1,1,64,0,0.285583," ","integrate(x^2*(C*x^2+B*x+A)*(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{1}{9} \, C c x^{9} + \frac{1}{8} \, B c x^{8} + \frac{1}{7} \, C b x^{7} + \frac{1}{7} \, A c x^{7} + \frac{1}{6} \, B b x^{6} + \frac{1}{5} \, C a x^{5} + \frac{1}{5} \, A b x^{5} + \frac{1}{4} \, B a x^{4} + \frac{1}{3} \, A a x^{3}"," ",0,"1/9*C*c*x^9 + 1/8*B*c*x^8 + 1/7*C*b*x^7 + 1/7*A*c*x^7 + 1/6*B*b*x^6 + 1/5*C*a*x^5 + 1/5*A*b*x^5 + 1/4*B*a*x^4 + 1/3*A*a*x^3","A",0
2,1,64,0,0.226545," ","integrate(x*(C*x^2+B*x+A)*(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{1}{8} \, C c x^{8} + \frac{1}{7} \, B c x^{7} + \frac{1}{6} \, C b x^{6} + \frac{1}{6} \, A c x^{6} + \frac{1}{5} \, B b x^{5} + \frac{1}{4} \, C a x^{4} + \frac{1}{4} \, A b x^{4} + \frac{1}{3} \, B a x^{3} + \frac{1}{2} \, A a x^{2}"," ",0,"1/8*C*c*x^8 + 1/7*B*c*x^7 + 1/6*C*b*x^6 + 1/6*A*c*x^6 + 1/5*B*b*x^5 + 1/4*C*a*x^4 + 1/4*A*b*x^4 + 1/3*B*a*x^3 + 1/2*A*a*x^2","A",0
3,1,61,0,0.377009," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{1}{7} \, C c x^{7} + \frac{1}{6} \, B c x^{6} + \frac{1}{5} \, C b x^{5} + \frac{1}{5} \, A c x^{5} + \frac{1}{4} \, B b x^{4} + \frac{1}{3} \, C a x^{3} + \frac{1}{3} \, A b x^{3} + \frac{1}{2} \, B a x^{2} + A a x"," ",0,"1/7*C*c*x^7 + 1/6*B*c*x^6 + 1/5*C*b*x^5 + 1/5*A*c*x^5 + 1/4*B*b*x^4 + 1/3*C*a*x^3 + 1/3*A*b*x^3 + 1/2*B*a*x^2 + A*a*x","A",0
4,1,60,0,0.372215," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x,x, algorithm=""giac"")","\frac{1}{6} \, C c x^{6} + \frac{1}{5} \, B c x^{5} + \frac{1}{4} \, C b x^{4} + \frac{1}{4} \, A c x^{4} + \frac{1}{3} \, B b x^{3} + \frac{1}{2} \, C a x^{2} + \frac{1}{2} \, A b x^{2} + B a x + A a \log\left({\left| x \right|}\right)"," ",0,"1/6*C*c*x^6 + 1/5*B*c*x^5 + 1/4*C*b*x^4 + 1/4*A*c*x^4 + 1/3*B*b*x^3 + 1/2*C*a*x^2 + 1/2*A*b*x^2 + B*a*x + A*a*log(abs(x))","A",0
5,1,57,0,0.298812," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x^2,x, algorithm=""giac"")","\frac{1}{5} \, C c x^{5} + \frac{1}{4} \, B c x^{4} + \frac{1}{3} \, C b x^{3} + \frac{1}{3} \, A c x^{3} + \frac{1}{2} \, B b x^{2} + C a x + A b x + B a \log\left({\left| x \right|}\right) - \frac{A a}{x}"," ",0,"1/5*C*c*x^5 + 1/4*B*c*x^4 + 1/3*C*b*x^3 + 1/3*A*c*x^3 + 1/2*B*b*x^2 + C*a*x + A*b*x + B*a*log(abs(x)) - A*a/x","A",0
6,1,58,0,0.290442," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x^3,x, algorithm=""giac"")","\frac{1}{4} \, C c x^{4} + \frac{1}{3} \, B c x^{3} + \frac{1}{2} \, C b x^{2} + \frac{1}{2} \, A c x^{2} + B b x + {\left(C a + A b\right)} \log\left({\left| x \right|}\right) - \frac{2 \, B a x + A a}{2 \, x^{2}}"," ",0,"1/4*C*c*x^4 + 1/3*B*c*x^3 + 1/2*C*b*x^2 + 1/2*A*c*x^2 + B*b*x + (C*a + A*b)*log(abs(x)) - 1/2*(2*B*a*x + A*a)/x^2","A",0
7,1,56,0,0.368923," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x^4,x, algorithm=""giac"")","\frac{1}{3} \, C c x^{3} + \frac{1}{2} \, B c x^{2} + C b x + A c x + B b \log\left({\left| x \right|}\right) - \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 + C*b*x + A*c*x + B*b*log(abs(x)) - 1/6*(3*B*a*x + 6*(C*a + A*b)*x^2 + 2*A*a)/x^3","A",0
8,1,57,0,0.287637," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x^5,x, algorithm=""giac"")","\frac{1}{2} \, C c x^{2} + B c x + {\left(C b + A c\right)} \log\left({\left| x \right|}\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(abs(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
9,1,57,0,0.258600," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x^6,x, algorithm=""giac"")","C c x + B c \log\left({\left| x \right|}\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(abs(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
10,1,60,0,0.390094," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x^7,x, algorithm=""giac"")","C c \log\left({\left| x \right|}\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(abs(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
11,1,154,0,0.406049," ","integrate(x^2*(C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{13} \, C c^{2} x^{13} + \frac{1}{12} \, B c^{2} x^{12} + \frac{2}{11} \, C b c x^{11} + \frac{1}{11} \, A c^{2} x^{11} + \frac{1}{5} \, B b c x^{10} + \frac{1}{9} \, C b^{2} x^{9} + \frac{2}{9} \, C a c x^{9} + \frac{2}{9} \, A b c x^{9} + \frac{1}{8} \, B b^{2} x^{8} + \frac{1}{4} \, B a c x^{8} + \frac{2}{7} \, C a b x^{7} + \frac{1}{7} \, A b^{2} x^{7} + \frac{2}{7} \, A a c x^{7} + \frac{1}{3} \, B a b x^{6} + \frac{1}{5} \, C a^{2} x^{5} + \frac{2}{5} \, A a b x^{5} + \frac{1}{4} \, B a^{2} x^{4} + \frac{1}{3} \, A a^{2} x^{3}"," ",0,"1/13*C*c^2*x^13 + 1/12*B*c^2*x^12 + 2/11*C*b*c*x^11 + 1/11*A*c^2*x^11 + 1/5*B*b*c*x^10 + 1/9*C*b^2*x^9 + 2/9*C*a*c*x^9 + 2/9*A*b*c*x^9 + 1/8*B*b^2*x^8 + 1/4*B*a*c*x^8 + 2/7*C*a*b*x^7 + 1/7*A*b^2*x^7 + 2/7*A*a*c*x^7 + 1/3*B*a*b*x^6 + 1/5*C*a^2*x^5 + 2/5*A*a*b*x^5 + 1/4*B*a^2*x^4 + 1/3*A*a^2*x^3","A",0
12,1,154,0,0.306271," ","integrate(x*(C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{12} \, C c^{2} x^{12} + \frac{1}{11} \, B c^{2} x^{11} + \frac{1}{5} \, C b c x^{10} + \frac{1}{10} \, A c^{2} x^{10} + \frac{2}{9} \, B b c x^{9} + \frac{1}{8} \, C b^{2} x^{8} + \frac{1}{4} \, C a c x^{8} + \frac{1}{4} \, A b c x^{8} + \frac{1}{7} \, B b^{2} x^{7} + \frac{2}{7} \, B a c x^{7} + \frac{1}{3} \, C a b x^{6} + \frac{1}{6} \, A b^{2} x^{6} + \frac{1}{3} \, A a c x^{6} + \frac{2}{5} \, B a b x^{5} + \frac{1}{4} \, C a^{2} x^{4} + \frac{1}{2} \, A a b x^{4} + \frac{1}{3} \, B a^{2} x^{3} + \frac{1}{2} \, A a^{2} x^{2}"," ",0,"1/12*C*c^2*x^12 + 1/11*B*c^2*x^11 + 1/5*C*b*c*x^10 + 1/10*A*c^2*x^10 + 2/9*B*b*c*x^9 + 1/8*C*b^2*x^8 + 1/4*C*a*c*x^8 + 1/4*A*b*c*x^8 + 1/7*B*b^2*x^7 + 2/7*B*a*c*x^7 + 1/3*C*a*b*x^6 + 1/6*A*b^2*x^6 + 1/3*A*a*c*x^6 + 2/5*B*a*b*x^5 + 1/4*C*a^2*x^4 + 1/2*A*a*b*x^4 + 1/3*B*a^2*x^3 + 1/2*A*a^2*x^2","A",0
13,1,151,0,0.299556," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{11} \, C c^{2} x^{11} + \frac{1}{10} \, B c^{2} x^{10} + \frac{2}{9} \, C b c x^{9} + \frac{1}{9} \, A c^{2} x^{9} + \frac{1}{4} \, B b c x^{8} + \frac{1}{7} \, C b^{2} x^{7} + \frac{2}{7} \, C a c x^{7} + \frac{2}{7} \, A b c x^{7} + \frac{1}{6} \, B b^{2} x^{6} + \frac{1}{3} \, B a c x^{6} + \frac{2}{5} \, C a b x^{5} + \frac{1}{5} \, A b^{2} x^{5} + \frac{2}{5} \, A a c x^{5} + \frac{1}{2} \, B a b x^{4} + \frac{1}{3} \, C a^{2} x^{3} + \frac{2}{3} \, A a b x^{3} + \frac{1}{2} \, B a^{2} x^{2} + A a^{2} x"," ",0,"1/11*C*c^2*x^11 + 1/10*B*c^2*x^10 + 2/9*C*b*c*x^9 + 1/9*A*c^2*x^9 + 1/4*B*b*c*x^8 + 1/7*C*b^2*x^7 + 2/7*C*a*c*x^7 + 2/7*A*b*c*x^7 + 1/6*B*b^2*x^6 + 1/3*B*a*c*x^6 + 2/5*C*a*b*x^5 + 1/5*A*b^2*x^5 + 2/5*A*a*c*x^5 + 1/2*B*a*b*x^4 + 1/3*C*a^2*x^3 + 2/3*A*a*b*x^3 + 1/2*B*a^2*x^2 + A*a^2*x","A",0
14,1,149,0,0.363991," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x,x, algorithm=""giac"")","\frac{1}{10} \, C c^{2} x^{10} + \frac{1}{9} \, B c^{2} x^{9} + \frac{1}{4} \, C b c x^{8} + \frac{1}{8} \, A c^{2} x^{8} + \frac{2}{7} \, B b c x^{7} + \frac{1}{6} \, C b^{2} x^{6} + \frac{1}{3} \, C a c x^{6} + \frac{1}{3} \, A b c x^{6} + \frac{1}{5} \, B b^{2} x^{5} + \frac{2}{5} \, B a c x^{5} + \frac{1}{2} \, C a b x^{4} + \frac{1}{4} \, A b^{2} x^{4} + \frac{1}{2} \, A a c x^{4} + \frac{2}{3} \, B a b x^{3} + \frac{1}{2} \, C a^{2} x^{2} + A a b x^{2} + B a^{2} x + A a^{2} \log\left({\left| x \right|}\right)"," ",0,"1/10*C*c^2*x^10 + 1/9*B*c^2*x^9 + 1/4*C*b*c*x^8 + 1/8*A*c^2*x^8 + 2/7*B*b*c*x^7 + 1/6*C*b^2*x^6 + 1/3*C*a*c*x^6 + 1/3*A*b*c*x^6 + 1/5*B*b^2*x^5 + 2/5*B*a*c*x^5 + 1/2*C*a*b*x^4 + 1/4*A*b^2*x^4 + 1/2*A*a*c*x^4 + 2/3*B*a*b*x^3 + 1/2*C*a^2*x^2 + A*a*b*x^2 + B*a^2*x + A*a^2*log(abs(x))","A",0
15,1,147,0,0.282296," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x^2,x, algorithm=""giac"")","\frac{1}{9} \, C c^{2} x^{9} + \frac{1}{8} \, B c^{2} x^{8} + \frac{2}{7} \, C b c x^{7} + \frac{1}{7} \, A c^{2} x^{7} + \frac{1}{3} \, B b c x^{6} + \frac{1}{5} \, C b^{2} x^{5} + \frac{2}{5} \, C a c x^{5} + \frac{2}{5} \, A b c x^{5} + \frac{1}{4} \, B b^{2} x^{4} + \frac{1}{2} \, B a c x^{4} + \frac{2}{3} \, C a b x^{3} + \frac{1}{3} \, A b^{2} x^{3} + \frac{2}{3} \, A a c x^{3} + B a b x^{2} + C a^{2} x + 2 \, A a b x + B a^{2} \log\left({\left| x \right|}\right) - \frac{A a^{2}}{x}"," ",0,"1/9*C*c^2*x^9 + 1/8*B*c^2*x^8 + 2/7*C*b*c*x^7 + 1/7*A*c^2*x^7 + 1/3*B*b*c*x^6 + 1/5*C*b^2*x^5 + 2/5*C*a*c*x^5 + 2/5*A*b*c*x^5 + 1/4*B*b^2*x^4 + 1/2*B*a*c*x^4 + 2/3*C*a*b*x^3 + 1/3*A*b^2*x^3 + 2/3*A*a*c*x^3 + B*a*b*x^2 + C*a^2*x + 2*A*a*b*x + B*a^2*log(abs(x)) - A*a^2/x","A",0
16,1,148,0,0.395444," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x^3,x, algorithm=""giac"")","\frac{1}{8} \, C c^{2} x^{8} + \frac{1}{7} \, B c^{2} x^{7} + \frac{1}{3} \, C b c x^{6} + \frac{1}{6} \, A c^{2} x^{6} + \frac{2}{5} \, B b c x^{5} + \frac{1}{4} \, C b^{2} x^{4} + \frac{1}{2} \, C a c x^{4} + \frac{1}{2} \, A b c x^{4} + \frac{1}{3} \, B b^{2} x^{3} + \frac{2}{3} \, B a c x^{3} + C a b x^{2} + \frac{1}{2} \, A b^{2} x^{2} + A a c x^{2} + 2 \, B a b x + {\left(C a^{2} + 2 \, A a b\right)} \log\left({\left| x \right|}\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 + 1/3*C*b*c*x^6 + 1/6*A*c^2*x^6 + 2/5*B*b*c*x^5 + 1/4*C*b^2*x^4 + 1/2*C*a*c*x^4 + 1/2*A*b*c*x^4 + 1/3*B*b^2*x^3 + 2/3*B*a*c*x^3 + C*a*b*x^2 + 1/2*A*b^2*x^2 + A*a*c*x^2 + 2*B*a*b*x + (C*a^2 + 2*A*a*b)*log(abs(x)) - 1/2*(2*B*a^2*x + A*a^2)/x^2","A",0
17,1,146,0,0.284003," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x^4,x, algorithm=""giac"")","\frac{1}{7} \, C c^{2} x^{7} + \frac{1}{6} \, B c^{2} x^{6} + \frac{2}{5} \, C b c x^{5} + \frac{1}{5} \, A c^{2} x^{5} + \frac{1}{2} \, B b c x^{4} + \frac{1}{3} \, C b^{2} x^{3} + \frac{2}{3} \, C a c x^{3} + \frac{2}{3} \, A b c x^{3} + \frac{1}{2} \, B b^{2} x^{2} + B a c x^{2} + 2 \, C a b x + A b^{2} x + 2 \, A a c x + 2 \, B a b \log\left({\left| x \right|}\right) - \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 + 2/5*C*b*c*x^5 + 1/5*A*c^2*x^5 + 1/2*B*b*c*x^4 + 1/3*C*b^2*x^3 + 2/3*C*a*c*x^3 + 2/3*A*b*c*x^3 + 1/2*B*b^2*x^2 + B*a*c*x^2 + 2*C*a*b*x + A*b^2*x + 2*A*a*c*x + 2*B*a*b*log(abs(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
18,1,142,0,0.376766," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x^5,x, algorithm=""giac"")","\frac{1}{6} \, C c^{2} x^{6} + \frac{1}{5} \, B c^{2} x^{5} + \frac{1}{2} \, C b c x^{4} + \frac{1}{4} \, A c^{2} x^{4} + \frac{2}{3} \, B b c x^{3} + \frac{1}{2} \, C b^{2} x^{2} + C a c x^{2} + A b c x^{2} + B b^{2} x + 2 \, B a c x + {\left(2 \, C a b + A b^{2} + 2 \, A a c\right)} \log\left({\left| x \right|}\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 + 1/2*C*b*c*x^4 + 1/4*A*c^2*x^4 + 2/3*B*b*c*x^3 + 1/2*C*b^2*x^2 + C*a*c*x^2 + A*b*c*x^2 + B*b^2*x + 2*B*a*c*x + (2*C*a*b + A*b^2 + 2*A*a*c)*log(abs(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
19,1,140,0,0.292289," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x^6,x, algorithm=""giac"")","\frac{1}{5} \, C c^{2} x^{5} + \frac{1}{4} \, B c^{2} x^{4} + \frac{2}{3} \, C b c x^{3} + \frac{1}{3} \, A c^{2} x^{3} + B b c x^{2} + C b^{2} x + 2 \, C a c x + 2 \, A b c x + {\left(B b^{2} + 2 \, B a c\right)} \log\left({\left| x \right|}\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 + 2/3*C*b*c*x^3 + 1/3*A*c^2*x^3 + B*b*c*x^2 + C*b^2*x + 2*C*a*c*x + 2*A*b*c*x + (B*b^2 + 2*B*a*c)*log(abs(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
20,1,141,0,0.395511," ","integrate((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x^7,x, algorithm=""giac"")","\frac{1}{4} \, C c^{2} x^{4} + \frac{1}{3} \, B c^{2} x^{3} + C b c x^{2} + \frac{1}{2} \, A c^{2} x^{2} + 2 \, B b c x + {\left(C b^{2} + 2 \, C a c + 2 \, A b c\right)} \log\left({\left| x \right|}\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 + C*b*c*x^2 + 1/2*A*c^2*x^2 + 2*B*b*c*x + (C*b^2 + 2*C*a*c + 2*A*b*c)*log(abs(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
21,1,5304,0,5.748865," ","integrate(x^4*(C*x^2+B*x+A)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{B b \log\left({\left| c x^{4} + b x^{2} + a \right|}\right)}{4 \, 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 {\left| c \right|} - 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 {\left| c \right|} - {\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}} x}{\sqrt{\frac{b c^{7} + \sqrt{b^{2} c^{14} - 4 \, a c^{15}}}{c^{8}}}}\right)}{8 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} - 2 \, a b^{3} c^{5} + 16 \, a^{3} c^{6} + 8 \, a^{2} b c^{6} + a b^{2} c^{6} - 4 \, a^{2} c^{7}\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 {\left| c \right|} + 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 {\left| c \right|} - {\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}} x}{\sqrt{\frac{b c^{7} - \sqrt{b^{2} c^{14} - 4 \, a c^{15}}}{c^{8}}}}\right)}{8 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} - 2 \, a b^{3} c^{5} + 16 \, a^{3} c^{6} + 8 \, a^{2} b c^{6} + a b^{2} c^{6} - 4 \, a^{2} c^{7}\right)} c^{2}} + \frac{2 \, C c^{2} x^{3} + 3 \, B c^{2} x^{2} - 6 \, C b c x + 6 \, A c^{2} x}{6 \, c^{3}} + \frac{{\left({\left(b^{7} - 10 \, a b^{5} c - 2 \, b^{6} c + 32 \, a^{2} b^{3} c^{2} + 12 \, a b^{4} c^{2} + b^{5} c^{2} - 32 \, a^{3} b c^{3} - 16 \, a^{2} b^{2} c^{3} - 6 \, a b^{3} c^{3} + 8 \, a^{2} b c^{4} - {\left(b^{6} - 10 \, a b^{4} c - 2 \, b^{5} c + 32 \, a^{2} b^{2} c^{2} + 12 \, a b^{3} c^{2} + b^{4} c^{2} - 32 \, a^{3} c^{3} - 16 \, a^{2} b c^{3} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| c \right|} + {\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 - 6 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} + 8 \, a^{2} b^{2} c^{3} + 4 \, a b^{3} c^{3} + b^{4} c^{3} - 2 \, a b^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{b c^{7} + \sqrt{b^{2} c^{14} - 4 \, a c^{15}}}{2 \, c^{8}}\right)}{16 \, {\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} {\left| c \right|}} + \frac{{\left({\left(b^{7} - 10 \, a b^{5} c - 2 \, b^{6} c + 32 \, a^{2} b^{3} c^{2} + 12 \, a b^{4} c^{2} + b^{5} c^{2} - 32 \, a^{3} b c^{3} - 16 \, a^{2} b^{2} c^{3} - 6 \, a b^{3} c^{3} + 8 \, a^{2} b c^{4} + {\left(b^{6} - 10 \, a b^{4} c - 2 \, b^{5} c + 32 \, a^{2} b^{2} c^{2} + 12 \, a b^{3} c^{2} + b^{4} c^{2} - 32 \, a^{3} c^{3} - 16 \, a^{2} b c^{3} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| c \right|} + {\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 - 6 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} + 8 \, a^{2} b^{2} c^{3} + 4 \, a b^{3} c^{3} + b^{4} c^{3} - 2 \, a b^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{b c^{7} - \sqrt{b^{2} c^{14} - 4 \, a c^{15}}}{2 \, c^{8}}\right)}{16 \, {\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} {\left| c \right|}}"," ",0,"-1/4*B*b*log(abs(c*x^4 + b*x^2 + a))/c^2 - 1/8*((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*(b^2 - 4*a*c)*b^3*c^3 + 8*(b^2 - 4*a*c)*a*b*c^4)*A*c^2 - (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*(b^2 - 4*a*c)*b^4*c^2 + 10*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*C*c^2 + 2*(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*(b^2 - 4*a*c)*a*b^2*c^4 + 8*(b^2 - 4*a*c)*a^2*c^5)*A*abs(c) - 2*(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*(b^2 - 4*a*c)*a*b^3*c^3 + 8*(b^2 - 4*a*c)*a^2*b*c^4)*C*abs(c) - (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*(b^2 - 4*a*c)*b^3*c^5 + 4*(b^2 - 4*a*c)*a*b*c^6)*A + (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*(b^2 - 4*a*c)*b^4*c^4 + 6*(b^2 - 4*a*c)*a*b^2*c^5)*C)*arctan(2*sqrt(1/2)*x/sqrt((b*c^7 + sqrt(b^2*c^14 - 4*a*c^15))/c^8))/((a*b^4*c^4 - 8*a^2*b^2*c^5 - 2*a*b^3*c^5 + 16*a^3*c^6 + 8*a^2*b*c^6 + a*b^2*c^6 - 4*a^2*c^7)*c^2) + 1/8*((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*(b^2 - 4*a*c)*b^3*c^3 + 8*(b^2 - 4*a*c)*a*b*c^4)*A*c^2 - (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*(b^2 - 4*a*c)*b^4*c^2 + 10*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*C*c^2 - 2*(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*(b^2 - 4*a*c)*a*b^2*c^4 - 8*(b^2 - 4*a*c)*a^2*c^5)*A*abs(c) + 2*(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*(b^2 - 4*a*c)*a*b^3*c^3 - 8*(b^2 - 4*a*c)*a^2*b*c^4)*C*abs(c) - (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*(b^2 - 4*a*c)*b^3*c^5 + 4*(b^2 - 4*a*c)*a*b*c^6)*A + (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*(b^2 - 4*a*c)*b^4*c^4 + 6*(b^2 - 4*a*c)*a*b^2*c^5)*C)*arctan(2*sqrt(1/2)*x/sqrt((b*c^7 - sqrt(b^2*c^14 - 4*a*c^15))/c^8))/((a*b^4*c^4 - 8*a^2*b^2*c^5 - 2*a*b^3*c^5 + 16*a^3*c^6 + 8*a^2*b*c^6 + a*b^2*c^6 - 4*a^2*c^7)*c^2) + 1/6*(2*C*c^2*x^3 + 3*B*c^2*x^2 - 6*C*b*c*x + 6*A*c^2*x)/c^3 + 1/16*((b^7 - 10*a*b^5*c - 2*b^6*c + 32*a^2*b^3*c^2 + 12*a*b^4*c^2 + b^5*c^2 - 32*a^3*b*c^3 - 16*a^2*b^2*c^3 - 6*a*b^3*c^3 + 8*a^2*b*c^4 - (b^6 - 10*a*b^4*c - 2*b^5*c + 32*a^2*b^2*c^2 + 12*a*b^3*c^2 + b^4*c^2 - 32*a^3*c^3 - 16*a^2*b*c^3 - 6*a*b^2*c^3 + 8*a^2*c^4)*sqrt(b^2 - 4*a*c))*B*abs(c) + (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 - (b^6*c - 6*a*b^4*c^2 - 2*b^5*c^2 + 8*a^2*b^2*c^3 + 4*a*b^3*c^3 + b^4*c^3 - 2*a*b^2*c^4)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(b*c^7 + sqrt(b^2*c^14 - 4*a*c^15))/c^8)/((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)*c^2*abs(c)) + 1/16*((b^7 - 10*a*b^5*c - 2*b^6*c + 32*a^2*b^3*c^2 + 12*a*b^4*c^2 + b^5*c^2 - 32*a^3*b*c^3 - 16*a^2*b^2*c^3 - 6*a*b^3*c^3 + 8*a^2*b*c^4 + (b^6 - 10*a*b^4*c - 2*b^5*c + 32*a^2*b^2*c^2 + 12*a*b^3*c^2 + b^4*c^2 - 32*a^3*c^3 - 16*a^2*b*c^3 - 6*a*b^2*c^3 + 8*a^2*c^4)*sqrt(b^2 - 4*a*c))*B*abs(c) + (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 + (b^6*c - 6*a*b^4*c^2 - 2*b^5*c^2 + 8*a^2*b^2*c^3 + 4*a*b^3*c^3 + b^4*c^3 - 2*a*b^2*c^4)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(b*c^7 - sqrt(b^2*c^14 - 4*a*c^15))/c^8)/((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)*c^2*abs(c))","B",0
22,1,3519,0,5.025220," ","integrate(x^3*(C*x^2+B*x+A)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(C b - A c\right)} \log\left({\left| c x^{4} + b x^{2} + a \right|}\right)}{4 \, c^{2}} + \frac{C c x^{2} + 2 \, B c x}{2 \, 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} 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)} B {\left| c \right|} - {\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)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c^{5} + \sqrt{b^{2} c^{10} - 4 \, a c^{11}}}{c^{6}}}}\right)}{8 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} - 2 \, a b^{3} c^{4} + 16 \, a^{3} c^{5} + 8 \, a^{2} b c^{5} + a b^{2} c^{5} - 4 \, a^{2} c^{6}\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} 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)} B {\left| c \right|} - {\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)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c^{5} - \sqrt{b^{2} c^{10} - 4 \, a c^{11}}}{c^{6}}}}\right)}{8 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} - 2 \, a b^{3} c^{4} + 16 \, a^{3} c^{5} + 8 \, a^{2} b c^{5} + a b^{2} c^{5} - 4 \, a^{2} c^{6}\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 {\left| c \right|} - {\left(b^{7} - 10 \, a b^{5} c - 2 \, b^{6} c + 32 \, a^{2} b^{3} c^{2} + 12 \, a b^{4} c^{2} + b^{5} c^{2} - 32 \, a^{3} b c^{3} - 16 \, a^{2} b^{2} c^{3} - 6 \, a b^{3} c^{3} + 8 \, a^{2} b c^{4} - {\left(b^{6} - 10 \, a b^{4} c - 2 \, b^{5} c + 32 \, a^{2} b^{2} c^{2} + 12 \, a b^{3} c^{2} + b^{4} c^{2} - 32 \, a^{3} c^{3} - 16 \, a^{2} b c^{3} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C {\left| c \right|} + {\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 - {\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 - 6 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} + 8 \, a^{2} b^{2} c^{3} + 4 \, a b^{3} c^{3} + b^{4} c^{3} - 2 \, a b^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C\right)} \log\left(x^{2} + \frac{b c^{5} + \sqrt{b^{2} c^{10} - 4 \, a c^{11}}}{2 \, c^{6}}\right)}{16 \, {\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} {\left| c \right|}} - \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 {\left| c \right|} - {\left(b^{7} - 10 \, a b^{5} c - 2 \, b^{6} c + 32 \, a^{2} b^{3} c^{2} + 12 \, a b^{4} c^{2} + b^{5} c^{2} - 32 \, a^{3} b c^{3} - 16 \, a^{2} b^{2} c^{3} - 6 \, a b^{3} c^{3} + 8 \, a^{2} b c^{4} + {\left(b^{6} - 10 \, a b^{4} c - 2 \, b^{5} c + 32 \, a^{2} b^{2} c^{2} + 12 \, a b^{3} c^{2} + b^{4} c^{2} - 32 \, a^{3} c^{3} - 16 \, a^{2} b c^{3} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C {\left| c \right|} + {\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 - {\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 - 6 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} + 8 \, a^{2} b^{2} c^{3} + 4 \, a b^{3} c^{3} + b^{4} c^{3} - 2 \, a b^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C\right)} \log\left(x^{2} + \frac{b c^{5} - \sqrt{b^{2} c^{10} - 4 \, a c^{11}}}{2 \, c^{6}}\right)}{16 \, {\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} {\left| c \right|}}"," ",0,"-1/4*(C*b - A*c)*log(abs(c*x^4 + b*x^2 + a))/c^2 + 1/2*(C*c*x^2 + 2*B*c*x)/c^2 - 1/8*((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*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*B*c^2 + 2*(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*(b^2 - 4*a*c)*a*b^2*c^3 + 8*(b^2 - 4*a*c)*a^2*c^4)*B*abs(c) - (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*(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*a*b*c^5)*B)*arctan(2*sqrt(1/2)*x/sqrt((b*c^5 + sqrt(b^2*c^10 - 4*a*c^11))/c^6))/((a*b^4*c^3 - 8*a^2*b^2*c^4 - 2*a*b^3*c^4 + 16*a^3*c^5 + 8*a^2*b*c^5 + a*b^2*c^5 - 4*a^2*c^6)*c^2) + 1/8*((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*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*B*c^2 - 2*(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*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*B*abs(c) - (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*(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*a*b*c^5)*B)*arctan(2*sqrt(1/2)*x/sqrt((b*c^5 - sqrt(b^2*c^10 - 4*a*c^11))/c^6))/((a*b^4*c^3 - 8*a^2*b^2*c^4 - 2*a*b^3*c^4 + 16*a^3*c^5 + 8*a^2*b*c^5 + a*b^2*c^5 - 4*a^2*c^6)*c^2) - 1/16*((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 - (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)*sqrt(b^2 - 4*a*c))*A*abs(c) - (b^7 - 10*a*b^5*c - 2*b^6*c + 32*a^2*b^3*c^2 + 12*a*b^4*c^2 + b^5*c^2 - 32*a^3*b*c^3 - 16*a^2*b^2*c^3 - 6*a*b^3*c^3 + 8*a^2*b*c^4 - (b^6 - 10*a*b^4*c - 2*b^5*c + 32*a^2*b^2*c^2 + 12*a*b^3*c^2 + b^4*c^2 - 32*a^3*c^3 - 16*a^2*b*c^3 - 6*a*b^2*c^3 + 8*a^2*c^4)*sqrt(b^2 - 4*a*c))*C*abs(c) + (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 + (b^5*c^2 - 4*a*b^3*c^3 - 2*b^4*c^3 + b^3*c^4)*sqrt(b^2 - 4*a*c))*A - (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 - (b^6*c - 6*a*b^4*c^2 - 2*b^5*c^2 + 8*a^2*b^2*c^3 + 4*a*b^3*c^3 + b^4*c^3 - 2*a*b^2*c^4)*sqrt(b^2 - 4*a*c))*C)*log(x^2 + 1/2*(b*c^5 + sqrt(b^2*c^10 - 4*a*c^11))/c^6)/((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)*c^2*abs(c)) - 1/16*((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 + (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)*sqrt(b^2 - 4*a*c))*A*abs(c) - (b^7 - 10*a*b^5*c - 2*b^6*c + 32*a^2*b^3*c^2 + 12*a*b^4*c^2 + b^5*c^2 - 32*a^3*b*c^3 - 16*a^2*b^2*c^3 - 6*a*b^3*c^3 + 8*a^2*b*c^4 + (b^6 - 10*a*b^4*c - 2*b^5*c + 32*a^2*b^2*c^2 + 12*a*b^3*c^2 + b^4*c^2 - 32*a^3*c^3 - 16*a^2*b*c^3 - 6*a*b^2*c^3 + 8*a^2*c^4)*sqrt(b^2 - 4*a*c))*C*abs(c) + (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 + (b^5*c^2 - 4*a*b^3*c^3 - 2*b^4*c^3 + b^3*c^4)*sqrt(b^2 - 4*a*c))*A - (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 + (b^6*c - 6*a*b^4*c^2 - 2*b^5*c^2 + 8*a^2*b^2*c^3 + 4*a*b^3*c^3 + b^4*c^3 - 2*a*b^2*c^4)*sqrt(b^2 - 4*a*c))*C)*log(x^2 + 1/2*(b*c^5 - sqrt(b^2*c^10 - 4*a*c^11))/c^6)/((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)*c^2*abs(c))","B",0
23,1,3843,0,5.565636," ","integrate(x^2*(C*x^2+B*x+A)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{C x}{c} + \frac{B \log\left({\left| c x^{4} + b x^{2} + a \right|}\right)}{4 \, c} + \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 {\left| c \right|} - {\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}} x}{\sqrt{\frac{b c^{3} + \sqrt{b^{2} c^{6} - 4 \, a c^{7}}}{c^{4}}}}\right)}{8 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} - 2 \, a b^{3} c^{4} + 16 \, a^{3} c^{5} + 8 \, a^{2} b c^{5} + a b^{2} c^{5} - 4 \, a^{2} c^{6}\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 {\left| c \right|} - {\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}} x}{\sqrt{\frac{b c^{3} - \sqrt{b^{2} c^{6} - 4 \, a c^{7}}}{c^{4}}}}\right)}{8 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} - 2 \, a b^{3} c^{4} + 16 \, a^{3} c^{5} + 8 \, a^{2} b c^{5} + a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} c^{2}} - \frac{{\left({\left(b^{6} - 8 \, a b^{4} c - 2 \, b^{5} c + 16 \, a^{2} b^{2} c^{2} + 8 \, a b^{3} c^{2} + b^{4} c^{2} - 4 \, a b^{2} c^{3} - {\left(b^{5} - 8 \, a b^{3} c - 2 \, b^{4} c + 16 \, a^{2} b c^{2} + 8 \, a b^{2} c^{2} + b^{3} c^{2} - 4 \, a b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| c \right|} + {\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 - 4 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + b^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{b c^{3} + \sqrt{b^{2} c^{6} - 4 \, a c^{7}}}{2 \, c^{4}}\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^{2} {\left| c \right|}} - \frac{{\left({\left(b^{6} - 8 \, a b^{4} c - 2 \, b^{5} c + 16 \, a^{2} b^{2} c^{2} + 8 \, a b^{3} c^{2} + b^{4} c^{2} - 4 \, a b^{2} c^{3} + {\left(b^{5} - 8 \, a b^{3} c - 2 \, b^{4} c + 16 \, a^{2} b c^{2} + 8 \, a b^{2} c^{2} + b^{3} c^{2} - 4 \, a b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| c \right|} + {\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 - 4 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + b^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{b c^{3} - \sqrt{b^{2} c^{6} - 4 \, a c^{7}}}{2 \, c^{4}}\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^{2} {\left| c \right|}}"," ",0,"C*x/c + 1/4*B*log(abs(c*x^4 + b*x^2 + a))/c + 1/8*((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*(b^2 - 4*a*c)*b^2*c^3 + 8*(b^2 - 4*a*c)*a*c^4)*A*c^2 - (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*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*C*c^2 - 2*(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*(b^2 - 4*a*c)*a*b^2*c^3 + 8*(b^2 - 4*a*c)*a^2*c^4)*C*abs(c) - (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*(b^2 - 4*a*c)*b^2*c^5)*A + (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*(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*a*b*c^5)*C)*arctan(2*sqrt(1/2)*x/sqrt((b*c^3 + sqrt(b^2*c^6 - 4*a*c^7))/c^4))/((a*b^4*c^3 - 8*a^2*b^2*c^4 - 2*a*b^3*c^4 + 16*a^3*c^5 + 8*a^2*b*c^5 + a*b^2*c^5 - 4*a^2*c^6)*c^2) - 1/8*((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*(b^2 - 4*a*c)*b^2*c^3 + 8*(b^2 - 4*a*c)*a*c^4)*A*c^2 - (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*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*C*c^2 + 2*(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*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*C*abs(c) - (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*(b^2 - 4*a*c)*b^2*c^5)*A + (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*(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*a*b*c^5)*C)*arctan(2*sqrt(1/2)*x/sqrt((b*c^3 - sqrt(b^2*c^6 - 4*a*c^7))/c^4))/((a*b^4*c^3 - 8*a^2*b^2*c^4 - 2*a*b^3*c^4 + 16*a^3*c^5 + 8*a^2*b*c^5 + a*b^2*c^5 - 4*a^2*c^6)*c^2) - 1/16*((b^6 - 8*a*b^4*c - 2*b^5*c + 16*a^2*b^2*c^2 + 8*a*b^3*c^2 + b^4*c^2 - 4*a*b^2*c^3 - (b^5 - 8*a*b^3*c - 2*b^4*c + 16*a^2*b*c^2 + 8*a*b^2*c^2 + b^3*c^2 - 4*a*b*c^3)*sqrt(b^2 - 4*a*c))*B*abs(c) + (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 - (b^5*c - 4*a*b^3*c^2 - 2*b^4*c^2 + b^3*c^3)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(b*c^3 + sqrt(b^2*c^6 - 4*a*c^7))/c^4)/((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)*c^2*abs(c)) - 1/16*((b^6 - 8*a*b^4*c - 2*b^5*c + 16*a^2*b^2*c^2 + 8*a*b^3*c^2 + b^4*c^2 - 4*a*b^2*c^3 + (b^5 - 8*a*b^3*c - 2*b^4*c + 16*a^2*b*c^2 + 8*a*b^2*c^2 + b^3*c^2 - 4*a*b*c^3)*sqrt(b^2 - 4*a*c))*B*abs(c) + (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 + (b^5*c - 4*a*b^3*c^2 - 2*b^4*c^2 + b^3*c^3)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(b*c^3 - sqrt(b^2*c^6 - 4*a*c^7))/c^4)/((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)*c^2*abs(c))","B",0
24,1,2369,0,5.358848," ","integrate(x*(C*x^2+B*x+A)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{C \log\left({\left| c x^{4} + b x^{2} + a \right|}\right)}{4 \, c} + \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)} B c^{2} - {\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)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c + \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{c^{2}}}}\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^{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)} B c^{2} - {\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)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c - \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{c^{2}}}}\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(2 \, {\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} - {\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)} \sqrt{b^{2} - 4 \, a c}\right)} A {\left| c \right|} - {\left(b^{6} - 8 \, a b^{4} c - 2 \, b^{5} c + 16 \, a^{2} b^{2} c^{2} + 8 \, a b^{3} c^{2} + b^{4} c^{2} - 4 \, a b^{2} c^{3} - {\left(b^{5} - 8 \, a b^{3} c - 2 \, b^{4} c + 16 \, a^{2} b c^{2} + 8 \, a b^{2} c^{2} + b^{3} c^{2} - 4 \, a b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C {\left| c \right|} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} - 2 \, b^{4} c^{3} + 16 \, a^{2} b c^{4} + 8 \, a b^{2} c^{4} + b^{3} c^{4} - 4 \, a b c^{5} + {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} - 2 \, b^{3} c^{3} + b^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A - {\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 - 4 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + b^{3} c^{3}\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^{2} {\left| c \right|}} + \frac{{\left(2 \, {\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} + {\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)} \sqrt{b^{2} - 4 \, a c}\right)} A {\left| c \right|} - {\left(b^{6} - 8 \, a b^{4} c - 2 \, b^{5} c + 16 \, a^{2} b^{2} c^{2} + 8 \, a b^{3} c^{2} + b^{4} c^{2} - 4 \, a b^{2} c^{3} + {\left(b^{5} - 8 \, a b^{3} c - 2 \, b^{4} c + 16 \, a^{2} b c^{2} + 8 \, a b^{2} c^{2} + b^{3} c^{2} - 4 \, a b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C {\left| c \right|} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} - 2 \, b^{4} c^{3} + 16 \, a^{2} b c^{4} + 8 \, a b^{2} c^{4} + b^{3} c^{4} - 4 \, a b c^{5} + {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} - 2 \, b^{3} c^{3} + b^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A - {\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 - 4 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + b^{3} c^{3}\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^{2} {\left| c \right|}}"," ",0,"1/4*C*log(abs(c*x^4 + b*x^2 + a))/c + 1/8*((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*(b^2 - 4*a*c)*b^2*c^2 + 8*(b^2 - 4*a*c)*a*c^3)*B*c^2 - (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*(b^2 - 4*a*c)*b^2*c^4)*B)*arctan(2*sqrt(1/2)*x/sqrt((b*c + sqrt(b^2*c^2 - 4*a*c^3))/c^2))/((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)*c^2) - 1/8*((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*(b^2 - 4*a*c)*b^2*c^2 + 8*(b^2 - 4*a*c)*a*c^3)*B*c^2 - (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*(b^2 - 4*a*c)*b^2*c^4)*B)*arctan(2*sqrt(1/2)*x/sqrt((b*c - sqrt(b^2*c^2 - 4*a*c^3))/c^2))/((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)*c^2) + 1/16*(2*(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 - (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)*sqrt(b^2 - 4*a*c))*A*abs(c) - (b^6 - 8*a*b^4*c - 2*b^5*c + 16*a^2*b^2*c^2 + 8*a*b^3*c^2 + b^4*c^2 - 4*a*b^2*c^3 - (b^5 - 8*a*b^3*c - 2*b^4*c + 16*a^2*b*c^2 + 8*a*b^2*c^2 + b^3*c^2 - 4*a*b*c^3)*sqrt(b^2 - 4*a*c))*C*abs(c) + 2*(b^5*c^2 - 8*a*b^3*c^3 - 2*b^4*c^3 + 16*a^2*b*c^4 + 8*a*b^2*c^4 + b^3*c^4 - 4*a*b*c^5 + (b^4*c^2 - 4*a*b^2*c^3 - 2*b^3*c^3 + b^2*c^4)*sqrt(b^2 - 4*a*c))*A - (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 - (b^5*c - 4*a*b^3*c^2 - 2*b^4*c^2 + b^3*c^3)*sqrt(b^2 - 4*a*c))*C)*log(x^2 + 1/2*(b*c + sqrt(b^2*c^2 - 4*a*c^3))/c^2)/((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)*c^2*abs(c)) + 1/16*(2*(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 + (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)*sqrt(b^2 - 4*a*c))*A*abs(c) - (b^6 - 8*a*b^4*c - 2*b^5*c + 16*a^2*b^2*c^2 + 8*a*b^3*c^2 + b^4*c^2 - 4*a*b^2*c^3 + (b^5 - 8*a*b^3*c - 2*b^4*c + 16*a^2*b*c^2 + 8*a*b^2*c^2 + b^3*c^2 - 4*a*b*c^3)*sqrt(b^2 - 4*a*c))*C*abs(c) + 2*(b^5*c^2 - 8*a*b^3*c^3 - 2*b^4*c^3 + 16*a^2*b*c^4 + 8*a*b^2*c^4 + b^3*c^4 - 4*a*b*c^5 + (b^4*c^2 - 4*a*b^2*c^3 - 2*b^3*c^3 + b^2*c^4)*sqrt(b^2 - 4*a*c))*A - (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 + (b^5*c - 4*a*b^3*c^2 - 2*b^4*c^2 + b^3*c^3)*sqrt(b^2 - 4*a*c))*C)*log(x^2 + 1/2*(b*c - sqrt(b^2*c^2 - 4*a*c^3))/c^2)/((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)*c^2*abs(c))","B",0
25,1,1616,0,4.372346," ","integrate((C*x^2+B*x+A)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(b^{2} c^{2} - 4 \, a c^{3} - 2 \, b c^{3} + c^{4}\right)} \sqrt{b^{2} - 4 \, a c} B \log\left(x^{2} + \frac{b + \sqrt{b^{2} - 4 \, a c}}{2 \, 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^{2}} + \frac{{\left(b^{2} c^{2} - 4 \, a c^{3} - 2 \, b c^{3} + c^{4}\right)} \sqrt{b^{2} - 4 \, a c} B \log\left(x^{2} + \frac{b - \sqrt{b^{2} - 4 \, a c}}{2 \, 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^{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} - 2 \, 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} + 8 \, a b c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} - 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 + \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} + 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} A + 2 \, {\left(2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{2}\right)} C\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)} {\left| c \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} - 2 \, 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} + 8 \, a b c^{3} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} - 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 + \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} + 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} A + 2 \, {\left(2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{2}\right)} C\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)} {\left| c \right|}}"," ",0,"-1/2*(b^2*c^2 - 4*a*c^3 - 2*b*c^3 + c^4)*sqrt(b^2 - 4*a*c)*B*log(x^2 + 1/2*(b + sqrt(b^2 - 4*a*c))/c)/((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)*c^2) + 1/2*(b^2*c^2 - 4*a*c^3 - 2*b*c^3 + c^4)*sqrt(b^2 - 4*a*c)*B*log(x^2 + 1/2*(b - sqrt(b^2 - 4*a*c))/c)/((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)*c^2) + 1/4*((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 - 2*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 + 8*a*b*c^3 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 - 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 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 + 2*(b^2 - 4*a*c)*b^2*c - 8*(b^2 - 4*a*c)*a*c^2 + 2*(b^2 - 4*a*c)*b*c^2)*A + 2*(2*a*b^2*c^2 - 8*a^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^2 - 2*(b^2 - 4*a*c)*a*c^2)*C)*arctan(2*sqrt(1/2)*x/sqrt((b + sqrt(b^2 - 4*a*c))/c))/((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)*abs(c)) + 1/4*((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 - 2*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 + 8*a*b*c^3 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 - 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 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b^2*c + 8*(b^2 - 4*a*c)*a*c^2 + 2*(b^2 - 4*a*c)*b*c^2)*A + 2*(2*a*b^2*c^2 - 8*a^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^2 - 2*(b^2 - 4*a*c)*a*c^2)*C)*arctan(2*sqrt(1/2)*x/sqrt((b - sqrt(b^2 - 4*a*c))/c))/((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)*abs(c))","B",0
26,1,2336,0,5.075364," ","integrate((C*x^2+B*x+A)/x/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{A \log\left({\left| c x^{4} + b x^{2} + a \right|}\right)}{4 \, a} + \frac{A \log\left({\left| x \right|}\right)}{a} + \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 {\left| c \right|} + {\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}} x}{\sqrt{\frac{a^{2} b c + \sqrt{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}{a^{2} c^{2}}}}\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}} + \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 {\left| c \right|} - {\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}} x}{\sqrt{\frac{a^{2} b c - \sqrt{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}{a^{2} c^{2}}}}\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}} - \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 {\left| c \right|} - 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 {\left| c \right|} + {\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{a^{2} b c + \sqrt{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}{2 \, a^{2} c^{2}}\right)}{16 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c - 2 \, a^{2} b^{3} c + 16 \, a^{4} c^{2} + 8 \, a^{3} b c^{2} + a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} c^{2} {\left| c \right|}} - \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 {\left| c \right|} - 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 {\left| c \right|} + {\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{a^{2} b c - \sqrt{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}{2 \, a^{2} c^{2}}\right)}{16 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c - 2 \, a^{2} b^{3} c + 16 \, a^{4} c^{2} + 8 \, a^{3} b c^{2} + a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} c^{2} {\left| c \right|}}"," ",0,"-1/4*A*log(abs(c*x^4 + b*x^2 + a))/a + A*log(abs(x))/a + 1/4*((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*(b^2 - 4*a*c)*b^2*c + 8*(b^2 - 4*a*c)*a*c^2)*B*abs(c) + (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*(b^2 - 4*a*c)*b*c^3)*B)*arctan(2*sqrt(1/2)*x/sqrt((a^2*b*c + sqrt(a^4*b^2*c^2 - 4*a^5*c^3))/(a^2*c^2)))/((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)*c^2) + 1/4*((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*(b^2 - 4*a*c)*b^2*c - 8*(b^2 - 4*a*c)*a*c^2)*B*abs(c) - (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*(b^2 - 4*a*c)*b*c^3)*B)*arctan(2*sqrt(1/2)*x/sqrt((a^2*b*c - sqrt(a^4*b^2*c^2 - 4*a^5*c^3))/(a^2*c^2)))/((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)*c^2) - 1/16*((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 - (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)*sqrt(b^2 - 4*a*c))*A*abs(c) - 2*(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 - (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)*sqrt(b^2 - 4*a*c))*C*abs(c) + (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 + (b^5*c^2 - 4*a*b^3*c^3 - 2*b^4*c^3 + b^3*c^4)*sqrt(b^2 - 4*a*c))*A - 2*(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 - (a*b^4*c^2 - 4*a^2*b^2*c^3 - 2*a*b^3*c^3 + a*b^2*c^4)*sqrt(b^2 - 4*a*c))*C)*log(x^2 + 1/2*(a^2*b*c + sqrt(a^4*b^2*c^2 - 4*a^5*c^3))/(a^2*c^2))/((a^2*b^4 - 8*a^3*b^2*c - 2*a^2*b^3*c + 16*a^4*c^2 + 8*a^3*b*c^2 + a^2*b^2*c^2 - 4*a^3*c^3)*c^2*abs(c)) - 1/16*((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 + (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)*sqrt(b^2 - 4*a*c))*A*abs(c) - 2*(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 + (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)*sqrt(b^2 - 4*a*c))*C*abs(c) + (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 + (b^5*c^2 - 4*a*b^3*c^3 - 2*b^4*c^3 + b^3*c^4)*sqrt(b^2 - 4*a*c))*A - 2*(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 + (a*b^4*c^2 - 4*a^2*b^2*c^3 - 2*a*b^3*c^3 + a*b^2*c^4)*sqrt(b^2 - 4*a*c))*C)*log(x^2 + 1/2*(a^2*b*c - sqrt(a^4*b^2*c^2 - 4*a^5*c^3))/(a^2*c^2))/((a^2*b^4 - 8*a^3*b^2*c - 2*a^2*b^3*c + 16*a^4*c^2 + 8*a^3*b*c^2 + a^2*b^2*c^2 - 4*a^3*c^3)*c^2*abs(c))","B",0
27,1,3507,0,5.392890," ","integrate((C*x^2+B*x+A)/x^2/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{B \log\left({\left| c x^{4} + b x^{2} + a \right|}\right)}{4 \, a} + \frac{B \log\left({\left| x \right|}\right)}{a} - \frac{A}{a x} - \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 {\left| c \right|} - 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 {\left| c \right|} + {\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}} x}{\sqrt{\frac{a^{2} b c + \sqrt{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}{a^{2} c^{2}}}}\right)}{8 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} - 2 \, a^{2} b^{3} c^{2} + 16 \, a^{4} c^{3} + 8 \, a^{3} b c^{3} + a^{2} b^{2} c^{3} - 4 \, a^{3} 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 {\left| c \right|} + 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 {\left| c \right|} + {\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}} x}{\sqrt{\frac{a^{2} b c - \sqrt{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}{a^{2} c^{2}}}}\right)}{8 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} - 2 \, a^{2} b^{3} c^{2} + 16 \, a^{4} c^{3} + 8 \, a^{3} b c^{3} + a^{2} b^{2} c^{3} - 4 \, a^{3} 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 {\left| c \right|} + {\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{a^{2} b c + \sqrt{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}{2 \, a^{2} c^{2}}\right)}{16 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c - 2 \, a^{2} b^{3} c + 16 \, a^{4} c^{2} + 8 \, a^{3} b c^{2} + a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} c^{2} {\left| c \right|}} - \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 {\left| c \right|} + {\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{a^{2} b c - \sqrt{a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}}}{2 \, a^{2} c^{2}}\right)}{16 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c - 2 \, a^{2} b^{3} c + 16 \, a^{4} c^{2} + 8 \, a^{3} b c^{2} + a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} c^{2} {\left| c \right|}}"," ",0,"-1/4*B*log(abs(c*x^4 + b*x^2 + a))/a + B*log(abs(x))/a - A/(a*x) - 1/8*((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*(b^2 - 4*a*c)*b^2*c^2 + 8*(b^2 - 4*a*c)*a*c^3)*A*c^2 + 2*(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*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*A*abs(c) - 2*(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*(b^2 - 4*a*c)*a*b^2*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3)*C*abs(c) + (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*(b^2 - 4*a*c)*b^2*c^4)*A - 2*(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*(b^2 - 4*a*c)*a*b*c^4)*C)*arctan(2*sqrt(1/2)*x/sqrt((a^2*b*c + sqrt(a^4*b^2*c^2 - 4*a^5*c^3))/(a^2*c^2)))/((a^2*b^4*c - 8*a^3*b^2*c^2 - 2*a^2*b^3*c^2 + 16*a^4*c^3 + 8*a^3*b*c^3 + a^2*b^2*c^3 - 4*a^3*c^4)*c^2) + 1/8*((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*(b^2 - 4*a*c)*b^2*c^2 + 8*(b^2 - 4*a*c)*a*c^3)*A*c^2 - 2*(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*(b^2 - 4*a*c)*b^3*c^2 - 8*(b^2 - 4*a*c)*a*b*c^3)*A*abs(c) + 2*(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*(b^2 - 4*a*c)*a*b^2*c^2 - 8*(b^2 - 4*a*c)*a^2*c^3)*C*abs(c) + (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*(b^2 - 4*a*c)*b^2*c^4)*A - 2*(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*(b^2 - 4*a*c)*a*b*c^4)*C)*arctan(2*sqrt(1/2)*x/sqrt((a^2*b*c - sqrt(a^4*b^2*c^2 - 4*a^5*c^3))/(a^2*c^2)))/((a^2*b^4*c - 8*a^3*b^2*c^2 - 2*a^2*b^3*c^2 + 16*a^4*c^3 + 8*a^3*b*c^3 + a^2*b^2*c^3 - 4*a^3*c^4)*c^2) - 1/16*((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 - (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)*sqrt(b^2 - 4*a*c))*B*abs(c) + (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 - (b^5*c^2 - 4*a*b^3*c^3 - 2*b^4*c^3 + b^3*c^4)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(a^2*b*c + sqrt(a^4*b^2*c^2 - 4*a^5*c^3))/(a^2*c^2))/((a^2*b^4 - 8*a^3*b^2*c - 2*a^2*b^3*c + 16*a^4*c^2 + 8*a^3*b*c^2 + a^2*b^2*c^2 - 4*a^3*c^3)*c^2*abs(c)) - 1/16*((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 + (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)*sqrt(b^2 - 4*a*c))*B*abs(c) + (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 + (b^5*c^2 - 4*a*b^3*c^3 - 2*b^4*c^3 + b^3*c^4)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(a^2*b*c - sqrt(a^4*b^2*c^2 - 4*a^5*c^3))/(a^2*c^2))/((a^2*b^4 - 8*a^3*b^2*c - 2*a^2*b^3*c + 16*a^4*c^2 + 8*a^3*b*c^2 + a^2*b^2*c^2 - 4*a^3*c^3)*c^2*abs(c))","B",0
28,1,3353,0,5.871984," ","integrate((C*x^2+B*x+A)/x^3/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(C a - A b\right)} \log\left({\left| c x^{4} + b x^{2} + a \right|}\right)}{4 \, a^{2}} + \frac{{\left(C a - A b\right)} \log\left({\left| x \right|}\right)}{a^{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)} B 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)} B {\left| c \right|} + {\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)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{4} b c + \sqrt{a^{8} b^{2} c^{2} - 4 \, a^{9} c^{3}}}{a^{4} c^{2}}}}\right)}{8 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} - 2 \, a^{2} b^{3} c^{2} + 16 \, a^{4} c^{3} + 8 \, a^{3} b c^{3} + a^{2} b^{2} c^{3} - 4 \, a^{3} 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)} B 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)} B {\left| c \right|} + {\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)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{4} b c - \sqrt{a^{8} b^{2} c^{2} - 4 \, a^{9} c^{3}}}{a^{4} c^{2}}}}\right)}{8 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} - 2 \, a^{2} b^{3} c^{2} + 16 \, a^{4} c^{3} + 8 \, a^{3} b c^{3} + a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\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)} A {\left| c \right|} - {\left(a b^{6} c - 8 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 16 \, a^{3} b^{2} c^{3} + 8 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 4 \, a^{2} b^{2} c^{4} - {\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}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C {\left| c \right|} + {\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)} A - {\left(a b^{6} c^{2} - 8 \, a^{2} b^{4} c^{3} - 2 \, a b^{5} c^{3} + 16 \, a^{3} b^{2} c^{4} + 8 \, a^{2} b^{3} c^{4} + a b^{4} c^{4} - 4 \, a^{2} b^{2} c^{5} - {\left(a b^{5} c^{2} - 4 \, a^{2} b^{3} c^{3} - 2 \, a b^{4} c^{3} + a b^{3} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C\right)} \log\left(x^{2} + \frac{a^{4} b c + \sqrt{a^{8} b^{2} c^{2} - 4 \, a^{9} c^{3}}}{2 \, a^{4} c^{2}}\right)}{16 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c - 2 \, a^{3} b^{3} c + 16 \, a^{5} c^{2} + 8 \, a^{4} b c^{2} + a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} c^{2} {\left| c \right|}} + \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)} A {\left| c \right|} - {\left(a b^{6} c - 8 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 16 \, a^{3} b^{2} c^{3} + 8 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 4 \, a^{2} b^{2} c^{4} + {\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}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C {\left| c \right|} - {\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)} A + {\left(a b^{6} c^{2} - 8 \, a^{2} b^{4} c^{3} - 2 \, a b^{5} c^{3} + 16 \, a^{3} b^{2} c^{4} + 8 \, a^{2} b^{3} c^{4} + a b^{4} c^{4} - 4 \, a^{2} b^{2} c^{5} + {\left(a b^{5} c^{2} - 4 \, a^{2} b^{3} c^{3} - 2 \, a b^{4} c^{3} + a b^{3} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C\right)} \log\left(x^{2} + \frac{a^{4} b c - \sqrt{a^{8} b^{2} c^{2} - 4 \, a^{9} c^{3}}}{2 \, a^{4} c^{2}}\right)}{16 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c - 2 \, a^{3} b^{3} c + 16 \, a^{5} c^{2} + 8 \, a^{4} b c^{2} + a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} c^{2} {\left| c \right|}} - \frac{2 \, B a x + A a}{2 \, a^{2} x^{2}}"," ",0,"-1/4*(C*a - A*b)*log(abs(c*x^4 + b*x^2 + a))/a^2 + (C*a - A*b)*log(abs(x))/a^2 - 1/8*((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*(b^2 - 4*a*c)*b^2*c^2 + 8*(b^2 - 4*a*c)*a*c^3)*B*c^2 + 2*(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*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*B*abs(c) + (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*(b^2 - 4*a*c)*b^2*c^4)*B)*arctan(2*sqrt(1/2)*x/sqrt((a^4*b*c + sqrt(a^8*b^2*c^2 - 4*a^9*c^3))/(a^4*c^2)))/((a^2*b^4*c - 8*a^3*b^2*c^2 - 2*a^2*b^3*c^2 + 16*a^4*c^3 + 8*a^3*b*c^3 + a^2*b^2*c^3 - 4*a^3*c^4)*c^2) + 1/8*((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*(b^2 - 4*a*c)*b^2*c^2 + 8*(b^2 - 4*a*c)*a*c^3)*B*c^2 - 2*(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*(b^2 - 4*a*c)*b^3*c^2 - 8*(b^2 - 4*a*c)*a*b*c^3)*B*abs(c) + (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*(b^2 - 4*a*c)*b^2*c^4)*B)*arctan(2*sqrt(1/2)*x/sqrt((a^4*b*c - sqrt(a^8*b^2*c^2 - 4*a^9*c^3))/(a^4*c^2)))/((a^2*b^4*c - 8*a^3*b^2*c^2 - 2*a^2*b^3*c^2 + 16*a^4*c^3 + 8*a^3*b*c^3 + a^2*b^2*c^3 - 4*a^3*c^4)*c^2) + 1/16*((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 - (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)*sqrt(b^2 - 4*a*c))*A*abs(c) - (a*b^6*c - 8*a^2*b^4*c^2 - 2*a*b^5*c^2 + 16*a^3*b^2*c^3 + 8*a^2*b^3*c^3 + a*b^4*c^3 - 4*a^2*b^2*c^4 - (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)*sqrt(b^2 - 4*a*c))*C*abs(c) + (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 + (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)*sqrt(b^2 - 4*a*c))*A - (a*b^6*c^2 - 8*a^2*b^4*c^3 - 2*a*b^5*c^3 + 16*a^3*b^2*c^4 + 8*a^2*b^3*c^4 + a*b^4*c^4 - 4*a^2*b^2*c^5 - (a*b^5*c^2 - 4*a^2*b^3*c^3 - 2*a*b^4*c^3 + a*b^3*c^4)*sqrt(b^2 - 4*a*c))*C)*log(x^2 + 1/2*(a^4*b*c + sqrt(a^8*b^2*c^2 - 4*a^9*c^3))/(a^4*c^2))/((a^3*b^4 - 8*a^4*b^2*c - 2*a^3*b^3*c + 16*a^5*c^2 + 8*a^4*b*c^2 + a^3*b^2*c^2 - 4*a^4*c^3)*c^2*abs(c)) + 1/16*((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 + (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)*sqrt(b^2 - 4*a*c))*A*abs(c) - (a*b^6*c - 8*a^2*b^4*c^2 - 2*a*b^5*c^2 + 16*a^3*b^2*c^3 + 8*a^2*b^3*c^3 + a*b^4*c^3 - 4*a^2*b^2*c^4 + (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)*sqrt(b^2 - 4*a*c))*C*abs(c) - (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 + (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)*sqrt(b^2 - 4*a*c))*A + (a*b^6*c^2 - 8*a^2*b^4*c^3 - 2*a*b^5*c^3 + 16*a^3*b^2*c^4 + 8*a^2*b^3*c^4 + a*b^4*c^4 - 4*a^2*b^2*c^5 + (a*b^5*c^2 - 4*a^2*b^3*c^3 - 2*a*b^4*c^3 + a*b^3*c^4)*sqrt(b^2 - 4*a*c))*C)*log(x^2 + 1/2*(a^4*b*c - sqrt(a^8*b^2*c^2 - 4*a^9*c^3))/(a^4*c^2))/((a^3*b^4 - 8*a^4*b^2*c - 2*a^3*b^3*c + 16*a^5*c^2 + 8*a^4*b*c^2 + a^3*b^2*c^2 - 4*a^4*c^3)*c^2*abs(c)) - 1/2*(2*B*a*x + A*a)/(a^2*x^2)","B",0
29,1,5219,0,8.470970," ","integrate(x^4*(C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{C b^{2} x^{3} - 2 \, C a c x^{3} - A b c x^{3} + B b^{2} x^{2} - 2 \, B a c x^{2} + C a b x - 2 \, A a c x + B a b}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}} + \frac{{\left({\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)} {\left(b^{2} c - 4 \, a c^{2}\right)}^{2} A + {\left(2 \, b^{4} c^{2} - 20 \, a b^{2} c^{3} + 48 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} + 10 \, \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 - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 12 \, \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} + 6 \, \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} + 12 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}^{2} C - 4 \, {\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 {\left| b^{2} c - 4 \, a c^{2} \right|} + 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 {\left| b^{2} c - 4 \, a c^{2} \right|} - {\left(2 \, b^{7} c^{5} - 8 \, a b^{5} c^{6} - 32 \, a^{2} b^{3} c^{7} + 128 \, a^{3} b c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{4} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{5} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{5} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{7}\right)} A - {\left(2 \, b^{8} c^{4} - 32 \, a b^{6} c^{5} + 160 \, a^{2} b^{4} c^{6} - 256 \, a^{3} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{4} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{4} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{5} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{6}\right)} C\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} c - 4 \, a b c^{2} + \sqrt{{\left(b^{3} c - 4 \, a b c^{2}\right)}^{2} - 4 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}}{b^{2} c^{2} - 4 \, a c^{3}}}}\right)}{16 \, {\left(a b^{6} c^{3} - 12 \, a^{2} b^{4} c^{4} - 2 \, a b^{5} c^{4} + 48 \, a^{3} b^{2} c^{5} + 16 \, a^{2} b^{3} c^{5} + a b^{4} c^{5} - 64 \, a^{4} c^{6} - 32 \, a^{3} b c^{6} - 8 \, a^{2} b^{2} c^{6} + 16 \, a^{3} c^{7}\right)} {\left| b^{2} c - 4 \, a c^{2} \right|} {\left| c \right|}} - \frac{{\left({\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)} {\left(b^{2} c - 4 \, a c^{2}\right)}^{2} A + {\left(2 \, b^{4} c^{2} - 20 \, a b^{2} c^{3} + 48 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} + 10 \, \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 - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 12 \, \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} + 6 \, \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} + 12 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}^{2} C + 4 \, {\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 {\left| b^{2} c - 4 \, a c^{2} \right|} - 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 {\left| b^{2} c - 4 \, a c^{2} \right|} - {\left(2 \, b^{7} c^{5} - 8 \, a b^{5} c^{6} - 32 \, a^{2} b^{3} c^{7} + 128 \, a^{3} b c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{4} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{5} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{5} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{7}\right)} A - {\left(2 \, b^{8} c^{4} - 32 \, a b^{6} c^{5} + 160 \, a^{2} b^{4} c^{6} - 256 \, a^{3} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{4} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{4} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{5} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{6}\right)} C\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} c - 4 \, a b c^{2} - \sqrt{{\left(b^{3} c - 4 \, a b c^{2}\right)}^{2} - 4 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}}{b^{2} c^{2} - 4 \, a c^{3}}}}\right)}{16 \, {\left(a b^{6} c^{3} - 12 \, a^{2} b^{4} c^{4} - 2 \, a b^{5} c^{4} + 48 \, a^{3} b^{2} c^{5} + 16 \, a^{2} b^{3} c^{5} + a b^{4} c^{5} - 64 \, a^{4} c^{6} - 32 \, a^{3} b c^{6} - 8 \, a^{2} b^{2} c^{6} + 16 \, a^{3} c^{7}\right)} {\left| b^{2} c - 4 \, a c^{2} \right|} {\left| c \right|}} - \frac{{\left({\left(b^{3} c - 4 \, a b c^{2} - 2 \, b^{2} c^{2} + b c^{3} + {\left(b^{2} c - 4 \, a c^{2} - 2 \, b c^{2} + c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| b^{2} c - 4 \, a c^{2} \right|} + {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} - 2 \, b^{4} c^{3} + 16 \, a^{2} b c^{4} + 8 \, a b^{2} c^{4} + b^{3} c^{4} - 4 \, a b c^{5} + {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} - 2 \, b^{3} c^{3} + b^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{b^{3} c - 4 \, a b c^{2} + \sqrt{{\left(b^{3} c - 4 \, a b c^{2}\right)}^{2} - 4 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}\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 - 4 \, a c^{2} \right|}} - \frac{{\left({\left(b^{3} c - 4 \, a b c^{2} - 2 \, b^{2} c^{2} + b c^{3} - {\left(b^{2} c - 4 \, a c^{2} - 2 \, b c^{2} + c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| b^{2} c - 4 \, a c^{2} \right|} - {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} - 2 \, b^{4} c^{3} + 16 \, a^{2} b c^{4} + 8 \, a b^{2} c^{4} + b^{3} c^{4} - 4 \, a b c^{5} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} - 2 \, b^{3} c^{3} + b^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{b^{3} c - 4 \, a b c^{2} - \sqrt{{\left(b^{3} c - 4 \, a b c^{2}\right)}^{2} - 4 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}\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 - 4 \, a c^{2} \right|}}"," ",0,"-1/2*(C*b^2*x^3 - 2*C*a*c*x^3 - A*b*c*x^3 + B*b^2*x^2 - 2*B*a*c*x^2 + C*a*b*x - 2*A*a*c*x + B*a*b)/((c*x^4 + b*x^2 + a)*(b^2*c - 4*a*c^2)) + 1/16*((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*(b^2 - 4*a*c)*b*c^3)*(b^2*c - 4*a*c^2)^2*A + (2*b^4*c^2 - 20*a*b^2*c^3 + 48*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 + 10*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 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 12*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 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^2*c^2 + 12*(b^2 - 4*a*c)*a*c^3)*(b^2*c - 4*a*c^2)^2*C - 4*(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*(b^2 - 4*a*c)*a*b^2*c^4 - 8*(b^2 - 4*a*c)*a^2*c^5)*A*abs(b^2*c - 4*a*c^2) + 2*(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*(b^2 - 4*a*c)*a*b^3*c^3 - 8*(b^2 - 4*a*c)*a^2*b*c^4)*C*abs(b^2*c - 4*a*c^2) - (2*b^7*c^5 - 8*a*b^5*c^6 - 32*a^2*b^3*c^7 + 128*a^3*b*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^4 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^5 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 - 2*(b^2 - 4*a*c)*b^5*c^5 + 32*(b^2 - 4*a*c)*a^2*b*c^7)*A - (2*b^8*c^4 - 32*a*b^6*c^5 + 160*a^2*b^4*c^6 - 256*a^3*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^3 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^4 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 2*(b^2 - 4*a*c)*b^6*c^4 + 24*(b^2 - 4*a*c)*a*b^4*c^5 - 64*(b^2 - 4*a*c)*a^2*b^2*c^6)*C)*arctan(2*sqrt(1/2)*x/sqrt((b^3*c - 4*a*b*c^2 + sqrt((b^3*c - 4*a*b*c^2)^2 - 4*(a*b^2*c - 4*a^2*c^2)*(b^2*c^2 - 4*a*c^3)))/(b^2*c^2 - 4*a*c^3)))/((a*b^6*c^3 - 12*a^2*b^4*c^4 - 2*a*b^5*c^4 + 48*a^3*b^2*c^5 + 16*a^2*b^3*c^5 + a*b^4*c^5 - 64*a^4*c^6 - 32*a^3*b*c^6 - 8*a^2*b^2*c^6 + 16*a^3*c^7)*abs(b^2*c - 4*a*c^2)*abs(c)) - 1/16*((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*(b^2 - 4*a*c)*b*c^3)*(b^2*c - 4*a*c^2)^2*A + (2*b^4*c^2 - 20*a*b^2*c^3 + 48*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 + 10*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 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 12*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 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^2*c^2 + 12*(b^2 - 4*a*c)*a*c^3)*(b^2*c - 4*a*c^2)^2*C + 4*(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*(b^2 - 4*a*c)*a*b^2*c^4 + 8*(b^2 - 4*a*c)*a^2*c^5)*A*abs(b^2*c - 4*a*c^2) - 2*(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*(b^2 - 4*a*c)*a*b^3*c^3 + 8*(b^2 - 4*a*c)*a^2*b*c^4)*C*abs(b^2*c - 4*a*c^2) - (2*b^7*c^5 - 8*a*b^5*c^6 - 32*a^2*b^3*c^7 + 128*a^3*b*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^4 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^5 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 - 2*(b^2 - 4*a*c)*b^5*c^5 + 32*(b^2 - 4*a*c)*a^2*b*c^7)*A - (2*b^8*c^4 - 32*a*b^6*c^5 + 160*a^2*b^4*c^6 - 256*a^3*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^3 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^4 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 2*(b^2 - 4*a*c)*b^6*c^4 + 24*(b^2 - 4*a*c)*a*b^4*c^5 - 64*(b^2 - 4*a*c)*a^2*b^2*c^6)*C)*arctan(2*sqrt(1/2)*x/sqrt((b^3*c - 4*a*b*c^2 - sqrt((b^3*c - 4*a*b*c^2)^2 - 4*(a*b^2*c - 4*a^2*c^2)*(b^2*c^2 - 4*a*c^3)))/(b^2*c^2 - 4*a*c^3)))/((a*b^6*c^3 - 12*a^2*b^4*c^4 - 2*a*b^5*c^4 + 48*a^3*b^2*c^5 + 16*a^2*b^3*c^5 + a*b^4*c^5 - 64*a^4*c^6 - 32*a^3*b*c^6 - 8*a^2*b^2*c^6 + 16*a^3*c^7)*abs(b^2*c - 4*a*c^2)*abs(c)) - 1/4*((b^3*c - 4*a*b*c^2 - 2*b^2*c^2 + b*c^3 + (b^2*c - 4*a*c^2 - 2*b*c^2 + c^3)*sqrt(b^2 - 4*a*c))*B*abs(b^2*c - 4*a*c^2) + (b^5*c^2 - 8*a*b^3*c^3 - 2*b^4*c^3 + 16*a^2*b*c^4 + 8*a*b^2*c^4 + b^3*c^4 - 4*a*b*c^5 + (b^4*c^2 - 4*a*b^2*c^3 - 2*b^3*c^3 + b^2*c^4)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(b^3*c - 4*a*b*c^2 + sqrt((b^3*c - 4*a*b*c^2)^2 - 4*(a*b^2*c - 4*a^2*c^2)*(b^2*c^2 - 4*a*c^3)))/(b^2*c^2 - 4*a*c^3))/((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)*c^2*abs(b^2*c - 4*a*c^2)) - 1/4*((b^3*c - 4*a*b*c^2 - 2*b^2*c^2 + b*c^3 - (b^2*c - 4*a*c^2 - 2*b*c^2 + c^3)*sqrt(b^2 - 4*a*c))*B*abs(b^2*c - 4*a*c^2) - (b^5*c^2 - 8*a*b^3*c^3 - 2*b^4*c^3 + 16*a^2*b*c^4 + 8*a*b^2*c^4 + b^3*c^4 - 4*a*b*c^5 - (b^4*c^2 - 4*a*b^2*c^3 - 2*b^3*c^3 + b^2*c^4)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(b^3*c - 4*a*b*c^2 - sqrt((b^3*c - 4*a*b*c^2)^2 - 4*(a*b^2*c - 4*a^2*c^2)*(b^2*c^2 - 4*a*c^3)))/(b^2*c^2 - 4*a*c^3))/((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)*c^2*abs(b^2*c - 4*a*c^2))","B",0
30,1,3228,0,5.368843," ","integrate(x^3*(C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{B b c x^{3} - C b^{2} x^{2} + 2 \, C a c x^{2} + A b c x^{2} + 2 \, B a c x - C a b + 2 \, A a c}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}} + \frac{{\left({\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 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 - \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 c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} B - 4 \, {\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)} B {\left| b^{2} - 4 \, a c \right|} - {\left(2 \, b^{7} c^{2} - 8 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 128 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 16 \, \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} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} - 4 \, a b c + \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{16 \, {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 48 \, a^{3} b^{2} c^{3} + 16 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 64 \, a^{4} c^{4} - 32 \, a^{3} b c^{4} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}} - \frac{{\left({\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} + 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 - \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 c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} B + 4 \, {\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)} B {\left| b^{2} - 4 \, a c \right|} - {\left(2 \, b^{7} c^{2} - 8 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 128 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 16 \, \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} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} - 4 \, a b c - \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{16 \, {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 48 \, a^{3} b^{2} c^{3} + 16 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 64 \, a^{4} c^{4} - 32 \, a^{3} b c^{4} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}} + \frac{{\left({\left(b^{4} c - 4 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} + b^{2} c^{3} + {\left(b^{3} c - 4 \, a b c^{2} - 2 \, b^{2} c^{2} + b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A {\left| b^{2} - 4 \, a c \right|} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2} - 2 \, a b^{2} c^{2} + a b c^{3} + {\left(a b^{2} c - 4 \, a^{2} c^{2} - 2 \, a b c^{2} + a c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C {\left| b^{2} - 4 \, a c \right|} - {\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 - 4 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + b^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A + 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 - 4 \, a^{2} b^{2} c^{2} - 2 \, a b^{3} c^{2} + a b^{2} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C\right)} \log\left(x^{2} + \frac{b^{3} - 4 \, a b c + \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\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^{2} {\left| b^{2} - 4 \, a c \right|}} + \frac{{\left({\left(b^{4} c - 4 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} + b^{2} c^{3} - {\left(b^{3} c - 4 \, a b c^{2} - 2 \, b^{2} c^{2} + b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A {\left| b^{2} - 4 \, a c \right|} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2} - 2 \, a b^{2} c^{2} + a b c^{3} - {\left(a b^{2} c - 4 \, a^{2} c^{2} - 2 \, a b c^{2} + a c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C {\left| b^{2} - 4 \, a c \right|} - {\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 - 4 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + b^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A + 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 - 4 \, a^{2} b^{2} c^{2} - 2 \, a b^{3} c^{2} + a b^{2} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C\right)} \log\left(x^{2} + \frac{b^{3} - 4 \, a b c - \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\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^{2} {\left| b^{2} - 4 \, a c \right|}}"," ",0,"1/2*(B*b*c*x^3 - C*b^2*x^2 + 2*C*a*c*x^2 + A*b*c*x^2 + 2*B*a*c*x - C*a*b + 2*A*a*c)/((c*x^4 + b*x^2 + a)*(b^2*c - 4*a*c^2)) + 1/16*((2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(b^2 - 4*a*c)^2*B - 4*(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*(b^2 - 4*a*c)*a*b^2*c^2 - 8*(b^2 - 4*a*c)*a^2*c^3)*B*abs(b^2 - 4*a*c) - (2*b^7*c^2 - 8*a*b^5*c^3 - 32*a^2*b^3*c^4 + 128*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 16*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)*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 32*(b^2 - 4*a*c)*a^2*b*c^4)*B)*arctan(2*sqrt(1/2)*x/sqrt((b^3 - 4*a*b*c + sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6*c - 12*a^2*b^4*c^2 - 2*a*b^5*c^2 + 48*a^3*b^2*c^3 + 16*a^2*b^3*c^3 + a*b^4*c^3 - 64*a^4*c^4 - 32*a^3*b*c^4 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*abs(b^2 - 4*a*c)*abs(c)) - 1/16*((2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(b^2 - 4*a*c)^2*B + 4*(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*(b^2 - 4*a*c)*a*b^2*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3)*B*abs(b^2 - 4*a*c) - (2*b^7*c^2 - 8*a*b^5*c^3 - 32*a^2*b^3*c^4 + 128*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 16*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)*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 32*(b^2 - 4*a*c)*a^2*b*c^4)*B)*arctan(2*sqrt(1/2)*x/sqrt((b^3 - 4*a*b*c - sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6*c - 12*a^2*b^4*c^2 - 2*a*b^5*c^2 + 48*a^3*b^2*c^3 + 16*a^2*b^3*c^3 + a*b^4*c^3 - 64*a^4*c^4 - 32*a^3*b*c^4 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*abs(b^2 - 4*a*c)*abs(c)) + 1/8*((b^4*c - 4*a*b^2*c^2 - 2*b^3*c^2 + b^2*c^3 + (b^3*c - 4*a*b*c^2 - 2*b^2*c^2 + b*c^3)*sqrt(b^2 - 4*a*c))*A*abs(b^2 - 4*a*c) - 2*(a*b^3*c - 4*a^2*b*c^2 - 2*a*b^2*c^2 + a*b*c^3 + (a*b^2*c - 4*a^2*c^2 - 2*a*b*c^2 + a*c^3)*sqrt(b^2 - 4*a*c))*C*abs(b^2 - 4*a*c) - (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 + (b^5*c - 4*a*b^3*c^2 - 2*b^4*c^2 + b^3*c^3)*sqrt(b^2 - 4*a*c))*A + 2*(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 + (a*b^4*c - 4*a^2*b^2*c^2 - 2*a*b^3*c^2 + a*b^2*c^3)*sqrt(b^2 - 4*a*c))*C)*log(x^2 + 1/2*(b^3 - 4*a*b*c + sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2))/((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)*c^2*abs(b^2 - 4*a*c)) + 1/8*((b^4*c - 4*a*b^2*c^2 - 2*b^3*c^2 + b^2*c^3 - (b^3*c - 4*a*b*c^2 - 2*b^2*c^2 + b*c^3)*sqrt(b^2 - 4*a*c))*A*abs(b^2 - 4*a*c) - 2*(a*b^3*c - 4*a^2*b*c^2 - 2*a*b^2*c^2 + a*b*c^3 - (a*b^2*c - 4*a^2*c^2 - 2*a*b*c^2 + a*c^3)*sqrt(b^2 - 4*a*c))*C*abs(b^2 - 4*a*c) - (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 - (b^5*c - 4*a*b^3*c^2 - 2*b^4*c^2 + b^3*c^3)*sqrt(b^2 - 4*a*c))*A + 2*(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 - (a*b^4*c - 4*a^2*b^2*c^2 - 2*a*b^3*c^2 + a*b^2*c^3)*sqrt(b^2 - 4*a*c))*C)*log(x^2 + 1/2*(b^3 - 4*a*b*c - sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2))/((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)*c^2*abs(b^2 - 4*a*c))","B",0
31,1,4440,0,7.049224," ","integrate(x^2*(C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{C b x^{3} - 2 \, A c x^{3} + B b x^{2} + 2 \, C a x - A b x + 2 \, B a}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} - 4 \, a c\right)}} - \frac{{\left(2 \, {\left(2 \, b^{2} c^{3} - 8 \, a c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{3}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} A - {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 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 - \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 c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} C - 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 {\left| b^{2} - 4 \, a c \right|} + 4 \, {\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 {\left| b^{2} - 4 \, a c \right|} - 4 \, {\left(2 \, b^{6} c^{3} - 16 \, a b^{4} c^{4} + 32 \, a^{2} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, \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^{2} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - \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 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4}\right)} A + {\left(2 \, b^{7} c^{2} - 8 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 128 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 16 \, \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} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} C\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} - 4 \, a b c + \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{16 \, {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 48 \, a^{3} b^{2} c^{3} + 16 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 64 \, a^{4} c^{4} - 32 \, a^{3} b c^{4} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}} + \frac{{\left(2 \, {\left(2 \, b^{2} c^{3} - 8 \, a c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{3}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} A - {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} + 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 - \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 c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} C + 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 {\left| b^{2} - 4 \, a c \right|} - 4 \, {\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 {\left| b^{2} - 4 \, a c \right|} - 4 \, {\left(2 \, b^{6} c^{3} - 16 \, a b^{4} c^{4} + 32 \, a^{2} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, \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^{2} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - \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 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4}\right)} A + {\left(2 \, b^{7} c^{2} - 8 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 128 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 16 \, \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} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} C\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} - 4 \, a b c - \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{16 \, {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 48 \, a^{3} b^{2} c^{3} + 16 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 64 \, a^{4} c^{4} - 32 \, a^{3} b c^{4} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}} + \frac{{\left({\left(b^{4} c - 4 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} + b^{2} c^{3} + {\left(b^{3} c - 4 \, a b c^{2} - 2 \, b^{2} c^{2} + b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| b^{2} - 4 \, a c \right|} - {\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 - 4 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + b^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{b^{3} - 4 \, a b c + \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\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^{2} {\left| b^{2} - 4 \, a c \right|}} + \frac{{\left({\left(b^{4} c - 4 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} + b^{2} c^{3} - {\left(b^{3} c - 4 \, a b c^{2} - 2 \, b^{2} c^{2} + b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| b^{2} - 4 \, a c \right|} - {\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 - 4 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + b^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{b^{3} - 4 \, a b c - \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\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^{2} {\left| b^{2} - 4 \, a c \right|}}"," ",0,"1/2*(C*b*x^3 - 2*A*c*x^3 + B*b*x^2 + 2*C*a*x - A*b*x + 2*B*a)/((c*x^4 + b*x^2 + a)*(b^2 - 4*a*c)) - 1/16*(2*(2*b^2*c^3 - 8*a*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*c^3 - 2*(b^2 - 4*a*c)*c^3)*(b^2 - 4*a*c)^2*A - (2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(b^2 - 4*a*c)^2*C - 2*(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*(b^2 - 4*a*c)*b^3*c^2 - 8*(b^2 - 4*a*c)*a*b*c^3)*A*abs(b^2 - 4*a*c) + 4*(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*(b^2 - 4*a*c)*a*b^2*c^2 - 8*(b^2 - 4*a*c)*a^2*c^3)*C*abs(b^2 - 4*a*c) - 4*(2*b^6*c^3 - 16*a*b^4*c^4 + 32*a^2*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*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^2*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 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*(b^2 - 4*a*c)*b^4*c^3 + 8*(b^2 - 4*a*c)*a*b^2*c^4)*A + (2*b^7*c^2 - 8*a*b^5*c^3 - 32*a^2*b^3*c^4 + 128*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 16*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)*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 32*(b^2 - 4*a*c)*a^2*b*c^4)*C)*arctan(2*sqrt(1/2)*x/sqrt((b^3 - 4*a*b*c + sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6*c - 12*a^2*b^4*c^2 - 2*a*b^5*c^2 + 48*a^3*b^2*c^3 + 16*a^2*b^3*c^3 + a*b^4*c^3 - 64*a^4*c^4 - 32*a^3*b*c^4 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*abs(b^2 - 4*a*c)*abs(c)) + 1/16*(2*(2*b^2*c^3 - 8*a*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*c^3 - 2*(b^2 - 4*a*c)*c^3)*(b^2 - 4*a*c)^2*A - (2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(b^2 - 4*a*c)^2*C + 2*(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*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*A*abs(b^2 - 4*a*c) - 4*(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*(b^2 - 4*a*c)*a*b^2*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3)*C*abs(b^2 - 4*a*c) - 4*(2*b^6*c^3 - 16*a*b^4*c^4 + 32*a^2*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*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^2*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 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*(b^2 - 4*a*c)*b^4*c^3 + 8*(b^2 - 4*a*c)*a*b^2*c^4)*A + (2*b^7*c^2 - 8*a*b^5*c^3 - 32*a^2*b^3*c^4 + 128*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 16*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)*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 32*(b^2 - 4*a*c)*a^2*b*c^4)*C)*arctan(2*sqrt(1/2)*x/sqrt((b^3 - 4*a*b*c - sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6*c - 12*a^2*b^4*c^2 - 2*a*b^5*c^2 + 48*a^3*b^2*c^3 + 16*a^2*b^3*c^3 + a*b^4*c^3 - 64*a^4*c^4 - 32*a^3*b*c^4 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*abs(b^2 - 4*a*c)*abs(c)) + 1/8*((b^4*c - 4*a*b^2*c^2 - 2*b^3*c^2 + b^2*c^3 + (b^3*c - 4*a*b*c^2 - 2*b^2*c^2 + b*c^3)*sqrt(b^2 - 4*a*c))*B*abs(b^2 - 4*a*c) - (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 + (b^5*c - 4*a*b^3*c^2 - 2*b^4*c^2 + b^3*c^3)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(b^3 - 4*a*b*c + sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2))/((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)*c^2*abs(b^2 - 4*a*c)) + 1/8*((b^4*c - 4*a*b^2*c^2 - 2*b^3*c^2 + b^2*c^3 - (b^3*c - 4*a*b*c^2 - 2*b^2*c^2 + b*c^3)*sqrt(b^2 - 4*a*c))*B*abs(b^2 - 4*a*c) - (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 - (b^5*c - 4*a*b^3*c^2 - 2*b^4*c^2 + b^3*c^3)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(b^3 - 4*a*b*c - sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2))/((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)*c^2*abs(b^2 - 4*a*c))","B",0
32,1,3013,0,5.172931," ","integrate(x*(C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{2 \, B c x^{3} - C b x^{2} + 2 \, A c x^{2} + B b x - 2 \, C a + A b}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} - 4 \, a c\right)}} - \frac{{\left({\left(2 \, b^{2} c^{2} - 8 \, a c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} B - {\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} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 32 \, a^{2} b 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}\right)} B {\left| b^{2} - 4 \, a c \right|} - 2 \, {\left(2 \, b^{6} c^{2} - 16 \, a b^{4} c^{3} + 32 \, a^{2} b^{2} c^{4} - \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 - 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} - 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} + 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 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} - 4 \, a b c + \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{8 \, {\left(a b^{6} - 12 \, a^{2} b^{4} c - 2 \, a b^{5} c + 48 \, a^{3} b^{2} c^{2} + 16 \, a^{2} b^{3} c^{2} + a b^{4} c^{2} - 64 \, a^{4} c^{3} - 32 \, a^{3} b c^{3} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}} + \frac{{\left({\left(2 \, b^{2} c^{2} - 8 \, a c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} B + {\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} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + 32 \, a^{2} b 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}\right)} B {\left| b^{2} - 4 \, a c \right|} - 2 \, {\left(2 \, b^{6} c^{2} - 16 \, a b^{4} c^{3} + 32 \, a^{2} b^{2} c^{4} - \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 - 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} - 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} + 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 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} - 4 \, a b c - \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{8 \, {\left(a b^{6} - 12 \, a^{2} b^{4} c - 2 \, a b^{5} c + 48 \, a^{3} b^{2} c^{2} + 16 \, a^{2} b^{3} c^{2} + a b^{4} c^{2} - 64 \, a^{4} c^{3} - 32 \, a^{3} b c^{3} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}} - \frac{{\left(2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3} - 2 \, b^{2} c^{3} + b c^{4} + {\left(b^{2} c^{2} - 4 \, a c^{3} - 2 \, b c^{3} + c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A {\left| b^{2} - 4 \, a c \right|} - {\left(b^{4} c - 4 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} + b^{2} c^{3} + {\left(b^{3} c - 4 \, a b c^{2} - 2 \, b^{2} c^{2} + b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C {\left| b^{2} - 4 \, a c \right|} - 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} - 2 \, b^{4} c^{3} + 16 \, a^{2} b c^{4} + 8 \, a b^{2} c^{4} + b^{3} c^{4} - 4 \, a b c^{5} + {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} - 2 \, b^{3} c^{3} + b^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A + {\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 - 4 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + b^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C\right)} \log\left(x^{2} + \frac{b^{3} - 4 \, a b c + \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\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^{2} {\left| b^{2} - 4 \, a c \right|}} - \frac{{\left(2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3} - 2 \, b^{2} c^{3} + b c^{4} - {\left(b^{2} c^{2} - 4 \, a c^{3} - 2 \, b c^{3} + c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A {\left| b^{2} - 4 \, a c \right|} - {\left(b^{4} c - 4 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} + b^{2} c^{3} - {\left(b^{3} c - 4 \, a b c^{2} - 2 \, b^{2} c^{2} + b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C {\left| b^{2} - 4 \, a c \right|} - 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} - 2 \, b^{4} c^{3} + 16 \, a^{2} b c^{4} + 8 \, a b^{2} c^{4} + b^{3} c^{4} - 4 \, a b c^{5} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} - 2 \, b^{3} c^{3} + b^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A + {\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 - 4 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + b^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C\right)} \log\left(x^{2} + \frac{b^{3} - 4 \, a b c - \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\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^{2} {\left| b^{2} - 4 \, a c \right|}}"," ",0,"-1/2*(2*B*c*x^3 - C*b*x^2 + 2*A*c*x^2 + B*b*x - 2*C*a + A*b)/((c*x^4 + b*x^2 + a)*(b^2 - 4*a*c)) - 1/8*((2*b^2*c^2 - 8*a*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*c^2 - 2*(b^2 - 4*a*c)*c^2)*(b^2 - 4*a*c)^2*B - (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 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 32*a^2*b*c^3 + 2*(b^2 - 4*a*c)*b^3*c - 8*(b^2 - 4*a*c)*a*b*c^2)*B*abs(b^2 - 4*a*c) - 2*(2*b^6*c^2 - 16*a*b^4*c^3 + 32*a^2*b^2*c^4 - 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 - 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 - 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 + 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*(b^2 - 4*a*c)*b^4*c^2 + 8*(b^2 - 4*a*c)*a*b^2*c^3)*B)*arctan(2*sqrt(1/2)*x/sqrt((b^3 - 4*a*b*c + sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6 - 12*a^2*b^4*c - 2*a*b^5*c + 48*a^3*b^2*c^2 + 16*a^2*b^3*c^2 + a*b^4*c^2 - 64*a^4*c^3 - 32*a^3*b*c^3 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*abs(b^2 - 4*a*c)*abs(c)) + 1/8*((2*b^2*c^2 - 8*a*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*c^2 - 2*(b^2 - 4*a*c)*c^2)*(b^2 - 4*a*c)^2*B + (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 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 + 32*a^2*b*c^3 - 2*(b^2 - 4*a*c)*b^3*c + 8*(b^2 - 4*a*c)*a*b*c^2)*B*abs(b^2 - 4*a*c) - 2*(2*b^6*c^2 - 16*a*b^4*c^3 + 32*a^2*b^2*c^4 - 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 - 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 - 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 + 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*(b^2 - 4*a*c)*b^4*c^2 + 8*(b^2 - 4*a*c)*a*b^2*c^3)*B)*arctan(2*sqrt(1/2)*x/sqrt((b^3 - 4*a*b*c - sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6 - 12*a^2*b^4*c - 2*a*b^5*c + 48*a^3*b^2*c^2 + 16*a^2*b^3*c^2 + a*b^4*c^2 - 64*a^4*c^3 - 32*a^3*b*c^3 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*abs(b^2 - 4*a*c)*abs(c)) - 1/8*(2*(b^3*c^2 - 4*a*b*c^3 - 2*b^2*c^3 + b*c^4 + (b^2*c^2 - 4*a*c^3 - 2*b*c^3 + c^4)*sqrt(b^2 - 4*a*c))*A*abs(b^2 - 4*a*c) - (b^4*c - 4*a*b^2*c^2 - 2*b^3*c^2 + b^2*c^3 + (b^3*c - 4*a*b*c^2 - 2*b^2*c^2 + b*c^3)*sqrt(b^2 - 4*a*c))*C*abs(b^2 - 4*a*c) - 2*(b^5*c^2 - 8*a*b^3*c^3 - 2*b^4*c^3 + 16*a^2*b*c^4 + 8*a*b^2*c^4 + b^3*c^4 - 4*a*b*c^5 + (b^4*c^2 - 4*a*b^2*c^3 - 2*b^3*c^3 + b^2*c^4)*sqrt(b^2 - 4*a*c))*A + (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 + (b^5*c - 4*a*b^3*c^2 - 2*b^4*c^2 + b^3*c^3)*sqrt(b^2 - 4*a*c))*C)*log(x^2 + 1/2*(b^3 - 4*a*b*c + sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2))/((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)*c^2*abs(b^2 - 4*a*c)) - 1/8*(2*(b^3*c^2 - 4*a*b*c^3 - 2*b^2*c^3 + b*c^4 - (b^2*c^2 - 4*a*c^3 - 2*b*c^3 + c^4)*sqrt(b^2 - 4*a*c))*A*abs(b^2 - 4*a*c) - (b^4*c - 4*a*b^2*c^2 - 2*b^3*c^2 + b^2*c^3 - (b^3*c - 4*a*b*c^2 - 2*b^2*c^2 + b*c^3)*sqrt(b^2 - 4*a*c))*C*abs(b^2 - 4*a*c) - 2*(b^5*c^2 - 8*a*b^3*c^3 - 2*b^4*c^3 + 16*a^2*b*c^4 + 8*a*b^2*c^4 + b^3*c^4 - 4*a*b*c^5 - (b^4*c^2 - 4*a*b^2*c^3 - 2*b^3*c^3 + b^2*c^4)*sqrt(b^2 - 4*a*c))*A + (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 - (b^5*c - 4*a*b^3*c^2 - 2*b^4*c^2 + b^3*c^3)*sqrt(b^2 - 4*a*c))*C)*log(x^2 + 1/2*(b^3 - 4*a*b*c - sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2))/((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)*c^2*abs(b^2 - 4*a*c))","B",0
33,1,5158,0,7.848756," ","integrate((C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{2 \, C a c x^{3} - A b c x^{3} + 2 \, B a c x^{2} + C a b x - A b^{2} x + 2 \, A a c x + B a b}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}} + \frac{{\left({\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 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 - \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 c^{2}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} A - 2 \, {\left(2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{2}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} C + 2 \, {\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} - 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 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 192 \, a^{4} c^{4} + 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} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3}\right)} A {\left| a b^{2} - 4 \, a^{2} c \right|} + 2 \, {\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} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, a^{4} b 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}\right)} C {\left| a b^{2} - 4 \, a^{2} c \right|} + {\left(2 \, a^{2} b^{7} c^{2} - 40 \, a^{3} b^{5} c^{3} + 224 \, a^{4} b^{3} c^{4} - 384 \, a^{5} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} A + 4 \, {\left(2 \, a^{3} b^{6} c^{2} - 16 \, a^{4} b^{4} c^{3} + 32 \, a^{5} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{3}\right)} C\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b^{3} - 4 \, a^{2} b c + \sqrt{{\left(a b^{3} - 4 \, a^{2} b c\right)}^{2} - 4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}}}{a b^{2} c - 4 \, a^{2} c^{2}}}}\right)}{16 \, {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c - 2 \, a^{3} b^{5} c + 48 \, a^{5} b^{2} c^{2} + 16 \, a^{4} b^{3} c^{2} + a^{3} b^{4} c^{2} - 64 \, a^{6} c^{3} - 32 \, a^{5} b c^{3} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|} {\left| c \right|}} - \frac{{\left({\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} + 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 - \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 c^{2}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} A - 2 \, {\left(2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{2}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} C - 2 \, {\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} - 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 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 192 \, a^{4} c^{4} - 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} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3}\right)} A {\left| a b^{2} - 4 \, a^{2} c \right|} - 2 \, {\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} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 32 \, a^{4} b 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}\right)} C {\left| a b^{2} - 4 \, a^{2} c \right|} + {\left(2 \, a^{2} b^{7} c^{2} - 40 \, a^{3} b^{5} c^{3} + 224 \, a^{4} b^{3} c^{4} - 384 \, a^{5} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} A + 4 \, {\left(2 \, a^{3} b^{6} c^{2} - 16 \, a^{4} b^{4} c^{3} + 32 \, a^{5} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{3}\right)} C\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b^{3} - 4 \, a^{2} b c - \sqrt{{\left(a b^{3} - 4 \, a^{2} b c\right)}^{2} - 4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}}}{a b^{2} c - 4 \, a^{2} c^{2}}}}\right)}{16 \, {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c - 2 \, a^{3} b^{5} c + 48 \, a^{5} b^{2} c^{2} + 16 \, a^{4} b^{3} c^{2} + a^{3} b^{4} c^{2} - 64 \, a^{6} c^{3} - 32 \, a^{5} b c^{3} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|} {\left| c \right|}} - \frac{{\left({\left(b^{3} c^{2} - 4 \, a b c^{3} - 2 \, b^{2} c^{3} + b c^{4} + {\left(b^{2} c^{2} - 4 \, a c^{3} - 2 \, b c^{3} + c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| a b^{2} - 4 \, a^{2} c \right|} - {\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)} B\right)} \log\left(x^{2} + \frac{a b^{3} - 4 \, a^{2} b c + \sqrt{{\left(a b^{3} - 4 \, a^{2} b c\right)}^{2} - 4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}}}{2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}}\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|}} - \frac{{\left({\left(b^{3} c^{2} - 4 \, a b c^{3} - 2 \, b^{2} c^{3} + b c^{4} - {\left(b^{2} c^{2} - 4 \, a c^{3} - 2 \, b c^{3} + c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| a b^{2} - 4 \, a^{2} c \right|} - {\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)} B\right)} \log\left(x^{2} + \frac{a b^{3} - 4 \, a^{2} b c - \sqrt{{\left(a b^{3} - 4 \, a^{2} b c\right)}^{2} - 4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}}}{2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}}\right)}{4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c - 2 \, a b^{3} c + 16 \, a^{3} c^{2} + 8 \, a^{2} b c^{2} + a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} c^{2} {\left| a b^{2} - 4 \, a^{2} c \right|}}"," ",0,"-1/2*(2*C*a*c*x^3 - A*b*c*x^3 + 2*B*a*c*x^2 + C*a*b*x - A*b^2*x + 2*A*a*c*x + B*a*b)/((c*x^4 + b*x^2 + a)*(a*b^2 - 4*a^2*c)) + 1/16*((2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(a*b^2 - 4*a^2*c)^2*A - 2*(2*a*b^2*c^2 - 8*a^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^2 - 2*(b^2 - 4*a*c)*a*c^2)*(a*b^2 - 4*a^2*c)^2*C + 2*(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 - 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*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 192*a^4*c^4 + 2*(b^2 - 4*a*c)*a*b^4*c - 20*(b^2 - 4*a*c)*a^2*b^2*c^2 + 48*(b^2 - 4*a*c)*a^3*c^3)*A*abs(a*b^2 - 4*a^2*c) + 2*(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 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*a^4*b*c^3 + 2*(b^2 - 4*a*c)*a^2*b^3*c - 8*(b^2 - 4*a*c)*a^3*b*c^2)*C*abs(a*b^2 - 4*a^2*c) + (2*a^2*b^7*c^2 - 40*a^3*b^5*c^3 + 224*a^4*b^3*c^4 - 384*a^5*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 - 2*(b^2 - 4*a*c)*a^2*b^5*c^2 + 32*(b^2 - 4*a*c)*a^3*b^3*c^3 - 96*(b^2 - 4*a*c)*a^4*b*c^4)*A + 4*(2*a^3*b^6*c^2 - 16*a^4*b^4*c^3 + 32*a^5*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 - 2*(b^2 - 4*a*c)*a^3*b^4*c^2 + 8*(b^2 - 4*a*c)*a^4*b^2*c^3)*C)*arctan(2*sqrt(1/2)*x/sqrt((a*b^3 - 4*a^2*b*c + sqrt((a*b^3 - 4*a^2*b*c)^2 - 4*(a^2*b^2 - 4*a^3*c)*(a*b^2*c - 4*a^2*c^2)))/(a*b^2*c - 4*a^2*c^2)))/((a^3*b^6 - 12*a^4*b^4*c - 2*a^3*b^5*c + 48*a^5*b^2*c^2 + 16*a^4*b^3*c^2 + a^3*b^4*c^2 - 64*a^6*c^3 - 32*a^5*b*c^3 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*abs(a*b^2 - 4*a^2*c)*abs(c)) - 1/16*((2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(a*b^2 - 4*a^2*c)^2*A - 2*(2*a*b^2*c^2 - 8*a^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^2 - 2*(b^2 - 4*a*c)*a*c^2)*(a*b^2 - 4*a^2*c)^2*C - 2*(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 - 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*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 - 192*a^4*c^4 - 2*(b^2 - 4*a*c)*a*b^4*c + 20*(b^2 - 4*a*c)*a^2*b^2*c^2 - 48*(b^2 - 4*a*c)*a^3*c^3)*A*abs(a*b^2 - 4*a^2*c) - 2*(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 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 + 32*a^4*b*c^3 - 2*(b^2 - 4*a*c)*a^2*b^3*c + 8*(b^2 - 4*a*c)*a^3*b*c^2)*C*abs(a*b^2 - 4*a^2*c) + (2*a^2*b^7*c^2 - 40*a^3*b^5*c^3 + 224*a^4*b^3*c^4 - 384*a^5*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 - 2*(b^2 - 4*a*c)*a^2*b^5*c^2 + 32*(b^2 - 4*a*c)*a^3*b^3*c^3 - 96*(b^2 - 4*a*c)*a^4*b*c^4)*A + 4*(2*a^3*b^6*c^2 - 16*a^4*b^4*c^3 + 32*a^5*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 - 2*(b^2 - 4*a*c)*a^3*b^4*c^2 + 8*(b^2 - 4*a*c)*a^4*b^2*c^3)*C)*arctan(2*sqrt(1/2)*x/sqrt((a*b^3 - 4*a^2*b*c - sqrt((a*b^3 - 4*a^2*b*c)^2 - 4*(a^2*b^2 - 4*a^3*c)*(a*b^2*c - 4*a^2*c^2)))/(a*b^2*c - 4*a^2*c^2)))/((a^3*b^6 - 12*a^4*b^4*c - 2*a^3*b^5*c + 48*a^5*b^2*c^2 + 16*a^4*b^3*c^2 + a^3*b^4*c^2 - 64*a^6*c^3 - 32*a^5*b*c^3 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*abs(a*b^2 - 4*a^2*c)*abs(c)) - 1/4*((b^3*c^2 - 4*a*b*c^3 - 2*b^2*c^3 + b*c^4 + (b^2*c^2 - 4*a*c^3 - 2*b*c^3 + c^4)*sqrt(b^2 - 4*a*c))*B*abs(a*b^2 - 4*a^2*c) - (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 + (a*b^4*c^2 - 4*a^2*b^2*c^3 - 2*a*b^3*c^3 + a*b^2*c^4)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(a*b^3 - 4*a^2*b*c + sqrt((a*b^3 - 4*a^2*b*c)^2 - 4*(a^2*b^2 - 4*a^3*c)*(a*b^2*c - 4*a^2*c^2)))/(a*b^2*c - 4*a^2*c^2))/((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)*c^2*abs(a*b^2 - 4*a^2*c)) - 1/4*((b^3*c^2 - 4*a*b*c^3 - 2*b^2*c^3 + b*c^4 - (b^2*c^2 - 4*a*c^3 - 2*b*c^3 + c^4)*sqrt(b^2 - 4*a*c))*B*abs(a*b^2 - 4*a^2*c) - (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 - (a*b^4*c^2 - 4*a^2*b^2*c^3 - 2*a*b^3*c^3 + a*b^2*c^4)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(a*b^3 - 4*a^2*b*c - sqrt((a*b^3 - 4*a^2*b*c)^2 - 4*(a^2*b^2 - 4*a^3*c)*(a*b^2*c - 4*a^2*c^2)))/(a*b^2*c - 4*a^2*c^2))/((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)*c^2*abs(a*b^2 - 4*a^2*c))","B",0
34,1,6022,0,6.552853," ","integrate((C*x^2+B*x+A)/x/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{A \log\left({\left| c x^{4} + b x^{2} + a \right|}\right)}{4 \, a^{2}} + \frac{A \log\left({\left| x \right|}\right)}{a^{2}} + \frac{{\left({\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)}^{2} {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 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 - \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 c^{2}\right)} B + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c - 18 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{2} - 2 \, a^{4} b^{8} c^{2} + 120 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{3} + 28 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{3} + 36 \, a^{5} b^{6} c^{3} - 352 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{4} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{4} - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{4} - 240 \, a^{6} b^{4} c^{4} + 384 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} c^{5} + 192 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{5} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{5} + 704 \, a^{7} b^{2} c^{5} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} c^{6} - 768 \, a^{8} c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{6} c^{2} - 28 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c^{3} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{4} - 192 \, {\left(b^{2} - 4 \, a c\right)} a^{7} c^{5}\right)} B {\left| a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} \right|} + {\left(2 \, a^{8} b^{11} c^{4} - 56 \, a^{9} b^{9} c^{5} + 576 \, a^{10} b^{7} c^{6} - 2816 \, a^{11} b^{5} c^{7} + 6656 \, a^{12} b^{3} c^{8} - 6144 \, a^{13} b c^{9} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{11} c^{2} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{9} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{10} c^{3} - 288 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{7} c^{4} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{8} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{9} c^{4} + 1408 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{5} c^{5} + 384 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{6} c^{5} + 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{7} c^{5} - 3328 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{3} c^{6} - 1280 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{4} c^{6} - 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{5} c^{6} + 3072 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{13} b c^{7} + 1536 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{2} c^{7} + 640 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{3} c^{7} - 768 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{12} b c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{9} c^{4} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{7} c^{5} - 384 \, {\left(b^{2} - 4 \, a c\right)} a^{10} b^{5} c^{6} + 1280 \, {\left(b^{2} - 4 \, a c\right)} a^{11} b^{3} c^{7} - 1536 \, {\left(b^{2} - 4 \, a c\right)} a^{12} b c^{8}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3} + \sqrt{{\left(a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3}\right)}^{2} - 4 \, {\left(a^{5} b^{4} c - 8 \, a^{6} b^{2} c^{2} + 16 \, a^{7} c^{3}\right)} {\left(a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}\right)}}}{a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}}}}\right)}{16 \, {\left(a^{6} b^{8} c - 16 \, a^{7} b^{6} c^{2} - 2 \, a^{6} b^{7} c^{2} + 96 \, a^{8} b^{4} c^{3} + 24 \, a^{7} b^{5} c^{3} + a^{6} b^{6} c^{3} - 256 \, a^{9} b^{2} c^{4} - 96 \, a^{8} b^{3} c^{4} - 12 \, a^{7} b^{4} c^{4} + 256 \, a^{10} c^{5} + 128 \, a^{9} b c^{5} + 48 \, a^{8} b^{2} c^{5} - 64 \, a^{9} c^{6}\right)} {\left| a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} \right|} {\left| c \right|}} - \frac{{\left({\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)}^{2} {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} + 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 - \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 c^{2}\right)} B - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c - 18 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{2} + 2 \, a^{4} b^{8} c^{2} + 120 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{3} + 28 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{3} - 36 \, a^{5} b^{6} c^{3} - 352 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{4} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{4} - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{4} + 240 \, a^{6} b^{4} c^{4} + 384 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} c^{5} + 192 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{5} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{5} - 704 \, a^{7} b^{2} c^{5} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} c^{6} + 768 \, a^{8} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{6} c^{2} + 28 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{4} + 192 \, {\left(b^{2} - 4 \, a c\right)} a^{7} c^{5}\right)} B {\left| a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} \right|} + {\left(2 \, a^{8} b^{11} c^{4} - 56 \, a^{9} b^{9} c^{5} + 576 \, a^{10} b^{7} c^{6} - 2816 \, a^{11} b^{5} c^{7} + 6656 \, a^{12} b^{3} c^{8} - 6144 \, a^{13} b c^{9} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{11} c^{2} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{9} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{10} c^{3} - 288 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{7} c^{4} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{8} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{9} c^{4} + 1408 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{5} c^{5} + 384 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{6} c^{5} + 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{7} c^{5} - 3328 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{3} c^{6} - 1280 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{4} c^{6} - 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{5} c^{6} + 3072 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{13} b c^{7} + 1536 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{2} c^{7} + 640 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{3} c^{7} - 768 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{12} b c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{9} c^{4} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{7} c^{5} - 384 \, {\left(b^{2} - 4 \, a c\right)} a^{10} b^{5} c^{6} + 1280 \, {\left(b^{2} - 4 \, a c\right)} a^{11} b^{3} c^{7} - 1536 \, {\left(b^{2} - 4 \, a c\right)} a^{12} b c^{8}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3} - \sqrt{{\left(a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3}\right)}^{2} - 4 \, {\left(a^{5} b^{4} c - 8 \, a^{6} b^{2} c^{2} + 16 \, a^{7} c^{3}\right)} {\left(a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}\right)}}}{a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}}}}\right)}{16 \, {\left(a^{6} b^{8} c - 16 \, a^{7} b^{6} c^{2} - 2 \, a^{6} b^{7} c^{2} + 96 \, a^{8} b^{4} c^{3} + 24 \, a^{7} b^{5} c^{3} + a^{6} b^{6} c^{3} - 256 \, a^{9} b^{2} c^{4} - 96 \, a^{8} b^{3} c^{4} - 12 \, a^{7} b^{4} c^{4} + 256 \, a^{10} c^{5} + 128 \, a^{9} b c^{5} + 48 \, a^{8} b^{2} c^{5} - 64 \, a^{9} c^{6}\right)} {\left| a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} \right|} {\left| c \right|}} - \frac{{\left({\left(b^{6} c - 10 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} + 24 \, a^{2} b^{2} c^{3} + 12 \, a b^{3} c^{3} + b^{4} c^{3} - 6 \, a b^{2} c^{4} + {\left(b^{5} c - 10 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + 24 \, a^{2} b c^{3} + 12 \, a b^{2} c^{3} + b^{3} c^{3} - 6 \, a b c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A {\left| a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} \right|} + 4 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3} - 2 \, a^{2} b^{2} c^{3} + a^{2} b c^{4} + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} - 2 \, a^{2} b c^{3} + a^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C {\left| a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} \right|} + {\left(a^{4} b^{10} c^{2} - 18 \, a^{5} b^{8} c^{3} - 2 \, a^{4} b^{9} c^{3} + 120 \, a^{6} b^{6} c^{4} + 28 \, a^{5} b^{7} c^{4} + a^{4} b^{8} c^{4} - 352 \, a^{7} b^{4} c^{5} - 128 \, a^{6} b^{5} c^{5} - 14 \, a^{5} b^{6} c^{5} + 384 \, a^{8} b^{2} c^{6} + 192 \, a^{7} b^{3} c^{6} + 64 \, a^{6} b^{4} c^{6} - 96 \, a^{7} b^{2} c^{7} + {\left(a^{4} b^{9} c^{2} - 14 \, a^{5} b^{7} c^{3} - 2 \, a^{4} b^{8} c^{3} + 64 \, a^{6} b^{5} c^{4} + 20 \, a^{5} b^{6} c^{4} + a^{4} b^{7} c^{4} - 96 \, a^{7} b^{3} c^{5} - 48 \, a^{6} b^{4} c^{5} - 10 \, a^{5} b^{5} c^{5} + 24 \, a^{6} b^{3} c^{6}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A + 4 \, {\left(a^{6} b^{7} c^{3} - 12 \, a^{7} b^{5} c^{4} - 2 \, a^{6} b^{6} c^{4} + 48 \, a^{8} b^{3} c^{5} + 16 \, a^{7} b^{4} c^{5} + a^{6} b^{5} c^{5} - 64 \, a^{9} b c^{6} - 32 \, a^{8} b^{2} c^{6} - 8 \, a^{7} b^{3} c^{6} + 16 \, a^{8} b c^{7} + {\left(a^{6} b^{6} c^{3} - 8 \, a^{7} b^{4} c^{4} - 2 \, a^{6} b^{5} c^{4} + 16 \, a^{8} b^{2} c^{5} + 8 \, a^{7} b^{3} c^{5} + a^{6} b^{4} c^{5} - 4 \, a^{7} b^{2} c^{6}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C\right)} \log\left(x^{2} + \frac{a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3} + \sqrt{{\left(a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3}\right)}^{2} - 4 \, {\left(a^{5} b^{4} c - 8 \, a^{6} b^{2} c^{2} + 16 \, a^{7} c^{3}\right)} {\left(a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}\right)}}}{2 \, {\left(a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}\right)}}\right)}{16 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c - 2 \, a^{3} b^{3} c + 16 \, a^{5} c^{2} + 8 \, a^{4} b c^{2} + a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} c^{2} {\left| a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} \right|}} - \frac{{\left({\left(b^{6} c - 10 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} + 24 \, a^{2} b^{2} c^{3} + 12 \, a b^{3} c^{3} + b^{4} c^{3} - 6 \, a b^{2} c^{4} - {\left(b^{5} c - 10 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + 24 \, a^{2} b c^{3} + 12 \, a b^{2} c^{3} + b^{3} c^{3} - 6 \, a b c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A {\left| a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} \right|} + 4 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3} - 2 \, a^{2} b^{2} c^{3} + a^{2} b c^{4} - {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} - 2 \, a^{2} b c^{3} + a^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C {\left| a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} \right|} - {\left(a^{4} b^{10} c^{2} - 18 \, a^{5} b^{8} c^{3} - 2 \, a^{4} b^{9} c^{3} + 120 \, a^{6} b^{6} c^{4} + 28 \, a^{5} b^{7} c^{4} + a^{4} b^{8} c^{4} - 352 \, a^{7} b^{4} c^{5} - 128 \, a^{6} b^{5} c^{5} - 14 \, a^{5} b^{6} c^{5} + 384 \, a^{8} b^{2} c^{6} + 192 \, a^{7} b^{3} c^{6} + 64 \, a^{6} b^{4} c^{6} - 96 \, a^{7} b^{2} c^{7} - {\left(a^{4} b^{9} c^{2} - 14 \, a^{5} b^{7} c^{3} - 2 \, a^{4} b^{8} c^{3} + 64 \, a^{6} b^{5} c^{4} + 20 \, a^{5} b^{6} c^{4} + a^{4} b^{7} c^{4} - 96 \, a^{7} b^{3} c^{5} - 48 \, a^{6} b^{4} c^{5} - 10 \, a^{5} b^{5} c^{5} + 24 \, a^{6} b^{3} c^{6}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A - 4 \, {\left(a^{6} b^{7} c^{3} - 12 \, a^{7} b^{5} c^{4} - 2 \, a^{6} b^{6} c^{4} + 48 \, a^{8} b^{3} c^{5} + 16 \, a^{7} b^{4} c^{5} + a^{6} b^{5} c^{5} - 64 \, a^{9} b c^{6} - 32 \, a^{8} b^{2} c^{6} - 8 \, a^{7} b^{3} c^{6} + 16 \, a^{8} b c^{7} - {\left(a^{6} b^{6} c^{3} - 8 \, a^{7} b^{4} c^{4} - 2 \, a^{6} b^{5} c^{4} + 16 \, a^{8} b^{2} c^{5} + 8 \, a^{7} b^{3} c^{5} + a^{6} b^{4} c^{5} - 4 \, a^{7} b^{2} c^{6}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C\right)} \log\left(x^{2} + \frac{a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3} - \sqrt{{\left(a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3}\right)}^{2} - 4 \, {\left(a^{5} b^{4} c - 8 \, a^{6} b^{2} c^{2} + 16 \, a^{7} c^{3}\right)} {\left(a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}\right)}}}{2 \, {\left(a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}\right)}}\right)}{16 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c - 2 \, a^{3} b^{3} c + 16 \, a^{5} c^{2} + 8 \, a^{4} b c^{2} + a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} c^{2} {\left| a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} \right|}} + \frac{B a b c x^{3} - C a^{2} b + A a b^{2} - 2 \, A a^{2} c - {\left(2 \, C a^{2} c - A a b c\right)} x^{2} + {\left(B a b^{2} - 2 \, B a^{2} c\right)} x}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} - 4 \, a c\right)} a^{2}}"," ",0,"-1/4*A*log(abs(c*x^4 + b*x^2 + a))/a^2 + A*log(abs(x))/a^2 + 1/16*((a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)^2*(2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*B + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c - 18*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^2 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^2 - 2*a^4*b^8*c^2 + 120*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^3 + 28*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^3 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^3 + 36*a^5*b^6*c^3 - 352*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^4 - 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^4 - 14*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^4 - 240*a^6*b^4*c^4 + 384*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*c^5 + 192*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b*c^5 + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^5 + 704*a^7*b^2*c^5 - 96*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*c^6 - 768*a^8*c^6 + 2*(b^2 - 4*a*c)*a^4*b^6*c^2 - 28*(b^2 - 4*a*c)*a^5*b^4*c^3 + 128*(b^2 - 4*a*c)*a^6*b^2*c^4 - 192*(b^2 - 4*a*c)*a^7*c^5)*B*abs(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3) + (2*a^8*b^11*c^4 - 56*a^9*b^9*c^5 + 576*a^10*b^7*c^6 - 2816*a^11*b^5*c^7 + 6656*a^12*b^3*c^8 - 6144*a^13*b*c^9 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^11*c^2 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^9*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^10*c^3 - 288*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^7*c^4 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^8*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^9*c^4 + 1408*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^5*c^5 + 384*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^6*c^5 + 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^7*c^5 - 3328*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^12*b^3*c^6 - 1280*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^4*c^6 - 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^5*c^6 + 3072*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^13*b*c^7 + 1536*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^12*b^2*c^7 + 640*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^3*c^7 - 768*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^12*b*c^8 - 2*(b^2 - 4*a*c)*a^8*b^9*c^4 + 48*(b^2 - 4*a*c)*a^9*b^7*c^5 - 384*(b^2 - 4*a*c)*a^10*b^5*c^6 + 1280*(b^2 - 4*a*c)*a^11*b^3*c^7 - 1536*(b^2 - 4*a*c)*a^12*b*c^8)*B)*arctan(2*sqrt(1/2)*x/sqrt((a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3 + sqrt((a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3)^2 - 4*(a^5*b^4*c - 8*a^6*b^2*c^2 + 16*a^7*c^3)*(a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4)))/(a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4)))/((a^6*b^8*c - 16*a^7*b^6*c^2 - 2*a^6*b^7*c^2 + 96*a^8*b^4*c^3 + 24*a^7*b^5*c^3 + a^6*b^6*c^3 - 256*a^9*b^2*c^4 - 96*a^8*b^3*c^4 - 12*a^7*b^4*c^4 + 256*a^10*c^5 + 128*a^9*b*c^5 + 48*a^8*b^2*c^5 - 64*a^9*c^6)*abs(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*abs(c)) - 1/16*((a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)^2*(2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*B - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c - 18*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^2 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^2 + 2*a^4*b^8*c^2 + 120*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^3 + 28*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^3 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^3 - 36*a^5*b^6*c^3 - 352*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^4 - 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^4 - 14*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^4 + 240*a^6*b^4*c^4 + 384*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*c^5 + 192*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^5 + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^5 - 704*a^7*b^2*c^5 - 96*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*c^6 + 768*a^8*c^6 - 2*(b^2 - 4*a*c)*a^4*b^6*c^2 + 28*(b^2 - 4*a*c)*a^5*b^4*c^3 - 128*(b^2 - 4*a*c)*a^6*b^2*c^4 + 192*(b^2 - 4*a*c)*a^7*c^5)*B*abs(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3) + (2*a^8*b^11*c^4 - 56*a^9*b^9*c^5 + 576*a^10*b^7*c^6 - 2816*a^11*b^5*c^7 + 6656*a^12*b^3*c^8 - 6144*a^13*b*c^9 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^11*c^2 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^9*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^10*c^3 - 288*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^7*c^4 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^8*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^9*c^4 + 1408*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^5*c^5 + 384*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^6*c^5 + 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^7*c^5 - 3328*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^12*b^3*c^6 - 1280*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^4*c^6 - 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^5*c^6 + 3072*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^13*b*c^7 + 1536*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^12*b^2*c^7 + 640*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^3*c^7 - 768*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^12*b*c^8 - 2*(b^2 - 4*a*c)*a^8*b^9*c^4 + 48*(b^2 - 4*a*c)*a^9*b^7*c^5 - 384*(b^2 - 4*a*c)*a^10*b^5*c^6 + 1280*(b^2 - 4*a*c)*a^11*b^3*c^7 - 1536*(b^2 - 4*a*c)*a^12*b*c^8)*B)*arctan(2*sqrt(1/2)*x/sqrt((a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3 - sqrt((a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3)^2 - 4*(a^5*b^4*c - 8*a^6*b^2*c^2 + 16*a^7*c^3)*(a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4)))/(a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4)))/((a^6*b^8*c - 16*a^7*b^6*c^2 - 2*a^6*b^7*c^2 + 96*a^8*b^4*c^3 + 24*a^7*b^5*c^3 + a^6*b^6*c^3 - 256*a^9*b^2*c^4 - 96*a^8*b^3*c^4 - 12*a^7*b^4*c^4 + 256*a^10*c^5 + 128*a^9*b*c^5 + 48*a^8*b^2*c^5 - 64*a^9*c^6)*abs(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*abs(c)) - 1/16*((b^6*c - 10*a*b^4*c^2 - 2*b^5*c^2 + 24*a^2*b^2*c^3 + 12*a*b^3*c^3 + b^4*c^3 - 6*a*b^2*c^4 + (b^5*c - 10*a*b^3*c^2 - 2*b^4*c^2 + 24*a^2*b*c^3 + 12*a*b^2*c^3 + b^3*c^3 - 6*a*b*c^4)*sqrt(b^2 - 4*a*c))*A*abs(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3) + 4*(a^2*b^3*c^2 - 4*a^3*b*c^3 - 2*a^2*b^2*c^3 + a^2*b*c^4 + (a^2*b^2*c^2 - 4*a^3*c^3 - 2*a^2*b*c^3 + a^2*c^4)*sqrt(b^2 - 4*a*c))*C*abs(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3) + (a^4*b^10*c^2 - 18*a^5*b^8*c^3 - 2*a^4*b^9*c^3 + 120*a^6*b^6*c^4 + 28*a^5*b^7*c^4 + a^4*b^8*c^4 - 352*a^7*b^4*c^5 - 128*a^6*b^5*c^5 - 14*a^5*b^6*c^5 + 384*a^8*b^2*c^6 + 192*a^7*b^3*c^6 + 64*a^6*b^4*c^6 - 96*a^7*b^2*c^7 + (a^4*b^9*c^2 - 14*a^5*b^7*c^3 - 2*a^4*b^8*c^3 + 64*a^6*b^5*c^4 + 20*a^5*b^6*c^4 + a^4*b^7*c^4 - 96*a^7*b^3*c^5 - 48*a^6*b^4*c^5 - 10*a^5*b^5*c^5 + 24*a^6*b^3*c^6)*sqrt(b^2 - 4*a*c))*A + 4*(a^6*b^7*c^3 - 12*a^7*b^5*c^4 - 2*a^6*b^6*c^4 + 48*a^8*b^3*c^5 + 16*a^7*b^4*c^5 + a^6*b^5*c^5 - 64*a^9*b*c^6 - 32*a^8*b^2*c^6 - 8*a^7*b^3*c^6 + 16*a^8*b*c^7 + (a^6*b^6*c^3 - 8*a^7*b^4*c^4 - 2*a^6*b^5*c^4 + 16*a^8*b^2*c^5 + 8*a^7*b^3*c^5 + a^6*b^4*c^5 - 4*a^7*b^2*c^6)*sqrt(b^2 - 4*a*c))*C)*log(x^2 + 1/2*(a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3 + sqrt((a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3)^2 - 4*(a^5*b^4*c - 8*a^6*b^2*c^2 + 16*a^7*c^3)*(a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4)))/(a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4))/((a^3*b^4 - 8*a^4*b^2*c - 2*a^3*b^3*c + 16*a^5*c^2 + 8*a^4*b*c^2 + a^3*b^2*c^2 - 4*a^4*c^3)*c^2*abs(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)) - 1/16*((b^6*c - 10*a*b^4*c^2 - 2*b^5*c^2 + 24*a^2*b^2*c^3 + 12*a*b^3*c^3 + b^4*c^3 - 6*a*b^2*c^4 - (b^5*c - 10*a*b^3*c^2 - 2*b^4*c^2 + 24*a^2*b*c^3 + 12*a*b^2*c^3 + b^3*c^3 - 6*a*b*c^4)*sqrt(b^2 - 4*a*c))*A*abs(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3) + 4*(a^2*b^3*c^2 - 4*a^3*b*c^3 - 2*a^2*b^2*c^3 + a^2*b*c^4 - (a^2*b^2*c^2 - 4*a^3*c^3 - 2*a^2*b*c^3 + a^2*c^4)*sqrt(b^2 - 4*a*c))*C*abs(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3) - (a^4*b^10*c^2 - 18*a^5*b^8*c^3 - 2*a^4*b^9*c^3 + 120*a^6*b^6*c^4 + 28*a^5*b^7*c^4 + a^4*b^8*c^4 - 352*a^7*b^4*c^5 - 128*a^6*b^5*c^5 - 14*a^5*b^6*c^5 + 384*a^8*b^2*c^6 + 192*a^7*b^3*c^6 + 64*a^6*b^4*c^6 - 96*a^7*b^2*c^7 - (a^4*b^9*c^2 - 14*a^5*b^7*c^3 - 2*a^4*b^8*c^3 + 64*a^6*b^5*c^4 + 20*a^5*b^6*c^4 + a^4*b^7*c^4 - 96*a^7*b^3*c^5 - 48*a^6*b^4*c^5 - 10*a^5*b^5*c^5 + 24*a^6*b^3*c^6)*sqrt(b^2 - 4*a*c))*A - 4*(a^6*b^7*c^3 - 12*a^7*b^5*c^4 - 2*a^6*b^6*c^4 + 48*a^8*b^3*c^5 + 16*a^7*b^4*c^5 + a^6*b^5*c^5 - 64*a^9*b*c^6 - 32*a^8*b^2*c^6 - 8*a^7*b^3*c^6 + 16*a^8*b*c^7 - (a^6*b^6*c^3 - 8*a^7*b^4*c^4 - 2*a^6*b^5*c^4 + 16*a^8*b^2*c^5 + 8*a^7*b^3*c^5 + a^6*b^4*c^5 - 4*a^7*b^2*c^6)*sqrt(b^2 - 4*a*c))*C)*log(x^2 + 1/2*(a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3 - sqrt((a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3)^2 - 4*(a^5*b^4*c - 8*a^6*b^2*c^2 + 16*a^7*c^3)*(a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4)))/(a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4))/((a^3*b^4 - 8*a^4*b^2*c - 2*a^3*b^3*c + 16*a^5*c^2 + 8*a^4*b*c^2 + a^3*b^2*c^2 - 4*a^4*c^3)*c^2*abs(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)) + 1/2*(B*a*b*c*x^3 - C*a^2*b + A*a*b^2 - 2*A*a^2*c - (2*C*a^2*c - A*a*b*c)*x^2 + (B*a*b^2 - 2*B*a^2*c)*x)/((c*x^4 + b*x^2 + a)*(b^2 - 4*a*c)*a^2)","B",0
35,1,9015,0,11.545034," ","integrate((C*x^2+B*x+A)/x^2/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{B \log\left({\left| c x^{4} + b x^{2} + a \right|}\right)}{4 \, a^{2}} + \frac{B \log\left({\left| x \right|}\right)}{a^{2}} + \frac{C a b c x^{4} - 3 \, A b^{2} c x^{4} + 10 \, A a c^{2} x^{4} + B a b c x^{3} + C a b^{2} x^{2} - 3 \, A b^{3} x^{2} - 2 \, C a^{2} c x^{2} + 11 \, A a b c x^{2} + B a b^{2} x - 2 \, B a^{2} c x - 2 \, A a b^{2} + 8 \, A a^{2} c}{2 \, {\left(c x^{5} + b x^{3} + a x\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}} - \frac{{\left({\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)}^{2} {\left(6 \, b^{4} c^{2} - 44 \, a b^{2} c^{3} + 80 \, a^{2} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 20 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} A - {\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)}^{2} {\left(2 \, a b^{3} c^{2} - 8 \, 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^{3} + 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 - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2}\right)} C + 2 \, {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{9} c - 49 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} c^{2} - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c^{2} - 6 \, a^{4} b^{9} c^{2} + 300 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c^{3} + 74 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{3} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{3} + 98 \, a^{5} b^{7} c^{3} - 816 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{4} - 304 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{4} - 37 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{4} - 600 \, a^{6} b^{5} c^{4} + 832 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{5} + 416 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} + 152 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{5} + 1632 \, a^{7} b^{3} c^{5} - 208 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{6} - 1664 \, a^{8} b c^{6} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{7} c^{2} - 74 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{5} c^{3} + 304 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{3} c^{4} - 416 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{5}\right)} A {\left| a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{8} c - 18 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{6} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} c^{2} - 2 \, a^{5} b^{8} c^{2} + 120 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{4} c^{3} + 28 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{3} + 36 \, a^{6} b^{6} c^{3} - 352 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{2} c^{4} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{4} - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{4} - 240 \, a^{7} b^{4} c^{4} + 384 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} c^{5} + 192 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{5} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} + 704 \, a^{8} b^{2} c^{5} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} c^{6} - 768 \, a^{9} c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{6} c^{2} - 28 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{4} c^{3} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{2} c^{4} - 192 \, {\left(b^{2} - 4 \, a c\right)} a^{8} c^{5}\right)} C {\left| a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} \right|} + {\left(6 \, a^{8} b^{12} c^{4} - 128 \, a^{9} b^{10} c^{5} + 1088 \, a^{10} b^{8} c^{6} - 4608 \, a^{11} b^{6} c^{7} + 9728 \, a^{12} b^{4} c^{8} - 8192 \, a^{13} b^{2} c^{9} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{12} c^{2} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{10} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{11} c^{3} - 544 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{8} c^{4} - 104 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{9} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{10} c^{4} + 2304 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{6} c^{5} + 672 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{7} c^{5} + 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{8} c^{5} - 4864 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{4} c^{6} - 1920 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{5} c^{6} - 336 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{6} c^{6} + 4096 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{13} b^{2} c^{7} + 2048 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{3} c^{7} + 960 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{4} c^{7} - 1024 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{2} c^{8} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{10} c^{4} + 104 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{8} c^{5} - 672 \, {\left(b^{2} - 4 \, a c\right)} a^{10} b^{6} c^{6} + 1920 \, {\left(b^{2} - 4 \, a c\right)} a^{11} b^{4} c^{7} - 2048 \, {\left(b^{2} - 4 \, a c\right)} a^{12} b^{2} c^{8}\right)} A - {\left(2 \, a^{9} b^{11} c^{4} - 56 \, a^{10} b^{9} c^{5} + 576 \, a^{11} b^{7} c^{6} - 2816 \, a^{12} b^{5} c^{7} + 6656 \, a^{13} b^{3} c^{8} - 6144 \, a^{14} b c^{9} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{11} c^{2} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{9} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{10} c^{3} - 288 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{7} c^{4} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{8} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{9} c^{4} + 1408 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{5} c^{5} + 384 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{6} c^{5} + 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{7} c^{5} - 3328 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{13} b^{3} c^{6} - 1280 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{4} c^{6} - 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{5} c^{6} + 3072 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{14} b c^{7} + 1536 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{13} b^{2} c^{7} + 640 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{3} c^{7} - 768 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{13} b c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{9} c^{4} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{10} b^{7} c^{5} - 384 \, {\left(b^{2} - 4 \, a c\right)} a^{11} b^{5} c^{6} + 1280 \, {\left(b^{2} - 4 \, a c\right)} a^{12} b^{3} c^{7} - 1536 \, {\left(b^{2} - 4 \, a c\right)} a^{13} b c^{8}\right)} C\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3} + \sqrt{{\left(a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3}\right)}^{2} - 4 \, {\left(a^{5} b^{4} c - 8 \, a^{6} b^{2} c^{2} + 16 \, a^{7} c^{3}\right)} {\left(a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}\right)}}}{a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}}}}\right)}{16 \, {\left(a^{7} b^{8} c - 16 \, a^{8} b^{6} c^{2} - 2 \, a^{7} b^{7} c^{2} + 96 \, a^{9} b^{4} c^{3} + 24 \, a^{8} b^{5} c^{3} + a^{7} b^{6} c^{3} - 256 \, a^{10} b^{2} c^{4} - 96 \, a^{9} b^{3} c^{4} - 12 \, a^{8} b^{4} c^{4} + 256 \, a^{11} c^{5} + 128 \, a^{10} b c^{5} + 48 \, a^{9} b^{2} c^{5} - 64 \, a^{10} c^{6}\right)} {\left| a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} \right|} {\left| c \right|}} + \frac{{\left({\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)}^{2} {\left(6 \, b^{4} c^{2} - 44 \, a b^{2} c^{3} + 80 \, a^{2} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 20 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} A - {\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)}^{2} {\left(2 \, a b^{3} c^{2} - 8 \, 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^{3} + 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 - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2}\right)} C - 2 \, {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{9} c - 49 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} c^{2} - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c^{2} + 6 \, a^{4} b^{9} c^{2} + 300 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c^{3} + 74 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{3} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{3} - 98 \, a^{5} b^{7} c^{3} - 816 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{4} - 304 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{4} - 37 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{4} + 600 \, a^{6} b^{5} c^{4} + 832 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{5} + 416 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} + 152 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{5} - 1632 \, a^{7} b^{3} c^{5} - 208 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{6} + 1664 \, a^{8} b c^{6} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{7} c^{2} + 74 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{5} c^{3} - 304 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{3} c^{4} + 416 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{5}\right)} A {\left| a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{8} c - 18 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{6} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} c^{2} + 2 \, a^{5} b^{8} c^{2} + 120 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{4} c^{3} + 28 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{3} - 36 \, a^{6} b^{6} c^{3} - 352 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{2} c^{4} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{4} - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{4} + 240 \, a^{7} b^{4} c^{4} + 384 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} c^{5} + 192 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{5} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} - 704 \, a^{8} b^{2} c^{5} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} c^{6} + 768 \, a^{9} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{6} c^{2} + 28 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{4} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{2} c^{4} + 192 \, {\left(b^{2} - 4 \, a c\right)} a^{8} c^{5}\right)} C {\left| a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} \right|} + {\left(6 \, a^{8} b^{12} c^{4} - 128 \, a^{9} b^{10} c^{5} + 1088 \, a^{10} b^{8} c^{6} - 4608 \, a^{11} b^{6} c^{7} + 9728 \, a^{12} b^{4} c^{8} - 8192 \, a^{13} b^{2} c^{9} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{12} c^{2} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{10} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{11} c^{3} - 544 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{8} c^{4} - 104 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{9} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{10} c^{4} + 2304 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{6} c^{5} + 672 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{7} c^{5} + 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{8} c^{5} - 4864 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{4} c^{6} - 1920 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{5} c^{6} - 336 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{6} c^{6} + 4096 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{13} b^{2} c^{7} + 2048 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{3} c^{7} + 960 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{4} c^{7} - 1024 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{2} c^{8} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{10} c^{4} + 104 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{8} c^{5} - 672 \, {\left(b^{2} - 4 \, a c\right)} a^{10} b^{6} c^{6} + 1920 \, {\left(b^{2} - 4 \, a c\right)} a^{11} b^{4} c^{7} - 2048 \, {\left(b^{2} - 4 \, a c\right)} a^{12} b^{2} c^{8}\right)} A - {\left(2 \, a^{9} b^{11} c^{4} - 56 \, a^{10} b^{9} c^{5} + 576 \, a^{11} b^{7} c^{6} - 2816 \, a^{12} b^{5} c^{7} + 6656 \, a^{13} b^{3} c^{8} - 6144 \, a^{14} b c^{9} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{11} c^{2} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{9} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{10} c^{3} - 288 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{7} c^{4} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{8} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{9} c^{4} + 1408 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{5} c^{5} + 384 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{6} c^{5} + 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{7} c^{5} - 3328 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{13} b^{3} c^{6} - 1280 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{4} c^{6} - 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{5} c^{6} + 3072 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{14} b c^{7} + 1536 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{13} b^{2} c^{7} + 640 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{3} c^{7} - 768 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{13} b c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{9} c^{4} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{10} b^{7} c^{5} - 384 \, {\left(b^{2} - 4 \, a c\right)} a^{11} b^{5} c^{6} + 1280 \, {\left(b^{2} - 4 \, a c\right)} a^{12} b^{3} c^{7} - 1536 \, {\left(b^{2} - 4 \, a c\right)} a^{13} b c^{8}\right)} C\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3} - \sqrt{{\left(a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3}\right)}^{2} - 4 \, {\left(a^{5} b^{4} c - 8 \, a^{6} b^{2} c^{2} + 16 \, a^{7} c^{3}\right)} {\left(a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}\right)}}}{a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}}}}\right)}{16 \, {\left(a^{7} b^{8} c - 16 \, a^{8} b^{6} c^{2} - 2 \, a^{7} b^{7} c^{2} + 96 \, a^{9} b^{4} c^{3} + 24 \, a^{8} b^{5} c^{3} + a^{7} b^{6} c^{3} - 256 \, a^{10} b^{2} c^{4} - 96 \, a^{9} b^{3} c^{4} - 12 \, a^{8} b^{4} c^{4} + 256 \, a^{11} c^{5} + 128 \, a^{10} b c^{5} + 48 \, a^{9} b^{2} c^{5} - 64 \, a^{10} c^{6}\right)} {\left| a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} \right|} {\left| c \right|}} - \frac{{\left({\left(b^{6} c - 10 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} + 24 \, a^{2} b^{2} c^{3} + 12 \, a b^{3} c^{3} + b^{4} c^{3} - 6 \, a b^{2} c^{4} + {\left(b^{5} c - 10 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + 24 \, a^{2} b c^{3} + 12 \, a b^{2} c^{3} + b^{3} c^{3} - 6 \, a b c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} \right|} - {\left(a^{4} b^{10} c^{2} - 18 \, a^{5} b^{8} c^{3} - 2 \, a^{4} b^{9} c^{3} + 120 \, a^{6} b^{6} c^{4} + 28 \, a^{5} b^{7} c^{4} + a^{4} b^{8} c^{4} - 352 \, a^{7} b^{4} c^{5} - 128 \, a^{6} b^{5} c^{5} - 14 \, a^{5} b^{6} c^{5} + 384 \, a^{8} b^{2} c^{6} + 192 \, a^{7} b^{3} c^{6} + 64 \, a^{6} b^{4} c^{6} - 96 \, a^{7} b^{2} c^{7} + {\left(a^{4} b^{9} c^{2} - 14 \, a^{5} b^{7} c^{3} - 2 \, a^{4} b^{8} c^{3} + 64 \, a^{6} b^{5} c^{4} + 20 \, a^{5} b^{6} c^{4} + a^{4} b^{7} c^{4} - 96 \, a^{7} b^{3} c^{5} - 48 \, a^{6} b^{4} c^{5} - 10 \, a^{5} b^{5} c^{5} + 24 \, a^{6} b^{3} c^{6}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3} + \sqrt{{\left(a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3}\right)}^{2} - 4 \, {\left(a^{5} b^{4} c - 8 \, a^{6} b^{2} c^{2} + 16 \, a^{7} c^{3}\right)} {\left(a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}\right)}}}{2 \, {\left(a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}\right)}}\right)}{16 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c - 2 \, a^{3} b^{3} c + 16 \, a^{5} c^{2} + 8 \, a^{4} b c^{2} + a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} c^{2} {\left| a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} \right|}} - \frac{{\left({\left(b^{6} c - 10 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} + 24 \, a^{2} b^{2} c^{3} + 12 \, a b^{3} c^{3} + b^{4} c^{3} - 6 \, a b^{2} c^{4} - {\left(b^{5} c - 10 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + 24 \, a^{2} b c^{3} + 12 \, a b^{2} c^{3} + b^{3} c^{3} - 6 \, a b c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} \right|} - {\left(a^{4} b^{10} c^{2} - 18 \, a^{5} b^{8} c^{3} - 2 \, a^{4} b^{9} c^{3} + 120 \, a^{6} b^{6} c^{4} + 28 \, a^{5} b^{7} c^{4} + a^{4} b^{8} c^{4} - 352 \, a^{7} b^{4} c^{5} - 128 \, a^{6} b^{5} c^{5} - 14 \, a^{5} b^{6} c^{5} + 384 \, a^{8} b^{2} c^{6} + 192 \, a^{7} b^{3} c^{6} + 64 \, a^{6} b^{4} c^{6} - 96 \, a^{7} b^{2} c^{7} - {\left(a^{4} b^{9} c^{2} - 14 \, a^{5} b^{7} c^{3} - 2 \, a^{4} b^{8} c^{3} + 64 \, a^{6} b^{5} c^{4} + 20 \, a^{5} b^{6} c^{4} + a^{4} b^{7} c^{4} - 96 \, a^{7} b^{3} c^{5} - 48 \, a^{6} b^{4} c^{5} - 10 \, a^{5} b^{5} c^{5} + 24 \, a^{6} b^{3} c^{6}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3} - \sqrt{{\left(a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3}\right)}^{2} - 4 \, {\left(a^{5} b^{4} c - 8 \, a^{6} b^{2} c^{2} + 16 \, a^{7} c^{3}\right)} {\left(a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}\right)}}}{2 \, {\left(a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}\right)}}\right)}{16 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c - 2 \, a^{3} b^{3} c + 16 \, a^{5} c^{2} + 8 \, a^{4} b c^{2} + a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} c^{2} {\left| a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3} \right|}}"," ",0,"-1/4*B*log(abs(c*x^4 + b*x^2 + a))/a^2 + B*log(abs(x))/a^2 + 1/2*(C*a*b*c*x^4 - 3*A*b^2*c*x^4 + 10*A*a*c^2*x^4 + B*a*b*c*x^3 + C*a*b^2*x^2 - 3*A*b^3*x^2 - 2*C*a^2*c*x^2 + 11*A*a*b*c*x^2 + B*a*b^2*x - 2*B*a^2*c*x - 2*A*a*b^2 + 8*A*a^2*c)/((c*x^5 + b*x^3 + a*x)*(a^2*b^2 - 4*a^3*c)) - 1/16*((a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)^2*(6*b^4*c^2 - 44*a*b^2*c^3 + 80*a^2*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 6*(b^2 - 4*a*c)*b^2*c^2 + 20*(b^2 - 4*a*c)*a*c^3)*A - (a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)^2*(2*a*b^3*c^2 - 8*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^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 2*(b^2 - 4*a*c)*a*b*c^2)*C + 2*(3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^9*c - 49*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^7*c^2 - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c^2 - 6*a^4*b^9*c^2 + 300*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c^3 + 74*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^3 + 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^3 + 98*a^5*b^7*c^3 - 816*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^4 - 304*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^4 - 37*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^4 - 600*a^6*b^5*c^4 + 832*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b*c^5 + 416*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 + 152*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^5 + 1632*a^7*b^3*c^5 - 208*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b*c^6 - 1664*a^8*b*c^6 + 6*(b^2 - 4*a*c)*a^4*b^7*c^2 - 74*(b^2 - 4*a*c)*a^5*b^5*c^3 + 304*(b^2 - 4*a*c)*a^6*b^3*c^4 - 416*(b^2 - 4*a*c)*a^7*b*c^5)*A*abs(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3) - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^8*c - 18*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^6*c^2 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^7*c^2 - 2*a^5*b^8*c^2 + 120*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^4*c^3 + 28*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c^3 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^3 + 36*a^6*b^6*c^3 - 352*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^2*c^4 - 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^4 - 14*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^4 - 240*a^7*b^4*c^4 + 384*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*c^5 + 192*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b*c^5 + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 + 704*a^8*b^2*c^5 - 96*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*c^6 - 768*a^9*c^6 + 2*(b^2 - 4*a*c)*a^5*b^6*c^2 - 28*(b^2 - 4*a*c)*a^6*b^4*c^3 + 128*(b^2 - 4*a*c)*a^7*b^2*c^4 - 192*(b^2 - 4*a*c)*a^8*c^5)*C*abs(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3) + (6*a^8*b^12*c^4 - 128*a^9*b^10*c^5 + 1088*a^10*b^8*c^6 - 4608*a^11*b^6*c^7 + 9728*a^12*b^4*c^8 - 8192*a^13*b^2*c^9 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^12*c^2 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^10*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^11*c^3 - 544*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^8*c^4 - 104*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^9*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^10*c^4 + 2304*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^6*c^5 + 672*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^7*c^5 + 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^8*c^5 - 4864*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^12*b^4*c^6 - 1920*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^5*c^6 - 336*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^6*c^6 + 4096*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^13*b^2*c^7 + 2048*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^12*b^3*c^7 + 960*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^4*c^7 - 1024*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^12*b^2*c^8 - 6*(b^2 - 4*a*c)*a^8*b^10*c^4 + 104*(b^2 - 4*a*c)*a^9*b^8*c^5 - 672*(b^2 - 4*a*c)*a^10*b^6*c^6 + 1920*(b^2 - 4*a*c)*a^11*b^4*c^7 - 2048*(b^2 - 4*a*c)*a^12*b^2*c^8)*A - (2*a^9*b^11*c^4 - 56*a^10*b^9*c^5 + 576*a^11*b^7*c^6 - 2816*a^12*b^5*c^7 + 6656*a^13*b^3*c^8 - 6144*a^14*b*c^9 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^11*c^2 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^9*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^10*c^3 - 288*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^7*c^4 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^8*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^9*c^4 + 1408*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^12*b^5*c^5 + 384*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^6*c^5 + 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^7*c^5 - 3328*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^13*b^3*c^6 - 1280*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^12*b^4*c^6 - 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^5*c^6 + 3072*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^14*b*c^7 + 1536*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^13*b^2*c^7 + 640*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^12*b^3*c^7 - 768*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^13*b*c^8 - 2*(b^2 - 4*a*c)*a^9*b^9*c^4 + 48*(b^2 - 4*a*c)*a^10*b^7*c^5 - 384*(b^2 - 4*a*c)*a^11*b^5*c^6 + 1280*(b^2 - 4*a*c)*a^12*b^3*c^7 - 1536*(b^2 - 4*a*c)*a^13*b*c^8)*C)*arctan(2*sqrt(1/2)*x/sqrt((a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3 + sqrt((a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3)^2 - 4*(a^5*b^4*c - 8*a^6*b^2*c^2 + 16*a^7*c^3)*(a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4)))/(a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4)))/((a^7*b^8*c - 16*a^8*b^6*c^2 - 2*a^7*b^7*c^2 + 96*a^9*b^4*c^3 + 24*a^8*b^5*c^3 + a^7*b^6*c^3 - 256*a^10*b^2*c^4 - 96*a^9*b^3*c^4 - 12*a^8*b^4*c^4 + 256*a^11*c^5 + 128*a^10*b*c^5 + 48*a^9*b^2*c^5 - 64*a^10*c^6)*abs(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*abs(c)) + 1/16*((a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)^2*(6*b^4*c^2 - 44*a*b^2*c^3 + 80*a^2*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 - 6*(b^2 - 4*a*c)*b^2*c^2 + 20*(b^2 - 4*a*c)*a*c^3)*A - (a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)^2*(2*a*b^3*c^2 - 8*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^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 2*(b^2 - 4*a*c)*a*b*c^2)*C - 2*(3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^9*c - 49*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^7*c^2 - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c^2 + 6*a^4*b^9*c^2 + 300*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c^3 + 74*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^3 + 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^3 - 98*a^5*b^7*c^3 - 816*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^4 - 304*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^4 - 37*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^4 + 600*a^6*b^5*c^4 + 832*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b*c^5 + 416*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 + 152*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^5 - 1632*a^7*b^3*c^5 - 208*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^6 + 1664*a^8*b*c^6 - 6*(b^2 - 4*a*c)*a^4*b^7*c^2 + 74*(b^2 - 4*a*c)*a^5*b^5*c^3 - 304*(b^2 - 4*a*c)*a^6*b^3*c^4 + 416*(b^2 - 4*a*c)*a^7*b*c^5)*A*abs(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3) + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^8*c - 18*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^6*c^2 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^7*c^2 + 2*a^5*b^8*c^2 + 120*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^4*c^3 + 28*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c^3 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^3 - 36*a^6*b^6*c^3 - 352*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^2*c^4 - 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^4 - 14*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^4 + 240*a^7*b^4*c^4 + 384*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*c^5 + 192*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b*c^5 + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 - 704*a^8*b^2*c^5 - 96*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*c^6 + 768*a^9*c^6 - 2*(b^2 - 4*a*c)*a^5*b^6*c^2 + 28*(b^2 - 4*a*c)*a^6*b^4*c^3 - 128*(b^2 - 4*a*c)*a^7*b^2*c^4 + 192*(b^2 - 4*a*c)*a^8*c^5)*C*abs(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3) + (6*a^8*b^12*c^4 - 128*a^9*b^10*c^5 + 1088*a^10*b^8*c^6 - 4608*a^11*b^6*c^7 + 9728*a^12*b^4*c^8 - 8192*a^13*b^2*c^9 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^12*c^2 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^10*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^11*c^3 - 544*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^8*c^4 - 104*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^9*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^10*c^4 + 2304*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^6*c^5 + 672*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^7*c^5 + 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^8*c^5 - 4864*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^12*b^4*c^6 - 1920*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^5*c^6 - 336*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^6*c^6 + 4096*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^13*b^2*c^7 + 2048*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^12*b^3*c^7 + 960*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^4*c^7 - 1024*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^12*b^2*c^8 - 6*(b^2 - 4*a*c)*a^8*b^10*c^4 + 104*(b^2 - 4*a*c)*a^9*b^8*c^5 - 672*(b^2 - 4*a*c)*a^10*b^6*c^6 + 1920*(b^2 - 4*a*c)*a^11*b^4*c^7 - 2048*(b^2 - 4*a*c)*a^12*b^2*c^8)*A - (2*a^9*b^11*c^4 - 56*a^10*b^9*c^5 + 576*a^11*b^7*c^6 - 2816*a^12*b^5*c^7 + 6656*a^13*b^3*c^8 - 6144*a^14*b*c^9 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^11*c^2 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^9*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^10*c^3 - 288*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^7*c^4 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^8*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^9*c^4 + 1408*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^12*b^5*c^5 + 384*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^6*c^5 + 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^7*c^5 - 3328*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^13*b^3*c^6 - 1280*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^12*b^4*c^6 - 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^5*c^6 + 3072*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^14*b*c^7 + 1536*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^13*b^2*c^7 + 640*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^12*b^3*c^7 - 768*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^13*b*c^8 - 2*(b^2 - 4*a*c)*a^9*b^9*c^4 + 48*(b^2 - 4*a*c)*a^10*b^7*c^5 - 384*(b^2 - 4*a*c)*a^11*b^5*c^6 + 1280*(b^2 - 4*a*c)*a^12*b^3*c^7 - 1536*(b^2 - 4*a*c)*a^13*b*c^8)*C)*arctan(2*sqrt(1/2)*x/sqrt((a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3 - sqrt((a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3)^2 - 4*(a^5*b^4*c - 8*a^6*b^2*c^2 + 16*a^7*c^3)*(a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4)))/(a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4)))/((a^7*b^8*c - 16*a^8*b^6*c^2 - 2*a^7*b^7*c^2 + 96*a^9*b^4*c^3 + 24*a^8*b^5*c^3 + a^7*b^6*c^3 - 256*a^10*b^2*c^4 - 96*a^9*b^3*c^4 - 12*a^8*b^4*c^4 + 256*a^11*c^5 + 128*a^10*b*c^5 + 48*a^9*b^2*c^5 - 64*a^10*c^6)*abs(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*abs(c)) - 1/16*((b^6*c - 10*a*b^4*c^2 - 2*b^5*c^2 + 24*a^2*b^2*c^3 + 12*a*b^3*c^3 + b^4*c^3 - 6*a*b^2*c^4 + (b^5*c - 10*a*b^3*c^2 - 2*b^4*c^2 + 24*a^2*b*c^3 + 12*a*b^2*c^3 + b^3*c^3 - 6*a*b*c^4)*sqrt(b^2 - 4*a*c))*B*abs(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3) - (a^4*b^10*c^2 - 18*a^5*b^8*c^3 - 2*a^4*b^9*c^3 + 120*a^6*b^6*c^4 + 28*a^5*b^7*c^4 + a^4*b^8*c^4 - 352*a^7*b^4*c^5 - 128*a^6*b^5*c^5 - 14*a^5*b^6*c^5 + 384*a^8*b^2*c^6 + 192*a^7*b^3*c^6 + 64*a^6*b^4*c^6 - 96*a^7*b^2*c^7 + (a^4*b^9*c^2 - 14*a^5*b^7*c^3 - 2*a^4*b^8*c^3 + 64*a^6*b^5*c^4 + 20*a^5*b^6*c^4 + a^4*b^7*c^4 - 96*a^7*b^3*c^5 - 48*a^6*b^4*c^5 - 10*a^5*b^5*c^5 + 24*a^6*b^3*c^6)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3 + sqrt((a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3)^2 - 4*(a^5*b^4*c - 8*a^6*b^2*c^2 + 16*a^7*c^3)*(a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4)))/(a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4))/((a^3*b^4 - 8*a^4*b^2*c - 2*a^3*b^3*c + 16*a^5*c^2 + 8*a^4*b*c^2 + a^3*b^2*c^2 - 4*a^4*c^3)*c^2*abs(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)) - 1/16*((b^6*c - 10*a*b^4*c^2 - 2*b^5*c^2 + 24*a^2*b^2*c^3 + 12*a*b^3*c^3 + b^4*c^3 - 6*a*b^2*c^4 - (b^5*c - 10*a*b^3*c^2 - 2*b^4*c^2 + 24*a^2*b*c^3 + 12*a*b^2*c^3 + b^3*c^3 - 6*a*b*c^4)*sqrt(b^2 - 4*a*c))*B*abs(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3) - (a^4*b^10*c^2 - 18*a^5*b^8*c^3 - 2*a^4*b^9*c^3 + 120*a^6*b^6*c^4 + 28*a^5*b^7*c^4 + a^4*b^8*c^4 - 352*a^7*b^4*c^5 - 128*a^6*b^5*c^5 - 14*a^5*b^6*c^5 + 384*a^8*b^2*c^6 + 192*a^7*b^3*c^6 + 64*a^6*b^4*c^6 - 96*a^7*b^2*c^7 - (a^4*b^9*c^2 - 14*a^5*b^7*c^3 - 2*a^4*b^8*c^3 + 64*a^6*b^5*c^4 + 20*a^5*b^6*c^4 + a^4*b^7*c^4 - 96*a^7*b^3*c^5 - 48*a^6*b^4*c^5 - 10*a^5*b^5*c^5 + 24*a^6*b^3*c^6)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3 - sqrt((a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3)^2 - 4*(a^5*b^4*c - 8*a^6*b^2*c^2 + 16*a^7*c^3)*(a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4)))/(a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4))/((a^3*b^4 - 8*a^4*b^2*c - 2*a^3*b^3*c + 16*a^5*c^2 + 8*a^4*b*c^2 + a^3*b^2*c^2 - 4*a^4*c^3)*c^2*abs(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3))","B",0
36,1,6938,0,7.564757," ","integrate((C*x^2+B*x+A)/x^3/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left({\left(a^{6} b^{4} c - 8 \, a^{7} b^{2} c^{2} + 16 \, a^{8} c^{3}\right)}^{2} {\left(6 \, b^{4} c^{2} - 44 \, a b^{2} c^{3} + 80 \, a^{2} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 20 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} B + 2 \, {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{9} c - 49 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{7} c^{2} - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{8} c^{2} - 6 \, a^{6} b^{9} c^{2} + 300 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{5} c^{3} + 74 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{6} c^{3} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{7} c^{3} + 98 \, a^{7} b^{7} c^{3} - 816 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{3} c^{4} - 304 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{4} c^{4} - 37 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{5} c^{4} - 600 \, a^{8} b^{5} c^{4} + 832 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b c^{5} + 416 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{2} c^{5} + 152 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{3} c^{5} + 1632 \, a^{9} b^{3} c^{5} - 208 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b c^{6} - 1664 \, a^{10} b c^{6} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{7} c^{2} - 74 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{5} c^{3} + 304 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{3} c^{4} - 416 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b c^{5}\right)} B {\left| a^{6} b^{4} c - 8 \, a^{7} b^{2} c^{2} + 16 \, a^{8} c^{3} \right|} + {\left(6 \, a^{12} b^{12} c^{4} - 128 \, a^{13} b^{10} c^{5} + 1088 \, a^{14} b^{8} c^{6} - 4608 \, a^{15} b^{6} c^{7} + 9728 \, a^{16} b^{4} c^{8} - 8192 \, a^{17} b^{2} c^{9} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{12} c^{2} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{13} b^{10} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{11} c^{3} - 544 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{14} b^{8} c^{4} - 104 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{13} b^{9} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{10} c^{4} + 2304 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{15} b^{6} c^{5} + 672 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{14} b^{7} c^{5} + 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{13} b^{8} c^{5} - 4864 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{16} b^{4} c^{6} - 1920 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{15} b^{5} c^{6} - 336 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{14} b^{6} c^{6} + 4096 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{17} b^{2} c^{7} + 2048 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{16} b^{3} c^{7} + 960 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{15} b^{4} c^{7} - 1024 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{16} b^{2} c^{8} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{12} b^{10} c^{4} + 104 \, {\left(b^{2} - 4 \, a c\right)} a^{13} b^{8} c^{5} - 672 \, {\left(b^{2} - 4 \, a c\right)} a^{14} b^{6} c^{6} + 1920 \, {\left(b^{2} - 4 \, a c\right)} a^{15} b^{4} c^{7} - 2048 \, {\left(b^{2} - 4 \, a c\right)} a^{16} b^{2} c^{8}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{6} b^{5} c - 8 \, a^{7} b^{3} c^{2} + 16 \, a^{8} b c^{3} + \sqrt{{\left(a^{6} b^{5} c - 8 \, a^{7} b^{3} c^{2} + 16 \, a^{8} b c^{3}\right)}^{2} - 4 \, {\left(a^{7} b^{4} c - 8 \, a^{8} b^{2} c^{2} + 16 \, a^{9} c^{3}\right)} {\left(a^{6} b^{4} c^{2} - 8 \, a^{7} b^{2} c^{3} + 16 \, a^{8} c^{4}\right)}}}{a^{6} b^{4} c^{2} - 8 \, a^{7} b^{2} c^{3} + 16 \, a^{8} c^{4}}}}\right)}{16 \, {\left(a^{9} b^{8} c - 16 \, a^{10} b^{6} c^{2} - 2 \, a^{9} b^{7} c^{2} + 96 \, a^{11} b^{4} c^{3} + 24 \, a^{10} b^{5} c^{3} + a^{9} b^{6} c^{3} - 256 \, a^{12} b^{2} c^{4} - 96 \, a^{11} b^{3} c^{4} - 12 \, a^{10} b^{4} c^{4} + 256 \, a^{13} c^{5} + 128 \, a^{12} b c^{5} + 48 \, a^{11} b^{2} c^{5} - 64 \, a^{12} c^{6}\right)} {\left| a^{6} b^{4} c - 8 \, a^{7} b^{2} c^{2} + 16 \, a^{8} c^{3} \right|} {\left| c \right|}} + \frac{{\left({\left(a^{6} b^{4} c - 8 \, a^{7} b^{2} c^{2} + 16 \, a^{8} c^{3}\right)}^{2} {\left(6 \, b^{4} c^{2} - 44 \, a b^{2} c^{3} + 80 \, a^{2} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 20 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} B - 2 \, {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{9} c - 49 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{7} c^{2} - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{8} c^{2} + 6 \, a^{6} b^{9} c^{2} + 300 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{5} c^{3} + 74 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{6} c^{3} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{7} c^{3} - 98 \, a^{7} b^{7} c^{3} - 816 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{3} c^{4} - 304 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{4} c^{4} - 37 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{5} c^{4} + 600 \, a^{8} b^{5} c^{4} + 832 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b c^{5} + 416 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{2} c^{5} + 152 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{3} c^{5} - 1632 \, a^{9} b^{3} c^{5} - 208 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b c^{6} + 1664 \, a^{10} b c^{6} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{7} c^{2} + 74 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{5} c^{3} - 304 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{3} c^{4} + 416 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b c^{5}\right)} B {\left| a^{6} b^{4} c - 8 \, a^{7} b^{2} c^{2} + 16 \, a^{8} c^{3} \right|} + {\left(6 \, a^{12} b^{12} c^{4} - 128 \, a^{13} b^{10} c^{5} + 1088 \, a^{14} b^{8} c^{6} - 4608 \, a^{15} b^{6} c^{7} + 9728 \, a^{16} b^{4} c^{8} - 8192 \, a^{17} b^{2} c^{9} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{12} c^{2} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{13} b^{10} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{11} c^{3} - 544 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{14} b^{8} c^{4} - 104 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{13} b^{9} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{10} c^{4} + 2304 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{15} b^{6} c^{5} + 672 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{14} b^{7} c^{5} + 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{13} b^{8} c^{5} - 4864 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{16} b^{4} c^{6} - 1920 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{15} b^{5} c^{6} - 336 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{14} b^{6} c^{6} + 4096 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{17} b^{2} c^{7} + 2048 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{16} b^{3} c^{7} + 960 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{15} b^{4} c^{7} - 1024 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{16} b^{2} c^{8} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{12} b^{10} c^{4} + 104 \, {\left(b^{2} - 4 \, a c\right)} a^{13} b^{8} c^{5} - 672 \, {\left(b^{2} - 4 \, a c\right)} a^{14} b^{6} c^{6} + 1920 \, {\left(b^{2} - 4 \, a c\right)} a^{15} b^{4} c^{7} - 2048 \, {\left(b^{2} - 4 \, a c\right)} a^{16} b^{2} c^{8}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{6} b^{5} c - 8 \, a^{7} b^{3} c^{2} + 16 \, a^{8} b c^{3} - \sqrt{{\left(a^{6} b^{5} c - 8 \, a^{7} b^{3} c^{2} + 16 \, a^{8} b c^{3}\right)}^{2} - 4 \, {\left(a^{7} b^{4} c - 8 \, a^{8} b^{2} c^{2} + 16 \, a^{9} c^{3}\right)} {\left(a^{6} b^{4} c^{2} - 8 \, a^{7} b^{2} c^{3} + 16 \, a^{8} c^{4}\right)}}}{a^{6} b^{4} c^{2} - 8 \, a^{7} b^{2} c^{3} + 16 \, a^{8} c^{4}}}}\right)}{16 \, {\left(a^{9} b^{8} c - 16 \, a^{10} b^{6} c^{2} - 2 \, a^{9} b^{7} c^{2} + 96 \, a^{11} b^{4} c^{3} + 24 \, a^{10} b^{5} c^{3} + a^{9} b^{6} c^{3} - 256 \, a^{12} b^{2} c^{4} - 96 \, a^{11} b^{3} c^{4} - 12 \, a^{10} b^{4} c^{4} + 256 \, a^{13} c^{5} + 128 \, a^{12} b c^{5} + 48 \, a^{11} b^{2} c^{5} - 64 \, a^{12} c^{6}\right)} {\left| a^{6} b^{4} c - 8 \, a^{7} b^{2} c^{2} + 16 \, a^{8} c^{3} \right|} {\left| c \right|}} - \frac{{\left(C a - 2 \, A b\right)} \log\left({\left| c x^{4} + b x^{2} + a \right|}\right)}{4 \, a^{3}} + \frac{{\left(C a - 2 \, A b\right)} \log\left({\left| x \right|}\right)}{a^{3}} + \frac{{\left(2 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} - 2 \, b^{6} c^{2} + 30 \, a^{2} b^{3} c^{3} + 12 \, a b^{4} c^{3} + b^{5} c^{3} - 24 \, a^{3} b c^{4} - 12 \, a^{2} b^{2} c^{4} - 6 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5} + {\left(b^{6} c - 10 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} + 30 \, a^{2} b^{2} c^{3} + 12 \, a b^{3} c^{3} + b^{4} c^{3} - 24 \, a^{3} c^{4} - 12 \, a^{2} b c^{4} - 6 \, a b^{2} c^{4} + 6 \, a^{2} c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A {\left| a^{6} b^{4} c - 8 \, a^{7} b^{2} c^{2} + 16 \, a^{8} c^{3} \right|} - {\left(a b^{6} c - 10 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 24 \, a^{3} b^{2} c^{3} + 12 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 6 \, a^{2} b^{2} c^{4} + {\left(a b^{5} c - 10 \, a^{2} b^{3} c^{2} - 2 \, a b^{4} c^{2} + 24 \, a^{3} b c^{3} + 12 \, a^{2} b^{2} c^{3} + a b^{3} c^{3} - 6 \, a^{2} b c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C {\left| a^{6} b^{4} c - 8 \, a^{7} b^{2} c^{2} + 16 \, a^{8} c^{3} \right|} - 2 \, {\left(a^{6} b^{11} c^{2} - 18 \, a^{7} b^{9} c^{3} - 2 \, a^{6} b^{10} c^{3} + 126 \, a^{8} b^{7} c^{4} + 28 \, a^{7} b^{8} c^{4} + a^{6} b^{9} c^{4} - 424 \, a^{9} b^{5} c^{5} - 140 \, a^{8} b^{6} c^{5} - 14 \, a^{7} b^{7} c^{5} + 672 \, a^{10} b^{3} c^{6} + 288 \, a^{9} b^{4} c^{6} + 70 \, a^{8} b^{5} c^{6} - 384 \, a^{11} b c^{7} - 192 \, a^{10} b^{2} c^{7} - 144 \, a^{9} b^{3} c^{7} + 96 \, a^{10} b c^{8} + {\left(a^{6} b^{10} c^{2} - 14 \, a^{7} b^{8} c^{3} - 2 \, a^{6} b^{9} c^{3} + 70 \, a^{8} b^{6} c^{4} + 20 \, a^{7} b^{7} c^{4} + a^{6} b^{8} c^{4} - 144 \, a^{9} b^{4} c^{5} - 60 \, a^{8} b^{5} c^{5} - 10 \, a^{7} b^{6} c^{5} + 96 \, a^{10} b^{2} c^{6} + 48 \, a^{9} b^{3} c^{6} + 30 \, a^{8} b^{4} c^{6} - 24 \, a^{9} b^{2} c^{7}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A + {\left(a^{7} b^{10} c^{2} - 18 \, a^{8} b^{8} c^{3} - 2 \, a^{7} b^{9} c^{3} + 120 \, a^{9} b^{6} c^{4} + 28 \, a^{8} b^{7} c^{4} + a^{7} b^{8} c^{4} - 352 \, a^{10} b^{4} c^{5} - 128 \, a^{9} b^{5} c^{5} - 14 \, a^{8} b^{6} c^{5} + 384 \, a^{11} b^{2} c^{6} + 192 \, a^{10} b^{3} c^{6} + 64 \, a^{9} b^{4} c^{6} - 96 \, a^{10} b^{2} c^{7} + {\left(a^{7} b^{9} c^{2} - 14 \, a^{8} b^{7} c^{3} - 2 \, a^{7} b^{8} c^{3} + 64 \, a^{9} b^{5} c^{4} + 20 \, a^{8} b^{6} c^{4} + a^{7} b^{7} c^{4} - 96 \, a^{10} b^{3} c^{5} - 48 \, a^{9} b^{4} c^{5} - 10 \, a^{8} b^{5} c^{5} + 24 \, a^{9} b^{3} c^{6}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C\right)} \log\left(x^{2} + \frac{a^{6} b^{5} c - 8 \, a^{7} b^{3} c^{2} + 16 \, a^{8} b c^{3} + \sqrt{{\left(a^{6} b^{5} c - 8 \, a^{7} b^{3} c^{2} + 16 \, a^{8} b c^{3}\right)}^{2} - 4 \, {\left(a^{7} b^{4} c - 8 \, a^{8} b^{2} c^{2} + 16 \, a^{9} c^{3}\right)} {\left(a^{6} b^{4} c^{2} - 8 \, a^{7} b^{2} c^{3} + 16 \, a^{8} c^{4}\right)}}}{2 \, {\left(a^{6} b^{4} c^{2} - 8 \, a^{7} b^{2} c^{3} + 16 \, a^{8} c^{4}\right)}}\right)}{16 \, {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c - 2 \, a^{4} b^{3} c + 16 \, a^{6} c^{2} + 8 \, a^{5} b c^{2} + a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} c^{2} {\left| a^{6} b^{4} c - 8 \, a^{7} b^{2} c^{2} + 16 \, a^{8} c^{3} \right|}} + \frac{{\left(2 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} - 2 \, b^{6} c^{2} + 30 \, a^{2} b^{3} c^{3} + 12 \, a b^{4} c^{3} + b^{5} c^{3} - 24 \, a^{3} b c^{4} - 12 \, a^{2} b^{2} c^{4} - 6 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5} - {\left(b^{6} c - 10 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} + 30 \, a^{2} b^{2} c^{3} + 12 \, a b^{3} c^{3} + b^{4} c^{3} - 24 \, a^{3} c^{4} - 12 \, a^{2} b c^{4} - 6 \, a b^{2} c^{4} + 6 \, a^{2} c^{5}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A {\left| a^{6} b^{4} c - 8 \, a^{7} b^{2} c^{2} + 16 \, a^{8} c^{3} \right|} - {\left(a b^{6} c - 10 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 24 \, a^{3} b^{2} c^{3} + 12 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 6 \, a^{2} b^{2} c^{4} - {\left(a b^{5} c - 10 \, a^{2} b^{3} c^{2} - 2 \, a b^{4} c^{2} + 24 \, a^{3} b c^{3} + 12 \, a^{2} b^{2} c^{3} + a b^{3} c^{3} - 6 \, a^{2} b c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C {\left| a^{6} b^{4} c - 8 \, a^{7} b^{2} c^{2} + 16 \, a^{8} c^{3} \right|} - 2 \, {\left(a^{6} b^{11} c^{2} - 18 \, a^{7} b^{9} c^{3} - 2 \, a^{6} b^{10} c^{3} + 126 \, a^{8} b^{7} c^{4} + 28 \, a^{7} b^{8} c^{4} + a^{6} b^{9} c^{4} - 424 \, a^{9} b^{5} c^{5} - 140 \, a^{8} b^{6} c^{5} - 14 \, a^{7} b^{7} c^{5} + 672 \, a^{10} b^{3} c^{6} + 288 \, a^{9} b^{4} c^{6} + 70 \, a^{8} b^{5} c^{6} - 384 \, a^{11} b c^{7} - 192 \, a^{10} b^{2} c^{7} - 144 \, a^{9} b^{3} c^{7} + 96 \, a^{10} b c^{8} - {\left(a^{6} b^{10} c^{2} - 14 \, a^{7} b^{8} c^{3} - 2 \, a^{6} b^{9} c^{3} + 70 \, a^{8} b^{6} c^{4} + 20 \, a^{7} b^{7} c^{4} + a^{6} b^{8} c^{4} - 144 \, a^{9} b^{4} c^{5} - 60 \, a^{8} b^{5} c^{5} - 10 \, a^{7} b^{6} c^{5} + 96 \, a^{10} b^{2} c^{6} + 48 \, a^{9} b^{3} c^{6} + 30 \, a^{8} b^{4} c^{6} - 24 \, a^{9} b^{2} c^{7}\right)} \sqrt{b^{2} - 4 \, a c}\right)} A + {\left(a^{7} b^{10} c^{2} - 18 \, a^{8} b^{8} c^{3} - 2 \, a^{7} b^{9} c^{3} + 120 \, a^{9} b^{6} c^{4} + 28 \, a^{8} b^{7} c^{4} + a^{7} b^{8} c^{4} - 352 \, a^{10} b^{4} c^{5} - 128 \, a^{9} b^{5} c^{5} - 14 \, a^{8} b^{6} c^{5} + 384 \, a^{11} b^{2} c^{6} + 192 \, a^{10} b^{3} c^{6} + 64 \, a^{9} b^{4} c^{6} - 96 \, a^{10} b^{2} c^{7} - {\left(a^{7} b^{9} c^{2} - 14 \, a^{8} b^{7} c^{3} - 2 \, a^{7} b^{8} c^{3} + 64 \, a^{9} b^{5} c^{4} + 20 \, a^{8} b^{6} c^{4} + a^{7} b^{7} c^{4} - 96 \, a^{10} b^{3} c^{5} - 48 \, a^{9} b^{4} c^{5} - 10 \, a^{8} b^{5} c^{5} + 24 \, a^{9} b^{3} c^{6}\right)} \sqrt{b^{2} - 4 \, a c}\right)} C\right)} \log\left(x^{2} + \frac{a^{6} b^{5} c - 8 \, a^{7} b^{3} c^{2} + 16 \, a^{8} b c^{3} - \sqrt{{\left(a^{6} b^{5} c - 8 \, a^{7} b^{3} c^{2} + 16 \, a^{8} b c^{3}\right)}^{2} - 4 \, {\left(a^{7} b^{4} c - 8 \, a^{8} b^{2} c^{2} + 16 \, a^{9} c^{3}\right)} {\left(a^{6} b^{4} c^{2} - 8 \, a^{7} b^{2} c^{3} + 16 \, a^{8} c^{4}\right)}}}{2 \, {\left(a^{6} b^{4} c^{2} - 8 \, a^{7} b^{2} c^{3} + 16 \, a^{8} c^{4}\right)}}\right)}{16 \, {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c - 2 \, a^{4} b^{3} c + 16 \, a^{6} c^{2} + 8 \, a^{5} b c^{2} + a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} c^{2} {\left| a^{6} b^{4} c - 8 \, a^{7} b^{2} c^{2} + 16 \, a^{8} c^{3} \right|}} - \frac{{\left(3 \, B a b^{2} c - 10 \, B a^{2} c^{2}\right)} x^{5} + A a^{2} b^{2} - 4 \, A a^{3} c - {\left(C a^{2} b c - 2 \, A a b^{2} c + 6 \, A a^{2} c^{2}\right)} x^{4} + {\left(3 \, B a b^{3} - 11 \, B a^{2} b c\right)} x^{3} - {\left(C a^{2} b^{2} - 2 \, A a b^{3} - 2 \, C a^{3} c + 7 \, A a^{2} b c\right)} x^{2} + 2 \, {\left(B a^{2} b^{2} - 4 \, B a^{3} c\right)} x}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} - 4 \, a c\right)} a^{3} x^{2}}"," ",0,"-1/16*((a^6*b^4*c - 8*a^7*b^2*c^2 + 16*a^8*c^3)^2*(6*b^4*c^2 - 44*a*b^2*c^3 + 80*a^2*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 6*(b^2 - 4*a*c)*b^2*c^2 + 20*(b^2 - 4*a*c)*a*c^3)*B + 2*(3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^9*c - 49*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^7*c^2 - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^8*c^2 - 6*a^6*b^9*c^2 + 300*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^3 + 74*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^6*c^3 + 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^7*c^3 + 98*a^7*b^7*c^3 - 816*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^4 - 304*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^4*c^4 - 37*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^5*c^4 - 600*a^8*b^5*c^4 + 832*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b*c^5 + 416*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^2*c^5 + 152*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^3*c^5 + 1632*a^9*b^3*c^5 - 208*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b*c^6 - 1664*a^10*b*c^6 + 6*(b^2 - 4*a*c)*a^6*b^7*c^2 - 74*(b^2 - 4*a*c)*a^7*b^5*c^3 + 304*(b^2 - 4*a*c)*a^8*b^3*c^4 - 416*(b^2 - 4*a*c)*a^9*b*c^5)*B*abs(a^6*b^4*c - 8*a^7*b^2*c^2 + 16*a^8*c^3) + (6*a^12*b^12*c^4 - 128*a^13*b^10*c^5 + 1088*a^14*b^8*c^6 - 4608*a^15*b^6*c^7 + 9728*a^16*b^4*c^8 - 8192*a^17*b^2*c^9 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^12*b^12*c^2 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^13*b^10*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^12*b^11*c^3 - 544*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^14*b^8*c^4 - 104*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^13*b^9*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^12*b^10*c^4 + 2304*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^15*b^6*c^5 + 672*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^14*b^7*c^5 + 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^13*b^8*c^5 - 4864*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^16*b^4*c^6 - 1920*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^15*b^5*c^6 - 336*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^14*b^6*c^6 + 4096*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^17*b^2*c^7 + 2048*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^16*b^3*c^7 + 960*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^15*b^4*c^7 - 1024*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^16*b^2*c^8 - 6*(b^2 - 4*a*c)*a^12*b^10*c^4 + 104*(b^2 - 4*a*c)*a^13*b^8*c^5 - 672*(b^2 - 4*a*c)*a^14*b^6*c^6 + 1920*(b^2 - 4*a*c)*a^15*b^4*c^7 - 2048*(b^2 - 4*a*c)*a^16*b^2*c^8)*B)*arctan(2*sqrt(1/2)*x/sqrt((a^6*b^5*c - 8*a^7*b^3*c^2 + 16*a^8*b*c^3 + sqrt((a^6*b^5*c - 8*a^7*b^3*c^2 + 16*a^8*b*c^3)^2 - 4*(a^7*b^4*c - 8*a^8*b^2*c^2 + 16*a^9*c^3)*(a^6*b^4*c^2 - 8*a^7*b^2*c^3 + 16*a^8*c^4)))/(a^6*b^4*c^2 - 8*a^7*b^2*c^3 + 16*a^8*c^4)))/((a^9*b^8*c - 16*a^10*b^6*c^2 - 2*a^9*b^7*c^2 + 96*a^11*b^4*c^3 + 24*a^10*b^5*c^3 + a^9*b^6*c^3 - 256*a^12*b^2*c^4 - 96*a^11*b^3*c^4 - 12*a^10*b^4*c^4 + 256*a^13*c^5 + 128*a^12*b*c^5 + 48*a^11*b^2*c^5 - 64*a^12*c^6)*abs(a^6*b^4*c - 8*a^7*b^2*c^2 + 16*a^8*c^3)*abs(c)) + 1/16*((a^6*b^4*c - 8*a^7*b^2*c^2 + 16*a^8*c^3)^2*(6*b^4*c^2 - 44*a*b^2*c^3 + 80*a^2*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 - 6*(b^2 - 4*a*c)*b^2*c^2 + 20*(b^2 - 4*a*c)*a*c^3)*B - 2*(3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^9*c - 49*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^7*c^2 - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^8*c^2 + 6*a^6*b^9*c^2 + 300*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^3 + 74*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^6*c^3 + 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^7*c^3 - 98*a^7*b^7*c^3 - 816*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^4 - 304*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^4*c^4 - 37*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^5*c^4 + 600*a^8*b^5*c^4 + 832*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b*c^5 + 416*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^2*c^5 + 152*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^3*c^5 - 1632*a^9*b^3*c^5 - 208*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b*c^6 + 1664*a^10*b*c^6 - 6*(b^2 - 4*a*c)*a^6*b^7*c^2 + 74*(b^2 - 4*a*c)*a^7*b^5*c^3 - 304*(b^2 - 4*a*c)*a^8*b^3*c^4 + 416*(b^2 - 4*a*c)*a^9*b*c^5)*B*abs(a^6*b^4*c - 8*a^7*b^2*c^2 + 16*a^8*c^3) + (6*a^12*b^12*c^4 - 128*a^13*b^10*c^5 + 1088*a^14*b^8*c^6 - 4608*a^15*b^6*c^7 + 9728*a^16*b^4*c^8 - 8192*a^17*b^2*c^9 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^12*b^12*c^2 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^13*b^10*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^12*b^11*c^3 - 544*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^14*b^8*c^4 - 104*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^13*b^9*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^12*b^10*c^4 + 2304*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^15*b^6*c^5 + 672*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^14*b^7*c^5 + 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^13*b^8*c^5 - 4864*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^16*b^4*c^6 - 1920*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^15*b^5*c^6 - 336*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^14*b^6*c^6 + 4096*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^17*b^2*c^7 + 2048*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^16*b^3*c^7 + 960*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^15*b^4*c^7 - 1024*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^16*b^2*c^8 - 6*(b^2 - 4*a*c)*a^12*b^10*c^4 + 104*(b^2 - 4*a*c)*a^13*b^8*c^5 - 672*(b^2 - 4*a*c)*a^14*b^6*c^6 + 1920*(b^2 - 4*a*c)*a^15*b^4*c^7 - 2048*(b^2 - 4*a*c)*a^16*b^2*c^8)*B)*arctan(2*sqrt(1/2)*x/sqrt((a^6*b^5*c - 8*a^7*b^3*c^2 + 16*a^8*b*c^3 - sqrt((a^6*b^5*c - 8*a^7*b^3*c^2 + 16*a^8*b*c^3)^2 - 4*(a^7*b^4*c - 8*a^8*b^2*c^2 + 16*a^9*c^3)*(a^6*b^4*c^2 - 8*a^7*b^2*c^3 + 16*a^8*c^4)))/(a^6*b^4*c^2 - 8*a^7*b^2*c^3 + 16*a^8*c^4)))/((a^9*b^8*c - 16*a^10*b^6*c^2 - 2*a^9*b^7*c^2 + 96*a^11*b^4*c^3 + 24*a^10*b^5*c^3 + a^9*b^6*c^3 - 256*a^12*b^2*c^4 - 96*a^11*b^3*c^4 - 12*a^10*b^4*c^4 + 256*a^13*c^5 + 128*a^12*b*c^5 + 48*a^11*b^2*c^5 - 64*a^12*c^6)*abs(a^6*b^4*c - 8*a^7*b^2*c^2 + 16*a^8*c^3)*abs(c)) - 1/4*(C*a - 2*A*b)*log(abs(c*x^4 + b*x^2 + a))/a^3 + (C*a - 2*A*b)*log(abs(x))/a^3 + 1/16*(2*(b^7*c - 10*a*b^5*c^2 - 2*b^6*c^2 + 30*a^2*b^3*c^3 + 12*a*b^4*c^3 + b^5*c^3 - 24*a^3*b*c^4 - 12*a^2*b^2*c^4 - 6*a*b^3*c^4 + 6*a^2*b*c^5 + (b^6*c - 10*a*b^4*c^2 - 2*b^5*c^2 + 30*a^2*b^2*c^3 + 12*a*b^3*c^3 + b^4*c^3 - 24*a^3*c^4 - 12*a^2*b*c^4 - 6*a*b^2*c^4 + 6*a^2*c^5)*sqrt(b^2 - 4*a*c))*A*abs(a^6*b^4*c - 8*a^7*b^2*c^2 + 16*a^8*c^3) - (a*b^6*c - 10*a^2*b^4*c^2 - 2*a*b^5*c^2 + 24*a^3*b^2*c^3 + 12*a^2*b^3*c^3 + a*b^4*c^3 - 6*a^2*b^2*c^4 + (a*b^5*c - 10*a^2*b^3*c^2 - 2*a*b^4*c^2 + 24*a^3*b*c^3 + 12*a^2*b^2*c^3 + a*b^3*c^3 - 6*a^2*b*c^4)*sqrt(b^2 - 4*a*c))*C*abs(a^6*b^4*c - 8*a^7*b^2*c^2 + 16*a^8*c^3) - 2*(a^6*b^11*c^2 - 18*a^7*b^9*c^3 - 2*a^6*b^10*c^3 + 126*a^8*b^7*c^4 + 28*a^7*b^8*c^4 + a^6*b^9*c^4 - 424*a^9*b^5*c^5 - 140*a^8*b^6*c^5 - 14*a^7*b^7*c^5 + 672*a^10*b^3*c^6 + 288*a^9*b^4*c^6 + 70*a^8*b^5*c^6 - 384*a^11*b*c^7 - 192*a^10*b^2*c^7 - 144*a^9*b^3*c^7 + 96*a^10*b*c^8 + (a^6*b^10*c^2 - 14*a^7*b^8*c^3 - 2*a^6*b^9*c^3 + 70*a^8*b^6*c^4 + 20*a^7*b^7*c^4 + a^6*b^8*c^4 - 144*a^9*b^4*c^5 - 60*a^8*b^5*c^5 - 10*a^7*b^6*c^5 + 96*a^10*b^2*c^6 + 48*a^9*b^3*c^6 + 30*a^8*b^4*c^6 - 24*a^9*b^2*c^7)*sqrt(b^2 - 4*a*c))*A + (a^7*b^10*c^2 - 18*a^8*b^8*c^3 - 2*a^7*b^9*c^3 + 120*a^9*b^6*c^4 + 28*a^8*b^7*c^4 + a^7*b^8*c^4 - 352*a^10*b^4*c^5 - 128*a^9*b^5*c^5 - 14*a^8*b^6*c^5 + 384*a^11*b^2*c^6 + 192*a^10*b^3*c^6 + 64*a^9*b^4*c^6 - 96*a^10*b^2*c^7 + (a^7*b^9*c^2 - 14*a^8*b^7*c^3 - 2*a^7*b^8*c^3 + 64*a^9*b^5*c^4 + 20*a^8*b^6*c^4 + a^7*b^7*c^4 - 96*a^10*b^3*c^5 - 48*a^9*b^4*c^5 - 10*a^8*b^5*c^5 + 24*a^9*b^3*c^6)*sqrt(b^2 - 4*a*c))*C)*log(x^2 + 1/2*(a^6*b^5*c - 8*a^7*b^3*c^2 + 16*a^8*b*c^3 + sqrt((a^6*b^5*c - 8*a^7*b^3*c^2 + 16*a^8*b*c^3)^2 - 4*(a^7*b^4*c - 8*a^8*b^2*c^2 + 16*a^9*c^3)*(a^6*b^4*c^2 - 8*a^7*b^2*c^3 + 16*a^8*c^4)))/(a^6*b^4*c^2 - 8*a^7*b^2*c^3 + 16*a^8*c^4))/((a^4*b^4 - 8*a^5*b^2*c - 2*a^4*b^3*c + 16*a^6*c^2 + 8*a^5*b*c^2 + a^4*b^2*c^2 - 4*a^5*c^3)*c^2*abs(a^6*b^4*c - 8*a^7*b^2*c^2 + 16*a^8*c^3)) + 1/16*(2*(b^7*c - 10*a*b^5*c^2 - 2*b^6*c^2 + 30*a^2*b^3*c^3 + 12*a*b^4*c^3 + b^5*c^3 - 24*a^3*b*c^4 - 12*a^2*b^2*c^4 - 6*a*b^3*c^4 + 6*a^2*b*c^5 - (b^6*c - 10*a*b^4*c^2 - 2*b^5*c^2 + 30*a^2*b^2*c^3 + 12*a*b^3*c^3 + b^4*c^3 - 24*a^3*c^4 - 12*a^2*b*c^4 - 6*a*b^2*c^4 + 6*a^2*c^5)*sqrt(b^2 - 4*a*c))*A*abs(a^6*b^4*c - 8*a^7*b^2*c^2 + 16*a^8*c^3) - (a*b^6*c - 10*a^2*b^4*c^2 - 2*a*b^5*c^2 + 24*a^3*b^2*c^3 + 12*a^2*b^3*c^3 + a*b^4*c^3 - 6*a^2*b^2*c^4 - (a*b^5*c - 10*a^2*b^3*c^2 - 2*a*b^4*c^2 + 24*a^3*b*c^3 + 12*a^2*b^2*c^3 + a*b^3*c^3 - 6*a^2*b*c^4)*sqrt(b^2 - 4*a*c))*C*abs(a^6*b^4*c - 8*a^7*b^2*c^2 + 16*a^8*c^3) - 2*(a^6*b^11*c^2 - 18*a^7*b^9*c^3 - 2*a^6*b^10*c^3 + 126*a^8*b^7*c^4 + 28*a^7*b^8*c^4 + a^6*b^9*c^4 - 424*a^9*b^5*c^5 - 140*a^8*b^6*c^5 - 14*a^7*b^7*c^5 + 672*a^10*b^3*c^6 + 288*a^9*b^4*c^6 + 70*a^8*b^5*c^6 - 384*a^11*b*c^7 - 192*a^10*b^2*c^7 - 144*a^9*b^3*c^7 + 96*a^10*b*c^8 - (a^6*b^10*c^2 - 14*a^7*b^8*c^3 - 2*a^6*b^9*c^3 + 70*a^8*b^6*c^4 + 20*a^7*b^7*c^4 + a^6*b^8*c^4 - 144*a^9*b^4*c^5 - 60*a^8*b^5*c^5 - 10*a^7*b^6*c^5 + 96*a^10*b^2*c^6 + 48*a^9*b^3*c^6 + 30*a^8*b^4*c^6 - 24*a^9*b^2*c^7)*sqrt(b^2 - 4*a*c))*A + (a^7*b^10*c^2 - 18*a^8*b^8*c^3 - 2*a^7*b^9*c^3 + 120*a^9*b^6*c^4 + 28*a^8*b^7*c^4 + a^7*b^8*c^4 - 352*a^10*b^4*c^5 - 128*a^9*b^5*c^5 - 14*a^8*b^6*c^5 + 384*a^11*b^2*c^6 + 192*a^10*b^3*c^6 + 64*a^9*b^4*c^6 - 96*a^10*b^2*c^7 - (a^7*b^9*c^2 - 14*a^8*b^7*c^3 - 2*a^7*b^8*c^3 + 64*a^9*b^5*c^4 + 20*a^8*b^6*c^4 + a^7*b^7*c^4 - 96*a^10*b^3*c^5 - 48*a^9*b^4*c^5 - 10*a^8*b^5*c^5 + 24*a^9*b^3*c^6)*sqrt(b^2 - 4*a*c))*C)*log(x^2 + 1/2*(a^6*b^5*c - 8*a^7*b^3*c^2 + 16*a^8*b*c^3 - sqrt((a^6*b^5*c - 8*a^7*b^3*c^2 + 16*a^8*b*c^3)^2 - 4*(a^7*b^4*c - 8*a^8*b^2*c^2 + 16*a^9*c^3)*(a^6*b^4*c^2 - 8*a^7*b^2*c^3 + 16*a^8*c^4)))/(a^6*b^4*c^2 - 8*a^7*b^2*c^3 + 16*a^8*c^4))/((a^4*b^4 - 8*a^5*b^2*c - 2*a^4*b^3*c + 16*a^6*c^2 + 8*a^5*b*c^2 + a^4*b^2*c^2 - 4*a^5*c^3)*c^2*abs(a^6*b^4*c - 8*a^7*b^2*c^2 + 16*a^8*c^3)) - 1/2*((3*B*a*b^2*c - 10*B*a^2*c^2)*x^5 + A*a^2*b^2 - 4*A*a^3*c - (C*a^2*b*c - 2*A*a*b^2*c + 6*A*a^2*c^2)*x^4 + (3*B*a*b^3 - 11*B*a^2*b*c)*x^3 - (C*a^2*b^2 - 2*A*a*b^3 - 2*C*a^3*c + 7*A*a^2*b*c)*x^2 + 2*(B*a^2*b^2 - 4*B*a^3*c)*x)/((c*x^4 + b*x^2 + a)*(b^2 - 4*a*c)*a^3*x^2)","B",0
37,1,7808,0,1.131290," ","integrate((d*x)^m*(C*x^2+B*x+A)*(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{\left(d x\right)^{m} C c^{3} m^{14} x^{15} + \left(d x\right)^{m} B c^{3} m^{14} x^{14} + 105 \, \left(d x\right)^{m} C c^{3} m^{13} x^{15} + 3 \, \left(d x\right)^{m} C b c^{2} m^{14} x^{13} + \left(d x\right)^{m} A c^{3} m^{14} x^{13} + 106 \, \left(d x\right)^{m} B c^{3} m^{13} x^{14} + 5005 \, \left(d x\right)^{m} C c^{3} m^{12} x^{15} + 3 \, \left(d x\right)^{m} B b c^{2} m^{14} x^{12} + 321 \, \left(d x\right)^{m} C b c^{2} m^{13} x^{13} + 107 \, \left(d x\right)^{m} A c^{3} m^{13} x^{13} + 5096 \, \left(d x\right)^{m} B c^{3} m^{12} x^{14} + 143325 \, \left(d x\right)^{m} C c^{3} m^{11} x^{15} + 3 \, \left(d x\right)^{m} C b^{2} c m^{14} x^{11} + 3 \, \left(d x\right)^{m} C a c^{2} m^{14} x^{11} + 3 \, \left(d x\right)^{m} A b c^{2} m^{14} x^{11} + 324 \, \left(d x\right)^{m} B b c^{2} m^{13} x^{12} + 15567 \, \left(d x\right)^{m} C b c^{2} m^{12} x^{13} + 5189 \, \left(d x\right)^{m} A c^{3} m^{12} x^{13} + 147056 \, \left(d x\right)^{m} B c^{3} m^{11} x^{14} + 2749747 \, \left(d x\right)^{m} C c^{3} m^{10} x^{15} + 3 \, \left(d x\right)^{m} B b^{2} c m^{14} x^{10} + 3 \, \left(d x\right)^{m} B a c^{2} m^{14} x^{10} + 327 \, \left(d x\right)^{m} C b^{2} c m^{13} x^{11} + 327 \, \left(d x\right)^{m} C a c^{2} m^{13} x^{11} + 327 \, \left(d x\right)^{m} A b c^{2} m^{13} x^{11} + 15852 \, \left(d x\right)^{m} B b c^{2} m^{12} x^{12} + 452829 \, \left(d x\right)^{m} C b c^{2} m^{11} x^{13} + 150943 \, \left(d x\right)^{m} A c^{3} m^{11} x^{13} + 2840838 \, \left(d x\right)^{m} B c^{3} m^{10} x^{14} + 37312275 \, \left(d x\right)^{m} C c^{3} m^{9} x^{15} + \left(d x\right)^{m} C b^{3} m^{14} x^{9} + 6 \, \left(d x\right)^{m} C a b c m^{14} x^{9} + 3 \, \left(d x\right)^{m} A b^{2} c m^{14} x^{9} + 3 \, \left(d x\right)^{m} A a c^{2} m^{14} x^{9} + 330 \, \left(d x\right)^{m} B b^{2} c m^{13} x^{10} + 330 \, \left(d x\right)^{m} B a c^{2} m^{13} x^{10} + 16143 \, \left(d x\right)^{m} C b^{2} c m^{12} x^{11} + 16143 \, \left(d x\right)^{m} C a c^{2} m^{12} x^{11} + 16143 \, \left(d x\right)^{m} A b c^{2} m^{12} x^{11} + 464976 \, \left(d x\right)^{m} B b c^{2} m^{11} x^{12} + 8812089 \, \left(d x\right)^{m} C b c^{2} m^{10} x^{13} + 2937363 \, \left(d x\right)^{m} A c^{3} m^{10} x^{13} + 38786748 \, \left(d x\right)^{m} B c^{3} m^{9} x^{14} + 368411615 \, \left(d x\right)^{m} C c^{3} m^{8} x^{15} + \left(d x\right)^{m} B b^{3} m^{14} x^{8} + 6 \, \left(d x\right)^{m} B a b c m^{14} x^{8} + 111 \, \left(d x\right)^{m} C b^{3} m^{13} x^{9} + 666 \, \left(d x\right)^{m} C a b c m^{13} x^{9} + 333 \, \left(d x\right)^{m} A b^{2} c m^{13} x^{9} + 333 \, \left(d x\right)^{m} A a c^{2} m^{13} x^{9} + 16440 \, \left(d x\right)^{m} B b^{2} c m^{12} x^{10} + 16440 \, \left(d x\right)^{m} B a c^{2} m^{12} x^{10} + 477627 \, \left(d x\right)^{m} C b^{2} c m^{11} x^{11} + 477627 \, \left(d x\right)^{m} C a c^{2} m^{11} x^{11} + 477627 \, \left(d x\right)^{m} A b c^{2} m^{11} x^{11} + 9119154 \, \left(d x\right)^{m} B b c^{2} m^{10} x^{12} + 121118283 \, \left(d x\right)^{m} C b c^{2} m^{9} x^{13} + 40372761 \, \left(d x\right)^{m} A c^{3} m^{9} x^{13} + 385081268 \, \left(d x\right)^{m} B c^{3} m^{8} x^{14} + 2681453775 \, \left(d x\right)^{m} C c^{3} m^{7} x^{15} + 3 \, \left(d x\right)^{m} C a b^{2} m^{14} x^{7} + \left(d x\right)^{m} A b^{3} m^{14} x^{7} + 3 \, \left(d x\right)^{m} C a^{2} c m^{14} x^{7} + 6 \, \left(d x\right)^{m} A a b c m^{14} x^{7} + 112 \, \left(d x\right)^{m} B b^{3} m^{13} x^{8} + 672 \, \left(d x\right)^{m} B a b c m^{13} x^{8} + 5581 \, \left(d x\right)^{m} C b^{3} m^{12} x^{9} + 33486 \, \left(d x\right)^{m} C a b c m^{12} x^{9} + 16743 \, \left(d x\right)^{m} A b^{2} c m^{12} x^{9} + 16743 \, \left(d x\right)^{m} A a c^{2} m^{12} x^{9} + 490800 \, \left(d x\right)^{m} B b^{2} c m^{11} x^{10} + 490800 \, \left(d x\right)^{m} B a c^{2} m^{11} x^{10} + 9444969 \, \left(d x\right)^{m} C b^{2} c m^{10} x^{11} + 9444969 \, \left(d x\right)^{m} C a c^{2} m^{10} x^{11} + 9444969 \, \left(d x\right)^{m} A b c^{2} m^{10} x^{11} + 126245592 \, \left(d x\right)^{m} B b c^{2} m^{9} x^{12} + 1209749541 \, \left(d x\right)^{m} C b c^{2} m^{8} x^{13} + 403249847 \, \left(d x\right)^{m} A c^{3} m^{8} x^{13} + 2816490248 \, \left(d x\right)^{m} B c^{3} m^{7} x^{14} + 14409322928 \, \left(d x\right)^{m} C c^{3} m^{6} x^{15} + 3 \, \left(d x\right)^{m} B a b^{2} m^{14} x^{6} + 3 \, \left(d x\right)^{m} B a^{2} c m^{14} x^{6} + 339 \, \left(d x\right)^{m} C a b^{2} m^{13} x^{7} + 113 \, \left(d x\right)^{m} A b^{3} m^{13} x^{7} + 339 \, \left(d x\right)^{m} C a^{2} c m^{13} x^{7} + 678 \, \left(d x\right)^{m} A a b c m^{13} x^{7} + 5684 \, \left(d x\right)^{m} B b^{3} m^{12} x^{8} + 34104 \, \left(d x\right)^{m} B a b c m^{12} x^{8} + 168171 \, \left(d x\right)^{m} C b^{3} m^{11} x^{9} + 1009026 \, \left(d x\right)^{m} C a b c m^{11} x^{9} + 504513 \, \left(d x\right)^{m} A b^{2} c m^{11} x^{9} + 504513 \, \left(d x\right)^{m} A a c^{2} m^{11} x^{9} + 9790866 \, \left(d x\right)^{m} B b^{2} c m^{10} x^{10} + 9790866 \, \left(d x\right)^{m} B a c^{2} m^{10} x^{10} + 131780781 \, \left(d x\right)^{m} C b^{2} c m^{9} x^{11} + 131780781 \, \left(d x\right)^{m} C a c^{2} m^{9} x^{11} + 131780781 \, \left(d x\right)^{m} A b c^{2} m^{9} x^{11} + 1269340116 \, \left(d x\right)^{m} B b c^{2} m^{8} x^{12} + 8896139967 \, \left(d x\right)^{m} C b c^{2} m^{7} x^{13} + 2965379989 \, \left(d x\right)^{m} A c^{3} m^{7} x^{13} + 15200266081 \, \left(d x\right)^{m} B c^{3} m^{6} x^{14} + 56663366760 \, \left(d x\right)^{m} C c^{3} m^{5} x^{15} + 3 \, \left(d x\right)^{m} C a^{2} b m^{14} x^{5} + 3 \, \left(d x\right)^{m} A a b^{2} m^{14} x^{5} + 3 \, \left(d x\right)^{m} A a^{2} c m^{14} x^{5} + 342 \, \left(d x\right)^{m} B a b^{2} m^{13} x^{6} + 342 \, \left(d x\right)^{m} B a^{2} c m^{13} x^{6} + 17367 \, \left(d x\right)^{m} C a b^{2} m^{12} x^{7} + 5789 \, \left(d x\right)^{m} A b^{3} m^{12} x^{7} + 17367 \, \left(d x\right)^{m} C a^{2} c m^{12} x^{7} + 34734 \, \left(d x\right)^{m} A a b c m^{12} x^{7} + 172928 \, \left(d x\right)^{m} B b^{3} m^{11} x^{8} + 1037568 \, \left(d x\right)^{m} B a b c m^{11} x^{8} + 3386083 \, \left(d x\right)^{m} C b^{3} m^{10} x^{9} + 20316498 \, \left(d x\right)^{m} C a b c m^{10} x^{9} + 10158249 \, \left(d x\right)^{m} A b^{2} c m^{10} x^{9} + 10158249 \, \left(d x\right)^{m} A a c^{2} m^{10} x^{9} + 137766780 \, \left(d x\right)^{m} B b^{2} c m^{9} x^{10} + 137766780 \, \left(d x\right)^{m} B a c^{2} m^{9} x^{10} + 1334698629 \, \left(d x\right)^{m} C b^{2} c m^{8} x^{11} + 1334698629 \, \left(d x\right)^{m} C a c^{2} m^{8} x^{11} + 1334698629 \, \left(d x\right)^{m} A b c^{2} m^{8} x^{11} + 9390802608 \, \left(d x\right)^{m} B b c^{2} m^{7} x^{12} + 48243569088 \, \left(d x\right)^{m} C b c^{2} m^{6} x^{13} + 16081189696 \, \left(d x\right)^{m} A c^{3} m^{6} x^{13} + 59999485546 \, \left(d x\right)^{m} B c^{3} m^{5} x^{14} 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\left(d x\right)^{m} B a^{2} b m x^{4} + 784604620800 \, \left(d x\right)^{m} C a^{2} b x^{5} + 784604620800 \, \left(d x\right)^{m} A a b^{2} x^{5} + 784604620800 \, \left(d x\right)^{m} A a^{2} c x^{5} + 1922666722704 \, \left(d x\right)^{m} A a^{3} m^{3} x + 2161577352960 \, \left(d x\right)^{m} B a^{3} m^{2} x^{2} + 1301090515200 \, \left(d x\right)^{m} C a^{3} m x^{3} + 3903271545600 \, \left(d x\right)^{m} A a^{2} b m x^{3} + 980755776000 \, \left(d x\right)^{m} B a^{2} b x^{4} + 3134328981120 \, \left(d x\right)^{m} A a^{3} m^{2} x + 1842662908800 \, \left(d x\right)^{m} B a^{3} m x^{2} + 435891456000 \, \left(d x\right)^{m} C a^{3} x^{3} + 1307674368000 \, \left(d x\right)^{m} A a^{2} b x^{3} + 3031488633600 \, \left(d x\right)^{m} A a^{3} m x + 653837184000 \, \left(d x\right)^{m} B a^{3} x^{2} + 1307674368000 \, \left(d x\right)^{m} A a^{3} x}{m^{15} + 120 \, m^{14} + 6580 \, m^{13} + 218400 \, m^{12} + 4899622 \, m^{11} + 78558480 \, m^{10} + 928095740 \, m^{9} + 8207628000 \, m^{8} + 54631129553 \, m^{7} + 272803210680 \, m^{6} + 1009672107080 \, m^{5} + 2706813345600 \, m^{4} + 5056995703824 \, m^{3} + 6165817614720 \, m^{2} + 4339163001600 \, m + 1307674368000}"," ",0,"((d*x)^m*C*c^3*m^14*x^15 + (d*x)^m*B*c^3*m^14*x^14 + 105*(d*x)^m*C*c^3*m^13*x^15 + 3*(d*x)^m*C*b*c^2*m^14*x^13 + (d*x)^m*A*c^3*m^14*x^13 + 106*(d*x)^m*B*c^3*m^13*x^14 + 5005*(d*x)^m*C*c^3*m^12*x^15 + 3*(d*x)^m*B*b*c^2*m^14*x^12 + 321*(d*x)^m*C*b*c^2*m^13*x^13 + 107*(d*x)^m*A*c^3*m^13*x^13 + 5096*(d*x)^m*B*c^3*m^12*x^14 + 143325*(d*x)^m*C*c^3*m^11*x^15 + 3*(d*x)^m*C*b^2*c*m^14*x^11 + 3*(d*x)^m*C*a*c^2*m^14*x^11 + 3*(d*x)^m*A*b*c^2*m^14*x^11 + 324*(d*x)^m*B*b*c^2*m^13*x^12 + 15567*(d*x)^m*C*b*c^2*m^12*x^13 + 5189*(d*x)^m*A*c^3*m^12*x^13 + 147056*(d*x)^m*B*c^3*m^11*x^14 + 2749747*(d*x)^m*C*c^3*m^10*x^15 + 3*(d*x)^m*B*b^2*c*m^14*x^10 + 3*(d*x)^m*B*a*c^2*m^14*x^10 + 327*(d*x)^m*C*b^2*c*m^13*x^11 + 327*(d*x)^m*C*a*c^2*m^13*x^11 + 327*(d*x)^m*A*b*c^2*m^13*x^11 + 15852*(d*x)^m*B*b*c^2*m^12*x^12 + 452829*(d*x)^m*C*b*c^2*m^11*x^13 + 150943*(d*x)^m*A*c^3*m^11*x^13 + 2840838*(d*x)^m*B*c^3*m^10*x^14 + 37312275*(d*x)^m*C*c^3*m^9*x^15 + (d*x)^m*C*b^3*m^14*x^9 + 6*(d*x)^m*C*a*b*c*m^14*x^9 + 3*(d*x)^m*A*b^2*c*m^14*x^9 + 3*(d*x)^m*A*a*c^2*m^14*x^9 + 330*(d*x)^m*B*b^2*c*m^13*x^10 + 330*(d*x)^m*B*a*c^2*m^13*x^10 + 16143*(d*x)^m*C*b^2*c*m^12*x^11 + 16143*(d*x)^m*C*a*c^2*m^12*x^11 + 16143*(d*x)^m*A*b*c^2*m^12*x^11 + 464976*(d*x)^m*B*b*c^2*m^11*x^12 + 8812089*(d*x)^m*C*b*c^2*m^10*x^13 + 2937363*(d*x)^m*A*c^3*m^10*x^13 + 38786748*(d*x)^m*B*c^3*m^9*x^14 + 368411615*(d*x)^m*C*c^3*m^8*x^15 + (d*x)^m*B*b^3*m^14*x^8 + 6*(d*x)^m*B*a*b*c*m^14*x^8 + 111*(d*x)^m*C*b^3*m^13*x^9 + 666*(d*x)^m*C*a*b*c*m^13*x^9 + 333*(d*x)^m*A*b^2*c*m^13*x^9 + 333*(d*x)^m*A*a*c^2*m^13*x^9 + 16440*(d*x)^m*B*b^2*c*m^12*x^10 + 16440*(d*x)^m*B*a*c^2*m^12*x^10 + 477627*(d*x)^m*C*b^2*c*m^11*x^11 + 477627*(d*x)^m*C*a*c^2*m^11*x^11 + 477627*(d*x)^m*A*b*c^2*m^11*x^11 + 9119154*(d*x)^m*B*b*c^2*m^10*x^12 + 121118283*(d*x)^m*C*b*c^2*m^9*x^13 + 40372761*(d*x)^m*A*c^3*m^9*x^13 + 385081268*(d*x)^m*B*c^3*m^8*x^14 + 2681453775*(d*x)^m*C*c^3*m^7*x^15 + 3*(d*x)^m*C*a*b^2*m^14*x^7 + (d*x)^m*A*b^3*m^14*x^7 + 3*(d*x)^m*C*a^2*c*m^14*x^7 + 6*(d*x)^m*A*a*b*c*m^14*x^7 + 112*(d*x)^m*B*b^3*m^13*x^8 + 672*(d*x)^m*B*a*b*c*m^13*x^8 + 5581*(d*x)^m*C*b^3*m^12*x^9 + 33486*(d*x)^m*C*a*b*c*m^12*x^9 + 16743*(d*x)^m*A*b^2*c*m^12*x^9 + 16743*(d*x)^m*A*a*c^2*m^12*x^9 + 490800*(d*x)^m*B*b^2*c*m^11*x^10 + 490800*(d*x)^m*B*a*c^2*m^11*x^10 + 9444969*(d*x)^m*C*b^2*c*m^10*x^11 + 9444969*(d*x)^m*C*a*c^2*m^10*x^11 + 9444969*(d*x)^m*A*b*c^2*m^10*x^11 + 126245592*(d*x)^m*B*b*c^2*m^9*x^12 + 1209749541*(d*x)^m*C*b*c^2*m^8*x^13 + 403249847*(d*x)^m*A*c^3*m^8*x^13 + 2816490248*(d*x)^m*B*c^3*m^7*x^14 + 14409322928*(d*x)^m*C*c^3*m^6*x^15 + 3*(d*x)^m*B*a*b^2*m^14*x^6 + 3*(d*x)^m*B*a^2*c*m^14*x^6 + 339*(d*x)^m*C*a*b^2*m^13*x^7 + 113*(d*x)^m*A*b^3*m^13*x^7 + 339*(d*x)^m*C*a^2*c*m^13*x^7 + 678*(d*x)^m*A*a*b*c*m^13*x^7 + 5684*(d*x)^m*B*b^3*m^12*x^8 + 34104*(d*x)^m*B*a*b*c*m^12*x^8 + 168171*(d*x)^m*C*b^3*m^11*x^9 + 1009026*(d*x)^m*C*a*b*c*m^11*x^9 + 504513*(d*x)^m*A*b^2*c*m^11*x^9 + 504513*(d*x)^m*A*a*c^2*m^11*x^9 + 9790866*(d*x)^m*B*b^2*c*m^10*x^10 + 9790866*(d*x)^m*B*a*c^2*m^10*x^10 + 131780781*(d*x)^m*C*b^2*c*m^9*x^11 + 131780781*(d*x)^m*C*a*c^2*m^9*x^11 + 131780781*(d*x)^m*A*b*c^2*m^9*x^11 + 1269340116*(d*x)^m*B*b*c^2*m^8*x^12 + 8896139967*(d*x)^m*C*b*c^2*m^7*x^13 + 2965379989*(d*x)^m*A*c^3*m^7*x^13 + 15200266081*(d*x)^m*B*c^3*m^6*x^14 + 56663366760*(d*x)^m*C*c^3*m^5*x^15 + 3*(d*x)^m*C*a^2*b*m^14*x^5 + 3*(d*x)^m*A*a*b^2*m^14*x^5 + 3*(d*x)^m*A*a^2*c*m^14*x^5 + 342*(d*x)^m*B*a*b^2*m^13*x^6 + 342*(d*x)^m*B*a^2*c*m^13*x^6 + 17367*(d*x)^m*C*a*b^2*m^12*x^7 + 5789*(d*x)^m*A*b^3*m^12*x^7 + 17367*(d*x)^m*C*a^2*c*m^12*x^7 + 34734*(d*x)^m*A*a*b*c*m^12*x^7 + 172928*(d*x)^m*B*b^3*m^11*x^8 + 1037568*(d*x)^m*B*a*b*c*m^11*x^8 + 3386083*(d*x)^m*C*b^3*m^10*x^9 + 20316498*(d*x)^m*C*a*b*c*m^10*x^9 + 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1008086865108*(d*x)^m*B*a*b^2*m^4*x^6 + 1008086865108*(d*x)^m*B*a^2*c*m^4*x^6 + 1826102786256*(d*x)^m*C*a*b^2*m^3*x^7 + 608700928752*(d*x)^m*A*b^3*m^3*x^7 + 1826102786256*(d*x)^m*C*a^2*c*m^3*x^7 + 3652205572512*(d*x)^m*A*a*b*c*m^3*x^7 + 705481831440*(d*x)^m*B*b^3*m^2*x^8 + 4232890988640*(d*x)^m*B*a*b*c*m^2*x^8 + 465985094400*(d*x)^m*C*b^3*m*x^9 + 2795910566400*(d*x)^m*C*a*b*c*m*x^9 + 1397955283200*(d*x)^m*A*b^2*c*m*x^9 + 1397955283200*(d*x)^m*A*a*c^2*m*x^9 + 392302310400*(d*x)^m*B*b^2*c*x^10 + 392302310400*(d*x)^m*B*a*c^2*x^10 + 854224943*(d*x)^m*A*a^3*m^8*x + 6629764856*(d*x)^m*B*a^3*m^7*x^2 + 36588367376*(d*x)^m*C*a^3*m^6*x^3 + 109765102128*(d*x)^m*A*a^2*b*m^6*x^3 + 426272198748*(d*x)^m*B*a^2*b*m^5*x^4 + 1145655530640*(d*x)^m*C*a^2*b*m^4*x^5 + 1145655530640*(d*x)^m*A*a*b^2*m^4*x^5 + 1145655530640*(d*x)^m*A*a^2*c*m^4*x^5 + 2071918846152*(d*x)^m*B*a*b^2*m^3*x^6 + 2071918846152*(d*x)^m*B*a^2*c*m^3*x^6 + 2388267607680*(d*x)^m*C*a*b^2*m^2*x^7 + 796089202560*(d*x)^m*A*b^3*m^2*x^7 + 2388267607680*(d*x)^m*C*a^2*c*m^2*x^7 + 4776535215360*(d*x)^m*A*a*b*c*m^2*x^7 + 521962963200*(d*x)^m*B*b^3*m*x^8 + 3131777779200*(d*x)^m*B*a*b*c*m*x^8 + 145297152000*(d*x)^m*C*b^3*x^9 + 871782912000*(d*x)^m*C*a*b*c*x^9 + 435891456000*(d*x)^m*A*b^2*c*x^9 + 435891456000*(d*x)^m*A*a*c^2*x^9 + 7353403057*(d*x)^m*A*a^3*m^7*x + 41371599841*(d*x)^m*B*a^3*m^6*x^2 + 163038108552*(d*x)^m*C*a^3*m^5*x^3 + 489114325656*(d*x)^m*A*a^2*b*m^5*x^3 + 1323927526248*(d*x)^m*B*a^2*b*m^4*x^4 + 2392162383600*(d*x)^m*C*a^2*b*m^3*x^5 + 2392162383600*(d*x)^m*A*a*b^2*m^3*x^5 + 2392162383600*(d*x)^m*A*a^2*c*m^3*x^5 + 2739474034560*(d*x)^m*B*a*b^2*m^2*x^6 + 2739474034560*(d*x)^m*B*a^2*c*m^2*x^6 + 1779579590400*(d*x)^m*C*a*b^2*m*x^7 + 593193196800*(d*x)^m*A*b^3*m*x^7 + 1779579590400*(d*x)^m*C*a^2*c*m*x^7 + 3559159180800*(d*x)^m*A*a*b*c*m*x^7 + 163459296000*(d*x)^m*B*b^3*x^8 + 980755776000*(d*x)^m*B*a*b*c*x^8 + 47277726496*(d*x)^m*A*a^3*m^6*x + 190060010998*(d*x)^m*B*a^3*m^5*x^2 + 520557781424*(d*x)^m*C*a^3*m^4*x^3 + 1561673344272*(d*x)^m*A*a^2*b*m^4*x^3 + 2824729931808*(d*x)^m*B*a^2*b*m^3*x^4 + 3210175193472*(d*x)^m*C*a^2*b*m^2*x^5 + 3210175193472*(d*x)^m*A*a*b^2*m^2*x^5 + 3210175193472*(d*x)^m*A*a^2*c*m^2*x^5 + 2060608636800*(d*x)^m*B*a*b^2*m*x^6 + 2060608636800*(d*x)^m*B*a^2*c*m*x^6 + 560431872000*(d*x)^m*C*a*b^2*x^7 + 186810624000*(d*x)^m*A*b^3*x^7 + 560431872000*(d*x)^m*C*a^2*c*x^7 + 1120863744000*(d*x)^m*A*a*b*c*x^7 + 225525484184*(d*x)^m*A*a^3*m^5*x + 629552085084*(d*x)^m*B*a^3*m^4*x^2 + 1145140001328*(d*x)^m*C*a^3*m^3*x^3 + 3435420003984*(d*x)^m*A*a^2*b*m^3*x^3 + 3872067384240*(d*x)^m*B*a^2*b*m^2*x^4 + 2446576876800*(d*x)^m*C*a^2*b*m*x^5 + 2446576876800*(d*x)^m*A*a*b^2*m*x^5 + 2446576876800*(d*x)^m*A*a^2*c*m*x^5 + 653837184000*(d*x)^m*B*a*b^2*x^6 + 653837184000*(d*x)^m*B*a^2*c*x^6 + 784146622896*(d*x)^m*A*a^3*m^4*x + 1447709175432*(d*x)^m*B*a^3*m^3*x^2 + 1621575699840*(d*x)^m*C*a^3*m^2*x^3 + 4864727099520*(d*x)^m*A*a^2*b*m^2*x^3 + 3009183307200*(d*x)^m*B*a^2*b*m*x^4 + 784604620800*(d*x)^m*C*a^2*b*x^5 + 784604620800*(d*x)^m*A*a*b^2*x^5 + 784604620800*(d*x)^m*A*a^2*c*x^5 + 1922666722704*(d*x)^m*A*a^3*m^3*x + 2161577352960*(d*x)^m*B*a^3*m^2*x^2 + 1301090515200*(d*x)^m*C*a^3*m*x^3 + 3903271545600*(d*x)^m*A*a^2*b*m*x^3 + 980755776000*(d*x)^m*B*a^2*b*x^4 + 3134328981120*(d*x)^m*A*a^3*m^2*x + 1842662908800*(d*x)^m*B*a^3*m*x^2 + 435891456000*(d*x)^m*C*a^3*x^3 + 1307674368000*(d*x)^m*A*a^2*b*x^3 + 3031488633600*(d*x)^m*A*a^3*m*x + 653837184000*(d*x)^m*B*a^3*x^2 + 1307674368000*(d*x)^m*A*a^3*x)/(m^15 + 120*m^14 + 6580*m^13 + 218400*m^12 + 4899622*m^11 + 78558480*m^10 + 928095740*m^9 + 8207628000*m^8 + 54631129553*m^7 + 272803210680*m^6 + 1009672107080*m^5 + 2706813345600*m^4 + 5056995703824*m^3 + 6165817614720*m^2 + 4339163001600*m + 1307674368000)","B",0
38,1,3203,0,0.725195," ","integrate((d*x)^m*(C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{\left(d x\right)^{m} C c^{2} m^{10} x^{11} + \left(d x\right)^{m} B c^{2} m^{10} x^{10} + 55 \, \left(d x\right)^{m} C c^{2} m^{9} x^{11} + 2 \, \left(d x\right)^{m} C b c m^{10} x^{9} + \left(d x\right)^{m} A c^{2} m^{10} x^{9} + 56 \, \left(d x\right)^{m} B c^{2} m^{9} x^{10} + 1320 \, \left(d x\right)^{m} C c^{2} m^{8} x^{11} + 2 \, \left(d x\right)^{m} B b c m^{10} x^{8} + 114 \, \left(d x\right)^{m} C b c m^{9} x^{9} + 57 \, \left(d x\right)^{m} A c^{2} m^{9} x^{9} + 1365 \, \left(d x\right)^{m} B c^{2} m^{8} x^{10} + 18150 \, \left(d x\right)^{m} C c^{2} m^{7} x^{11} + \left(d x\right)^{m} C b^{2} m^{10} x^{7} + 2 \, \left(d x\right)^{m} C a c m^{10} x^{7} + 2 \, \left(d x\right)^{m} A b c m^{10} x^{7} + 116 \, \left(d x\right)^{m} B b c m^{9} x^{8} + 2824 \, \left(d x\right)^{m} C b c m^{8} x^{9} + 1412 \, \left(d x\right)^{m} A c^{2} m^{8} x^{9} + 19020 \, \left(d x\right)^{m} B c^{2} m^{7} x^{10} + 157773 \, \left(d x\right)^{m} C c^{2} m^{6} x^{11} + \left(d x\right)^{m} B b^{2} m^{10} x^{6} + 2 \, \left(d x\right)^{m} B a c m^{10} x^{6} + 59 \, \left(d x\right)^{m} C b^{2} m^{9} x^{7} + 118 \, \left(d x\right)^{m} C a c m^{9} x^{7} + 118 \, \left(d x\right)^{m} A b c m^{9} x^{7} + 2922 \, \left(d x\right)^{m} B b c m^{8} x^{8} + 39924 \, \left(d x\right)^{m} C b c m^{7} x^{9} + 19962 \, \left(d x\right)^{m} A c^{2} m^{7} x^{9} + 167223 \, \left(d x\right)^{m} B c^{2} m^{6} x^{10} + 902055 \, \left(d x\right)^{m} C c^{2} m^{5} x^{11} + 2 \, \left(d x\right)^{m} C a b m^{10} x^{5} + \left(d x\right)^{m} A b^{2} m^{10} x^{5} + 2 \, \left(d x\right)^{m} A a c m^{10} x^{5} + 60 \, \left(d x\right)^{m} B b^{2} m^{9} x^{6} + 120 \, \left(d x\right)^{m} B a c m^{9} x^{6} + 1512 \, \left(d x\right)^{m} C b^{2} m^{8} x^{7} + 3024 \, \left(d x\right)^{m} C a c m^{8} x^{7} + 3024 \, \left(d x\right)^{m} A b c m^{8} x^{7} + 41964 \, \left(d x\right)^{m} B b c m^{7} x^{8} + 355530 \, \left(d x\right)^{m} C b c m^{6} x^{9} + 177765 \, \left(d x\right)^{m} A c^{2} m^{6} x^{9} + 965328 \, \left(d x\right)^{m} B c^{2} m^{5} x^{10} + 3416930 \, \left(d x\right)^{m} C c^{2} m^{4} x^{11} + 2 \, \left(d x\right)^{m} B a b m^{10} x^{4} + 122 \, \left(d x\right)^{m} C a b m^{9} x^{5} + 61 \, \left(d x\right)^{m} A b^{2} m^{9} x^{5} + 122 \, \left(d x\right)^{m} A a c m^{9} x^{5} + 1565 \, \left(d x\right)^{m} B b^{2} m^{8} x^{6} + 3130 \, \left(d x\right)^{m} B a c m^{8} x^{6} + 22086 \, \left(d x\right)^{m} C b^{2} m^{7} x^{7} + 44172 \, \left(d x\right)^{m} C a c m^{7} x^{7} + 44172 \, \left(d x\right)^{m} A b c m^{7} x^{7} + 379134 \, \left(d x\right)^{m} B b c m^{6} x^{8} + 2075346 \, \left(d x\right)^{m} C b c m^{5} x^{9} + 1037673 \, \left(d x\right)^{m} A c^{2} m^{5} x^{9} + 3686255 \, \left(d x\right)^{m} B c^{2} m^{4} x^{10} + 8409500 \, \left(d x\right)^{m} C c^{2} m^{3} x^{11} + \left(d x\right)^{m} C a^{2} m^{10} x^{3} + 2 \, \left(d x\right)^{m} A a b m^{10} x^{3} + 124 \, \left(d x\right)^{m} B a b m^{9} x^{4} + 3240 \, \left(d x\right)^{m} C a b m^{8} x^{5} + 1620 \, \left(d x\right)^{m} A b^{2} m^{8} x^{5} + 3240 \, \left(d x\right)^{m} A a c m^{8} x^{5} + 23280 \, \left(d x\right)^{m} B b^{2} m^{7} x^{6} + 46560 \, \left(d x\right)^{m} B a c m^{7} x^{6} + 202821 \, \left(d x\right)^{m} C b^{2} m^{6} x^{7} + 405642 \, \left(d x\right)^{m} C a c m^{6} x^{7} + 405642 \, \left(d x\right)^{m} A b c m^{6} x^{7} + 2242044 \, \left(d x\right)^{m} B b c m^{5} x^{8} + 8000956 \, \left(d x\right)^{m} C b c m^{4} x^{9} + 4000478 \, \left(d x\right)^{m} A c^{2} m^{4} x^{9} + 9133180 \, \left(d x\right)^{m} B c^{2} m^{3} x^{10} + 12753576 \, \left(d x\right)^{m} C c^{2} m^{2} x^{11} + \left(d x\right)^{m} B a^{2} m^{10} x^{2} + 63 \, \left(d x\right)^{m} C a^{2} m^{9} x^{3} + 126 \, \left(d x\right)^{m} A a b m^{9} x^{3} + 3354 \, \left(d x\right)^{m} B a b m^{8} x^{4} + 49140 \, \left(d x\right)^{m} C a b m^{7} x^{5} + 24570 \, \left(d x\right)^{m} A b^{2} m^{7} x^{5} + 49140 \, \left(d x\right)^{m} A a c m^{7} x^{5} + 217743 \, \left(d x\right)^{m} B b^{2} m^{6} x^{6} + 435486 \, \left(d x\right)^{m} B a c m^{6} x^{6} + 1217811 \, \left(d x\right)^{m} C b^{2} m^{5} x^{7} + 2435622 \, \left(d x\right)^{m} C a c m^{5} x^{7} + 2435622 \, \left(d x\right)^{m} A b c m^{5} x^{7} + 8742718 \, \left(d x\right)^{m} B b c m^{4} x^{8} + 19982856 \, \left(d x\right)^{m} C b c m^{3} x^{9} + 9991428 \, \left(d x\right)^{m} A c^{2} m^{3} x^{9} + 13926276 \, \left(d x\right)^{m} B c^{2} m^{2} x^{10} + 10628640 \, \left(d x\right)^{m} C c^{2} m x^{11} + \left(d x\right)^{m} A a^{2} m^{10} x + 64 \, \left(d x\right)^{m} B a^{2} m^{9} x^{2} + 1736 \, \left(d x\right)^{m} C a^{2} m^{8} x^{3} + 3472 \, \left(d x\right)^{m} A a b m^{8} x^{3} + 51924 \, \left(d x\right)^{m} B a b m^{7} x^{4} + 469146 \, \left(d x\right)^{m} C a b m^{6} x^{5} + 234573 \, \left(d x\right)^{m} A b^{2} m^{6} x^{5} + 469146 \, \left(d x\right)^{m} A a c m^{6} x^{5} + 1331100 \, \left(d x\right)^{m} B b^{2} m^{5} x^{6} + 2662200 \, \left(d x\right)^{m} B a c m^{5} x^{6} + 4814858 \, \left(d x\right)^{m} C b^{2} m^{4} x^{7} + 9629716 \, \left(d x\right)^{m} C a c m^{4} x^{7} + 9629716 \, \left(d x\right)^{m} A b c m^{4} x^{7} + 22049716 \, \left(d x\right)^{m} B b c m^{3} x^{8} + 30670448 \, \left(d x\right)^{m} C b c m^{2} x^{9} + 15335224 \, \left(d x\right)^{m} A c^{2} m^{2} x^{9} + 11655216 \, \left(d x\right)^{m} B c^{2} m x^{10} + 3628800 \, \left(d x\right)^{m} C c^{2} x^{11} + 65 \, \left(d x\right)^{m} A a^{2} m^{9} x + 1797 \, \left(d x\right)^{m} B a^{2} m^{8} x^{2} + 27462 \, \left(d x\right)^{m} C a^{2} m^{7} x^{3} + 54924 \, \left(d x\right)^{m} A a b m^{7} x^{3} + 507150 \, \left(d x\right)^{m} B a b m^{6} x^{4} + 2929386 \, \left(d x\right)^{m} C a b m^{5} x^{5} + 1464693 \, \left(d x\right)^{m} A b^{2} m^{5} x^{5} + 2929386 \, \left(d x\right)^{m} A a c m^{5} x^{5} + 5352935 \, \left(d x\right)^{m} B b^{2} m^{4} x^{6} + 10705870 \, \left(d x\right)^{m} B a c m^{4} x^{6} + 12291724 \, \left(d x\right)^{m} C b^{2} m^{3} x^{7} + 24583448 \, \left(d x\right)^{m} C a c m^{3} x^{7} + 24583448 \, \left(d x\right)^{m} A b c m^{3} x^{7} + 34118424 \, \left(d x\right)^{m} B b c m^{2} x^{8} + 25801920 \, \left(d x\right)^{m} C b c m x^{9} + 12900960 \, \left(d x\right)^{m} A c^{2} m x^{9} + 3991680 \, \left(d x\right)^{m} B c^{2} x^{10} + 1860 \, \left(d x\right)^{m} A a^{2} m^{8} x + 29076 \, \left(d x\right)^{m} B a^{2} m^{7} x^{2} + 275037 \, \left(d x\right)^{m} C a^{2} m^{6} x^{3} + 550074 \, \left(d x\right)^{m} A a b m^{6} x^{3} + 3246516 \, \left(d x\right)^{m} B a b m^{5} x^{4} + 12032140 \, \left(d x\right)^{m} C a b m^{4} x^{5} + 6016070 \, \left(d x\right)^{m} A b^{2} m^{4} x^{5} + 12032140 \, \left(d x\right)^{m} A a c m^{4} x^{5} + 13878120 \, \left(d x\right)^{m} B b^{2} m^{3} x^{6} + 27756240 \, \left(d x\right)^{m} B a c m^{3} x^{6} + 19216008 \, \left(d x\right)^{m} C b^{2} m^{2} x^{7} + 38432016 \, \left(d x\right)^{m} C a c m^{2} x^{7} + 38432016 \, \left(d x\right)^{m} A b c m^{2} x^{7} + 28888560 \, \left(d x\right)^{m} B b c m x^{8} + 8870400 \, \left(d x\right)^{m} C b c x^{9} + 4435200 \, \left(d x\right)^{m} A c^{2} x^{9} + 30810 \, \left(d x\right)^{m} A a^{2} m^{7} x + 299271 \, \left(d x\right)^{m} B a^{2} m^{6} x^{2} + 1812447 \, \left(d x\right)^{m} C a^{2} m^{5} x^{3} + 3624894 \, \left(d x\right)^{m} A a b m^{5} x^{3} + 13693006 \, \left(d x\right)^{m} B a b m^{4} x^{4} + 31830760 \, \left(d x\right)^{m} C a b m^{3} x^{5} + 15915380 \, \left(d x\right)^{m} A b^{2} m^{3} x^{5} + 31830760 \, \left(d x\right)^{m} A a c m^{3} x^{5} + 21989356 \, \left(d x\right)^{m} B b^{2} m^{2} x^{6} + 43978712 \, \left(d x\right)^{m} B a c m^{2} x^{6} + 16405920 \, \left(d x\right)^{m} C b^{2} m x^{7} + 32811840 \, \left(d x\right)^{m} C a c m x^{7} + 32811840 \, \left(d x\right)^{m} A b c m x^{7} + 9979200 \, \left(d x\right)^{m} B b c x^{8} + 326613 \, \left(d x\right)^{m} A a^{2} m^{6} x + 2039016 \, \left(d x\right)^{m} B a^{2} m^{5} x^{2} + 7902194 \, \left(d x\right)^{m} C a^{2} m^{4} x^{3} + 15804388 \, \left(d x\right)^{m} A a b m^{4} x^{3} + 37219436 \, \left(d x\right)^{m} B a b m^{3} x^{4} + 51362352 \, \left(d x\right)^{m} C a b m^{2} x^{5} + 25681176 \, \left(d x\right)^{m} A b^{2} m^{2} x^{5} + 51362352 \, \left(d x\right)^{m} A a c m^{2} x^{5} + 18981840 \, \left(d x\right)^{m} B b^{2} m x^{6} + 37963680 \, \left(d x\right)^{m} B a c m x^{6} + 5702400 \, \left(d x\right)^{m} C b^{2} x^{7} + 11404800 \, \left(d x\right)^{m} C a c x^{7} + 11404800 \, \left(d x\right)^{m} A b c x^{7} + 2310945 \, \left(d x\right)^{m} A a^{2} m^{5} x + 9261503 \, \left(d x\right)^{m} B a^{2} m^{4} x^{2} + 22289148 \, \left(d x\right)^{m} C a^{2} m^{3} x^{3} + 44578296 \, \left(d x\right)^{m} A a b m^{3} x^{3} + 61638408 \, \left(d x\right)^{m} B a b m^{2} x^{4} + 45024192 \, \left(d x\right)^{m} C a b m x^{5} + 22512096 \, \left(d x\right)^{m} A b^{2} m x^{5} + 45024192 \, \left(d x\right)^{m} A a c m x^{5} + 6652800 \, \left(d x\right)^{m} B b^{2} x^{6} + 13305600 \, \left(d x\right)^{m} B a c x^{6} + 11028590 \, \left(d x\right)^{m} A a^{2} m^{4} x + 27472724 \, \left(d x\right)^{m} B a^{2} m^{3} x^{2} + 38390632 \, \left(d x\right)^{m} C a^{2} m^{2} x^{3} + 76781264 \, \left(d x\right)^{m} A a b m^{2} x^{3} + 55282320 \, \left(d x\right)^{m} B a b m x^{4} + 15966720 \, \left(d x\right)^{m} C a b x^{5} + 7983360 \, \left(d x\right)^{m} A b^{2} x^{5} + 15966720 \, \left(d x\right)^{m} A a c x^{5} + 34967140 \, \left(d x\right)^{m} A a^{2} m^{3} x + 50312628 \, \left(d x\right)^{m} B a^{2} m^{2} x^{2} + 35746080 \, \left(d x\right)^{m} C a^{2} m x^{3} + 71492160 \, \left(d x\right)^{m} A a b m x^{3} + 19958400 \, \left(d x\right)^{m} B a b x^{4} + 70290936 \, \left(d x\right)^{m} A a^{2} m^{2} x + 50292720 \, \left(d x\right)^{m} B a^{2} m x^{2} + 13305600 \, \left(d x\right)^{m} C a^{2} x^{3} + 26611200 \, \left(d x\right)^{m} A a b x^{3} + 80627040 \, \left(d x\right)^{m} A a^{2} m x + 19958400 \, \left(d x\right)^{m} B a^{2} x^{2} + 39916800 \, \left(d x\right)^{m} A a^{2} x}{m^{11} + 66 \, m^{10} + 1925 \, m^{9} + 32670 \, m^{8} + 357423 \, m^{7} + 2637558 \, m^{6} + 13339535 \, m^{5} + 45995730 \, m^{4} + 105258076 \, m^{3} + 150917976 \, m^{2} + 120543840 \, m + 39916800}"," ",0,"((d*x)^m*C*c^2*m^10*x^11 + (d*x)^m*B*c^2*m^10*x^10 + 55*(d*x)^m*C*c^2*m^9*x^11 + 2*(d*x)^m*C*b*c*m^10*x^9 + (d*x)^m*A*c^2*m^10*x^9 + 56*(d*x)^m*B*c^2*m^9*x^10 + 1320*(d*x)^m*C*c^2*m^8*x^11 + 2*(d*x)^m*B*b*c*m^10*x^8 + 114*(d*x)^m*C*b*c*m^9*x^9 + 57*(d*x)^m*A*c^2*m^9*x^9 + 1365*(d*x)^m*B*c^2*m^8*x^10 + 18150*(d*x)^m*C*c^2*m^7*x^11 + (d*x)^m*C*b^2*m^10*x^7 + 2*(d*x)^m*C*a*c*m^10*x^7 + 2*(d*x)^m*A*b*c*m^10*x^7 + 116*(d*x)^m*B*b*c*m^9*x^8 + 2824*(d*x)^m*C*b*c*m^8*x^9 + 1412*(d*x)^m*A*c^2*m^8*x^9 + 19020*(d*x)^m*B*c^2*m^7*x^10 + 157773*(d*x)^m*C*c^2*m^6*x^11 + (d*x)^m*B*b^2*m^10*x^6 + 2*(d*x)^m*B*a*c*m^10*x^6 + 59*(d*x)^m*C*b^2*m^9*x^7 + 118*(d*x)^m*C*a*c*m^9*x^7 + 118*(d*x)^m*A*b*c*m^9*x^7 + 2922*(d*x)^m*B*b*c*m^8*x^8 + 39924*(d*x)^m*C*b*c*m^7*x^9 + 19962*(d*x)^m*A*c^2*m^7*x^9 + 167223*(d*x)^m*B*c^2*m^6*x^10 + 902055*(d*x)^m*C*c^2*m^5*x^11 + 2*(d*x)^m*C*a*b*m^10*x^5 + (d*x)^m*A*b^2*m^10*x^5 + 2*(d*x)^m*A*a*c*m^10*x^5 + 60*(d*x)^m*B*b^2*m^9*x^6 + 120*(d*x)^m*B*a*c*m^9*x^6 + 1512*(d*x)^m*C*b^2*m^8*x^7 + 3024*(d*x)^m*C*a*c*m^8*x^7 + 3024*(d*x)^m*A*b*c*m^8*x^7 + 41964*(d*x)^m*B*b*c*m^7*x^8 + 355530*(d*x)^m*C*b*c*m^6*x^9 + 177765*(d*x)^m*A*c^2*m^6*x^9 + 965328*(d*x)^m*B*c^2*m^5*x^10 + 3416930*(d*x)^m*C*c^2*m^4*x^11 + 2*(d*x)^m*B*a*b*m^10*x^4 + 122*(d*x)^m*C*a*b*m^9*x^5 + 61*(d*x)^m*A*b^2*m^9*x^5 + 122*(d*x)^m*A*a*c*m^9*x^5 + 1565*(d*x)^m*B*b^2*m^8*x^6 + 3130*(d*x)^m*B*a*c*m^8*x^6 + 22086*(d*x)^m*C*b^2*m^7*x^7 + 44172*(d*x)^m*C*a*c*m^7*x^7 + 44172*(d*x)^m*A*b*c*m^7*x^7 + 379134*(d*x)^m*B*b*c*m^6*x^8 + 2075346*(d*x)^m*C*b*c*m^5*x^9 + 1037673*(d*x)^m*A*c^2*m^5*x^9 + 3686255*(d*x)^m*B*c^2*m^4*x^10 + 8409500*(d*x)^m*C*c^2*m^3*x^11 + (d*x)^m*C*a^2*m^10*x^3 + 2*(d*x)^m*A*a*b*m^10*x^3 + 124*(d*x)^m*B*a*b*m^9*x^4 + 3240*(d*x)^m*C*a*b*m^8*x^5 + 1620*(d*x)^m*A*b^2*m^8*x^5 + 3240*(d*x)^m*A*a*c*m^8*x^5 + 23280*(d*x)^m*B*b^2*m^7*x^6 + 46560*(d*x)^m*B*a*c*m^7*x^6 + 202821*(d*x)^m*C*b^2*m^6*x^7 + 405642*(d*x)^m*C*a*c*m^6*x^7 + 405642*(d*x)^m*A*b*c*m^6*x^7 + 2242044*(d*x)^m*B*b*c*m^5*x^8 + 8000956*(d*x)^m*C*b*c*m^4*x^9 + 4000478*(d*x)^m*A*c^2*m^4*x^9 + 9133180*(d*x)^m*B*c^2*m^3*x^10 + 12753576*(d*x)^m*C*c^2*m^2*x^11 + (d*x)^m*B*a^2*m^10*x^2 + 63*(d*x)^m*C*a^2*m^9*x^3 + 126*(d*x)^m*A*a*b*m^9*x^3 + 3354*(d*x)^m*B*a*b*m^8*x^4 + 49140*(d*x)^m*C*a*b*m^7*x^5 + 24570*(d*x)^m*A*b^2*m^7*x^5 + 49140*(d*x)^m*A*a*c*m^7*x^5 + 217743*(d*x)^m*B*b^2*m^6*x^6 + 435486*(d*x)^m*B*a*c*m^6*x^6 + 1217811*(d*x)^m*C*b^2*m^5*x^7 + 2435622*(d*x)^m*C*a*c*m^5*x^7 + 2435622*(d*x)^m*A*b*c*m^5*x^7 + 8742718*(d*x)^m*B*b*c*m^4*x^8 + 19982856*(d*x)^m*C*b*c*m^3*x^9 + 9991428*(d*x)^m*A*c^2*m^3*x^9 + 13926276*(d*x)^m*B*c^2*m^2*x^10 + 10628640*(d*x)^m*C*c^2*m*x^11 + (d*x)^m*A*a^2*m^10*x + 64*(d*x)^m*B*a^2*m^9*x^2 + 1736*(d*x)^m*C*a^2*m^8*x^3 + 3472*(d*x)^m*A*a*b*m^8*x^3 + 51924*(d*x)^m*B*a*b*m^7*x^4 + 469146*(d*x)^m*C*a*b*m^6*x^5 + 234573*(d*x)^m*A*b^2*m^6*x^5 + 469146*(d*x)^m*A*a*c*m^6*x^5 + 1331100*(d*x)^m*B*b^2*m^5*x^6 + 2662200*(d*x)^m*B*a*c*m^5*x^6 + 4814858*(d*x)^m*C*b^2*m^4*x^7 + 9629716*(d*x)^m*C*a*c*m^4*x^7 + 9629716*(d*x)^m*A*b*c*m^4*x^7 + 22049716*(d*x)^m*B*b*c*m^3*x^8 + 30670448*(d*x)^m*C*b*c*m^2*x^9 + 15335224*(d*x)^m*A*c^2*m^2*x^9 + 11655216*(d*x)^m*B*c^2*m*x^10 + 3628800*(d*x)^m*C*c^2*x^11 + 65*(d*x)^m*A*a^2*m^9*x + 1797*(d*x)^m*B*a^2*m^8*x^2 + 27462*(d*x)^m*C*a^2*m^7*x^3 + 54924*(d*x)^m*A*a*b*m^7*x^3 + 507150*(d*x)^m*B*a*b*m^6*x^4 + 2929386*(d*x)^m*C*a*b*m^5*x^5 + 1464693*(d*x)^m*A*b^2*m^5*x^5 + 2929386*(d*x)^m*A*a*c*m^5*x^5 + 5352935*(d*x)^m*B*b^2*m^4*x^6 + 10705870*(d*x)^m*B*a*c*m^4*x^6 + 12291724*(d*x)^m*C*b^2*m^3*x^7 + 24583448*(d*x)^m*C*a*c*m^3*x^7 + 24583448*(d*x)^m*A*b*c*m^3*x^7 + 34118424*(d*x)^m*B*b*c*m^2*x^8 + 25801920*(d*x)^m*C*b*c*m*x^9 + 12900960*(d*x)^m*A*c^2*m*x^9 + 3991680*(d*x)^m*B*c^2*x^10 + 1860*(d*x)^m*A*a^2*m^8*x + 29076*(d*x)^m*B*a^2*m^7*x^2 + 275037*(d*x)^m*C*a^2*m^6*x^3 + 550074*(d*x)^m*A*a*b*m^6*x^3 + 3246516*(d*x)^m*B*a*b*m^5*x^4 + 12032140*(d*x)^m*C*a*b*m^4*x^5 + 6016070*(d*x)^m*A*b^2*m^4*x^5 + 12032140*(d*x)^m*A*a*c*m^4*x^5 + 13878120*(d*x)^m*B*b^2*m^3*x^6 + 27756240*(d*x)^m*B*a*c*m^3*x^6 + 19216008*(d*x)^m*C*b^2*m^2*x^7 + 38432016*(d*x)^m*C*a*c*m^2*x^7 + 38432016*(d*x)^m*A*b*c*m^2*x^7 + 28888560*(d*x)^m*B*b*c*m*x^8 + 8870400*(d*x)^m*C*b*c*x^9 + 4435200*(d*x)^m*A*c^2*x^9 + 30810*(d*x)^m*A*a^2*m^7*x + 299271*(d*x)^m*B*a^2*m^6*x^2 + 1812447*(d*x)^m*C*a^2*m^5*x^3 + 3624894*(d*x)^m*A*a*b*m^5*x^3 + 13693006*(d*x)^m*B*a*b*m^4*x^4 + 31830760*(d*x)^m*C*a*b*m^3*x^5 + 15915380*(d*x)^m*A*b^2*m^3*x^5 + 31830760*(d*x)^m*A*a*c*m^3*x^5 + 21989356*(d*x)^m*B*b^2*m^2*x^6 + 43978712*(d*x)^m*B*a*c*m^2*x^6 + 16405920*(d*x)^m*C*b^2*m*x^7 + 32811840*(d*x)^m*C*a*c*m*x^7 + 32811840*(d*x)^m*A*b*c*m*x^7 + 9979200*(d*x)^m*B*b*c*x^8 + 326613*(d*x)^m*A*a^2*m^6*x + 2039016*(d*x)^m*B*a^2*m^5*x^2 + 7902194*(d*x)^m*C*a^2*m^4*x^3 + 15804388*(d*x)^m*A*a*b*m^4*x^3 + 37219436*(d*x)^m*B*a*b*m^3*x^4 + 51362352*(d*x)^m*C*a*b*m^2*x^5 + 25681176*(d*x)^m*A*b^2*m^2*x^5 + 51362352*(d*x)^m*A*a*c*m^2*x^5 + 18981840*(d*x)^m*B*b^2*m*x^6 + 37963680*(d*x)^m*B*a*c*m*x^6 + 5702400*(d*x)^m*C*b^2*x^7 + 11404800*(d*x)^m*C*a*c*x^7 + 11404800*(d*x)^m*A*b*c*x^7 + 2310945*(d*x)^m*A*a^2*m^5*x + 9261503*(d*x)^m*B*a^2*m^4*x^2 + 22289148*(d*x)^m*C*a^2*m^3*x^3 + 44578296*(d*x)^m*A*a*b*m^3*x^3 + 61638408*(d*x)^m*B*a*b*m^2*x^4 + 45024192*(d*x)^m*C*a*b*m*x^5 + 22512096*(d*x)^m*A*b^2*m*x^5 + 45024192*(d*x)^m*A*a*c*m*x^5 + 6652800*(d*x)^m*B*b^2*x^6 + 13305600*(d*x)^m*B*a*c*x^6 + 11028590*(d*x)^m*A*a^2*m^4*x + 27472724*(d*x)^m*B*a^2*m^3*x^2 + 38390632*(d*x)^m*C*a^2*m^2*x^3 + 76781264*(d*x)^m*A*a*b*m^2*x^3 + 55282320*(d*x)^m*B*a*b*m*x^4 + 15966720*(d*x)^m*C*a*b*x^5 + 7983360*(d*x)^m*A*b^2*x^5 + 15966720*(d*x)^m*A*a*c*x^5 + 34967140*(d*x)^m*A*a^2*m^3*x + 50312628*(d*x)^m*B*a^2*m^2*x^2 + 35746080*(d*x)^m*C*a^2*m*x^3 + 71492160*(d*x)^m*A*a*b*m*x^3 + 19958400*(d*x)^m*B*a*b*x^4 + 70290936*(d*x)^m*A*a^2*m^2*x + 50292720*(d*x)^m*B*a^2*m*x^2 + 13305600*(d*x)^m*C*a^2*x^3 + 26611200*(d*x)^m*A*a*b*x^3 + 80627040*(d*x)^m*A*a^2*m*x + 19958400*(d*x)^m*B*a^2*x^2 + 39916800*(d*x)^m*A*a^2*x)/(m^11 + 66*m^10 + 1925*m^9 + 32670*m^8 + 357423*m^7 + 2637558*m^6 + 13339535*m^5 + 45995730*m^4 + 105258076*m^3 + 150917976*m^2 + 120543840*m + 39916800)","B",0
39,1,914,0,0.532711," ","integrate((d*x)^m*(C*x^2+B*x+A)*(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{\left(d x\right)^{m} C c m^{6} x^{7} + \left(d x\right)^{m} B c m^{6} x^{6} + 21 \, \left(d x\right)^{m} C c m^{5} x^{7} + \left(d x\right)^{m} C b m^{6} x^{5} + \left(d x\right)^{m} A c m^{6} x^{5} + 22 \, \left(d x\right)^{m} B c m^{5} x^{6} + 175 \, \left(d x\right)^{m} C c m^{4} x^{7} + \left(d x\right)^{m} B b m^{6} x^{4} + 23 \, \left(d x\right)^{m} C b m^{5} x^{5} + 23 \, \left(d x\right)^{m} A c m^{5} x^{5} + 190 \, \left(d x\right)^{m} B c m^{4} x^{6} + 735 \, \left(d x\right)^{m} C c m^{3} x^{7} + \left(d x\right)^{m} C a m^{6} x^{3} + \left(d x\right)^{m} A b m^{6} x^{3} + 24 \, \left(d x\right)^{m} B b m^{5} x^{4} + 207 \, \left(d x\right)^{m} C b m^{4} x^{5} + 207 \, \left(d x\right)^{m} A c m^{4} x^{5} + 820 \, \left(d x\right)^{m} B c m^{3} x^{6} + 1624 \, \left(d x\right)^{m} C c m^{2} x^{7} + \left(d x\right)^{m} B a m^{6} x^{2} + 25 \, \left(d x\right)^{m} C a m^{5} x^{3} + 25 \, \left(d x\right)^{m} A b m^{5} x^{3} + 226 \, \left(d x\right)^{m} B b m^{4} x^{4} + 925 \, \left(d x\right)^{m} C b m^{3} x^{5} + 925 \, \left(d x\right)^{m} A c m^{3} x^{5} + 1849 \, \left(d x\right)^{m} B c m^{2} x^{6} + 1764 \, \left(d x\right)^{m} C c m x^{7} + \left(d x\right)^{m} A a m^{6} x + 26 \, \left(d x\right)^{m} B a m^{5} x^{2} + 247 \, \left(d x\right)^{m} C a m^{4} x^{3} + 247 \, \left(d x\right)^{m} A b m^{4} x^{3} + 1056 \, \left(d x\right)^{m} B b m^{3} x^{4} + 2144 \, \left(d x\right)^{m} C b m^{2} x^{5} + 2144 \, \left(d x\right)^{m} A c m^{2} x^{5} + 2038 \, \left(d x\right)^{m} B c m x^{6} + 720 \, \left(d x\right)^{m} C c x^{7} + 27 \, \left(d x\right)^{m} A a m^{5} x + 270 \, \left(d x\right)^{m} B a m^{4} x^{2} + 1219 \, \left(d x\right)^{m} C a m^{3} x^{3} + 1219 \, \left(d x\right)^{m} A b m^{3} x^{3} + 2545 \, \left(d x\right)^{m} B b m^{2} x^{4} + 2412 \, \left(d x\right)^{m} C b m x^{5} + 2412 \, \left(d x\right)^{m} A c m x^{5} + 840 \, \left(d x\right)^{m} B c x^{6} + 295 \, \left(d x\right)^{m} A a m^{4} x + 1420 \, \left(d x\right)^{m} B a m^{3} x^{2} + 3112 \, \left(d x\right)^{m} C a m^{2} x^{3} + 3112 \, \left(d x\right)^{m} A b m^{2} x^{3} + 2952 \, \left(d x\right)^{m} B b m x^{4} + 1008 \, \left(d x\right)^{m} C b x^{5} + 1008 \, \left(d x\right)^{m} A c x^{5} + 1665 \, \left(d x\right)^{m} A a m^{3} x + 3929 \, \left(d x\right)^{m} B a m^{2} x^{2} + 3796 \, \left(d x\right)^{m} C a m x^{3} + 3796 \, \left(d x\right)^{m} A b m x^{3} + 1260 \, \left(d x\right)^{m} B b x^{4} + 5104 \, \left(d x\right)^{m} A a m^{2} x + 5274 \, \left(d x\right)^{m} B a m x^{2} + 1680 \, \left(d x\right)^{m} C a x^{3} + 1680 \, \left(d x\right)^{m} A b x^{3} + 8028 \, \left(d x\right)^{m} A a m x + 2520 \, \left(d x\right)^{m} B a x^{2} + 5040 \, \left(d x\right)^{m} A a x}{m^{7} + 28 \, m^{6} + 322 \, m^{5} + 1960 \, m^{4} + 6769 \, m^{3} + 13132 \, m^{2} + 13068 \, m + 5040}"," ",0,"((d*x)^m*C*c*m^6*x^7 + (d*x)^m*B*c*m^6*x^6 + 21*(d*x)^m*C*c*m^5*x^7 + (d*x)^m*C*b*m^6*x^5 + (d*x)^m*A*c*m^6*x^5 + 22*(d*x)^m*B*c*m^5*x^6 + 175*(d*x)^m*C*c*m^4*x^7 + (d*x)^m*B*b*m^6*x^4 + 23*(d*x)^m*C*b*m^5*x^5 + 23*(d*x)^m*A*c*m^5*x^5 + 190*(d*x)^m*B*c*m^4*x^6 + 735*(d*x)^m*C*c*m^3*x^7 + (d*x)^m*C*a*m^6*x^3 + (d*x)^m*A*b*m^6*x^3 + 24*(d*x)^m*B*b*m^5*x^4 + 207*(d*x)^m*C*b*m^4*x^5 + 207*(d*x)^m*A*c*m^4*x^5 + 820*(d*x)^m*B*c*m^3*x^6 + 1624*(d*x)^m*C*c*m^2*x^7 + (d*x)^m*B*a*m^6*x^2 + 25*(d*x)^m*C*a*m^5*x^3 + 25*(d*x)^m*A*b*m^5*x^3 + 226*(d*x)^m*B*b*m^4*x^4 + 925*(d*x)^m*C*b*m^3*x^5 + 925*(d*x)^m*A*c*m^3*x^5 + 1849*(d*x)^m*B*c*m^2*x^6 + 1764*(d*x)^m*C*c*m*x^7 + (d*x)^m*A*a*m^6*x + 26*(d*x)^m*B*a*m^5*x^2 + 247*(d*x)^m*C*a*m^4*x^3 + 247*(d*x)^m*A*b*m^4*x^3 + 1056*(d*x)^m*B*b*m^3*x^4 + 2144*(d*x)^m*C*b*m^2*x^5 + 2144*(d*x)^m*A*c*m^2*x^5 + 2038*(d*x)^m*B*c*m*x^6 + 720*(d*x)^m*C*c*x^7 + 27*(d*x)^m*A*a*m^5*x + 270*(d*x)^m*B*a*m^4*x^2 + 1219*(d*x)^m*C*a*m^3*x^3 + 1219*(d*x)^m*A*b*m^3*x^3 + 2545*(d*x)^m*B*b*m^2*x^4 + 2412*(d*x)^m*C*b*m*x^5 + 2412*(d*x)^m*A*c*m*x^5 + 840*(d*x)^m*B*c*x^6 + 295*(d*x)^m*A*a*m^4*x + 1420*(d*x)^m*B*a*m^3*x^2 + 3112*(d*x)^m*C*a*m^2*x^3 + 3112*(d*x)^m*A*b*m^2*x^3 + 2952*(d*x)^m*B*b*m*x^4 + 1008*(d*x)^m*C*b*x^5 + 1008*(d*x)^m*A*c*x^5 + 1665*(d*x)^m*A*a*m^3*x + 3929*(d*x)^m*B*a*m^2*x^2 + 3796*(d*x)^m*C*a*m*x^3 + 3796*(d*x)^m*A*b*m*x^3 + 1260*(d*x)^m*B*b*x^4 + 5104*(d*x)^m*A*a*m^2*x + 5274*(d*x)^m*B*a*m*x^2 + 1680*(d*x)^m*C*a*x^3 + 1680*(d*x)^m*A*b*x^3 + 8028*(d*x)^m*A*a*m*x + 2520*(d*x)^m*B*a*x^2 + 5040*(d*x)^m*A*a*x)/(m^7 + 28*m^6 + 322*m^5 + 1960*m^4 + 6769*m^3 + 13132*m^2 + 13068*m + 5040)","B",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=""giac"")","\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=""giac"")","\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
42,1,4440,0,7.038295," ","integrate(x^2*(C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{C b x^{3} - 2 \, A c x^{3} + B b x^{2} + 2 \, C a x - A b x + 2 \, B a}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} - 4 \, a c\right)}} - \frac{{\left(2 \, {\left(2 \, b^{2} c^{3} - 8 \, a c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{3}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} A - {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 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 - \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 c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} C - 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 {\left| b^{2} - 4 \, a c \right|} + 4 \, {\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 {\left| b^{2} - 4 \, a c \right|} - 4 \, {\left(2 \, b^{6} c^{3} - 16 \, a b^{4} c^{4} + 32 \, a^{2} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, \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^{2} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - \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 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4}\right)} A + {\left(2 \, b^{7} c^{2} - 8 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 128 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 16 \, \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} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} C\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} - 4 \, a b c + \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{16 \, {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 48 \, a^{3} b^{2} c^{3} + 16 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 64 \, a^{4} c^{4} - 32 \, a^{3} b c^{4} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}} + \frac{{\left(2 \, {\left(2 \, b^{2} c^{3} - 8 \, a c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{3}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} A - {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} + 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 - \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 c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} C + 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 {\left| b^{2} - 4 \, a c \right|} - 4 \, {\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 {\left| b^{2} - 4 \, a c \right|} - 4 \, {\left(2 \, b^{6} c^{3} - 16 \, a b^{4} c^{4} + 32 \, a^{2} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, \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^{2} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - \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 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4}\right)} A + {\left(2 \, b^{7} c^{2} - 8 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 128 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 16 \, \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} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} C\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} - 4 \, a b c - \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{16 \, {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 48 \, a^{3} b^{2} c^{3} + 16 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 64 \, a^{4} c^{4} - 32 \, a^{3} b c^{4} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}} + \frac{{\left({\left(b^{4} c - 4 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} + b^{2} c^{3} + {\left(b^{3} c - 4 \, a b c^{2} - 2 \, b^{2} c^{2} + b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| b^{2} - 4 \, a c \right|} - {\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 - 4 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + b^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{b^{3} - 4 \, a b c + \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\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^{2} {\left| b^{2} - 4 \, a c \right|}} + \frac{{\left({\left(b^{4} c - 4 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} + b^{2} c^{3} - {\left(b^{3} c - 4 \, a b c^{2} - 2 \, b^{2} c^{2} + b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| b^{2} - 4 \, a c \right|} - {\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 - 4 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + b^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{b^{3} - 4 \, a b c - \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\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^{2} {\left| b^{2} - 4 \, a c \right|}}"," ",0,"1/2*(C*b*x^3 - 2*A*c*x^3 + B*b*x^2 + 2*C*a*x - A*b*x + 2*B*a)/((c*x^4 + b*x^2 + a)*(b^2 - 4*a*c)) - 1/16*(2*(2*b^2*c^3 - 8*a*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*c^3 - 2*(b^2 - 4*a*c)*c^3)*(b^2 - 4*a*c)^2*A - (2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(b^2 - 4*a*c)^2*C - 2*(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*(b^2 - 4*a*c)*b^3*c^2 - 8*(b^2 - 4*a*c)*a*b*c^3)*A*abs(b^2 - 4*a*c) + 4*(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*(b^2 - 4*a*c)*a*b^2*c^2 - 8*(b^2 - 4*a*c)*a^2*c^3)*C*abs(b^2 - 4*a*c) - 4*(2*b^6*c^3 - 16*a*b^4*c^4 + 32*a^2*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*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^2*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 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*(b^2 - 4*a*c)*b^4*c^3 + 8*(b^2 - 4*a*c)*a*b^2*c^4)*A + (2*b^7*c^2 - 8*a*b^5*c^3 - 32*a^2*b^3*c^4 + 128*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 16*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)*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 32*(b^2 - 4*a*c)*a^2*b*c^4)*C)*arctan(2*sqrt(1/2)*x/sqrt((b^3 - 4*a*b*c + sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6*c - 12*a^2*b^4*c^2 - 2*a*b^5*c^2 + 48*a^3*b^2*c^3 + 16*a^2*b^3*c^3 + a*b^4*c^3 - 64*a^4*c^4 - 32*a^3*b*c^4 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*abs(b^2 - 4*a*c)*abs(c)) + 1/16*(2*(2*b^2*c^3 - 8*a*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*c^3 - 2*(b^2 - 4*a*c)*c^3)*(b^2 - 4*a*c)^2*A - (2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(b^2 - 4*a*c)^2*C + 2*(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*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*A*abs(b^2 - 4*a*c) - 4*(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*(b^2 - 4*a*c)*a*b^2*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3)*C*abs(b^2 - 4*a*c) - 4*(2*b^6*c^3 - 16*a*b^4*c^4 + 32*a^2*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*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^2*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 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*(b^2 - 4*a*c)*b^4*c^3 + 8*(b^2 - 4*a*c)*a*b^2*c^4)*A + (2*b^7*c^2 - 8*a*b^5*c^3 - 32*a^2*b^3*c^4 + 128*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 16*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)*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 32*(b^2 - 4*a*c)*a^2*b*c^4)*C)*arctan(2*sqrt(1/2)*x/sqrt((b^3 - 4*a*b*c - sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6*c - 12*a^2*b^4*c^2 - 2*a*b^5*c^2 + 48*a^3*b^2*c^3 + 16*a^2*b^3*c^3 + a*b^4*c^3 - 64*a^4*c^4 - 32*a^3*b*c^4 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*abs(b^2 - 4*a*c)*abs(c)) + 1/8*((b^4*c - 4*a*b^2*c^2 - 2*b^3*c^2 + b^2*c^3 + (b^3*c - 4*a*b*c^2 - 2*b^2*c^2 + b*c^3)*sqrt(b^2 - 4*a*c))*B*abs(b^2 - 4*a*c) - (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 + (b^5*c - 4*a*b^3*c^2 - 2*b^4*c^2 + b^3*c^3)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(b^3 - 4*a*b*c + sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2))/((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)*c^2*abs(b^2 - 4*a*c)) + 1/8*((b^4*c - 4*a*b^2*c^2 - 2*b^3*c^2 + b^2*c^3 - (b^3*c - 4*a*b*c^2 - 2*b^2*c^2 + b*c^3)*sqrt(b^2 - 4*a*c))*B*abs(b^2 - 4*a*c) - (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 - (b^5*c - 4*a*b^3*c^2 - 2*b^4*c^2 + b^3*c^3)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(b^3 - 4*a*b*c - sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2))/((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)*c^2*abs(b^2 - 4*a*c))","B",0
43,1,4440,0,7.134569," ","integrate(x*(C*x^3+B*x^2+A*x)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{C b x^{3} - 2 \, A c x^{3} + B b x^{2} + 2 \, C a x - A b x + 2 \, B a}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} - 4 \, a c\right)}} - \frac{{\left(2 \, {\left(2 \, b^{2} c^{3} - 8 \, a c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{3}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} A - {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 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 - \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 c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} C - 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 {\left| b^{2} - 4 \, a c \right|} + 4 \, {\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 {\left| b^{2} - 4 \, a c \right|} - 4 \, {\left(2 \, b^{6} c^{3} - 16 \, a b^{4} c^{4} + 32 \, a^{2} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, \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^{2} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - \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 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4}\right)} A + {\left(2 \, b^{7} c^{2} - 8 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 128 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 16 \, \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} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} C\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} - 4 \, a b c + \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{16 \, {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 48 \, a^{3} b^{2} c^{3} + 16 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 64 \, a^{4} c^{4} - 32 \, a^{3} b c^{4} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}} + \frac{{\left(2 \, {\left(2 \, b^{2} c^{3} - 8 \, a c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{3}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} A - {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} + 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 - \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 c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} C + 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 {\left| b^{2} - 4 \, a c \right|} - 4 \, {\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 {\left| b^{2} - 4 \, a c \right|} - 4 \, {\left(2 \, b^{6} c^{3} - 16 \, a b^{4} c^{4} + 32 \, a^{2} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, \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^{2} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - \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 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4}\right)} A + {\left(2 \, b^{7} c^{2} - 8 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 128 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 16 \, \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} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} C\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} - 4 \, a b c - \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{16 \, {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 48 \, a^{3} b^{2} c^{3} + 16 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 64 \, a^{4} c^{4} - 32 \, a^{3} b c^{4} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}} + \frac{{\left({\left(b^{4} c - 4 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} + b^{2} c^{3} + {\left(b^{3} c - 4 \, a b c^{2} - 2 \, b^{2} c^{2} + b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| b^{2} - 4 \, a c \right|} - {\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 - 4 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + b^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{b^{3} - 4 \, a b c + \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\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^{2} {\left| b^{2} - 4 \, a c \right|}} + \frac{{\left({\left(b^{4} c - 4 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} + b^{2} c^{3} - {\left(b^{3} c - 4 \, a b c^{2} - 2 \, b^{2} c^{2} + b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| b^{2} - 4 \, a c \right|} - {\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 - 4 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + b^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{b^{3} - 4 \, a b c - \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\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^{2} {\left| b^{2} - 4 \, a c \right|}}"," ",0,"1/2*(C*b*x^3 - 2*A*c*x^3 + B*b*x^2 + 2*C*a*x - A*b*x + 2*B*a)/((c*x^4 + b*x^2 + a)*(b^2 - 4*a*c)) - 1/16*(2*(2*b^2*c^3 - 8*a*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*c^3 - 2*(b^2 - 4*a*c)*c^3)*(b^2 - 4*a*c)^2*A - (2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(b^2 - 4*a*c)^2*C - 2*(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*(b^2 - 4*a*c)*b^3*c^2 - 8*(b^2 - 4*a*c)*a*b*c^3)*A*abs(b^2 - 4*a*c) + 4*(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*(b^2 - 4*a*c)*a*b^2*c^2 - 8*(b^2 - 4*a*c)*a^2*c^3)*C*abs(b^2 - 4*a*c) - 4*(2*b^6*c^3 - 16*a*b^4*c^4 + 32*a^2*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*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^2*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 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*(b^2 - 4*a*c)*b^4*c^3 + 8*(b^2 - 4*a*c)*a*b^2*c^4)*A + (2*b^7*c^2 - 8*a*b^5*c^3 - 32*a^2*b^3*c^4 + 128*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 16*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)*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 32*(b^2 - 4*a*c)*a^2*b*c^4)*C)*arctan(2*sqrt(1/2)*x/sqrt((b^3 - 4*a*b*c + sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6*c - 12*a^2*b^4*c^2 - 2*a*b^5*c^2 + 48*a^3*b^2*c^3 + 16*a^2*b^3*c^3 + a*b^4*c^3 - 64*a^4*c^4 - 32*a^3*b*c^4 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*abs(b^2 - 4*a*c)*abs(c)) + 1/16*(2*(2*b^2*c^3 - 8*a*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*c^3 - 2*(b^2 - 4*a*c)*c^3)*(b^2 - 4*a*c)^2*A - (2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(b^2 - 4*a*c)^2*C + 2*(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*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*A*abs(b^2 - 4*a*c) - 4*(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*(b^2 - 4*a*c)*a*b^2*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3)*C*abs(b^2 - 4*a*c) - 4*(2*b^6*c^3 - 16*a*b^4*c^4 + 32*a^2*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*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^2*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 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*(b^2 - 4*a*c)*b^4*c^3 + 8*(b^2 - 4*a*c)*a*b^2*c^4)*A + (2*b^7*c^2 - 8*a*b^5*c^3 - 32*a^2*b^3*c^4 + 128*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 16*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)*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 32*(b^2 - 4*a*c)*a^2*b*c^4)*C)*arctan(2*sqrt(1/2)*x/sqrt((b^3 - 4*a*b*c - sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6*c - 12*a^2*b^4*c^2 - 2*a*b^5*c^2 + 48*a^3*b^2*c^3 + 16*a^2*b^3*c^3 + a*b^4*c^3 - 64*a^4*c^4 - 32*a^3*b*c^4 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*abs(b^2 - 4*a*c)*abs(c)) + 1/8*((b^4*c - 4*a*b^2*c^2 - 2*b^3*c^2 + b^2*c^3 + (b^3*c - 4*a*b*c^2 - 2*b^2*c^2 + b*c^3)*sqrt(b^2 - 4*a*c))*B*abs(b^2 - 4*a*c) - (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 + (b^5*c - 4*a*b^3*c^2 - 2*b^4*c^2 + b^3*c^3)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(b^3 - 4*a*b*c + sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2))/((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)*c^2*abs(b^2 - 4*a*c)) + 1/8*((b^4*c - 4*a*b^2*c^2 - 2*b^3*c^2 + b^2*c^3 - (b^3*c - 4*a*b*c^2 - 2*b^2*c^2 + b*c^3)*sqrt(b^2 - 4*a*c))*B*abs(b^2 - 4*a*c) - (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 - (b^5*c - 4*a*b^3*c^2 - 2*b^4*c^2 + b^3*c^3)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(b^3 - 4*a*b*c - sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2))/((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)*c^2*abs(b^2 - 4*a*c))","B",0
44,1,4439,0,6.896461," ","integrate((C*x^4+B*x^3+A*x^2)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{C b x^{3} - 2 \, A c x^{3} + B b x^{2} + 2 \, C a x - A b x + 2 \, B a}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} - 4 \, a c\right)}} - \frac{{\left(2 \, {\left(2 \, b^{2} c^{3} - 8 \, a c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{3}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} A - {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 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 - \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 c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} C - 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 {\left| b^{2} - 4 \, a c \right|} + 4 \, {\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 {\left| b^{2} - 4 \, a c \right|} - 4 \, {\left(2 \, b^{6} c^{3} - 16 \, a b^{4} c^{4} + 32 \, a^{2} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, \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^{2} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - \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 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4}\right)} A + {\left(2 \, b^{7} c^{2} - 8 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 128 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 16 \, \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} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} C\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} - 4 \, a b c + \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{16 \, {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 48 \, a^{3} b^{2} c^{3} + 16 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 64 \, a^{4} c^{4} - 32 \, a^{3} b c^{4} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}} + \frac{{\left(2 \, {\left(2 \, b^{2} c^{3} - 8 \, a c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{3}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} A - {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} + 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 - \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 c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} C + 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 {\left| b^{2} - 4 \, a c \right|} - 4 \, {\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 {\left| b^{2} - 4 \, a c \right|} - 4 \, {\left(2 \, b^{6} c^{3} - 16 \, a b^{4} c^{4} + 32 \, a^{2} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, \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^{2} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - \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 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4}\right)} A + {\left(2 \, b^{7} c^{2} - 8 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 128 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 16 \, \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} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} C\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} - 4 \, a b c - \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{16 \, {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 48 \, a^{3} b^{2} c^{3} + 16 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 64 \, a^{4} c^{4} - 32 \, a^{3} b c^{4} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}} + \frac{{\left({\left(b^{4} c - 4 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} + b^{2} c^{3} + {\left(b^{3} c - 4 \, a b c^{2} - 2 \, b^{2} c^{2} + b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| b^{2} - 4 \, a c \right|} - {\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 - 4 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + b^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{b^{3} - 4 \, a b c + \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\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^{2} {\left| b^{2} - 4 \, a c \right|}} + \frac{{\left({\left(b^{4} c - 4 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} + b^{2} c^{3} - {\left(b^{3} c - 4 \, a b c^{2} - 2 \, b^{2} c^{2} + b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| b^{2} - 4 \, a c \right|} + {\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 - 4 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + b^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{b^{3} - 4 \, a b c - \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\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^{2} {\left| b^{2} - 4 \, a c \right|}}"," ",0,"1/2*(C*b*x^3 - 2*A*c*x^3 + B*b*x^2 + 2*C*a*x - A*b*x + 2*B*a)/((c*x^4 + b*x^2 + a)*(b^2 - 4*a*c)) - 1/16*(2*(2*b^2*c^3 - 8*a*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*c^3 - 2*(b^2 - 4*a*c)*c^3)*(b^2 - 4*a*c)^2*A - (2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(b^2 - 4*a*c)^2*C - 2*(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*(b^2 - 4*a*c)*b^3*c^2 - 8*(b^2 - 4*a*c)*a*b*c^3)*A*abs(b^2 - 4*a*c) + 4*(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*(b^2 - 4*a*c)*a*b^2*c^2 - 8*(b^2 - 4*a*c)*a^2*c^3)*C*abs(b^2 - 4*a*c) - 4*(2*b^6*c^3 - 16*a*b^4*c^4 + 32*a^2*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*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^2*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 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*(b^2 - 4*a*c)*b^4*c^3 + 8*(b^2 - 4*a*c)*a*b^2*c^4)*A + (2*b^7*c^2 - 8*a*b^5*c^3 - 32*a^2*b^3*c^4 + 128*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 16*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)*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 32*(b^2 - 4*a*c)*a^2*b*c^4)*C)*arctan(2*sqrt(1/2)*x/sqrt((b^3 - 4*a*b*c + sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6*c - 12*a^2*b^4*c^2 - 2*a*b^5*c^2 + 48*a^3*b^2*c^3 + 16*a^2*b^3*c^3 + a*b^4*c^3 - 64*a^4*c^4 - 32*a^3*b*c^4 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*abs(b^2 - 4*a*c)*abs(c)) + 1/16*(2*(2*b^2*c^3 - 8*a*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*c^3 - 2*(b^2 - 4*a*c)*c^3)*(b^2 - 4*a*c)^2*A - (2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(b^2 - 4*a*c)^2*C + 2*(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*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*A*abs(b^2 - 4*a*c) - 4*(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*(b^2 - 4*a*c)*a*b^2*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3)*C*abs(b^2 - 4*a*c) - 4*(2*b^6*c^3 - 16*a*b^4*c^4 + 32*a^2*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*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^2*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 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*(b^2 - 4*a*c)*b^4*c^3 + 8*(b^2 - 4*a*c)*a*b^2*c^4)*A + (2*b^7*c^2 - 8*a*b^5*c^3 - 32*a^2*b^3*c^4 + 128*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 16*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)*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 32*(b^2 - 4*a*c)*a^2*b*c^4)*C)*arctan(2*sqrt(1/2)*x/sqrt((b^3 - 4*a*b*c - sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6*c - 12*a^2*b^4*c^2 - 2*a*b^5*c^2 + 48*a^3*b^2*c^3 + 16*a^2*b^3*c^3 + a*b^4*c^3 - 64*a^4*c^4 - 32*a^3*b*c^4 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*abs(b^2 - 4*a*c)*abs(c)) + 1/8*((b^4*c - 4*a*b^2*c^2 - 2*b^3*c^2 + b^2*c^3 + (b^3*c - 4*a*b*c^2 - 2*b^2*c^2 + b*c^3)*sqrt(b^2 - 4*a*c))*B*abs(b^2 - 4*a*c) - (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 + (b^5*c - 4*a*b^3*c^2 - 2*b^4*c^2 + b^3*c^3)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(b^3 - 4*a*b*c + sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2))/((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)*c^2*abs(b^2 - 4*a*c)) + 1/8*((b^4*c - 4*a*b^2*c^2 - 2*b^3*c^2 + b^2*c^3 - (b^3*c - 4*a*b*c^2 - 2*b^2*c^2 + b*c^3)*sqrt(b^2 - 4*a*c))*B*abs(b^2 - 4*a*c) + (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 - (b^5*c - 4*a*b^3*c^2 - 2*b^4*c^2 + b^3*c^3)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(b^3 - 4*a*b*c - sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2))/((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)*c^2*abs(b^2 - 4*a*c))","B",0
45,1,4439,0,7.311037," ","integrate((C*x^5+B*x^4+A*x^3)/x/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{C b x^{3} - 2 \, A c x^{3} + B b x^{2} + 2 \, C a x - A b x + 2 \, B a}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} - 4 \, a c\right)}} - \frac{{\left(2 \, {\left(2 \, b^{2} c^{3} - 8 \, a c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{3}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} A - {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 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 - \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 c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} C - 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 {\left| b^{2} - 4 \, a c \right|} + 4 \, {\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 {\left| b^{2} - 4 \, a c \right|} - 4 \, {\left(2 \, b^{6} c^{3} - 16 \, a b^{4} c^{4} + 32 \, a^{2} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, \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^{2} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - \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 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4}\right)} A + {\left(2 \, b^{7} c^{2} - 8 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 128 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 16 \, \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} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} C\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} - 4 \, a b c + \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{16 \, {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 48 \, a^{3} b^{2} c^{3} + 16 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 64 \, a^{4} c^{4} - 32 \, a^{3} b c^{4} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}} + \frac{{\left(2 \, {\left(2 \, b^{2} c^{3} - 8 \, a c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{3}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} A - {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} + 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 - \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 c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} C + 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 {\left| b^{2} - 4 \, a c \right|} - 4 \, {\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 {\left| b^{2} - 4 \, a c \right|} - 4 \, {\left(2 \, b^{6} c^{3} - 16 \, a b^{4} c^{4} + 32 \, a^{2} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, \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^{2} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - \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 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4}\right)} A + {\left(2 \, b^{7} c^{2} - 8 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 128 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 16 \, \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} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} C\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} - 4 \, a b c - \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{16 \, {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 48 \, a^{3} b^{2} c^{3} + 16 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 64 \, a^{4} c^{4} - 32 \, a^{3} b c^{4} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}} + \frac{{\left({\left(b^{4} c - 4 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} + b^{2} c^{3} + {\left(b^{3} c - 4 \, a b c^{2} - 2 \, b^{2} c^{2} + b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| b^{2} - 4 \, a c \right|} - {\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 - 4 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + b^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{b^{3} - 4 \, a b c + \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\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^{2} {\left| b^{2} - 4 \, a c \right|}} + \frac{{\left({\left(b^{4} c - 4 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} + b^{2} c^{3} - {\left(b^{3} c - 4 \, a b c^{2} - 2 \, b^{2} c^{2} + b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| b^{2} - 4 \, a c \right|} + {\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 - 4 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + b^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{b^{3} - 4 \, a b c - \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\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^{2} {\left| b^{2} - 4 \, a c \right|}}"," ",0,"1/2*(C*b*x^3 - 2*A*c*x^3 + B*b*x^2 + 2*C*a*x - A*b*x + 2*B*a)/((c*x^4 + b*x^2 + a)*(b^2 - 4*a*c)) - 1/16*(2*(2*b^2*c^3 - 8*a*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*c^3 - 2*(b^2 - 4*a*c)*c^3)*(b^2 - 4*a*c)^2*A - (2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(b^2 - 4*a*c)^2*C - 2*(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*(b^2 - 4*a*c)*b^3*c^2 - 8*(b^2 - 4*a*c)*a*b*c^3)*A*abs(b^2 - 4*a*c) + 4*(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*(b^2 - 4*a*c)*a*b^2*c^2 - 8*(b^2 - 4*a*c)*a^2*c^3)*C*abs(b^2 - 4*a*c) - 4*(2*b^6*c^3 - 16*a*b^4*c^4 + 32*a^2*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*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^2*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 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*(b^2 - 4*a*c)*b^4*c^3 + 8*(b^2 - 4*a*c)*a*b^2*c^4)*A + (2*b^7*c^2 - 8*a*b^5*c^3 - 32*a^2*b^3*c^4 + 128*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 16*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)*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 32*(b^2 - 4*a*c)*a^2*b*c^4)*C)*arctan(2*sqrt(1/2)*x/sqrt((b^3 - 4*a*b*c + sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6*c - 12*a^2*b^4*c^2 - 2*a*b^5*c^2 + 48*a^3*b^2*c^3 + 16*a^2*b^3*c^3 + a*b^4*c^3 - 64*a^4*c^4 - 32*a^3*b*c^4 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*abs(b^2 - 4*a*c)*abs(c)) + 1/16*(2*(2*b^2*c^3 - 8*a*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*c^3 - 2*(b^2 - 4*a*c)*c^3)*(b^2 - 4*a*c)^2*A - (2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(b^2 - 4*a*c)^2*C + 2*(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*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*A*abs(b^2 - 4*a*c) - 4*(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*(b^2 - 4*a*c)*a*b^2*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3)*C*abs(b^2 - 4*a*c) - 4*(2*b^6*c^3 - 16*a*b^4*c^4 + 32*a^2*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*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^2*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 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*(b^2 - 4*a*c)*b^4*c^3 + 8*(b^2 - 4*a*c)*a*b^2*c^4)*A + (2*b^7*c^2 - 8*a*b^5*c^3 - 32*a^2*b^3*c^4 + 128*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 16*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)*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 32*(b^2 - 4*a*c)*a^2*b*c^4)*C)*arctan(2*sqrt(1/2)*x/sqrt((b^3 - 4*a*b*c - sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6*c - 12*a^2*b^4*c^2 - 2*a*b^5*c^2 + 48*a^3*b^2*c^3 + 16*a^2*b^3*c^3 + a*b^4*c^3 - 64*a^4*c^4 - 32*a^3*b*c^4 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*abs(b^2 - 4*a*c)*abs(c)) + 1/8*((b^4*c - 4*a*b^2*c^2 - 2*b^3*c^2 + b^2*c^3 + (b^3*c - 4*a*b*c^2 - 2*b^2*c^2 + b*c^3)*sqrt(b^2 - 4*a*c))*B*abs(b^2 - 4*a*c) - (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 + (b^5*c - 4*a*b^3*c^2 - 2*b^4*c^2 + b^3*c^3)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(b^3 - 4*a*b*c + sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2))/((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)*c^2*abs(b^2 - 4*a*c)) + 1/8*((b^4*c - 4*a*b^2*c^2 - 2*b^3*c^2 + b^2*c^3 - (b^3*c - 4*a*b*c^2 - 2*b^2*c^2 + b*c^3)*sqrt(b^2 - 4*a*c))*B*abs(b^2 - 4*a*c) + (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 - (b^5*c - 4*a*b^3*c^2 - 2*b^4*c^2 + b^3*c^3)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(b^3 - 4*a*b*c - sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2))/((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)*c^2*abs(b^2 - 4*a*c))","B",0
46,1,4439,0,6.836172," ","integrate((C*x^6+B*x^5+A*x^4)/x^2/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{C b x^{3} - 2 \, A c x^{3} + B b x^{2} + 2 \, C a x - A b x + 2 \, B a}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} - 4 \, a c\right)}} - \frac{{\left(2 \, {\left(2 \, b^{2} c^{3} - 8 \, a c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{3}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} A - {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} + 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 - \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 c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} C - 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 {\left| b^{2} - 4 \, a c \right|} + 4 \, {\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 {\left| b^{2} - 4 \, a c \right|} - 4 \, {\left(2 \, b^{6} c^{3} - 16 \, a b^{4} c^{4} + 32 \, a^{2} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, \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^{2} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - \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 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4}\right)} A + {\left(2 \, b^{7} c^{2} - 8 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 128 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 16 \, \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} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} C\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} - 4 \, a b c + \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{16 \, {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 48 \, a^{3} b^{2} c^{3} + 16 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 64 \, a^{4} c^{4} - 32 \, a^{3} b c^{4} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}} + \frac{{\left(2 \, {\left(2 \, b^{2} c^{3} - 8 \, a c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{3}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} A - {\left(2 \, b^{3} c^{2} - 8 \, a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} + 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 - \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 c^{2}\right)} {\left(b^{2} - 4 \, a c\right)}^{2} C + 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 {\left| b^{2} - 4 \, a c \right|} - 4 \, {\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 {\left| b^{2} - 4 \, a c \right|} - 4 \, {\left(2 \, b^{6} c^{3} - 16 \, a b^{4} c^{4} + 32 \, a^{2} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, \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^{2} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - \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 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4}\right)} A + {\left(2 \, b^{7} c^{2} - 8 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 128 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 16 \, \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} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} C\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} - 4 \, a b c - \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{16 \, {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 48 \, a^{3} b^{2} c^{3} + 16 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} - 64 \, a^{4} c^{4} - 32 \, a^{3} b c^{4} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} {\left| b^{2} - 4 \, a c \right|} {\left| c \right|}} + \frac{{\left({\left(b^{4} c - 4 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} + b^{2} c^{3} + {\left(b^{3} c - 4 \, a b c^{2} - 2 \, b^{2} c^{2} + b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| b^{2} - 4 \, a c \right|} - {\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 - 4 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + b^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{b^{3} - 4 \, a b c + \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\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^{2} {\left| b^{2} - 4 \, a c \right|}} + \frac{{\left({\left(b^{4} c - 4 \, a b^{2} c^{2} - 2 \, b^{3} c^{2} + b^{2} c^{3} - {\left(b^{3} c - 4 \, a b c^{2} - 2 \, b^{2} c^{2} + b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B {\left| b^{2} - 4 \, a c \right|} + {\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 - 4 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} + b^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} B\right)} \log\left(x^{2} + \frac{b^{3} - 4 \, a b c - \sqrt{{\left(b^{3} - 4 \, a b c\right)}^{2} - 4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\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^{2} {\left| b^{2} - 4 \, a c \right|}}"," ",0,"1/2*(C*b*x^3 - 2*A*c*x^3 + B*b*x^2 + 2*C*a*x - A*b*x + 2*B*a)/((c*x^4 + b*x^2 + a)*(b^2 - 4*a*c)) - 1/16*(2*(2*b^2*c^3 - 8*a*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*c^3 - 2*(b^2 - 4*a*c)*c^3)*(b^2 - 4*a*c)^2*A - (2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(b^2 - 4*a*c)^2*C - 2*(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*(b^2 - 4*a*c)*b^3*c^2 - 8*(b^2 - 4*a*c)*a*b*c^3)*A*abs(b^2 - 4*a*c) + 4*(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*(b^2 - 4*a*c)*a*b^2*c^2 - 8*(b^2 - 4*a*c)*a^2*c^3)*C*abs(b^2 - 4*a*c) - 4*(2*b^6*c^3 - 16*a*b^4*c^4 + 32*a^2*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*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^2*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 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*(b^2 - 4*a*c)*b^4*c^3 + 8*(b^2 - 4*a*c)*a*b^2*c^4)*A + (2*b^7*c^2 - 8*a*b^5*c^3 - 32*a^2*b^3*c^4 + 128*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 16*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)*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 32*(b^2 - 4*a*c)*a^2*b*c^4)*C)*arctan(2*sqrt(1/2)*x/sqrt((b^3 - 4*a*b*c + sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6*c - 12*a^2*b^4*c^2 - 2*a*b^5*c^2 + 48*a^3*b^2*c^3 + 16*a^2*b^3*c^3 + a*b^4*c^3 - 64*a^4*c^4 - 32*a^3*b*c^4 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*abs(b^2 - 4*a*c)*abs(c)) + 1/16*(2*(2*b^2*c^3 - 8*a*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*c^3 - 2*(b^2 - 4*a*c)*c^3)*(b^2 - 4*a*c)^2*A - (2*b^3*c^2 - 8*a*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*(b^2 - 4*a*c)^2*C + 2*(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*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*A*abs(b^2 - 4*a*c) - 4*(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*(b^2 - 4*a*c)*a*b^2*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3)*C*abs(b^2 - 4*a*c) - 4*(2*b^6*c^3 - 16*a*b^4*c^4 + 32*a^2*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*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^2*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 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*(b^2 - 4*a*c)*b^4*c^3 + 8*(b^2 - 4*a*c)*a*b^2*c^4)*A + (2*b^7*c^2 - 8*a*b^5*c^3 - 32*a^2*b^3*c^4 + 128*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 16*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)*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 + 32*(b^2 - 4*a*c)*a^2*b*c^4)*C)*arctan(2*sqrt(1/2)*x/sqrt((b^3 - 4*a*b*c - sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/((a*b^6*c - 12*a^2*b^4*c^2 - 2*a*b^5*c^2 + 48*a^3*b^2*c^3 + 16*a^2*b^3*c^3 + a*b^4*c^3 - 64*a^4*c^4 - 32*a^3*b*c^4 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*abs(b^2 - 4*a*c)*abs(c)) + 1/8*((b^4*c - 4*a*b^2*c^2 - 2*b^3*c^2 + b^2*c^3 + (b^3*c - 4*a*b*c^2 - 2*b^2*c^2 + b*c^3)*sqrt(b^2 - 4*a*c))*B*abs(b^2 - 4*a*c) - (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 + (b^5*c - 4*a*b^3*c^2 - 2*b^4*c^2 + b^3*c^3)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(b^3 - 4*a*b*c + sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2))/((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)*c^2*abs(b^2 - 4*a*c)) + 1/8*((b^4*c - 4*a*b^2*c^2 - 2*b^3*c^2 + b^2*c^3 - (b^3*c - 4*a*b*c^2 - 2*b^2*c^2 + b*c^3)*sqrt(b^2 - 4*a*c))*B*abs(b^2 - 4*a*c) + (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 - (b^5*c - 4*a*b^3*c^2 - 2*b^4*c^2 + b^3*c^3)*sqrt(b^2 - 4*a*c))*B)*log(x^2 + 1/2*(b^3 - 4*a*b*c - sqrt((b^3 - 4*a*b*c)^2 - 4*(a*b^2 - 4*a^2*c)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2))/((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)*c^2*abs(b^2 - 4*a*c))","B",0
47,1,306,0,1.868224," ","integrate(x^7*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{3 \, c^{3} f x^{8} - 4 \, b c^{2} f x^{6} + 4 \, c^{3} x^{6} e + 6 \, c^{3} d x^{4} + 6 \, b^{2} c f x^{4} - 6 \, a c^{2} f x^{4} - 6 \, b c^{2} x^{4} e - 12 \, b c^{2} d x^{2} - 12 \, b^{3} f x^{2} + 24 \, a b c f x^{2} + 12 \, b^{2} c x^{2} e - 12 \, a c^{2} x^{2} e}{24 \, c^{4}} + \frac{{\left(b^{2} c^{2} d - a c^{3} d + b^{4} f - 3 \, a b^{2} c f + a^{2} c^{2} f - b^{3} c e + 2 \, a b c^{2} e\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, c^{5}} - \frac{{\left(b^{3} c^{2} d - 3 \, a b c^{3} d + b^{5} f - 5 \, a b^{3} c f + 5 \, a^{2} b c^{2} f - b^{4} c e + 4 \, a b^{2} c^{2} e - 2 \, a^{2} c^{3} e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} c^{5}}"," ",0,"1/24*(3*c^3*f*x^8 - 4*b*c^2*f*x^6 + 4*c^3*x^6*e + 6*c^3*d*x^4 + 6*b^2*c*f*x^4 - 6*a*c^2*f*x^4 - 6*b*c^2*x^4*e - 12*b*c^2*d*x^2 - 12*b^3*f*x^2 + 24*a*b*c*f*x^2 + 12*b^2*c*x^2*e - 12*a*c^2*x^2*e)/c^4 + 1/4*(b^2*c^2*d - a*c^3*d + b^4*f - 3*a*b^2*c*f + a^2*c^2*f - b^3*c*e + 2*a*b*c^2*e)*log(c*x^4 + b*x^2 + a)/c^5 - 1/2*(b^3*c^2*d - 3*a*b*c^3*d + b^5*f - 5*a*b^3*c*f + 5*a^2*b*c^2*f - b^4*c*e + 4*a*b^2*c^2*e - 2*a^2*c^3*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^5)","A",0
48,1,214,0,2.004756," ","integrate(x^5*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{2 \, c^{2} f x^{6} - 3 \, b c f x^{4} + 3 \, c^{2} x^{4} e + 6 \, c^{2} d x^{2} + 6 \, b^{2} f x^{2} - 6 \, a c f x^{2} - 6 \, b c x^{2} e}{12 \, c^{3}} - \frac{{\left(b c^{2} d + b^{3} f - 2 \, a b c f - b^{2} c e + a c^{2} e\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, c^{4}} + \frac{{\left(b^{2} c^{2} d - 2 \, a c^{3} d + b^{4} f - 4 \, a b^{2} c f + 2 \, a^{2} c^{2} f - b^{3} c e + 3 \, a b c^{2} e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} c^{4}}"," ",0,"1/12*(2*c^2*f*x^6 - 3*b*c*f*x^4 + 3*c^2*x^4*e + 6*c^2*d*x^2 + 6*b^2*f*x^2 - 6*a*c*f*x^2 - 6*b*c*x^2*e)/c^3 - 1/4*(b*c^2*d + b^3*f - 2*a*b*c*f - b^2*c*e + a*c^2*e)*log(c*x^4 + b*x^2 + a)/c^4 + 1/2*(b^2*c^2*d - 2*a*c^3*d + b^4*f - 4*a*b^2*c*f + 2*a^2*c^2*f - b^3*c*e + 3*a*b*c^2*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^4)","A",0
49,1,141,0,1.987026," ","integrate(x^3*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{c f x^{4} - 2 \, b f x^{2} + 2 \, c x^{2} e}{4 \, c^{2}} + \frac{{\left(c^{2} d + b^{2} f - a c f - b c e\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, c^{3}} - \frac{{\left(b c^{2} d + b^{3} f - 3 \, a b c f - b^{2} c e + 2 \, a c^{2} e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} c^{3}}"," ",0,"1/4*(c*f*x^4 - 2*b*f*x^2 + 2*c*x^2*e)/c^2 + 1/4*(c^2*d + b^2*f - a*c*f - b*c*e)*log(c*x^4 + b*x^2 + a)/c^3 - 1/2*(b*c^2*d + b^3*f - 3*a*b*c*f - b^2*c*e + 2*a*c^2*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^3)","A",0
50,1,99,0,1.779895," ","integrate(x*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{f x^{2}}{2 \, c} - \frac{{\left(b f - c e\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, c^{2}} + \frac{{\left(2 \, c^{2} d + b^{2} f - 2 \, a c f - b c e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} c^{2}}"," ",0,"1/2*f*x^2/c - 1/4*(b*f - c*e)*log(c*x^4 + b*x^2 + a)/c^2 + 1/2*(2*c^2*d + b^2*f - 2*a*c*f - b*c*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^2)","A",0
51,1,97,0,1.902568," ","integrate((f*x^4+e*x^2+d)/x/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{d \log\left(x^{2}\right)}{2 \, a} - \frac{{\left(c d - a f\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, a c} - \frac{{\left(b c d + a b f - 2 \, a c e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} a c}"," ",0,"1/2*d*log(x^2)/a - 1/4*(c*d - a*f)*log(c*x^4 + b*x^2 + a)/(a*c) - 1/2*(b*c*d + a*b*f - 2*a*c*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a*c)","A",0
52,1,135,0,1.777409," ","integrate((f*x^4+e*x^2+d)/x^3/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{{\left(b d - a e\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, a^{2}} - \frac{{\left(b d - a e\right)} \log\left(x^{2}\right)}{2 \, a^{2}} + \frac{{\left(b^{2} d - 2 \, a c d + 2 \, a^{2} f - a b e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} a^{2}} + \frac{b d x^{2} - a x^{2} e - a d}{2 \, a^{2} x^{2}}"," ",0,"1/4*(b*d - a*e)*log(c*x^4 + b*x^2 + a)/a^2 - 1/2*(b*d - a*e)*log(x^2)/a^2 + 1/2*(b^2*d - 2*a*c*d + 2*a^2*f - a*b*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a^2) + 1/2*(b*d*x^2 - a*x^2*e - a*d)/(a^2*x^2)","A",0
53,1,212,0,1.718997," ","integrate((f*x^4+e*x^2+d)/x^5/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(b^{2} d - a c d + a^{2} f - a b e\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, a^{3}} + \frac{{\left(b^{2} d - a c d + a^{2} f - a b e\right)} \log\left(x^{2}\right)}{2 \, a^{3}} - \frac{{\left(b^{3} d - 3 \, a b c d + a^{2} b f - a b^{2} e + 2 \, a^{2} c e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} a^{3}} - \frac{3 \, b^{2} d x^{4} - 3 \, a c d x^{4} + 3 \, a^{2} f x^{4} - 3 \, a b x^{4} e - 2 \, a b d x^{2} + 2 \, a^{2} x^{2} e + a^{2} d}{4 \, a^{3} x^{4}}"," ",0,"-1/4*(b^2*d - a*c*d + a^2*f - a*b*e)*log(c*x^4 + b*x^2 + a)/a^3 + 1/2*(b^2*d - a*c*d + a^2*f - a*b*e)*log(x^2)/a^3 - 1/2*(b^3*d - 3*a*b*c*d + a^2*b*f - a*b^2*e + 2*a^2*c*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a^3) - 1/4*(3*b^2*d*x^4 - 3*a*c*d*x^4 + 3*a^2*f*x^4 - 3*a*b*x^4*e - 2*a*b*d*x^2 + 2*a^2*x^2*e + a^2*d)/(a^3*x^4)","A",0
54,1,313,0,1.941145," ","integrate((f*x^4+e*x^2+d)/x^7/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{{\left(b^{3} d - 2 \, a b c d + a^{2} b f - a b^{2} e + a^{2} c e\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, a^{4}} - \frac{{\left(b^{3} d - 2 \, a b c d + a^{2} b f - a b^{2} e + a^{2} c e\right)} \log\left(x^{2}\right)}{2 \, a^{4}} + \frac{{\left(b^{4} d - 4 \, a b^{2} c d + 2 \, a^{2} c^{2} d + a^{2} b^{2} f - 2 \, a^{3} c f - a b^{3} e + 3 \, a^{2} b c e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} a^{4}} + \frac{11 \, b^{3} d x^{6} - 22 \, a b c d x^{6} + 11 \, a^{2} b f x^{6} - 11 \, a b^{2} x^{6} e + 11 \, a^{2} c x^{6} e - 6 \, a b^{2} d x^{4} + 6 \, a^{2} c d x^{4} - 6 \, a^{3} f x^{4} + 6 \, a^{2} b x^{4} e + 3 \, a^{2} b d x^{2} - 3 \, a^{3} x^{2} e - 2 \, a^{3} d}{12 \, a^{4} x^{6}}"," ",0,"1/4*(b^3*d - 2*a*b*c*d + a^2*b*f - a*b^2*e + a^2*c*e)*log(c*x^4 + b*x^2 + a)/a^4 - 1/2*(b^3*d - 2*a*b*c*d + a^2*b*f - a*b^2*e + a^2*c*e)*log(x^2)/a^4 + 1/2*(b^4*d - 4*a*b^2*c*d + 2*a^2*c^2*d + a^2*b^2*f - 2*a^3*c*f - a*b^3*e + 3*a^2*b*c*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a^4) + 1/12*(11*b^3*d*x^6 - 22*a*b*c*d*x^6 + 11*a^2*b*f*x^6 - 11*a*b^2*x^6*e + 11*a^2*c*x^6*e - 6*a*b^2*d*x^4 + 6*a^2*c*d*x^4 - 6*a^3*f*x^4 + 6*a^2*b*x^4*e + 3*a^2*b*d*x^2 - 3*a^3*x^2*e - 2*a^3*d)/(a^4*x^6)","A",0
55,1,7243,0,5.025173," ","integrate(x^4*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left({\left(2 \, b^{5} c^{4} - 16 \, a b^{3} c^{5} + 32 \, 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} + 8 \, \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} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 8 \, \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} + 4 \, \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} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5}\right)} c^{2} d + {\left(2 \, b^{7} c^{2} - 20 \, a b^{5} c^{3} + 64 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} 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^{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} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 12 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} c^{2} f - {\left(2 \, b^{6} c^{3} - 18 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 32 \, a^{3} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} 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^{4} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 10 \, {\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)} c^{2} e + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} + 2 \, a b^{4} c^{5} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} - 16 \, a^{2} b^{2} c^{6} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{7} + 32 \, a^{3} c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{6}\right)} d {\left| c \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} - 9 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + 2 \, a b^{6} c^{3} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} + 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - 18 \, a^{2} b^{4} c^{4} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} - 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + 48 \, a^{3} b^{2} c^{5} + 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} - 32 \, a^{4} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{3} + 10 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{5}\right)} f {\left| c \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} + 2 \, a b^{5} c^{4} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - 16 \, a^{2} b^{3} c^{5} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} + 32 \, a^{3} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{5}\right)} {\left| c \right|} e - {\left(2 \, b^{5} c^{6} - 12 \, a b^{3} c^{7} + 16 \, a^{2} b c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} 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^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{5} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{6} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{6} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{7}\right)} d - {\left(2 \, b^{7} c^{4} - 16 \, a b^{5} c^{5} + 36 \, a^{2} b^{3} c^{6} - 16 \, a^{3} b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{3} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{5} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{6}\right)} f + {\left(2 \, b^{6} c^{5} - 14 \, a b^{4} c^{6} + 24 \, a^{2} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{3} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{4} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{5} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{5} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{6}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c^{5} + \sqrt{b^{2} c^{10} - 4 \, a c^{11}}}{c^{6}}}}\right)}{8 \, {\left(a b^{4} c^{5} - 8 \, a^{2} b^{2} c^{6} - 2 \, a b^{3} c^{6} + 16 \, a^{3} c^{7} + 8 \, a^{2} b c^{7} + a b^{2} c^{7} - 4 \, a^{2} c^{8}\right)} c^{2}} + \frac{{\left({\left(2 \, b^{5} c^{4} - 16 \, a b^{3} c^{5} + 32 \, 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} + 8 \, \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} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 8 \, \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} + 4 \, \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} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5}\right)} c^{2} d + {\left(2 \, b^{7} c^{2} - 20 \, a b^{5} c^{3} + 64 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} 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^{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} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 12 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} c^{2} f - {\left(2 \, b^{6} c^{3} - 18 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 32 \, a^{3} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} 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^{4} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 10 \, {\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)} c^{2} e - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - 2 \, a b^{4} c^{5} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} + 16 \, a^{2} b^{2} c^{6} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{7} - 32 \, a^{3} c^{7} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{5} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{6}\right)} d {\left| c \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} - 9 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} - 2 \, a b^{6} c^{3} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} + 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} + 18 \, a^{2} b^{4} c^{4} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} - 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} - 48 \, a^{3} b^{2} c^{5} + 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{6} + 32 \, a^{4} c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{3} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{5}\right)} f {\left| c \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - 2 \, a b^{5} c^{4} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} + 16 \, a^{2} b^{3} c^{5} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} - 32 \, a^{3} b c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{5}\right)} {\left| c \right|} e - {\left(2 \, b^{5} c^{6} - 12 \, a b^{3} c^{7} + 16 \, a^{2} b c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} 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^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{5} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{6} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{6} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{7}\right)} d - {\left(2 \, b^{7} c^{4} - 16 \, a b^{5} c^{5} + 36 \, a^{2} b^{3} c^{6} - 16 \, a^{3} b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{3} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{5} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{6}\right)} f + {\left(2 \, b^{6} c^{5} - 14 \, a b^{4} c^{6} + 24 \, a^{2} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{3} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{4} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{5} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{5} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{6}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c^{5} - \sqrt{b^{2} c^{10} - 4 \, a c^{11}}}{c^{6}}}}\right)}{8 \, {\left(a b^{4} c^{5} - 8 \, a^{2} b^{2} c^{6} - 2 \, a b^{3} c^{6} + 16 \, a^{3} c^{7} + 8 \, a^{2} b c^{7} + a b^{2} c^{7} - 4 \, a^{2} c^{8}\right)} c^{2}} + \frac{3 \, c^{4} f x^{5} - 5 \, b c^{3} f x^{3} + 5 \, c^{4} x^{3} e + 15 \, c^{4} d x + 15 \, b^{2} c^{2} f x - 15 \, a c^{3} f x - 15 \, b c^{3} x e}{15 \, c^{5}}"," ",0,"-1/8*((2*b^5*c^4 - 16*a*b^3*c^5 + 32*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 + 8*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 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 8*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 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 2*(b^2 - 4*a*c)*b^3*c^4 + 8*(b^2 - 4*a*c)*a*b*c^5)*c^2*d + (2*b^7*c^2 - 20*a*b^5*c^3 + 64*a^2*b^3*c^4 - 64*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*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^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 - 2*(b^2 - 4*a*c)*b^5*c^2 + 12*(b^2 - 4*a*c)*a*b^3*c^3 - 16*(b^2 - 4*a*c)*a^2*b*c^4)*c^2*f - (2*b^6*c^3 - 18*a*b^4*c^4 + 48*a^2*b^2*c^5 - 32*a^3*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*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^4 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 2*(b^2 - 4*a*c)*b^4*c^3 + 10*(b^2 - 4*a*c)*a*b^2*c^4 - 8*(b^2 - 4*a*c)*a^2*c^5)*c^2*e + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 + 2*a*b^4*c^5 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^6 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - 16*a^2*b^2*c^6 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^7 + 32*a^3*c^7 - 2*(b^2 - 4*a*c)*a*b^2*c^5 + 8*(b^2 - 4*a*c)*a^2*c^6)*d*abs(c) + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^2 - 9*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 + 2*a*b^6*c^3 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 + 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - 18*a^2*b^4*c^4 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 - 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + 48*a^3*b^2*c^5 + 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^6 - 32*a^4*c^6 - 2*(b^2 - 4*a*c)*a*b^4*c^3 + 10*(b^2 - 4*a*c)*a^2*b^2*c^4 - 8*(b^2 - 4*a*c)*a^3*c^5)*f*abs(c) - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 + 2*a*b^5*c^4 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - 16*a^2*b^3*c^5 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 + 32*a^3*b*c^6 - 2*(b^2 - 4*a*c)*a*b^3*c^4 + 8*(b^2 - 4*a*c)*a^2*b*c^5)*abs(c)*e - (2*b^5*c^6 - 12*a*b^3*c^7 + 16*a^2*b*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*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^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^5 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^6 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^7 - 2*(b^2 - 4*a*c)*b^3*c^6 + 4*(b^2 - 4*a*c)*a*b*c^7)*d - (2*b^7*c^4 - 16*a*b^5*c^5 + 36*a^2*b^3*c^6 - 16*a^3*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^3 - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 - 2*(b^2 - 4*a*c)*b^5*c^4 + 8*(b^2 - 4*a*c)*a*b^3*c^5 - 4*(b^2 - 4*a*c)*a^2*b*c^6)*f + (2*b^6*c^5 - 14*a*b^4*c^6 + 24*a^2*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^3 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^4 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^5 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - 2*(b^2 - 4*a*c)*b^4*c^5 + 6*(b^2 - 4*a*c)*a*b^2*c^6)*e)*arctan(2*sqrt(1/2)*x/sqrt((b*c^5 + sqrt(b^2*c^10 - 4*a*c^11))/c^6))/((a*b^4*c^5 - 8*a^2*b^2*c^6 - 2*a*b^3*c^6 + 16*a^3*c^7 + 8*a^2*b*c^7 + a*b^2*c^7 - 4*a^2*c^8)*c^2) + 1/8*((2*b^5*c^4 - 16*a*b^3*c^5 + 32*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 + 8*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 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 8*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 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 2*(b^2 - 4*a*c)*b^3*c^4 + 8*(b^2 - 4*a*c)*a*b*c^5)*c^2*d + (2*b^7*c^2 - 20*a*b^5*c^3 + 64*a^2*b^3*c^4 - 64*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*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^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 - 2*(b^2 - 4*a*c)*b^5*c^2 + 12*(b^2 - 4*a*c)*a*b^3*c^3 - 16*(b^2 - 4*a*c)*a^2*b*c^4)*c^2*f - (2*b^6*c^3 - 18*a*b^4*c^4 + 48*a^2*b^2*c^5 - 32*a^3*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*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^4 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 2*(b^2 - 4*a*c)*b^4*c^3 + 10*(b^2 - 4*a*c)*a*b^2*c^4 - 8*(b^2 - 4*a*c)*a^2*c^5)*c^2*e - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - 2*a*b^4*c^5 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^6 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 + 16*a^2*b^2*c^6 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^7 - 32*a^3*c^7 + 2*(b^2 - 4*a*c)*a*b^2*c^5 - 8*(b^2 - 4*a*c)*a^2*c^6)*d*abs(c) - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^2 - 9*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 - 2*a*b^6*c^3 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 + 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 + 18*a^2*b^4*c^4 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 - 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 48*a^3*b^2*c^5 + 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^6 + 32*a^4*c^6 + 2*(b^2 - 4*a*c)*a*b^4*c^3 - 10*(b^2 - 4*a*c)*a^2*b^2*c^4 + 8*(b^2 - 4*a*c)*a^3*c^5)*f*abs(c) + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - 2*a*b^5*c^4 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 + 16*a^2*b^3*c^5 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 - 32*a^3*b*c^6 + 2*(b^2 - 4*a*c)*a*b^3*c^4 - 8*(b^2 - 4*a*c)*a^2*b*c^5)*abs(c)*e - (2*b^5*c^6 - 12*a*b^3*c^7 + 16*a^2*b*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*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^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^5 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^6 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^7 - 2*(b^2 - 4*a*c)*b^3*c^6 + 4*(b^2 - 4*a*c)*a*b*c^7)*d - (2*b^7*c^4 - 16*a*b^5*c^5 + 36*a^2*b^3*c^6 - 16*a^3*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^3 - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^6 - 2*(b^2 - 4*a*c)*b^5*c^4 + 8*(b^2 - 4*a*c)*a*b^3*c^5 - 4*(b^2 - 4*a*c)*a^2*b*c^6)*f + (2*b^6*c^5 - 14*a*b^4*c^6 + 24*a^2*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^3 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^4 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^5 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^6 - 2*(b^2 - 4*a*c)*b^4*c^5 + 6*(b^2 - 4*a*c)*a*b^2*c^6)*e)*arctan(2*sqrt(1/2)*x/sqrt((b*c^5 - sqrt(b^2*c^10 - 4*a*c^11))/c^6))/((a*b^4*c^5 - 8*a^2*b^2*c^6 - 2*a*b^3*c^6 + 16*a^3*c^7 + 8*a^2*b*c^7 + a*b^2*c^7 - 4*a^2*c^8)*c^2) + 1/15*(3*c^4*f*x^5 - 5*b*c^3*f*x^3 + 5*c^4*x^3*e + 15*c^4*d*x + 15*b^2*c^2*f*x - 15*a*c^3*f*x - 15*b*c^3*x*e)/c^5","B",0
56,1,5461,0,4.754590," ","integrate(x^2*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left({\left(2 \, b^{4} c^{4} - 16 \, a b^{2} 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} + 8 \, \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} - 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^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{5}\right)} c^{2} d + {\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^{2} f - {\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)} c^{2} e - 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)} f {\left| c \right|} + 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)} {\left| c \right|} e - {\left(2 \, b^{4} c^{6} - 8 \, a b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} 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^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{6}\right)} d - {\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)} f + {\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)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c^{3} + \sqrt{b^{2} c^{6} - 4 \, a c^{7}}}{c^{4}}}}\right)}{8 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} - 2 \, a b^{3} c^{5} + 16 \, a^{3} c^{6} + 8 \, a^{2} b c^{6} + a b^{2} c^{6} - 4 \, a^{2} c^{7}\right)} c^{2}} - \frac{{\left({\left(2 \, b^{4} c^{4} - 16 \, a b^{2} 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} + 8 \, \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} - 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^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{5}\right)} c^{2} d + {\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^{2} f - {\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)} c^{2} e - 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)} f {\left| c \right|} + 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)} {\left| c \right|} e - {\left(2 \, b^{4} c^{6} - 8 \, a b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} 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^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{6}\right)} d - {\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)} f + {\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)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c^{3} - \sqrt{b^{2} c^{6} - 4 \, a c^{7}}}{c^{4}}}}\right)}{8 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} - 2 \, a b^{3} c^{5} + 16 \, a^{3} c^{6} + 8 \, a^{2} b c^{6} + a b^{2} c^{6} - 4 \, a^{2} c^{7}\right)} c^{2}} + \frac{c^{2} f x^{3} - 3 \, b c f x + 3 \, c^{2} x e}{3 \, c^{3}}"," ",0,"-1/8*((2*b^4*c^4 - 16*a*b^2*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 + 8*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 - 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*(b^2 - 4*a*c)*b^2*c^4 + 8*(b^2 - 4*a*c)*a*c^5)*c^2*d + (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*(b^2 - 4*a*c)*b^4*c^2 + 10*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*c^2*f - (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*(b^2 - 4*a*c)*b^3*c^3 + 8*(b^2 - 4*a*c)*a*b*c^4)*c^2*e - 2*(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*(b^2 - 4*a*c)*a*b^3*c^3 + 8*(b^2 - 4*a*c)*a^2*b*c^4)*f*abs(c) + 2*(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*(b^2 - 4*a*c)*a*b^2*c^4 + 8*(b^2 - 4*a*c)*a^2*c^5)*abs(c)*e - (2*b^4*c^6 - 8*a*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*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^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^6 - 2*(b^2 - 4*a*c)*b^2*c^6)*d - (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*(b^2 - 4*a*c)*b^4*c^4 + 6*(b^2 - 4*a*c)*a*b^2*c^5)*f + (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*(b^2 - 4*a*c)*b^3*c^5 + 4*(b^2 - 4*a*c)*a*b*c^6)*e)*arctan(2*sqrt(1/2)*x/sqrt((b*c^3 + sqrt(b^2*c^6 - 4*a*c^7))/c^4))/((a*b^4*c^4 - 8*a^2*b^2*c^5 - 2*a*b^3*c^5 + 16*a^3*c^6 + 8*a^2*b*c^6 + a*b^2*c^6 - 4*a^2*c^7)*c^2) - 1/8*((2*b^4*c^4 - 16*a*b^2*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 + 8*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 - 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*(b^2 - 4*a*c)*b^2*c^4 + 8*(b^2 - 4*a*c)*a*c^5)*c^2*d + (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*(b^2 - 4*a*c)*b^4*c^2 + 10*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*c^2*f - (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*(b^2 - 4*a*c)*b^3*c^3 + 8*(b^2 - 4*a*c)*a*b*c^4)*c^2*e - 2*(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*(b^2 - 4*a*c)*a*b^3*c^3 - 8*(b^2 - 4*a*c)*a^2*b*c^4)*f*abs(c) + 2*(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*(b^2 - 4*a*c)*a*b^2*c^4 - 8*(b^2 - 4*a*c)*a^2*c^5)*abs(c)*e - (2*b^4*c^6 - 8*a*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*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^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^6 - 2*(b^2 - 4*a*c)*b^2*c^6)*d - (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*(b^2 - 4*a*c)*b^4*c^4 + 6*(b^2 - 4*a*c)*a*b^2*c^5)*f + (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*(b^2 - 4*a*c)*b^3*c^5 + 4*(b^2 - 4*a*c)*a*b*c^6)*e)*arctan(2*sqrt(1/2)*x/sqrt((b*c^3 - sqrt(b^2*c^6 - 4*a*c^7))/c^4))/((a*b^4*c^4 - 8*a^2*b^2*c^5 - 2*a*b^3*c^5 + 16*a^3*c^6 + 8*a^2*b*c^6 + a*b^2*c^6 - 4*a^2*c^7)*c^2) + 1/3*(c^2*f*x^3 - 3*b*c*f*x + 3*c^2*x*e)/c^3","B",0
57,1,4086,0,3.907548," ","integrate((f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{f x}{c} - \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)} c^{2} f - {\left(2 \, b^{4} c^{3} - 16 \, a b^{2} c^{4} + 32 \, a^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} c^{2} e - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 2 \, b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} - 16 \, a b^{2} c^{5} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{6} + 32 \, a^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{5}\right)} d {\left| c \right|} + 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)} f {\left| c \right|} - 2 \, {\left(2 \, b^{3} c^{6} - 8 \, a b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{6}\right)} d - {\left(2 \, b^{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)} f + {\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)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c + \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{c^{2}}}}\right)}{8 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} - 2 \, a b^{3} c^{4} + 16 \, a^{3} c^{5} + 8 \, a^{2} b c^{5} + a b^{2} c^{5} - 4 \, a^{2} c^{6}\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)} c^{2} f - {\left(2 \, b^{4} c^{3} - 16 \, a b^{2} c^{4} + 32 \, a^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} c^{2} e + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} - 2 \, b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} + 16 \, a b^{2} c^{5} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{6} - 32 \, a^{2} c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{5}\right)} d {\left| c \right|} - 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)} f {\left| c \right|} - 2 \, {\left(2 \, b^{3} c^{6} - 8 \, a b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{6}\right)} d - {\left(2 \, b^{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)} f + {\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)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c - \sqrt{b^{2} c^{2} - 4 \, a c^{3}}}{c^{2}}}}\right)}{8 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} - 2 \, a b^{3} c^{4} + 16 \, a^{3} c^{5} + 8 \, a^{2} b c^{5} + a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} c^{2}}"," ",0,"f*x/c - 1/8*((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*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*c^2*f - (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*(b^2 - 4*a*c)*b^2*c^3 + 8*(b^2 - 4*a*c)*a*c^4)*c^2*e - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 2*b^4*c^4 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^5 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^5 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^5 - 16*a*b^2*c^5 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^6 + 32*a^2*c^6 - 2*(b^2 - 4*a*c)*b^2*c^4 + 8*(b^2 - 4*a*c)*a*c^5)*d*abs(c) + 2*(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*(b^2 - 4*a*c)*a*b^2*c^3 + 8*(b^2 - 4*a*c)*a^2*c^4)*f*abs(c) - 2*(2*b^3*c^6 - 8*a*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^6 - 2*(b^2 - 4*a*c)*b*c^6)*d - (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*(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*a*b*c^5)*f + (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*(b^2 - 4*a*c)*b^2*c^5)*e)*arctan(2*sqrt(1/2)*x/sqrt((b*c + sqrt(b^2*c^2 - 4*a*c^3))/c^2))/((a*b^4*c^3 - 8*a^2*b^2*c^4 - 2*a*b^3*c^4 + 16*a^3*c^5 + 8*a^2*b*c^5 + a*b^2*c^5 - 4*a^2*c^6)*c^2) + 1/8*((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*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3)*c^2*f - (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*(b^2 - 4*a*c)*b^2*c^3 + 8*(b^2 - 4*a*c)*a*c^4)*c^2*e + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^4 - 2*b^4*c^4 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^5 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^5 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^5 + 16*a*b^2*c^5 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^6 - 32*a^2*c^6 + 2*(b^2 - 4*a*c)*b^2*c^4 - 8*(b^2 - 4*a*c)*a*c^5)*d*abs(c) - 2*(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*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*f*abs(c) - 2*(2*b^3*c^6 - 8*a*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^6 - 2*(b^2 - 4*a*c)*b*c^6)*d - (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*(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*a*b*c^5)*f + (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*(b^2 - 4*a*c)*b^2*c^5)*e)*arctan(2*sqrt(1/2)*x/sqrt((b*c - sqrt(b^2*c^2 - 4*a*c^3))/c^2))/((a*b^4*c^3 - 8*a^2*b^2*c^4 - 2*a*b^3*c^4 + 16*a^3*c^5 + 8*a^2*b*c^5 + a*b^2*c^5 - 4*a^2*c^6)*c^2)","B",0
58,1,3988,0,5.935836," ","integrate((f*x^4+e*x^2+d)/x^2/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{d}{a x} - \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^{2} d - {\left(2 \, a b^{4} c^{2} - 16 \, a^{2} b^{2} 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} + 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 - 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^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} a^{2} f + 2 \, {\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} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 32 \, a^{3} b 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}\right)} d {\left| a \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 2 \, a^{2} b^{4} 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} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 16 \, a^{3} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 32 \, a^{4} c^{4} + 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)} {\left| a \right|} e + {\left(2 \, a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} 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} + 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} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3}\right)} d + {\left(2 \, a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{2}\right)} f - 2 \, {\left(2 \, a^{3} b^{3} c^{3} - 8 \, 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^{3} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{2} + 2 \, \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^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b + \sqrt{a^{2} b^{2} - 4 \, a^{3} c}}{a c}}}\right)}{8 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} - 2 \, a^{3} b^{3} c^{2} + 16 \, a^{5} c^{3} + 8 \, a^{4} b c^{3} + a^{3} b^{2} c^{3} - 4 \, a^{4} c^{4}\right)} {\left| a \right|} {\left| c \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^{2} d - {\left(2 \, a b^{4} c^{2} - 16 \, a^{2} b^{2} 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} + 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 - 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^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} a^{2} f - 2 \, {\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} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 32 \, a^{3} b 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}\right)} d {\left| a \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 2 \, a^{2} b^{4} 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} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 16 \, a^{3} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 32 \, a^{4} c^{4} - 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)} {\left| a \right|} e + {\left(2 \, a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} 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} + 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} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3}\right)} d + {\left(2 \, a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{2}\right)} f - 2 \, {\left(2 \, a^{3} b^{3} c^{3} - 8 \, 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^{3} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{2} + 2 \, \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^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b - \sqrt{a^{2} b^{2} - 4 \, a^{3} c}}{a c}}}\right)}{8 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} - 2 \, a^{3} b^{3} c^{2} + 16 \, a^{5} c^{3} + 8 \, a^{4} b c^{3} + a^{3} b^{2} c^{3} - 4 \, a^{4} c^{4}\right)} {\left| a \right|} {\left| c \right|}}"," ",0,"-d/(a*x) - 1/8*((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*(b^2 - 4*a*c)*b^2*c^3 + 8*(b^2 - 4*a*c)*a*c^4)*a^2*d - (2*a*b^4*c^2 - 16*a^2*b^2*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 + 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 - 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*(b^2 - 4*a*c)*a*b^2*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3)*a^2*f + 2*(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 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 32*a^3*b*c^4 + 2*(b^2 - 4*a*c)*a*b^3*c^2 - 8*(b^2 - 4*a*c)*a^2*b*c^3)*d*abs(a) - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - 2*a^2*b^4*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 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 16*a^3*b^2*c^3 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 - 32*a^4*c^4 + 2*(b^2 - 4*a*c)*a^2*b^2*c^2 - 8*(b^2 - 4*a*c)*a^3*c^3)*abs(a)*e + (2*a^2*b^4*c^3 - 8*a^3*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*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 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 2*(b^2 - 4*a*c)*a^2*b^2*c^3)*d + (2*a^3*b^4*c^2 - 8*a^4*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 - 2*(b^2 - 4*a*c)*a^3*b^2*c^2)*f - 2*(2*a^3*b^3*c^3 - 8*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^3*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^2 + 2*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^3 - 2*(b^2 - 4*a*c)*a^3*b*c^3)*e)*arctan(2*sqrt(1/2)*x/sqrt((a*b + sqrt(a^2*b^2 - 4*a^3*c))/(a*c)))/((a^3*b^4*c - 8*a^4*b^2*c^2 - 2*a^3*b^3*c^2 + 16*a^5*c^3 + 8*a^4*b*c^3 + a^3*b^2*c^3 - 4*a^4*c^4)*abs(a)*abs(c)) + 1/8*((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*(b^2 - 4*a*c)*b^2*c^3 + 8*(b^2 - 4*a*c)*a*c^4)*a^2*d - (2*a*b^4*c^2 - 16*a^2*b^2*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 + 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 - 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*(b^2 - 4*a*c)*a*b^2*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3)*a^2*f - 2*(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 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 32*a^3*b*c^4 - 2*(b^2 - 4*a*c)*a*b^3*c^2 + 8*(b^2 - 4*a*c)*a^2*b*c^3)*d*abs(a) + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + 2*a^2*b^4*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 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 16*a^3*b^2*c^3 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 32*a^4*c^4 - 2*(b^2 - 4*a*c)*a^2*b^2*c^2 + 8*(b^2 - 4*a*c)*a^3*c^3)*abs(a)*e + (2*a^2*b^4*c^3 - 8*a^3*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*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 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 2*(b^2 - 4*a*c)*a^2*b^2*c^3)*d + (2*a^3*b^4*c^2 - 8*a^4*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 - 2*(b^2 - 4*a*c)*a^3*b^2*c^2)*f - 2*(2*a^3*b^3*c^3 - 8*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^3*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^2 + 2*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^3 - 2*(b^2 - 4*a*c)*a^3*b*c^3)*e)*arctan(2*sqrt(1/2)*x/sqrt((a*b - sqrt(a^2*b^2 - 4*a^3*c))/(a*c)))/((a^3*b^4*c - 8*a^4*b^2*c^2 - 2*a^3*b^3*c^2 + 16*a^5*c^3 + 8*a^4*b*c^3 + a^3*b^2*c^3 - 4*a^4*c^4)*abs(a)*abs(c))","B",0
59,1,3813,0,3.442431," ","integrate((f*x^4+e*x^2+d)/x^4/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\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{a^{2} b + \sqrt{a^{4} b^{2} - 4 \, a^{5} c}}{a^{2} c}}}\right)}{4 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c - 2 \, a^{3} b^{3} c + 16 \, a^{5} c^{2} + 8 \, a^{4} b c^{2} + a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} {\left| c \right|}} + \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{a^{2} b - \sqrt{a^{4} b^{2} - 4 \, a^{5} c}}{a^{2} c}}}\right)}{4 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c - 2 \, a^{3} b^{3} c + 16 \, a^{5} c^{2} + 8 \, a^{4} b c^{2} + a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} {\left| c \right|}} + \frac{3 \, b d x^{2} - 3 \, a x^{2} e - a d}{3 \, a^{2} x^{3}}"," ",0,"1/4*((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*(b^2 - 4*a*c)*b^4*c - 10*(b^2 - 4*a*c)*a*b^2*c^2 - 2*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3 + 6*(b^2 - 4*a*c)*a*b*c^3)*d + (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*(b^2 - 4*a*c)*a^2*b^2*c - 8*(b^2 - 4*a*c)*a^3*c^2 - 2*(b^2 - 4*a*c)*a^2*b*c^2)*f - (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*(b^2 - 4*a*c)*a*b^3*c - 8*(b^2 - 4*a*c)*a^2*b*c^2 - 2*(b^2 - 4*a*c)*a*b^2*c^2 + 4*(b^2 - 4*a*c)*a^2*c^3)*e)*arctan(2*sqrt(1/2)*x/sqrt((a^2*b + sqrt(a^4*b^2 - 4*a^5*c))/(a^2*c)))/((a^3*b^4 - 8*a^4*b^2*c - 2*a^3*b^3*c + 16*a^5*c^2 + 8*a^4*b*c^2 + a^3*b^2*c^2 - 4*a^4*c^3)*abs(c)) + 1/4*((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*(b^2 - 4*a*c)*b^4*c + 10*(b^2 - 4*a*c)*a*b^2*c^2 + 2*(b^2 - 4*a*c)*b^3*c^2 - 8*(b^2 - 4*a*c)*a^2*c^3 - 6*(b^2 - 4*a*c)*a*b*c^3)*d + (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*(b^2 - 4*a*c)*a^2*b^2*c + 8*(b^2 - 4*a*c)*a^3*c^2 + 2*(b^2 - 4*a*c)*a^2*b*c^2)*f - (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*(b^2 - 4*a*c)*a*b^3*c + 8*(b^2 - 4*a*c)*a^2*b*c^2 + 2*(b^2 - 4*a*c)*a*b^2*c^2 - 4*(b^2 - 4*a*c)*a^2*c^3)*e)*arctan(2*sqrt(1/2)*x/sqrt((a^2*b - sqrt(a^4*b^2 - 4*a^5*c))/(a^2*c)))/((a^3*b^4 - 8*a^4*b^2*c - 2*a^3*b^3*c + 16*a^5*c^2 + 8*a^4*b*c^2 + a^3*b^2*c^2 - 4*a^4*c^3)*abs(c)) + 1/3*(3*b*d*x^2 - 3*a*x^2*e - a*d)/(a^2*x^3)","B",0
60,1,6718,0,7.015025," ","integrate((f*x^4+e*x^2+d)/x^6/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left({\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)} a^{2} d + {\left(2 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} 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} + 8 \, \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 - 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^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3}\right)} a^{2} f - {\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)} a^{2} e + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, a b^{7} c + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 12 \, \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} + 20 \, a^{2} b^{5} c^{2} - 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 64 \, a^{3} b^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 64 \, a^{4} b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c - 12 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3}\right)} d {\left| a \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c - 2 \, a^{3} b^{5} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{2} + 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} + 16 \, a^{4} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 32 \, a^{5} b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{2}\right)} f {\left| a \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} - 9 \, \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 + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} + 10 \, \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} + 18 \, a^{3} b^{4} c^{2} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 48 \, a^{4} b^{2} c^{3} + 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 32 \, a^{5} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{3}\right)} {\left| a \right|} e + {\left(2 \, a^{2} b^{6} c^{2} - 14 \, a^{3} b^{4} c^{3} + 24 \, a^{4} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{2} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{3}\right)} d + {\left(2 \, a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{2}\right)} f - {\left(2 \, a^{3} b^{5} c^{2} - 12 \, a^{4} b^{3} c^{3} + 16 \, a^{5} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{3}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{3} b + \sqrt{a^{6} b^{2} - 4 \, a^{7} c}}{a^{3} c}}}\right)}{8 \, {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c - 2 \, a^{5} b^{3} c + 16 \, a^{7} c^{2} + 8 \, a^{6} b c^{2} + a^{5} b^{2} c^{2} - 4 \, a^{6} c^{3}\right)} {\left| a \right|} {\left| c \right|}} + \frac{{\left({\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)} a^{2} d + {\left(2 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} 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} + 8 \, \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 - 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^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3}\right)} a^{2} f - {\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)} a^{2} e - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c + 2 \, a b^{7} c + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 12 \, \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} - 20 \, a^{2} b^{5} c^{2} - 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 64 \, a^{3} b^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 64 \, a^{4} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c + 12 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3}\right)} d {\left| a \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c + 2 \, a^{3} b^{5} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{2} + 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} - 16 \, a^{4} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} + 32 \, a^{5} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{2}\right)} f {\left| a \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} - 9 \, \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 + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} + 10 \, \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} - 18 \, a^{3} b^{4} c^{2} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} + 48 \, a^{4} b^{2} c^{3} + 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} - 32 \, a^{5} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c + 10 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{3}\right)} {\left| a \right|} e + {\left(2 \, a^{2} b^{6} c^{2} - 14 \, a^{3} b^{4} c^{3} + 24 \, a^{4} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{2} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{3}\right)} d + {\left(2 \, a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{2}\right)} f - {\left(2 \, a^{3} b^{5} c^{2} - 12 \, a^{4} b^{3} c^{3} + 16 \, a^{5} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{3}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{3} b - \sqrt{a^{6} b^{2} - 4 \, a^{7} c}}{a^{3} c}}}\right)}{8 \, {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c - 2 \, a^{5} b^{3} c + 16 \, a^{7} c^{2} + 8 \, a^{6} b c^{2} + a^{5} b^{2} c^{2} - 4 \, a^{6} c^{3}\right)} {\left| a \right|} {\left| c \right|}} - \frac{15 \, b^{2} d x^{4} - 15 \, a c d x^{4} + 15 \, a^{2} f x^{4} - 15 \, a b x^{4} e - 5 \, a b d x^{2} + 5 \, a^{2} x^{2} e + 3 \, a^{2} d}{15 \, a^{3} x^{5}}"," ",0,"-1/8*((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*(b^2 - 4*a*c)*b^4*c^2 + 10*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*a^2*d + (2*a^2*b^4*c^2 - 16*a^3*b^2*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 + 8*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 - 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*(b^2 - 4*a*c)*a^2*b^2*c^2 + 8*(b^2 - 4*a*c)*a^3*c^3)*a^2*f - (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*(b^2 - 4*a*c)*a*b^3*c^2 + 8*(b^2 - 4*a*c)*a^2*b*c^3)*a^2*e + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7 - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c - 2*a*b^7*c + 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + 12*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 + 20*a^2*b^5*c^2 - 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 64*a^3*b^3*c^3 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 64*a^4*b*c^4 + 2*(b^2 - 4*a*c)*a*b^5*c - 12*(b^2 - 4*a*c)*a^2*b^3*c^2 + 16*(b^2 - 4*a*c)*a^3*b*c^3)*d*abs(a) + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c - 2*a^3*b^5*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^2 + 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 + 16*a^4*b^3*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 - 32*a^5*b*c^3 + 2*(b^2 - 4*a*c)*a^3*b^3*c - 8*(b^2 - 4*a*c)*a^4*b*c^2)*f*abs(a) - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6 - 9*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 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^2 + 10*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 + 18*a^3*b^4*c^2 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*c^3 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 - 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 48*a^4*b^2*c^3 + 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^4 + 32*a^5*c^4 + 2*(b^2 - 4*a*c)*a^2*b^4*c - 10*(b^2 - 4*a*c)*a^3*b^2*c^2 + 8*(b^2 - 4*a*c)*a^4*c^3)*abs(a)*e + (2*a^2*b^6*c^2 - 14*a^3*b^4*c^3 + 24*a^4*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^2 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 2*(b^2 - 4*a*c)*a^2*b^4*c^2 + 6*(b^2 - 4*a*c)*a^3*b^2*c^3)*d + (2*a^4*b^4*c^2 - 8*a^5*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^2 - 2*(b^2 - 4*a*c)*a^4*b^2*c^2)*f - (2*a^3*b^5*c^2 - 12*a^4*b^3*c^3 + 16*a^5*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^2 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 - 2*(b^2 - 4*a*c)*a^3*b^3*c^2 + 4*(b^2 - 4*a*c)*a^4*b*c^3)*e)*arctan(2*sqrt(1/2)*x/sqrt((a^3*b + sqrt(a^6*b^2 - 4*a^7*c))/(a^3*c)))/((a^5*b^4 - 8*a^6*b^2*c - 2*a^5*b^3*c + 16*a^7*c^2 + 8*a^6*b*c^2 + a^5*b^2*c^2 - 4*a^6*c^3)*abs(a)*abs(c)) + 1/8*((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*(b^2 - 4*a*c)*b^4*c^2 + 10*(b^2 - 4*a*c)*a*b^2*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4)*a^2*d + (2*a^2*b^4*c^2 - 16*a^3*b^2*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 + 8*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 - 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*(b^2 - 4*a*c)*a^2*b^2*c^2 + 8*(b^2 - 4*a*c)*a^3*c^3)*a^2*f - (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*(b^2 - 4*a*c)*a*b^3*c^2 + 8*(b^2 - 4*a*c)*a^2*b*c^3)*a^2*e - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7 - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c + 2*a*b^7*c + 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + 12*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 - 20*a^2*b^5*c^2 - 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 + 64*a^3*b^3*c^3 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 - 64*a^4*b*c^4 - 2*(b^2 - 4*a*c)*a*b^5*c + 12*(b^2 - 4*a*c)*a^2*b^3*c^2 - 16*(b^2 - 4*a*c)*a^3*b*c^3)*d*abs(a) - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c + 2*a^3*b^5*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^2 + 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 - 16*a^4*b^3*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 + 32*a^5*b*c^3 - 2*(b^2 - 4*a*c)*a^3*b^3*c + 8*(b^2 - 4*a*c)*a^4*b*c^2)*f*abs(a) + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6 - 9*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 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^2 + 10*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 - 18*a^3*b^4*c^2 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*c^3 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 - 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 + 48*a^4*b^2*c^3 + 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^4 - 32*a^5*c^4 - 2*(b^2 - 4*a*c)*a^2*b^4*c + 10*(b^2 - 4*a*c)*a^3*b^2*c^2 - 8*(b^2 - 4*a*c)*a^4*c^3)*abs(a)*e + (2*a^2*b^6*c^2 - 14*a^3*b^4*c^3 + 24*a^4*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^2 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 2*(b^2 - 4*a*c)*a^2*b^4*c^2 + 6*(b^2 - 4*a*c)*a^3*b^2*c^3)*d + (2*a^4*b^4*c^2 - 8*a^5*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^2 - 2*(b^2 - 4*a*c)*a^4*b^2*c^2)*f - (2*a^3*b^5*c^2 - 12*a^4*b^3*c^3 + 16*a^5*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^2 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 - 2*(b^2 - 4*a*c)*a^3*b^3*c^2 + 4*(b^2 - 4*a*c)*a^4*b*c^3)*e)*arctan(2*sqrt(1/2)*x/sqrt((a^3*b - sqrt(a^6*b^2 - 4*a^7*c))/(a^3*c)))/((a^5*b^4 - 8*a^6*b^2*c - 2*a^5*b^3*c + 16*a^7*c^2 + 8*a^6*b*c^2 + a^5*b^2*c^2 - 4*a^6*c^3)*abs(a)*abs(c)) - 1/15*(15*b^2*d*x^4 - 15*a*c*d*x^4 + 15*a^2*f*x^4 - 15*a*b*x^4*e - 5*a*b*d*x^2 + 5*a^2*x^2*e + 3*a^2*d)/(a^3*x^5)","B",0
61,1,424,0,1.951652," ","integrate(x^7*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(b^{3} c^{2} d - 6 \, a b c^{3} d + 3 \, b^{5} f - 20 \, a b^{3} c f + 30 \, a^{2} b c^{2} f - 2 \, b^{4} c e + 12 \, a b^{2} c^{2} e - 12 \, a^{2} c^{3} e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{b^{2} c^{3} d x^{4} - 4 \, a c^{4} d x^{4} + 3 \, b^{4} c f x^{4} - 14 \, a b^{2} c^{2} f x^{4} + 8 \, a^{2} c^{3} f x^{4} - 2 \, b^{3} c^{2} x^{4} e + 8 \, a b c^{3} x^{4} e - b^{3} c^{2} d x^{2} + 2 \, a b c^{3} d x^{2} + b^{5} f x^{2} - 4 \, a b^{3} c f x^{2} - 2 \, a^{2} b c^{2} f x^{2} + 4 \, a^{2} c^{3} x^{2} e - a b^{2} c^{2} d + a b^{4} f - 6 \, a^{2} b^{2} c f + 4 \, a^{3} c^{2} f + 2 \, a^{2} b c^{2} e}{4 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} {\left(c x^{4} + b x^{2} + a\right)}} + \frac{{\left(c^{2} d + 3 \, b^{2} f - 2 \, a c f - 2 \, b c e\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, c^{4}} + \frac{c^{2} f x^{4} - 4 \, b c f x^{2} + 2 \, c^{2} x^{2} e}{4 \, c^{4}}"," ",0,"-1/2*(b^3*c^2*d - 6*a*b*c^3*d + 3*b^5*f - 20*a*b^3*c*f + 30*a^2*b*c^2*f - 2*b^4*c*e + 12*a*b^2*c^2*e - 12*a^2*c^3*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^4 - 4*a*c^5)*sqrt(-b^2 + 4*a*c)) - 1/4*(b^2*c^3*d*x^4 - 4*a*c^4*d*x^4 + 3*b^4*c*f*x^4 - 14*a*b^2*c^2*f*x^4 + 8*a^2*c^3*f*x^4 - 2*b^3*c^2*x^4*e + 8*a*b*c^3*x^4*e - b^3*c^2*d*x^2 + 2*a*b*c^3*d*x^2 + b^5*f*x^2 - 4*a*b^3*c*f*x^2 - 2*a^2*b*c^2*f*x^2 + 4*a^2*c^3*x^2*e - a*b^2*c^2*d + a*b^4*f - 6*a^2*b^2*c*f + 4*a^3*c^2*f + 2*a^2*b*c^2*e)/((b^2*c^4 - 4*a*c^5)*(c*x^4 + b*x^2 + a)) + 1/4*(c^2*d + 3*b^2*f - 2*a*c*f - 2*b*c*e)*log(c*x^4 + b*x^2 + a)/c^4 + 1/4*(c^2*f*x^4 - 4*b*c*f*x^2 + 2*c^2*x^2*e)/c^4","A",0
62,1,279,0,1.864519," ","integrate(x^5*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{f x^{2}}{2 \, c^{2}} - \frac{{\left(4 \, a c^{3} d - 2 \, b^{4} f + 12 \, a b^{2} c f - 12 \, a^{2} c^{2} f + b^{3} c e - 6 \, a b c^{2} e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{2 \, b^{3} f x^{4} - 8 \, a b c f x^{4} - b^{2} c x^{4} e + 4 \, a c^{2} x^{4} e - 2 \, b^{2} c d x^{2} + 4 \, a c^{2} d x^{2} - 4 \, a^{2} c f x^{2} + b^{3} x^{2} e - 2 \, a b c x^{2} e - 2 \, a b c d - 2 \, a^{2} b f + a b^{2} e}{4 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}} - \frac{{\left(2 \, b f - c e\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, c^{3}}"," ",0,"1/2*f*x^2/c^2 - 1/2*(4*a*c^3*d - 2*b^4*f + 12*a*b^2*c*f - 12*a^2*c^2*f + b^3*c*e - 6*a*b*c^2*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^3 - 4*a*c^4)*sqrt(-b^2 + 4*a*c)) + 1/4*(2*b^3*f*x^4 - 8*a*b*c*f*x^4 - b^2*c*x^4*e + 4*a*c^2*x^4*e - 2*b^2*c*d*x^2 + 4*a*c^2*d*x^2 - 4*a^2*c*f*x^2 + b^3*x^2*e - 2*a*b*c*x^2*e - 2*a*b*c*d - 2*a^2*b*f + a*b^2*e)/((c*x^4 + b*x^2 + a)*(b^2*c^2 - 4*a*c^3)) - 1/4*(2*b*f - c*e)*log(c*x^4 + b*x^2 + a)/c^3","A",0
63,1,195,0,1.838349," ","integrate(x^3*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(2 \, b c^{2} d - b^{3} f + 6 \, a b c f - 4 \, a c^{2} e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{f \log\left(c x^{4} + b x^{2} + a\right)}{4 \, c^{2}} + \frac{2 \, a c^{2} d + a b^{2} f - 2 \, a^{2} c f - a b c e + {\left(b c^{2} d + b^{3} f - 3 \, a b c f - b^{2} c e + 2 \, a c^{2} e\right)} x^{2}}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} - 4 \, a c\right)} c^{2}}"," ",0,"1/2*(2*b*c^2*d - b^3*f + 6*a*b*c*f - 4*a*c^2*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^2 - 4*a*c^3)*sqrt(-b^2 + 4*a*c)) + 1/4*f*log(c*x^4 + b*x^2 + a)/c^2 + 1/2*(2*a*c^2*d + a*b^2*f - 2*a^2*c*f - a*b*c*e + (b*c^2*d + b^3*f - 3*a*b*c*f - b^2*c*e + 2*a*c^2*e)*x^2)/((c*x^4 + b*x^2 + a)*(b^2 - 4*a*c)*c^2)","A",0
64,1,140,0,2.166830," ","integrate(x*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, c d + 2 \, a f - b e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, c^{2} d x^{2} + b^{2} f x^{2} - 2 \, a c f x^{2} - b c x^{2} e + b c d + a b f - 2 \, a c e}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}"," ",0,"-(2*c*d + 2*a*f - b*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) - 1/2*(2*c^2*d*x^2 + b^2*f*x^2 - 2*a*c*f*x^2 - b*c*x^2*e + b*c*d + a*b*f - 2*a*c*e)/((c*x^4 + b*x^2 + a)*(b^2*c - 4*a*c^2))","A",0
65,1,227,0,2.000855," ","integrate((f*x^4+e*x^2+d)/x/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(b^{3} d - 6 \, a b c d - 2 \, a^{2} b f + 4 \, a^{2} c e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{d \log\left(c x^{4} + b x^{2} + a\right)}{4 \, a^{2}} + \frac{d \log\left(x^{2}\right)}{2 \, a^{2}} + \frac{b^{2} c d x^{4} - 4 \, a c^{2} d x^{4} + b^{3} d x^{2} - 2 \, a b c d x^{2} + 2 \, a^{2} b f x^{2} - 4 \, a^{2} c x^{2} e + 3 \, a b^{2} d - 8 \, a^{2} c d + 4 \, a^{3} f - 2 \, a^{2} b e}{4 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}}"," ",0,"-1/2*(b^3*d - 6*a*b*c*d - 2*a^2*b*f + 4*a^2*c*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((a^2*b^2 - 4*a^3*c)*sqrt(-b^2 + 4*a*c)) - 1/4*d*log(c*x^4 + b*x^2 + a)/a^2 + 1/2*d*log(x^2)/a^2 + 1/4*(b^2*c*d*x^4 - 4*a*c^2*d*x^4 + b^3*d*x^2 - 2*a*b*c*d*x^2 + 2*a^2*b*f*x^2 - 4*a^2*c*x^2*e + 3*a*b^2*d - 8*a^2*c*d + 4*a^3*f - 2*a^2*b*e)/((c*x^4 + b*x^2 + a)*(a^2*b^2 - 4*a^3*c))","A",0
66,1,287,0,1.846173," ","integrate((f*x^4+e*x^2+d)/x^3/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(2 \, b^{4} d - 12 \, a b^{2} c d + 12 \, a^{2} c^{2} d - 4 \, a^{3} c f - a b^{3} e + 6 \, a^{2} b c e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, b^{2} c d x^{4} - 6 \, a c^{2} d x^{4} + 2 \, a^{2} c f x^{4} - a b c x^{4} e + 2 \, b^{3} d x^{2} - 7 \, a b c d x^{2} + a^{2} b f x^{2} - a b^{2} x^{2} e + 2 \, a^{2} c x^{2} e + a b^{2} d - 4 \, a^{2} c d}{2 \, {\left(c x^{6} + b x^{4} + a x^{2}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}} + \frac{{\left(2 \, b d - a e\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, a^{3}} - \frac{{\left(2 \, b d - a e\right)} \log\left(x^{2}\right)}{2 \, a^{3}}"," ",0,"1/2*(2*b^4*d - 12*a*b^2*c*d + 12*a^2*c^2*d - 4*a^3*c*f - a*b^3*e + 6*a^2*b*c*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((a^3*b^2 - 4*a^4*c)*sqrt(-b^2 + 4*a*c)) - 1/2*(2*b^2*c*d*x^4 - 6*a*c^2*d*x^4 + 2*a^2*c*f*x^4 - a*b*c*x^4*e + 2*b^3*d*x^2 - 7*a*b*c*d*x^2 + a^2*b*f*x^2 - a*b^2*x^2*e + 2*a^2*c*x^2*e + a*b^2*d - 4*a^2*c*d)/((c*x^6 + b*x^4 + a*x^2)*(a^2*b^2 - 4*a^3*c)) + 1/4*(2*b*d - a*e)*log(c*x^4 + b*x^2 + a)/a^3 - 1/2*(2*b*d - a*e)*log(x^2)/a^3","A",0
67,1,535,0,1.887542," ","integrate((f*x^4+e*x^2+d)/x^5/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(3 \, b^{5} d - 20 \, a b^{3} c d + 30 \, a^{2} b c^{2} d + a^{2} b^{3} f - 6 \, a^{3} b c f - 2 \, a b^{4} e + 12 \, a^{2} b^{2} c e - 12 \, a^{3} c^{2} e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{3 \, b^{4} c d x^{4} - 14 \, a b^{2} c^{2} d x^{4} + 8 \, a^{2} c^{3} d x^{4} + a^{2} b^{2} c f x^{4} - 4 \, a^{3} c^{2} f x^{4} - 2 \, a b^{3} c x^{4} e + 8 \, a^{2} b c^{2} x^{4} e + 3 \, b^{5} d x^{2} - 12 \, a b^{3} c d x^{2} + 2 \, a^{2} b c^{2} d x^{2} + a^{2} b^{3} f x^{2} - 2 \, a^{3} b c f x^{2} - 2 \, a b^{4} x^{2} e + 6 \, a^{2} b^{2} c x^{2} e + 4 \, a^{3} c^{2} x^{2} e + 5 \, a b^{4} d - 22 \, a^{2} b^{2} c d + 12 \, a^{3} c^{2} d + 3 \, a^{3} b^{2} f - 8 \, a^{4} c f - 4 \, a^{2} b^{3} e + 14 \, a^{3} b c e}{4 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} {\left(c x^{4} + b x^{2} + a\right)}} - \frac{{\left(3 \, b^{2} d - 2 \, a c d + a^{2} f - 2 \, a b e\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, a^{4}} + \frac{{\left(3 \, b^{2} d - 2 \, a c d + a^{2} f - 2 \, a b e\right)} \log\left(x^{2}\right)}{2 \, a^{4}} - \frac{9 \, b^{2} d x^{4} - 6 \, a c d x^{4} + 3 \, a^{2} f x^{4} - 6 \, a b x^{4} e - 4 \, a b d x^{2} + 2 \, a^{2} x^{2} e + a^{2} d}{4 \, a^{4} x^{4}}"," ",0,"-1/2*(3*b^5*d - 20*a*b^3*c*d + 30*a^2*b*c^2*d + a^2*b^3*f - 6*a^3*b*c*f - 2*a*b^4*e + 12*a^2*b^2*c*e - 12*a^3*c^2*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((a^4*b^2 - 4*a^5*c)*sqrt(-b^2 + 4*a*c)) + 1/4*(3*b^4*c*d*x^4 - 14*a*b^2*c^2*d*x^4 + 8*a^2*c^3*d*x^4 + a^2*b^2*c*f*x^4 - 4*a^3*c^2*f*x^4 - 2*a*b^3*c*x^4*e + 8*a^2*b*c^2*x^4*e + 3*b^5*d*x^2 - 12*a*b^3*c*d*x^2 + 2*a^2*b*c^2*d*x^2 + a^2*b^3*f*x^2 - 2*a^3*b*c*f*x^2 - 2*a*b^4*x^2*e + 6*a^2*b^2*c*x^2*e + 4*a^3*c^2*x^2*e + 5*a*b^4*d - 22*a^2*b^2*c*d + 12*a^3*c^2*d + 3*a^3*b^2*f - 8*a^4*c*f - 4*a^2*b^3*e + 14*a^3*b*c*e)/((a^4*b^2 - 4*a^5*c)*(c*x^4 + b*x^2 + a)) - 1/4*(3*b^2*d - 2*a*c*d + a^2*f - 2*a*b*e)*log(c*x^4 + b*x^2 + a)/a^4 + 1/2*(3*b^2*d - 2*a*c*d + a^2*f - 2*a*b*e)*log(x^2)/a^4 - 1/4*(9*b^2*d*x^4 - 6*a*c*d*x^4 + 3*a^2*f*x^4 - 6*a*b*x^4*e - 4*a*b*d*x^2 + 2*a^2*x^2*e + a^2*d)/(a^4*x^4)","A",0
68,1,8957,0,9.044460," ","integrate(x^6*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{b^{2} c^{2} d x^{3} - 2 \, a c^{3} d x^{3} + b^{4} f x^{3} - 4 \, a b^{2} c f x^{3} + 2 \, a^{2} c^{2} f x^{3} - b^{3} c x^{3} e + 3 \, a b c^{2} x^{3} e + a b c^{2} d x + a b^{3} f x - 3 \, a^{2} b c f x - a b^{2} c x e + 2 \, a^{2} c^{2} x e}{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} {\left(c x^{4} + b x^{2} + a\right)}} + \frac{{\left({\left(2 \, b^{4} c^{4} - 20 \, a b^{2} c^{5} + 48 \, 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} + 10 \, \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} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 12 \, \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} + 6 \, \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^{2} c^{4} + 12 \, {\left(b^{2} - 4 \, a c\right)} a c^{5}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}^{2} d + {\left(10 \, b^{6} c^{2} - 88 \, a b^{4} c^{3} + 220 \, a^{2} b^{2} c^{4} - 112 \, 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} + 44 \, \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 - 110 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 48 \, \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} + 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 14 \, \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^{4} c^{2} + 48 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 28 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}^{2} f - {\left(6 \, b^{5} c^{3} - 50 \, a b^{3} c^{4} + 104 \, 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 + 25 \, \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} - 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 26 \, \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} + 13 \, \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^{3} c^{3} + 26 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}^{2} e + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{6} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{7} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{7} - 2 \, a b^{5} c^{7} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{8} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{8} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{8} + 16 \, a^{2} b^{3} c^{8} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{9} - 32 \, a^{3} b c^{9} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{7} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{8}\right)} d {\left| b^{2} c^{3} - 4 \, a c^{4} \right|} + 2 \, {\left(5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{4} - 59 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{5} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{5} - 10 \, a b^{7} c^{5} + 232 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{6} + 78 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{6} + 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{6} + 118 \, a^{2} b^{5} c^{6} - 304 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{7} - 152 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{7} - 39 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{7} - 464 \, a^{3} b^{3} c^{7} + 76 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{8} + 608 \, a^{4} b c^{8} + 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{5} - 78 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{6} + 152 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{7}\right)} f {\left| b^{2} c^{3} - 4 \, a c^{4} \right|} - 2 \, {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{5} - 34 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{6} - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{6} - 6 \, a b^{6} c^{6} + 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{7} + 44 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{7} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{7} + 68 \, a^{2} b^{4} c^{7} - 160 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{8} - 80 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{8} - 22 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{8} - 256 \, a^{3} b^{2} c^{8} + 40 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{9} + 320 \, a^{4} c^{9} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{6} - 44 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{7} + 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{8}\right)} {\left| b^{2} c^{3} - 4 \, a c^{4} \right|} e - {\left(2 \, b^{8} c^{10} - 32 \, a b^{6} c^{11} + 160 \, a^{2} b^{4} c^{12} - 256 \, a^{3} b^{2} c^{13} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{8} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{9} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{9} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{10} - 24 \, \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^{10} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{11} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{11} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{11} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{12} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{10} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{11} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{12}\right)} d - {\left(10 \, b^{10} c^{8} - 148 \, a b^{8} c^{9} + 808 \, a^{2} b^{6} c^{10} - 1920 \, a^{3} b^{4} c^{11} + 1664 \, a^{4} b^{2} c^{12} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{10} c^{6} + 74 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{8} c^{7} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{9} c^{7} - 404 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{8} - 108 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{8} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{8} + 960 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{9} + 376 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{9} + 54 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{9} - 832 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{10} - 416 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{10} - 188 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{10} + 208 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{11} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{8} c^{8} + 108 \, {\left(b^{2} - 4 \, a c\right)} a b^{6} c^{9} - 376 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{10} + 416 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{11}\right)} f + {\left(6 \, b^{9} c^{9} - 86 \, a b^{7} c^{10} + 440 \, a^{2} b^{5} c^{11} - 928 \, a^{3} b^{3} c^{12} + 640 \, a^{4} b c^{13} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{9} c^{7} + 43 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{8} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{8} - 220 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{9} - 62 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{9} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{9} + 464 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{10} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{10} + 31 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{10} - 320 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{11} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{11} - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{11} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{12} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{7} c^{9} + 62 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{10} - 192 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{11} + 160 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{12}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} c^{3} - 4 \, a b c^{4} + \sqrt{{\left(b^{3} c^{3} - 4 \, a b c^{4}\right)}^{2} - 4 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} {\left(b^{2} c^{4} - 4 \, a c^{5}\right)}}}{b^{2} c^{4} - 4 \, a c^{5}}}}\right)}{16 \, {\left(a b^{6} c^{7} - 12 \, a^{2} b^{4} c^{8} - 2 \, a b^{5} c^{8} + 48 \, a^{3} b^{2} c^{9} + 16 \, a^{2} b^{3} c^{9} + a b^{4} c^{9} - 64 \, a^{4} c^{10} - 32 \, a^{3} b c^{10} - 8 \, a^{2} b^{2} c^{10} + 16 \, a^{3} c^{11}\right)} {\left| b^{2} c^{3} - 4 \, a c^{4} \right|} {\left| c \right|}} + \frac{{\left({\left(2 \, b^{4} c^{4} - 20 \, a b^{2} c^{5} + 48 \, 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} + 10 \, \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} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 12 \, \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} + 6 \, \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^{2} c^{4} + 12 \, {\left(b^{2} - 4 \, a c\right)} a c^{5}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}^{2} d + {\left(10 \, b^{6} c^{2} - 88 \, a b^{4} c^{3} + 220 \, a^{2} b^{2} c^{4} - 112 \, 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} + 44 \, \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 - 110 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 48 \, \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} + 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 14 \, \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^{4} c^{2} + 48 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 28 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}^{2} f - {\left(6 \, b^{5} c^{3} - 50 \, a b^{3} c^{4} + 104 \, 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 + 25 \, \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} - 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 26 \, \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} + 13 \, \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^{3} c^{3} + 26 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}^{2} e + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{6} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{7} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{7} + 2 \, a b^{5} c^{7} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{8} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{8} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{8} - 16 \, a^{2} b^{3} c^{8} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{9} + 32 \, a^{3} b c^{9} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{7} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{8}\right)} d {\left| b^{2} c^{3} - 4 \, a c^{4} \right|} + 2 \, {\left(5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{4} - 59 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{5} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{5} + 10 \, a b^{7} c^{5} + 232 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{6} + 78 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{6} + 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{6} - 118 \, a^{2} b^{5} c^{6} - 304 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{7} - 152 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{7} - 39 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{7} + 464 \, a^{3} b^{3} c^{7} + 76 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{8} - 608 \, a^{4} b c^{8} - 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{5} + 78 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{6} - 152 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{7}\right)} f {\left| b^{2} c^{3} - 4 \, a c^{4} \right|} - 2 \, {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{5} - 34 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{6} - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{6} + 6 \, a b^{6} c^{6} + 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{7} + 44 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{7} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{7} - 68 \, a^{2} b^{4} c^{7} - 160 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{8} - 80 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{8} - 22 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{8} + 256 \, a^{3} b^{2} c^{8} + 40 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{9} - 320 \, a^{4} c^{9} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{6} + 44 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{7} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{8}\right)} {\left| b^{2} c^{3} - 4 \, a c^{4} \right|} e - {\left(2 \, b^{8} c^{10} - 32 \, a b^{6} c^{11} + 160 \, a^{2} b^{4} c^{12} - 256 \, a^{3} b^{2} c^{13} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{8} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{9} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{9} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{10} - 24 \, \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^{10} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{11} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{11} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{11} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{12} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{10} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{11} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{12}\right)} d - {\left(10 \, b^{10} c^{8} - 148 \, a b^{8} c^{9} + 808 \, a^{2} b^{6} c^{10} - 1920 \, a^{3} b^{4} c^{11} + 1664 \, a^{4} b^{2} c^{12} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{10} c^{6} + 74 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{8} c^{7} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{9} c^{7} - 404 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{8} - 108 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{8} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{8} + 960 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{9} + 376 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{9} + 54 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{9} - 832 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{10} - 416 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{10} - 188 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{10} + 208 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{11} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{8} c^{8} + 108 \, {\left(b^{2} - 4 \, a c\right)} a b^{6} c^{9} - 376 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{10} + 416 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{11}\right)} f + {\left(6 \, b^{9} c^{9} - 86 \, a b^{7} c^{10} + 440 \, a^{2} b^{5} c^{11} - 928 \, a^{3} b^{3} c^{12} + 640 \, a^{4} b c^{13} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{9} c^{7} + 43 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{8} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{8} - 220 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{9} - 62 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{9} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{9} + 464 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{10} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{10} + 31 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{10} - 320 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{11} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{11} - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{11} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{12} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{7} c^{9} + 62 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{10} - 192 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{11} + 160 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{12}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} c^{3} - 4 \, a b c^{4} - \sqrt{{\left(b^{3} c^{3} - 4 \, a b c^{4}\right)}^{2} - 4 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} {\left(b^{2} c^{4} - 4 \, a c^{5}\right)}}}{b^{2} c^{4} - 4 \, a c^{5}}}}\right)}{16 \, {\left(a b^{6} c^{7} - 12 \, a^{2} b^{4} c^{8} - 2 \, a b^{5} c^{8} + 48 \, a^{3} b^{2} c^{9} + 16 \, a^{2} b^{3} c^{9} + a b^{4} c^{9} - 64 \, a^{4} c^{10} - 32 \, a^{3} b c^{10} - 8 \, a^{2} b^{2} c^{10} + 16 \, a^{3} c^{11}\right)} {\left| b^{2} c^{3} - 4 \, a c^{4} \right|} {\left| c \right|}} + \frac{c^{4} f x^{3} - 6 \, b c^{3} f x + 3 \, c^{4} x e}{3 \, c^{6}}"," ",0,"-1/2*(b^2*c^2*d*x^3 - 2*a*c^3*d*x^3 + b^4*f*x^3 - 4*a*b^2*c*f*x^3 + 2*a^2*c^2*f*x^3 - b^3*c*x^3*e + 3*a*b*c^2*x^3*e + a*b*c^2*d*x + a*b^3*f*x - 3*a^2*b*c*f*x - a*b^2*c*x*e + 2*a^2*c^2*x*e)/((b^2*c^3 - 4*a*c^4)*(c*x^4 + b*x^2 + a)) + 1/16*((2*b^4*c^4 - 20*a*b^2*c^5 + 48*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 + 10*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 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 12*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 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^5 - 2*(b^2 - 4*a*c)*b^2*c^4 + 12*(b^2 - 4*a*c)*a*c^5)*(b^2*c^3 - 4*a*c^4)^2*d + (10*b^6*c^2 - 88*a*b^4*c^3 + 220*a^2*b^2*c^4 - 112*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 + 44*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 - 110*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 48*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 + 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 10*(b^2 - 4*a*c)*b^4*c^2 + 48*(b^2 - 4*a*c)*a*b^2*c^3 - 28*(b^2 - 4*a*c)*a^2*c^4)*(b^2*c^3 - 4*a*c^4)^2*f - (6*b^5*c^3 - 50*a*b^3*c^4 + 104*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 + 25*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 - 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 26*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 + 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - 6*(b^2 - 4*a*c)*b^3*c^3 + 26*(b^2 - 4*a*c)*a*b*c^4)*(b^2*c^3 - 4*a*c^4)^2*e + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^6 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^7 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^7 - 2*a*b^5*c^7 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^8 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^8 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^8 + 16*a^2*b^3*c^8 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^9 - 32*a^3*b*c^9 + 2*(b^2 - 4*a*c)*a*b^3*c^7 - 8*(b^2 - 4*a*c)*a^2*b*c^8)*d*abs(b^2*c^3 - 4*a*c^4) + 2*(5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^4 - 59*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^5 - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^5 - 10*a*b^7*c^5 + 232*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^6 + 78*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^6 + 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^6 + 118*a^2*b^5*c^6 - 304*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^7 - 152*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^7 - 39*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^7 - 464*a^3*b^3*c^7 + 76*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^8 + 608*a^4*b*c^8 + 10*(b^2 - 4*a*c)*a*b^5*c^5 - 78*(b^2 - 4*a*c)*a^2*b^3*c^6 + 152*(b^2 - 4*a*c)*a^3*b*c^7)*f*abs(b^2*c^3 - 4*a*c^4) - 2*(3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^5 - 34*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^6 - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^6 - 6*a*b^6*c^6 + 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^7 + 44*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^7 + 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^7 + 68*a^2*b^4*c^7 - 160*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^8 - 80*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^8 - 22*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^8 - 256*a^3*b^2*c^8 + 40*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^9 + 320*a^4*c^9 + 6*(b^2 - 4*a*c)*a*b^4*c^6 - 44*(b^2 - 4*a*c)*a^2*b^2*c^7 + 80*(b^2 - 4*a*c)*a^3*c^8)*abs(b^2*c^3 - 4*a*c^4)*e - (2*b^8*c^10 - 32*a*b^6*c^11 + 160*a^2*b^4*c^12 - 256*a^3*b^2*c^13 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^8 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^9 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^9 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^10 - 24*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^10 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^11 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^11 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^11 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^12 - 2*(b^2 - 4*a*c)*b^6*c^10 + 24*(b^2 - 4*a*c)*a*b^4*c^11 - 64*(b^2 - 4*a*c)*a^2*b^2*c^12)*d - (10*b^10*c^8 - 148*a*b^8*c^9 + 808*a^2*b^6*c^10 - 1920*a^3*b^4*c^11 + 1664*a^4*b^2*c^12 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^10*c^6 + 74*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^8*c^7 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^9*c^7 - 404*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^8 - 108*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^8 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^8 + 960*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^9 + 376*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^9 + 54*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^9 - 832*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^10 - 416*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^10 - 188*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^10 + 208*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^11 - 10*(b^2 - 4*a*c)*b^8*c^8 + 108*(b^2 - 4*a*c)*a*b^6*c^9 - 376*(b^2 - 4*a*c)*a^2*b^4*c^10 + 416*(b^2 - 4*a*c)*a^3*b^2*c^11)*f + (6*b^9*c^9 - 86*a*b^7*c^10 + 440*a^2*b^5*c^11 - 928*a^3*b^3*c^12 + 640*a^4*b*c^13 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^9*c^7 + 43*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^8 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^8 - 220*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^9 - 62*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^9 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^9 + 464*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^10 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^10 + 31*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^10 - 320*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^11 - 160*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^11 - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^11 + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^12 - 6*(b^2 - 4*a*c)*b^7*c^9 + 62*(b^2 - 4*a*c)*a*b^5*c^10 - 192*(b^2 - 4*a*c)*a^2*b^3*c^11 + 160*(b^2 - 4*a*c)*a^3*b*c^12)*e)*arctan(2*sqrt(1/2)*x/sqrt((b^3*c^3 - 4*a*b*c^4 + sqrt((b^3*c^3 - 4*a*b*c^4)^2 - 4*(a*b^2*c^3 - 4*a^2*c^4)*(b^2*c^4 - 4*a*c^5)))/(b^2*c^4 - 4*a*c^5)))/((a*b^6*c^7 - 12*a^2*b^4*c^8 - 2*a*b^5*c^8 + 48*a^3*b^2*c^9 + 16*a^2*b^3*c^9 + a*b^4*c^9 - 64*a^4*c^10 - 32*a^3*b*c^10 - 8*a^2*b^2*c^10 + 16*a^3*c^11)*abs(b^2*c^3 - 4*a*c^4)*abs(c)) + 1/16*((2*b^4*c^4 - 20*a*b^2*c^5 + 48*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 + 10*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 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 12*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 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^5 - 2*(b^2 - 4*a*c)*b^2*c^4 + 12*(b^2 - 4*a*c)*a*c^5)*(b^2*c^3 - 4*a*c^4)^2*d + (10*b^6*c^2 - 88*a*b^4*c^3 + 220*a^2*b^2*c^4 - 112*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 + 44*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 - 110*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 48*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 + 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 10*(b^2 - 4*a*c)*b^4*c^2 + 48*(b^2 - 4*a*c)*a*b^2*c^3 - 28*(b^2 - 4*a*c)*a^2*c^4)*(b^2*c^3 - 4*a*c^4)^2*f - (6*b^5*c^3 - 50*a*b^3*c^4 + 104*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 + 25*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 - 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 26*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 + 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - 6*(b^2 - 4*a*c)*b^3*c^3 + 26*(b^2 - 4*a*c)*a*b*c^4)*(b^2*c^3 - 4*a*c^4)^2*e + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^6 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^7 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^7 + 2*a*b^5*c^7 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^8 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^8 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^8 - 16*a^2*b^3*c^8 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^9 + 32*a^3*b*c^9 - 2*(b^2 - 4*a*c)*a*b^3*c^7 + 8*(b^2 - 4*a*c)*a^2*b*c^8)*d*abs(b^2*c^3 - 4*a*c^4) + 2*(5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^4 - 59*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^5 - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^5 + 10*a*b^7*c^5 + 232*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^6 + 78*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^6 + 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^6 - 118*a^2*b^5*c^6 - 304*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^7 - 152*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^7 - 39*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^7 + 464*a^3*b^3*c^7 + 76*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^8 - 608*a^4*b*c^8 - 10*(b^2 - 4*a*c)*a*b^5*c^5 + 78*(b^2 - 4*a*c)*a^2*b^3*c^6 - 152*(b^2 - 4*a*c)*a^3*b*c^7)*f*abs(b^2*c^3 - 4*a*c^4) - 2*(3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^5 - 34*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^6 - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^6 + 6*a*b^6*c^6 + 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^7 + 44*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^7 + 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^7 - 68*a^2*b^4*c^7 - 160*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^8 - 80*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^8 - 22*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^8 + 256*a^3*b^2*c^8 + 40*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^9 - 320*a^4*c^9 - 6*(b^2 - 4*a*c)*a*b^4*c^6 + 44*(b^2 - 4*a*c)*a^2*b^2*c^7 - 80*(b^2 - 4*a*c)*a^3*c^8)*abs(b^2*c^3 - 4*a*c^4)*e - (2*b^8*c^10 - 32*a*b^6*c^11 + 160*a^2*b^4*c^12 - 256*a^3*b^2*c^13 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^8 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^9 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^9 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^10 - 24*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^10 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^11 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^11 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^11 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^12 - 2*(b^2 - 4*a*c)*b^6*c^10 + 24*(b^2 - 4*a*c)*a*b^4*c^11 - 64*(b^2 - 4*a*c)*a^2*b^2*c^12)*d - (10*b^10*c^8 - 148*a*b^8*c^9 + 808*a^2*b^6*c^10 - 1920*a^3*b^4*c^11 + 1664*a^4*b^2*c^12 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^10*c^6 + 74*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^8*c^7 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^9*c^7 - 404*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^8 - 108*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^8 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^8 + 960*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^9 + 376*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^9 + 54*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^9 - 832*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^10 - 416*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^10 - 188*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^10 + 208*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^11 - 10*(b^2 - 4*a*c)*b^8*c^8 + 108*(b^2 - 4*a*c)*a*b^6*c^9 - 376*(b^2 - 4*a*c)*a^2*b^4*c^10 + 416*(b^2 - 4*a*c)*a^3*b^2*c^11)*f + (6*b^9*c^9 - 86*a*b^7*c^10 + 440*a^2*b^5*c^11 - 928*a^3*b^3*c^12 + 640*a^4*b*c^13 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^9*c^7 + 43*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^8 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^8 - 220*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^9 - 62*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^9 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^9 + 464*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^10 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^10 + 31*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^10 - 320*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^11 - 160*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^11 - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^11 + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^12 - 6*(b^2 - 4*a*c)*b^7*c^9 + 62*(b^2 - 4*a*c)*a*b^5*c^10 - 192*(b^2 - 4*a*c)*a^2*b^3*c^11 + 160*(b^2 - 4*a*c)*a^3*b*c^12)*e)*arctan(2*sqrt(1/2)*x/sqrt((b^3*c^3 - 4*a*b*c^4 - sqrt((b^3*c^3 - 4*a*b*c^4)^2 - 4*(a*b^2*c^3 - 4*a^2*c^4)*(b^2*c^4 - 4*a*c^5)))/(b^2*c^4 - 4*a*c^5)))/((a*b^6*c^7 - 12*a^2*b^4*c^8 - 2*a*b^5*c^8 + 48*a^3*b^2*c^9 + 16*a^2*b^3*c^9 + a*b^4*c^9 - 64*a^4*c^10 - 32*a^3*b*c^10 - 8*a^2*b^2*c^10 + 16*a^3*c^11)*abs(b^2*c^3 - 4*a*c^4)*abs(c)) + 1/3*(c^4*f*x^3 - 6*b*c^3*f*x + 3*c^4*x*e)/c^6","B",0
69,1,7496,0,8.250053," ","integrate(x^4*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{f x}{c^{2}} + \frac{b c^{2} d x^{3} + b^{3} f x^{3} - 3 \, a b c f x^{3} - b^{2} c x^{3} e + 2 \, a c^{2} x^{3} e + 2 \, a c^{2} d x + a b^{2} f x - 2 \, a^{2} c f x - a b c x e}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}} + \frac{{\left({\left(2 \, b^{3} c^{4} - 8 \, a b c^{5} - \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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{4}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}^{2} d - {\left(6 \, b^{5} c^{2} - 50 \, a b^{3} c^{3} + 104 \, a^{2} b c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 25 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 26 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 13 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 26 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}^{2} f + {\left(2 \, b^{4} c^{3} - 20 \, a b^{2} c^{4} + 48 \, 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 + 10 \, \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} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 12 \, \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} + 6 \, \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} + 12 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}^{2} e - 4 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{6} + 2 \, a b^{4} c^{6} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{7} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{7} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{7} - 16 \, a^{2} b^{2} c^{7} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{8} + 32 \, a^{3} c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{6} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{7}\right)} d {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} - 2 \, {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{3} - 34 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} + 6 \, a b^{6} c^{4} + 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 44 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 68 \, a^{2} b^{4} c^{5} - 160 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{6} - 80 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 22 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} + 256 \, a^{3} b^{2} c^{6} + 40 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{7} - 320 \, a^{4} c^{7} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{4} + 44 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{5} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{6}\right)} f {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} + 2 \, a b^{5} c^{5} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{6} - 16 \, a^{2} b^{3} c^{6} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{7} + 32 \, a^{3} b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{5} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{6}\right)} {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} e - {\left(2 \, b^{7} c^{8} - 8 \, a b^{5} c^{9} - 32 \, a^{2} b^{3} c^{10} + 128 \, a^{3} b c^{11} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{7} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{7} + 16 \, \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} b^{5} c^{8} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{9} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{9} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{10} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{8} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{10}\right)} d + {\left(6 \, b^{9} c^{6} - 86 \, a b^{7} c^{7} + 440 \, a^{2} b^{5} c^{8} - 928 \, a^{3} b^{3} c^{9} + 640 \, a^{4} b c^{10} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{9} c^{4} + 43 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{5} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{5} - 220 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{6} - 62 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} + 464 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{7} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{7} + 31 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{7} - 320 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{8} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{8} - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{8} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{9} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{7} c^{6} + 62 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{7} - 192 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{8} + 160 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{9}\right)} f - {\left(2 \, b^{8} c^{7} - 32 \, a b^{6} c^{8} + 160 \, a^{2} b^{4} c^{9} - 256 \, a^{3} b^{2} c^{10} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{5} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{6} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{7} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{7} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{8} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{8} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{8} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{9} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{7} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{8} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{9}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} c^{2} - 4 \, a b c^{3} + \sqrt{{\left(b^{3} c^{2} - 4 \, a b c^{3}\right)}^{2} - 4 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}}{b^{2} c^{3} - 4 \, a c^{4}}}}\right)}{16 \, {\left(a b^{6} c^{5} - 12 \, a^{2} b^{4} c^{6} - 2 \, a b^{5} c^{6} + 48 \, a^{3} b^{2} c^{7} + 16 \, a^{2} b^{3} c^{7} + a b^{4} c^{7} - 64 \, a^{4} c^{8} - 32 \, a^{3} b c^{8} - 8 \, a^{2} b^{2} c^{8} + 16 \, a^{3} c^{9}\right)} {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} {\left| c \right|}} - \frac{{\left({\left(2 \, b^{3} c^{4} - 8 \, a b c^{5} - \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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{4}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}^{2} d - {\left(6 \, b^{5} c^{2} - 50 \, a b^{3} c^{3} + 104 \, a^{2} b c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 25 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 26 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 13 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 26 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}^{2} f + {\left(2 \, b^{4} c^{3} - 20 \, a b^{2} c^{4} + 48 \, 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 + 10 \, \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} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 12 \, \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} + 6 \, \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} + 12 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}^{2} e + 4 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{6} - 2 \, a b^{4} c^{6} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{7} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{7} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{7} + 16 \, a^{2} b^{2} c^{7} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{8} - 32 \, a^{3} c^{8} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{6} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{7}\right)} d {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} + 2 \, {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{3} - 34 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} - 6 \, a b^{6} c^{4} + 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 44 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} + 68 \, a^{2} b^{4} c^{5} - 160 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{6} - 80 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 22 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 256 \, a^{3} b^{2} c^{6} + 40 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{7} + 320 \, a^{4} c^{7} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{4} - 44 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{5} + 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{6}\right)} f {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 2 \, a b^{5} c^{5} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{6} + 16 \, a^{2} b^{3} c^{6} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{7} - 32 \, a^{3} b c^{7} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{5} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{6}\right)} {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} e - {\left(2 \, b^{7} c^{8} - 8 \, a b^{5} c^{9} - 32 \, a^{2} b^{3} c^{10} + 128 \, a^{3} b c^{11} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{7} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{7} + 16 \, \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} b^{5} c^{8} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{9} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{9} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{10} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{8} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{10}\right)} d + {\left(6 \, b^{9} c^{6} - 86 \, a b^{7} c^{7} + 440 \, a^{2} b^{5} c^{8} - 928 \, a^{3} b^{3} c^{9} + 640 \, a^{4} b c^{10} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{9} c^{4} + 43 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{5} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{5} - 220 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{6} - 62 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} + 464 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{7} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{7} + 31 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{7} - 320 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{8} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{8} - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{8} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{9} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{7} c^{6} + 62 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{7} - 192 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{8} + 160 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{9}\right)} f - {\left(2 \, b^{8} c^{7} - 32 \, a b^{6} c^{8} + 160 \, a^{2} b^{4} c^{9} - 256 \, a^{3} b^{2} c^{10} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{5} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{6} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{7} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{7} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{8} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{8} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{8} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{9} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{7} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{8} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{9}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} c^{2} - 4 \, a b c^{3} - \sqrt{{\left(b^{3} c^{2} - 4 \, a b c^{3}\right)}^{2} - 4 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}}{b^{2} c^{3} - 4 \, a c^{4}}}}\right)}{16 \, {\left(a b^{6} c^{5} - 12 \, a^{2} b^{4} c^{6} - 2 \, a b^{5} c^{6} + 48 \, a^{3} b^{2} c^{7} + 16 \, a^{2} b^{3} c^{7} + a b^{4} c^{7} - 64 \, a^{4} c^{8} - 32 \, a^{3} b c^{8} - 8 \, a^{2} b^{2} c^{8} + 16 \, a^{3} c^{9}\right)} {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} {\left| c \right|}}"," ",0,"f*x/c^2 + 1/2*(b*c^2*d*x^3 + b^3*f*x^3 - 3*a*b*c*f*x^3 - b^2*c*x^3*e + 2*a*c^2*x^3*e + 2*a*c^2*d*x + a*b^2*f*x - 2*a^2*c*f*x - a*b*c*x*e)/((c*x^4 + b*x^2 + a)*(b^2*c^2 - 4*a*c^3)) + 1/16*((2*b^3*c^4 - 8*a*b*c^5 - 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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^4 - 2*(b^2 - 4*a*c)*b*c^4)*(b^2*c^2 - 4*a*c^3)^2*d - (6*b^5*c^2 - 50*a*b^3*c^3 + 104*a^2*b*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 25*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 26*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 6*(b^2 - 4*a*c)*b^3*c^2 + 26*(b^2 - 4*a*c)*a*b*c^3)*(b^2*c^2 - 4*a*c^3)^2*f + (2*b^4*c^3 - 20*a*b^2*c^4 + 48*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 + 10*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 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 12*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 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^4 - 2*(b^2 - 4*a*c)*b^2*c^3 + 12*(b^2 - 4*a*c)*a*c^4)*(b^2*c^2 - 4*a*c^3)^2*e - 4*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^6 + 2*a*b^4*c^6 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^7 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^7 - 16*a^2*b^2*c^7 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^8 + 32*a^3*c^8 - 2*(b^2 - 4*a*c)*a*b^2*c^6 + 8*(b^2 - 4*a*c)*a^2*c^7)*d*abs(-b^2*c^2 + 4*a*c^3) - 2*(3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 - 34*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 + 6*a*b^6*c^4 + 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 44*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 68*a^2*b^4*c^5 - 160*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^6 - 80*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 22*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + 256*a^3*b^2*c^6 + 40*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^7 - 320*a^4*c^7 - 6*(b^2 - 4*a*c)*a*b^4*c^4 + 44*(b^2 - 4*a*c)*a^2*b^2*c^5 - 80*(b^2 - 4*a*c)*a^3*c^6)*f*abs(-b^2*c^2 + 4*a*c^3) + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 + 2*a*b^5*c^5 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^6 - 16*a^2*b^3*c^6 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 + 32*a^3*b*c^7 - 2*(b^2 - 4*a*c)*a*b^3*c^5 + 8*(b^2 - 4*a*c)*a^2*b*c^6)*abs(-b^2*c^2 + 4*a*c^3)*e - (2*b^7*c^8 - 8*a*b^5*c^9 - 32*a^2*b^3*c^10 + 128*a^3*b*c^11 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^6 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^7 + 16*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)*b^5*c^8 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^9 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^10 - 2*(b^2 - 4*a*c)*b^5*c^8 + 32*(b^2 - 4*a*c)*a^2*b*c^10)*d + (6*b^9*c^6 - 86*a*b^7*c^7 + 440*a^2*b^5*c^8 - 928*a^3*b^3*c^9 + 640*a^4*b*c^10 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^9*c^4 + 43*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^5 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^5 - 220*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^6 - 62*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^6 + 464*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^7 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 + 31*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 - 320*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^8 - 160*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^8 - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^9 - 6*(b^2 - 4*a*c)*b^7*c^6 + 62*(b^2 - 4*a*c)*a*b^5*c^7 - 192*(b^2 - 4*a*c)*a^2*b^3*c^8 + 160*(b^2 - 4*a*c)*a^3*b*c^9)*f - (2*b^8*c^7 - 32*a*b^6*c^8 + 160*a^2*b^4*c^9 - 256*a^3*b^2*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^5 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^6 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^6 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^7 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^8 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^8 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 - 2*(b^2 - 4*a*c)*b^6*c^7 + 24*(b^2 - 4*a*c)*a*b^4*c^8 - 64*(b^2 - 4*a*c)*a^2*b^2*c^9)*e)*arctan(2*sqrt(1/2)*x/sqrt((b^3*c^2 - 4*a*b*c^3 + sqrt((b^3*c^2 - 4*a*b*c^3)^2 - 4*(a*b^2*c^2 - 4*a^2*c^3)*(b^2*c^3 - 4*a*c^4)))/(b^2*c^3 - 4*a*c^4)))/((a*b^6*c^5 - 12*a^2*b^4*c^6 - 2*a*b^5*c^6 + 48*a^3*b^2*c^7 + 16*a^2*b^3*c^7 + a*b^4*c^7 - 64*a^4*c^8 - 32*a^3*b*c^8 - 8*a^2*b^2*c^8 + 16*a^3*c^9)*abs(-b^2*c^2 + 4*a*c^3)*abs(c)) - 1/16*((2*b^3*c^4 - 8*a*b*c^5 - 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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^4 - 2*(b^2 - 4*a*c)*b*c^4)*(b^2*c^2 - 4*a*c^3)^2*d - (6*b^5*c^2 - 50*a*b^3*c^3 + 104*a^2*b*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 + 25*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 26*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 6*(b^2 - 4*a*c)*b^3*c^2 + 26*(b^2 - 4*a*c)*a*b*c^3)*(b^2*c^2 - 4*a*c^3)^2*f + (2*b^4*c^3 - 20*a*b^2*c^4 + 48*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 + 10*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 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 12*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 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^4 - 2*(b^2 - 4*a*c)*b^2*c^3 + 12*(b^2 - 4*a*c)*a*c^4)*(b^2*c^2 - 4*a*c^3)^2*e + 4*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^6 - 2*a*b^4*c^6 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^7 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^7 + 16*a^2*b^2*c^7 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^8 - 32*a^3*c^8 + 2*(b^2 - 4*a*c)*a*b^2*c^6 - 8*(b^2 - 4*a*c)*a^2*c^7)*d*abs(-b^2*c^2 + 4*a*c^3) + 2*(3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 - 34*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - 6*a*b^6*c^4 + 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 44*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 + 68*a^2*b^4*c^5 - 160*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^6 - 80*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 22*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 256*a^3*b^2*c^6 + 40*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^7 + 320*a^4*c^7 + 6*(b^2 - 4*a*c)*a*b^4*c^4 - 44*(b^2 - 4*a*c)*a^2*b^2*c^5 + 80*(b^2 - 4*a*c)*a^3*c^6)*f*abs(-b^2*c^2 + 4*a*c^3) - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 2*a*b^5*c^5 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^6 + 16*a^2*b^3*c^6 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 - 32*a^3*b*c^7 + 2*(b^2 - 4*a*c)*a*b^3*c^5 - 8*(b^2 - 4*a*c)*a^2*b*c^6)*abs(-b^2*c^2 + 4*a*c^3)*e - (2*b^7*c^8 - 8*a*b^5*c^9 - 32*a^2*b^3*c^10 + 128*a^3*b*c^11 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^6 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^7 + 16*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)*b^5*c^8 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^9 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^10 - 2*(b^2 - 4*a*c)*b^5*c^8 + 32*(b^2 - 4*a*c)*a^2*b*c^10)*d + (6*b^9*c^6 - 86*a*b^7*c^7 + 440*a^2*b^5*c^8 - 928*a^3*b^3*c^9 + 640*a^4*b*c^10 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^9*c^4 + 43*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^5 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^5 - 220*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^6 - 62*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^6 + 464*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^7 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 + 31*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 - 320*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^8 - 160*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^8 - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^9 - 6*(b^2 - 4*a*c)*b^7*c^6 + 62*(b^2 - 4*a*c)*a*b^5*c^7 - 192*(b^2 - 4*a*c)*a^2*b^3*c^8 + 160*(b^2 - 4*a*c)*a^3*b*c^9)*f - (2*b^8*c^7 - 32*a*b^6*c^8 + 160*a^2*b^4*c^9 - 256*a^3*b^2*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^5 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^6 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^6 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^7 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^8 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^8 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 - 2*(b^2 - 4*a*c)*b^6*c^7 + 24*(b^2 - 4*a*c)*a*b^4*c^8 - 64*(b^2 - 4*a*c)*a^2*b^2*c^9)*e)*arctan(2*sqrt(1/2)*x/sqrt((b^3*c^2 - 4*a*b*c^3 - sqrt((b^3*c^2 - 4*a*b*c^3)^2 - 4*(a*b^2*c^2 - 4*a^2*c^3)*(b^2*c^3 - 4*a*c^4)))/(b^2*c^3 - 4*a*c^4)))/((a*b^6*c^5 - 12*a^2*b^4*c^6 - 2*a*b^5*c^6 + 48*a^3*b^2*c^7 + 16*a^2*b^3*c^7 + a*b^4*c^7 - 64*a^4*c^8 - 32*a^3*b*c^8 - 8*a^2*b^2*c^8 + 16*a^3*c^9)*abs(-b^2*c^2 + 4*a*c^3)*abs(c))","B",0
70,1,6208,0,6.810925," ","integrate(x^2*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{2 \, c^{2} d x^{3} + b^{2} f x^{3} - 2 \, a c f x^{3} - b c x^{3} e + b c d x + a b f x - 2 \, a c x e}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}} - \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)} {\left(b^{2} c - 4 \, a c^{2}\right)}^{2} d - {\left(2 \, b^{4} c^{2} - 20 \, a b^{2} c^{3} + 48 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} + 10 \, \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 - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 12 \, \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} + 6 \, \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} + 12 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}^{2} f - {\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)} {\left(b^{2} c - 4 \, a c^{2}\right)}^{2} e - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} - 2 \, b^{5} c^{4} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} + 16 \, a b^{3} c^{5} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{6} - 32 \, a^{2} b c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5}\right)} d {\left| b^{2} c - 4 \, a c^{2} \right|} - 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)} f {\left| b^{2} c - 4 \, a c^{2} \right|} + 4 \, {\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)} {\left| b^{2} c - 4 \, a c^{2} \right|} e - 4 \, {\left(2 \, b^{6} c^{6} - 16 \, a b^{4} c^{7} + 32 \, a^{2} b^{2} c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{5} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{6} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{6} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{7}\right)} d + {\left(2 \, b^{8} c^{4} - 32 \, a b^{6} c^{5} + 160 \, a^{2} b^{4} c^{6} - 256 \, a^{3} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{4} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{4} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{5} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{6}\right)} f + {\left(2 \, b^{7} c^{5} - 8 \, a b^{5} c^{6} - 32 \, a^{2} b^{3} c^{7} + 128 \, a^{3} b c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{4} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{5} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{5} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{7}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} c - 4 \, a b c^{2} + \sqrt{{\left(b^{3} c - 4 \, a b c^{2}\right)}^{2} - 4 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}}{b^{2} c^{2} - 4 \, a c^{3}}}}\right)}{16 \, {\left(a b^{6} c^{3} - 12 \, a^{2} b^{4} c^{4} - 2 \, a b^{5} c^{4} + 48 \, a^{3} b^{2} c^{5} + 16 \, a^{2} b^{3} c^{5} + a b^{4} c^{5} - 64 \, a^{4} c^{6} - 32 \, a^{3} b c^{6} - 8 \, a^{2} b^{2} c^{6} + 16 \, a^{3} c^{7}\right)} {\left| b^{2} c - 4 \, a c^{2} \right|} {\left| c \right|}} + \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)} {\left(b^{2} c - 4 \, a c^{2}\right)}^{2} d - {\left(2 \, b^{4} c^{2} - 20 \, a b^{2} c^{3} + 48 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} + 10 \, \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 - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 12 \, \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} + 6 \, \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} + 12 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}^{2} f - {\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)} {\left(b^{2} c - 4 \, a c^{2}\right)}^{2} e + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} + 2 \, b^{5} c^{4} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} - 16 \, a b^{3} c^{5} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{6} + 32 \, a^{2} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5}\right)} d {\left| b^{2} c - 4 \, a c^{2} \right|} + 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)} f {\left| b^{2} c - 4 \, a c^{2} \right|} - 4 \, {\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)} {\left| b^{2} c - 4 \, a c^{2} \right|} e - 4 \, {\left(2 \, b^{6} c^{6} - 16 \, a b^{4} c^{7} + 32 \, a^{2} b^{2} c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{5} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{6} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{6} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{7}\right)} d + {\left(2 \, b^{8} c^{4} - 32 \, a b^{6} c^{5} + 160 \, a^{2} b^{4} c^{6} - 256 \, a^{3} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{4} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{4} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{5} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{6}\right)} f + {\left(2 \, b^{7} c^{5} - 8 \, a b^{5} c^{6} - 32 \, a^{2} b^{3} c^{7} + 128 \, a^{3} b c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{4} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{5} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{5} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{7}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} c - 4 \, a b c^{2} - \sqrt{{\left(b^{3} c - 4 \, a b c^{2}\right)}^{2} - 4 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}}{b^{2} c^{2} - 4 \, a c^{3}}}}\right)}{16 \, {\left(a b^{6} c^{3} - 12 \, a^{2} b^{4} c^{4} - 2 \, a b^{5} c^{4} + 48 \, a^{3} b^{2} c^{5} + 16 \, a^{2} b^{3} c^{5} + a b^{4} c^{5} - 64 \, a^{4} c^{6} - 32 \, a^{3} b c^{6} - 8 \, a^{2} b^{2} c^{6} + 16 \, a^{3} c^{7}\right)} {\left| b^{2} c - 4 \, a c^{2} \right|} {\left| c \right|}}"," ",0,"-1/2*(2*c^2*d*x^3 + b^2*f*x^3 - 2*a*c*f*x^3 - b*c*x^3*e + b*c*d*x + a*b*f*x - 2*a*c*x*e)/((c*x^4 + b*x^2 + a)*(b^2*c - 4*a*c^2)) - 1/16*(2*(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*(b^2 - 4*a*c)*c^4)*(b^2*c - 4*a*c^2)^2*d - (2*b^4*c^2 - 20*a*b^2*c^3 + 48*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 + 10*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 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 12*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 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^2*c^2 + 12*(b^2 - 4*a*c)*a*c^3)*(b^2*c - 4*a*c^2)^2*f - (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*(b^2 - 4*a*c)*b*c^3)*(b^2*c - 4*a*c^2)^2*e - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^3 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^4 - 2*b^5*c^4 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^5 + 16*a*b^3*c^5 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^6 - 32*a^2*b*c^6 + 2*(b^2 - 4*a*c)*b^3*c^4 - 8*(b^2 - 4*a*c)*a*b*c^5)*d*abs(b^2*c - 4*a*c^2) - 2*(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*(b^2 - 4*a*c)*a*b^3*c^3 - 8*(b^2 - 4*a*c)*a^2*b*c^4)*f*abs(b^2*c - 4*a*c^2) + 4*(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*(b^2 - 4*a*c)*a*b^2*c^4 - 8*(b^2 - 4*a*c)*a^2*c^5)*abs(b^2*c - 4*a*c^2)*e - 4*(2*b^6*c^6 - 16*a*b^4*c^7 + 32*a^2*b^2*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^5 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^6 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^7 - 2*(b^2 - 4*a*c)*b^4*c^6 + 8*(b^2 - 4*a*c)*a*b^2*c^7)*d + (2*b^8*c^4 - 32*a*b^6*c^5 + 160*a^2*b^4*c^6 - 256*a^3*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^3 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^4 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 2*(b^2 - 4*a*c)*b^6*c^4 + 24*(b^2 - 4*a*c)*a*b^4*c^5 - 64*(b^2 - 4*a*c)*a^2*b^2*c^6)*f + (2*b^7*c^5 - 8*a*b^5*c^6 - 32*a^2*b^3*c^7 + 128*a^3*b*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^4 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^5 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 - 2*(b^2 - 4*a*c)*b^5*c^5 + 32*(b^2 - 4*a*c)*a^2*b*c^7)*e)*arctan(2*sqrt(1/2)*x/sqrt((b^3*c - 4*a*b*c^2 + sqrt((b^3*c - 4*a*b*c^2)^2 - 4*(a*b^2*c - 4*a^2*c^2)*(b^2*c^2 - 4*a*c^3)))/(b^2*c^2 - 4*a*c^3)))/((a*b^6*c^3 - 12*a^2*b^4*c^4 - 2*a*b^5*c^4 + 48*a^3*b^2*c^5 + 16*a^2*b^3*c^5 + a*b^4*c^5 - 64*a^4*c^6 - 32*a^3*b*c^6 - 8*a^2*b^2*c^6 + 16*a^3*c^7)*abs(b^2*c - 4*a*c^2)*abs(c)) + 1/16*(2*(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*(b^2 - 4*a*c)*c^4)*(b^2*c - 4*a*c^2)^2*d - (2*b^4*c^2 - 20*a*b^2*c^3 + 48*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 + 10*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 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 12*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 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^2*c^2 + 12*(b^2 - 4*a*c)*a*c^3)*(b^2*c - 4*a*c^2)^2*f - (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*(b^2 - 4*a*c)*b*c^3)*(b^2*c - 4*a*c^2)^2*e + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^3 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^4 + 2*b^5*c^4 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^5 - 16*a*b^3*c^5 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^6 + 32*a^2*b*c^6 - 2*(b^2 - 4*a*c)*b^3*c^4 + 8*(b^2 - 4*a*c)*a*b*c^5)*d*abs(b^2*c - 4*a*c^2) + 2*(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*(b^2 - 4*a*c)*a*b^3*c^3 + 8*(b^2 - 4*a*c)*a^2*b*c^4)*f*abs(b^2*c - 4*a*c^2) - 4*(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*(b^2 - 4*a*c)*a*b^2*c^4 + 8*(b^2 - 4*a*c)*a^2*c^5)*abs(b^2*c - 4*a*c^2)*e - 4*(2*b^6*c^6 - 16*a*b^4*c^7 + 32*a^2*b^2*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^5 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^6 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^7 - 2*(b^2 - 4*a*c)*b^4*c^6 + 8*(b^2 - 4*a*c)*a*b^2*c^7)*d + (2*b^8*c^4 - 32*a*b^6*c^5 + 160*a^2*b^4*c^6 - 256*a^3*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^3 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^4 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 2*(b^2 - 4*a*c)*b^6*c^4 + 24*(b^2 - 4*a*c)*a*b^4*c^5 - 64*(b^2 - 4*a*c)*a^2*b^2*c^6)*f + (2*b^7*c^5 - 8*a*b^5*c^6 - 32*a^2*b^3*c^7 + 128*a^3*b*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^4 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^5 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 - 2*(b^2 - 4*a*c)*b^5*c^5 + 32*(b^2 - 4*a*c)*a^2*b*c^7)*e)*arctan(2*sqrt(1/2)*x/sqrt((b^3*c - 4*a*b*c^2 - sqrt((b^3*c - 4*a*b*c^2)^2 - 4*(a*b^2*c - 4*a^2*c^2)*(b^2*c^2 - 4*a*c^3)))/(b^2*c^2 - 4*a*c^3)))/((a*b^6*c^3 - 12*a^2*b^4*c^4 - 2*a*b^5*c^4 + 48*a^3*b^2*c^5 + 16*a^2*b^3*c^5 + a*b^4*c^5 - 64*a^4*c^6 - 32*a^3*b*c^6 - 8*a^2*b^2*c^6 + 16*a^3*c^7)*abs(b^2*c - 4*a*c^2)*abs(c))","B",0
71,1,6356,0,6.973314," ","integrate((f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{b c d x^{3} + a b f x^{3} - 2 \, a c x^{3} e + b^{2} d x - 2 \, a c d x + 2 \, a^{2} f x - a b x e}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}} + \frac{{\left({\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)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} d + {\left(2 \, a b^{3} c^{2} - 8 \, 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^{3} + 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 - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} f - 2 \, {\left(2 \, a b^{2} c^{3} - 8 \, a^{2} c^{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} a^{2} c^{2} + 2 \, \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} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} e + 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)} d {\left| a b^{2} - 4 \, a^{2} c \right|} - 4 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} - 2 \, a^{3} b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} + 16 \, a^{4} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} - 32 \, a^{5} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{3}\right)} f {\left| a b^{2} - 4 \, a^{2} c \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} - 2 \, a^{2} b^{5} c^{2} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 16 \, a^{3} b^{3} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 32 \, a^{4} b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|} e + {\left(2 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 224 \, a^{4} b^{3} c^{5} - 384 \, a^{5} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{3} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{4} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{5}\right)} d - {\left(2 \, a^{3} b^{7} c^{2} - 8 \, a^{4} b^{5} c^{3} - 32 \, a^{5} b^{3} c^{4} + 128 \, a^{6} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{4}\right)} f + 4 \, {\left(2 \, a^{3} b^{6} c^{3} - 16 \, a^{4} b^{4} c^{4} + 32 \, a^{5} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b^{3} - 4 \, a^{2} b c + \sqrt{{\left(a b^{3} - 4 \, a^{2} b c\right)}^{2} - 4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}}}{a b^{2} c - 4 \, a^{2} c^{2}}}}\right)}{16 \, {\left(a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} - 2 \, a^{3} b^{5} c^{2} + 48 \, a^{5} b^{2} c^{3} + 16 \, a^{4} b^{3} c^{3} + a^{3} b^{4} c^{3} - 64 \, a^{6} c^{4} - 32 \, a^{5} b c^{4} - 8 \, a^{4} b^{2} c^{4} + 16 \, a^{5} c^{5}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|} {\left| c \right|}} - \frac{{\left({\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)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} d + {\left(2 \, a b^{3} c^{2} - 8 \, 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^{3} + 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 - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} f - 2 \, {\left(2 \, a b^{2} c^{3} - 8 \, a^{2} c^{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} a^{2} c^{2} + 2 \, \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} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(a b^{2} - 4 \, a^{2} c\right)}^{2} e - 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)} d {\left| a b^{2} - 4 \, a^{2} c \right|} + 4 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 2 \, a^{3} b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 16 \, a^{4} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 32 \, a^{5} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{3}\right)} f {\left| a b^{2} - 4 \, a^{2} c \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 2 \, a^{2} b^{5} c^{2} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 16 \, a^{3} b^{3} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 32 \, a^{4} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|} e + {\left(2 \, a^{2} b^{7} c^{3} - 40 \, a^{3} b^{5} c^{4} + 224 \, a^{4} b^{3} c^{5} - 384 \, a^{5} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{3} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{4} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{5}\right)} d - {\left(2 \, a^{3} b^{7} c^{2} - 8 \, a^{4} b^{5} c^{3} - 32 \, a^{5} b^{3} c^{4} + 128 \, a^{6} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{4}\right)} f + 4 \, {\left(2 \, a^{3} b^{6} c^{3} - 16 \, a^{4} b^{4} c^{4} + 32 \, a^{5} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b^{3} - 4 \, a^{2} b c - \sqrt{{\left(a b^{3} - 4 \, a^{2} b c\right)}^{2} - 4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}}}{a b^{2} c - 4 \, a^{2} c^{2}}}}\right)}{16 \, {\left(a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} - 2 \, a^{3} b^{5} c^{2} + 48 \, a^{5} b^{2} c^{3} + 16 \, a^{4} b^{3} c^{3} + a^{3} b^{4} c^{3} - 64 \, a^{6} c^{4} - 32 \, a^{5} b c^{4} - 8 \, a^{4} b^{2} c^{4} + 16 \, a^{5} c^{5}\right)} {\left| a b^{2} - 4 \, a^{2} c \right|} {\left| c \right|}}"," ",0,"1/2*(b*c*d*x^3 + a*b*f*x^3 - 2*a*c*x^3*e + b^2*d*x - 2*a*c*d*x + 2*a^2*f*x - a*b*x*e)/((c*x^4 + b*x^2 + a)*(a*b^2 - 4*a^2*c)) + 1/16*((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*(b^2 - 4*a*c)*b*c^3)*(a*b^2 - 4*a^2*c)^2*d + (2*a*b^3*c^2 - 8*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^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 2*(b^2 - 4*a*c)*a*b*c^2)*(a*b^2 - 4*a^2*c)^2*f - 2*(2*a*b^2*c^3 - 8*a^2*c^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)*a^2*c^2 + 2*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)*a*c^3 - 2*(b^2 - 4*a*c)*a*c^3)*(a*b^2 - 4*a^2*c)^2*e + 2*(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*(b^2 - 4*a*c)*a*b^4*c^2 - 20*(b^2 - 4*a*c)*a^2*b^2*c^3 + 48*(b^2 - 4*a*c)*a^3*c^4)*d*abs(a*b^2 - 4*a^2*c) - 4*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^2 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 - 2*a^3*b^4*c^2 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*c^3 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 + 16*a^4*b^2*c^3 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^4 - 32*a^5*c^4 + 2*(b^2 - 4*a*c)*a^3*b^2*c^2 - 8*(b^2 - 4*a*c)*a^4*c^3)*f*abs(a*b^2 - 4*a^2*c) + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 - 2*a^2*b^5*c^2 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 + 16*a^3*b^3*c^3 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 - 32*a^4*b*c^4 + 2*(b^2 - 4*a*c)*a^2*b^3*c^2 - 8*(b^2 - 4*a*c)*a^3*b*c^3)*abs(a*b^2 - 4*a^2*c)*e + (2*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 224*a^4*b^3*c^5 - 384*a^5*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 - 2*(b^2 - 4*a*c)*a^2*b^5*c^3 + 32*(b^2 - 4*a*c)*a^3*b^3*c^4 - 96*(b^2 - 4*a*c)*a^4*b*c^5)*d - (2*a^3*b^7*c^2 - 8*a^4*b^5*c^3 - 32*a^5*b^3*c^4 + 128*a^6*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 - 2*(b^2 - 4*a*c)*a^3*b^5*c^2 + 32*(b^2 - 4*a*c)*a^5*b*c^4)*f + 4*(2*a^3*b^6*c^3 - 16*a^4*b^4*c^4 + 32*a^5*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 2*(b^2 - 4*a*c)*a^3*b^4*c^3 + 8*(b^2 - 4*a*c)*a^4*b^2*c^4)*e)*arctan(2*sqrt(1/2)*x/sqrt((a*b^3 - 4*a^2*b*c + sqrt((a*b^3 - 4*a^2*b*c)^2 - 4*(a^2*b^2 - 4*a^3*c)*(a*b^2*c - 4*a^2*c^2)))/(a*b^2*c - 4*a^2*c^2)))/((a^3*b^6*c - 12*a^4*b^4*c^2 - 2*a^3*b^5*c^2 + 48*a^5*b^2*c^3 + 16*a^4*b^3*c^3 + a^3*b^4*c^3 - 64*a^6*c^4 - 32*a^5*b*c^4 - 8*a^4*b^2*c^4 + 16*a^5*c^5)*abs(a*b^2 - 4*a^2*c)*abs(c)) - 1/16*((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*(b^2 - 4*a*c)*b*c^3)*(a*b^2 - 4*a^2*c)^2*d + (2*a*b^3*c^2 - 8*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^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 2*(b^2 - 4*a*c)*a*b*c^2)*(a*b^2 - 4*a^2*c)^2*f - 2*(2*a*b^2*c^3 - 8*a^2*c^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)*a^2*c^2 + 2*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)*a*c^3 - 2*(b^2 - 4*a*c)*a*c^3)*(a*b^2 - 4*a^2*c)^2*e - 2*(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*(b^2 - 4*a*c)*a*b^4*c^2 + 20*(b^2 - 4*a*c)*a^2*b^2*c^3 - 48*(b^2 - 4*a*c)*a^3*c^4)*d*abs(a*b^2 - 4*a^2*c) + 4*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^2 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + 2*a^3*b^4*c^2 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*c^3 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 16*a^4*b^2*c^3 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^4 + 32*a^5*c^4 - 2*(b^2 - 4*a*c)*a^3*b^2*c^2 + 8*(b^2 - 4*a*c)*a^4*c^3)*f*abs(a*b^2 - 4*a^2*c) - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + 2*a^2*b^5*c^2 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 16*a^3*b^3*c^3 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 32*a^4*b*c^4 - 2*(b^2 - 4*a*c)*a^2*b^3*c^2 + 8*(b^2 - 4*a*c)*a^3*b*c^3)*abs(a*b^2 - 4*a^2*c)*e + (2*a^2*b^7*c^3 - 40*a^3*b^5*c^4 + 224*a^4*b^3*c^5 - 384*a^5*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 - 2*(b^2 - 4*a*c)*a^2*b^5*c^3 + 32*(b^2 - 4*a*c)*a^3*b^3*c^4 - 96*(b^2 - 4*a*c)*a^4*b*c^5)*d - (2*a^3*b^7*c^2 - 8*a^4*b^5*c^3 - 32*a^5*b^3*c^4 + 128*a^6*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 - 2*(b^2 - 4*a*c)*a^3*b^5*c^2 + 32*(b^2 - 4*a*c)*a^5*b*c^4)*f + 4*(2*a^3*b^6*c^3 - 16*a^4*b^4*c^4 + 32*a^5*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 2*(b^2 - 4*a*c)*a^3*b^4*c^3 + 8*(b^2 - 4*a*c)*a^4*b^2*c^4)*e)*arctan(2*sqrt(1/2)*x/sqrt((a*b^3 - 4*a^2*b*c - sqrt((a*b^3 - 4*a^2*b*c)^2 - 4*(a^2*b^2 - 4*a^3*c)*(a*b^2*c - 4*a^2*c^2)))/(a*b^2*c - 4*a^2*c^2)))/((a^3*b^6*c - 12*a^4*b^4*c^2 - 2*a^3*b^5*c^2 + 48*a^5*b^2*c^3 + 16*a^4*b^3*c^3 + a^3*b^4*c^3 - 64*a^6*c^4 - 32*a^5*b*c^4 - 8*a^4*b^2*c^4 + 16*a^5*c^5)*abs(a*b^2 - 4*a^2*c)*abs(c))","B",0
72,1,7182,0,7.093450," ","integrate((f*x^4+e*x^2+d)/x^2/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{3 \, b^{2} c d x^{4} - 10 \, a c^{2} d x^{4} + 2 \, a^{2} c f x^{4} - a b c x^{4} e + 3 \, b^{3} d x^{2} - 11 \, a b c d x^{2} + a^{2} b f x^{2} - a b^{2} x^{2} e + 2 \, a^{2} c x^{2} e + 2 \, a b^{2} d - 8 \, a^{2} c d}{2 \, {\left(c x^{5} + b x^{3} + a x\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}} - \frac{{\left({\left(6 \, b^{4} c^{2} - 44 \, a b^{2} c^{3} + 80 \, a^{2} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 20 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}^{2} d + 2 \, {\left(2 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{2}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}^{2} f - {\left(2 \, a b^{3} c^{2} - 8 \, 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^{3} + 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 - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}^{2} e + 2 \, {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} - 37 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c - 6 \, a^{2} b^{7} c + 152 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} + 50 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 74 \, a^{3} b^{5} c^{2} - 208 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} - 104 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 25 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 304 \, a^{4} b^{3} c^{3} + 52 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} + 416 \, a^{5} b c^{4} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c - 50 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{2} + 104 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{3}\right)} d {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c - 2 \, a^{4} b^{5} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} + 16 \, a^{5} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} - 32 \, a^{6} b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{2}\right)} f {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c - 2 \, a^{3} b^{6} c + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} + 28 \, a^{4} b^{4} c^{2} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{3} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 128 \, a^{5} b^{2} c^{3} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{4} + 192 \, a^{6} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c - 20 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{2} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{5} c^{3}\right)} {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} e + {\left(6 \, a^{4} b^{8} c^{2} - 80 \, a^{5} b^{6} c^{3} + 352 \, a^{6} b^{4} c^{4} - 512 \, a^{7} b^{2} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{2} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{2} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{3} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{3} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{3} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{6} c^{2} + 56 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{4}\right)} d - 4 \, {\left(2 \, a^{6} b^{6} c^{2} - 16 \, a^{7} b^{4} c^{3} + 32 \, a^{8} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{6} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{4} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{2} c^{3}\right)} f - {\left(2 \, a^{5} b^{7} c^{2} - 40 \, a^{6} b^{5} c^{3} + 224 \, a^{7} b^{3} c^{4} - 384 \, a^{8} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{2} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{3} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{3} c^{3} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{2} b^{3} - 4 \, a^{3} b c + \sqrt{{\left(a^{2} b^{3} - 4 \, a^{3} b c\right)}^{2} - 4 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}}}\right)}{16 \, {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c - 2 \, a^{5} b^{5} c + 48 \, a^{7} b^{2} c^{2} + 16 \, a^{6} b^{3} c^{2} + a^{5} b^{4} c^{2} - 64 \, a^{8} c^{3} - 32 \, a^{7} b c^{3} - 8 \, a^{6} b^{2} c^{3} + 16 \, a^{7} c^{4}\right)} {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} {\left| c \right|}} + \frac{{\left({\left(6 \, b^{4} c^{2} - 44 \, a b^{2} c^{3} + 80 \, a^{2} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 20 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}^{2} d + 2 \, {\left(2 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{2}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}^{2} f - {\left(2 \, a b^{3} c^{2} - 8 \, 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^{3} + 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 - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}^{2} e - 2 \, {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} - 37 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c + 6 \, a^{2} b^{7} c + 152 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} + 50 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} - 74 \, a^{3} b^{5} c^{2} - 208 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} - 104 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 25 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} + 304 \, a^{4} b^{3} c^{3} + 52 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 416 \, a^{5} b c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c + 50 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{2} - 104 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{3}\right)} d {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c + 2 \, a^{4} b^{5} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} - 16 \, a^{5} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} + 32 \, a^{6} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{2}\right)} f {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c + 2 \, a^{3} b^{6} c + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - 28 \, a^{4} b^{4} c^{2} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{3} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} + 128 \, a^{5} b^{2} c^{3} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{4} - 192 \, a^{6} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{2} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{5} c^{3}\right)} {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} e + {\left(6 \, a^{4} b^{8} c^{2} - 80 \, a^{5} b^{6} c^{3} + 352 \, a^{6} b^{4} c^{4} - 512 \, a^{7} b^{2} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{2} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{2} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{3} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{3} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{3} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{6} c^{2} + 56 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{4}\right)} d - 4 \, {\left(2 \, a^{6} b^{6} c^{2} - 16 \, a^{7} b^{4} c^{3} + 32 \, a^{8} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{6} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{4} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{2} c^{3}\right)} f - {\left(2 \, a^{5} b^{7} c^{2} - 40 \, a^{6} b^{5} c^{3} + 224 \, a^{7} b^{3} c^{4} - 384 \, a^{8} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{2} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{3} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{3} c^{3} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{2} b^{3} - 4 \, a^{3} b c - \sqrt{{\left(a^{2} b^{3} - 4 \, a^{3} b c\right)}^{2} - 4 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}}}\right)}{16 \, {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c - 2 \, a^{5} b^{5} c + 48 \, a^{7} b^{2} c^{2} + 16 \, a^{6} b^{3} c^{2} + a^{5} b^{4} c^{2} - 64 \, a^{8} c^{3} - 32 \, a^{7} b c^{3} - 8 \, a^{6} b^{2} c^{3} + 16 \, a^{7} c^{4}\right)} {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} {\left| c \right|}}"," ",0,"-1/2*(3*b^2*c*d*x^4 - 10*a*c^2*d*x^4 + 2*a^2*c*f*x^4 - a*b*c*x^4*e + 3*b^3*d*x^2 - 11*a*b*c*d*x^2 + a^2*b*f*x^2 - a*b^2*x^2*e + 2*a^2*c*x^2*e + 2*a*b^2*d - 8*a^2*c*d)/((c*x^5 + b*x^3 + a*x)*(a^2*b^2 - 4*a^3*c)) - 1/16*((6*b^4*c^2 - 44*a*b^2*c^3 + 80*a^2*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^3 - 6*(b^2 - 4*a*c)*b^2*c^2 + 20*(b^2 - 4*a*c)*a*c^3)*(a^2*b^2 - 4*a^3*c)^2*d + 2*(2*a^2*b^2*c^2 - 8*a^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 2*(b^2 - 4*a*c)*a^2*c^2)*(a^2*b^2 - 4*a^3*c)^2*f - (2*a*b^3*c^2 - 8*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^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 2*(b^2 - 4*a*c)*a*b*c^2)*(a^2*b^2 - 4*a^3*c)^2*e + 2*(3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7 - 37*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c - 6*a^2*b^7*c + 152*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 + 50*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 + 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 + 74*a^3*b^5*c^2 - 208*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 - 104*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 - 25*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 - 304*a^4*b^3*c^3 + 52*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 + 416*a^5*b*c^4 + 6*(b^2 - 4*a*c)*a^2*b^5*c - 50*(b^2 - 4*a*c)*a^3*b^3*c^2 + 104*(b^2 - 4*a*c)*a^4*b*c^3)*d*abs(a^2*b^2 - 4*a^3*c) - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c - 2*a^4*b^5*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 + 16*a^5*b^3*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 - 32*a^6*b*c^3 + 2*(b^2 - 4*a*c)*a^4*b^3*c - 8*(b^2 - 4*a*c)*a^5*b*c^2)*f*abs(a^2*b^2 - 4*a^3*c) - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6 - 14*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c - 2*a^3*b^6*c + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^2 + 20*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 + 28*a^4*b^4*c^2 - 96*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*c^3 - 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 - 128*a^5*b^2*c^3 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*c^4 + 192*a^6*c^4 + 2*(b^2 - 4*a*c)*a^3*b^4*c - 20*(b^2 - 4*a*c)*a^4*b^2*c^2 + 48*(b^2 - 4*a*c)*a^5*c^3)*abs(a^2*b^2 - 4*a^3*c)*e + (6*a^4*b^8*c^2 - 80*a^5*b^6*c^3 + 352*a^6*b^4*c^4 - 512*a^7*b^2*c^5 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^8 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^2 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^3 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^3 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^4 - 6*(b^2 - 4*a*c)*a^4*b^6*c^2 + 56*(b^2 - 4*a*c)*a^5*b^4*c^3 - 128*(b^2 - 4*a*c)*a^6*b^2*c^4)*d - 4*(2*a^6*b^6*c^2 - 16*a^7*b^4*c^3 + 32*a^8*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^6 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^2*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^3 - 2*(b^2 - 4*a*c)*a^6*b^4*c^2 + 8*(b^2 - 4*a*c)*a^7*b^2*c^3)*f - (2*a^5*b^7*c^2 - 40*a^6*b^5*c^3 + 224*a^7*b^3*c^4 - 384*a^8*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^7 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^2 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b*c^3 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^3 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b*c^4 - 2*(b^2 - 4*a*c)*a^5*b^5*c^2 + 32*(b^2 - 4*a*c)*a^6*b^3*c^3 - 96*(b^2 - 4*a*c)*a^7*b*c^4)*e)*arctan(2*sqrt(1/2)*x/sqrt((a^2*b^3 - 4*a^3*b*c + sqrt((a^2*b^3 - 4*a^3*b*c)^2 - 4*(a^3*b^2 - 4*a^4*c)*(a^2*b^2*c - 4*a^3*c^2)))/(a^2*b^2*c - 4*a^3*c^2)))/((a^5*b^6 - 12*a^6*b^4*c - 2*a^5*b^5*c + 48*a^7*b^2*c^2 + 16*a^6*b^3*c^2 + a^5*b^4*c^2 - 64*a^8*c^3 - 32*a^7*b*c^3 - 8*a^6*b^2*c^3 + 16*a^7*c^4)*abs(a^2*b^2 - 4*a^3*c)*abs(c)) + 1/16*((6*b^4*c^2 - 44*a*b^2*c^3 + 80*a^2*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^3 - 6*(b^2 - 4*a*c)*b^2*c^2 + 20*(b^2 - 4*a*c)*a*c^3)*(a^2*b^2 - 4*a^3*c)^2*d + 2*(2*a^2*b^2*c^2 - 8*a^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 2*(b^2 - 4*a*c)*a^2*c^2)*(a^2*b^2 - 4*a^3*c)^2*f - (2*a*b^3*c^2 - 8*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^3 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 2*(b^2 - 4*a*c)*a*b*c^2)*(a^2*b^2 - 4*a^3*c)^2*e - 2*(3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7 - 37*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c + 6*a^2*b^7*c + 152*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 + 50*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 + 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 - 74*a^3*b^5*c^2 - 208*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 - 104*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 - 25*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 + 304*a^4*b^3*c^3 + 52*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 - 416*a^5*b*c^4 - 6*(b^2 - 4*a*c)*a^2*b^5*c + 50*(b^2 - 4*a*c)*a^3*b^3*c^2 - 104*(b^2 - 4*a*c)*a^4*b*c^3)*d*abs(a^2*b^2 - 4*a^3*c) + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c + 2*a^4*b^5*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 - 16*a^5*b^3*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 + 32*a^6*b*c^3 - 2*(b^2 - 4*a*c)*a^4*b^3*c + 8*(b^2 - 4*a*c)*a^5*b*c^2)*f*abs(a^2*b^2 - 4*a^3*c) + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6 - 14*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c + 2*a^3*b^6*c + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^2 + 20*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 - 28*a^4*b^4*c^2 - 96*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*c^3 - 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 + 128*a^5*b^2*c^3 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*c^4 - 192*a^6*c^4 - 2*(b^2 - 4*a*c)*a^3*b^4*c + 20*(b^2 - 4*a*c)*a^4*b^2*c^2 - 48*(b^2 - 4*a*c)*a^5*c^3)*abs(a^2*b^2 - 4*a^3*c)*e + (6*a^4*b^8*c^2 - 80*a^5*b^6*c^3 + 352*a^6*b^4*c^4 - 512*a^7*b^2*c^5 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^8 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^2 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^3 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^3 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^4 - 6*(b^2 - 4*a*c)*a^4*b^6*c^2 + 56*(b^2 - 4*a*c)*a^5*b^4*c^3 - 128*(b^2 - 4*a*c)*a^6*b^2*c^4)*d - 4*(2*a^6*b^6*c^2 - 16*a^7*b^4*c^3 + 32*a^8*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^6 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^2*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^3 - 2*(b^2 - 4*a*c)*a^6*b^4*c^2 + 8*(b^2 - 4*a*c)*a^7*b^2*c^3)*f - (2*a^5*b^7*c^2 - 40*a^6*b^5*c^3 + 224*a^7*b^3*c^4 - 384*a^8*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^7 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^2 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b*c^3 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^3 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^4 - 2*(b^2 - 4*a*c)*a^5*b^5*c^2 + 32*(b^2 - 4*a*c)*a^6*b^3*c^3 - 96*(b^2 - 4*a*c)*a^7*b*c^4)*e)*arctan(2*sqrt(1/2)*x/sqrt((a^2*b^3 - 4*a^3*b*c - sqrt((a^2*b^3 - 4*a^3*b*c)^2 - 4*(a^3*b^2 - 4*a^4*c)*(a^2*b^2*c - 4*a^3*c^2)))/(a^2*b^2*c - 4*a^3*c^2)))/((a^5*b^6 - 12*a^6*b^4*c - 2*a^5*b^5*c + 48*a^7*b^2*c^2 + 16*a^6*b^3*c^2 + a^5*b^4*c^2 - 64*a^8*c^3 - 32*a^7*b*c^3 - 8*a^6*b^2*c^3 + 16*a^7*c^4)*abs(a^2*b^2 - 4*a^3*c)*abs(c))","B",0
73,1,8660,0,8.590658," ","integrate((f*x^4+e*x^2+d)/x^4/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{b^{3} c d x^{3} - 3 \, a b c^{2} d x^{3} + a^{2} b c f x^{3} - a b^{2} c x^{3} e + 2 \, a^{2} c^{2} x^{3} e + b^{4} d x - 4 \, a b^{2} c d x + 2 \, a^{2} c^{2} d x + a^{2} b^{2} f x - 2 \, a^{3} c f x - a b^{3} x e + 3 \, a^{2} b c x e}{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} {\left(c x^{4} + b x^{2} + a\right)}} + \frac{{\left({\left(10 \, b^{5} c^{2} - 78 \, a b^{3} c^{3} + 152 \, a^{2} b c^{4} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 39 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 76 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 38 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 19 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 38 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}^{2} d + {\left(2 \, a^{2} b^{3} c^{2} - 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 c^{2}\right)} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}^{2} f - {\left(6 \, a b^{4} c^{2} - 44 \, a^{2} b^{2} c^{3} + 80 \, a^{3} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}^{2} e + 2 \, {\left(5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{8} - 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c - 10 \, a^{3} b^{8} c + 286 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{2} + 88 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{2} + 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{2} + 128 \, a^{4} b^{6} c^{2} - 496 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{3} - 220 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{3} - 44 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{3} - 572 \, a^{5} b^{4} c^{3} + 224 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} c^{4} + 112 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{4} + 110 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{4} + 992 \, a^{6} b^{2} c^{4} - 56 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{5} - 448 \, a^{7} c^{5} + 10 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{6} c - 88 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{4} c^{2} + 220 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{2} c^{3} - 112 \, {\left(b^{2} - 4 \, a c\right)} a^{6} c^{4}\right)} d {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c - 2 \, a^{5} b^{6} c + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{2} + 28 \, a^{6} b^{4} c^{2} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} c^{3} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{3} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{3} - 128 \, a^{7} b^{2} c^{3} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} c^{4} + 192 \, a^{8} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c - 20 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{2} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{7} c^{3}\right)} f {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} - 2 \, {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} - 37 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c - 6 \, a^{4} b^{7} c + 152 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{2} + 50 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{2} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{2} + 74 \, a^{5} b^{5} c^{2} - 208 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{3} - 104 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{3} - 25 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{3} - 304 \, a^{6} b^{3} c^{3} + 52 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{4} + 416 \, a^{7} b c^{4} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{5} c - 50 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{3} c^{2} + 104 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b c^{3}\right)} {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} e + {\left(10 \, a^{6} b^{9} c^{2} - 138 \, a^{7} b^{7} c^{3} + 680 \, a^{8} b^{5} c^{4} - 1376 \, a^{9} b^{3} c^{5} + 896 \, a^{10} b c^{6} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{9} + 69 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{7} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{8} c - 340 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{5} c^{2} - 98 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{6} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{7} c^{2} + 688 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{3} c^{3} + 288 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{4} c^{3} + 49 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{5} c^{3} - 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b c^{4} - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{2} c^{4} - 144 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{3} c^{4} + 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b c^{5} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{7} c^{2} + 98 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{5} c^{3} - 288 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{3} c^{4} + 224 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b c^{5}\right)} d + {\left(2 \, a^{8} b^{7} c^{2} - 40 \, a^{9} b^{5} c^{3} + 224 \, a^{10} b^{3} c^{4} - 384 \, a^{11} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{7} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{6} c - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{3} c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{5} c^{2} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b c^{3} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{3} c^{3} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{10} b c^{4}\right)} f - {\left(6 \, a^{7} b^{8} c^{2} - 80 \, a^{8} b^{6} c^{3} + 352 \, a^{9} b^{4} c^{4} - 512 \, a^{10} b^{2} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{8} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{6} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{7} c - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{4} c^{2} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{5} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{6} c^{2} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{2} c^{3} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{3} c^{3} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{4} c^{3} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{2} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{6} c^{2} + 56 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{4} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{2} c^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{3} b^{3} - 4 \, a^{4} b c + \sqrt{{\left(a^{3} b^{3} - 4 \, a^{4} b c\right)}^{2} - 4 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)}}}{a^{3} b^{2} c - 4 \, a^{4} c^{2}}}}\right)}{16 \, {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c - 2 \, a^{7} b^{5} c + 48 \, a^{9} b^{2} c^{2} + 16 \, a^{8} b^{3} c^{2} + a^{7} b^{4} c^{2} - 64 \, a^{10} c^{3} - 32 \, a^{9} b c^{3} - 8 \, a^{8} b^{2} c^{3} + 16 \, a^{9} c^{4}\right)} {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} {\left| c \right|}} - \frac{{\left({\left(10 \, b^{5} c^{2} - 78 \, a b^{3} c^{3} + 152 \, a^{2} b c^{4} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 39 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 76 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 38 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 19 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 38 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}^{2} d + {\left(2 \, a^{2} b^{3} c^{2} - 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 c^{2}\right)} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}^{2} f - {\left(6 \, a b^{4} c^{2} - 44 \, a^{2} b^{2} c^{3} + 80 \, a^{3} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}^{2} e - 2 \, {\left(5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{8} - 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c + 10 \, a^{3} b^{8} c + 286 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{2} + 88 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{2} + 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{2} - 128 \, a^{4} b^{6} c^{2} - 496 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{3} - 220 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{3} - 44 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{3} + 572 \, a^{5} b^{4} c^{3} + 224 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} c^{4} + 112 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{4} + 110 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{4} - 992 \, a^{6} b^{2} c^{4} - 56 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{5} + 448 \, a^{7} c^{5} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{6} c + 88 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{4} c^{2} - 220 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{2} c^{3} + 112 \, {\left(b^{2} - 4 \, a c\right)} a^{6} c^{4}\right)} d {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c + 2 \, a^{5} b^{6} c + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{2} - 28 \, a^{6} b^{4} c^{2} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} c^{3} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{3} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{3} + 128 \, a^{7} b^{2} c^{3} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} c^{4} - 192 \, a^{8} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{2} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{7} c^{3}\right)} f {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} + 2 \, {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} - 37 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c + 6 \, a^{4} b^{7} c + 152 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{2} + 50 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{2} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{2} - 74 \, a^{5} b^{5} c^{2} - 208 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{3} - 104 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{3} - 25 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{3} + 304 \, a^{6} b^{3} c^{3} + 52 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{4} - 416 \, a^{7} b c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{5} c + 50 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{3} c^{2} - 104 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b c^{3}\right)} {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} e + {\left(10 \, a^{6} b^{9} c^{2} - 138 \, a^{7} b^{7} c^{3} + 680 \, a^{8} b^{5} c^{4} - 1376 \, a^{9} b^{3} c^{5} + 896 \, a^{10} b c^{6} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{9} + 69 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{7} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{8} c - 340 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{5} c^{2} - 98 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{6} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{7} c^{2} + 688 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{3} c^{3} + 288 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{4} c^{3} + 49 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{5} c^{3} - 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b c^{4} - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{2} c^{4} - 144 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{3} c^{4} + 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b c^{5} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{7} c^{2} + 98 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{5} c^{3} - 288 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{3} c^{4} + 224 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b c^{5}\right)} d + {\left(2 \, a^{8} b^{7} c^{2} - 40 \, a^{9} b^{5} c^{3} + 224 \, a^{10} b^{3} c^{4} - 384 \, a^{11} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{7} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{6} c - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{3} c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{5} c^{2} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b c^{3} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{3} c^{3} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{10} b c^{4}\right)} f - {\left(6 \, a^{7} b^{8} c^{2} - 80 \, a^{8} b^{6} c^{3} + 352 \, a^{9} b^{4} c^{4} - 512 \, a^{10} b^{2} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{8} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{6} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{7} c - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{4} c^{2} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{5} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{6} c^{2} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{2} c^{3} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{3} c^{3} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{4} c^{3} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{2} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{6} c^{2} + 56 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{4} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{2} c^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{3} b^{3} - 4 \, a^{4} b c - \sqrt{{\left(a^{3} b^{3} - 4 \, a^{4} b c\right)}^{2} - 4 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)}}}{a^{3} b^{2} c - 4 \, a^{4} c^{2}}}}\right)}{16 \, {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c - 2 \, a^{7} b^{5} c + 48 \, a^{9} b^{2} c^{2} + 16 \, a^{8} b^{3} c^{2} + a^{7} b^{4} c^{2} - 64 \, a^{10} c^{3} - 32 \, a^{9} b c^{3} - 8 \, a^{8} b^{2} c^{3} + 16 \, a^{9} c^{4}\right)} {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} {\left| c \right|}} + \frac{6 \, b d x^{2} - 3 \, a x^{2} e - a d}{3 \, a^{3} x^{3}}"," ",0,"1/2*(b^3*c*d*x^3 - 3*a*b*c^2*d*x^3 + a^2*b*c*f*x^3 - a*b^2*c*x^3*e + 2*a^2*c^2*x^3*e + b^4*d*x - 4*a*b^2*c*d*x + 2*a^2*c^2*d*x + a^2*b^2*f*x - 2*a^3*c*f*x - a*b^3*x*e + 3*a^2*b*c*x*e)/((a^3*b^2 - 4*a^4*c)*(c*x^4 + b*x^2 + a)) + 1/16*((10*b^5*c^2 - 78*a*b^3*c^3 + 152*a^2*b*c^4 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 + 39*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 76*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 38*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 19*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 10*(b^2 - 4*a*c)*b^3*c^2 + 38*(b^2 - 4*a*c)*a*b*c^3)*(a^3*b^2 - 4*a^4*c)^2*d + (2*a^2*b^3*c^2 - 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*(b^2 - 4*a*c)*a^2*b*c^2)*(a^3*b^2 - 4*a^4*c)^2*f - (6*a*b^4*c^2 - 44*a^2*b^2*c^3 + 80*a^3*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 6*(b^2 - 4*a*c)*a*b^2*c^2 + 20*(b^2 - 4*a*c)*a^2*c^3)*(a^3*b^2 - 4*a^4*c)^2*e + 2*(5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^8 - 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c - 10*a^3*b^8*c + 286*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 + 88*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^2 + 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^2 + 128*a^4*b^6*c^2 - 496*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 - 220*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^3 - 44*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^3 - 572*a^5*b^4*c^3 + 224*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*c^4 + 112*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^4 + 110*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^4 + 992*a^6*b^2*c^4 - 56*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*c^5 - 448*a^7*c^5 + 10*(b^2 - 4*a*c)*a^3*b^6*c - 88*(b^2 - 4*a*c)*a^4*b^4*c^2 + 220*(b^2 - 4*a*c)*a^5*b^2*c^3 - 112*(b^2 - 4*a*c)*a^6*c^4)*d*abs(a^3*b^2 - 4*a^4*c) + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6 - 14*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c - 2*a^5*b^6*c + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^2 + 20*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 + 28*a^6*b^4*c^2 - 96*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*c^3 - 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b*c^3 - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 - 128*a^7*b^2*c^3 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*c^4 + 192*a^8*c^4 + 2*(b^2 - 4*a*c)*a^5*b^4*c - 20*(b^2 - 4*a*c)*a^6*b^2*c^2 + 48*(b^2 - 4*a*c)*a^7*c^3)*f*abs(a^3*b^2 - 4*a^4*c) - 2*(3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7 - 37*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c - 6*a^4*b^7*c + 152*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^2 + 50*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 + 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^2 + 74*a^5*b^5*c^2 - 208*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b*c^3 - 104*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 - 25*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^3 - 304*a^6*b^3*c^3 + 52*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^4 + 416*a^7*b*c^4 + 6*(b^2 - 4*a*c)*a^4*b^5*c - 50*(b^2 - 4*a*c)*a^5*b^3*c^2 + 104*(b^2 - 4*a*c)*a^6*b*c^3)*abs(a^3*b^2 - 4*a^4*c)*e + (10*a^6*b^9*c^2 - 138*a^7*b^7*c^3 + 680*a^8*b^5*c^4 - 1376*a^9*b^3*c^5 + 896*a^10*b*c^6 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^9 + 69*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^7*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^8*c - 340*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 - 98*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^6*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^7*c^2 + 688*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 + 288*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^4*c^3 + 49*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^5*c^3 - 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b*c^4 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^2*c^4 - 144*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^3*c^4 + 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b*c^5 - 10*(b^2 - 4*a*c)*a^6*b^7*c^2 + 98*(b^2 - 4*a*c)*a^7*b^5*c^3 - 288*(b^2 - 4*a*c)*a^8*b^3*c^4 + 224*(b^2 - 4*a*c)*a^9*b*c^5)*d + (2*a^8*b^7*c^2 - 40*a^9*b^5*c^3 + 224*a^10*b^3*c^4 - 384*a^11*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^7 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^6*c - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^3*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b*c^3 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b*c^4 - 2*(b^2 - 4*a*c)*a^8*b^5*c^2 + 32*(b^2 - 4*a*c)*a^9*b^3*c^3 - 96*(b^2 - 4*a*c)*a^10*b*c^4)*f - (6*a^7*b^8*c^2 - 80*a^8*b^6*c^3 + 352*a^9*b^4*c^4 - 512*a^10*b^2*c^5 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^8 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^6*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^7*c - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^4*c^2 - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^6*c^2 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^2*c^3 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^4*c^3 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^2*c^4 - 6*(b^2 - 4*a*c)*a^7*b^6*c^2 + 56*(b^2 - 4*a*c)*a^8*b^4*c^3 - 128*(b^2 - 4*a*c)*a^9*b^2*c^4)*e)*arctan(2*sqrt(1/2)*x/sqrt((a^3*b^3 - 4*a^4*b*c + sqrt((a^3*b^3 - 4*a^4*b*c)^2 - 4*(a^4*b^2 - 4*a^5*c)*(a^3*b^2*c - 4*a^4*c^2)))/(a^3*b^2*c - 4*a^4*c^2)))/((a^7*b^6 - 12*a^8*b^4*c - 2*a^7*b^5*c + 48*a^9*b^2*c^2 + 16*a^8*b^3*c^2 + a^7*b^4*c^2 - 64*a^10*c^3 - 32*a^9*b*c^3 - 8*a^8*b^2*c^3 + 16*a^9*c^4)*abs(a^3*b^2 - 4*a^4*c)*abs(c)) - 1/16*((10*b^5*c^2 - 78*a*b^3*c^3 + 152*a^2*b*c^4 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 39*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 76*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 38*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 19*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 10*(b^2 - 4*a*c)*b^3*c^2 + 38*(b^2 - 4*a*c)*a*b*c^3)*(a^3*b^2 - 4*a^4*c)^2*d + (2*a^2*b^3*c^2 - 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*(b^2 - 4*a*c)*a^2*b*c^2)*(a^3*b^2 - 4*a^4*c)^2*f - (6*a*b^4*c^2 - 44*a^2*b^2*c^3 + 80*a^3*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 6*(b^2 - 4*a*c)*a*b^2*c^2 + 20*(b^2 - 4*a*c)*a^2*c^3)*(a^3*b^2 - 4*a^4*c)^2*e - 2*(5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^8 - 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c + 10*a^3*b^8*c + 286*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 + 88*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^2 + 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^2 - 128*a^4*b^6*c^2 - 496*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 - 220*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^3 - 44*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^3 + 572*a^5*b^4*c^3 + 224*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*c^4 + 112*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^4 + 110*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^4 - 992*a^6*b^2*c^4 - 56*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*c^5 + 448*a^7*c^5 - 10*(b^2 - 4*a*c)*a^3*b^6*c + 88*(b^2 - 4*a*c)*a^4*b^4*c^2 - 220*(b^2 - 4*a*c)*a^5*b^2*c^3 + 112*(b^2 - 4*a*c)*a^6*c^4)*d*abs(a^3*b^2 - 4*a^4*c) - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6 - 14*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c + 2*a^5*b^6*c + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^2 + 20*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 - 28*a^6*b^4*c^2 - 96*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*c^3 - 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^3 - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 + 128*a^7*b^2*c^3 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*c^4 - 192*a^8*c^4 - 2*(b^2 - 4*a*c)*a^5*b^4*c + 20*(b^2 - 4*a*c)*a^6*b^2*c^2 - 48*(b^2 - 4*a*c)*a^7*c^3)*f*abs(a^3*b^2 - 4*a^4*c) + 2*(3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^7 - 37*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c + 6*a^4*b^7*c + 152*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^2 + 50*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 + 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^2 - 74*a^5*b^5*c^2 - 208*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^3 - 104*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 - 25*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^3 + 304*a^6*b^3*c^3 + 52*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^4 - 416*a^7*b*c^4 - 6*(b^2 - 4*a*c)*a^4*b^5*c + 50*(b^2 - 4*a*c)*a^5*b^3*c^2 - 104*(b^2 - 4*a*c)*a^6*b*c^3)*abs(a^3*b^2 - 4*a^4*c)*e + (10*a^6*b^9*c^2 - 138*a^7*b^7*c^3 + 680*a^8*b^5*c^4 - 1376*a^9*b^3*c^5 + 896*a^10*b*c^6 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^9 + 69*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^7*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^8*c - 340*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 - 98*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^6*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^7*c^2 + 688*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 + 288*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^4*c^3 + 49*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^5*c^3 - 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b*c^4 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^2*c^4 - 144*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^3*c^4 + 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b*c^5 - 10*(b^2 - 4*a*c)*a^6*b^7*c^2 + 98*(b^2 - 4*a*c)*a^7*b^5*c^3 - 288*(b^2 - 4*a*c)*a^8*b^3*c^4 + 224*(b^2 - 4*a*c)*a^9*b*c^5)*d + (2*a^8*b^7*c^2 - 40*a^9*b^5*c^3 + 224*a^10*b^3*c^4 - 384*a^11*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^7 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^6*c - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^3*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b*c^3 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b*c^4 - 2*(b^2 - 4*a*c)*a^8*b^5*c^2 + 32*(b^2 - 4*a*c)*a^9*b^3*c^3 - 96*(b^2 - 4*a*c)*a^10*b*c^4)*f - (6*a^7*b^8*c^2 - 80*a^8*b^6*c^3 + 352*a^9*b^4*c^4 - 512*a^10*b^2*c^5 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^8 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^6*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^7*c - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^4*c^2 - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^6*c^2 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^2*c^3 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^4*c^3 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^2*c^4 - 6*(b^2 - 4*a*c)*a^7*b^6*c^2 + 56*(b^2 - 4*a*c)*a^8*b^4*c^3 - 128*(b^2 - 4*a*c)*a^9*b^2*c^4)*e)*arctan(2*sqrt(1/2)*x/sqrt((a^3*b^3 - 4*a^4*b*c - sqrt((a^3*b^3 - 4*a^4*b*c)^2 - 4*(a^4*b^2 - 4*a^5*c)*(a^3*b^2*c - 4*a^4*c^2)))/(a^3*b^2*c - 4*a^4*c^2)))/((a^7*b^6 - 12*a^8*b^4*c - 2*a^7*b^5*c + 48*a^9*b^2*c^2 + 16*a^8*b^3*c^2 + a^7*b^4*c^2 - 64*a^10*c^3 - 32*a^9*b*c^3 - 8*a^8*b^2*c^3 + 16*a^9*c^4)*abs(a^3*b^2 - 4*a^4*c)*abs(c)) + 1/3*(6*b*d*x^2 - 3*a*x^2*e - a*d)/(a^3*x^3)","B",0
74,1,63,0,0.361526," ","integrate(x^9*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x, algorithm=""giac"")","\frac{5}{8} \, x^{8} - \frac{9}{2} \, x^{6} + \frac{49}{2} \, x^{4} - \frac{293}{2} \, x^{2} - \frac{394 \, x^{4} + 767 \, x^{2} + 374}{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*(394*x^4 + 767*x^2 + 374)/(x^4 + 3*x^2 + 2) + 392*log(x^2 + 2) + 2*log(x^2 + 1)","A",0
75,1,58,0,0.322652," ","integrate(x^7*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x, algorithm=""giac"")","\frac{5}{6} \, x^{6} - \frac{27}{4} \, x^{4} + 49 \, x^{2} + \frac{293 \, x^{4} + 465 \, x^{2} + 174}{4 \, {\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 + 1/4*(293*x^4 + 465*x^2 + 174)/(x^4 + 3*x^2 + 2) - 144*log(x^2 + 2) - 5/2*log(x^2 + 1)","A",0
76,1,53,0,0.367355," ","integrate(x^5*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x, algorithm=""giac"")","\frac{5}{4} \, x^{4} - \frac{27}{2} \, x^{2} - \frac{49 \, x^{4} + 44 \, x^{2} - 4}{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*(49*x^4 + 44*x^2 - 4)/(x^4 + 3*x^2 + 2) + 46*log(x^2 + 2) + 3*log(x^2 + 1)","A",0
77,1,45,0,0.390439," ","integrate(x^3*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x, algorithm=""giac"")","\frac{5}{2} \, x^{2} - \frac{51 \, x^{2} + 50}{2 \, {\left(x^{2} + 2\right)} {\left(x^{2} + 1\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^2 + 2)*(x^2 + 1)) - 10*log(x^2 + 2) - 7/2*log(x^2 + 1)","A",0
78,1,40,0,0.354148," ","integrate(x*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x, algorithm=""giac"")","\frac{25 \, x^{2} + 24}{2 \, {\left(x^{2} + 2\right)} {\left(x^{2} + 1\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^2 + 2)*(x^2 + 1)) - 3/2*log(x^2 + 2) + 4*log(x^2 + 1)","A",0
79,1,47,0,0.377147," ","integrate((5*x^6+3*x^4+x^2+4)/x/(x^4+3*x^2+2)^2,x, algorithm=""giac"")","\frac{x^{4} - 21 \, x^{2} - 20}{4 \, {\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,"1/4*(x^4 - 21*x^2 - 20)/(x^4 + 3*x^2 + 2) + 4*log(x^2 + 2) - 9/2*log(x^2 + 1) + 1/2*log(x^2)","A",0
80,1,53,0,0.373771," ","integrate((5*x^6+3*x^4+x^2+4)/x^3/(x^4+3*x^2+2)^2,x, algorithm=""giac"")","\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
81,1,66,0,0.340806," ","integrate((5*x^6+3*x^4+x^2+4)/x^5/(x^4+3*x^2+2)^2,x, algorithm=""giac"")","\frac{23 \, x^{4} + 51 \, x^{2} + 36}{16 \, {\left(x^{4} + 3 \, x^{2} + 2\right)}} - \frac{69 \, x^{4} - 22 \, x^{2} + 4}{16 \, x^{4}} + \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,"1/16*(23*x^4 + 51*x^2 + 36)/(x^4 + 3*x^2 + 2) - 1/16*(69*x^4 - 22*x^2 + 4)/x^4 + 21/8*log(x^2 + 2) - 11/2*log(x^2 + 1) + 23/8*log(x^2)","A",0
82,1,58,0,0.331465," ","integrate(x^8*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x, algorithm=""giac"")","\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
83,1,51,0,0.313978," ","integrate(x^6*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x, algorithm=""giac"")","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
84,1,48,0,0.306061," ","integrate(x^4*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x, algorithm=""giac"")","\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
85,1,43,0,0.340256," ","integrate(x^2*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x, algorithm=""giac"")","-\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
86,1,40,0,0.338683," ","integrate((5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x, algorithm=""giac"")","-\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
87,1,45,0,0.384249," ","integrate((5*x^6+3*x^4+x^2+4)/x^2/(x^4+3*x^2+2)^2,x, algorithm=""giac"")","\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
88,1,52,0,0.386450," ","integrate((5*x^6+3*x^4+x^2+4)/x^4/(x^4+3*x^2+2)^2,x, algorithm=""giac"")","-\frac{71}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) - \frac{9 \, x^{3} + 5 \, x}{8 \, {\left(x^{4} + 3 \, x^{2} + 2\right)}} + \frac{33 \, x^{2} - 4}{12 \, x^{3}} + \frac{21}{2} \, \arctan\left(x\right)"," ",0,"-71/16*sqrt(2)*arctan(1/2*sqrt(2)*x) - 1/8*(9*x^3 + 5*x)/(x^4 + 3*x^2 + 2) + 1/12*(33*x^2 - 4)/x^3 + 21/2*arctan(x)","A",0
89,1,57,0,0.342546," ","integrate((5*x^6+3*x^4+x^2+4)/x^6/(x^4+3*x^2+2)^2,x, algorithm=""giac"")","\frac{97}{32} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) + \frac{5 \, x^{3} - 3 \, x}{16 \, {\left(x^{4} + 3 \, x^{2} + 2\right)}} - \frac{345 \, x^{4} - 55 \, x^{2} + 12}{60 \, x^{5}} - \frac{23}{2} \, \arctan\left(x\right)"," ",0,"97/32*sqrt(2)*arctan(1/2*sqrt(2)*x) + 1/16*(5*x^3 - 3*x)/(x^4 + 3*x^2 + 2) - 1/60*(345*x^4 - 55*x^2 + 12)/x^5 - 23/2*arctan(x)","A",0
90,1,62,0,0.449856," ","integrate((5*x^6+3*x^4+x^2+4)/x^8/(x^4+3*x^2+2)^2,x, algorithm=""giac"")","-\frac{123}{64} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) + \frac{3 \, x^{3} + 19 \, x}{32 \, {\left(x^{4} + 3 \, x^{2} + 2\right)}} + \frac{14385 \, x^{6} - 3220 \, x^{4} + 924 \, x^{2} - 240}{1680 \, x^{7}} + \frac{25}{2} \, \arctan\left(x\right)"," ",0,"-123/64*sqrt(2)*arctan(1/2*sqrt(2)*x) + 1/32*(3*x^3 + 19*x)/(x^4 + 3*x^2 + 2) + 1/1680*(14385*x^6 - 3220*x^4 + 924*x^2 - 240)/x^7 + 25/2*arctan(x)","A",0
91,1,61,0,0.316861," ","integrate(x^10*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^3,x, algorithm=""giac"")","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^{4} + 3 \, x^{2} + 2\right)}^{2}} + \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^4 + 3*x^2 + 2)^2 + 477/8*arctan(x)","A",0
92,1,58,0,0.413736," ","integrate(x^8*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^3,x, algorithm=""giac"")","\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^{4} + 3 \, x^{2} + 2\right)}^{2}} - \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^4 + 3*x^2 + 2)^2 - 449/8*arctan(x)","A",0
93,1,53,0,0.323927," ","integrate(x^6*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^3,x, algorithm=""giac"")","-\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^{4} + 3 \, x^{2} + 2\right)}^{2}} + \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^4 + 3*x^2 + 2)^2 + 413/8*arctan(x)","A",0
94,1,50,0,0.344950," ","integrate(x^4*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^3,x, algorithm=""giac"")","\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^{4} + 3 \, x^{2} + 2\right)}^{2}} - \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^4 + 3*x^2 + 2)^2 - 369/8*arctan(x)","A",0
95,1,50,0,0.379308," ","integrate(x^2*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^3,x, algorithm=""giac"")","-\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^{4} + 3 \, x^{2} + 2\right)}^{2}} + \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^4 + 3*x^2 + 2)^2 + 317/8*arctan(x)","A",0
96,1,50,0,0.327908," ","integrate((5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^3,x, algorithm=""giac"")","\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^{4} + 3 \, x^{2} + 2\right)}^{2}} - \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^4 + 3*x^2 + 2)^2 - 257/8*arctan(x)","A",0
97,1,55,0,0.338490," ","integrate((5*x^6+3*x^4+x^2+4)/x^2/(x^4+3*x^2+2)^3,x, algorithm=""giac"")","-\frac{1119}{64} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) - \frac{347 \, x^{7} + 1588 \, x^{5} + 2291 \, x^{3} + 1058 \, x}{32 \, {\left(x^{4} + 3 \, x^{2} + 2\right)}^{2}} - \frac{1}{2 \, x} + \frac{189}{8} \, \arctan\left(x\right)"," ",0,"-1119/64*sqrt(2)*arctan(1/2*sqrt(2)*x) - 1/32*(347*x^7 + 1588*x^5 + 2291*x^3 + 1058*x)/(x^4 + 3*x^2 + 2)^2 - 1/2/x + 189/8*arctan(x)","A",0
98,1,62,0,0.361287," ","integrate((5*x^6+3*x^4+x^2+4)/x^4/(x^4+3*x^2+2)^3,x, algorithm=""giac"")","\frac{1611}{128} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) + \frac{571 \, x^{7} + 2664 \, x^{5} + 3959 \, x^{3} + 1882 \, x}{64 \, {\left(x^{4} + 3 \, x^{2} + 2\right)}^{2}} + \frac{51 \, x^{2} - 4}{24 \, x^{3}} - \frac{113}{8} \, \arctan\left(x\right)"," ",0,"1611/128*sqrt(2)*arctan(1/2*sqrt(2)*x) + 1/64*(571*x^7 + 2664*x^5 + 3959*x^3 + 1882*x)/(x^4 + 3*x^2 + 2)^2 + 1/24*(51*x^2 - 4)/x^3 - 113/8*arctan(x)","A",0
99,1,67,0,0.356029," ","integrate((5*x^6+3*x^4+x^2+4)/x^6/(x^4+3*x^2+2)^3,x, algorithm=""giac"")","-\frac{2207}{256} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right) - \frac{999 \, x^{7} + 4768 \, x^{5} + 7291 \, x^{3} + 3554 \, x}{128 \, {\left(x^{4} + 3 \, x^{2} + 2\right)}^{2}} - \frac{1395 \, x^{4} - 170 \, x^{2} + 24}{240 \, x^{5}} + \frac{29}{8} \, \arctan\left(x\right)"," ",0,"-2207/256*sqrt(2)*arctan(1/2*sqrt(2)*x) - 1/128*(999*x^7 + 4768*x^5 + 7291*x^3 + 3554*x)/(x^4 + 3*x^2 + 2)^2 - 1/240*(1395*x^4 - 170*x^2 + 24)/x^5 + 29/8*arctan(x)","A",0
100,1,76,0,1.017620," ","integrate(x^9*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x, algorithm=""giac"")","\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{366 \, x^{4} + 557 \, x^{2} + 723}{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)) + 1/8*(366*x^4 + 557*x^2 + 723)/(x^4 + 2*x^2 + 3) - 183/4*log(x^4 + 2*x^2 + 3)","A",0
101,1,71,0,1.168682," ","integrate(x^7*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x, algorithm=""giac"")","\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{76 \, x^{4} + 27 \, x^{2} + 153}{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)) - 1/8*(76*x^4 + 27*x^2 + 153)/(x^4 + 2*x^2 + 3) + 19/2*log(x^4 + 2*x^2 + 3)","A",0
102,1,66,0,1.090452," ","integrate(x^5*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x, algorithm=""giac"")","\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{38 \, x^{4} + 101 \, x^{2} + 39}{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)) - 1/8*(38*x^4 + 101*x^2 + 39)/(x^4 + 2*x^2 + 3) + 19/4*log(x^4 + 2*x^2 + 3)","A",0
103,1,54,0,1.184469," ","integrate(x^3*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x, algorithm=""giac"")","\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
104,1,49,0,1.133272," ","integrate(x*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x, algorithm=""giac"")","-\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
105,1,62,0,1.103302," ","integrate((5*x^6+3*x^4+x^2+4)/x/(x^4+2*x^2+3)^2,x, algorithm=""giac"")","\frac{89}{144} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x^{2} + 1\right)}\right) + \frac{8 \, x^{4} - 59 \, x^{2} + 99}{72 \, {\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)) + 1/72*(8*x^4 - 59*x^2 + 99)/(x^4 + 2*x^2 + 3) - 1/9*log(x^4 + 2*x^2 + 3) + 2/9*log(x^2)","A",0
106,1,66,0,1.072457," ","integrate((5*x^6+3*x^4+x^2+4)/x^3/(x^4+2*x^2+3)^2,x, algorithm=""giac"")","-\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
107,1,79,0,1.164740," ","integrate((5*x^6+3*x^4+x^2+4)/x^5/(x^4+2*x^2+3)^2,x, algorithm=""giac"")","\frac{125}{432} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x^{2} + 1\right)}\right) + \frac{26 \, x^{4} + 177 \, x^{2} + 253}{216 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}} - \frac{39 \, x^{4} - 26 \, x^{2} + 12}{108 \, x^{4}} - \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)) + 1/216*(26*x^4 + 177*x^2 + 253)/(x^4 + 2*x^2 + 3) - 1/108*(39*x^4 - 26*x^2 + 12)/x^4 - 13/108*log(x^4 + 2*x^2 + 3) + 13/54*log(x^2)","A",0
108,1,84,0,1.165257," ","integrate((5*x^6+3*x^4+x^2+4)/x^7/(x^4+2*x^2+3)^2,x, algorithm=""giac"")","-\frac{1237}{3888} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x^{2} + 1\right)}\right) + \frac{122 \, x^{4} - 281 \, x^{2} + 441}{1944 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}} - \frac{671 \, x^{6} + 702 \, x^{4} - 351 \, x^{2} + 216}{2916 \, x^{6}} - \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)) + 1/1944*(122*x^4 - 281*x^2 + 441)/(x^4 + 2*x^2 + 3) - 1/2916*(671*x^6 + 702*x^4 - 351*x^2 + 216)/x^6 - 61/972*log(x^4 + 2*x^2 + 3) + 61/486*log(x^2)","A",0
109,1,585,0,1.887064," ","integrate(x^8*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x, algorithm=""giac"")","\frac{5}{7} \, x^{7} - \frac{17}{5} \, x^{5} + \frac{19}{3} \, x^{3} + \frac{1}{20736} \, \sqrt{2} {\left(1339 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 24102 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 24102 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 1339 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} - 35532 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} + 35532 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x + 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) + \frac{1}{20736} \, \sqrt{2} {\left(1339 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 24102 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 24102 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 1339 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} - 35532 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} + 35532 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x - 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) + \frac{1}{41472} \, \sqrt{2} {\left(24102 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 1339 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 1339 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 24102 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 35532 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} - 35532 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} + 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) - \frac{1}{41472} \, \sqrt{2} {\left(24102 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 1339 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 1339 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 24102 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 35532 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} - 35532 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} - 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) + 38 \, x + \frac{25 \, {\left(5 \, x^{3} + 3 \, x\right)}}{8 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}}"," ",0,"5/7*x^7 - 17/5*x^5 + 19/3*x^3 + 1/20736*sqrt(2)*(1339*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 24102*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 24102*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 1339*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) - 35532*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) + 35532*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x + 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) + 1/20736*sqrt(2)*(1339*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 24102*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 24102*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 1339*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) - 35532*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) + 35532*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x - 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) + 1/41472*sqrt(2)*(24102*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 1339*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 1339*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 24102*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 35532*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) - 35532*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 + 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) - 1/41472*sqrt(2)*(24102*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 1339*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 1339*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 24102*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 35532*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) - 35532*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 - 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) + 38*x + 25/8*(5*x^3 + 3*x)/(x^4 + 2*x^2 + 3)","B",0
110,1,576,0,1.850852," ","integrate(x^6*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x, algorithm=""giac"")","x^{5} - \frac{17}{3} \, x^{3} - \frac{1}{2304} \, \sqrt{2} {\left(31 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 558 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 558 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 31 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 2124 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} - 2124 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x + 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) - \frac{1}{2304} \, \sqrt{2} {\left(31 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 558 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 558 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 31 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 2124 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} - 2124 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x - 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) - \frac{1}{4608} \, \sqrt{2} {\left(558 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 31 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 31 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 558 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} + 2124 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} + 2124 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} + 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) + \frac{1}{4608} \, \sqrt{2} {\left(558 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 31 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 31 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 558 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} + 2124 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} + 2124 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} - 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) + 19 \, x - \frac{25 \, {\left(x^{3} - 3 \, x\right)}}{8 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}}"," ",0,"x^5 - 17/3*x^3 - 1/2304*sqrt(2)*(31*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 558*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 558*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 31*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) + 2124*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) - 2124*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x + 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) - 1/2304*sqrt(2)*(31*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 558*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 558*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 31*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) + 2124*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) - 2124*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x - 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) - 1/4608*sqrt(2)*(558*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 31*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 31*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 558*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) + 2124*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) + 2124*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 + 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) + 1/4608*sqrt(2)*(558*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 31*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 31*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 558*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) + 2124*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) + 2124*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 - 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) + 19*x - 25/8*(x^3 - 3*x)/(x^4 + 2*x^2 + 3)","B",0
111,1,573,0,1.854111," ","integrate(x^4*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x, algorithm=""giac"")","\frac{5}{3} \, x^{3} - \frac{1}{20736} \, \sqrt{2} {\left(127 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 2286 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 2286 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 127 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} - 17388 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} + 17388 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x + 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) - \frac{1}{20736} \, \sqrt{2} {\left(127 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 2286 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 2286 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 127 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} - 17388 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} + 17388 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x - 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) - \frac{1}{41472} \, \sqrt{2} {\left(2286 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 127 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 127 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 2286 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 17388 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} - 17388 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} + 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) + \frac{1}{41472} \, \sqrt{2} {\left(2286 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 127 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 127 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 2286 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 17388 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} - 17388 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} - 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) - 17 \, x - \frac{25 \, {\left(x^{3} + 3 \, x\right)}}{8 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}}"," ",0,"5/3*x^3 - 1/20736*sqrt(2)*(127*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 2286*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 2286*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 127*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) - 17388*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) + 17388*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x + 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) - 1/20736*sqrt(2)*(127*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 2286*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 2286*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 127*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) - 17388*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) + 17388*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x - 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) - 1/41472*sqrt(2)*(2286*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 127*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 127*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 2286*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 17388*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) - 17388*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 + 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) + 1/41472*sqrt(2)*(2286*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 127*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 127*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 2286*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 17388*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) - 17388*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 - 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) - 17*x - 25/8*(x^3 + 3*x)/(x^4 + 2*x^2 + 3)","B",0
112,1,566,0,1.824913," ","integrate(x^2*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x, algorithm=""giac"")","\frac{1}{6912} \, \sqrt{2} {\left(37 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 666 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 666 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 37 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} - 1740 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} + 1740 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x + 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) + \frac{1}{6912} \, \sqrt{2} {\left(37 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 666 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 666 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 37 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} - 1740 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} + 1740 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x - 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) + \frac{1}{13824} \, \sqrt{2} {\left(666 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 37 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 37 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 666 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 1740 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} - 1740 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} + 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) - \frac{1}{13824} \, \sqrt{2} {\left(666 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 37 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 37 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 666 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 1740 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} - 1740 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} - 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) + 5 \, x + \frac{25 \, {\left(x^{3} + x\right)}}{8 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}}"," ",0,"1/6912*sqrt(2)*(37*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 666*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 666*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 37*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) - 1740*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) + 1740*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x + 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) + 1/6912*sqrt(2)*(37*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 666*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 666*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 37*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) - 1740*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) + 1740*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x - 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) + 1/13824*sqrt(2)*(666*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 37*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 37*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 666*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 1740*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) - 1740*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 + 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) - 1/13824*sqrt(2)*(666*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 37*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 37*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 666*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 1740*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) - 1740*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 - 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) + 5*x + 25/8*(x^3 + x)/(x^4 + 2*x^2 + 3)","B",0
113,1,565,0,1.818192," ","integrate((5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x, algorithm=""giac"")","-\frac{1}{62208} \, \sqrt{2} {\left(95 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 1710 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 1710 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 95 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} - 252 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} + 252 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x + 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) - \frac{1}{62208} \, \sqrt{2} {\left(95 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 1710 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 1710 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 95 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} - 252 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} + 252 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x - 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) - \frac{1}{124416} \, \sqrt{2} {\left(1710 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 95 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 95 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 1710 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 252 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} - 252 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} + 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) + \frac{1}{124416} \, \sqrt{2} {\left(1710 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 95 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 95 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 1710 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 252 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} - 252 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} - 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) - \frac{25 \, {\left(x^{3} - x\right)}}{24 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}}"," ",0,"-1/62208*sqrt(2)*(95*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 1710*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 1710*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 95*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) - 252*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) + 252*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x + 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) - 1/62208*sqrt(2)*(95*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 1710*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 1710*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 95*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) - 252*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) + 252*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x - 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) - 1/124416*sqrt(2)*(1710*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 95*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 95*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 1710*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 252*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) - 252*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 + 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) + 1/124416*sqrt(2)*(1710*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 95*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 95*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 1710*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 252*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) - 252*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 - 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) - 25/24*(x^3 - x)/(x^4 + 2*x^2 + 3)","B",0
114,1,572,0,1.936819," ","integrate((5*x^6+3*x^4+x^2+4)/x^2/(x^4+2*x^2+3)^2,x, algorithm=""giac"")","\frac{1}{62208} \, \sqrt{2} {\left(19 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 342 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 342 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 19 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 252 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} - 252 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x + 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) + \frac{1}{62208} \, \sqrt{2} {\left(19 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 342 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 342 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 19 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 252 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} - 252 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x - 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) + \frac{1}{124416} \, \sqrt{2} {\left(342 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 19 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 19 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 342 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} + 252 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} + 252 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} + 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) - \frac{1}{124416} \, \sqrt{2} {\left(342 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 19 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 19 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 342 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} + 252 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} + 252 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} - 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) - \frac{19 \, x^{4} + 63 \, x^{2} + 32}{24 \, {\left(x^{5} + 2 \, x^{3} + 3 \, x\right)}}"," ",0,"1/62208*sqrt(2)*(19*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 342*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 342*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 19*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) + 252*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) - 252*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x + 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) + 1/62208*sqrt(2)*(19*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 342*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 342*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 19*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) + 252*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) - 252*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x - 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) + 1/124416*sqrt(2)*(342*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 19*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 19*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 342*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) + 252*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) + 252*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 + 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) - 1/124416*sqrt(2)*(342*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 19*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 19*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 342*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) + 252*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) + 252*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 - 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) - 1/24*(19*x^4 + 63*x^2 + 32)/(x^5 + 2*x^3 + 3*x)","B",0
115,1,579,0,1.850921," ","integrate((5*x^6+3*x^4+x^2+4)/x^4/(x^4+2*x^2+3)^2,x, algorithm=""giac"")","-\frac{1}{559872} \, \sqrt{2} {\left(229 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 4122 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 4122 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 229 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} - 4932 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} + 4932 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x + 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) - \frac{1}{559872} \, \sqrt{2} {\left(229 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 4122 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 4122 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 229 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} - 4932 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} + 4932 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x - 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) - \frac{1}{1119744} \, \sqrt{2} {\left(4122 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 229 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 229 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 4122 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 4932 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} - 4932 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} + 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) + \frac{1}{1119744} \, \sqrt{2} {\left(4122 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 229 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 229 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 4122 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 4932 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} - 4932 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} - 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) + \frac{25 \, {\left(5 \, x^{3} + 7 \, x\right)}}{216 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}} + \frac{13 \, x^{2} - 4}{27 \, x^{3}}"," ",0,"-1/559872*sqrt(2)*(229*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 4122*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 4122*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 229*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) - 4932*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) + 4932*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x + 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) - 1/559872*sqrt(2)*(229*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 4122*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 4122*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 229*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) - 4932*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) + 4932*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x - 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) - 1/1119744*sqrt(2)*(4122*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 229*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 229*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 4122*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 4932*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) - 4932*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 + 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) + 1/1119744*sqrt(2)*(4122*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 229*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 229*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 4122*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 4932*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) - 4932*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 - 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) + 25/216*(5*x^3 + 7*x)/(x^4 + 2*x^2 + 3) + 1/27*(13*x^2 - 4)/x^3","B",0
116,1,584,0,1.784682," ","integrate((5*x^6+3*x^4+x^2+4)/x^6/(x^4+2*x^2+3)^2,x, algorithm=""giac"")","\frac{1}{1679616} \, \sqrt{2} {\left(487 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 8766 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 8766 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 487 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 16668 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} - 16668 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x + 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) + \frac{1}{1679616} \, \sqrt{2} {\left(487 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 8766 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 8766 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 487 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 16668 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} - 16668 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x - 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) + \frac{1}{3359232} \, \sqrt{2} {\left(8766 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 487 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 487 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 8766 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} + 16668 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} + 16668 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} + 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) - \frac{1}{3359232} \, \sqrt{2} {\left(8766 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 487 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 487 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 8766 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} + 16668 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} + 16668 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} - 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) - \frac{25 \, {\left(7 \, x^{3} - x\right)}}{648 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}} - \frac{195 \, x^{4} - 65 \, x^{2} + 36}{405 \, x^{5}}"," ",0,"1/1679616*sqrt(2)*(487*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 8766*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 8766*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 487*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) + 16668*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) - 16668*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x + 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) + 1/1679616*sqrt(2)*(487*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 8766*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 8766*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 487*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) + 16668*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) - 16668*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x - 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) + 1/3359232*sqrt(2)*(8766*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 487*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 487*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 8766*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) + 16668*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) + 16668*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 + 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) - 1/3359232*sqrt(2)*(8766*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 487*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 487*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 8766*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) + 16668*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) + 16668*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 - 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) - 25/648*(7*x^3 - x)/(x^4 + 2*x^2 + 3) - 1/405*(195*x^4 - 65*x^2 + 36)/x^5","B",0
117,1,588,0,2.694170," ","integrate(x^10*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^3,x, algorithm=""giac"")","x^{5} - 9 \, x^{3} - \frac{1}{13824} \, \sqrt{2} {\left(37 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 666 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 666 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 37 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 41823 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} - 41823 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x + 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) - \frac{1}{13824} \, \sqrt{2} {\left(37 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 666 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 666 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 37 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 41823 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} - 41823 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x - 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) - \frac{1}{27648} \, \sqrt{2} {\left(666 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 37 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 37 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 666 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} + 41823 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} + 41823 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} + 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) + \frac{1}{27648} \, \sqrt{2} {\left(666 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 37 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 37 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 666 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} + 41823 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} + 41823 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} - 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) + 58 \, x + \frac{252 \, x^{7} + 3809 \, x^{5} + 6666 \, x^{3} + 8415 \, x}{64 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}^{2}}"," ",0,"x^5 - 9*x^3 - 1/13824*sqrt(2)*(37*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 666*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 666*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 37*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) + 41823*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) - 41823*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x + 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) - 1/13824*sqrt(2)*(37*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 666*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 666*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 37*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) + 41823*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) - 41823*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x - 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) - 1/27648*sqrt(2)*(666*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 37*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 37*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 666*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) + 41823*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) + 41823*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 + 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) + 1/27648*sqrt(2)*(666*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 37*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 37*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 666*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) + 41823*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) + 41823*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 - 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) + 58*x + 1/64*(252*x^7 + 3809*x^5 + 6666*x^3 + 8415*x)/(x^4 + 2*x^2 + 3)^2","B",0
118,1,585,0,2.588274," ","integrate(x^8*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^3,x, algorithm=""giac"")","\frac{5}{3} \, x^{3} - \frac{7}{55296} \, \sqrt{2} {\left(137 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 2466 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 2466 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 137 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} - 11232 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} + 11232 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x + 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) - \frac{7}{55296} \, \sqrt{2} {\left(137 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 2466 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 2466 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 137 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} - 11232 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} + 11232 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x - 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) - \frac{7}{110592} \, \sqrt{2} {\left(2466 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 137 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 137 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 2466 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 11232 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} - 11232 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} + 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) + \frac{7}{110592} \, \sqrt{2} {\left(2466 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 137 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 137 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 2466 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 11232 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} - 11232 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} - 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) - 27 \, x - \frac{835 \, x^{7} + 3138 \, x^{5} + 4941 \, x^{3} + 4104 \, x}{64 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}^{2}}"," ",0,"5/3*x^3 - 7/55296*sqrt(2)*(137*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 2466*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 2466*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 137*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) - 11232*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) + 11232*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x + 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) - 7/55296*sqrt(2)*(137*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 2466*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 2466*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 137*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) - 11232*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) + 11232*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x - 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) - 7/110592*sqrt(2)*(2466*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 137*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 137*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 2466*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 11232*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) - 11232*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 + 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) + 7/110592*sqrt(2)*(2466*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 137*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 137*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 2466*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 11232*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) - 11232*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 - 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) - 27*x - 1/64*(835*x^7 + 3138*x^5 + 4941*x^3 + 4104*x)/(x^4 + 2*x^2 + 3)^2","B",0
119,1,580,0,2.612440," ","integrate(x^6*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^3,x, algorithm=""giac"")","\frac{1}{82944} \, \sqrt{2} {\left(661 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 11898 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 11898 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 661 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} - 20466 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} + 20466 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x + 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) + \frac{1}{82944} \, \sqrt{2} {\left(661 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 11898 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 11898 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 661 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} - 20466 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} + 20466 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x - 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) + \frac{1}{165888} \, \sqrt{2} {\left(11898 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 661 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 661 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 11898 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 20466 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} - 20466 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} + 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) - \frac{1}{165888} \, \sqrt{2} {\left(11898 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 661 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 661 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 11898 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 20466 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} - 20466 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} - 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) + 5 \, x + \frac{406 \, x^{7} + 889 \, x^{5} + 1272 \, x^{3} + 531 \, x}{64 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}^{2}}"," ",0,"1/82944*sqrt(2)*(661*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 11898*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 11898*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 661*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) - 20466*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) + 20466*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x + 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) + 1/82944*sqrt(2)*(661*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 11898*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 11898*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 661*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) - 20466*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) + 20466*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x - 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) + 1/165888*sqrt(2)*(11898*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 661*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 661*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 11898*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 20466*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) - 20466*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 + 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) - 1/165888*sqrt(2)*(11898*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 661*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 661*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 11898*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 20466*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) - 20466*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 - 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) + 5*x + 1/64*(406*x^7 + 889*x^5 + 1272*x^3 + 531*x)/(x^4 + 2*x^2 + 3)^2","B",0
120,1,577,0,2.599668," ","integrate(x^4*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^3,x, algorithm=""giac"")","-\frac{1}{18432} \, \sqrt{2} {\left(29 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 522 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 522 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 29 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 552 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} - 552 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x + 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) - \frac{1}{18432} \, \sqrt{2} {\left(29 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 522 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 522 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 29 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 552 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} - 552 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x - 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) - \frac{1}{36864} \, \sqrt{2} {\left(522 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 29 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 29 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 522 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} + 552 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} + 552 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} + 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) + \frac{1}{36864} \, \sqrt{2} {\left(522 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 29 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 29 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 522 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} + 552 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} + 552 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} - 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) - \frac{59 \, x^{7} - 120 \, x^{5} - 199 \, x^{3} - 414 \, x}{64 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}^{2}}"," ",0,"-1/18432*sqrt(2)*(29*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 522*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 522*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 29*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) + 552*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) - 552*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x + 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) - 1/18432*sqrt(2)*(29*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 522*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 522*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 29*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) + 552*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) - 552*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x - 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) - 1/36864*sqrt(2)*(522*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 29*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 29*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 522*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) + 552*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) + 552*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 + 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) + 1/36864*sqrt(2)*(522*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 29*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 29*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 522*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) + 552*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) + 552*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 - 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) - 1/64*(59*x^7 - 120*x^5 - 199*x^3 - 414*x)/(x^4 + 2*x^2 + 3)^2","B",0
121,1,577,0,2.688353," ","integrate(x^2*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^3,x, algorithm=""giac"")","\frac{11}{124416} \, \sqrt{2} {\left(2 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 36 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 36 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 2 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 207 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} - 207 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x + 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) + \frac{11}{124416} \, \sqrt{2} {\left(2 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 36 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 36 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 2 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 207 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} - 207 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x - 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) + \frac{11}{248832} \, \sqrt{2} {\left(36 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 2 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 2 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 36 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} + 207 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} + 207 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} + 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) - \frac{11}{248832} \, \sqrt{2} {\left(36 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 2 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 2 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 36 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} + 207 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} + 207 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} - 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) - \frac{88 \, x^{7} + 529 \, x^{5} + 670 \, x^{3} + 759 \, x}{192 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}^{2}}"," ",0,"11/124416*sqrt(2)*(2*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 36*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 36*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 2*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) + 207*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) - 207*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x + 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) + 11/124416*sqrt(2)*(2*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 36*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 36*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 2*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) + 207*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) - 207*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x - 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) + 11/248832*sqrt(2)*(36*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 2*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 2*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 36*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) + 207*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) + 207*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 + 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) - 11/248832*sqrt(2)*(36*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 2*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 2*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 36*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) + 207*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) + 207*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 - 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) - 1/192*(88*x^7 + 529*x^5 + 670*x^3 + 759*x)/(x^4 + 2*x^2 + 3)^2","B",0
122,1,577,0,2.618100," ","integrate((5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^3,x, algorithm=""giac"")","-\frac{1}{165888} \, \sqrt{2} {\left(17 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 306 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 306 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 17 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 144 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} - 144 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x + 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) - \frac{1}{165888} \, \sqrt{2} {\left(17 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 306 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 306 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 17 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 144 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} - 144 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x - 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) - \frac{1}{331776} \, \sqrt{2} {\left(306 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 17 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 17 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 306 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} + 144 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} + 144 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} + 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) + \frac{1}{331776} \, \sqrt{2} {\left(306 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 17 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 17 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 306 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} + 144 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} + 144 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} - 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) + \frac{51 \, x^{7} + 166 \, x^{5} + 181 \, x^{3} + 292 \, x}{192 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}^{2}}"," ",0,"-1/165888*sqrt(2)*(17*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 306*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 306*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 17*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) + 144*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) - 144*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x + 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) - 1/165888*sqrt(2)*(17*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 306*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 306*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 17*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) + 144*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) - 144*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x - 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) - 1/331776*sqrt(2)*(306*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 17*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 17*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 306*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) + 144*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) + 144*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 + 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) + 1/331776*sqrt(2)*(306*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 17*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 17*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 306*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) + 144*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) + 144*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 - 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) + 1/192*(51*x^7 + 166*x^5 + 181*x^3 + 292*x)/(x^4 + 2*x^2 + 3)^2","B",0
123,1,582,0,3.265749," ","integrate((5*x^6+3*x^4+x^2+4)/x^2/(x^4+2*x^2+3)^3,x, algorithm=""giac"")","\frac{1}{746496} \, \sqrt{2} {\left(83 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 1494 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 1494 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 83 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} - 3114 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} + 3114 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x + 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) + \frac{1}{746496} \, \sqrt{2} {\left(83 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 1494 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 1494 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 83 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} - 3114 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} + 3114 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x - 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) + \frac{1}{1492992} \, \sqrt{2} {\left(1494 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 83 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 83 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 1494 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 3114 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} - 3114 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} + 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) - \frac{1}{1492992} \, \sqrt{2} {\left(1494 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 83 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 83 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 1494 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 3114 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} - 3114 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} - 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) - \frac{242 \, x^{7} + 809 \, x^{5} + 1676 \, x^{3} + 2475 \, x}{1728 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}^{2}} - \frac{4}{27 \, x}"," ",0,"1/746496*sqrt(2)*(83*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 1494*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 1494*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 83*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) - 3114*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) + 3114*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x + 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) + 1/746496*sqrt(2)*(83*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 1494*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 1494*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 83*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) - 3114*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) + 3114*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x - 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) + 1/1492992*sqrt(2)*(1494*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 83*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 83*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 1494*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 3114*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) - 3114*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 + 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) - 1/1492992*sqrt(2)*(1494*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 83*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 83*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 1494*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 3114*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) - 3114*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 - 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) - 1/1728*(242*x^7 + 809*x^5 + 1676*x^3 + 2475*x)/(x^4 + 2*x^2 + 3)^2 - 4/27/x","B",0
124,1,589,0,2.991200," ","integrate((5*x^6+3*x^4+x^2+4)/x^4/(x^4+2*x^2+3)^3,x, algorithm=""giac"")","-\frac{1}{13436928} \, \sqrt{2} {\left(2369 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 42642 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 42642 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 2369 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} - 80712 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} + 80712 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x + 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) - \frac{1}{13436928} \, \sqrt{2} {\left(2369 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 42642 \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 42642 \cdot 3^{\frac{3}{4}} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} + 2369 \cdot 3^{\frac{3}{4}} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} - 80712 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{6 \, \sqrt{3} + 18} + 80712 \cdot 3^{\frac{1}{4}} \sqrt{-6 \, \sqrt{3} + 18}\right)} \arctan\left(\frac{3^{\frac{3}{4}} {\left(x - 3^{\frac{1}{4}} \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}\right)}}{3 \, \sqrt{\frac{1}{6} \, \sqrt{3} + \frac{1}{2}}}\right) - \frac{1}{26873856} \, \sqrt{2} {\left(42642 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 2369 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 2369 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 42642 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 80712 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} - 80712 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} + 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) + \frac{1}{26873856} \, \sqrt{2} {\left(42642 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(\sqrt{3} + 3\right)} \sqrt{-6 \, \sqrt{3} + 18} - 2369 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(-6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 2369 \cdot 3^{\frac{3}{4}} {\left(6 \, \sqrt{3} + 18\right)}^{\frac{3}{2}} + 42642 \cdot 3^{\frac{3}{4}} \sqrt{6 \, \sqrt{3} + 18} {\left(\sqrt{3} - 3\right)} - 80712 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{-6 \, \sqrt{3} + 18} - 80712 \cdot 3^{\frac{1}{4}} \sqrt{6 \, \sqrt{3} + 18}\right)} \log\left(x^{2} - 2 \cdot 3^{\frac{1}{4}} x \sqrt{-\frac{1}{6} \, \sqrt{3} + \frac{1}{2}} + \sqrt{3}\right) + \frac{1025 \, x^{7} + 3524 \, x^{5} + 7523 \, x^{3} + 6522 \, x}{5184 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}^{2}} + \frac{21 \, x^{2} - 4}{81 \, x^{3}}"," ",0,"-1/13436928*sqrt(2)*(2369*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 42642*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 42642*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 2369*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) - 80712*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) + 80712*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x + 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) - 1/13436928*sqrt(2)*(2369*3^(3/4)*sqrt(2)*(6*sqrt(3) + 18)^(3/2) + 42642*3^(3/4)*sqrt(2)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 42642*3^(3/4)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) + 2369*3^(3/4)*(-6*sqrt(3) + 18)^(3/2) - 80712*3^(1/4)*sqrt(2)*sqrt(6*sqrt(3) + 18) + 80712*3^(1/4)*sqrt(-6*sqrt(3) + 18))*arctan(1/3*3^(3/4)*(x - 3^(1/4)*sqrt(-1/6*sqrt(3) + 1/2))/sqrt(1/6*sqrt(3) + 1/2)) - 1/26873856*sqrt(2)*(42642*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 2369*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 2369*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 42642*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 80712*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) - 80712*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 + 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) + 1/26873856*sqrt(2)*(42642*3^(3/4)*sqrt(2)*(sqrt(3) + 3)*sqrt(-6*sqrt(3) + 18) - 2369*3^(3/4)*sqrt(2)*(-6*sqrt(3) + 18)^(3/2) + 2369*3^(3/4)*(6*sqrt(3) + 18)^(3/2) + 42642*3^(3/4)*sqrt(6*sqrt(3) + 18)*(sqrt(3) - 3) - 80712*3^(1/4)*sqrt(2)*sqrt(-6*sqrt(3) + 18) - 80712*3^(1/4)*sqrt(6*sqrt(3) + 18))*log(x^2 - 2*3^(1/4)*x*sqrt(-1/6*sqrt(3) + 1/2) + sqrt(3)) + 1/5184*(1025*x^7 + 3524*x^5 + 7523*x^3 + 6522*x)/(x^4 + 2*x^2 + 3)^2 + 1/81*(21*x^2 - 4)/x^3","B",0
125,1,146,0,1.897949," ","integrate(x*(g*x^6+f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{c g x^{4} + 2 \, c f x^{2} - 2 \, b g x^{2}}{4 \, c^{2}} - \frac{{\left(b c f - b^{2} g + a c g - c^{2} e\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, c^{3}} + \frac{{\left(2 \, c^{3} d + b^{2} c f - 2 \, a c^{2} f - b^{3} g + 3 \, a b c g - b c^{2} e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} c^{3}}"," ",0,"1/4*(c*g*x^4 + 2*c*f*x^2 - 2*b*g*x^2)/c^2 - 1/4*(b*c*f - b^2*g + a*c*g - c^2*e)*log(c*x^4 + b*x^2 + a)/c^3 + 1/2*(2*c^3*d + b^2*c*f - 2*a*c^2*f - b^3*g + 3*a*b*c*g - b*c^2*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^3)","A",0
126,1,10761,0,9.952752," ","integrate(x^4*(g*x^6+f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{b c^{3} d x^{3} + b^{3} c f x^{3} - 3 \, a b c^{2} f x^{3} - b^{4} g x^{3} + 4 \, a b^{2} c g x^{3} - 2 \, a^{2} c^{2} g x^{3} - b^{2} c^{2} x^{3} e + 2 \, a c^{3} x^{3} e + 2 \, a c^{3} d x + a b^{2} c f x - 2 \, a^{2} c^{2} f x - a b^{3} g x + 3 \, a^{2} b c g x - a b c^{2} x e}{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} {\left(c x^{4} + b x^{2} + a\right)}} + \frac{{\left({\left(2 \, b^{3} c^{5} - 8 \, a b c^{6} - \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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{5}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}^{2} d - {\left(6 \, b^{5} c^{3} - 50 \, a b^{3} c^{4} + 104 \, 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 + 25 \, \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} - 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 26 \, \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} + 13 \, \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^{3} c^{3} + 26 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}^{2} f + {\left(10 \, b^{6} c^{2} - 88 \, a b^{4} c^{3} + 220 \, a^{2} b^{2} c^{4} - 112 \, 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} + 44 \, \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 - 110 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 48 \, \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} + 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 14 \, \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^{4} c^{2} + 48 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 28 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}^{2} g + {\left(2 \, b^{4} c^{4} - 20 \, a b^{2} c^{5} + 48 \, 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} + 10 \, \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} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 12 \, \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} + 6 \, \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^{2} c^{4} + 12 \, {\left(b^{2} - 4 \, a c\right)} a c^{5}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}^{2} e - 4 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{7} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{8} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{8} - 2 \, a b^{4} c^{8} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{9} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{9} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{9} + 16 \, a^{2} b^{2} c^{9} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{10} - 32 \, a^{3} c^{10} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{8} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{9}\right)} d {\left| b^{2} c^{3} - 4 \, a c^{4} \right|} - 2 \, {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{5} - 34 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{6} - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{6} - 6 \, a b^{6} c^{6} + 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{7} + 44 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{7} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{7} + 68 \, a^{2} b^{4} c^{7} - 160 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{8} - 80 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{8} - 22 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{8} - 256 \, a^{3} b^{2} c^{8} + 40 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{9} + 320 \, a^{4} c^{9} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{6} - 44 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{7} + 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{8}\right)} f {\left| b^{2} c^{3} - 4 \, a c^{4} \right|} + 2 \, {\left(5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{4} - 59 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{5} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{5} - 10 \, a b^{7} c^{5} + 232 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{6} + 78 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{6} + 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{6} + 118 \, a^{2} b^{5} c^{6} - 304 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{7} - 152 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{7} - 39 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{7} - 464 \, a^{3} b^{3} c^{7} + 76 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{8} + 608 \, a^{4} b c^{8} + 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{5} - 78 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{6} + 152 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{7}\right)} g {\left| b^{2} c^{3} - 4 \, a c^{4} \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{6} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{7} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{7} - 2 \, a b^{5} c^{7} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{8} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{8} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{8} + 16 \, a^{2} b^{3} c^{8} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{9} - 32 \, a^{3} b c^{9} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{7} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{8}\right)} {\left| b^{2} c^{3} - 4 \, a c^{4} \right|} e - {\left(2 \, b^{7} c^{11} - 8 \, a b^{5} c^{12} - 32 \, a^{2} b^{3} c^{13} + 128 \, a^{3} b c^{14} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{9} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{10} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{10} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{11} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{11} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{12} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{12} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{13} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{11} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{13}\right)} d + {\left(6 \, b^{9} c^{9} - 86 \, a b^{7} c^{10} + 440 \, a^{2} b^{5} c^{11} - 928 \, a^{3} b^{3} c^{12} + 640 \, a^{4} b c^{13} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{9} c^{7} + 43 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{8} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{8} - 220 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{9} - 62 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{9} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{9} + 464 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{10} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{10} + 31 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{10} - 320 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{11} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{11} - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{11} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{12} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{7} c^{9} + 62 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{10} - 192 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{11} + 160 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{12}\right)} f - {\left(10 \, b^{10} c^{8} - 148 \, a b^{8} c^{9} + 808 \, a^{2} b^{6} c^{10} - 1920 \, a^{3} b^{4} c^{11} + 1664 \, a^{4} b^{2} c^{12} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{10} c^{6} + 74 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{8} c^{7} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{9} c^{7} - 404 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{8} - 108 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{8} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{8} + 960 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{9} + 376 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{9} + 54 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{9} - 832 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{10} - 416 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{10} - 188 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{10} + 208 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{11} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{8} c^{8} + 108 \, {\left(b^{2} - 4 \, a c\right)} a b^{6} c^{9} - 376 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{10} + 416 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{11}\right)} g - {\left(2 \, b^{8} c^{10} - 32 \, a b^{6} c^{11} + 160 \, a^{2} b^{4} c^{12} - 256 \, a^{3} b^{2} c^{13} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{8} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{9} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{9} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{10} - 24 \, \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^{10} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{11} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{11} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{11} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{12} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{10} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{11} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{12}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} c^{3} - 4 \, a b c^{4} + \sqrt{{\left(b^{3} c^{3} - 4 \, a b c^{4}\right)}^{2} - 4 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} {\left(b^{2} c^{4} - 4 \, a c^{5}\right)}}}{b^{2} c^{4} - 4 \, a c^{5}}}}\right)}{16 \, {\left(a b^{6} c^{7} - 12 \, a^{2} b^{4} c^{8} - 2 \, a b^{5} c^{8} + 48 \, a^{3} b^{2} c^{9} + 16 \, a^{2} b^{3} c^{9} + a b^{4} c^{9} - 64 \, a^{4} c^{10} - 32 \, a^{3} b c^{10} - 8 \, a^{2} b^{2} c^{10} + 16 \, a^{3} c^{11}\right)} {\left| b^{2} c^{3} - 4 \, a c^{4} \right|} {\left| c \right|}} + \frac{{\left({\left(2 \, b^{3} c^{5} - 8 \, a b c^{6} - \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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{5}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}^{2} d - {\left(6 \, b^{5} c^{3} - 50 \, a b^{3} c^{4} + 104 \, 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 + 25 \, \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} - 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 26 \, \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} + 13 \, \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^{3} c^{3} + 26 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}^{2} f + {\left(10 \, b^{6} c^{2} - 88 \, a b^{4} c^{3} + 220 \, a^{2} b^{2} c^{4} - 112 \, 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} + 44 \, \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 - 110 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 48 \, \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} + 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 14 \, \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^{4} c^{2} + 48 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 28 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}^{2} g + {\left(2 \, b^{4} c^{4} - 20 \, a b^{2} c^{5} + 48 \, 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} + 10 \, \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} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 12 \, \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} + 6 \, \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^{2} c^{4} + 12 \, {\left(b^{2} - 4 \, a c\right)} a c^{5}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}^{2} e - 4 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{7} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{8} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{8} + 2 \, a b^{4} c^{8} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{9} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{9} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{9} - 16 \, a^{2} b^{2} c^{9} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{10} + 32 \, a^{3} c^{10} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{8} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{9}\right)} d {\left| b^{2} c^{3} - 4 \, a c^{4} \right|} - 2 \, {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{5} - 34 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{6} - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{6} + 6 \, a b^{6} c^{6} + 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{7} + 44 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{7} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{7} - 68 \, a^{2} b^{4} c^{7} - 160 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{8} - 80 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{8} - 22 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{8} + 256 \, a^{3} b^{2} c^{8} + 40 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{9} - 320 \, a^{4} c^{9} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{6} + 44 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{7} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{8}\right)} f {\left| b^{2} c^{3} - 4 \, a c^{4} \right|} + 2 \, {\left(5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{4} - 59 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{5} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{5} + 10 \, a b^{7} c^{5} + 232 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{6} + 78 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{6} + 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{6} - 118 \, a^{2} b^{5} c^{6} - 304 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{7} - 152 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{7} - 39 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{7} + 464 \, a^{3} b^{3} c^{7} + 76 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{8} - 608 \, a^{4} b c^{8} - 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{5} + 78 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{6} - 152 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{7}\right)} g {\left| b^{2} c^{3} - 4 \, a c^{4} \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{6} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{7} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{7} + 2 \, a b^{5} c^{7} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{8} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{8} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{8} - 16 \, a^{2} b^{3} c^{8} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{9} + 32 \, a^{3} b c^{9} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{7} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{8}\right)} {\left| b^{2} c^{3} - 4 \, a c^{4} \right|} e - {\left(2 \, b^{7} c^{11} - 8 \, a b^{5} c^{12} - 32 \, a^{2} b^{3} c^{13} + 128 \, a^{3} b c^{14} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{9} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{10} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{10} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{11} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{11} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{12} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{12} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{13} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{11} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{13}\right)} d + {\left(6 \, b^{9} c^{9} - 86 \, a b^{7} c^{10} + 440 \, a^{2} b^{5} c^{11} - 928 \, a^{3} b^{3} c^{12} + 640 \, a^{4} b c^{13} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{9} c^{7} + 43 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{8} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{8} - 220 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{9} - 62 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{9} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{9} + 464 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{10} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{10} + 31 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{10} - 320 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{11} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{11} - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{11} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{12} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{7} c^{9} + 62 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{10} - 192 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{11} + 160 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{12}\right)} f - {\left(10 \, b^{10} c^{8} - 148 \, a b^{8} c^{9} + 808 \, a^{2} b^{6} c^{10} - 1920 \, a^{3} b^{4} c^{11} + 1664 \, a^{4} b^{2} c^{12} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{10} c^{6} + 74 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{8} c^{7} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{9} c^{7} - 404 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{8} - 108 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{8} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{8} + 960 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{9} + 376 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{9} + 54 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{9} - 832 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{10} - 416 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{10} - 188 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{10} + 208 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{11} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{8} c^{8} + 108 \, {\left(b^{2} - 4 \, a c\right)} a b^{6} c^{9} - 376 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{10} + 416 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{11}\right)} g - {\left(2 \, b^{8} c^{10} - 32 \, a b^{6} c^{11} + 160 \, a^{2} b^{4} c^{12} - 256 \, a^{3} b^{2} c^{13} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{8} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{9} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{9} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{10} - 24 \, \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^{10} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{11} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{11} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{11} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{12} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{10} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{11} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{12}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} c^{3} - 4 \, a b c^{4} - \sqrt{{\left(b^{3} c^{3} - 4 \, a b c^{4}\right)}^{2} - 4 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} {\left(b^{2} c^{4} - 4 \, a c^{5}\right)}}}{b^{2} c^{4} - 4 \, a c^{5}}}}\right)}{16 \, {\left(a b^{6} c^{7} - 12 \, a^{2} b^{4} c^{8} - 2 \, a b^{5} c^{8} + 48 \, a^{3} b^{2} c^{9} + 16 \, a^{2} b^{3} c^{9} + a b^{4} c^{9} - 64 \, a^{4} c^{10} - 32 \, a^{3} b c^{10} - 8 \, a^{2} b^{2} c^{10} + 16 \, a^{3} c^{11}\right)} {\left| b^{2} c^{3} - 4 \, a c^{4} \right|} {\left| c \right|}} + \frac{c^{4} g x^{3} + 3 \, c^{4} f x - 6 \, b c^{3} g x}{3 \, c^{6}}"," ",0,"1/2*(b*c^3*d*x^3 + b^3*c*f*x^3 - 3*a*b*c^2*f*x^3 - b^4*g*x^3 + 4*a*b^2*c*g*x^3 - 2*a^2*c^2*g*x^3 - b^2*c^2*x^3*e + 2*a*c^3*x^3*e + 2*a*c^3*d*x + a*b^2*c*f*x - 2*a^2*c^2*f*x - a*b^3*g*x + 3*a^2*b*c*g*x - a*b*c^2*x*e)/((b^2*c^3 - 4*a*c^4)*(c*x^4 + b*x^2 + a)) + 1/16*((2*b^3*c^5 - 8*a*b*c^6 - 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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^5 - 2*(b^2 - 4*a*c)*b*c^5)*(b^2*c^3 - 4*a*c^4)^2*d - (6*b^5*c^3 - 50*a*b^3*c^4 + 104*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 + 25*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 - 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 26*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 + 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - 6*(b^2 - 4*a*c)*b^3*c^3 + 26*(b^2 - 4*a*c)*a*b*c^4)*(b^2*c^3 - 4*a*c^4)^2*f + (10*b^6*c^2 - 88*a*b^4*c^3 + 220*a^2*b^2*c^4 - 112*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 + 44*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 - 110*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 48*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 + 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 10*(b^2 - 4*a*c)*b^4*c^2 + 48*(b^2 - 4*a*c)*a*b^2*c^3 - 28*(b^2 - 4*a*c)*a^2*c^4)*(b^2*c^3 - 4*a*c^4)^2*g + (2*b^4*c^4 - 20*a*b^2*c^5 + 48*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 + 10*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 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 12*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 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^5 - 2*(b^2 - 4*a*c)*b^2*c^4 + 12*(b^2 - 4*a*c)*a*c^5)*(b^2*c^3 - 4*a*c^4)^2*e - 4*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^7 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^8 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^8 - 2*a*b^4*c^8 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^9 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^9 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^9 + 16*a^2*b^2*c^9 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^10 - 32*a^3*c^10 + 2*(b^2 - 4*a*c)*a*b^2*c^8 - 8*(b^2 - 4*a*c)*a^2*c^9)*d*abs(b^2*c^3 - 4*a*c^4) - 2*(3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^5 - 34*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^6 - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^6 - 6*a*b^6*c^6 + 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^7 + 44*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^7 + 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^7 + 68*a^2*b^4*c^7 - 160*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^8 - 80*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^8 - 22*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^8 - 256*a^3*b^2*c^8 + 40*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^9 + 320*a^4*c^9 + 6*(b^2 - 4*a*c)*a*b^4*c^6 - 44*(b^2 - 4*a*c)*a^2*b^2*c^7 + 80*(b^2 - 4*a*c)*a^3*c^8)*f*abs(b^2*c^3 - 4*a*c^4) + 2*(5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^4 - 59*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^5 - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^5 - 10*a*b^7*c^5 + 232*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^6 + 78*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^6 + 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^6 + 118*a^2*b^5*c^6 - 304*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^7 - 152*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^7 - 39*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^7 - 464*a^3*b^3*c^7 + 76*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^8 + 608*a^4*b*c^8 + 10*(b^2 - 4*a*c)*a*b^5*c^5 - 78*(b^2 - 4*a*c)*a^2*b^3*c^6 + 152*(b^2 - 4*a*c)*a^3*b*c^7)*g*abs(b^2*c^3 - 4*a*c^4) + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^6 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^7 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^7 - 2*a*b^5*c^7 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^8 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^8 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^8 + 16*a^2*b^3*c^8 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^9 - 32*a^3*b*c^9 + 2*(b^2 - 4*a*c)*a*b^3*c^7 - 8*(b^2 - 4*a*c)*a^2*b*c^8)*abs(b^2*c^3 - 4*a*c^4)*e - (2*b^7*c^11 - 8*a*b^5*c^12 - 32*a^2*b^3*c^13 + 128*a^3*b*c^14 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^9 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^10 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^10 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^11 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^11 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^12 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^12 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^13 - 2*(b^2 - 4*a*c)*b^5*c^11 + 32*(b^2 - 4*a*c)*a^2*b*c^13)*d + (6*b^9*c^9 - 86*a*b^7*c^10 + 440*a^2*b^5*c^11 - 928*a^3*b^3*c^12 + 640*a^4*b*c^13 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^9*c^7 + 43*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^8 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^8 - 220*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^9 - 62*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^9 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^9 + 464*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^10 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^10 + 31*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^10 - 320*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^11 - 160*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^11 - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^11 + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^12 - 6*(b^2 - 4*a*c)*b^7*c^9 + 62*(b^2 - 4*a*c)*a*b^5*c^10 - 192*(b^2 - 4*a*c)*a^2*b^3*c^11 + 160*(b^2 - 4*a*c)*a^3*b*c^12)*f - (10*b^10*c^8 - 148*a*b^8*c^9 + 808*a^2*b^6*c^10 - 1920*a^3*b^4*c^11 + 1664*a^4*b^2*c^12 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^10*c^6 + 74*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^8*c^7 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^9*c^7 - 404*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^8 - 108*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^8 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^8 + 960*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^9 + 376*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^9 + 54*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^9 - 832*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^10 - 416*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^10 - 188*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^10 + 208*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^11 - 10*(b^2 - 4*a*c)*b^8*c^8 + 108*(b^2 - 4*a*c)*a*b^6*c^9 - 376*(b^2 - 4*a*c)*a^2*b^4*c^10 + 416*(b^2 - 4*a*c)*a^3*b^2*c^11)*g - (2*b^8*c^10 - 32*a*b^6*c^11 + 160*a^2*b^4*c^12 - 256*a^3*b^2*c^13 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^8 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^9 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^9 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^10 - 24*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^10 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^11 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^11 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^11 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^12 - 2*(b^2 - 4*a*c)*b^6*c^10 + 24*(b^2 - 4*a*c)*a*b^4*c^11 - 64*(b^2 - 4*a*c)*a^2*b^2*c^12)*e)*arctan(2*sqrt(1/2)*x/sqrt((b^3*c^3 - 4*a*b*c^4 + sqrt((b^3*c^3 - 4*a*b*c^4)^2 - 4*(a*b^2*c^3 - 4*a^2*c^4)*(b^2*c^4 - 4*a*c^5)))/(b^2*c^4 - 4*a*c^5)))/((a*b^6*c^7 - 12*a^2*b^4*c^8 - 2*a*b^5*c^8 + 48*a^3*b^2*c^9 + 16*a^2*b^3*c^9 + a*b^4*c^9 - 64*a^4*c^10 - 32*a^3*b*c^10 - 8*a^2*b^2*c^10 + 16*a^3*c^11)*abs(b^2*c^3 - 4*a*c^4)*abs(c)) + 1/16*((2*b^3*c^5 - 8*a*b*c^6 - 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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^5 - 2*(b^2 - 4*a*c)*b*c^5)*(b^2*c^3 - 4*a*c^4)^2*d - (6*b^5*c^3 - 50*a*b^3*c^4 + 104*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 + 25*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 - 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 26*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 + 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - 6*(b^2 - 4*a*c)*b^3*c^3 + 26*(b^2 - 4*a*c)*a*b*c^4)*(b^2*c^3 - 4*a*c^4)^2*f + (10*b^6*c^2 - 88*a*b^4*c^3 + 220*a^2*b^2*c^4 - 112*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 + 44*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 - 110*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 48*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 + 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 10*(b^2 - 4*a*c)*b^4*c^2 + 48*(b^2 - 4*a*c)*a*b^2*c^3 - 28*(b^2 - 4*a*c)*a^2*c^4)*(b^2*c^3 - 4*a*c^4)^2*g + (2*b^4*c^4 - 20*a*b^2*c^5 + 48*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 + 10*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 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 12*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 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^5 - 2*(b^2 - 4*a*c)*b^2*c^4 + 12*(b^2 - 4*a*c)*a*c^5)*(b^2*c^3 - 4*a*c^4)^2*e - 4*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^7 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^8 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^8 + 2*a*b^4*c^8 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^9 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^9 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^9 - 16*a^2*b^2*c^9 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^10 + 32*a^3*c^10 - 2*(b^2 - 4*a*c)*a*b^2*c^8 + 8*(b^2 - 4*a*c)*a^2*c^9)*d*abs(b^2*c^3 - 4*a*c^4) - 2*(3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^5 - 34*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^6 - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^6 + 6*a*b^6*c^6 + 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^7 + 44*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^7 + 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^7 - 68*a^2*b^4*c^7 - 160*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^8 - 80*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^8 - 22*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^8 + 256*a^3*b^2*c^8 + 40*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^9 - 320*a^4*c^9 - 6*(b^2 - 4*a*c)*a*b^4*c^6 + 44*(b^2 - 4*a*c)*a^2*b^2*c^7 - 80*(b^2 - 4*a*c)*a^3*c^8)*f*abs(b^2*c^3 - 4*a*c^4) + 2*(5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^4 - 59*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^5 - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^5 + 10*a*b^7*c^5 + 232*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^6 + 78*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^6 + 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^6 - 118*a^2*b^5*c^6 - 304*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^7 - 152*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^7 - 39*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^7 + 464*a^3*b^3*c^7 + 76*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^8 - 608*a^4*b*c^8 - 10*(b^2 - 4*a*c)*a*b^5*c^5 + 78*(b^2 - 4*a*c)*a^2*b^3*c^6 - 152*(b^2 - 4*a*c)*a^3*b*c^7)*g*abs(b^2*c^3 - 4*a*c^4) + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^6 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^7 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^7 + 2*a*b^5*c^7 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^8 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^8 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^8 - 16*a^2*b^3*c^8 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^9 + 32*a^3*b*c^9 - 2*(b^2 - 4*a*c)*a*b^3*c^7 + 8*(b^2 - 4*a*c)*a^2*b*c^8)*abs(b^2*c^3 - 4*a*c^4)*e - (2*b^7*c^11 - 8*a*b^5*c^12 - 32*a^2*b^3*c^13 + 128*a^3*b*c^14 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^9 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^10 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^10 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^11 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^11 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^12 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^12 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^13 - 2*(b^2 - 4*a*c)*b^5*c^11 + 32*(b^2 - 4*a*c)*a^2*b*c^13)*d + (6*b^9*c^9 - 86*a*b^7*c^10 + 440*a^2*b^5*c^11 - 928*a^3*b^3*c^12 + 640*a^4*b*c^13 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^9*c^7 + 43*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^8 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^8 - 220*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^9 - 62*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^9 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^9 + 464*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^10 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^10 + 31*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^10 - 320*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^11 - 160*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^11 - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^11 + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^12 - 6*(b^2 - 4*a*c)*b^7*c^9 + 62*(b^2 - 4*a*c)*a*b^5*c^10 - 192*(b^2 - 4*a*c)*a^2*b^3*c^11 + 160*(b^2 - 4*a*c)*a^3*b*c^12)*f - (10*b^10*c^8 - 148*a*b^8*c^9 + 808*a^2*b^6*c^10 - 1920*a^3*b^4*c^11 + 1664*a^4*b^2*c^12 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^10*c^6 + 74*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^8*c^7 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^9*c^7 - 404*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^8 - 108*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^8 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^8 + 960*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^9 + 376*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^9 + 54*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^9 - 832*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^10 - 416*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^10 - 188*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^10 + 208*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^11 - 10*(b^2 - 4*a*c)*b^8*c^8 + 108*(b^2 - 4*a*c)*a*b^6*c^9 - 376*(b^2 - 4*a*c)*a^2*b^4*c^10 + 416*(b^2 - 4*a*c)*a^3*b^2*c^11)*g - (2*b^8*c^10 - 32*a*b^6*c^11 + 160*a^2*b^4*c^12 - 256*a^3*b^2*c^13 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^8 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^9 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^9 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^10 - 24*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^10 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^11 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^11 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^11 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^12 - 2*(b^2 - 4*a*c)*b^6*c^10 + 24*(b^2 - 4*a*c)*a*b^4*c^11 - 64*(b^2 - 4*a*c)*a^2*b^2*c^12)*e)*arctan(2*sqrt(1/2)*x/sqrt((b^3*c^3 - 4*a*b*c^4 - sqrt((b^3*c^3 - 4*a*b*c^4)^2 - 4*(a*b^2*c^3 - 4*a^2*c^4)*(b^2*c^4 - 4*a*c^5)))/(b^2*c^4 - 4*a*c^5)))/((a*b^6*c^7 - 12*a^2*b^4*c^8 - 2*a*b^5*c^8 + 48*a^3*b^2*c^9 + 16*a^2*b^3*c^9 + a*b^4*c^9 - 64*a^4*c^10 - 32*a^3*b*c^10 - 8*a^2*b^2*c^10 + 16*a^3*c^11)*abs(b^2*c^3 - 4*a*c^4)*abs(c)) + 1/3*(c^4*g*x^3 + 3*c^4*f*x - 6*b*c^3*g*x)/c^6","B",0
127,1,9170,0,8.920893," ","integrate(x^2*(g*x^6+f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{g x}{c^{2}} - \frac{2 \, c^{3} d x^{3} + b^{2} c f x^{3} - 2 \, a c^{2} f x^{3} - b^{3} g x^{3} + 3 \, a b c g x^{3} - b c^{2} x^{3} e + b c^{2} d x + a b c f x - a b^{2} g x + 2 \, a^{2} c g x - 2 \, a c^{2} x e}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}} - \frac{{\left(2 \, {\left(2 \, b^{2} c^{5} - 8 \, a c^{6} - \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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{5}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}^{2} d - {\left(2 \, b^{4} c^{3} - 20 \, a b^{2} c^{4} + 48 \, 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 + 10 \, \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} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 12 \, \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} + 6 \, \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} + 12 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}^{2} f + {\left(6 \, b^{5} c^{2} - 50 \, a b^{3} c^{3} + 104 \, a^{2} b c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 25 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 26 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 13 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 26 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}^{2} g - {\left(2 \, b^{3} c^{4} - 8 \, a b c^{5} - \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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{4}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}^{2} e - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{6} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{6} + 2 \, b^{5} c^{6} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{7} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{7} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{7} - 16 \, a b^{3} c^{7} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{8} + 32 \, a^{2} b c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{6} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{7}\right)} d {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} + 2 \, a b^{5} c^{5} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{6} - 16 \, a^{2} b^{3} c^{6} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{7} + 32 \, a^{3} b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{5} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{6}\right)} f {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} + 2 \, {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{3} - 34 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} + 6 \, a b^{6} c^{4} + 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 44 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 68 \, a^{2} b^{4} c^{5} - 160 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{6} - 80 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 22 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} + 256 \, a^{3} b^{2} c^{6} + 40 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{7} - 320 \, a^{4} c^{7} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{4} + 44 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{5} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{6}\right)} g {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} + 4 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{6} + 2 \, a b^{4} c^{6} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{7} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{7} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{7} - 16 \, a^{2} b^{2} c^{7} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{8} + 32 \, a^{3} c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{6} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{7}\right)} {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} e - 4 \, {\left(2 \, b^{6} c^{9} - 16 \, a b^{4} c^{10} + 32 \, a^{2} b^{2} c^{11} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{7} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{8} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{8} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{9} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{9} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{9} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{10} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{9} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{10}\right)} d + {\left(2 \, b^{8} c^{7} - 32 \, a b^{6} c^{8} + 160 \, a^{2} b^{4} c^{9} - 256 \, a^{3} b^{2} c^{10} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{5} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{6} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{7} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{7} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{8} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{8} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{8} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{9} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{7} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{8} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{9}\right)} f - {\left(6 \, b^{9} c^{6} - 86 \, a b^{7} c^{7} + 440 \, a^{2} b^{5} c^{8} - 928 \, a^{3} b^{3} c^{9} + 640 \, a^{4} b c^{10} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{9} c^{4} + 43 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{5} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{5} - 220 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{6} - 62 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} + 464 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{7} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{7} + 31 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{7} - 320 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{8} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{8} - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{8} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{9} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{7} c^{6} + 62 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{7} - 192 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{8} + 160 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{9}\right)} g + {\left(2 \, b^{7} c^{8} - 8 \, a b^{5} c^{9} - 32 \, a^{2} b^{3} c^{10} + 128 \, a^{3} b c^{11} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{7} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{7} + 16 \, \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} b^{5} c^{8} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{9} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{9} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{10} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{8} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{10}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} c^{2} - 4 \, a b c^{3} + \sqrt{{\left(b^{3} c^{2} - 4 \, a b c^{3}\right)}^{2} - 4 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}}{b^{2} c^{3} - 4 \, a c^{4}}}}\right)}{16 \, {\left(a b^{6} c^{5} - 12 \, a^{2} b^{4} c^{6} - 2 \, a b^{5} c^{6} + 48 \, a^{3} b^{2} c^{7} + 16 \, a^{2} b^{3} c^{7} + a b^{4} c^{7} - 64 \, a^{4} c^{8} - 32 \, a^{3} b c^{8} - 8 \, a^{2} b^{2} c^{8} + 16 \, a^{3} c^{9}\right)} {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} {\left| c \right|}} + \frac{{\left(2 \, {\left(2 \, b^{2} c^{5} - 8 \, a c^{6} - \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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{5}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}^{2} d - {\left(2 \, b^{4} c^{3} - 20 \, a b^{2} c^{4} + 48 \, 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 + 10 \, \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} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 12 \, \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} + 6 \, \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} + 12 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}^{2} f + {\left(6 \, b^{5} c^{2} - 50 \, a b^{3} c^{3} + 104 \, a^{2} b c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 25 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 26 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 13 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 26 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}^{2} g - {\left(2 \, b^{3} c^{4} - 8 \, a b c^{5} - \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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{4}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}^{2} e + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{6} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{6} - 2 \, b^{5} c^{6} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{7} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{7} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{7} + 16 \, a b^{3} c^{7} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{8} - 32 \, a^{2} b c^{8} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{6} - 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{7}\right)} d {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 2 \, a b^{5} c^{5} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{6} + 16 \, a^{2} b^{3} c^{6} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{7} - 32 \, a^{3} b c^{7} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{5} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{6}\right)} f {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} - 2 \, {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{3} - 34 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} - 6 \, a b^{6} c^{4} + 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 44 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} + 68 \, a^{2} b^{4} c^{5} - 160 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{6} - 80 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 22 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 256 \, a^{3} b^{2} c^{6} + 40 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{7} + 320 \, a^{4} c^{7} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{4} - 44 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{5} + 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{6}\right)} g {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} - 4 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{6} - 2 \, a b^{4} c^{6} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{7} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{7} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{7} + 16 \, a^{2} b^{2} c^{7} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{8} - 32 \, a^{3} c^{8} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{6} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{7}\right)} {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} e - 4 \, {\left(2 \, b^{6} c^{9} - 16 \, a b^{4} c^{10} + 32 \, a^{2} b^{2} c^{11} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{7} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{8} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{8} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{9} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{9} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{9} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{10} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{9} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{10}\right)} d + {\left(2 \, b^{8} c^{7} - 32 \, a b^{6} c^{8} + 160 \, a^{2} b^{4} c^{9} - 256 \, a^{3} b^{2} c^{10} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{5} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{6} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{7} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{7} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{8} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{8} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{8} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{9} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{7} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{8} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{9}\right)} f - {\left(6 \, b^{9} c^{6} - 86 \, a b^{7} c^{7} + 440 \, a^{2} b^{5} c^{8} - 928 \, a^{3} b^{3} c^{9} + 640 \, a^{4} b c^{10} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{9} c^{4} + 43 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{5} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{5} - 220 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{6} - 62 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} + 464 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{7} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{7} + 31 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{7} - 320 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{8} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{8} - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{8} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{9} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{7} c^{6} + 62 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{7} - 192 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{8} + 160 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{9}\right)} g + {\left(2 \, b^{7} c^{8} - 8 \, a b^{5} c^{9} - 32 \, a^{2} b^{3} c^{10} + 128 \, a^{3} b c^{11} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{7} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{7} + 16 \, \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} b^{5} c^{8} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{9} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{9} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{10} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{8} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{10}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{3} c^{2} - 4 \, a b c^{3} - \sqrt{{\left(b^{3} c^{2} - 4 \, a b c^{3}\right)}^{2} - 4 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}}{b^{2} c^{3} - 4 \, a c^{4}}}}\right)}{16 \, {\left(a b^{6} c^{5} - 12 \, a^{2} b^{4} c^{6} - 2 \, a b^{5} c^{6} + 48 \, a^{3} b^{2} c^{7} + 16 \, a^{2} b^{3} c^{7} + a b^{4} c^{7} - 64 \, a^{4} c^{8} - 32 \, a^{3} b c^{8} - 8 \, a^{2} b^{2} c^{8} + 16 \, a^{3} c^{9}\right)} {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} {\left| c \right|}}"," ",0,"g*x/c^2 - 1/2*(2*c^3*d*x^3 + b^2*c*f*x^3 - 2*a*c^2*f*x^3 - b^3*g*x^3 + 3*a*b*c*g*x^3 - b*c^2*x^3*e + b*c^2*d*x + a*b*c*f*x - a*b^2*g*x + 2*a^2*c*g*x - 2*a*c^2*x*e)/((c*x^4 + b*x^2 + a)*(b^2*c^2 - 4*a*c^3)) - 1/16*(2*(2*b^2*c^5 - 8*a*c^6 - 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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*c^5 - 2*(b^2 - 4*a*c)*c^5)*(b^2*c^2 - 4*a*c^3)^2*d - (2*b^4*c^3 - 20*a*b^2*c^4 + 48*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 + 10*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 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 12*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 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^4 - 2*(b^2 - 4*a*c)*b^2*c^3 + 12*(b^2 - 4*a*c)*a*c^4)*(b^2*c^2 - 4*a*c^3)^2*f + (6*b^5*c^2 - 50*a*b^3*c^3 + 104*a^2*b*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 25*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 26*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 6*(b^2 - 4*a*c)*b^3*c^2 + 26*(b^2 - 4*a*c)*a*b*c^3)*(b^2*c^2 - 4*a*c^3)^2*g - (2*b^3*c^4 - 8*a*b*c^5 - 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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^4 - 2*(b^2 - 4*a*c)*b*c^4)*(b^2*c^2 - 4*a*c^3)^2*e - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^6 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^6 + 2*b^5*c^6 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^7 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^7 - 16*a*b^3*c^7 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^8 + 32*a^2*b*c^8 - 2*(b^2 - 4*a*c)*b^3*c^6 + 8*(b^2 - 4*a*c)*a*b*c^7)*d*abs(-b^2*c^2 + 4*a*c^3) - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 + 2*a*b^5*c^5 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^6 - 16*a^2*b^3*c^6 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 + 32*a^3*b*c^7 - 2*(b^2 - 4*a*c)*a*b^3*c^5 + 8*(b^2 - 4*a*c)*a^2*b*c^6)*f*abs(-b^2*c^2 + 4*a*c^3) + 2*(3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 - 34*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 + 6*a*b^6*c^4 + 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 44*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 68*a^2*b^4*c^5 - 160*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^6 - 80*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 22*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + 256*a^3*b^2*c^6 + 40*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^7 - 320*a^4*c^7 - 6*(b^2 - 4*a*c)*a*b^4*c^4 + 44*(b^2 - 4*a*c)*a^2*b^2*c^5 - 80*(b^2 - 4*a*c)*a^3*c^6)*g*abs(-b^2*c^2 + 4*a*c^3) + 4*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^6 + 2*a*b^4*c^6 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^7 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^7 - 16*a^2*b^2*c^7 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^8 + 32*a^3*c^8 - 2*(b^2 - 4*a*c)*a*b^2*c^6 + 8*(b^2 - 4*a*c)*a^2*c^7)*abs(-b^2*c^2 + 4*a*c^3)*e - 4*(2*b^6*c^9 - 16*a*b^4*c^10 + 32*a^2*b^2*c^11 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^7 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^8 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^8 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^9 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^9 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^10 - 2*(b^2 - 4*a*c)*b^4*c^9 + 8*(b^2 - 4*a*c)*a*b^2*c^10)*d + (2*b^8*c^7 - 32*a*b^6*c^8 + 160*a^2*b^4*c^9 - 256*a^3*b^2*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^5 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^6 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^6 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^7 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^8 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^8 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 - 2*(b^2 - 4*a*c)*b^6*c^7 + 24*(b^2 - 4*a*c)*a*b^4*c^8 - 64*(b^2 - 4*a*c)*a^2*b^2*c^9)*f - (6*b^9*c^6 - 86*a*b^7*c^7 + 440*a^2*b^5*c^8 - 928*a^3*b^3*c^9 + 640*a^4*b*c^10 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^9*c^4 + 43*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^5 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^5 - 220*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^6 - 62*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^6 + 464*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^7 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 + 31*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 - 320*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^8 - 160*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^8 - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^9 - 6*(b^2 - 4*a*c)*b^7*c^6 + 62*(b^2 - 4*a*c)*a*b^5*c^7 - 192*(b^2 - 4*a*c)*a^2*b^3*c^8 + 160*(b^2 - 4*a*c)*a^3*b*c^9)*g + (2*b^7*c^8 - 8*a*b^5*c^9 - 32*a^2*b^3*c^10 + 128*a^3*b*c^11 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^6 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^7 + 16*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)*b^5*c^8 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^9 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^10 - 2*(b^2 - 4*a*c)*b^5*c^8 + 32*(b^2 - 4*a*c)*a^2*b*c^10)*e)*arctan(2*sqrt(1/2)*x/sqrt((b^3*c^2 - 4*a*b*c^3 + sqrt((b^3*c^2 - 4*a*b*c^3)^2 - 4*(a*b^2*c^2 - 4*a^2*c^3)*(b^2*c^3 - 4*a*c^4)))/(b^2*c^3 - 4*a*c^4)))/((a*b^6*c^5 - 12*a^2*b^4*c^6 - 2*a*b^5*c^6 + 48*a^3*b^2*c^7 + 16*a^2*b^3*c^7 + a*b^4*c^7 - 64*a^4*c^8 - 32*a^3*b*c^8 - 8*a^2*b^2*c^8 + 16*a^3*c^9)*abs(-b^2*c^2 + 4*a*c^3)*abs(c)) + 1/16*(2*(2*b^2*c^5 - 8*a*c^6 - 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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*c^5 - 2*(b^2 - 4*a*c)*c^5)*(b^2*c^2 - 4*a*c^3)^2*d - (2*b^4*c^3 - 20*a*b^2*c^4 + 48*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 + 10*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 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 12*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 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^4 - 2*(b^2 - 4*a*c)*b^2*c^3 + 12*(b^2 - 4*a*c)*a*c^4)*(b^2*c^2 - 4*a*c^3)^2*f + (6*b^5*c^2 - 50*a*b^3*c^3 + 104*a^2*b*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 + 25*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 26*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 6*(b^2 - 4*a*c)*b^3*c^2 + 26*(b^2 - 4*a*c)*a*b*c^3)*(b^2*c^2 - 4*a*c^3)^2*g - (2*b^3*c^4 - 8*a*b*c^5 - 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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^4 - 2*(b^2 - 4*a*c)*b*c^4)*(b^2*c^2 - 4*a*c^3)^2*e + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^6 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^6 - 2*b^5*c^6 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^7 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^7 + 16*a*b^3*c^7 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^8 - 32*a^2*b*c^8 + 2*(b^2 - 4*a*c)*b^3*c^6 - 8*(b^2 - 4*a*c)*a*b*c^7)*d*abs(-b^2*c^2 + 4*a*c^3) + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 2*a*b^5*c^5 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^6 + 16*a^2*b^3*c^6 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 - 32*a^3*b*c^7 + 2*(b^2 - 4*a*c)*a*b^3*c^5 - 8*(b^2 - 4*a*c)*a^2*b*c^6)*f*abs(-b^2*c^2 + 4*a*c^3) - 2*(3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 - 34*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - 6*a*b^6*c^4 + 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 44*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 + 68*a^2*b^4*c^5 - 160*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^6 - 80*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 22*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 256*a^3*b^2*c^6 + 40*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^7 + 320*a^4*c^7 + 6*(b^2 - 4*a*c)*a*b^4*c^4 - 44*(b^2 - 4*a*c)*a^2*b^2*c^5 + 80*(b^2 - 4*a*c)*a^3*c^6)*g*abs(-b^2*c^2 + 4*a*c^3) - 4*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^6 - 2*a*b^4*c^6 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^7 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^7 + 16*a^2*b^2*c^7 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^8 - 32*a^3*c^8 + 2*(b^2 - 4*a*c)*a*b^2*c^6 - 8*(b^2 - 4*a*c)*a^2*c^7)*abs(-b^2*c^2 + 4*a*c^3)*e - 4*(2*b^6*c^9 - 16*a*b^4*c^10 + 32*a^2*b^2*c^11 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^7 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^8 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^8 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^9 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^9 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^10 - 2*(b^2 - 4*a*c)*b^4*c^9 + 8*(b^2 - 4*a*c)*a*b^2*c^10)*d + (2*b^8*c^7 - 32*a*b^6*c^8 + 160*a^2*b^4*c^9 - 256*a^3*b^2*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^5 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^6 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^6 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^7 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^8 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^8 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 - 2*(b^2 - 4*a*c)*b^6*c^7 + 24*(b^2 - 4*a*c)*a*b^4*c^8 - 64*(b^2 - 4*a*c)*a^2*b^2*c^9)*f - (6*b^9*c^6 - 86*a*b^7*c^7 + 440*a^2*b^5*c^8 - 928*a^3*b^3*c^9 + 640*a^4*b*c^10 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^9*c^4 + 43*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^5 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^5 - 220*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^6 - 62*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^6 + 464*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^7 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 + 31*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 - 320*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^8 - 160*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^8 - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^9 - 6*(b^2 - 4*a*c)*b^7*c^6 + 62*(b^2 - 4*a*c)*a*b^5*c^7 - 192*(b^2 - 4*a*c)*a^2*b^3*c^8 + 160*(b^2 - 4*a*c)*a^3*b*c^9)*g + (2*b^7*c^8 - 8*a*b^5*c^9 - 32*a^2*b^3*c^10 + 128*a^3*b*c^11 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^6 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^7 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^7 + 16*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)*b^5*c^8 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^9 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^10 - 2*(b^2 - 4*a*c)*b^5*c^8 + 32*(b^2 - 4*a*c)*a^2*b*c^10)*e)*arctan(2*sqrt(1/2)*x/sqrt((b^3*c^2 - 4*a*b*c^3 - sqrt((b^3*c^2 - 4*a*b*c^3)^2 - 4*(a*b^2*c^2 - 4*a^2*c^3)*(b^2*c^3 - 4*a*c^4)))/(b^2*c^3 - 4*a*c^4)))/((a*b^6*c^5 - 12*a^2*b^4*c^6 - 2*a*b^5*c^6 + 48*a^3*b^2*c^7 + 16*a^2*b^3*c^7 + a*b^4*c^7 - 64*a^4*c^8 - 32*a^3*b*c^8 - 8*a^2*b^2*c^8 + 16*a^3*c^9)*abs(-b^2*c^2 + 4*a*c^3)*abs(c))","B",0
128,1,8913,0,8.513985," ","integrate((g*x^6+f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{b c^{2} d x^{3} + a b c f x^{3} - a b^{2} g x^{3} + 2 \, a^{2} c g x^{3} - 2 \, a c^{2} x^{3} e + b^{2} c d x - 2 \, a c^{2} d x + 2 \, a^{2} c f x - a^{2} b g x - a b c x e}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}} + \frac{{\left({\left(2 \, b^{3} c^{4} - 8 \, a b c^{5} - \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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{4}\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}^{2} d + {\left(2 \, a b^{3} c^{3} - 8 \, a^{2} b 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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 2 \, \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} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}^{2} f + {\left(2 \, a b^{4} c^{2} - 20 \, a^{2} b^{2} c^{3} + 48 \, 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} + 10 \, \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 - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} - 12 \, \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} + 6 \, \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^{2} c^{2} + 12 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}^{2} g - 2 \, {\left(2 \, a b^{2} c^{4} - 8 \, a^{2} c^{5} - \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 \, \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} a c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}^{2} e + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{3} - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} - 2 \, a b^{6} c^{4} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} + 28 \, a^{2} b^{4} c^{5} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{6} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 128 \, a^{3} b^{2} c^{6} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{7} + 192 \, a^{4} c^{7} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{4} - 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{5} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{6}\right)} d {\left| a b^{2} c - 4 \, a^{2} c^{2} \right|} - 4 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 2 \, a^{3} b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{5} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 16 \, a^{4} b^{2} c^{5} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{6} - 32 \, a^{5} c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{5}\right)} f {\left| a b^{2} c - 4 \, a^{2} c^{2} \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 2 \, a^{3} b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} + 16 \, a^{4} b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} - 32 \, a^{5} b c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} g {\left| a b^{2} c - 4 \, a^{2} c^{2} \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 2 \, a^{2} b^{5} c^{4} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + 16 \, a^{3} b^{3} c^{5} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 32 \, a^{4} b c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{5}\right)} {\left| a b^{2} c - 4 \, a^{2} c^{2} \right|} e + {\left(2 \, a^{2} b^{7} c^{6} - 40 \, a^{3} b^{5} c^{7} + 224 \, a^{4} b^{3} c^{8} - 384 \, a^{5} b c^{9} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c^{4} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{5} - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{6} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{6} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{7} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{7} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{7} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{6} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{7} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{8}\right)} d - {\left(2 \, a^{3} b^{7} c^{5} - 8 \, a^{4} b^{5} c^{6} - 32 \, a^{5} b^{3} c^{7} + 128 \, a^{6} b c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{4} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{5} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{6} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{6} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{5} c^{5} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{7}\right)} f - {\left(2 \, a^{3} b^{8} c^{4} - 32 \, a^{4} b^{6} c^{5} + 160 \, a^{5} b^{4} c^{6} - 256 \, a^{6} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{8} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{4} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{4} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{5} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{5} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{6} c^{4} + 24 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{4} c^{5} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{2} c^{6}\right)} g + 4 \, {\left(2 \, a^{3} b^{6} c^{6} - 16 \, a^{4} b^{4} c^{7} + 32 \, a^{5} b^{2} c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{5} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{6} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{6} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{6} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{7}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b^{3} c - 4 \, a^{2} b c^{2} + \sqrt{{\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)}^{2} - 4 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}}}\right)}{16 \, {\left(a^{3} b^{6} c^{3} - 12 \, a^{4} b^{4} c^{4} - 2 \, a^{3} b^{5} c^{4} + 48 \, a^{5} b^{2} c^{5} + 16 \, a^{4} b^{3} c^{5} + a^{3} b^{4} c^{5} - 64 \, a^{6} c^{6} - 32 \, a^{5} b c^{6} - 8 \, a^{4} b^{2} c^{6} + 16 \, a^{5} c^{7}\right)} {\left| a b^{2} c - 4 \, a^{2} c^{2} \right|} {\left| c \right|}} - \frac{{\left({\left(2 \, b^{3} c^{4} - 8 \, a b c^{5} - \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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{4}\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}^{2} d + {\left(2 \, a b^{3} c^{3} - 8 \, a^{2} b 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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 2 \, \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} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}^{2} f + {\left(2 \, a b^{4} c^{2} - 20 \, a^{2} b^{2} c^{3} + 48 \, 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} + 10 \, \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 - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} - 12 \, \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} + 6 \, \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^{2} c^{2} + 12 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}^{2} g - 2 \, {\left(2 \, a b^{2} c^{4} - 8 \, a^{2} c^{5} - \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 \, \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} a c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)}^{2} e - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{3} - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} + 2 \, a b^{6} c^{4} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{5} - 28 \, a^{2} b^{4} c^{5} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{6} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} + 128 \, a^{3} b^{2} c^{6} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{7} - 192 \, a^{4} c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{4} + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{5} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{6}\right)} d {\left| a b^{2} c - 4 \, a^{2} c^{2} \right|} + 4 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} + 2 \, a^{3} b^{4} c^{4} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{5} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} - 16 \, a^{4} b^{2} c^{5} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{6} + 32 \, a^{5} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{5}\right)} f {\left| a b^{2} c - 4 \, a^{2} c^{2} \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} + 2 \, a^{3} b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 16 \, a^{4} b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} + 32 \, a^{5} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} g {\left| a b^{2} c - 4 \, a^{2} c^{2} \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} + 2 \, a^{2} b^{5} c^{4} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} - 16 \, a^{3} b^{3} c^{5} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} + 32 \, a^{4} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{5}\right)} {\left| a b^{2} c - 4 \, a^{2} c^{2} \right|} e + {\left(2 \, a^{2} b^{7} c^{6} - 40 \, a^{3} b^{5} c^{7} + 224 \, a^{4} b^{3} c^{8} - 384 \, a^{5} b c^{9} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c^{4} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{5} - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{6} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{6} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{7} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{7} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{7} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{6} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{7} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{8}\right)} d - {\left(2 \, a^{3} b^{7} c^{5} - 8 \, a^{4} b^{5} c^{6} - 32 \, a^{5} b^{3} c^{7} + 128 \, a^{6} b c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{4} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{5} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{6} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{6} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{5} c^{5} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{7}\right)} f - {\left(2 \, a^{3} b^{8} c^{4} - 32 \, a^{4} b^{6} c^{5} + 160 \, a^{5} b^{4} c^{6} - 256 \, a^{6} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{8} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{4} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{4} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{5} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{5} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{6} c^{4} + 24 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{4} c^{5} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{2} c^{6}\right)} g + 4 \, {\left(2 \, a^{3} b^{6} c^{6} - 16 \, a^{4} b^{4} c^{7} + 32 \, a^{5} b^{2} c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{5} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{6} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{6} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{6} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{7}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b^{3} c - 4 \, a^{2} b c^{2} - \sqrt{{\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)}^{2} - 4 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}}}\right)}{16 \, {\left(a^{3} b^{6} c^{3} - 12 \, a^{4} b^{4} c^{4} - 2 \, a^{3} b^{5} c^{4} + 48 \, a^{5} b^{2} c^{5} + 16 \, a^{4} b^{3} c^{5} + a^{3} b^{4} c^{5} - 64 \, a^{6} c^{6} - 32 \, a^{5} b c^{6} - 8 \, a^{4} b^{2} c^{6} + 16 \, a^{5} c^{7}\right)} {\left| a b^{2} c - 4 \, a^{2} c^{2} \right|} {\left| c \right|}}"," ",0,"1/2*(b*c^2*d*x^3 + a*b*c*f*x^3 - a*b^2*g*x^3 + 2*a^2*c*g*x^3 - 2*a*c^2*x^3*e + b^2*c*d*x - 2*a*c^2*d*x + 2*a^2*c*f*x - a^2*b*g*x - a*b*c*x*e)/((c*x^4 + b*x^2 + a)*(a*b^2*c - 4*a^2*c^2)) + 1/16*((2*b^3*c^4 - 8*a*b*c^5 - 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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b*c^4 - 2*(b^2 - 4*a*c)*b*c^4)*(a*b^2*c - 4*a^2*c^2)^2*d + (2*a*b^3*c^3 - 8*a^2*b*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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 2*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)*a*b*c^3 - 2*(b^2 - 4*a*c)*a*b*c^3)*(a*b^2*c - 4*a^2*c^2)^2*f + (2*a*b^4*c^2 - 20*a^2*b^2*c^3 + 48*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 + 10*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 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^2 - 12*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 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 2*(b^2 - 4*a*c)*a*b^2*c^2 + 12*(b^2 - 4*a*c)*a^2*c^3)*(a*b^2*c - 4*a^2*c^2)^2*g - 2*(2*a*b^2*c^4 - 8*a^2*c^5 - 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*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)*a*c^4 - 2*(b^2 - 4*a*c)*a*c^4)*(a*b^2*c - 4*a^2*c^2)^2*e + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 - 14*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 - 2*a*b^6*c^4 + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 20*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 + 28*a^2*b^4*c^5 - 96*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^6 - 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 128*a^3*b^2*c^6 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^7 + 192*a^4*c^7 + 2*(b^2 - 4*a*c)*a*b^4*c^4 - 20*(b^2 - 4*a*c)*a^2*b^2*c^5 + 48*(b^2 - 4*a*c)*a^3*c^6)*d*abs(a*b^2*c - 4*a^2*c^2) - 4*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 2*a^3*b^4*c^4 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*c^5 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 16*a^4*b^2*c^5 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^6 - 32*a^5*c^6 + 2*(b^2 - 4*a*c)*a^3*b^2*c^4 - 8*(b^2 - 4*a*c)*a^4*c^5)*f*abs(a*b^2*c - 4*a^2*c^2) + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 2*a^3*b^5*c^3 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 + 16*a^4*b^3*c^4 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 - 32*a^5*b*c^5 + 2*(b^2 - 4*a*c)*a^3*b^3*c^3 - 8*(b^2 - 4*a*c)*a^4*b*c^4)*g*abs(a*b^2*c - 4*a^2*c^2) + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 2*a^2*b^5*c^4 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + 16*a^3*b^3*c^5 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 32*a^4*b*c^6 + 2*(b^2 - 4*a*c)*a^2*b^3*c^4 - 8*(b^2 - 4*a*c)*a^3*b*c^5)*abs(a*b^2*c - 4*a^2*c^2)*e + (2*a^2*b^7*c^6 - 40*a^3*b^5*c^7 + 224*a^4*b^3*c^8 - 384*a^5*b*c^9 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c^4 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^5 - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^6 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^6 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^7 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^7 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^7 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^8 - 2*(b^2 - 4*a*c)*a^2*b^5*c^6 + 32*(b^2 - 4*a*c)*a^3*b^3*c^7 - 96*(b^2 - 4*a*c)*a^4*b*c^8)*d - (2*a^3*b^7*c^5 - 8*a^4*b^5*c^6 - 32*a^5*b^3*c^7 + 128*a^6*b*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^4 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^5 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^6 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^6 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^7 - 2*(b^2 - 4*a*c)*a^3*b^5*c^5 + 32*(b^2 - 4*a*c)*a^5*b*c^7)*f - (2*a^3*b^8*c^4 - 32*a^4*b^6*c^5 + 160*a^5*b^4*c^6 - 256*a^6*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^8*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c^3 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^4 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^4 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^5 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^5 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^5 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^6 - 2*(b^2 - 4*a*c)*a^3*b^6*c^4 + 24*(b^2 - 4*a*c)*a^4*b^4*c^5 - 64*(b^2 - 4*a*c)*a^5*b^2*c^6)*g + 4*(2*a^3*b^6*c^6 - 16*a^4*b^4*c^7 + 32*a^5*b^2*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^5 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^6 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^6 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^7 - 2*(b^2 - 4*a*c)*a^3*b^4*c^6 + 8*(b^2 - 4*a*c)*a^4*b^2*c^7)*e)*arctan(2*sqrt(1/2)*x/sqrt((a*b^3*c - 4*a^2*b*c^2 + sqrt((a*b^3*c - 4*a^2*b*c^2)^2 - 4*(a^2*b^2*c - 4*a^3*c^2)*(a*b^2*c^2 - 4*a^2*c^3)))/(a*b^2*c^2 - 4*a^2*c^3)))/((a^3*b^6*c^3 - 12*a^4*b^4*c^4 - 2*a^3*b^5*c^4 + 48*a^5*b^2*c^5 + 16*a^4*b^3*c^5 + a^3*b^4*c^5 - 64*a^6*c^6 - 32*a^5*b*c^6 - 8*a^4*b^2*c^6 + 16*a^5*c^7)*abs(a*b^2*c - 4*a^2*c^2)*abs(c)) - 1/16*((2*b^3*c^4 - 8*a*b*c^5 - 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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b*c^4 - 2*(b^2 - 4*a*c)*b*c^4)*(a*b^2*c - 4*a^2*c^2)^2*d + (2*a*b^3*c^3 - 8*a^2*b*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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 2*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)*a*b*c^3 - 2*(b^2 - 4*a*c)*a*b*c^3)*(a*b^2*c - 4*a^2*c^2)^2*f + (2*a*b^4*c^2 - 20*a^2*b^2*c^3 + 48*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 + 10*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 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^2 - 12*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 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 2*(b^2 - 4*a*c)*a*b^2*c^2 + 12*(b^2 - 4*a*c)*a^2*c^3)*(a*b^2*c - 4*a^2*c^2)^2*g - 2*(2*a*b^2*c^4 - 8*a^2*c^5 - 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*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)*a*c^4 - 2*(b^2 - 4*a*c)*a*c^4)*(a*b^2*c - 4*a^2*c^2)^2*e - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^3 - 14*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 + 2*a*b^6*c^4 + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 20*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^5 - 28*a^2*b^4*c^5 - 96*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^6 - 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + 128*a^3*b^2*c^6 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^7 - 192*a^4*c^7 - 2*(b^2 - 4*a*c)*a*b^4*c^4 + 20*(b^2 - 4*a*c)*a^2*b^2*c^5 - 48*(b^2 - 4*a*c)*a^3*c^6)*d*abs(a*b^2*c - 4*a^2*c^2) + 4*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 + 2*a^3*b^4*c^4 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*c^5 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 - 16*a^4*b^2*c^5 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^6 + 32*a^5*c^6 - 2*(b^2 - 4*a*c)*a^3*b^2*c^4 + 8*(b^2 - 4*a*c)*a^4*c^5)*f*abs(a*b^2*c - 4*a^2*c^2) - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 + 2*a^3*b^5*c^3 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 16*a^4*b^3*c^4 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 + 32*a^5*b*c^5 - 2*(b^2 - 4*a*c)*a^3*b^3*c^3 + 8*(b^2 - 4*a*c)*a^4*b*c^4)*g*abs(a*b^2*c - 4*a^2*c^2) - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 + 2*a^2*b^5*c^4 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 - 16*a^3*b^3*c^5 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 + 32*a^4*b*c^6 - 2*(b^2 - 4*a*c)*a^2*b^3*c^4 + 8*(b^2 - 4*a*c)*a^3*b*c^5)*abs(a*b^2*c - 4*a^2*c^2)*e + (2*a^2*b^7*c^6 - 40*a^3*b^5*c^7 + 224*a^4*b^3*c^8 - 384*a^5*b*c^9 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c^4 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^5 - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^6 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^6 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^7 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^7 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^7 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^8 - 2*(b^2 - 4*a*c)*a^2*b^5*c^6 + 32*(b^2 - 4*a*c)*a^3*b^3*c^7 - 96*(b^2 - 4*a*c)*a^4*b*c^8)*d - (2*a^3*b^7*c^5 - 8*a^4*b^5*c^6 - 32*a^5*b^3*c^7 + 128*a^6*b*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^4 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^5 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^6 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^6 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^7 - 2*(b^2 - 4*a*c)*a^3*b^5*c^5 + 32*(b^2 - 4*a*c)*a^5*b*c^7)*f - (2*a^3*b^8*c^4 - 32*a^4*b^6*c^5 + 160*a^5*b^4*c^6 - 256*a^6*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^8*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c^3 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^4 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^4 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^5 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^5 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^5 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^6 - 2*(b^2 - 4*a*c)*a^3*b^6*c^4 + 24*(b^2 - 4*a*c)*a^4*b^4*c^5 - 64*(b^2 - 4*a*c)*a^5*b^2*c^6)*g + 4*(2*a^3*b^6*c^6 - 16*a^4*b^4*c^7 + 32*a^5*b^2*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^5 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^6 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^6 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^7 - 2*(b^2 - 4*a*c)*a^3*b^4*c^6 + 8*(b^2 - 4*a*c)*a^4*b^2*c^7)*e)*arctan(2*sqrt(1/2)*x/sqrt((a*b^3*c - 4*a^2*b*c^2 - sqrt((a*b^3*c - 4*a^2*b*c^2)^2 - 4*(a^2*b^2*c - 4*a^3*c^2)*(a*b^2*c^2 - 4*a^2*c^3)))/(a*b^2*c^2 - 4*a^2*c^3)))/((a^3*b^6*c^3 - 12*a^4*b^4*c^4 - 2*a^3*b^5*c^4 + 48*a^5*b^2*c^5 + 16*a^4*b^3*c^5 + a^3*b^4*c^5 - 64*a^6*c^6 - 32*a^5*b*c^6 - 8*a^4*b^2*c^6 + 16*a^5*c^7)*abs(a*b^2*c - 4*a^2*c^2)*abs(c))","B",0
129,1,9176,0,8.303197," ","integrate((g*x^6+f*x^4+e*x^2+d)/x^2/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{3 \, b^{2} c d x^{4} - 10 \, a c^{2} d x^{4} + 2 \, a^{2} c f x^{4} - a^{2} b g x^{4} - a b c x^{4} e + 3 \, b^{3} d x^{2} - 11 \, a b c d x^{2} + a^{2} b f x^{2} - 2 \, a^{3} g x^{2} - a b^{2} x^{2} e + 2 \, a^{2} c x^{2} e + 2 \, a b^{2} d - 8 \, a^{2} c d}{2 \, {\left(c x^{5} + b x^{3} + a x\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}} - \frac{{\left({\left(6 \, b^{4} c^{3} - 44 \, a b^{2} c^{4} + 80 \, a^{2} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} + 20 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}^{2} d + 2 \, {\left(2 \, a^{2} b^{2} c^{3} - 8 \, a^{3} 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 + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{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^{2} c^{3}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}^{2} f - {\left(2 \, a^{2} b^{3} c^{2} - 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 c^{2}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}^{2} g - {\left(2 \, a b^{3} c^{3} - 8 \, a^{2} b 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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 2 \, \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} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}^{2} e + 2 \, {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c - 37 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} - 6 \, a^{2} b^{7} c^{2} + 152 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} + 50 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} + 74 \, a^{3} b^{5} c^{3} - 208 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} - 104 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} - 25 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 304 \, a^{4} b^{3} c^{4} + 52 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} + 416 \, a^{5} b c^{5} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} - 50 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} + 104 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} d {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{2} - 2 \, a^{4} b^{5} c^{2} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} + 16 \, a^{5} b^{3} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} - 32 \, a^{6} b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{3} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{3}\right)} f {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} + 4 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{2} - 2 \, a^{5} b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} + 16 \, a^{6} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{4} - 32 \, a^{7} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{6} c^{3}\right)} g {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} - 2 \, a^{3} b^{6} c^{2} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} + 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} + 28 \, a^{4} b^{4} c^{3} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{4} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} - 128 \, a^{5} b^{2} c^{4} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{5} + 192 \, a^{6} c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{2} - 20 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{3} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{5} c^{4}\right)} {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} e + {\left(6 \, a^{4} b^{8} c^{3} - 80 \, a^{5} b^{6} c^{4} + 352 \, a^{6} b^{4} c^{5} - 512 \, a^{7} b^{2} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{2} - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{3} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{3} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{3} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{4} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{4} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{4} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{6} c^{3} + 56 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c^{4} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{5}\right)} d - 4 \, {\left(2 \, a^{6} b^{6} c^{3} - 16 \, a^{7} b^{4} c^{4} + 32 \, a^{8} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{6} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{4} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{2} c^{4}\right)} f + {\left(2 \, a^{6} b^{7} c^{2} - 8 \, a^{7} b^{5} c^{3} - 32 \, a^{8} b^{3} c^{4} + 128 \, a^{9} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{6} c + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b c^{4}\right)} g - {\left(2 \, a^{5} b^{7} c^{3} - 40 \, a^{6} b^{5} c^{4} + 224 \, a^{7} b^{3} c^{5} - 384 \, a^{8} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} c + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{2} - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{3} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{4} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{4} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{4} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{5} c^{3} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{3} c^{4} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{5}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{2} b^{3} - 4 \, a^{3} b c + \sqrt{{\left(a^{2} b^{3} - 4 \, a^{3} b c\right)}^{2} - 4 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}}}\right)}{16 \, {\left(a^{5} b^{6} c - 12 \, a^{6} b^{4} c^{2} - 2 \, a^{5} b^{5} c^{2} + 48 \, a^{7} b^{2} c^{3} + 16 \, a^{6} b^{3} c^{3} + a^{5} b^{4} c^{3} - 64 \, a^{8} c^{4} - 32 \, a^{7} b c^{4} - 8 \, a^{6} b^{2} c^{4} + 16 \, a^{7} c^{5}\right)} {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} {\left| c \right|}} + \frac{{\left({\left(6 \, b^{4} c^{3} - 44 \, a b^{2} c^{4} + 80 \, a^{2} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} + 20 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}^{2} d + 2 \, {\left(2 \, a^{2} b^{2} c^{3} - 8 \, a^{3} 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 + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{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^{2} c^{3}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}^{2} f - {\left(2 \, a^{2} b^{3} c^{2} - 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 c^{2}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}^{2} g - {\left(2 \, a b^{3} c^{3} - 8 \, a^{2} b 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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 2 \, \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} a b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}^{2} e - 2 \, {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c - 37 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} + 6 \, a^{2} b^{7} c^{2} + 152 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} + 50 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} - 74 \, a^{3} b^{5} c^{3} - 208 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} - 104 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} - 25 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} + 304 \, a^{4} b^{3} c^{4} + 52 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} - 416 \, a^{5} b c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} + 50 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} - 104 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} d {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{2} + 2 \, a^{4} b^{5} c^{2} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 16 \, a^{5} b^{3} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} + 32 \, a^{6} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{3}\right)} f {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} - 4 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{2} + 2 \, a^{5} b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} - 16 \, a^{6} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{4} + 32 \, a^{7} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{6} c^{3}\right)} g {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} + 2 \, a^{3} b^{6} c^{2} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} + 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 28 \, a^{4} b^{4} c^{3} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{4} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} + 128 \, a^{5} b^{2} c^{4} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{5} - 192 \, a^{6} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{2} + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{3} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{5} c^{4}\right)} {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} e + {\left(6 \, a^{4} b^{8} c^{3} - 80 \, a^{5} b^{6} c^{4} + 352 \, a^{6} b^{4} c^{5} - 512 \, a^{7} b^{2} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{2} - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{3} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{3} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{3} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{4} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{4} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{4} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{6} c^{3} + 56 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c^{4} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{5}\right)} d - 4 \, {\left(2 \, a^{6} b^{6} c^{3} - 16 \, a^{7} b^{4} c^{4} + 32 \, a^{8} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{6} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{4} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{2} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{2} c^{4}\right)} f + {\left(2 \, a^{6} b^{7} c^{2} - 8 \, a^{7} b^{5} c^{3} - 32 \, a^{8} b^{3} c^{4} + 128 \, a^{9} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{7} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{6} c + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b c^{4}\right)} g - {\left(2 \, a^{5} b^{7} c^{3} - 40 \, a^{6} b^{5} c^{4} + 224 \, a^{7} b^{3} c^{5} - 384 \, a^{8} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} c + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{2} - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{3} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{3} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{4} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{4} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{4} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{5} c^{3} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{3} c^{4} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{5}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{2} b^{3} - 4 \, a^{3} b c - \sqrt{{\left(a^{2} b^{3} - 4 \, a^{3} b c\right)}^{2} - 4 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}}}\right)}{16 \, {\left(a^{5} b^{6} c - 12 \, a^{6} b^{4} c^{2} - 2 \, a^{5} b^{5} c^{2} + 48 \, a^{7} b^{2} c^{3} + 16 \, a^{6} b^{3} c^{3} + a^{5} b^{4} c^{3} - 64 \, a^{8} c^{4} - 32 \, a^{7} b c^{4} - 8 \, a^{6} b^{2} c^{4} + 16 \, a^{7} c^{5}\right)} {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} {\left| c \right|}}"," ",0,"-1/2*(3*b^2*c*d*x^4 - 10*a*c^2*d*x^4 + 2*a^2*c*f*x^4 - a^2*b*g*x^4 - a*b*c*x^4*e + 3*b^3*d*x^2 - 11*a*b*c*d*x^2 + a^2*b*f*x^2 - 2*a^3*g*x^2 - a*b^2*x^2*e + 2*a^2*c*x^2*e + 2*a*b^2*d - 8*a^2*c*d)/((c*x^5 + b*x^3 + a*x)*(a^2*b^2 - 4*a^3*c)) - 1/16*((6*b^4*c^3 - 44*a*b^2*c^4 + 80*a^2*c^5 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^3 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^4 - 6*(b^2 - 4*a*c)*b^2*c^3 + 20*(b^2 - 4*a*c)*a*c^4)*(a^2*b^2 - 4*a^3*c)^2*d + 2*(2*a^2*b^2*c^3 - 8*a^3*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 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 2*(b^2 - 4*a*c)*a^2*c^3)*(a^2*b^2 - 4*a^3*c)^2*f - (2*a^2*b^3*c^2 - 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*(b^2 - 4*a*c)*a^2*b*c^2)*(a^2*b^2 - 4*a^3*c)^2*g - (2*a*b^3*c^3 - 8*a^2*b*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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 2*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)*a*b*c^3 - 2*(b^2 - 4*a*c)*a*b*c^3)*(a^2*b^2 - 4*a^3*c)^2*e + 2*(3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c - 37*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 - 6*a^2*b^7*c^2 + 152*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 + 50*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 + 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 + 74*a^3*b^5*c^3 - 208*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 - 104*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 25*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 304*a^4*b^3*c^4 + 52*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 + 416*a^5*b*c^5 + 6*(b^2 - 4*a*c)*a^2*b^5*c^2 - 50*(b^2 - 4*a*c)*a^3*b^3*c^3 + 104*(b^2 - 4*a*c)*a^4*b*c^4)*d*abs(a^2*b^2 - 4*a^3*c) - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^2 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^2 - 2*a^4*b^5*c^2 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^3 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 + 16*a^5*b^3*c^3 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 - 32*a^6*b*c^4 + 2*(b^2 - 4*a*c)*a^4*b^3*c^2 - 8*(b^2 - 4*a*c)*a^5*b*c^3)*f*abs(a^2*b^2 - 4*a^3*c) + 4*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^2 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^2 - 2*a^5*b^4*c^2 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*c^3 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^3 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 + 16*a^6*b^2*c^3 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*c^4 - 32*a^7*c^4 + 2*(b^2 - 4*a*c)*a^5*b^2*c^2 - 8*(b^2 - 4*a*c)*a^6*c^3)*g*abs(a^2*b^2 - 4*a^3*c) - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c - 14*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^2 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 - 2*a^3*b^6*c^2 + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 + 20*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 + 28*a^4*b^4*c^3 - 96*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*c^4 - 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 128*a^5*b^2*c^4 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*c^5 + 192*a^6*c^5 + 2*(b^2 - 4*a*c)*a^3*b^4*c^2 - 20*(b^2 - 4*a*c)*a^4*b^2*c^3 + 48*(b^2 - 4*a*c)*a^5*c^4)*abs(a^2*b^2 - 4*a^3*c)*e + (6*a^4*b^8*c^3 - 80*a^5*b^6*c^4 + 352*a^6*b^4*c^5 - 512*a^7*b^2*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^2 - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^3 - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^3 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^3 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^4 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^4 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^4 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^5 - 6*(b^2 - 4*a*c)*a^4*b^6*c^3 + 56*(b^2 - 4*a*c)*a^5*b^4*c^4 - 128*(b^2 - 4*a*c)*a^6*b^2*c^5)*d - 4*(2*a^6*b^6*c^3 - 16*a^7*b^4*c^4 + 32*a^8*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^6*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^4*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^4 - 2*(b^2 - 4*a*c)*a^6*b^4*c^3 + 8*(b^2 - 4*a*c)*a^7*b^2*c^4)*f + (2*a^6*b^7*c^2 - 8*a^7*b^5*c^3 - 32*a^8*b^3*c^4 + 128*a^9*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^6*c + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b*c^4 - 2*(b^2 - 4*a*c)*a^6*b^5*c^2 + 32*(b^2 - 4*a*c)*a^8*b*c^4)*g - (2*a^5*b^7*c^3 - 40*a^6*b^5*c^4 + 224*a^7*b^3*c^5 - 384*a^8*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^7*c + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^2 - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^3 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b*c^4 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^4 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^4 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b*c^5 - 2*(b^2 - 4*a*c)*a^5*b^5*c^3 + 32*(b^2 - 4*a*c)*a^6*b^3*c^4 - 96*(b^2 - 4*a*c)*a^7*b*c^5)*e)*arctan(2*sqrt(1/2)*x/sqrt((a^2*b^3 - 4*a^3*b*c + sqrt((a^2*b^3 - 4*a^3*b*c)^2 - 4*(a^3*b^2 - 4*a^4*c)*(a^2*b^2*c - 4*a^3*c^2)))/(a^2*b^2*c - 4*a^3*c^2)))/((a^5*b^6*c - 12*a^6*b^4*c^2 - 2*a^5*b^5*c^2 + 48*a^7*b^2*c^3 + 16*a^6*b^3*c^3 + a^5*b^4*c^3 - 64*a^8*c^4 - 32*a^7*b*c^4 - 8*a^6*b^2*c^4 + 16*a^7*c^5)*abs(a^2*b^2 - 4*a^3*c)*abs(c)) + 1/16*((6*b^4*c^3 - 44*a*b^2*c^4 + 80*a^2*c^5 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^3 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^4 - 6*(b^2 - 4*a*c)*b^2*c^3 + 20*(b^2 - 4*a*c)*a*c^4)*(a^2*b^2 - 4*a^3*c)^2*d + 2*(2*a^2*b^2*c^3 - 8*a^3*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 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 2*(b^2 - 4*a*c)*a^2*c^3)*(a^2*b^2 - 4*a^3*c)^2*f - (2*a^2*b^3*c^2 - 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*(b^2 - 4*a*c)*a^2*b*c^2)*(a^2*b^2 - 4*a^3*c)^2*g - (2*a*b^3*c^3 - 8*a^2*b*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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 2*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)*a*b*c^3 - 2*(b^2 - 4*a*c)*a*b*c^3)*(a^2*b^2 - 4*a^3*c)^2*e - 2*(3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c - 37*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 + 6*a^2*b^7*c^2 + 152*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 + 50*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 + 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 - 74*a^3*b^5*c^3 - 208*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 - 104*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 25*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 + 304*a^4*b^3*c^4 + 52*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 - 416*a^5*b*c^5 - 6*(b^2 - 4*a*c)*a^2*b^5*c^2 + 50*(b^2 - 4*a*c)*a^3*b^3*c^3 - 104*(b^2 - 4*a*c)*a^4*b*c^4)*d*abs(a^2*b^2 - 4*a^3*c) + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^2 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^2 + 2*a^4*b^5*c^2 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^3 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 16*a^5*b^3*c^3 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 + 32*a^6*b*c^4 - 2*(b^2 - 4*a*c)*a^4*b^3*c^2 + 8*(b^2 - 4*a*c)*a^5*b*c^3)*f*abs(a^2*b^2 - 4*a^3*c) - 4*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^2 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^2 + 2*a^5*b^4*c^2 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*c^3 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^3 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 - 16*a^6*b^2*c^3 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*c^4 + 32*a^7*c^4 - 2*(b^2 - 4*a*c)*a^5*b^2*c^2 + 8*(b^2 - 4*a*c)*a^6*c^3)*g*abs(a^2*b^2 - 4*a^3*c) + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c - 14*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^2 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + 2*a^3*b^6*c^2 + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 + 20*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 28*a^4*b^4*c^3 - 96*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*c^4 - 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + 128*a^5*b^2*c^4 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*c^5 - 192*a^6*c^5 - 2*(b^2 - 4*a*c)*a^3*b^4*c^2 + 20*(b^2 - 4*a*c)*a^4*b^2*c^3 - 48*(b^2 - 4*a*c)*a^5*c^4)*abs(a^2*b^2 - 4*a^3*c)*e + (6*a^4*b^8*c^3 - 80*a^5*b^6*c^4 + 352*a^6*b^4*c^5 - 512*a^7*b^2*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^2 - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^3 - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^3 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^3 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^4 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^4 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^4 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^5 - 6*(b^2 - 4*a*c)*a^4*b^6*c^3 + 56*(b^2 - 4*a*c)*a^5*b^4*c^4 - 128*(b^2 - 4*a*c)*a^6*b^2*c^5)*d - 4*(2*a^6*b^6*c^3 - 16*a^7*b^4*c^4 + 32*a^8*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^6*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^4*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^2*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^4 - 2*(b^2 - 4*a*c)*a^6*b^4*c^3 + 8*(b^2 - 4*a*c)*a^7*b^2*c^4)*f + (2*a^6*b^7*c^2 - 8*a^7*b^5*c^3 - 32*a^8*b^3*c^4 + 128*a^9*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^7 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^6*c + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b*c^4 - 2*(b^2 - 4*a*c)*a^6*b^5*c^2 + 32*(b^2 - 4*a*c)*a^8*b*c^4)*g - (2*a^5*b^7*c^3 - 40*a^6*b^5*c^4 + 224*a^7*b^3*c^5 - 384*a^8*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^7*c + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^2 - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^3 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^3 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b*c^4 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^4 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^4 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^5 - 2*(b^2 - 4*a*c)*a^5*b^5*c^3 + 32*(b^2 - 4*a*c)*a^6*b^3*c^4 - 96*(b^2 - 4*a*c)*a^7*b*c^5)*e)*arctan(2*sqrt(1/2)*x/sqrt((a^2*b^3 - 4*a^3*b*c - sqrt((a^2*b^3 - 4*a^3*b*c)^2 - 4*(a^3*b^2 - 4*a^4*c)*(a^2*b^2*c - 4*a^3*c^2)))/(a^2*b^2*c - 4*a^3*c^2)))/((a^5*b^6*c - 12*a^6*b^4*c^2 - 2*a^5*b^5*c^2 + 48*a^7*b^2*c^3 + 16*a^6*b^3*c^3 + a^5*b^4*c^3 - 64*a^8*c^4 - 32*a^7*b*c^4 - 8*a^6*b^2*c^4 + 16*a^7*c^5)*abs(a^2*b^2 - 4*a^3*c)*abs(c))","B",0
130,1,10422,0,9.055101," ","integrate((g*x^6+f*x^4+e*x^2+d)/x^4/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{b^{3} c d x^{3} - 3 \, a b c^{2} d x^{3} + a^{2} b c f x^{3} - 2 \, a^{3} c g x^{3} - a b^{2} c x^{3} e + 2 \, a^{2} c^{2} x^{3} e + b^{4} d x - 4 \, a b^{2} c d x + 2 \, a^{2} c^{2} d x + a^{2} b^{2} f x - 2 \, a^{3} c f x - a^{3} b g x - a b^{3} x e + 3 \, a^{2} b c x e}{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} {\left(c x^{4} + b x^{2} + a\right)}} + \frac{{\left({\left(10 \, b^{5} c^{2} - 78 \, a b^{3} c^{3} + 152 \, a^{2} b c^{4} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 39 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 76 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 38 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 19 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 38 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}^{2} d + {\left(2 \, a^{2} b^{3} c^{2} - 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 c^{2}\right)} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}^{2} f - 2 \, {\left(2 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{2}\right)} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}^{2} g - {\left(6 \, a b^{4} c^{2} - 44 \, a^{2} b^{2} c^{3} + 80 \, a^{3} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}^{2} e + 2 \, {\left(5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{8} - 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c - 10 \, a^{3} b^{8} c + 286 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{2} + 88 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{2} + 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{2} + 128 \, a^{4} b^{6} c^{2} - 496 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{3} - 220 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{3} - 44 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{3} - 572 \, a^{5} b^{4} c^{3} + 224 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} c^{4} + 112 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{4} + 110 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{4} + 992 \, a^{6} b^{2} c^{4} - 56 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{5} - 448 \, a^{7} c^{5} + 10 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{6} c - 88 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{4} c^{2} + 220 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{2} c^{3} - 112 \, {\left(b^{2} - 4 \, a c\right)} a^{6} c^{4}\right)} d {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} - 14 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c - 2 \, a^{5} b^{6} c + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{2} + 28 \, a^{6} b^{4} c^{2} - 96 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} c^{3} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{3} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{3} - 128 \, a^{7} b^{2} c^{3} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} c^{4} + 192 \, a^{8} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c - 20 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{2} + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{7} c^{3}\right)} f {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c - 2 \, a^{6} b^{5} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{2} + 16 \, a^{7} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{3} - 32 \, a^{8} b c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{2}\right)} g {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} - 2 \, {\left(3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} - 37 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c - 6 \, a^{4} b^{7} c + 152 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{2} + 50 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{2} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{2} + 74 \, a^{5} b^{5} c^{2} - 208 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{3} - 104 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{3} - 25 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{3} - 304 \, a^{6} b^{3} c^{3} + 52 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{4} + 416 \, a^{7} b c^{4} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{5} c - 50 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{3} c^{2} + 104 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b c^{3}\right)} {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} e + {\left(10 \, a^{6} b^{9} c^{2} - 138 \, a^{7} b^{7} c^{3} + 680 \, a^{8} b^{5} c^{4} - 1376 \, a^{9} b^{3} c^{5} + 896 \, a^{10} b c^{6} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{9} + 69 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{7} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{8} c - 340 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{5} c^{2} - 98 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{6} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{7} c^{2} + 688 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{3} c^{3} + 288 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{4} c^{3} + 49 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{5} c^{3} - 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b c^{4} - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{2} c^{4} - 144 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{3} c^{4} + 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b c^{5} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{7} c^{2} + 98 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{5} c^{3} - 288 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{3} c^{4} + 224 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b c^{5}\right)} d + {\left(2 \, a^{8} b^{7} c^{2} - 40 \, a^{9} b^{5} c^{3} + 224 \, a^{10} b^{3} c^{4} - 384 \, a^{11} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{7} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{6} c - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{3} c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{5} c^{2} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b c^{3} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{3} c^{3} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{10} b c^{4}\right)} f + 4 \, {\left(2 \, a^{9} b^{6} c^{2} - 16 \, a^{10} b^{4} c^{3} + 32 \, a^{11} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{6} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{5} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{4} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{4} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{10} b^{2} c^{3}\right)} g - {\left(6 \, a^{7} b^{8} c^{2} - 80 \, a^{8} b^{6} c^{3} + 352 \, a^{9} b^{4} c^{4} - 512 \, a^{10} b^{2} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{8} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{6} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{7} c - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{4} c^{2} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{5} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{6} c^{2} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{2} c^{3} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{3} c^{3} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{4} c^{3} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{2} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{6} c^{2} + 56 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{4} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{2} c^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{3} b^{3} - 4 \, a^{4} b c + \sqrt{{\left(a^{3} b^{3} - 4 \, a^{4} b c\right)}^{2} - 4 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)}}}{a^{3} b^{2} c - 4 \, a^{4} c^{2}}}}\right)}{16 \, {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c - 2 \, a^{7} b^{5} c + 48 \, a^{9} b^{2} c^{2} + 16 \, a^{8} b^{3} c^{2} + a^{7} b^{4} c^{2} - 64 \, a^{10} c^{3} - 32 \, a^{9} b c^{3} - 8 \, a^{8} b^{2} c^{3} + 16 \, a^{9} c^{4}\right)} {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} {\left| c \right|}} - \frac{{\left({\left(10 \, b^{5} c^{2} - 78 \, a b^{3} c^{3} + 152 \, a^{2} b c^{4} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 39 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 76 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 38 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 19 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 38 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}^{2} d + {\left(2 \, a^{2} b^{3} c^{2} - 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 c^{2}\right)} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}^{2} f - 2 \, {\left(2 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{2}\right)} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}^{2} g - {\left(6 \, a b^{4} c^{2} - 44 \, a^{2} b^{2} c^{3} + 80 \, a^{3} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}^{2} e - 2 \, {\left(5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{8} - 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c + 10 \, a^{3} b^{8} c + 286 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{2} + 88 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{2} + 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{2} - 128 \, a^{4} b^{6} c^{2} - 496 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{3} - 220 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{3} - 44 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{3} + 572 \, a^{5} b^{4} c^{3} + 224 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} c^{4} + 112 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{4} + 110 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{4} - 992 \, a^{6} b^{2} c^{4} - 56 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{5} + 448 \, a^{7} c^{5} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{6} c + 88 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{4} c^{2} - 220 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{2} c^{3} + 112 \, {\left(b^{2} - 4 \, a c\right)} a^{6} c^{4}\right)} d {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} - 14 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c + 2 \, a^{5} b^{6} c + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{2} - 28 \, a^{6} b^{4} c^{2} - 96 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} c^{3} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{3} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{3} + 128 \, a^{7} b^{2} c^{3} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} c^{4} - 192 \, a^{8} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{2} - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{7} c^{3}\right)} f {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c + 2 \, a^{6} b^{5} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{2} - 16 \, a^{7} b^{3} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{3} + 32 \, a^{8} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{2}\right)} g {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} + 2 \, {\left(3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} - 37 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c + 6 \, a^{4} b^{7} c + 152 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{2} + 50 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{2} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{2} - 74 \, a^{5} b^{5} c^{2} - 208 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{3} - 104 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{3} - 25 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{3} + 304 \, a^{6} b^{3} c^{3} + 52 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{4} - 416 \, a^{7} b c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{5} c + 50 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{3} c^{2} - 104 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b c^{3}\right)} {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} e + {\left(10 \, a^{6} b^{9} c^{2} - 138 \, a^{7} b^{7} c^{3} + 680 \, a^{8} b^{5} c^{4} - 1376 \, a^{9} b^{3} c^{5} + 896 \, a^{10} b c^{6} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{9} + 69 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{7} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{8} c - 340 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{5} c^{2} - 98 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{6} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{7} c^{2} + 688 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{3} c^{3} + 288 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{4} c^{3} + 49 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{5} c^{3} - 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b c^{4} - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{2} c^{4} - 144 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{3} c^{4} + 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b c^{5} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{7} c^{2} + 98 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{5} c^{3} - 288 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{3} c^{4} + 224 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b c^{5}\right)} d + {\left(2 \, a^{8} b^{7} c^{2} - 40 \, a^{9} b^{5} c^{3} + 224 \, a^{10} b^{3} c^{4} - 384 \, a^{11} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{7} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{6} c - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{3} c^{2} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{5} c^{2} + 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b c^{3} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{2} c^{3} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{3} c^{3} - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{5} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{3} c^{3} - 96 \, {\left(b^{2} - 4 \, a c\right)} a^{10} b c^{4}\right)} f + 4 \, {\left(2 \, a^{9} b^{6} c^{2} - 16 \, a^{10} b^{4} c^{3} + 32 \, a^{11} b^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{6} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{5} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{4} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{4} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{10} b^{2} c^{3}\right)} g - {\left(6 \, a^{7} b^{8} c^{2} - 80 \, a^{8} b^{6} c^{3} + 352 \, a^{9} b^{4} c^{4} - 512 \, a^{10} b^{2} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{8} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{6} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{7} c - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{4} c^{2} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{5} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{6} c^{2} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{2} c^{3} + 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{3} c^{3} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{4} c^{3} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{2} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{6} c^{2} + 56 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{4} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{2} c^{4}\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{3} b^{3} - 4 \, a^{4} b c - \sqrt{{\left(a^{3} b^{3} - 4 \, a^{4} b c\right)}^{2} - 4 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)}}}{a^{3} b^{2} c - 4 \, a^{4} c^{2}}}}\right)}{16 \, {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c - 2 \, a^{7} b^{5} c + 48 \, a^{9} b^{2} c^{2} + 16 \, a^{8} b^{3} c^{2} + a^{7} b^{4} c^{2} - 64 \, a^{10} c^{3} - 32 \, a^{9} b c^{3} - 8 \, a^{8} b^{2} c^{3} + 16 \, a^{9} c^{4}\right)} {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} {\left| c \right|}} + \frac{6 \, b d x^{2} - 3 \, a x^{2} e - a d}{3 \, a^{3} x^{3}}"," ",0,"1/2*(b^3*c*d*x^3 - 3*a*b*c^2*d*x^3 + a^2*b*c*f*x^3 - 2*a^3*c*g*x^3 - a*b^2*c*x^3*e + 2*a^2*c^2*x^3*e + b^4*d*x - 4*a*b^2*c*d*x + 2*a^2*c^2*d*x + a^2*b^2*f*x - 2*a^3*c*f*x - a^3*b*g*x - a*b^3*x*e + 3*a^2*b*c*x*e)/((a^3*b^2 - 4*a^4*c)*(c*x^4 + b*x^2 + a)) + 1/16*((10*b^5*c^2 - 78*a*b^3*c^3 + 152*a^2*b*c^4 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 + 39*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 76*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 38*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 19*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 10*(b^2 - 4*a*c)*b^3*c^2 + 38*(b^2 - 4*a*c)*a*b*c^3)*(a^3*b^2 - 4*a^4*c)^2*d + (2*a^2*b^3*c^2 - 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*(b^2 - 4*a*c)*a^2*b*c^2)*(a^3*b^2 - 4*a^4*c)^2*f - 2*(2*a^3*b^2*c^2 - 8*a^4*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^2 - 2*(b^2 - 4*a*c)*a^3*c^2)*(a^3*b^2 - 4*a^4*c)^2*g - (6*a*b^4*c^2 - 44*a^2*b^2*c^3 + 80*a^3*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 6*(b^2 - 4*a*c)*a*b^2*c^2 + 20*(b^2 - 4*a*c)*a^2*c^3)*(a^3*b^2 - 4*a^4*c)^2*e + 2*(5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^8 - 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c - 10*a^3*b^8*c + 286*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 + 88*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^2 + 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^2 + 128*a^4*b^6*c^2 - 496*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 - 220*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^3 - 44*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^3 - 572*a^5*b^4*c^3 + 224*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*c^4 + 112*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^4 + 110*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^4 + 992*a^6*b^2*c^4 - 56*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*c^5 - 448*a^7*c^5 + 10*(b^2 - 4*a*c)*a^3*b^6*c - 88*(b^2 - 4*a*c)*a^4*b^4*c^2 + 220*(b^2 - 4*a*c)*a^5*b^2*c^3 - 112*(b^2 - 4*a*c)*a^6*c^4)*d*abs(a^3*b^2 - 4*a^4*c) + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6 - 14*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c - 2*a^5*b^6*c + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^2 + 20*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 + 28*a^6*b^4*c^2 - 96*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*c^3 - 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b*c^3 - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 - 128*a^7*b^2*c^3 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*c^4 + 192*a^8*c^4 + 2*(b^2 - 4*a*c)*a^5*b^4*c - 20*(b^2 - 4*a*c)*a^6*b^2*c^2 + 48*(b^2 - 4*a*c)*a^7*c^3)*f*abs(a^3*b^2 - 4*a^4*c) + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^5 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c - 2*a^6*b^5*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^2 + 16*a^7*b^3*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b*c^3 - 32*a^8*b*c^3 + 2*(b^2 - 4*a*c)*a^6*b^3*c - 8*(b^2 - 4*a*c)*a^7*b*c^2)*g*abs(a^3*b^2 - 4*a^4*c) - 2*(3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7 - 37*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c - 6*a^4*b^7*c + 152*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^2 + 50*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 + 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^2 + 74*a^5*b^5*c^2 - 208*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b*c^3 - 104*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 - 25*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^3 - 304*a^6*b^3*c^3 + 52*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^4 + 416*a^7*b*c^4 + 6*(b^2 - 4*a*c)*a^4*b^5*c - 50*(b^2 - 4*a*c)*a^5*b^3*c^2 + 104*(b^2 - 4*a*c)*a^6*b*c^3)*abs(a^3*b^2 - 4*a^4*c)*e + (10*a^6*b^9*c^2 - 138*a^7*b^7*c^3 + 680*a^8*b^5*c^4 - 1376*a^9*b^3*c^5 + 896*a^10*b*c^6 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^9 + 69*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^7*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^8*c - 340*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 - 98*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^6*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^7*c^2 + 688*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 + 288*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^4*c^3 + 49*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^5*c^3 - 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b*c^4 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^2*c^4 - 144*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^3*c^4 + 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b*c^5 - 10*(b^2 - 4*a*c)*a^6*b^7*c^2 + 98*(b^2 - 4*a*c)*a^7*b^5*c^3 - 288*(b^2 - 4*a*c)*a^8*b^3*c^4 + 224*(b^2 - 4*a*c)*a^9*b*c^5)*d + (2*a^8*b^7*c^2 - 40*a^9*b^5*c^3 + 224*a^10*b^3*c^4 - 384*a^11*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^7 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^6*c - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^3*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b*c^3 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b*c^4 - 2*(b^2 - 4*a*c)*a^8*b^5*c^2 + 32*(b^2 - 4*a*c)*a^9*b^3*c^3 - 96*(b^2 - 4*a*c)*a^10*b*c^4)*f + 4*(2*a^9*b^6*c^2 - 16*a^10*b^4*c^3 + 32*a^11*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^6 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^5*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^2*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^4*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^2*c^3 - 2*(b^2 - 4*a*c)*a^9*b^4*c^2 + 8*(b^2 - 4*a*c)*a^10*b^2*c^3)*g - (6*a^7*b^8*c^2 - 80*a^8*b^6*c^3 + 352*a^9*b^4*c^4 - 512*a^10*b^2*c^5 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^8 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^6*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^7*c - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^4*c^2 - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^6*c^2 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^2*c^3 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^4*c^3 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^2*c^4 - 6*(b^2 - 4*a*c)*a^7*b^6*c^2 + 56*(b^2 - 4*a*c)*a^8*b^4*c^3 - 128*(b^2 - 4*a*c)*a^9*b^2*c^4)*e)*arctan(2*sqrt(1/2)*x/sqrt((a^3*b^3 - 4*a^4*b*c + sqrt((a^3*b^3 - 4*a^4*b*c)^2 - 4*(a^4*b^2 - 4*a^5*c)*(a^3*b^2*c - 4*a^4*c^2)))/(a^3*b^2*c - 4*a^4*c^2)))/((a^7*b^6 - 12*a^8*b^4*c - 2*a^7*b^5*c + 48*a^9*b^2*c^2 + 16*a^8*b^3*c^2 + a^7*b^4*c^2 - 64*a^10*c^3 - 32*a^9*b*c^3 - 8*a^8*b^2*c^3 + 16*a^9*c^4)*abs(a^3*b^2 - 4*a^4*c)*abs(c)) - 1/16*((10*b^5*c^2 - 78*a*b^3*c^3 + 152*a^2*b*c^4 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 39*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 76*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 38*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 19*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 10*(b^2 - 4*a*c)*b^3*c^2 + 38*(b^2 - 4*a*c)*a*b*c^3)*(a^3*b^2 - 4*a^4*c)^2*d + (2*a^2*b^3*c^2 - 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*(b^2 - 4*a*c)*a^2*b*c^2)*(a^3*b^2 - 4*a^4*c)^2*f - 2*(2*a^3*b^2*c^2 - 8*a^4*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^2 - 2*(b^2 - 4*a*c)*a^3*c^2)*(a^3*b^2 - 4*a^4*c)^2*g - (6*a*b^4*c^2 - 44*a^2*b^2*c^3 + 80*a^3*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 - 6*(b^2 - 4*a*c)*a*b^2*c^2 + 20*(b^2 - 4*a*c)*a^2*c^3)*(a^3*b^2 - 4*a^4*c)^2*e - 2*(5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^8 - 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c + 10*a^3*b^8*c + 286*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 + 88*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^2 + 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^2 - 128*a^4*b^6*c^2 - 496*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 - 220*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^3 - 44*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^3 + 572*a^5*b^4*c^3 + 224*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*c^4 + 112*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^4 + 110*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^4 - 992*a^6*b^2*c^4 - 56*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*c^5 + 448*a^7*c^5 - 10*(b^2 - 4*a*c)*a^3*b^6*c + 88*(b^2 - 4*a*c)*a^4*b^4*c^2 - 220*(b^2 - 4*a*c)*a^5*b^2*c^3 + 112*(b^2 - 4*a*c)*a^6*c^4)*d*abs(a^3*b^2 - 4*a^4*c) - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6 - 14*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c + 2*a^5*b^6*c + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^2 + 20*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 - 28*a^6*b^4*c^2 - 96*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*c^3 - 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^3 - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 + 128*a^7*b^2*c^3 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*c^4 - 192*a^8*c^4 - 2*(b^2 - 4*a*c)*a^5*b^4*c + 20*(b^2 - 4*a*c)*a^6*b^2*c^2 - 48*(b^2 - 4*a*c)*a^7*c^3)*f*abs(a^3*b^2 - 4*a^4*c) - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^5 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c + 2*a^6*b^5*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^2 - 16*a^7*b^3*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^3 + 32*a^8*b*c^3 - 2*(b^2 - 4*a*c)*a^6*b^3*c + 8*(b^2 - 4*a*c)*a^7*b*c^2)*g*abs(a^3*b^2 - 4*a^4*c) + 2*(3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^7 - 37*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c + 6*a^4*b^7*c + 152*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^2 + 50*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 + 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^2 - 74*a^5*b^5*c^2 - 208*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^3 - 104*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 - 25*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^3 + 304*a^6*b^3*c^3 + 52*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^4 - 416*a^7*b*c^4 - 6*(b^2 - 4*a*c)*a^4*b^5*c + 50*(b^2 - 4*a*c)*a^5*b^3*c^2 - 104*(b^2 - 4*a*c)*a^6*b*c^3)*abs(a^3*b^2 - 4*a^4*c)*e + (10*a^6*b^9*c^2 - 138*a^7*b^7*c^3 + 680*a^8*b^5*c^4 - 1376*a^9*b^3*c^5 + 896*a^10*b*c^6 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^9 + 69*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^7*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^8*c - 340*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 - 98*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^6*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^7*c^2 + 688*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 + 288*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^4*c^3 + 49*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^5*c^3 - 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b*c^4 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^2*c^4 - 144*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^3*c^4 + 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b*c^5 - 10*(b^2 - 4*a*c)*a^6*b^7*c^2 + 98*(b^2 - 4*a*c)*a^7*b^5*c^3 - 288*(b^2 - 4*a*c)*a^8*b^3*c^4 + 224*(b^2 - 4*a*c)*a^9*b*c^5)*d + (2*a^8*b^7*c^2 - 40*a^9*b^5*c^3 + 224*a^10*b^3*c^4 - 384*a^11*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^7 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^6*c - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^3*c^2 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 + 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b*c^3 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^2*c^3 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b*c^4 - 2*(b^2 - 4*a*c)*a^8*b^5*c^2 + 32*(b^2 - 4*a*c)*a^9*b^3*c^3 - 96*(b^2 - 4*a*c)*a^10*b*c^4)*f + 4*(2*a^9*b^6*c^2 - 16*a^10*b^4*c^3 + 32*a^11*b^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^6 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^5*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^2*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^4*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^2*c^3 - 2*(b^2 - 4*a*c)*a^9*b^4*c^2 + 8*(b^2 - 4*a*c)*a^10*b^2*c^3)*g - (6*a^7*b^8*c^2 - 80*a^8*b^6*c^3 + 352*a^9*b^4*c^4 - 512*a^10*b^2*c^5 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^8 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^6*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^7*c - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^4*c^2 - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^6*c^2 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^2*c^3 + 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^4*c^3 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^2*c^4 - 6*(b^2 - 4*a*c)*a^7*b^6*c^2 + 56*(b^2 - 4*a*c)*a^8*b^4*c^3 - 128*(b^2 - 4*a*c)*a^9*b^2*c^4)*e)*arctan(2*sqrt(1/2)*x/sqrt((a^3*b^3 - 4*a^4*b*c - sqrt((a^3*b^3 - 4*a^4*b*c)^2 - 4*(a^4*b^2 - 4*a^5*c)*(a^3*b^2*c - 4*a^4*c^2)))/(a^3*b^2*c - 4*a^4*c^2)))/((a^7*b^6 - 12*a^8*b^4*c - 2*a^7*b^5*c + 48*a^9*b^2*c^2 + 16*a^8*b^3*c^2 + a^7*b^4*c^2 - 64*a^10*c^3 - 32*a^9*b*c^3 - 8*a^8*b^2*c^3 + 16*a^9*c^4)*abs(a^3*b^2 - 4*a^4*c)*abs(c)) + 1/3*(6*b*d*x^2 - 3*a*x^2*e - a*d)/(a^3*x^3)","B",0
131,1,58,0,0.608773," ","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=""giac"")","{\left(c x^{4} + b x^{2} + a\right)}^{p} c x^{7} + {\left(c x^{4} + b x^{2} + a\right)}^{p} b x^{5} + {\left(c x^{4} + b x^{2} + a\right)}^{p} a x^{3}"," ",0,"(c*x^4 + b*x^2 + a)^p*c*x^7 + (c*x^4 + b*x^2 + a)^p*b*x^5 + (c*x^4 + b*x^2 + a)^p*a*x^3","B",0
132,1,269,0,0.894196," ","integrate(x^5*(c*x^4+b*x^2+a)/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","-\frac{1}{315} \, {\left({\left({\left({\left({\left(5 \, {\left({\left(7 \, {\left({\left(x e + d\right)} c e^{\left(-9\right)} - 8 \, c d e^{\left(-9\right)}\right)} {\left(x e + d\right)} + 3 \, {\left(68 \, c d^{2} e^{81} + 3 \, b e^{83}\right)} e^{\left(-90\right)}\right)} {\left(x e + d\right)} - 2 \, {\left(220 \, c d^{3} e^{81} + 27 \, b d e^{83}\right)} e^{\left(-90\right)}\right)} {\left(x e + d\right)} + {\left(3098 \, c d^{4} e^{81} + 729 \, b d^{2} e^{83} + 63 \, a e^{85}\right)} e^{\left(-90\right)}\right)} {\left(x e + d\right)} - 36 \, {\left(82 \, c d^{5} e^{81} + 31 \, b d^{3} e^{83} + 7 \, a d e^{85}\right)} e^{\left(-90\right)}\right)} {\left(x e + d\right)} + 21 \, {\left(92 \, c d^{6} e^{81} + 51 \, b d^{4} e^{83} + 22 \, a d^{2} e^{85}\right)} e^{\left(-90\right)}\right)} {\left(x e + d\right)} - 210 \, {\left(4 \, c d^{7} e^{81} + 3 \, b d^{5} e^{83} + 2 \, a d^{3} e^{85}\right)} e^{\left(-90\right)}\right)} {\left(x e + d\right)} + 315 \, {\left(c d^{8} e^{81} + b d^{6} e^{83} + a d^{4} e^{85}\right)} e^{\left(-90\right)}\right)} \sqrt{x e + d} \sqrt{-x e + d} e^{\left(-1\right)}"," ",0,"-1/315*(((((5*((7*((x*e + d)*c*e^(-9) - 8*c*d*e^(-9))*(x*e + d) + 3*(68*c*d^2*e^81 + 3*b*e^83)*e^(-90))*(x*e + d) - 2*(220*c*d^3*e^81 + 27*b*d*e^83)*e^(-90))*(x*e + d) + (3098*c*d^4*e^81 + 729*b*d^2*e^83 + 63*a*e^85)*e^(-90))*(x*e + d) - 36*(82*c*d^5*e^81 + 31*b*d^3*e^83 + 7*a*d*e^85)*e^(-90))*(x*e + d) + 21*(92*c*d^6*e^81 + 51*b*d^4*e^83 + 22*a*d^2*e^85)*e^(-90))*(x*e + d) - 210*(4*c*d^7*e^81 + 3*b*d^5*e^83 + 2*a*d^3*e^85)*e^(-90))*(x*e + d) + 315*(c*d^8*e^81 + b*d^6*e^83 + a*d^4*e^85)*e^(-90))*sqrt(x*e + d)*sqrt(-x*e + d)*e^(-1)","A",0
133,1,194,0,0.748514," ","integrate(x^3*(c*x^4+b*x^2+a)/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","-\frac{1}{105} \, {\left({\left({\left(3 \, {\left({\left(5 \, {\left({\left(x e + d\right)} c e^{\left(-7\right)} - 6 \, c d e^{\left(-7\right)}\right)} {\left(x e + d\right)} + {\left(81 \, c d^{2} e^{49} + 7 \, b e^{51}\right)} e^{\left(-56\right)}\right)} {\left(x e + d\right)} - 4 \, {\left(31 \, c d^{3} e^{49} + 7 \, b d e^{51}\right)} e^{\left(-56\right)}\right)} {\left(x e + d\right)} + 7 \, {\left(51 \, c d^{4} e^{49} + 22 \, b d^{2} e^{51} + 5 \, a e^{53}\right)} e^{\left(-56\right)}\right)} {\left(x e + d\right)} - 70 \, {\left(3 \, c d^{5} e^{49} + 2 \, b d^{3} e^{51} + a d e^{53}\right)} e^{\left(-56\right)}\right)} {\left(x e + d\right)} + 105 \, {\left(c d^{6} e^{49} + b d^{4} e^{51} + a d^{2} e^{53}\right)} e^{\left(-56\right)}\right)} \sqrt{x e + d} \sqrt{-x e + d} e^{\left(-1\right)}"," ",0,"-1/105*(((3*((5*((x*e + d)*c*e^(-7) - 6*c*d*e^(-7))*(x*e + d) + (81*c*d^2*e^49 + 7*b*e^51)*e^(-56))*(x*e + d) - 4*(31*c*d^3*e^49 + 7*b*d*e^51)*e^(-56))*(x*e + d) + 7*(51*c*d^4*e^49 + 22*b*d^2*e^51 + 5*a*e^53)*e^(-56))*(x*e + d) - 70*(3*c*d^5*e^49 + 2*b*d^3*e^51 + a*d*e^53)*e^(-56))*(x*e + d) + 105*(c*d^6*e^49 + b*d^4*e^51 + a*d^2*e^53)*e^(-56))*sqrt(x*e + d)*sqrt(-x*e + d)*e^(-1)","A",0
134,1,121,0,0.626155," ","integrate(x*(c*x^4+b*x^2+a)/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","-\frac{1}{15} \, {\left({\left({\left(3 \, {\left({\left(x e + d\right)} c e^{\left(-5\right)} - 4 \, c d e^{\left(-5\right)}\right)} {\left(x e + d\right)} + {\left(22 \, c d^{2} e^{25} + 5 \, b e^{27}\right)} e^{\left(-30\right)}\right)} {\left(x e + d\right)} - 10 \, {\left(2 \, c d^{3} e^{25} + b d e^{27}\right)} e^{\left(-30\right)}\right)} {\left(x e + d\right)} + 15 \, {\left(c d^{4} e^{25} + b d^{2} e^{27} + a e^{29}\right)} e^{\left(-30\right)}\right)} \sqrt{x e + d} \sqrt{-x e + d} e^{\left(-1\right)}"," ",0,"-1/15*(((3*((x*e + d)*c*e^(-5) - 4*c*d*e^(-5))*(x*e + d) + (22*c*d^2*e^25 + 5*b*e^27)*e^(-30))*(x*e + d) - 10*(2*c*d^3*e^25 + b*d*e^27)*e^(-30))*(x*e + d) + 15*(c*d^4*e^25 + b*d^2*e^27 + a*e^29)*e^(-30))*sqrt(x*e + d)*sqrt(-x*e + d)*e^(-1)","A",0
135,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)/x/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: schur row 1 1.55494e-10Francis algorithm not precise enough for[1.0,-220.862474643,10162.5484803,-174574.213802,1032773.91614]schur row 1 3.66198e-10Francis algorithm not precise enough for[1.0,-467.909596927,45612.3731035,-1659969.6644,20804885.8013]Bad conditionned root j= 2 value 38.9905751966 ratio 0.000133135092941 mindist 0.00241522618125-a*ln(abs(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1))+2))/d+a*ln(abs(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1))-2))/d+2*((-24*c*exp(1)^12/144/exp(1)^16*sqrt(d+x*exp(1))*sqrt(d+x*exp(1))+48*c*exp(1)^12*d/144/exp(1)^16)*sqrt(d+x*exp(1))*sqrt(d+x*exp(1))+(-72*c*exp(1)^12*d^2-72*exp(1)^14*b)/144/exp(1)^16)*sqrt(d+x*exp(1))*sqrt(-d-x*exp(1)+2*d)","F(-2)",0
136,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)/x^3/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: schur row 1 1.55494e-10Francis algorithm not precise enough for[1.0,-220.862474643,10162.5484803,-174574.213802,1032773.91614]schur row 1 3.66198e-10Francis algorithm not precise enough for[1.0,-467.909596927,45612.3731035,-1659969.6644,20804885.8013]Bad conditionned root j= 2 value 38.9905751966 ratio 0.000133135092941 mindist 0.002415226181251/exp(1)*(-(2*a*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^3*exp(1)^3+8*a*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))*exp(1)^3)/d^3/((2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^2-4)^2-1/2*(a*exp(1)^3+2*b*d^2*exp(1))*ln(abs(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1))+2))/d^3+1/2*(a*exp(1)^3+2*b*d^2*exp(1))*ln(abs(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1))-2))/d^3-2*c*exp(1)/2/exp(1)^2*sqrt(d+x*exp(1))*sqrt(-d-x*exp(1)+2*d))","F(-2)",0
137,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)/x^5/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: schur row 1 1.55494e-10Francis algorithm not precise enough for[1.0,-220.862474643,10162.5484803,-174574.213802,1032773.91614]schur row 1 3.66198e-10Francis algorithm not precise enough for[1.0,-467.909596927,45612.3731035,-1659969.6644,20804885.8013]Bad conditionned root j= 2 value 38.9905751966 ratio 0.000133135092941 mindist 0.002415226181251/exp(1)*(1/2*(-5*a*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^7*exp(1)^5-4*b*d^2*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^7*exp(1)^3-12*a*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^5*exp(1)^5+16*b*d^2*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^5*exp(1)^3-48*a*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^3*exp(1)^5+64*b*d^2*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^3*exp(1)^3-320*a*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))*exp(1)^5-256*b*d^2*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))*exp(1)^3)/d^5/((2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^2-4)^4-1/8*(3*a*exp(1)^5+4*b*d^2*exp(1)^3+8*c*d^4*exp(1))*ln(abs(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1))+2))/d^5+1/8*(3*a*exp(1)^5+4*b*d^2*exp(1)^3+8*c*d^4*exp(1))*ln(abs(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1))-2))/d^5)","F(-2)",0
138,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)/x^7/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: schur row 1 1.55494e-10Francis algorithm not precise enough for[1.0,-220.862474643,10162.5484803,-174574.213802,1032773.91614]schur row 1 3.66198e-10Francis algorithm not precise enough for[1.0,-467.909596927,45612.3731035,-1659969.6644,20804885.8013]Bad conditionned root j= 2 value 38.9905751966 ratio 0.000133135092941 mindist 0.002415226181251/exp(1)*(-1/12*(33*a*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^11*exp(1)^7+30*b*d^2*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^11*exp(1)^5+24*c*d^4*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^11*exp(1)^3+20*a*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^9*exp(1)^7-168*b*d^2*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^9*exp(1)^5-288*c*d^4*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^9*exp(1)^3+1440*a*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^7*exp(1)^7+192*b*d^2*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^7*exp(1)^5+768*c*d^4*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^7*exp(1)^3+5760*a*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^5*exp(1)^7+768*b*d^2*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^5*exp(1)^5+3072*c*d^4*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^5*exp(1)^3+1280*a*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^3*exp(1)^7-10752*b*d^2*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^3*exp(1)^5-18432*c*d^4*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^3*exp(1)^3+33792*a*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))*exp(1)^7+30720*b*d^2*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))*exp(1)^5+24576*c*d^4*(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))*exp(1)^3)/d^7/((2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1)))^2-4)^6-1/16*(5*a*exp(1)^7+6*b*d^2*exp(1)^5+8*c*d^4*exp(1)^3)*ln(abs(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1))+2))/d^7+1/16*(5*a*exp(1)^7+6*b*d^2*exp(1)^5+8*c*d^4*exp(1)^3)*ln(abs(2*sqrt(d+x*exp(1))/(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))-1/2*(2*sqrt(2)*sqrt(d)-2*sqrt(-d-x*exp(1)+2*d))/sqrt(d+x*exp(1))-2))/d^7)","F(-2)",0
139,1,208,0,0.749344," ","integrate(x^2*(c*x^4+b*x^2+a)/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{1}{48} \, {\left(6 \, {\left(5 \, c d^{6} + 6 \, b d^{4} e^{2} + 8 \, a d^{2} e^{4}\right)} \arcsin\left(\frac{\sqrt{2} \sqrt{x e + d}}{2 \, \sqrt{d}}\right) e^{\left(-6\right)} - {\left({\left(2 \, {\left({\left(4 \, {\left({\left(x e + d\right)} c e^{\left(-6\right)} - 5 \, c d e^{\left(-6\right)}\right)} {\left(x e + d\right)} + 3 \, {\left(15 \, c d^{2} e^{36} + 2 \, b e^{38}\right)} e^{\left(-42\right)}\right)} {\left(x e + d\right)} - {\left(55 \, c d^{3} e^{36} + 18 \, b d e^{38}\right)} e^{\left(-42\right)}\right)} {\left(x e + d\right)} + {\left(85 \, c d^{4} e^{36} + 54 \, b d^{2} e^{38} + 24 \, a e^{40}\right)} e^{\left(-42\right)}\right)} {\left(x e + d\right)} - 3 \, {\left(11 \, c d^{5} e^{36} + 10 \, b d^{3} e^{38} + 8 \, a d e^{40}\right)} e^{\left(-42\right)}\right)} \sqrt{x e + d} \sqrt{-x e + d}\right)} e^{\left(-1\right)}"," ",0,"1/48*(6*(5*c*d^6 + 6*b*d^4*e^2 + 8*a*d^2*e^4)*arcsin(1/2*sqrt(2)*sqrt(x*e + d)/sqrt(d))*e^(-6) - ((2*((4*((x*e + d)*c*e^(-6) - 5*c*d*e^(-6))*(x*e + d) + 3*(15*c*d^2*e^36 + 2*b*e^38)*e^(-42))*(x*e + d) - (55*c*d^3*e^36 + 18*b*d*e^38)*e^(-42))*(x*e + d) + (85*c*d^4*e^36 + 54*b*d^2*e^38 + 24*a*e^40)*e^(-42))*(x*e + d) - 3*(11*c*d^5*e^36 + 10*b*d^3*e^38 + 8*a*d*e^40)*e^(-42))*sqrt(x*e + d)*sqrt(-x*e + d))*e^(-1)","A",0
140,1,135,0,0.594801," ","integrate((c*x^4+b*x^2+a)/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(2 \, {\left(3 \, c d^{4} + 4 \, b d^{2} e^{2} + 8 \, a e^{4}\right)} \arcsin\left(\frac{\sqrt{2} \sqrt{x e + d}}{2 \, \sqrt{d}}\right) e^{\left(-4\right)} - {\left({\left(2 \, {\left({\left(x e + d\right)} c e^{\left(-4\right)} - 3 \, c d e^{\left(-4\right)}\right)} {\left(x e + d\right)} + {\left(9 \, c d^{2} e^{16} + 4 \, b e^{18}\right)} e^{\left(-20\right)}\right)} {\left(x e + d\right)} - {\left(5 \, c d^{3} e^{16} + 4 \, b d e^{18}\right)} e^{\left(-20\right)}\right)} \sqrt{x e + d} \sqrt{-x e + d}\right)} e^{\left(-1\right)}"," ",0,"1/8*(2*(3*c*d^4 + 4*b*d^2*e^2 + 8*a*e^4)*arcsin(1/2*sqrt(2)*sqrt(x*e + d)/sqrt(d))*e^(-4) - ((2*((x*e + d)*c*e^(-4) - 3*c*d*e^(-4))*(x*e + d) + (9*c*d^2*e^16 + 4*b*e^18)*e^(-20))*(x*e + d) - (5*c*d^3*e^16 + 4*b*d*e^18)*e^(-20))*sqrt(x*e + d)*sqrt(-x*e + d))*e^(-1)","A",0
141,1,257,0,1.046288," ","integrate((c*x^4+b*x^2+a)/x^2/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left({\left(\pi + 2 \, \arctan\left(\frac{\sqrt{x e + d} {\left(\frac{{\left(\sqrt{2} \sqrt{d} - \sqrt{-x e + d}\right)}^{2}}{x e + d} - 1\right)}}{2 \, {\left(\sqrt{2} \sqrt{d} - \sqrt{-x e + d}\right)}}\right)\right)} {\left(c d^{2} + 2 \, b e^{2}\right)} e^{\left(-2\right)} - {\left({\left(x e + d\right)} c e^{\left(-2\right)} - c d e^{\left(-2\right)}\right)} \sqrt{x e + d} \sqrt{-x e + d} - \frac{8 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)} e^{2}}{{\left({\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{2} - 4\right)} d^{2}}\right)} e^{\left(-1\right)}"," ",0,"1/2*((pi + 2*arctan(1/2*sqrt(x*e + d)*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))^2/(x*e + d) - 1)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d))))*(c*d^2 + 2*b*e^2)*e^(-2) - ((x*e + d)*c*e^(-2) - c*d*e^(-2))*sqrt(x*e + d)*sqrt(-x*e + d) - 8*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))*e^2/((((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^2 - 4)*d^2))*e^(-1)","B",0
142,1,555,0,1.466616," ","integrate((c*x^4+b*x^2+a)/x^4/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, {\left(3 \, {\left(\pi + 2 \, \arctan\left(\frac{\sqrt{x e + d} {\left(\frac{{\left(\sqrt{2} \sqrt{d} - \sqrt{-x e + d}\right)}^{2}}{x e + d} - 1\right)}}{2 \, {\left(\sqrt{2} \sqrt{d} - \sqrt{-x e + d}\right)}}\right)\right)} c - \frac{4 \, {\left(3 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{5} e^{2} + 3 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{5} e^{4} - 24 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{3} e^{2} - 8 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{3} e^{4} + 48 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)} e^{2} + 48 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)} e^{4}\right)}}{{\left({\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{2} - 4\right)}^{3} d^{4}}\right)} e^{\left(-1\right)}"," ",0,"1/3*(3*(pi + 2*arctan(1/2*sqrt(x*e + d)*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))^2/(x*e + d) - 1)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d))))*c - 4*(3*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^5*e^2 + 3*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^5*e^4 - 24*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^3*e^2 - 8*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^3*e^4 + 48*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))*e^2 + 48*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))*e^4)/((((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^2 - 4)^3*d^4))*e^(-1)","B",0
143,1,1103,0,2.545779," ","integrate((c*x^4+b*x^2+a)/x^6/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","-\frac{4 \, {\left(15 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{9} e^{2} + 15 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{9} e^{4} - 240 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{7} e^{2} + 15 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{9} e^{6} - 160 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{7} e^{4} + 1440 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{5} e^{2} - 80 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{7} e^{6} + 800 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{5} e^{4} - 3840 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{3} e^{2} + 928 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{5} e^{6} - 2560 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{3} e^{4} + 3840 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)} e^{2} - 1280 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{3} e^{6} + 3840 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)} e^{4} + 3840 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)} e^{6}\right)} e^{\left(-1\right)}}{15 \, {\left({\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{2} - 4\right)}^{5} d^{6}}"," ",0,"-4/15*(15*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^9*e^2 + 15*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^9*e^4 - 240*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^7*e^2 + 15*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^9*e^6 - 160*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^7*e^4 + 1440*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^5*e^2 - 80*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^7*e^6 + 800*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^5*e^4 - 3840*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^3*e^2 + 928*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^5*e^6 - 2560*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^3*e^4 + 3840*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))*e^2 - 1280*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^3*e^6 + 3840*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))*e^4 + 3840*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))*e^6)*e^(-1)/((((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^2 - 4)^5*d^6)","B",0
144,1,1517,0,4.731378," ","integrate((c*x^4+b*x^2+a)/x^8/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","-\frac{4 \, {\left(105 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{13} e^{4} + 105 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{13} e^{6} - 1960 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{11} e^{4} + 105 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{13} e^{8} - 1400 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{11} e^{6} + 16240 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{9} e^{4} - 840 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{11} e^{8} + 12656 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{9} e^{6} - 80640 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{7} e^{4} + 14448 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{9} e^{8} - 69888 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{7} e^{6} + 259840 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{5} e^{4} - 40704 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{7} e^{8} + 202496 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{5} e^{6} - 501760 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{3} e^{4} + 231168 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{5} e^{8} - 358400 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{3} e^{6} + 430080 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)} e^{4} - 215040 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{3} e^{8} + 430080 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)} e^{6} + 430080 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)} e^{8}\right)} e^{\left(-1\right)}}{105 \, {\left({\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{2} - 4\right)}^{7} d^{8}}"," ",0,"-4/105*(105*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^13*e^4 + 105*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^13*e^6 - 1960*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^11*e^4 + 105*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^13*e^8 - 1400*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^11*e^6 + 16240*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^9*e^4 - 840*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^11*e^8 + 12656*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^9*e^6 - 80640*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^7*e^4 + 14448*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^9*e^8 - 69888*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^7*e^6 + 259840*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^5*e^4 - 40704*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^7*e^8 + 202496*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^5*e^6 - 501760*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^3*e^4 + 231168*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^5*e^8 - 358400*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^3*e^6 + 430080*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))*e^4 - 215040*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^3*e^8 + 430080*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))*e^6 + 430080*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))*e^8)*e^(-1)/((((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^2 - 4)^7*d^8)","B",0
145,1,1931,0,7.348466," ","integrate((c*x^4+b*x^2+a)/x^10/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","-\frac{4 \, {\left(315 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{17} e^{6} + 315 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{17} e^{8} - 6720 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{15} e^{6} + 315 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{17} e^{10} - 5040 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{15} e^{8} + 76608 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{13} e^{6} - 3360 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{15} e^{10} + 68544 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{13} e^{8} - 580608 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{11} e^{6} + 76608 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{13} e^{10} - 509184 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{11} e^{8} + 2892288 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{9} e^{6} - 327168 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{11} e^{10} + 2363904 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{9} e^{8} - 9289728 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{7} e^{6} + 2728448 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{9} e^{10} - 8146944 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{7} e^{8} + 19611648 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{5} e^{6} - 5234688 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{7} e^{10} + 17547264 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{5} e^{8} - 27525120 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{3} e^{6} + 19611648 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{5} e^{10} - 20643840 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{3} e^{8} + 20643840 \, c d^{4} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)} e^{6} - 13762560 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{3} e^{10} + 20643840 \, b d^{2} {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)} e^{8} + 20643840 \, a {\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)} e^{10}\right)} e^{\left(-1\right)}}{315 \, {\left({\left(\frac{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}{\sqrt{x e + d}} - \frac{\sqrt{x e + d}}{\sqrt{2} \sqrt{d} - \sqrt{-x e + d}}\right)}^{2} - 4\right)}^{9} d^{10}}"," ",0,"-4/315*(315*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^17*e^6 + 315*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^17*e^8 - 6720*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^15*e^6 + 315*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^17*e^10 - 5040*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^15*e^8 + 76608*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^13*e^6 - 3360*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^15*e^10 + 68544*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^13*e^8 - 580608*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^11*e^6 + 76608*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^13*e^10 - 509184*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^11*e^8 + 2892288*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^9*e^6 - 327168*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^11*e^10 + 2363904*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^9*e^8 - 9289728*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^7*e^6 + 2728448*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^9*e^10 - 8146944*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^7*e^8 + 19611648*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^5*e^6 - 5234688*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^7*e^10 + 17547264*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^5*e^8 - 27525120*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^3*e^6 + 19611648*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^5*e^10 - 20643840*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^3*e^8 + 20643840*c*d^4*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))*e^6 - 13762560*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^3*e^10 + 20643840*b*d^2*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))*e^8 + 20643840*a*((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))*e^10)*e^(-1)/((((sqrt(2)*sqrt(d) - sqrt(-x*e + d))/sqrt(x*e + d) - sqrt(x*e + d)/(sqrt(2)*sqrt(d) - sqrt(-x*e + d)))^2 - 4)^9*d^10)","B",0
