, x^{2} + 3}\,{d x}"," ",0,"-25/24*(x^3 - x)/(x^4 + 2*x^2 + 3) + 1/24*integrate((95*x^2 + 7)/(x^4 + 2*x^2 + 3), x)","F",0
114,0,0,0,0.000000," ","integrate((5*x^6+3*x^4+x^2+4)/x^2/(x^4+2*x^2+3)^2,x, algorithm=""maxima"")","-\frac{19 \, x^{4} + 63 \, x^{2} + 32}{24 \, {\left(x^{5} + 2 \, x^{3} + 3 \, x\right)}} - \frac{1}{24} \, \int \frac{19 \, x^{2} - 7}{x^{4} + 2 \, x^{2} + 3}\,{d x}"," ",0,"-1/24*(19*x^4 + 63*x^2 + 32)/(x^5 + 2*x^3 + 3*x) - 1/24*integrate((19*x^2 - 7)/(x^4 + 2*x^2 + 3), x)","F",0
115,0,0,0,0.000000," ","integrate((5*x^6+3*x^4+x^2+4)/x^4/(x^4+2*x^2+3)^2,x, algorithm=""maxima"")","\frac{229 \, x^{6} + 351 \, x^{4} + 248 \, x^{2} - 96}{216 \, {\left(x^{7} + 2 \, x^{5} + 3 \, x^{3}\right)}} + \frac{1}{216} \, \int \frac{229 \, x^{2} + 137}{x^{4} + 2 \, x^{2} + 3}\,{d x}"," ",0,"1/216*(229*x^6 + 351*x^4 + 248*x^2 - 96)/(x^7 + 2*x^5 + 3*x^3) + 1/216*integrate((229*x^2 + 137)/(x^4 + 2*x^2 + 3), x)","F",0
116,0,0,0,0.000000," ","integrate((5*x^6+3*x^4+x^2+4)/x^6/(x^4+2*x^2+3)^2,x, algorithm=""maxima"")","-\frac{2435 \, x^{8} + 2475 \, x^{6} + 3928 \, x^{4} - 984 \, x^{2} + 864}{3240 \, {\left(x^{9} + 2 \, x^{7} + 3 \, x^{5}\right)}} - \frac{1}{648} \, \int \frac{487 \, x^{2} - 463}{x^{4} + 2 \, x^{2} + 3}\,{d x}"," ",0,"-1/3240*(2435*x^8 + 2475*x^6 + 3928*x^4 - 984*x^2 + 864)/(x^9 + 2*x^7 + 3*x^5) - 1/648*integrate((487*x^2 - 463)/(x^4 + 2*x^2 + 3), x)","F",0
117,0,0,0,0.000000," ","integrate(x^10*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^3,x, algorithm=""maxima"")","x^{5} - 9 \, x^{3} + 58 \, x + \frac{252 \, x^{7} + 3809 \, x^{5} + 6666 \, x^{3} + 8415 \, x}{64 \, {\left(x^{8} + 4 \, x^{6} + 10 \, x^{4} + 12 \, x^{2} + 9\right)}} + \frac{3}{64} \, \int \frac{148 \, x^{2} - 4647}{x^{4} + 2 \, x^{2} + 3}\,{d x}"," ",0,"x^5 - 9*x^3 + 58*x + 1/64*(252*x^7 + 3809*x^5 + 6666*x^3 + 8415*x)/(x^8 + 4*x^6 + 10*x^4 + 12*x^2 + 9) + 3/64*integrate((148*x^2 - 4647)/(x^4 + 2*x^2 + 3), x)","F",0
118,0,0,0,0.000000," ","integrate(x^8*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^3,x, algorithm=""maxima"")","\frac{5}{3} \, x^{3} - 27 \, x - \frac{835 \, x^{7} + 3138 \, x^{5} + 4941 \, x^{3} + 4104 \, x}{64 \, {\left(x^{8} + 4 \, x^{6} + 10 \, x^{4} + 12 \, x^{2} + 9\right)}} + \frac{21}{64} \, \int \frac{137 \, x^{2} + 312}{x^{4} + 2 \, x^{2} + 3}\,{d x}"," ",0,"5/3*x^3 - 27*x - 1/64*(835*x^7 + 3138*x^5 + 4941*x^3 + 4104*x)/(x^8 + 4*x^6 + 10*x^4 + 12*x^2 + 9) + 21/64*integrate((137*x^2 + 312)/(x^4 + 2*x^2 + 3), x)","F",0
119,0,0,0,0.000000," ","integrate(x^6*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^3,x, algorithm=""maxima"")","5 \, x + \frac{406 \, x^{7} + 889 \, x^{5} + 1272 \, x^{3} + 531 \, x}{64 \, {\left(x^{8} + 4 \, x^{6} + 10 \, x^{4} + 12 \, x^{2} + 9\right)}} - \frac{1}{64} \, \int \frac{1322 \, x^{2} + 1137}{x^{4} + 2 \, x^{2} + 3}\,{d x}"," ",0,"5*x + 1/64*(406*x^7 + 889*x^5 + 1272*x^3 + 531*x)/(x^8 + 4*x^6 + 10*x^4 + 12*x^2 + 9) - 1/64*integrate((1322*x^2 + 1137)/(x^4 + 2*x^2 + 3), x)","F",0
120,0,0,0,0.000000," ","integrate(x^4*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^3,x, algorithm=""maxima"")","-\frac{59 \, x^{7} - 120 \, x^{5} - 199 \, x^{3} - 414 \, x}{64 \, {\left(x^{8} + 4 \, x^{6} + 10 \, x^{4} + 12 \, x^{2} + 9\right)}} + \frac{3}{64} \, \int \frac{87 \, x^{2} - 46}{x^{4} + 2 \, x^{2} + 3}\,{d x}"," ",0,"-1/64*(59*x^7 - 120*x^5 - 199*x^3 - 414*x)/(x^8 + 4*x^6 + 10*x^4 + 12*x^2 + 9) + 3/64*integrate((87*x^2 - 46)/(x^4 + 2*x^2 + 3), x)","F",0
121,0,0,0,0.000000," ","integrate(x^2*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^3,x, algorithm=""maxima"")","-\frac{88 \, x^{7} + 529 \, x^{5} + 670 \, x^{3} + 759 \, x}{192 \, {\left(x^{8} + 4 \, x^{6} + 10 \, x^{4} + 12 \, x^{2} + 9\right)}} - \frac{11}{192} \, \int \frac{8 \, x^{2} - 23}{x^{4} + 2 \, x^{2} + 3}\,{d x}"," ",0,"-1/192*(88*x^7 + 529*x^5 + 670*x^3 + 759*x)/(x^8 + 4*x^6 + 10*x^4 + 12*x^2 + 9) - 11/192*integrate((8*x^2 - 23)/(x^4 + 2*x^2 + 3), x)","F",0
122,0,0,0,0.000000," ","integrate((5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^3,x, algorithm=""maxima"")","\frac{51 \, x^{7} + 166 \, x^{5} + 181 \, x^{3} + 292 \, x}{192 \, {\left(x^{8} + 4 \, x^{6} + 10 \, x^{4} + 12 \, x^{2} + 9\right)}} + \frac{1}{64} \, \int \frac{17 \, x^{2} - 4}{x^{4} + 2 \, x^{2} + 3}\,{d x}"," ",0,"1/192*(51*x^7 + 166*x^5 + 181*x^3 + 292*x)/(x^8 + 4*x^6 + 10*x^4 + 12*x^2 + 9) + 1/64*integrate((17*x^2 - 4)/(x^4 + 2*x^2 + 3), x)","F",0
123,0,0,0,0.000000," ","integrate((5*x^6+3*x^4+x^2+4)/x^2/(x^4+2*x^2+3)^3,x, algorithm=""maxima"")","-\frac{166 \, x^{8} + 611 \, x^{6} + 1412 \, x^{4} + 1849 \, x^{2} + 768}{576 \, {\left(x^{9} + 4 \, x^{7} + 10 \, x^{5} + 12 \, x^{3} + 9 \, x\right)}} - \frac{1}{576} \, \int \frac{166 \, x^{2} + 173}{x^{4} + 2 \, x^{2} + 3}\,{d x}"," ",0,"-1/576*(166*x^8 + 611*x^6 + 1412*x^4 + 1849*x^2 + 768)/(x^9 + 4*x^7 + 10*x^5 + 12*x^3 + 9*x) - 1/576*integrate((166*x^2 + 173)/(x^4 + 2*x^2 + 3), x)","F",0
124,0,0,0,0.000000," ","integrate((5*x^6+3*x^4+x^2+4)/x^4/(x^4+2*x^2+3)^3,x, algorithm=""maxima"")","\frac{2369 \, x^{10} + 8644 \, x^{8} + 19939 \, x^{6} + 20090 \, x^{4} + 9024 \, x^{2} - 2304}{5184 \, {\left(x^{11} + 4 \, x^{9} + 10 \, x^{7} + 12 \, x^{5} + 9 \, x^{3}\right)}} + \frac{1}{5184} \, \int \frac{2369 \, x^{2} + 2242}{x^{4} + 2 \, x^{2} + 3}\,{d x}"," ",0,"1/5184*(2369*x^10 + 8644*x^8 + 19939*x^6 + 20090*x^4 + 9024*x^2 - 2304)/(x^11 + 4*x^9 + 10*x^7 + 12*x^5 + 9*x^3) + 1/5184*integrate((2369*x^2 + 2242)/(x^4 + 2*x^2 + 3), x)","F",0
125,-2,0,0,0.000000," ","integrate(x*(g*x^6+f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
126,0,0,0,0.000000," ","integrate(x^4*(g*x^6+f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(b c^{3} d - {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} e + {\left(b^{3} c - 3 \, a b c^{2}\right)} f - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} g\right)} x^{3} + {\left(2 \, a c^{3} d - a b c^{2} e + {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} f - {\left(a b^{3} - 3 \, a^{2} b c\right)} g\right)} x}{2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{4} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x^{2}\right)}} + \frac{-\int \frac{2 \, a c^{3} d - a b c^{2} e - {\left(b c^{3} d + {\left(b^{2} c^{2} - 6 \, a c^{3}\right)} e - {\left(3 \, b^{3} c - 13 \, a b c^{2}\right)} f + {\left(5 \, b^{4} - 24 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} g\right)} x^{2} + {\left(3 \, a b^{2} c - 10 \, a^{2} c^{2}\right)} f - {\left(5 \, a b^{3} - 19 \, a^{2} b c\right)} g}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}} + \frac{c g x^{3} + 3 \, {\left(c f - 2 \, b g\right)} x}{3 \, c^{3}}"," ",0,"1/2*((b*c^3*d - (b^2*c^2 - 2*a*c^3)*e + (b^3*c - 3*a*b*c^2)*f - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*g)*x^3 + (2*a*c^3*d - a*b*c^2*e + (a*b^2*c - 2*a^2*c^2)*f - (a*b^3 - 3*a^2*b*c)*g)*x)/(a*b^2*c^3 - 4*a^2*c^4 + (b^2*c^4 - 4*a*c^5)*x^4 + (b^3*c^3 - 4*a*b*c^4)*x^2) + 1/2*integrate(-(2*a*c^3*d - a*b*c^2*e - (b*c^3*d + (b^2*c^2 - 6*a*c^3)*e - (3*b^3*c - 13*a*b*c^2)*f + (5*b^4 - 24*a*b^2*c + 14*a^2*c^2)*g)*x^2 + (3*a*b^2*c - 10*a^2*c^2)*f - (5*a*b^3 - 19*a^2*b*c)*g)/(c*x^4 + b*x^2 + a), x)/(b^2*c^3 - 4*a*c^4) + 1/3*(c*g*x^3 + 3*(c*f - 2*b*g)*x)/c^3","F",0
127,0,0,0,0.000000," ","integrate(x^2*(g*x^6+f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(2 \, c^{3} d - b c^{2} e + {\left(b^{2} c - 2 \, a c^{2}\right)} f - {\left(b^{3} - 3 \, a b c\right)} g\right)} x^{3} + {\left(b c^{2} d - 2 \, a c^{2} e + a b c f - {\left(a b^{2} - 2 \, a^{2} c\right)} g\right)} x}{2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{4} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2}\right)}} + \frac{g x}{c^{2}} + \frac{\frac{{\left({\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 2 \, b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 16 \, a b^{3} c^{4} + 2 \, b^{4} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 32 \, a^{2} b c^{5} - 32 \, a^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{5}\right)} d + {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 2 \, a b^{5} c^{2} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 16 \, a^{2} b^{3} c^{3} - 2 \, a b^{4} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 32 \, a^{3} b c^{4} + 32 \, a^{2} b^{2} c^{4} - 96 \, a^{3} c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a 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^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 24 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} f - {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 34 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 6 \, a b^{6} c + 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 44 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 68 \, a^{2} b^{4} c^{2} - 6 \, a b^{5} c^{2} - 160 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 80 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 22 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 256 \, a^{3} b^{2} c^{3} + 56 \, a^{2} b^{3} c^{3} + 40 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 320 \, a^{4} c^{4} - 128 \, a^{3} b c^{4} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 28 \, \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 + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a 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} b c^{3} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c - 44 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3} - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} g - 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 \, a b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 32 \, a^{3} c^{5} - 16 \, a^{2} b c^{5} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{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^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{4} + 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} - 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} e\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^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 2 \, b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} - 16 \, a b^{3} c^{4} - 2 \, b^{4} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{5} + 32 \, a^{2} b c^{5} + 32 \, a^{2} c^{6} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{5}\right)} d + {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, a b^{5} c^{2} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 16 \, a^{2} b^{3} c^{3} + 2 \, a b^{4} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 32 \, a^{3} b c^{4} - 32 \, a^{2} b^{2} c^{4} + 96 \, a^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a 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^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 24 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} f - {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 34 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 6 \, a b^{6} c + 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 44 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 68 \, a^{2} b^{4} c^{2} + 6 \, a b^{5} c^{2} - 160 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 80 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 22 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 256 \, a^{3} b^{2} c^{3} - 56 \, a^{2} b^{3} c^{3} + 40 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 320 \, a^{4} c^{4} + 128 \, a^{3} b c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} + 28 \, \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 - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a 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} b c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c + 44 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} g - 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 \, a b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 32 \, a^{3} c^{5} + 16 \, a^{2} b c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{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^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{4} - 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} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} e\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(b^{2} c^{2} - 4 \, a c^{3}\right)}}"," ",0,"-1/2*((2*c^3*d - b*c^2*e + (b^2*c - 2*a*c^2)*f - (b^3 - 3*a*b*c)*g)*x^3 + (b*c^2*d - 2*a*c^2*e + a*b*c*f - (a*b^2 - 2*a^2*c)*g)*x)/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^4 + (b^3*c^2 - 4*a*b*c^3)*x^2) + g*x/c^2 + 1/2*integrate((b*c^2*d - 2*a*c^2*e + a*b*c*f - (2*c^3*d - b*c^2*e - (b^2*c - 6*a*c^2)*f + (3*b^3 - 13*a*b*c)*g)*x^2 - (3*a*b^2 - 10*a^2*c)*g)/(c*x^4 + b*x^2 + a), x)/(b^2*c^2 - 4*a*c^3)","F",0
128,0,0,0,0.000000," ","integrate((g*x^6+f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(b c^{2} d - 2 \, a c^{2} e + a b c f - {\left(a b^{2} - 2 \, a^{2} c\right)} g\right)} x^{3} - {\left(a b c e - 2 \, a^{2} c f + a^{2} b g - {\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{-\int \frac{a b c e - 2 \, a^{2} c f + a^{2} b g + {\left(b c^{2} d - 2 \, a c^{2} e + a b c f + {\left(a b^{2} - 6 \, a^{2} c\right)} g\right)} x^{2} + {\left(b^{2} c - 6 \, a c^{2}\right)} d}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}}"," ",0,"1/2*((b*c^2*d - 2*a*c^2*e + a*b*c*f - (a*b^2 - 2*a^2*c)*g)*x^3 - (a*b*c*e - 2*a^2*c*f + a^2*b*g - (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*c*e - 2*a^2*c*f + a^2*b*g + (b*c^2*d - 2*a*c^2*e + a*b*c*f + (a*b^2 - 6*a^2*c)*g)*x^2 + (b^2*c - 6*a*c^2)*d)/(c*x^4 + b*x^2 + a), x)/(a*b^2*c - 4*a^2*c^2)","F",0
129,0,0,0,0.000000," ","integrate((g*x^6+f*x^4+e*x^2+d)/x^2/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(a b c e - 2 \, a^{2} c f + a^{2} b g - {\left(3 \, b^{2} c - 10 \, a c^{2}\right)} d\right)} x^{4} - {\left(a^{2} b f - 2 \, a^{3} g + {\left(3 \, b^{3} - 11 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e\right)} x^{2} - 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d}{2 \, {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)}} + \frac{-\frac{{\left({\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} - 37 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 6 \, b^{7} c + 152 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 50 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 74 \, a b^{5} c^{2} + 6 \, b^{6} c^{2} - 208 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 104 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 25 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 304 \, a^{2} b^{3} c^{3} - 62 \, a b^{4} c^{3} + 52 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 416 \, a^{3} b c^{4} + 192 \, a^{2} b^{2} c^{4} - 160 \, a^{3} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} + 31 \, \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 - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 38 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 19 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 6 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c - 50 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 104 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} + 38 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 40 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} d - {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, a^{2} b^{5} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{2} + 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} + 16 \, a^{3} b^{3} c^{2} + 2 \, a^{2} b^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, a^{4} b c^{3} - 32 \, a^{4} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3}\right)} f + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} - 8 \, \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^{3} b^{3} c - 2 \, a^{3} b^{4} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 16 \, a^{4} b^{2} c^{2} + 4 \, a^{3} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 32 \, a^{5} c^{3} - 16 \, a^{4} b c^{3} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c + 4 \, \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^{3} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{2} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2}\right)} g - {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 14 \, \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 \, a b^{6} c + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 20 \, \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} + 28 \, a^{2} b^{4} c^{2} + 2 \, a b^{5} c^{2} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 128 \, a^{3} b^{2} c^{3} - 24 \, a^{2} b^{3} c^{3} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 192 \, a^{4} c^{4} + 64 \, a^{3} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} + 12 \, \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 - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 16 \, \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 b^{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^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c - 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3} + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} e\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(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} - 37 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 6 \, b^{7} c + 152 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 50 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 74 \, a b^{5} c^{2} - 6 \, b^{6} c^{2} - 208 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 104 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 25 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 304 \, a^{2} b^{3} c^{3} + 62 \, a b^{4} c^{3} + 52 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 416 \, a^{3} b c^{4} - 192 \, a^{2} b^{2} c^{4} + 160 \, a^{3} c^{5} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} - 31 \, \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 + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 38 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 19 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c + 50 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 6 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} - 104 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} - 38 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 40 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} d - {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c + 2 \, a^{2} b^{5} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{2} + 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} - 16 \, a^{3} b^{3} c^{2} - 2 \, a^{2} b^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 32 \, a^{4} b c^{3} + 32 \, a^{4} c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3}\right)} f + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} - 8 \, \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^{3} b^{3} c + 2 \, a^{3} b^{4} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} - 16 \, a^{4} b^{2} c^{2} - 4 \, a^{3} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} + 32 \, a^{5} c^{3} + 16 \, a^{4} b c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c - 4 \, \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^{3} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2}\right)} g - {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 14 \, \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 \, a b^{6} c + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 20 \, \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} - 28 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 128 \, a^{3} b^{2} c^{3} + 24 \, a^{2} b^{3} c^{3} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 192 \, a^{4} c^{4} - 64 \, a^{3} b c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 12 \, \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 + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 16 \, \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 b^{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^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3} - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} e\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^{2} b^{2} - 4 \, a^{3} c\right)}}"," ",0,"1/2*((a*b*c*e - 2*a^2*c*f + a^2*b*g - (3*b^2*c - 10*a*c^2)*d)*x^4 - (a^2*b*f - 2*a^3*g + (3*b^3 - 11*a*b*c)*d - (a*b^2 - 2*a^2*c)*e)*x^2 - 2*(a*b^2 - 4*a^2*c)*d)/((a^2*b^2*c - 4*a^3*c^2)*x^5 + (a^2*b^3 - 4*a^3*b*c)*x^3 + (a^3*b^2 - 4*a^4*c)*x) + 1/2*integrate((a^2*b*f - 2*a^3*g + (a*b*c*e - 2*a^2*c*f + a^2*b*g - (3*b^2*c - 10*a*c^2)*d)*x^2 - (3*b^3 - 13*a*b*c)*d + (a*b^2 - 6*a^2*c)*e)/(c*x^4 + b*x^2 + a), x)/(a^2*b^2 - 4*a^3*c)","F",0
130,0,0,0,0.000000," ","integrate((g*x^6+f*x^4+e*x^2+d)/x^4/(c*x^4+b*x^2+a)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(a^{2} b c f - 2 \, a^{3} c g + {\left(5 \, b^{3} c - 19 \, a b c^{2}\right)} d - {\left(3 \, a b^{2} c - 10 \, a^{2} c^{2}\right)} e\right)} x^{6} - {\left(3 \, a^{3} b g - {\left(15 \, b^{4} - 62 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} d + 3 \, {\left(3 \, a b^{3} - 11 \, a^{2} b c\right)} e - 3 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} f\right)} x^{4} + 2 \, {\left(5 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d - 3 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e\right)} x^{2} - 2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d}{6 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}\right)}} - \frac{-\int \frac{a^{3} b g + {\left(a^{2} b c f - 2 \, a^{3} c g + {\left(5 \, b^{3} c - 19 \, a b c^{2}\right)} d - {\left(3 \, a b^{2} c - 10 \, a^{2} c^{2}\right)} e\right)} x^{2} + {\left(5 \, b^{4} - 24 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} d - {\left(3 \, a b^{3} - 13 \, a^{2} b c\right)} e + {\left(a^{2} b^{2} - 6 \, a^{3} c\right)} f}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}}"," ",0,"1/6*(3*(a^2*b*c*f - 2*a^3*c*g + (5*b^3*c - 19*a*b*c^2)*d - (3*a*b^2*c - 10*a^2*c^2)*e)*x^6 - (3*a^3*b*g - (15*b^4 - 62*a*b^2*c + 14*a^2*c^2)*d + 3*(3*a*b^3 - 11*a^2*b*c)*e - 3*(a^2*b^2 - 2*a^3*c)*f)*x^4 + 2*(5*(a*b^3 - 4*a^2*b*c)*d - 3*(a^2*b^2 - 4*a^3*c)*e)*x^2 - 2*(a^2*b^2 - 4*a^3*c)*d)/((a^3*b^2*c - 4*a^4*c^2)*x^7 + (a^3*b^3 - 4*a^4*b*c)*x^5 + (a^4*b^2 - 4*a^5*c)*x^3) - 1/2*integrate(-(a^3*b*g + (a^2*b*c*f - 2*a^3*c*g + (5*b^3*c - 19*a*b*c^2)*d - (3*a*b^2*c - 10*a^2*c^2)*e)*x^2 + (5*b^4 - 24*a*b^2*c + 14*a^2*c^2)*d - (3*a*b^3 - 13*a^2*b*c)*e + (a^2*b^2 - 6*a^3*c)*f)/(c*x^4 + b*x^2 + a), x)/(a^3*b^2 - 4*a^4*c)","F",0
131,1,31,0,1.027867," ","integrate(x^2*(c*x^4+b*x^2+a)^p*(3*a+b*(5+2*p)*x^2+c*(7+4*p)*x^4),x, algorithm=""maxima"")","{\left(c x^{7} + b x^{5} + a x^{3}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{p}"," ",0,"(c*x^7 + b*x^5 + a*x^3)*(c*x^4 + b*x^2 + a)^p","A",0
132,1,295,0,1.025525," ","integrate(x^5*(c*x^4+b*x^2+a)/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-e^{2} x^{2} + d^{2}} c x^{8}}{9 \, e^{2}} - \frac{8 \, \sqrt{-e^{2} x^{2} + d^{2}} c d^{2} x^{6}}{63 \, e^{4}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} b x^{6}}{7 \, e^{2}} - \frac{16 \, \sqrt{-e^{2} x^{2} + d^{2}} c d^{4} x^{4}}{105 \, e^{6}} - \frac{6 \, \sqrt{-e^{2} x^{2} + d^{2}} b d^{2} x^{4}}{35 \, e^{4}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} a x^{4}}{5 \, e^{2}} - \frac{64 \, \sqrt{-e^{2} x^{2} + d^{2}} c d^{6} x^{2}}{315 \, e^{8}} - \frac{8 \, \sqrt{-e^{2} x^{2} + d^{2}} b d^{4} x^{2}}{35 \, e^{6}} - \frac{4 \, \sqrt{-e^{2} x^{2} + d^{2}} a d^{2} x^{2}}{15 \, e^{4}} - \frac{128 \, \sqrt{-e^{2} x^{2} + d^{2}} c d^{8}}{315 \, e^{10}} - \frac{16 \, \sqrt{-e^{2} x^{2} + d^{2}} b d^{6}}{35 \, e^{8}} - \frac{8 \, \sqrt{-e^{2} x^{2} + d^{2}} a d^{4}}{15 \, e^{6}}"," ",0,"-1/9*sqrt(-e^2*x^2 + d^2)*c*x^8/e^2 - 8/63*sqrt(-e^2*x^2 + d^2)*c*d^2*x^6/e^4 - 1/7*sqrt(-e^2*x^2 + d^2)*b*x^6/e^2 - 16/105*sqrt(-e^2*x^2 + d^2)*c*d^4*x^4/e^6 - 6/35*sqrt(-e^2*x^2 + d^2)*b*d^2*x^4/e^4 - 1/5*sqrt(-e^2*x^2 + d^2)*a*x^4/e^2 - 64/315*sqrt(-e^2*x^2 + d^2)*c*d^6*x^2/e^8 - 8/35*sqrt(-e^2*x^2 + d^2)*b*d^4*x^2/e^6 - 4/15*sqrt(-e^2*x^2 + d^2)*a*d^2*x^2/e^4 - 128/315*sqrt(-e^2*x^2 + d^2)*c*d^8/e^10 - 16/35*sqrt(-e^2*x^2 + d^2)*b*d^6/e^8 - 8/15*sqrt(-e^2*x^2 + d^2)*a*d^4/e^6","A",0
133,1,217,0,1.061955," ","integrate(x^3*(c*x^4+b*x^2+a)/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-e^{2} x^{2} + d^{2}} c x^{6}}{7 \, e^{2}} - \frac{6 \, \sqrt{-e^{2} x^{2} + d^{2}} c d^{2} x^{4}}{35 \, e^{4}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} b x^{4}}{5 \, e^{2}} - \frac{8 \, \sqrt{-e^{2} x^{2} + d^{2}} c d^{4} x^{2}}{35 \, e^{6}} - \frac{4 \, \sqrt{-e^{2} x^{2} + d^{2}} b d^{2} x^{2}}{15 \, e^{4}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} a x^{2}}{3 \, e^{2}} - \frac{16 \, \sqrt{-e^{2} x^{2} + d^{2}} c d^{6}}{35 \, e^{8}} - \frac{8 \, \sqrt{-e^{2} x^{2} + d^{2}} b d^{4}}{15 \, e^{6}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} a d^{2}}{3 \, e^{4}}"," ",0,"-1/7*sqrt(-e^2*x^2 + d^2)*c*x^6/e^2 - 6/35*sqrt(-e^2*x^2 + d^2)*c*d^2*x^4/e^4 - 1/5*sqrt(-e^2*x^2 + d^2)*b*x^4/e^2 - 8/35*sqrt(-e^2*x^2 + d^2)*c*d^4*x^2/e^6 - 4/15*sqrt(-e^2*x^2 + d^2)*b*d^2*x^2/e^4 - 1/3*sqrt(-e^2*x^2 + d^2)*a*x^2/e^2 - 16/35*sqrt(-e^2*x^2 + d^2)*c*d^6/e^8 - 8/15*sqrt(-e^2*x^2 + d^2)*b*d^4/e^6 - 2/3*sqrt(-e^2*x^2 + d^2)*a*d^2/e^4","A",0
134,1,139,0,1.032236," ","integrate(x*(c*x^4+b*x^2+a)/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-e^{2} x^{2} + d^{2}} c x^{4}}{5 \, e^{2}} - \frac{4 \, \sqrt{-e^{2} x^{2} + d^{2}} c d^{2} x^{2}}{15 \, e^{4}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} b x^{2}}{3 \, e^{2}} - \frac{8 \, \sqrt{-e^{2} x^{2} + d^{2}} c d^{4}}{15 \, e^{6}} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} b d^{2}}{3 \, e^{4}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} a}{e^{2}}"," ",0,"-1/5*sqrt(-e^2*x^2 + d^2)*c*x^4/e^2 - 4/15*sqrt(-e^2*x^2 + d^2)*c*d^2*x^2/e^4 - 1/3*sqrt(-e^2*x^2 + d^2)*b*x^2/e^2 - 8/15*sqrt(-e^2*x^2 + d^2)*c*d^4/e^6 - 2/3*sqrt(-e^2*x^2 + d^2)*b*d^2/e^4 - sqrt(-e^2*x^2 + d^2)*a/e^2","A",0
135,1,105,0,1.004480," ","integrate((c*x^4+b*x^2+a)/x/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-e^{2} x^{2} + d^{2}} c x^{2}}{3 \, e^{2}} - \frac{a \log\left(\frac{2 \, d^{2}}{{\left| x \right|}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} d}{{\left| x \right|}}\right)}{d} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} c d^{2}}{3 \, e^{4}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} b}{e^{2}}"," ",0,"-1/3*sqrt(-e^2*x^2 + d^2)*c*x^2/e^2 - a*log(2*d^2/abs(x) + 2*sqrt(-e^2*x^2 + d^2)*d/abs(x))/d - 2/3*sqrt(-e^2*x^2 + d^2)*c*d^2/e^4 - sqrt(-e^2*x^2 + d^2)*b/e^2","A",0
136,1,123,0,1.016989," ","integrate((c*x^4+b*x^2+a)/x^3/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""maxima"")","-\frac{b \log\left(\frac{2 \, d^{2}}{{\left| x \right|}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} d}{{\left| x \right|}}\right)}{d} - \frac{a e^{2} \log\left(\frac{2 \, d^{2}}{{\left| x \right|}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} d}{{\left| x \right|}}\right)}{2 \, d^{3}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} c}{e^{2}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} a}{2 \, d^{2} x^{2}}"," ",0,"-b*log(2*d^2/abs(x) + 2*sqrt(-e^2*x^2 + d^2)*d/abs(x))/d - 1/2*a*e^2*log(2*d^2/abs(x) + 2*sqrt(-e^2*x^2 + d^2)*d/abs(x))/d^3 - sqrt(-e^2*x^2 + d^2)*c/e^2 - 1/2*sqrt(-e^2*x^2 + d^2)*a/(d^2*x^2)","A",0
137,1,193,0,1.033677," ","integrate((c*x^4+b*x^2+a)/x^5/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""maxima"")","-\frac{c \log\left(\frac{2 \, d^{2}}{{\left| x \right|}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} d}{{\left| x \right|}}\right)}{d} - \frac{b e^{2} \log\left(\frac{2 \, d^{2}}{{\left| x \right|}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} d}{{\left| x \right|}}\right)}{2 \, d^{3}} - \frac{3 \, a e^{4} \log\left(\frac{2 \, d^{2}}{{\left| x \right|}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} d}{{\left| x \right|}}\right)}{8 \, d^{5}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} b}{2 \, d^{2} x^{2}} - \frac{3 \, \sqrt{-e^{2} x^{2} + d^{2}} a e^{2}}{8 \, d^{4} x^{2}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} a}{4 \, d^{2} x^{4}}"," ",0,"-c*log(2*d^2/abs(x) + 2*sqrt(-e^2*x^2 + d^2)*d/abs(x))/d - 1/2*b*e^2*log(2*d^2/abs(x) + 2*sqrt(-e^2*x^2 + d^2)*d/abs(x))/d^3 - 3/8*a*e^4*log(2*d^2/abs(x) + 2*sqrt(-e^2*x^2 + d^2)*d/abs(x))/d^5 - 1/2*sqrt(-e^2*x^2 + d^2)*b/(d^2*x^2) - 3/8*sqrt(-e^2*x^2 + d^2)*a*e^2/(d^4*x^2) - 1/4*sqrt(-e^2*x^2 + d^2)*a/(d^2*x^4)","A",0
138,1,271,0,1.033104," ","integrate((c*x^4+b*x^2+a)/x^7/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""maxima"")","-\frac{c e^{2} \log\left(\frac{2 \, d^{2}}{{\left| x \right|}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} d}{{\left| x \right|}}\right)}{2 \, d^{3}} - \frac{3 \, b e^{4} \log\left(\frac{2 \, d^{2}}{{\left| x \right|}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} d}{{\left| x \right|}}\right)}{8 \, d^{5}} - \frac{5 \, a e^{6} \log\left(\frac{2 \, d^{2}}{{\left| x \right|}} + \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} d}{{\left| x \right|}}\right)}{16 \, d^{7}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} c}{2 \, d^{2} x^{2}} - \frac{3 \, \sqrt{-e^{2} x^{2} + d^{2}} b e^{2}}{8 \, d^{4} x^{2}} - \frac{5 \, \sqrt{-e^{2} x^{2} + d^{2}} a e^{4}}{16 \, d^{6} x^{2}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} b}{4 \, d^{2} x^{4}} - \frac{5 \, \sqrt{-e^{2} x^{2} + d^{2}} a e^{2}}{24 \, d^{4} x^{4}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} a}{6 \, d^{2} x^{6}}"," ",0,"-1/2*c*e^2*log(2*d^2/abs(x) + 2*sqrt(-e^2*x^2 + d^2)*d/abs(x))/d^3 - 3/8*b*e^4*log(2*d^2/abs(x) + 2*sqrt(-e^2*x^2 + d^2)*d/abs(x))/d^5 - 5/16*a*e^6*log(2*d^2/abs(x) + 2*sqrt(-e^2*x^2 + d^2)*d/abs(x))/d^7 - 1/2*sqrt(-e^2*x^2 + d^2)*c/(d^2*x^2) - 3/8*sqrt(-e^2*x^2 + d^2)*b*e^2/(d^4*x^2) - 5/16*sqrt(-e^2*x^2 + d^2)*a*e^4/(d^6*x^2) - 1/4*sqrt(-e^2*x^2 + d^2)*b/(d^2*x^4) - 5/24*sqrt(-e^2*x^2 + d^2)*a*e^2/(d^4*x^4) - 1/6*sqrt(-e^2*x^2 + d^2)*a/(d^2*x^6)","A",0
139,1,190,0,1.106329," ","integrate(x^2*(c*x^4+b*x^2+a)/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-e^{2} x^{2} + d^{2}} c x^{5}}{6 \, e^{2}} - \frac{5 \, \sqrt{-e^{2} x^{2} + d^{2}} c d^{2} x^{3}}{24 \, e^{4}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} b x^{3}}{4 \, e^{2}} + \frac{5 \, c d^{6} \arcsin\left(\frac{e x}{d}\right)}{16 \, e^{7}} + \frac{3 \, b d^{4} \arcsin\left(\frac{e x}{d}\right)}{8 \, e^{5}} + \frac{a d^{2} \arcsin\left(\frac{e x}{d}\right)}{2 \, e^{3}} - \frac{5 \, \sqrt{-e^{2} x^{2} + d^{2}} c d^{4} x}{16 \, e^{6}} - \frac{3 \, \sqrt{-e^{2} x^{2} + d^{2}} b d^{2} x}{8 \, e^{4}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} a x}{2 \, e^{2}}"," ",0,"-1/6*sqrt(-e^2*x^2 + d^2)*c*x^5/e^2 - 5/24*sqrt(-e^2*x^2 + d^2)*c*d^2*x^3/e^4 - 1/4*sqrt(-e^2*x^2 + d^2)*b*x^3/e^2 + 5/16*c*d^6*arcsin(e*x/d)/e^7 + 3/8*b*d^4*arcsin(e*x/d)/e^5 + 1/2*a*d^2*arcsin(e*x/d)/e^3 - 5/16*sqrt(-e^2*x^2 + d^2)*c*d^4*x/e^6 - 3/8*sqrt(-e^2*x^2 + d^2)*b*d^2*x/e^4 - 1/2*sqrt(-e^2*x^2 + d^2)*a*x/e^2","A",0
140,1,113,0,1.018351," ","integrate((c*x^4+b*x^2+a)/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-e^{2} x^{2} + d^{2}} c x^{3}}{4 \, e^{2}} + \frac{3 \, c d^{4} \arcsin\left(\frac{e x}{d}\right)}{8 \, e^{5}} + \frac{b d^{2} \arcsin\left(\frac{e x}{d}\right)}{2 \, e^{3}} + \frac{a \arcsin\left(\frac{e x}{d}\right)}{e} - \frac{3 \, \sqrt{-e^{2} x^{2} + d^{2}} c d^{2} x}{8 \, e^{4}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} b x}{2 \, e^{2}}"," ",0,"-1/4*sqrt(-e^2*x^2 + d^2)*c*x^3/e^2 + 3/8*c*d^4*arcsin(e*x/d)/e^5 + 1/2*b*d^2*arcsin(e*x/d)/e^3 + a*arcsin(e*x/d)/e - 3/8*sqrt(-e^2*x^2 + d^2)*c*d^2*x/e^4 - 1/2*sqrt(-e^2*x^2 + d^2)*b*x/e^2","A",0
141,1,73,0,1.051673," ","integrate((c*x^4+b*x^2+a)/x^2/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""maxima"")","\frac{c d^{2} \arcsin\left(\frac{e x}{d}\right)}{2 \, e^{3}} + \frac{b \arcsin\left(\frac{e x}{d}\right)}{e} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} c x}{2 \, e^{2}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} a}{d^{2} x}"," ",0,"1/2*c*d^2*arcsin(e*x/d)/e^3 + b*arcsin(e*x/d)/e - 1/2*sqrt(-e^2*x^2 + d^2)*c*x/e^2 - sqrt(-e^2*x^2 + d^2)*a/(d^2*x)","A",0
142,1,85,0,1.004616," ","integrate((c*x^4+b*x^2+a)/x^4/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""maxima"")","\frac{c \arcsin\left(\frac{e x}{d}\right)}{e} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} b}{d^{2} x} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} a e^{2}}{3 \, d^{4} x} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} a}{3 \, d^{2} x^{3}}"," ",0,"c*arcsin(e*x/d)/e - sqrt(-e^2*x^2 + d^2)*b/(d^2*x) - 2/3*sqrt(-e^2*x^2 + d^2)*a*e^2/(d^4*x) - 1/3*sqrt(-e^2*x^2 + d^2)*a/(d^2*x^3)","A",0
143,1,148,0,1.018855," ","integrate((c*x^4+b*x^2+a)/x^6/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-e^{2} x^{2} + d^{2}} c}{d^{2} x} - \frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} b e^{2}}{3 \, d^{4} x} - \frac{8 \, \sqrt{-e^{2} x^{2} + d^{2}} a e^{4}}{15 \, d^{6} x} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} b}{3 \, d^{2} x^{3}} - \frac{4 \, \sqrt{-e^{2} x^{2} + d^{2}} a e^{2}}{15 \, d^{4} x^{3}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} a}{5 \, d^{2} x^{5}}"," ",0,"-sqrt(-e^2*x^2 + d^2)*c/(d^2*x) - 2/3*sqrt(-e^2*x^2 + d^2)*b*e^2/(d^4*x) - 8/15*sqrt(-e^2*x^2 + d^2)*a*e^4/(d^6*x) - 1/3*sqrt(-e^2*x^2 + d^2)*b/(d^2*x^3) - 4/15*sqrt(-e^2*x^2 + d^2)*a*e^2/(d^4*x^3) - 1/5*sqrt(-e^2*x^2 + d^2)*a/(d^2*x^5)","A",0
144,1,226,0,1.010096," ","integrate((c*x^4+b*x^2+a)/x^8/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-e^{2} x^{2} + d^{2}} c e^{2}}{3 \, d^{4} x} - \frac{8 \, \sqrt{-e^{2} x^{2} + d^{2}} b e^{4}}{15 \, d^{6} x} - \frac{16 \, \sqrt{-e^{2} x^{2} + d^{2}} a e^{6}}{35 \, d^{8} x} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} c}{3 \, d^{2} x^{3}} - \frac{4 \, \sqrt{-e^{2} x^{2} + d^{2}} b e^{2}}{15 \, d^{4} x^{3}} - \frac{8 \, \sqrt{-e^{2} x^{2} + d^{2}} a e^{4}}{35 \, d^{6} x^{3}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} b}{5 \, d^{2} x^{5}} - \frac{6 \, \sqrt{-e^{2} x^{2} + d^{2}} a e^{2}}{35 \, d^{4} x^{5}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} a}{7 \, d^{2} x^{7}}"," ",0,"-2/3*sqrt(-e^2*x^2 + d^2)*c*e^2/(d^4*x) - 8/15*sqrt(-e^2*x^2 + d^2)*b*e^4/(d^6*x) - 16/35*sqrt(-e^2*x^2 + d^2)*a*e^6/(d^8*x) - 1/3*sqrt(-e^2*x^2 + d^2)*c/(d^2*x^3) - 4/15*sqrt(-e^2*x^2 + d^2)*b*e^2/(d^4*x^3) - 8/35*sqrt(-e^2*x^2 + d^2)*a*e^4/(d^6*x^3) - 1/5*sqrt(-e^2*x^2 + d^2)*b/(d^2*x^5) - 6/35*sqrt(-e^2*x^2 + d^2)*a*e^2/(d^4*x^5) - 1/7*sqrt(-e^2*x^2 + d^2)*a/(d^2*x^7)","A",0
145,1,304,0,1.030909," ","integrate((c*x^4+b*x^2+a)/x^10/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""maxima"")","-\frac{8 \, \sqrt{-e^{2} x^{2} + d^{2}} c e^{4}}{15 \, d^{6} x} - \frac{16 \, \sqrt{-e^{2} x^{2} + d^{2}} b e^{6}}{35 \, d^{8} x} - \frac{128 \, \sqrt{-e^{2} x^{2} + d^{2}} a e^{8}}{315 \, d^{10} x} - \frac{4 \, \sqrt{-e^{2} x^{2} + d^{2}} c e^{2}}{15 \, d^{4} x^{3}} - \frac{8 \, \sqrt{-e^{2} x^{2} + d^{2}} b e^{4}}{35 \, d^{6} x^{3}} - \frac{64 \, \sqrt{-e^{2} x^{2} + d^{2}} a e^{6}}{315 \, d^{8} x^{3}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} c}{5 \, d^{2} x^{5}} - \frac{6 \, \sqrt{-e^{2} x^{2} + d^{2}} b e^{2}}{35 \, d^{4} x^{5}} - \frac{16 \, \sqrt{-e^{2} x^{2} + d^{2}} a e^{4}}{105 \, d^{6} x^{5}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} b}{7 \, d^{2} x^{7}} - \frac{8 \, \sqrt{-e^{2} x^{2} + d^{2}} a e^{2}}{63 \, d^{4} x^{7}} - \frac{\sqrt{-e^{2} x^{2} + d^{2}} a}{9 \, d^{2} x^{9}}"," ",0,"-8/15*sqrt(-e^2*x^2 + d^2)*c*e^4/(d^6*x) - 16/35*sqrt(-e^2*x^2 + d^2)*b*e^6/(d^8*x) - 128/315*sqrt(-e^2*x^2 + d^2)*a*e^8/(d^10*x) - 4/15*sqrt(-e^2*x^2 + d^2)*c*e^2/(d^4*x^3) - 8/35*sqrt(-e^2*x^2 + d^2)*b*e^4/(d^6*x^3) - 64/315*sqrt(-e^2*x^2 + d^2)*a*e^6/(d^8*x^3) - 1/5*sqrt(-e^2*x^2 + d^2)*c/(d^2*x^5) - 6/35*sqrt(-e^2*x^2 + d^2)*b*e^2/(d^4*x^5) - 16/105*sqrt(-e^2*x^2 + d^2)*a*e^4/(d^6*x^5) - 1/7*sqrt(-e^2*x^2 + d^2)*b/(d^2*x^7) - 8/63*sqrt(-e^2*x^2 + d^2)*a*e^2/(d^4*x^7) - 1/9*sqrt(-e^2*x^2 + d^2)*a/(d^2*x^9)","A",0
