1,1,131,0,0.261167," ","integrate(x^3*(e*x^2+d)*(c*x^4+a)^5,x, algorithm=""giac"")","\frac{1}{26} \, c^{5} x^{26} e + \frac{1}{24} \, c^{5} d x^{24} + \frac{5}{22} \, a c^{4} x^{22} e + \frac{1}{4} \, a c^{4} d x^{20} + \frac{5}{9} \, a^{2} c^{3} x^{18} e + \frac{5}{8} \, a^{2} c^{3} d x^{16} + \frac{5}{7} \, a^{3} c^{2} x^{14} e + \frac{5}{6} \, a^{3} c^{2} d x^{12} + \frac{1}{2} \, a^{4} c x^{10} e + \frac{5}{8} \, a^{4} c d x^{8} + \frac{1}{6} \, a^{5} x^{6} e + \frac{1}{4} \, a^{5} d x^{4}"," ",0,"1/26*c^5*x^26*e + 1/24*c^5*d*x^24 + 5/22*a*c^4*x^22*e + 1/4*a*c^4*d*x^20 + 5/9*a^2*c^3*x^18*e + 5/8*a^2*c^3*d*x^16 + 5/7*a^3*c^2*x^14*e + 5/6*a^3*c^2*d*x^12 + 1/2*a^4*c*x^10*e + 5/8*a^4*c*d*x^8 + 1/6*a^5*x^6*e + 1/4*a^5*d*x^4","A",0
2,1,131,0,0.193366," ","integrate(x^2*(e*x^2+d)*(c*x^4+a)^5,x, algorithm=""giac"")","\frac{1}{25} \, c^{5} x^{25} e + \frac{1}{23} \, c^{5} d x^{23} + \frac{5}{21} \, a c^{4} x^{21} e + \frac{5}{19} \, a c^{4} d x^{19} + \frac{10}{17} \, a^{2} c^{3} x^{17} e + \frac{2}{3} \, a^{2} c^{3} d x^{15} + \frac{10}{13} \, a^{3} c^{2} x^{13} e + \frac{10}{11} \, a^{3} c^{2} d x^{11} + \frac{5}{9} \, a^{4} c x^{9} e + \frac{5}{7} \, a^{4} c d x^{7} + \frac{1}{5} \, a^{5} x^{5} e + \frac{1}{3} \, a^{5} d x^{3}"," ",0,"1/25*c^5*x^25*e + 1/23*c^5*d*x^23 + 5/21*a*c^4*x^21*e + 5/19*a*c^4*d*x^19 + 10/17*a^2*c^3*x^17*e + 2/3*a^2*c^3*d*x^15 + 10/13*a^3*c^2*x^13*e + 10/11*a^3*c^2*d*x^11 + 5/9*a^4*c*x^9*e + 5/7*a^4*c*d*x^7 + 1/5*a^5*x^5*e + 1/3*a^5*d*x^3","A",0
3,1,130,0,0.179516," ","integrate(x*(e*x^2+d)*(c*x^4+a)^5,x, algorithm=""giac"")","\frac{1}{24} \, c^{5} x^{24} e + \frac{1}{22} \, c^{5} d x^{22} + \frac{1}{4} \, a c^{4} x^{20} e + \frac{5}{18} \, a c^{4} d x^{18} + \frac{5}{8} \, a^{2} c^{3} x^{16} e + \frac{5}{7} \, a^{2} c^{3} d x^{14} + \frac{5}{6} \, a^{3} c^{2} x^{12} e + a^{3} c^{2} d x^{10} + \frac{5}{8} \, a^{4} c x^{8} e + \frac{5}{6} \, a^{4} c d x^{6} + \frac{1}{4} \, a^{5} x^{4} e + \frac{1}{2} \, a^{5} d x^{2}"," ",0,"1/24*c^5*x^24*e + 1/22*c^5*d*x^22 + 1/4*a*c^4*x^20*e + 5/18*a*c^4*d*x^18 + 5/8*a^2*c^3*x^16*e + 5/7*a^2*c^3*d*x^14 + 5/6*a^3*c^2*x^12*e + a^3*c^2*d*x^10 + 5/8*a^4*c*x^8*e + 5/6*a^4*c*d*x^6 + 1/4*a^5*x^4*e + 1/2*a^5*d*x^2","A",0
4,1,127,0,0.220615," ","integrate((e*x^2+d)*(c*x^4+a)^5,x, algorithm=""giac"")","\frac{1}{23} \, c^{5} x^{23} e + \frac{1}{21} \, c^{5} d x^{21} + \frac{5}{19} \, a c^{4} x^{19} e + \frac{5}{17} \, a c^{4} d x^{17} + \frac{2}{3} \, a^{2} c^{3} x^{15} e + \frac{10}{13} \, a^{2} c^{3} d x^{13} + \frac{10}{11} \, a^{3} c^{2} x^{11} e + \frac{10}{9} \, a^{3} c^{2} d x^{9} + \frac{5}{7} \, a^{4} c x^{7} e + a^{4} c d x^{5} + \frac{1}{3} \, a^{5} x^{3} e + a^{5} d x"," ",0,"1/23*c^5*x^23*e + 1/21*c^5*d*x^21 + 5/19*a*c^4*x^19*e + 5/17*a*c^4*d*x^17 + 2/3*a^2*c^3*x^15*e + 10/13*a^2*c^3*d*x^13 + 10/11*a^3*c^2*x^11*e + 10/9*a^3*c^2*d*x^9 + 5/7*a^4*c*x^7*e + a^4*c*d*x^5 + 1/3*a^5*x^3*e + a^5*d*x","A",0
5,1,131,0,0.197467," ","integrate((e*x^2+d)*(c*x^4+a)^5/x,x, algorithm=""giac"")","\frac{1}{22} \, c^{5} x^{22} e + \frac{1}{20} \, c^{5} d x^{20} + \frac{5}{18} \, a c^{4} x^{18} e + \frac{5}{16} \, a c^{4} d x^{16} + \frac{5}{7} \, a^{2} c^{3} x^{14} e + \frac{5}{6} \, a^{2} c^{3} d x^{12} + a^{3} c^{2} x^{10} e + \frac{5}{4} \, a^{3} c^{2} d x^{8} + \frac{5}{6} \, a^{4} c x^{6} e + \frac{5}{4} \, a^{4} c d x^{4} + \frac{1}{2} \, a^{5} x^{2} e + \frac{1}{2} \, a^{5} d \log\left(x^{2}\right)"," ",0,"1/22*c^5*x^22*e + 1/20*c^5*d*x^20 + 5/18*a*c^4*x^18*e + 5/16*a*c^4*d*x^16 + 5/7*a^2*c^3*x^14*e + 5/6*a^2*c^3*d*x^12 + a^3*c^2*x^10*e + 5/4*a^3*c^2*d*x^8 + 5/6*a^4*c*x^6*e + 5/4*a^4*c*d*x^4 + 1/2*a^5*x^2*e + 1/2*a^5*d*log(x^2)","A",0
6,1,127,0,0.195321," ","integrate((e*x^2+d)*(c*x^4+a)^5/x^2,x, algorithm=""giac"")","\frac{1}{21} \, c^{5} x^{21} e + \frac{1}{19} \, c^{5} d x^{19} + \frac{5}{17} \, a c^{4} x^{17} e + \frac{1}{3} \, a c^{4} d x^{15} + \frac{10}{13} \, a^{2} c^{3} x^{13} e + \frac{10}{11} \, a^{2} c^{3} d x^{11} + \frac{10}{9} \, a^{3} c^{2} x^{9} e + \frac{10}{7} \, a^{3} c^{2} d x^{7} + a^{4} c x^{5} e + \frac{5}{3} \, a^{4} c d x^{3} + a^{5} x e - \frac{a^{5} d}{x}"," ",0,"1/21*c^5*x^21*e + 1/19*c^5*d*x^19 + 5/17*a*c^4*x^17*e + 1/3*a*c^4*d*x^15 + 10/13*a^2*c^3*x^13*e + 10/11*a^2*c^3*d*x^11 + 10/9*a^3*c^2*x^9*e + 10/7*a^3*c^2*d*x^7 + a^4*c*x^5*e + 5/3*a^4*c*d*x^3 + a^5*x*e - a^5*d/x","A",0
7,1,142,0,0.207741," ","integrate((e*x^2+d)*(c*x^4+a)^5/x^3,x, algorithm=""giac"")","\frac{1}{20} \, c^{5} x^{20} e + \frac{1}{18} \, c^{5} d x^{18} + \frac{5}{16} \, a c^{4} x^{16} e + \frac{5}{14} \, a c^{4} d x^{14} + \frac{5}{6} \, a^{2} c^{3} x^{12} e + a^{2} c^{3} d x^{10} + \frac{5}{4} \, a^{3} c^{2} x^{8} e + \frac{5}{3} \, a^{3} c^{2} d x^{6} + \frac{5}{4} \, a^{4} c x^{4} e + \frac{5}{2} \, a^{4} c d x^{2} + \frac{1}{2} \, a^{5} e \log\left(x^{2}\right) - \frac{a^{5} x^{2} e + a^{5} d}{2 \, x^{2}}"," ",0,"1/20*c^5*x^20*e + 1/18*c^5*d*x^18 + 5/16*a*c^4*x^16*e + 5/14*a*c^4*d*x^14 + 5/6*a^2*c^3*x^12*e + a^2*c^3*d*x^10 + 5/4*a^3*c^2*x^8*e + 5/3*a^3*c^2*d*x^6 + 5/4*a^4*c*x^4*e + 5/2*a^4*c*d*x^2 + 1/2*a^5*e*log(x^2) - 1/2*(a^5*x^2*e + a^5*d)/x^2","A",0
8,1,54,0,0.232858," ","integrate(x^5*(3*x^2+2)*(x^4+5)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(2 \, x^{4} + 5\right)} \sqrt{x^{4} + 5} x^{2} + \frac{3}{10} \, {\left(x^{4} + 5\right)}^{\frac{5}{2}} - \frac{5}{2} \, {\left(x^{4} + 5\right)}^{\frac{3}{2}} + \frac{25}{8} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/8*(2*x^4 + 5)*sqrt(x^4 + 5)*x^2 + 3/10*(x^4 + 5)^(5/2) - 5/2*(x^4 + 5)^(3/2) + 25/8*log(-x^2 + sqrt(x^4 + 5))","A",0
9,1,45,0,0.233314," ","integrate(x^3*(3*x^2+2)*(x^4+5)^(1/2),x, algorithm=""giac"")","\frac{3}{16} \, {\left(2 \, x^{4} + 5\right)} \sqrt{x^{4} + 5} x^{2} + \frac{1}{3} \, {\left(x^{4} + 5\right)}^{\frac{3}{2}} + \frac{75}{16} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"3/16*(2*x^4 + 5)*sqrt(x^4 + 5)*x^2 + 1/3*(x^4 + 5)^(3/2) + 75/16*log(-x^2 + sqrt(x^4 + 5))","A",0
10,1,38,0,0.197357," ","integrate(x*(3*x^2+2)*(x^4+5)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{x^{4} + 5} x^{2} + \frac{1}{2} \, {\left(x^{4} + 5\right)}^{\frac{3}{2}} - \frac{5}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/2*sqrt(x^4 + 5)*x^2 + 1/2*(x^4 + 5)^(3/2) - 5/2*log(-x^2 + sqrt(x^4 + 5))","A",0
11,1,76,0,0.212746," ","integrate((3*x^2+2)*(x^4+5)^(1/2)/x,x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{x^{4} + 5} {\left(3 \, x^{2} + 4\right)} + \sqrt{5} \log\left(-\frac{x^{2} + \sqrt{5} - \sqrt{x^{4} + 5}}{x^{2} - \sqrt{5} - \sqrt{x^{4} + 5}}\right) - \frac{15}{4} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/4*sqrt(x^4 + 5)*(3*x^2 + 4) + sqrt(5)*log(-(x^2 + sqrt(5) - sqrt(x^4 + 5))/(x^2 - sqrt(5) - sqrt(x^4 + 5))) - 15/4*log(-x^2 + sqrt(x^4 + 5))","A",0
12,1,91,0,0.245049," ","integrate((3*x^2+2)*(x^4+5)^(1/2)/x^3,x, algorithm=""giac"")","\frac{3}{2} \, \sqrt{5} \log\left(-\frac{x^{2} + \sqrt{5} - \sqrt{x^{4} + 5}}{x^{2} - \sqrt{5} - \sqrt{x^{4} + 5}}\right) + \frac{3}{2} \, \sqrt{x^{4} + 5} + \frac{10}{{\left(x^{2} - \sqrt{x^{4} + 5}\right)}^{2} - 5} - \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"3/2*sqrt(5)*log(-(x^2 + sqrt(5) - sqrt(x^4 + 5))/(x^2 - sqrt(5) - sqrt(x^4 + 5))) + 3/2*sqrt(x^4 + 5) + 10/((x^2 - sqrt(x^4 + 5))^2 - 5) - log(-x^2 + sqrt(x^4 + 5))","A",0
13,1,129,0,0.243970," ","integrate((3*x^2+2)*(x^4+5)^(1/2)/x^5,x, algorithm=""giac"")","\frac{1}{10} \, \sqrt{5} \log\left(-\frac{x^{2} + \sqrt{5} - \sqrt{x^{4} + 5}}{x^{2} - \sqrt{5} - \sqrt{x^{4} + 5}}\right) + \frac{{\left(x^{2} - \sqrt{x^{4} + 5}\right)}^{3} + 15 \, {\left(x^{2} - \sqrt{x^{4} + 5}\right)}^{2} + 5 \, x^{2} - 5 \, \sqrt{x^{4} + 5} - 75}{{\left({\left(x^{2} - \sqrt{x^{4} + 5}\right)}^{2} - 5\right)}^{2}} - \frac{3}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/10*sqrt(5)*log(-(x^2 + sqrt(5) - sqrt(x^4 + 5))/(x^2 - sqrt(5) - sqrt(x^4 + 5))) + ((x^2 - sqrt(x^4 + 5))^3 + 15*(x^2 - sqrt(x^4 + 5))^2 + 5*x^2 - 5*sqrt(x^4 + 5) - 75)/((x^2 - sqrt(x^4 + 5))^2 - 5)^2 - 3/2*log(-x^2 + sqrt(x^4 + 5))","B",0
14,1,116,0,0.231704," ","integrate((3*x^2+2)*(x^4+5)^(1/2)/x^7,x, algorithm=""giac"")","\frac{3}{20} \, \sqrt{5} \log\left(-\frac{x^{2} + \sqrt{5} - \sqrt{x^{4} + 5}}{x^{2} - \sqrt{5} - \sqrt{x^{4} + 5}}\right) + \frac{9 \, {\left(x^{2} - \sqrt{x^{4} + 5}\right)}^{5} + 12 \, {\left(x^{2} - \sqrt{x^{4} + 5}\right)}^{4} - 225 \, x^{2} + 225 \, \sqrt{x^{4} + 5} + 100}{6 \, {\left({\left(x^{2} - \sqrt{x^{4} + 5}\right)}^{2} - 5\right)}^{3}}"," ",0,"3/20*sqrt(5)*log(-(x^2 + sqrt(5) - sqrt(x^4 + 5))/(x^2 - sqrt(5) - sqrt(x^4 + 5))) + 1/6*(9*(x^2 - sqrt(x^4 + 5))^5 + 12*(x^2 - sqrt(x^4 + 5))^4 - 225*x^2 + 225*sqrt(x^4 + 5) + 100)/((x^2 - sqrt(x^4 + 5))^2 - 5)^3","B",0
15,0,0,0,0.000000," ","integrate(x^4*(3*x^2+2)*(x^4+5)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + 5} {\left(3 \, x^{2} + 2\right)} x^{4}\,{d x}"," ",0,"integrate(sqrt(x^4 + 5)*(3*x^2 + 2)*x^4, x)","F",0
16,0,0,0,0.000000," ","integrate(x^2*(3*x^2+2)*(x^4+5)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + 5} {\left(3 \, x^{2} + 2\right)} x^{2}\,{d x}"," ",0,"integrate(sqrt(x^4 + 5)*(3*x^2 + 2)*x^2, x)","F",0
17,0,0,0,0.000000," ","integrate((3*x^2+2)*(x^4+5)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + 5} {\left(3 \, x^{2} + 2\right)}\,{d x}"," ",0,"integrate(sqrt(x^4 + 5)*(3*x^2 + 2), x)","F",0
18,0,0,0,0.000000," ","integrate((3*x^2+2)*(x^4+5)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 5} {\left(3 \, x^{2} + 2\right)}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(x^4 + 5)*(3*x^2 + 2)/x^2, x)","F",0
19,0,0,0,0.000000," ","integrate((3*x^2+2)*(x^4+5)^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 5} {\left(3 \, x^{2} + 2\right)}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(x^4 + 5)*(3*x^2 + 2)/x^4, x)","F",0
20,1,80,0,0.246652," ","integrate(x^5*(3*x^2+2)*(x^4+5)^(3/2),x, algorithm=""giac"")","\frac{3}{14} \, {\left(x^{4} + 5\right)}^{\frac{7}{2}} + \frac{1}{48} \, {\left(2 \, {\left(4 \, x^{4} + 5\right)} x^{4} - 75\right)} \sqrt{x^{4} + 5} x^{2} + \frac{5}{8} \, {\left(2 \, x^{4} + 5\right)} \sqrt{x^{4} + 5} x^{2} - \frac{3}{2} \, {\left(x^{4} + 5\right)}^{\frac{5}{2}} + \frac{125}{16} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"3/14*(x^4 + 5)^(7/2) + 1/48*(2*(4*x^4 + 5)*x^4 - 75)*sqrt(x^4 + 5)*x^2 + 5/8*(2*x^4 + 5)*sqrt(x^4 + 5)*x^2 - 3/2*(x^4 + 5)^(5/2) + 125/16*log(-x^2 + sqrt(x^4 + 5))","A",0
21,1,71,0,0.204556," ","integrate(x^3*(3*x^2+2)*(x^4+5)^(3/2),x, algorithm=""giac"")","\frac{1}{32} \, {\left(2 \, {\left(4 \, x^{4} + 5\right)} x^{4} - 75\right)} \sqrt{x^{4} + 5} x^{2} + \frac{15}{16} \, {\left(2 \, x^{4} + 5\right)} \sqrt{x^{4} + 5} x^{2} + \frac{1}{5} \, {\left(x^{4} + 5\right)}^{\frac{5}{2}} + \frac{375}{32} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/32*(2*(4*x^4 + 5)*x^4 - 75)*sqrt(x^4 + 5)*x^2 + 15/16*(2*x^4 + 5)*sqrt(x^4 + 5)*x^2 + 1/5*(x^4 + 5)^(5/2) + 375/32*log(-x^2 + sqrt(x^4 + 5))","A",0
22,1,57,0,0.241528," ","integrate(x*(3*x^2+2)*(x^4+5)^(3/2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(2 \, x^{4} + 5\right)} \sqrt{x^{4} + 5} x^{2} + \frac{3}{10} \, {\left(x^{4} + 5\right)}^{\frac{5}{2}} + \frac{5}{2} \, \sqrt{x^{4} + 5} x^{2} - \frac{75}{8} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/8*(2*x^4 + 5)*sqrt(x^4 + 5)*x^2 + 3/10*(x^4 + 5)^(5/2) + 5/2*sqrt(x^4 + 5)*x^2 - 75/8*log(-x^2 + sqrt(x^4 + 5))","A",0
23,1,90,0,0.260767," ","integrate((3*x^2+2)*(x^4+5)^(3/2)/x,x, algorithm=""giac"")","\frac{1}{48} \, \sqrt{x^{4} + 5} {\left({\left(2 \, {\left(9 \, x^{2} + 8\right)} x^{2} + 225\right)} x^{2} + 320\right)} + 5 \, \sqrt{5} \log\left(-\frac{x^{2} + \sqrt{5} - \sqrt{x^{4} + 5}}{x^{2} - \sqrt{5} - \sqrt{x^{4} + 5}}\right) - \frac{225}{16} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/48*sqrt(x^4 + 5)*((2*(9*x^2 + 8)*x^2 + 225)*x^2 + 320) + 5*sqrt(5)*log(-(x^2 + sqrt(5) - sqrt(x^4 + 5))/(x^2 - sqrt(5) - sqrt(x^4 + 5))) - 225/16*log(-x^2 + sqrt(x^4 + 5))","A",0
24,1,102,0,0.257883," ","integrate((3*x^2+2)*(x^4+5)^(3/2)/x^3,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{x^{4} + 5} {\left({\left(x^{2} + 1\right)} x^{2} + 20\right)} + \frac{15}{2} \, \sqrt{5} \log\left(-\frac{x^{2} + \sqrt{5} - \sqrt{x^{4} + 5}}{x^{2} - \sqrt{5} - \sqrt{x^{4} + 5}}\right) + \frac{50}{{\left(x^{2} - \sqrt{x^{4} + 5}\right)}^{2} - 5} - \frac{15}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/2*sqrt(x^4 + 5)*((x^2 + 1)*x^2 + 20) + 15/2*sqrt(5)*log(-(x^2 + sqrt(5) - sqrt(x^4 + 5))/(x^2 - sqrt(5) - sqrt(x^4 + 5))) + 50/((x^2 - sqrt(x^4 + 5))^2 - 5) - 15/2*log(-x^2 + sqrt(x^4 + 5))","A",0
25,1,146,0,0.254966," ","integrate((3*x^2+2)*(x^4+5)^(3/2)/x^5,x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{x^{4} + 5} {\left(3 \, x^{2} + 4\right)} + \frac{3}{2} \, \sqrt{5} \log\left(-\frac{x^{2} + \sqrt{5} - \sqrt{x^{4} + 5}}{x^{2} - \sqrt{5} - \sqrt{x^{4} + 5}}\right) + \frac{5 \, {\left({\left(x^{2} - \sqrt{x^{4} + 5}\right)}^{3} + 15 \, {\left(x^{2} - \sqrt{x^{4} + 5}\right)}^{2} + 5 \, x^{2} - 5 \, \sqrt{x^{4} + 5} - 75\right)}}{{\left({\left(x^{2} - \sqrt{x^{4} + 5}\right)}^{2} - 5\right)}^{2}} - \frac{45}{4} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/4*sqrt(x^4 + 5)*(3*x^2 + 4) + 3/2*sqrt(5)*log(-(x^2 + sqrt(5) - sqrt(x^4 + 5))/(x^2 - sqrt(5) - sqrt(x^4 + 5))) + 5*((x^2 - sqrt(x^4 + 5))^3 + 15*(x^2 - sqrt(x^4 + 5))^2 + 5*x^2 - 5*sqrt(x^4 + 5) - 75)/((x^2 - sqrt(x^4 + 5))^2 - 5)^2 - 45/4*log(-x^2 + sqrt(x^4 + 5))","B",0
26,1,158,0,0.269795," ","integrate((3*x^2+2)*(x^4+5)^(3/2)/x^7,x, algorithm=""giac"")","\frac{9}{4} \, \sqrt{5} \log\left(-\frac{x^{2} + \sqrt{5} - \sqrt{x^{4} + 5}}{x^{2} - \sqrt{5} - \sqrt{x^{4} + 5}}\right) + \frac{3}{2} \, \sqrt{x^{4} + 5} + \frac{5 \, {\left(9 \, {\left(x^{2} - \sqrt{x^{4} + 5}\right)}^{5} + 24 \, {\left(x^{2} - \sqrt{x^{4} + 5}\right)}^{4} - 120 \, {\left(x^{2} - \sqrt{x^{4} + 5}\right)}^{2} - 225 \, x^{2} + 225 \, \sqrt{x^{4} + 5} + 400\right)}}{6 \, {\left({\left(x^{2} - \sqrt{x^{4} + 5}\right)}^{2} - 5\right)}^{3}} - \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"9/4*sqrt(5)*log(-(x^2 + sqrt(5) - sqrt(x^4 + 5))/(x^2 - sqrt(5) - sqrt(x^4 + 5))) + 3/2*sqrt(x^4 + 5) + 5/6*(9*(x^2 - sqrt(x^4 + 5))^5 + 24*(x^2 - sqrt(x^4 + 5))^4 - 120*(x^2 - sqrt(x^4 + 5))^2 - 225*x^2 + 225*sqrt(x^4 + 5) + 400)/((x^2 - sqrt(x^4 + 5))^2 - 5)^3 - log(-x^2 + sqrt(x^4 + 5))","B",0
27,0,0,0,0.000000," ","integrate(x^4*(3*x^2+2)*(x^4+5)^(3/2),x, algorithm=""giac"")","\int {\left(x^{4} + 5\right)}^{\frac{3}{2}} {\left(3 \, x^{2} + 2\right)} x^{4}\,{d x}"," ",0,"integrate((x^4 + 5)^(3/2)*(3*x^2 + 2)*x^4, x)","F",0
28,0,0,0,0.000000," ","integrate(x^2*(3*x^2+2)*(x^4+5)^(3/2),x, algorithm=""giac"")","\int {\left(x^{4} + 5\right)}^{\frac{3}{2}} {\left(3 \, x^{2} + 2\right)} x^{2}\,{d x}"," ",0,"integrate((x^4 + 5)^(3/2)*(3*x^2 + 2)*x^2, x)","F",0
29,0,0,0,0.000000," ","integrate((3*x^2+2)*(x^4+5)^(3/2),x, algorithm=""giac"")","\int {\left(x^{4} + 5\right)}^{\frac{3}{2}} {\left(3 \, x^{2} + 2\right)}\,{d x}"," ",0,"integrate((x^4 + 5)^(3/2)*(3*x^2 + 2), x)","F",0
30,0,0,0,0.000000," ","integrate((3*x^2+2)*(x^4+5)^(3/2)/x^2,x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 5\right)}^{\frac{3}{2}} {\left(3 \, x^{2} + 2\right)}}{x^{2}}\,{d x}"," ",0,"integrate((x^4 + 5)^(3/2)*(3*x^2 + 2)/x^2, x)","F",0
31,0,0,0,0.000000," ","integrate((3*x^2+2)*(x^4+5)^(3/2)/x^4,x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 5\right)}^{\frac{3}{2}} {\left(3 \, x^{2} + 2\right)}}{x^{4}}\,{d x}"," ",0,"integrate((x^4 + 5)^(3/2)*(3*x^2 + 2)/x^4, x)","F",0
32,1,46,0,0.188565," ","integrate(x^7*(3*x^2+2)/(x^4+5)^(1/2),x, algorithm=""giac"")","\frac{1}{48} \, \sqrt{x^{4} + 5} {\left({\left(2 \, {\left(9 \, x^{2} + 8\right)} x^{2} - 135\right)} x^{2} - 160\right)} - \frac{225}{16} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/48*sqrt(x^4 + 5)*((2*(9*x^2 + 8)*x^2 - 135)*x^2 - 160) - 225/16*log(-x^2 + sqrt(x^4 + 5))","A",0
33,1,37,0,0.215591," ","integrate(x^5*(3*x^2+2)/(x^4+5)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{x^{4} + 5} {\left({\left(x^{2} + 1\right)} x^{2} - 10\right)} + \frac{5}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/2*sqrt(x^4 + 5)*((x^2 + 1)*x^2 - 10) + 5/2*log(-x^2 + sqrt(x^4 + 5))","A",0
34,1,33,0,0.216254," ","integrate(x^3*(3*x^2+2)/(x^4+5)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{x^{4} + 5} {\left(3 \, x^{2} + 4\right)} + \frac{15}{4} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/4*sqrt(x^4 + 5)*(3*x^2 + 4) + 15/4*log(-x^2 + sqrt(x^4 + 5))","A",0
35,1,26,0,0.196210," ","integrate(x*(3*x^2+2)/(x^4+5)^(1/2),x, algorithm=""giac"")","\frac{3}{2} \, \sqrt{x^{4} + 5} - \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"3/2*sqrt(x^4 + 5) - log(-x^2 + sqrt(x^4 + 5))","A",0
36,1,61,0,0.204549," ","integrate((3*x^2+2)/x/(x^4+5)^(1/2),x, algorithm=""giac"")","\frac{1}{5} \, \sqrt{5} \log\left(-\frac{x^{2} + \sqrt{5} - \sqrt{x^{4} + 5}}{x^{2} - \sqrt{5} - \sqrt{x^{4} + 5}}\right) - \frac{3}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/5*sqrt(5)*log(-(x^2 + sqrt(5) - sqrt(x^4 + 5))/(x^2 - sqrt(5) - sqrt(x^4 + 5))) - 3/2*log(-x^2 + sqrt(x^4 + 5))","B",0
37,1,66,0,0.215876," ","integrate((3*x^2+2)/x^3/(x^4+5)^(1/2),x, algorithm=""giac"")","\frac{3}{10} \, \sqrt{5} \log\left(-\frac{x^{2} + \sqrt{5} - \sqrt{x^{4} + 5}}{x^{2} - \sqrt{5} - \sqrt{x^{4} + 5}}\right) + \frac{2}{{\left(x^{2} - \sqrt{x^{4} + 5}\right)}^{2} - 5}"," ",0,"3/10*sqrt(5)*log(-(x^2 + sqrt(5) - sqrt(x^4 + 5))/(x^2 - sqrt(5) - sqrt(x^4 + 5))) + 2/((x^2 - sqrt(x^4 + 5))^2 - 5)","B",0
38,1,114,0,0.216939," ","integrate((3*x^2+2)/x^5/(x^4+5)^(1/2),x, algorithm=""giac"")","-\frac{1}{50} \, \sqrt{5} \log\left(-\frac{x^{2} + \sqrt{5} - \sqrt{x^{4} + 5}}{x^{2} - \sqrt{5} - \sqrt{x^{4} + 5}}\right) + \frac{{\left(x^{2} - \sqrt{x^{4} + 5}\right)}^{3} + 15 \, {\left(x^{2} - \sqrt{x^{4} + 5}\right)}^{2} + 5 \, x^{2} - 5 \, \sqrt{x^{4} + 5} - 75}{5 \, {\left({\left(x^{2} - \sqrt{x^{4} + 5}\right)}^{2} - 5\right)}^{2}}"," ",0,"-1/50*sqrt(5)*log(-(x^2 + sqrt(5) - sqrt(x^4 + 5))/(x^2 - sqrt(5) - sqrt(x^4 + 5))) + 1/5*((x^2 - sqrt(x^4 + 5))^3 + 15*(x^2 - sqrt(x^4 + 5))^2 + 5*x^2 - 5*sqrt(x^4 + 5) - 75)/((x^2 - sqrt(x^4 + 5))^2 - 5)^2","B",0
39,0,0,0,0.000000," ","integrate(x^4*(3*x^2+2)/(x^4+5)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{2} + 2\right)} x^{4}}{\sqrt{x^{4} + 5}}\,{d x}"," ",0,"integrate((3*x^2 + 2)*x^4/sqrt(x^4 + 5), x)","F",0
40,0,0,0,0.000000," ","integrate(x^2*(3*x^2+2)/(x^4+5)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{2} + 2\right)} x^{2}}{\sqrt{x^{4} + 5}}\,{d x}"," ",0,"integrate((3*x^2 + 2)*x^2/sqrt(x^4 + 5), x)","F",0
41,0,0,0,0.000000," ","integrate((3*x^2+2)/(x^4+5)^(1/2),x, algorithm=""giac"")","\int \frac{3 \, x^{2} + 2}{\sqrt{x^{4} + 5}}\,{d x}"," ",0,"integrate((3*x^2 + 2)/sqrt(x^4 + 5), x)","F",0
42,0,0,0,0.000000," ","integrate((3*x^2+2)/x^2/(x^4+5)^(1/2),x, algorithm=""giac"")","\int \frac{3 \, x^{2} + 2}{\sqrt{x^{4} + 5} x^{2}}\,{d x}"," ",0,"integrate((3*x^2 + 2)/(sqrt(x^4 + 5)*x^2), x)","F",0
43,0,0,0,0.000000," ","integrate((3*x^2+2)/x^4/(x^4+5)^(1/2),x, algorithm=""giac"")","\int \frac{3 \, x^{2} + 2}{\sqrt{x^{4} + 5} x^{4}}\,{d x}"," ",0,"integrate((3*x^2 + 2)/(sqrt(x^4 + 5)*x^4), x)","F",0
44,1,45,0,0.206707," ","integrate(x^7*(3*x^2+2)/(x^4+5)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(3 \, x^{2} + 4\right)} x^{2} + 45\right)} x^{2} + 40}{4 \, \sqrt{x^{4} + 5}} + \frac{45}{4} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/4*(((3*x^2 + 4)*x^2 + 45)*x^2 + 40)/sqrt(x^4 + 5) + 45/4*log(-x^2 + sqrt(x^4 + 5))","A",0
45,1,39,0,0.232075," ","integrate(x^5*(3*x^2+2)/(x^4+5)^(3/2),x, algorithm=""giac"")","\frac{{\left(3 \, x^{2} - 2\right)} x^{2} + 30}{2 \, \sqrt{x^{4} + 5}} - \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/2*((3*x^2 - 2)*x^2 + 30)/sqrt(x^4 + 5) - log(-x^2 + sqrt(x^4 + 5))","A",0
46,1,33,0,0.253575," ","integrate(x^3*(3*x^2+2)/(x^4+5)^(3/2),x, algorithm=""giac"")","-\frac{3 \, x^{2} + 2}{2 \, \sqrt{x^{4} + 5}} - \frac{3}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"-1/2*(3*x^2 + 2)/sqrt(x^4 + 5) - 3/2*log(-x^2 + sqrt(x^4 + 5))","A",0
47,1,16,0,0.244555," ","integrate(x*(3*x^2+2)/(x^4+5)^(3/2),x, algorithm=""giac"")","\frac{2 \, x^{2} - 15}{10 \, \sqrt{x^{4} + 5}}"," ",0,"1/10*(2*x^2 - 15)/sqrt(x^4 + 5)","A",0
48,1,61,0,0.253140," ","integrate((3*x^2+2)/x/(x^4+5)^(3/2),x, algorithm=""giac"")","\frac{1}{25} \, \sqrt{5} \log\left(x^{2} + \sqrt{5} - \sqrt{x^{4} + 5}\right) - \frac{1}{25} \, \sqrt{5} \log\left(-x^{2} + \sqrt{5} + \sqrt{x^{4} + 5}\right) + \frac{3 \, x^{2} + 2}{10 \, \sqrt{x^{4} + 5}}"," ",0,"1/25*sqrt(5)*log(x^2 + sqrt(5) - sqrt(x^4 + 5)) - 1/25*sqrt(5)*log(-x^2 + sqrt(5) + sqrt(x^4 + 5)) + 1/10*(3*x^2 + 2)/sqrt(x^4 + 5)","A",0
49,1,82,0,0.243306," ","integrate((3*x^2+2)/x^3/(x^4+5)^(3/2),x, algorithm=""giac"")","\frac{3}{50} \, \sqrt{5} \log\left(-\frac{x^{2} + \sqrt{5} - \sqrt{x^{4} + 5}}{x^{2} - \sqrt{5} - \sqrt{x^{4} + 5}}\right) - \frac{2 \, x^{2} - 15}{50 \, \sqrt{x^{4} + 5}} + \frac{2}{5 \, {\left({\left(x^{2} - \sqrt{x^{4} + 5}\right)}^{2} - 5\right)}}"," ",0,"3/50*sqrt(5)*log(-(x^2 + sqrt(5) - sqrt(x^4 + 5))/(x^2 - sqrt(5) - sqrt(x^4 + 5))) - 1/50*(2*x^2 - 15)/sqrt(x^4 + 5) + 2/5/((x^2 - sqrt(x^4 + 5))^2 - 5)","A",0
50,0,0,0,0.000000," ","integrate(x^4*(3*x^2+2)/(x^4+5)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{2} + 2\right)} x^{4}}{{\left(x^{4} + 5\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((3*x^2 + 2)*x^4/(x^4 + 5)^(3/2), x)","F",0
51,0,0,0,0.000000," ","integrate(x^2*(3*x^2+2)/(x^4+5)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{2} + 2\right)} x^{2}}{{\left(x^{4} + 5\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((3*x^2 + 2)*x^2/(x^4 + 5)^(3/2), x)","F",0
52,0,0,0,0.000000," ","integrate((3*x^2+2)/(x^4+5)^(3/2),x, algorithm=""giac"")","\int \frac{3 \, x^{2} + 2}{{\left(x^{4} + 5\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((3*x^2 + 2)/(x^4 + 5)^(3/2), x)","F",0
53,0,0,0,0.000000," ","integrate((3*x^2+2)/x^2/(x^4+5)^(3/2),x, algorithm=""giac"")","\int \frac{3 \, x^{2} + 2}{{\left(x^{4} + 5\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate((3*x^2 + 2)/((x^4 + 5)^(3/2)*x^2), x)","F",0
54,0,0,0,0.000000," ","integrate((3*x^2+2)/x^4/(x^4+5)^(3/2),x, algorithm=""giac"")","\int \frac{3 \, x^{2} + 2}{{\left(x^{4} + 5\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate((3*x^2 + 2)/((x^4 + 5)^(3/2)*x^4), x)","F",0
55,1,3752,0,0.459464," ","integrate((f*x)^m*(e*x^2+d)*(x^4+2*x^2+1)^5,x, algorithm=""giac"")","\frac{\left(f x\right)^{m} m^{11} x^{23} e + 121 \, \left(f x\right)^{m} m^{10} x^{23} e + \left(f x\right)^{m} d m^{11} x^{21} + 10 \, \left(f x\right)^{m} m^{11} x^{21} e + 6435 \, \left(f x\right)^{m} m^{9} x^{23} e + 123 \, \left(f x\right)^{m} d m^{10} x^{21} + 1230 \, \left(f x\right)^{m} m^{10} x^{21} e + 197835 \, \left(f x\right)^{m} m^{8} x^{23} e + 10 \, \left(f x\right)^{m} d m^{11} x^{19} + 6635 \, \left(f x\right)^{m} d m^{9} x^{21} + 45 \, \left(f x\right)^{m} m^{11} x^{19} e + 66350 \, \left(f x\right)^{m} m^{9} x^{21} e + 3889578 \, \left(f x\right)^{m} m^{7} x^{23} e + 1250 \, \left(f x\right)^{m} d m^{10} x^{19} + 206505 \, \left(f x\right)^{m} d m^{8} x^{21} + 5625 \, \left(f x\right)^{m} m^{10} x^{19} e + 2065050 \, \left(f x\right)^{m} m^{8} x^{21} e + 51069018 \, \left(f x\right)^{m} m^{6} x^{23} e + 45 \, \left(f x\right)^{m} d m^{11} x^{17} + 68430 \, \left(f x\right)^{m} d m^{9} x^{19} + 4103178 \, \left(f x\right)^{m} d m^{7} x^{21} + 120 \, \left(f x\right)^{m} m^{11} x^{17} e + 307935 \, \left(f x\right)^{m} m^{9} x^{19} e + 41031780 \, \left(f x\right)^{m} m^{7} x^{21} e + 453714470 \, \left(f x\right)^{m} m^{5} x^{23} e + 5715 \, \left(f x\right)^{m} d m^{10} x^{17} + 2158230 \, \left(f x\right)^{m} d m^{8} x^{19} + 54362574 \, \left(f x\right)^{m} d m^{6} x^{21} + 15240 \, \left(f x\right)^{m} m^{10} x^{17} e + 9712035 \, \left(f x\right)^{m} m^{8} x^{19} e + 543625740 \, \left(f x\right)^{m} m^{6} x^{21} e + 2702025590 \, \left(f x\right)^{m} m^{4} x^{23} e + 120 \, \left(f x\right)^{m} d m^{11} x^{15} + 317655 \, \left(f x\right)^{m} d m^{9} x^{17} + 43391460 \, \left(f x\right)^{m} d m^{7} x^{19} + 486687830 \, \left(f x\right)^{m} d m^{5} x^{21} + 210 \, \left(f x\right)^{m} m^{11} x^{15} e + 847080 \, \left(f x\right)^{m} m^{9} x^{17} e + 195261570 \, \left(f x\right)^{m} m^{7} x^{19} e + 4866878300 \, \left(f x\right)^{m} m^{5} x^{21} e + 10431670821 \, \left(f x\right)^{m} m^{3} x^{23} e + 15480 \, \left(f x\right)^{m} d m^{10} x^{15} + 10162665 \, \left(f x\right)^{m} d m^{8} x^{17} + 580855380 \, \left(f x\right)^{m} d m^{6} x^{19} + 2917013970 \, \left(f x\right)^{m} d m^{4} x^{21} + 27090 \, \left(f x\right)^{m} m^{10} x^{15} e + 27100440 \, \left(f x\right)^{m} m^{8} x^{17} e + 2613849210 \, \left(f x\right)^{m} m^{6} x^{19} e + 29170139700 \, \left(f x\right)^{m} m^{4} x^{21} e + 24372200061 \, \left(f x\right)^{m} m^{2} x^{23} e + 210 \, \left(f x\right)^{m} d m^{11} x^{13} + 873960 \, \left(f x\right)^{m} d m^{9} x^{15} + 207024930 \, \left(f x\right)^{m} d m^{7} x^{17} + 5246766620 \, \left(f x\right)^{m} d m^{5} x^{19} + 11320966021 \, \left(f x\right)^{m} d m^{3} x^{21} + 252 \, \left(f x\right)^{m} m^{11} x^{13} e + 1529430 \, \left(f x\right)^{m} m^{9} x^{15} e + 552066480 \, \left(f x\right)^{m} m^{7} x^{17} e + 23610449790 \, \left(f x\right)^{m} m^{5} x^{19} e + 113209660210 \, \left(f x\right)^{m} m^{3} x^{21} e + 29985521895 \, \left(f x\right)^{m} m x^{23} e + 27510 \, \left(f x\right)^{m} d m^{10} x^{13} + 28391400 \, \left(f x\right)^{m} d m^{8} x^{15} + 2804395230 \, \left(f x\right)^{m} d m^{6} x^{17} + 31686018220 \, \left(f x\right)^{m} d m^{4} x^{19} + 26560342503 \, \left(f x\right)^{m} d m^{2} x^{21} + 33012 \, \left(f x\right)^{m} m^{10} x^{13} e + 49684950 \, \left(f x\right)^{m} m^{8} x^{15} e + 7478387280 \, \left(f x\right)^{m} m^{6} x^{17} e + 142587081990 \, \left(f x\right)^{m} m^{4} x^{19} e + 265603425030 \, \left(f x\right)^{m} m^{2} x^{21} e + 13749310575 \, \left(f x\right)^{m} x^{23} e + 252 \, \left(f x\right)^{m} d m^{11} x^{11} + 1578150 \, \left(f x\right)^{m} d m^{9} x^{13} + 586902960 \, \left(f x\right)^{m} d m^{7} x^{15} + 25598865870 \, \left(f x\right)^{m} d m^{5} x^{17} + 123748247730 \, \left(f x\right)^{m} d m^{3} x^{19} + 32778930735 \, \left(f x\right)^{m} d m x^{21} + 210 \, \left(f x\right)^{m} m^{11} x^{11} e + 1893780 \, \left(f x\right)^{m} m^{9} x^{13} e + 1027080180 \, \left(f x\right)^{m} m^{7} x^{15} e + 68263642320 \, \left(f x\right)^{m} m^{5} x^{17} e + 556867114785 \, \left(f x\right)^{m} m^{3} x^{19} e + 327789307350 \, \left(f x\right)^{m} m x^{21} e + 33516 \, \left(f x\right)^{m} d m^{10} x^{11} + 52110450 \, \left(f x\right)^{m} d m^{8} x^{13} + 8059973040 \, \left(f x\right)^{m} d m^{6} x^{15} + 156004908210 \, \left(f x\right)^{m} d m^{4} x^{17} + 291789582570 \, \left(f x\right)^{m} d m^{2} x^{19} + 15058768725 \, \left(f x\right)^{m} d x^{21} + 27930 \, \left(f x\right)^{m} m^{10} x^{11} e + 62532540 \, \left(f x\right)^{m} m^{8} x^{13} e + 14104952820 \, \left(f x\right)^{m} m^{6} x^{15} e + 416013088560 \, \left(f x\right)^{m} m^{4} x^{17} e + 1313053121565 \, \left(f x\right)^{m} m^{2} x^{19} e + 150587687250 \, \left(f x\right)^{m} x^{21} e + 210 \, \left(f x\right)^{m} d m^{11} x^{9} + 1954260 \, \left(f x\right)^{m} d m^{9} x^{11} + 1094918580 \, \left(f x\right)^{m} d m^{7} x^{13} + 74496630480 \, \left(f x\right)^{m} d m^{5} x^{15} + 613938233025 \, \left(f x\right)^{m} d m^{3} x^{17} + 361459164150 \, \left(f x\right)^{m} d m x^{19} + 120 \, \left(f x\right)^{m} m^{11} x^{9} e + 1628550 \, \left(f x\right)^{m} m^{9} x^{11} e + 1313902296 \, \left(f x\right)^{m} m^{7} x^{13} e + 130369103340 \, \left(f x\right)^{m} m^{5} x^{15} e + 1637168621400 \, \left(f x\right)^{m} m^{3} x^{17} e + 1626566238675 \, \left(f x\right)^{m} m x^{19} e + 28350 \, \left(f x\right)^{m} d m^{10} x^{9} + 65654820 \, \left(f x\right)^{m} d m^{8} x^{11} + 15277213980 \, \left(f x\right)^{m} d m^{6} x^{13} + 459045550800 \, \left(f x\right)^{m} d m^{4} x^{15} + 1456578341055 \, \left(f x\right)^{m} d m^{2} x^{17} + 166439022750 \, \left(f x\right)^{m} d x^{19} + 16200 \, \left(f x\right)^{m} m^{10} x^{9} e + 54712350 \, \left(f x\right)^{m} m^{8} x^{11} e + 18332656776 \, \left(f x\right)^{m} m^{6} x^{13} e + 803329713900 \, \left(f x\right)^{m} m^{4} x^{15} e + 3884208909480 \, 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x^{7} + 18217524780 \, \left(f x\right)^{m} d m^{6} x^{9} + 1212454199880 \, \left(f x\right)^{m} d m^{4} x^{11} + 8695750818510 \, \left(f x\right)^{m} d m^{2} x^{13} + 2529873145800 \, \left(f x\right)^{m} d x^{15} + 1390 \, \left(f x\right)^{m} m^{10} x^{5} e + 12961215 \, \left(f x\right)^{m} m^{8} x^{7} e + 10410014160 \, \left(f x\right)^{m} m^{6} x^{9} e + 1010378499900 \, \left(f x\right)^{m} m^{4} x^{11} e + 10434900982212 \, \left(f x\right)^{m} m^{2} x^{13} e + 4427278005150 \, \left(f x\right)^{m} x^{15} e + 10 \, \left(f x\right)^{m} d m^{11} x^{3} + 383535 \, \left(f x\right)^{m} d m^{9} x^{5} + 770831280 \, \left(f x\right)^{m} d m^{7} x^{7} + 177985672620 \, \left(f x\right)^{m} d m^{5} x^{9} + 4952725167852 \, \left(f x\right)^{m} d m^{3} x^{11} + 10969925251950 \, \left(f x\right)^{m} d m x^{13} + \left(f x\right)^{m} m^{11} x^{3} e + 85230 \, \left(f x\right)^{m} m^{9} x^{5} e + 289061730 \, \left(f x\right)^{m} m^{7} x^{7} e + 101706098640 \, \left(f x\right)^{m} m^{5} x^{9} e + 4127270973210 \, \left(f x\right)^{m} m^{3} x^{11} e + 13163910302340 \, \left(f x\right)^{m} m x^{13} e + 1410 \, \left(f x\right)^{m} d m^{10} x^{3} + 13645125 \, \left(f x\right)^{m} d m^{8} x^{5} + 11467698480 \, \left(f x\right)^{m} d m^{6} x^{7} + 1156995210420 \, \left(f x\right)^{m} d m^{4} x^{9} + 12123781647516 \, \left(f x\right)^{m} d m^{2} x^{11} + 5108397698250 \, \left(f x\right)^{m} d x^{13} + 141 \, \left(f x\right)^{m} m^{10} x^{3} e + 3032250 \, \left(f x\right)^{m} m^{8} x^{5} e + 4300386930 \, \left(f x\right)^{m} m^{6} x^{7} e + 661140120240 \, \left(f x\right)^{m} m^{4} x^{9} e + 10103151372930 \, \left(f x\right)^{m} m^{2} x^{11} e + 6130077237900 \, \left(f x\right)^{m} x^{13} e + \left(f x\right)^{m} d m^{11} x + 87950 \, \left(f x\right)^{m} d m^{9} x^{3} + 311564610 \, \left(f x\right)^{m} d m^{7} x^{5} + 115122336720 \, \left(f x\right)^{m} d m^{5} x^{7} + 4828477578330 \, \left(f x\right)^{m} d m^{3} x^{9} + 15456024948420 \, \left(f 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x\right)^{m} d m^{3} x^{7} + 15593181033150 \, \left(f x\right)^{m} d m x^{9} + 7481418 \, \left(f x\right)^{m} m^{7} x^{3} e + 10987467740 \, \left(f x\right)^{m} m^{5} x^{5} e + 1243095213825 \, \left(f x\right)^{m} m^{3} x^{7} e + 8910389161800 \, \left(f x\right)^{m} m x^{9} e + 336765 \, \left(f x\right)^{m} d m^{8} x + 1180850580 \, \left(f x\right)^{m} d m^{6} x^{3} + 343967603850 \, \left(f x\right)^{m} d m^{4} x^{5} + 8511631481880 \, \left(f x\right)^{m} d m^{2} x^{7} + 7378796675250 \, \left(f x\right)^{m} d x^{9} + 118085058 \, \left(f x\right)^{m} m^{6} x^{3} e + 76437245300 \, \left(f x\right)^{m} m^{4} x^{5} e + 3191861805705 \, \left(f x\right)^{m} m^{2} x^{7} e + 4216455243000 \, \left(f x\right)^{m} x^{9} e + 8103018 \, \left(f x\right)^{m} d m^{7} x + 12740467100 \, \left(f x\right)^{m} d m^{5} x^{3} + 1546183653345 \, \left(f x\right)^{m} d m^{3} x^{5} + 11284114422600 \, \left(f x\right)^{m} d m x^{7} + 1274046710 \, \left(f x\right)^{m} m^{5} x^{3} e + 343596367410 \, \left(f x\right)^{m} m^{3} x^{5} e + 4231542908475 \, \left(f x\right)^{m} m x^{7} e + 132426294 \, \left(f x\right)^{m} d m^{6} x + 93153182700 \, \left(f x\right)^{m} d m^{4} x^{3} + 4162610035755 \, \left(f x\right)^{m} d m^{2} x^{5} + 5421156741000 \, \left(f x\right)^{m} d x^{7} + 9315318270 \, \left(f x\right)^{m} m^{4} x^{3} e + 925024452390 \, \left(f x\right)^{m} m^{2} x^{5} e + 2032933777875 \, \left(f x\right)^{m} x^{7} e + 1495875590 \, \left(f x\right)^{m} d m^{5} x + 446323045810 \, \left(f x\right)^{m} d m^{3} x^{3} + 5761525369635 \, \left(f x\right)^{m} d m x^{5} + 44632304581 \, \left(f x\right)^{m} m^{3} x^{3} e + 1280338971030 \, \left(f x\right)^{m} m x^{5} e + 11641582810 \, \left(f x\right)^{m} d m^{4} x + 1304037152010 \, \left(f x\right)^{m} d m^{2} x^{3} + 2846107289025 \, \left(f x\right)^{m} d x^{5} + 130403715201 \, \left(f x\right)^{m} m^{2} x^{3} e + 632468286450 \, \left(f x\right)^{m} x^{5} e + 60936676581 \, \left(f x\right)^{m} d m^{3} x + 1993349776950 \, \left(f x\right)^{m} d m x^{3} + 199334977695 \, \left(f x\right)^{m} m x^{3} e + 203363952363 \, \left(f x\right)^{m} d m^{2} x + 1054113810750 \, \left(f x\right)^{m} d x^{3} + 105411381075 \, \left(f x\right)^{m} x^{3} e + 387182170935 \, \left(f x\right)^{m} d m x + 316234143225 \, \left(f x\right)^{m} d x}{m^{12} + 144 \, m^{11} + 9218 \, m^{10} + 345840 \, m^{9} + 8439783 \, m^{8} + 140529312 \, m^{7} + 1628301884 \, m^{6} + 13137458400 \, m^{5} + 72578259391 \, m^{4} + 264300628944 \, m^{3} + 590546123298 \, m^{2} + 703416314160 \, m + 316234143225}"," ",0,"((f*x)^m*m^11*x^23*e + 121*(f*x)^m*m^10*x^23*e + (f*x)^m*d*m^11*x^21 + 10*(f*x)^m*m^11*x^21*e + 6435*(f*x)^m*m^9*x^23*e + 123*(f*x)^m*d*m^10*x^21 + 1230*(f*x)^m*m^10*x^21*e + 197835*(f*x)^m*m^8*x^23*e + 10*(f*x)^m*d*m^11*x^19 + 6635*(f*x)^m*d*m^9*x^21 + 45*(f*x)^m*m^11*x^19*e + 66350*(f*x)^m*m^9*x^21*e + 3889578*(f*x)^m*m^7*x^23*e + 1250*(f*x)^m*d*m^10*x^19 + 206505*(f*x)^m*d*m^8*x^21 + 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68263642320*(f*x)^m*m^5*x^17*e + 556867114785*(f*x)^m*m^3*x^19*e + 327789307350*(f*x)^m*m*x^21*e + 33516*(f*x)^m*d*m^10*x^11 + 52110450*(f*x)^m*d*m^8*x^13 + 8059973040*(f*x)^m*d*m^6*x^15 + 156004908210*(f*x)^m*d*m^4*x^17 + 291789582570*(f*x)^m*d*m^2*x^19 + 15058768725*(f*x)^m*d*x^21 + 27930*(f*x)^m*m^10*x^11*e + 62532540*(f*x)^m*m^8*x^13*e + 14104952820*(f*x)^m*m^6*x^15*e + 416013088560*(f*x)^m*m^4*x^17*e + 1313053121565*(f*x)^m*m^2*x^19*e + 150587687250*(f*x)^m*x^21*e + 210*(f*x)^m*d*m^11*x^9 + 1954260*(f*x)^m*d*m^9*x^11 + 1094918580*(f*x)^m*d*m^7*x^13 + 74496630480*(f*x)^m*d*m^5*x^15 + 613938233025*(f*x)^m*d*m^3*x^17 + 361459164150*(f*x)^m*d*m*x^19 + 120*(f*x)^m*m^11*x^9*e + 1628550*(f*x)^m*m^9*x^11*e + 1313902296*(f*x)^m*m^7*x^13*e + 130369103340*(f*x)^m*m^5*x^15*e + 1637168621400*(f*x)^m*m^3*x^17*e + 1626566238675*(f*x)^m*m*x^19*e + 28350*(f*x)^m*d*m^10*x^9 + 65654820*(f*x)^m*d*m^8*x^11 + 15277213980*(f*x)^m*d*m^6*x^13 + 459045550800*(f*x)^m*d*m^4*x^15 + 1456578341055*(f*x)^m*d*m^2*x^17 + 166439022750*(f*x)^m*d*x^19 + 16200*(f*x)^m*m^10*x^9*e + 54712350*(f*x)^m*m^8*x^11*e + 18332656776*(f*x)^m*m^6*x^13*e + 803329713900*(f*x)^m*m^4*x^15*e + 3884208909480*(f*x)^m*m^2*x^17*e + 748975602375*(f*x)^m*x^19*e + 120*(f*x)^m*d*m^11*x^7 + 1680630*(f*x)^m*d*m^9*x^9 + 1404622296*(f*x)^m*d*m^7*x^11 + 143339613900*(f*x)^m*d*m^5*x^13 + 1823707864920*(f*x)^m*d*m^3*x^15 + 1812743750475*(f*x)^m*d*m*x^17 + 45*(f*x)^m*m^11*x^7*e + 960360*(f*x)^m*m^9*x^9*e + 1170518580*(f*x)^m*m^7*x^11*e + 172007536680*(f*x)^m*m^5*x^13*e + 3191488763610*(f*x)^m*m^3*x^15*e + 4833983334600*(f*x)^m*m*x^17*e + 16440*(f*x)^m*d*m^10*x^7 + 57500730*(f*x)^m*d*m^8*x^9 + 19962541368*(f*x)^m*d*m^6*x^11 + 895451283300*(f*x)^m*d*m^4*x^13 + 4360457499480*(f*x)^m*d*m^2*x^15 + 837090379125*(f*x)^m*d*x^17 + 6165*(f*x)^m*m^10*x^7*e + 32857560*(f*x)^m*m^8*x^9*e + 16635451140*(f*x)^m*m^6*x^11*e + 1074541539960*(f*x)^m*m^4*x^13*e + 7630800624090*(f*x)^m*m^2*x^15*e + 2232241011000*(f*x)^m*x^17*e + 45*(f*x)^m*d*m^11*x^5 + 991080*(f*x)^m*d*m^9*x^7 + 1254847860*(f*x)^m*d*m^7*x^9 + 190744119720*(f*x)^m*d*m^5*x^11 + 3600567789210*(f*x)^m*d*m^3*x^13 + 5458672303560*(f*x)^m*d*m*x^15 + 10*(f*x)^m*m^11*x^5*e + 371655*(f*x)^m*m^9*x^7*e + 717055920*(f*x)^m*m^7*x^9*e + 158953433100*(f*x)^m*m^5*x^11*e + 4320681347052*(f*x)^m*m^3*x^13*e + 9552676531230*(f*x)^m*m*x^15*e + 6255*(f*x)^m*d*m^10*x^5 + 34563240*(f*x)^m*d*m^8*x^7 + 18217524780*(f*x)^m*d*m^6*x^9 + 1212454199880*(f*x)^m*d*m^4*x^11 + 8695750818510*(f*x)^m*d*m^2*x^13 + 2529873145800*(f*x)^m*d*x^15 + 1390*(f*x)^m*m^10*x^5*e + 12961215*(f*x)^m*m^8*x^7*e + 10410014160*(f*x)^m*m^6*x^9*e + 1010378499900*(f*x)^m*m^4*x^11*e + 10434900982212*(f*x)^m*m^2*x^13*e + 4427278005150*(f*x)^m*x^15*e + 10*(f*x)^m*d*m^11*x^3 + 383535*(f*x)^m*d*m^9*x^5 + 770831280*(f*x)^m*d*m^7*x^7 + 177985672620*(f*x)^m*d*m^5*x^9 + 4952725167852*(f*x)^m*d*m^3*x^11 + 10969925251950*(f*x)^m*d*m*x^13 + (f*x)^m*m^11*x^3*e + 85230*(f*x)^m*m^9*x^5*e + 289061730*(f*x)^m*m^7*x^7*e + 101706098640*(f*x)^m*m^5*x^9*e + 4127270973210*(f*x)^m*m^3*x^11*e + 13163910302340*(f*x)^m*m*x^13*e + 1410*(f*x)^m*d*m^10*x^3 + 13645125*(f*x)^m*d*m^8*x^5 + 11467698480*(f*x)^m*d*m^6*x^7 + 1156995210420*(f*x)^m*d*m^4*x^9 + 12123781647516*(f*x)^m*d*m^2*x^11 + 5108397698250*(f*x)^m*d*x^13 + 141*(f*x)^m*m^10*x^3*e + 3032250*(f*x)^m*m^8*x^5*e + 4300386930*(f*x)^m*m^6*x^7*e + 661140120240*(f*x)^m*m^4*x^9*e + 10103151372930*(f*x)^m*m^2*x^11*e + 6130077237900*(f*x)^m*x^13*e + (f*x)^m*d*m^11*x + 87950*(f*x)^m*d*m^9*x^3 + 311564610*(f*x)^m*d*m^7*x^5 + 115122336720*(f*x)^m*d*m^5*x^7 + 4828477578330*(f*x)^m*d*m^3*x^9 + 15456024948420*(f*x)^m*d*m*x^11 + 8795*(f*x)^m*m^9*x^3*e + 69236580*(f*x)^m*m^7*x^5*e + 43170876270*(f*x)^m*m^5*x^7*e + 2759130044760*(f*x)^m*m^3*x^9*e + 12880020790350*(f*x)^m*m*x^11*e + 143*(f*x)^m*d*m^10*x + 3194550*(f*x)^m*d*m^8*x^3 + 4765995990*(f*x)^m*d*m^6*x^5 + 770638650960*(f*x)^m*d*m^4*x^7 + 12046833873270*(f*x)^m*d*m^2*x^9 + 7244636735700*(f*x)^m*d*x^11 + 319455*(f*x)^m*m^8*x^3*e + 1059110220*(f*x)^m*m^6*x^5*e + 288989494110*(f*x)^m*m^4*x^7*e + 6883905070440*(f*x)^m*m^2*x^9*e + 6037197279750*(f*x)^m*x^11*e + 9075*(f*x)^m*d*m^9*x + 74814180*(f*x)^m*d*m^7*x^3 + 49443604830*(f*x)^m*d*m^5*x^5 + 3314920570200*(f*x)^m*d*m^3*x^7 + 15593181033150*(f*x)^m*d*m*x^9 + 7481418*(f*x)^m*m^7*x^3*e + 10987467740*(f*x)^m*m^5*x^5*e + 1243095213825*(f*x)^m*m^3*x^7*e + 8910389161800*(f*x)^m*m*x^9*e + 336765*(f*x)^m*d*m^8*x + 1180850580*(f*x)^m*d*m^6*x^3 + 343967603850*(f*x)^m*d*m^4*x^5 + 8511631481880*(f*x)^m*d*m^2*x^7 + 7378796675250*(f*x)^m*d*x^9 + 118085058*(f*x)^m*m^6*x^3*e + 76437245300*(f*x)^m*m^4*x^5*e + 3191861805705*(f*x)^m*m^2*x^7*e + 4216455243000*(f*x)^m*x^9*e + 8103018*(f*x)^m*d*m^7*x + 12740467100*(f*x)^m*d*m^5*x^3 + 1546183653345*(f*x)^m*d*m^3*x^5 + 11284114422600*(f*x)^m*d*m*x^7 + 1274046710*(f*x)^m*m^5*x^3*e + 343596367410*(f*x)^m*m^3*x^5*e + 4231542908475*(f*x)^m*m*x^7*e + 132426294*(f*x)^m*d*m^6*x + 93153182700*(f*x)^m*d*m^4*x^3 + 4162610035755*(f*x)^m*d*m^2*x^5 + 5421156741000*(f*x)^m*d*x^7 + 9315318270*(f*x)^m*m^4*x^3*e + 925024452390*(f*x)^m*m^2*x^5*e + 2032933777875*(f*x)^m*x^7*e + 1495875590*(f*x)^m*d*m^5*x + 446323045810*(f*x)^m*d*m^3*x^3 + 5761525369635*(f*x)^m*d*m*x^5 + 44632304581*(f*x)^m*m^3*x^3*e + 1280338971030*(f*x)^m*m*x^5*e + 11641582810*(f*x)^m*d*m^4*x + 1304037152010*(f*x)^m*d*m^2*x^3 + 2846107289025*(f*x)^m*d*x^5 + 130403715201*(f*x)^m*m^2*x^3*e + 632468286450*(f*x)^m*x^5*e + 60936676581*(f*x)^m*d*m^3*x + 1993349776950*(f*x)^m*d*m*x^3 + 199334977695*(f*x)^m*m*x^3*e + 203363952363*(f*x)^m*d*m^2*x + 1054113810750*(f*x)^m*d*x^3 + 105411381075*(f*x)^m*x^3*e + 387182170935*(f*x)^m*d*m*x + 316234143225*(f*x)^m*d*x)/(m^12 + 144*m^11 + 9218*m^10 + 345840*m^9 + 8439783*m^8 + 140529312*m^7 + 1628301884*m^6 + 13137458400*m^5 + 72578259391*m^4 + 264300628944*m^3 + 590546123298*m^2 + 703416314160*m + 316234143225)","B",0
56,1,143,0,0.278033," ","integrate(x^5*(e*x^2+d)*(x^4+2*x^2+1)^5,x, algorithm=""giac"")","\frac{1}{28} \, x^{28} e + \frac{1}{26} \, d x^{26} + \frac{5}{13} \, x^{26} e + \frac{5}{12} \, d x^{24} + \frac{15}{8} \, x^{24} e + \frac{45}{22} \, d x^{22} + \frac{60}{11} \, x^{22} e + 6 \, d x^{20} + \frac{21}{2} \, x^{20} e + \frac{35}{3} \, d x^{18} + 14 \, x^{18} e + \frac{63}{4} \, d x^{16} + \frac{105}{8} \, x^{16} e + 15 \, d x^{14} + \frac{60}{7} \, x^{14} e + 10 \, d x^{12} + \frac{15}{4} \, x^{12} e + \frac{9}{2} \, d x^{10} + x^{10} e + \frac{5}{4} \, d x^{8} + \frac{1}{8} \, x^{8} e + \frac{1}{6} \, d x^{6}"," ",0,"1/28*x^28*e + 1/26*d*x^26 + 5/13*x^26*e + 5/12*d*x^24 + 15/8*x^24*e + 45/22*d*x^22 + 60/11*x^22*e + 6*d*x^20 + 21/2*x^20*e + 35/3*d*x^18 + 14*x^18*e + 63/4*d*x^16 + 105/8*x^16*e + 15*d*x^14 + 60/7*x^14*e + 10*d*x^12 + 15/4*x^12*e + 9/2*d*x^10 + x^10*e + 5/4*d*x^8 + 1/8*x^8*e + 1/6*d*x^6","B",0
57,1,144,0,0.296339," ","integrate(x^4*(e*x^2+d)*(x^4+2*x^2+1)^5,x, algorithm=""giac"")","\frac{1}{27} \, x^{27} e + \frac{1}{25} \, d x^{25} + \frac{2}{5} \, x^{25} e + \frac{10}{23} \, d x^{23} + \frac{45}{23} \, x^{23} e + \frac{15}{7} \, d x^{21} + \frac{40}{7} \, x^{21} e + \frac{120}{19} \, d x^{19} + \frac{210}{19} \, x^{19} e + \frac{210}{17} \, d x^{17} + \frac{252}{17} \, x^{17} e + \frac{84}{5} \, d x^{15} + 14 \, x^{15} e + \frac{210}{13} \, d x^{13} + \frac{120}{13} \, x^{13} e + \frac{120}{11} \, d x^{11} + \frac{45}{11} \, x^{11} e + 5 \, d x^{9} + \frac{10}{9} \, x^{9} e + \frac{10}{7} \, d x^{7} + \frac{1}{7} \, x^{7} e + \frac{1}{5} \, d x^{5}"," ",0,"1/27*x^27*e + 1/25*d*x^25 + 2/5*x^25*e + 10/23*d*x^23 + 45/23*x^23*e + 15/7*d*x^21 + 40/7*x^21*e + 120/19*d*x^19 + 210/19*x^19*e + 210/17*d*x^17 + 252/17*x^17*e + 84/5*d*x^15 + 14*x^15*e + 210/13*d*x^13 + 120/13*x^13*e + 120/11*d*x^11 + 45/11*x^11*e + 5*d*x^9 + 10/9*x^9*e + 10/7*d*x^7 + 1/7*x^7*e + 1/5*d*x^5","A",0
58,1,144,0,0.399556," ","integrate(x^3*(e*x^2+d)*(x^4+2*x^2+1)^5,x, algorithm=""giac"")","\frac{1}{26} \, x^{26} e + \frac{1}{24} \, d x^{24} + \frac{5}{12} \, x^{24} e + \frac{5}{11} \, d x^{22} + \frac{45}{22} \, x^{22} e + \frac{9}{4} \, d x^{20} + 6 \, x^{20} e + \frac{20}{3} \, d x^{18} + \frac{35}{3} \, x^{18} e + \frac{105}{8} \, d x^{16} + \frac{63}{4} \, x^{16} e + 18 \, d x^{14} + 15 \, x^{14} e + \frac{35}{2} \, d x^{12} + 10 \, x^{12} e + 12 \, d x^{10} + \frac{9}{2} \, x^{10} e + \frac{45}{8} \, d x^{8} + \frac{5}{4} \, x^{8} e + \frac{5}{3} \, d x^{6} + \frac{1}{6} \, x^{6} e + \frac{1}{4} \, d x^{4}"," ",0,"1/26*x^26*e + 1/24*d*x^24 + 5/12*x^24*e + 5/11*d*x^22 + 45/22*x^22*e + 9/4*d*x^20 + 6*x^20*e + 20/3*d*x^18 + 35/3*x^18*e + 105/8*d*x^16 + 63/4*x^16*e + 18*d*x^14 + 15*x^14*e + 35/2*d*x^12 + 10*x^12*e + 12*d*x^10 + 9/2*x^10*e + 45/8*d*x^8 + 5/4*x^8*e + 5/3*d*x^6 + 1/6*x^6*e + 1/4*d*x^4","B",0
59,1,144,0,0.287818," ","integrate(x^2*(e*x^2+d)*(x^4+2*x^2+1)^5,x, algorithm=""giac"")","\frac{1}{25} \, x^{25} e + \frac{1}{23} \, d x^{23} + \frac{10}{23} \, x^{23} e + \frac{10}{21} \, d x^{21} + \frac{15}{7} \, x^{21} e + \frac{45}{19} \, d x^{19} + \frac{120}{19} \, x^{19} e + \frac{120}{17} \, d x^{17} + \frac{210}{17} \, x^{17} e + 14 \, d x^{15} + \frac{84}{5} \, x^{15} e + \frac{252}{13} \, d x^{13} + \frac{210}{13} \, x^{13} e + \frac{210}{11} \, d x^{11} + \frac{120}{11} \, x^{11} e + \frac{40}{3} \, d x^{9} + 5 \, x^{9} e + \frac{45}{7} \, d x^{7} + \frac{10}{7} \, x^{7} e + 2 \, d x^{5} + \frac{1}{5} \, x^{5} e + \frac{1}{3} \, d x^{3}"," ",0,"1/25*x^25*e + 1/23*d*x^23 + 10/23*x^23*e + 10/21*d*x^21 + 15/7*x^21*e + 45/19*d*x^19 + 120/19*x^19*e + 120/17*d*x^17 + 210/17*x^17*e + 14*d*x^15 + 84/5*x^15*e + 252/13*d*x^13 + 210/13*x^13*e + 210/11*d*x^11 + 120/11*x^11*e + 40/3*d*x^9 + 5*x^9*e + 45/7*d*x^7 + 10/7*x^7*e + 2*d*x^5 + 1/5*x^5*e + 1/3*d*x^3","A",0
60,1,144,0,0.313732," ","integrate(x*(e*x^2+d)*(x^4+2*x^2+1)^5,x, algorithm=""giac"")","\frac{1}{24} \, x^{24} e + \frac{1}{22} \, d x^{22} + \frac{5}{11} \, x^{22} e + \frac{1}{2} \, d x^{20} + \frac{9}{4} \, x^{20} e + \frac{5}{2} \, d x^{18} + \frac{20}{3} \, x^{18} e + \frac{15}{2} \, d x^{16} + \frac{105}{8} \, x^{16} e + 15 \, d x^{14} + 18 \, x^{14} e + 21 \, d x^{12} + \frac{35}{2} \, x^{12} e + 21 \, d x^{10} + 12 \, x^{10} e + 15 \, d x^{8} + \frac{45}{8} \, x^{8} e + \frac{15}{2} \, d x^{6} + \frac{5}{3} \, x^{6} e + \frac{5}{2} \, d x^{4} + \frac{1}{4} \, x^{4} e + \frac{1}{2} \, d x^{2}"," ",0,"1/24*x^24*e + 1/22*d*x^22 + 5/11*x^22*e + 1/2*d*x^20 + 9/4*x^20*e + 5/2*d*x^18 + 20/3*x^18*e + 15/2*d*x^16 + 105/8*x^16*e + 15*d*x^14 + 18*x^14*e + 21*d*x^12 + 35/2*x^12*e + 21*d*x^10 + 12*x^10*e + 15*d*x^8 + 45/8*x^8*e + 15/2*d*x^6 + 5/3*x^6*e + 5/2*d*x^4 + 1/4*x^4*e + 1/2*d*x^2","B",0
61,1,141,0,0.362472," ","integrate((e*x^2+d)*(x^4+2*x^2+1)^5,x, algorithm=""giac"")","\frac{1}{23} \, x^{23} e + \frac{1}{21} \, d x^{21} + \frac{10}{21} \, x^{21} e + \frac{10}{19} \, d x^{19} + \frac{45}{19} \, x^{19} e + \frac{45}{17} \, d x^{17} + \frac{120}{17} \, x^{17} e + 8 \, d x^{15} + 14 \, x^{15} e + \frac{210}{13} \, d x^{13} + \frac{252}{13} \, x^{13} e + \frac{252}{11} \, d x^{11} + \frac{210}{11} \, x^{11} e + \frac{70}{3} \, d x^{9} + \frac{40}{3} \, x^{9} e + \frac{120}{7} \, d x^{7} + \frac{45}{7} \, x^{7} e + 9 \, d x^{5} + 2 \, x^{5} e + \frac{10}{3} \, d x^{3} + \frac{1}{3} \, x^{3} e + d x"," ",0,"1/23*x^23*e + 1/21*d*x^21 + 10/21*x^21*e + 10/19*d*x^19 + 45/19*x^19*e + 45/17*d*x^17 + 120/17*x^17*e + 8*d*x^15 + 14*x^15*e + 210/13*d*x^13 + 252/13*x^13*e + 252/11*d*x^11 + 210/11*x^11*e + 70/3*d*x^9 + 40/3*x^9*e + 120/7*d*x^7 + 45/7*x^7*e + 9*d*x^5 + 2*x^5*e + 10/3*d*x^3 + 1/3*x^3*e + d*x","A",0
62,1,145,0,0.266624," ","integrate((e*x^2+d)*(x^4+2*x^2+1)^5/x,x, algorithm=""giac"")","\frac{1}{22} \, x^{22} e + \frac{1}{20} \, d x^{20} + \frac{1}{2} \, x^{20} e + \frac{5}{9} \, d x^{18} + \frac{5}{2} \, x^{18} e + \frac{45}{16} \, d x^{16} + \frac{15}{2} \, x^{16} e + \frac{60}{7} \, d x^{14} + 15 \, x^{14} e + \frac{35}{2} \, d x^{12} + 21 \, x^{12} e + \frac{126}{5} \, d x^{10} + 21 \, x^{10} e + \frac{105}{4} \, d x^{8} + 15 \, x^{8} e + 20 \, d x^{6} + \frac{15}{2} \, x^{6} e + \frac{45}{4} \, d x^{4} + \frac{5}{2} \, x^{4} e + 5 \, d x^{2} + \frac{1}{2} \, x^{2} e + \frac{1}{2} \, d \log\left(x^{2}\right)"," ",0,"1/22*x^22*e + 1/20*d*x^20 + 1/2*x^20*e + 5/9*d*x^18 + 5/2*x^18*e + 45/16*d*x^16 + 15/2*x^16*e + 60/7*d*x^14 + 15*x^14*e + 35/2*d*x^12 + 21*x^12*e + 126/5*d*x^10 + 21*x^10*e + 105/4*d*x^8 + 15*x^8*e + 20*d*x^6 + 15/2*x^6*e + 45/4*d*x^4 + 5/2*x^4*e + 5*d*x^2 + 1/2*x^2*e + 1/2*d*log(x^2)","A",0
63,1,139,0,0.360968," ","integrate((e*x^2+d)*(x^4+2*x^2+1)^5/x^2,x, algorithm=""giac"")","\frac{1}{21} \, x^{21} e + \frac{1}{19} \, d x^{19} + \frac{10}{19} \, x^{19} e + \frac{10}{17} \, d x^{17} + \frac{45}{17} \, x^{17} e + 3 \, d x^{15} + 8 \, x^{15} e + \frac{120}{13} \, d x^{13} + \frac{210}{13} \, x^{13} e + \frac{210}{11} \, d x^{11} + \frac{252}{11} \, x^{11} e + 28 \, d x^{9} + \frac{70}{3} \, x^{9} e + 30 \, d x^{7} + \frac{120}{7} \, x^{7} e + 24 \, d x^{5} + 9 \, x^{5} e + 15 \, d x^{3} + \frac{10}{3} \, x^{3} e + 10 \, d x + x e - \frac{d}{x}"," ",0,"1/21*x^21*e + 1/19*d*x^19 + 10/19*x^19*e + 10/17*d*x^17 + 45/17*x^17*e + 3*d*x^15 + 8*x^15*e + 120/13*d*x^13 + 210/13*x^13*e + 210/11*d*x^11 + 252/11*x^11*e + 28*d*x^9 + 70/3*x^9*e + 30*d*x^7 + 120/7*x^7*e + 24*d*x^5 + 9*x^5*e + 15*d*x^3 + 10/3*x^3*e + 10*d*x + x*e - d/x","A",0
64,1,156,0,0.263450," ","integrate((e*x^2+d)*(x^4+2*x^2+1)^5/x^3,x, algorithm=""giac"")","\frac{1}{20} \, x^{20} e + \frac{1}{18} \, d x^{18} + \frac{5}{9} \, x^{18} e + \frac{5}{8} \, d x^{16} + \frac{45}{16} \, x^{16} e + \frac{45}{14} \, d x^{14} + \frac{60}{7} \, x^{14} e + 10 \, d x^{12} + \frac{35}{2} \, x^{12} e + 21 \, d x^{10} + \frac{126}{5} \, x^{10} e + \frac{63}{2} \, d x^{8} + \frac{105}{4} \, x^{8} e + 35 \, d x^{6} + 20 \, x^{6} e + 30 \, d x^{4} + \frac{45}{4} \, x^{4} e + \frac{45}{2} \, d x^{2} + 5 \, x^{2} e + \frac{1}{2} \, {\left(10 \, d + e\right)} \log\left(x^{2}\right) - \frac{10 \, d x^{2} + x^{2} e + d}{2 \, x^{2}}"," ",0,"1/20*x^20*e + 1/18*d*x^18 + 5/9*x^18*e + 5/8*d*x^16 + 45/16*x^16*e + 45/14*d*x^14 + 60/7*x^14*e + 10*d*x^12 + 35/2*x^12*e + 21*d*x^10 + 126/5*x^10*e + 63/2*d*x^8 + 105/4*x^8*e + 35*d*x^6 + 20*x^6*e + 30*d*x^4 + 45/4*x^4*e + 45/2*d*x^2 + 5*x^2*e + 1/2*(10*d + e)*log(x^2) - 1/2*(10*d*x^2 + x^2*e + d)/x^2","A",0
65,1,1848,0,0.619249," ","integrate((f*x)^m*(x^2+1)*(x^4+2*x^2+1)^5,x, algorithm=""giac"")","\frac{\left(f x\right)^{m} m^{11} x^{23} + 121 \, \left(f x\right)^{m} m^{10} x^{23} + 11 \, \left(f x\right)^{m} m^{11} x^{21} + 6435 \, \left(f x\right)^{m} m^{9} x^{23} + 1353 \, \left(f x\right)^{m} m^{10} x^{21} + 197835 \, \left(f x\right)^{m} m^{8} x^{23} + 55 \, \left(f x\right)^{m} m^{11} x^{19} + 72985 \, \left(f x\right)^{m} m^{9} x^{21} + 3889578 \, \left(f x\right)^{m} m^{7} x^{23} + 6875 \, \left(f x\right)^{m} m^{10} x^{19} + 2271555 \, \left(f x\right)^{m} m^{8} x^{21} + 51069018 \, \left(f x\right)^{m} m^{6} x^{23} + 165 \, \left(f x\right)^{m} m^{11} x^{17} + 376365 \, \left(f x\right)^{m} m^{9} x^{19} + 45134958 \, \left(f x\right)^{m} m^{7} x^{21} + 453714470 \, \left(f x\right)^{m} m^{5} x^{23} + 20955 \, \left(f x\right)^{m} m^{10} x^{17} + 11870265 \, \left(f x\right)^{m} m^{8} x^{19} + 597988314 \, \left(f x\right)^{m} m^{6} x^{21} + 2702025590 \, \left(f x\right)^{m} m^{4} x^{23} + 330 \, \left(f x\right)^{m} m^{11} x^{15} + 1164735 \, \left(f x\right)^{m} m^{9} x^{17} + 238653030 \, \left(f x\right)^{m} m^{7} x^{19} + 5353566130 \, \left(f x\right)^{m} m^{5} x^{21} + 10431670821 \, \left(f x\right)^{m} m^{3} x^{23} + 42570 \, \left(f x\right)^{m} m^{10} x^{15} + 37263105 \, \left(f x\right)^{m} m^{8} x^{17} + 3194704590 \, \left(f x\right)^{m} m^{6} x^{19} + 32087153670 \, \left(f x\right)^{m} m^{4} x^{21} + 24372200061 \, \left(f x\right)^{m} m^{2} x^{23} + 462 \, \left(f x\right)^{m} m^{11} x^{13} + 2403390 \, \left(f x\right)^{m} m^{9} x^{15} + 759091410 \, \left(f x\right)^{m} m^{7} x^{17} + 28857216410 \, \left(f x\right)^{m} m^{5} x^{19} + 124530626231 \, \left(f x\right)^{m} m^{3} x^{21} + 29985521895 \, \left(f x\right)^{m} m x^{23} + 60522 \, \left(f x\right)^{m} m^{10} x^{13} + 78076350 \, \left(f x\right)^{m} m^{8} x^{15} + 10282782510 \, \left(f x\right)^{m} m^{6} x^{17} + 174273100210 \, \left(f x\right)^{m} m^{4} x^{19} + 292163767533 \, \left(f x\right)^{m} m^{2} x^{21} + 13749310575 \, \left(f x\right)^{m} x^{23} + 462 \, \left(f x\right)^{m} m^{11} x^{11} + 3471930 \, \left(f x\right)^{m} m^{9} x^{13} + 1613983140 \, \left(f x\right)^{m} m^{7} x^{15} + 93862508190 \, \left(f x\right)^{m} m^{5} x^{17} + 680615362515 \, \left(f x\right)^{m} m^{3} x^{19} + 360568238085 \, \left(f x\right)^{m} m x^{21} + 61446 \, \left(f x\right)^{m} m^{10} x^{11} + 114642990 \, \left(f x\right)^{m} m^{8} x^{13} + 22164925860 \, \left(f x\right)^{m} m^{6} x^{15} + 572017996770 \, \left(f x\right)^{m} m^{4} x^{17} + 1604842704135 \, \left(f x\right)^{m} m^{2} x^{19} + 165646455975 \, \left(f x\right)^{m} x^{21} + 330 \, \left(f x\right)^{m} m^{11} x^{9} + 3582810 \, \left(f x\right)^{m} m^{9} x^{11} + 2408820876 \, \left(f x\right)^{m} m^{7} x^{13} + 204865733820 \, \left(f x\right)^{m} m^{5} x^{15} + 2251106854425 \, \left(f x\right)^{m} m^{3} x^{17} + 1988025402825 \, \left(f x\right)^{m} m x^{19} + 44550 \, \left(f x\right)^{m} m^{10} x^{9} + 120367170 \, \left(f x\right)^{m} m^{8} x^{11} + 33609870756 \, \left(f x\right)^{m} m^{6} x^{13} + 1262375264700 \, \left(f x\right)^{m} m^{4} x^{15} + 5340787250535 \, \left(f x\right)^{m} m^{2} x^{17} + 915414625125 \, \left(f x\right)^{m} x^{19} + 165 \, \left(f x\right)^{m} m^{11} x^{7} + 2640990 \, \left(f x\right)^{m} m^{9} x^{9} + 2575140876 \, \left(f x\right)^{m} m^{7} x^{11} + 315347150580 \, \left(f x\right)^{m} m^{5} x^{13} + 5015196628530 \, \left(f x\right)^{m} m^{3} x^{15} + 6646727085075 \, \left(f x\right)^{m} m x^{17} + 22605 \, \left(f x\right)^{m} m^{10} x^{7} + 90358290 \, \left(f x\right)^{m} m^{8} x^{9} + 36597992508 \, \left(f x\right)^{m} m^{6} x^{11} + 1969992823260 \, \left(f x\right)^{m} m^{4} x^{13} + 11991258123570 \, \left(f x\right)^{m} m^{2} x^{15} + 3069331390125 \, \left(f x\right)^{m} x^{17} + 55 \, \left(f x\right)^{m} m^{11} x^{5} + 1362735 \, \left(f x\right)^{m} m^{9} x^{7} + 1971903780 \, \left(f x\right)^{m} m^{7} x^{9} + 349697552820 \, \left(f x\right)^{m} m^{5} x^{11} + 7921249136262 \, \left(f x\right)^{m} m^{3} x^{13} + 15011348834790 \, \left(f x\right)^{m} m x^{15} + 7645 \, \left(f x\right)^{m} m^{10} x^{5} + 47524455 \, \left(f x\right)^{m} m^{8} x^{7} + 28627538940 \, \left(f x\right)^{m} m^{6} x^{9} + 2222832699780 \, \left(f x\right)^{m} m^{4} x^{11} + 19130651800722 \, \left(f x\right)^{m} m^{2} x^{13} + 6957151150950 \, \left(f x\right)^{m} x^{15} + 11 \, \left(f x\right)^{m} m^{11} x^{3} + 468765 \, \left(f x\right)^{m} m^{9} x^{5} + 1059893010 \, \left(f x\right)^{m} m^{7} x^{7} + 279691771260 \, \left(f x\right)^{m} m^{5} x^{9} + 9079996141062 \, \left(f x\right)^{m} m^{3} x^{11} + 24133835554290 \, \left(f x\right)^{m} m x^{13} + 1551 \, \left(f x\right)^{m} m^{10} x^{3} + 16677375 \, \left(f x\right)^{m} m^{8} x^{5} + 15768085410 \, \left(f x\right)^{m} m^{6} x^{7} + 1818135330660 \, \left(f x\right)^{m} m^{4} x^{9} + 22226933020446 \, \left(f x\right)^{m} m^{2} x^{11} + 11238474936150 \, \left(f x\right)^{m} x^{13} + \left(f x\right)^{m} m^{11} x + 96745 \, \left(f x\right)^{m} m^{9} x^{3} + 380801190 \, \left(f x\right)^{m} m^{7} x^{5} + 158293212990 \, \left(f x\right)^{m} m^{5} x^{7} + 7587607623090 \, \left(f x\right)^{m} m^{3} x^{9} + 28336045738770 \, \left(f x\right)^{m} m x^{11} + 143 \, \left(f x\right)^{m} m^{10} x + 3514005 \, \left(f x\right)^{m} m^{8} x^{3} + 5825106210 \, \left(f x\right)^{m} m^{6} x^{5} + 1059628145070 \, \left(f x\right)^{m} m^{4} x^{7} + 18930738943710 \, \left(f x\right)^{m} m^{2} x^{9} + 13281834015450 \, \left(f x\right)^{m} x^{11} + 9075 \, \left(f x\right)^{m} m^{9} x + 82295598 \, \left(f x\right)^{m} m^{7} x^{3} + 60431072570 \, \left(f x\right)^{m} m^{5} x^{5} + 4558015784025 \, \left(f x\right)^{m} m^{3} x^{7} + 24503570194950 \, \left(f x\right)^{m} m x^{9} + 336765 \, \left(f x\right)^{m} m^{8} x + 1298935638 \, \left(f x\right)^{m} m^{6} x^{3} + 420404849150 \, \left(f x\right)^{m} m^{4} x^{5} + 11703493287585 \, \left(f x\right)^{m} m^{2} x^{7} + 11595251918250 \, \left(f x\right)^{m} x^{9} + 8103018 \, \left(f x\right)^{m} m^{7} x + 14014513810 \, \left(f x\right)^{m} m^{5} x^{3} + 1889780020755 \, \left(f x\right)^{m} m^{3} x^{5} + 15515657331075 \, \left(f x\right)^{m} m x^{7} + 132426294 \, \left(f x\right)^{m} m^{6} x + 102468500970 \, \left(f x\right)^{m} m^{4} x^{3} + 5087634488145 \, \left(f x\right)^{m} m^{2} x^{5} + 7454090518875 \, \left(f x\right)^{m} x^{7} + 1495875590 \, \left(f x\right)^{m} m^{5} x + 490955350391 \, \left(f x\right)^{m} m^{3} x^{3} + 7041864340665 \, \left(f x\right)^{m} m x^{5} + 11641582810 \, \left(f x\right)^{m} m^{4} x + 1434440867211 \, \left(f x\right)^{m} m^{2} x^{3} + 3478575575475 \, \left(f x\right)^{m} x^{5} + 60936676581 \, \left(f x\right)^{m} m^{3} x + 2192684754645 \, \left(f x\right)^{m} m x^{3} + 203363952363 \, \left(f x\right)^{m} m^{2} x + 1159525191825 \, \left(f x\right)^{m} x^{3} + 387182170935 \, \left(f x\right)^{m} m x + 316234143225 \, \left(f x\right)^{m} x}{m^{12} + 144 \, m^{11} + 9218 \, m^{10} + 345840 \, m^{9} + 8439783 \, m^{8} + 140529312 \, m^{7} + 1628301884 \, m^{6} + 13137458400 \, m^{5} + 72578259391 \, m^{4} + 264300628944 \, m^{3} + 590546123298 \, m^{2} + 703416314160 \, m + 316234143225}"," ",0,"((f*x)^m*m^11*x^23 + 121*(f*x)^m*m^10*x^23 + 11*(f*x)^m*m^11*x^21 + 6435*(f*x)^m*m^9*x^23 + 1353*(f*x)^m*m^10*x^21 + 197835*(f*x)^m*m^8*x^23 + 55*(f*x)^m*m^11*x^19 + 72985*(f*x)^m*m^9*x^21 + 3889578*(f*x)^m*m^7*x^23 + 6875*(f*x)^m*m^10*x^19 + 2271555*(f*x)^m*m^8*x^21 + 51069018*(f*x)^m*m^6*x^23 + 165*(f*x)^m*m^11*x^17 + 376365*(f*x)^m*m^9*x^19 + 45134958*(f*x)^m*m^7*x^21 + 453714470*(f*x)^m*m^5*x^23 + 20955*(f*x)^m*m^10*x^17 + 11870265*(f*x)^m*m^8*x^19 + 597988314*(f*x)^m*m^6*x^21 + 2702025590*(f*x)^m*m^4*x^23 + 330*(f*x)^m*m^11*x^15 + 1164735*(f*x)^m*m^9*x^17 + 238653030*(f*x)^m*m^7*x^19 + 5353566130*(f*x)^m*m^5*x^21 + 10431670821*(f*x)^m*m^3*x^23 + 42570*(f*x)^m*m^10*x^15 + 37263105*(f*x)^m*m^8*x^17 + 3194704590*(f*x)^m*m^6*x^19 + 32087153670*(f*x)^m*m^4*x^21 + 24372200061*(f*x)^m*m^2*x^23 + 462*(f*x)^m*m^11*x^13 + 2403390*(f*x)^m*m^9*x^15 + 759091410*(f*x)^m*m^7*x^17 + 28857216410*(f*x)^m*m^5*x^19 + 124530626231*(f*x)^m*m^3*x^21 + 29985521895*(f*x)^m*m*x^23 + 60522*(f*x)^m*m^10*x^13 + 78076350*(f*x)^m*m^8*x^15 + 10282782510*(f*x)^m*m^6*x^17 + 174273100210*(f*x)^m*m^4*x^19 + 292163767533*(f*x)^m*m^2*x^21 + 13749310575*(f*x)^m*x^23 + 462*(f*x)^m*m^11*x^11 + 3471930*(f*x)^m*m^9*x^13 + 1613983140*(f*x)^m*m^7*x^15 + 93862508190*(f*x)^m*m^5*x^17 + 680615362515*(f*x)^m*m^3*x^19 + 360568238085*(f*x)^m*m*x^21 + 61446*(f*x)^m*m^10*x^11 + 114642990*(f*x)^m*m^8*x^13 + 22164925860*(f*x)^m*m^6*x^15 + 572017996770*(f*x)^m*m^4*x^17 + 1604842704135*(f*x)^m*m^2*x^19 + 165646455975*(f*x)^m*x^21 + 330*(f*x)^m*m^11*x^9 + 3582810*(f*x)^m*m^9*x^11 + 2408820876*(f*x)^m*m^7*x^13 + 204865733820*(f*x)^m*m^5*x^15 + 2251106854425*(f*x)^m*m^3*x^17 + 1988025402825*(f*x)^m*m*x^19 + 44550*(f*x)^m*m^10*x^9 + 120367170*(f*x)^m*m^8*x^11 + 33609870756*(f*x)^m*m^6*x^13 + 1262375264700*(f*x)^m*m^4*x^15 + 5340787250535*(f*x)^m*m^2*x^17 + 915414625125*(f*x)^m*x^19 + 165*(f*x)^m*m^11*x^7 + 2640990*(f*x)^m*m^9*x^9 + 2575140876*(f*x)^m*m^7*x^11 + 315347150580*(f*x)^m*m^5*x^13 + 5015196628530*(f*x)^m*m^3*x^15 + 6646727085075*(f*x)^m*m*x^17 + 22605*(f*x)^m*m^10*x^7 + 90358290*(f*x)^m*m^8*x^9 + 36597992508*(f*x)^m*m^6*x^11 + 1969992823260*(f*x)^m*m^4*x^13 + 11991258123570*(f*x)^m*m^2*x^15 + 3069331390125*(f*x)^m*x^17 + 55*(f*x)^m*m^11*x^5 + 1362735*(f*x)^m*m^9*x^7 + 1971903780*(f*x)^m*m^7*x^9 + 349697552820*(f*x)^m*m^5*x^11 + 7921249136262*(f*x)^m*m^3*x^13 + 15011348834790*(f*x)^m*m*x^15 + 7645*(f*x)^m*m^10*x^5 + 47524455*(f*x)^m*m^8*x^7 + 28627538940*(f*x)^m*m^6*x^9 + 2222832699780*(f*x)^m*m^4*x^11 + 19130651800722*(f*x)^m*m^2*x^13 + 6957151150950*(f*x)^m*x^15 + 11*(f*x)^m*m^11*x^3 + 468765*(f*x)^m*m^9*x^5 + 1059893010*(f*x)^m*m^7*x^7 + 279691771260*(f*x)^m*m^5*x^9 + 9079996141062*(f*x)^m*m^3*x^11 + 24133835554290*(f*x)^m*m*x^13 + 1551*(f*x)^m*m^10*x^3 + 16677375*(f*x)^m*m^8*x^5 + 15768085410*(f*x)^m*m^6*x^7 + 1818135330660*(f*x)^m*m^4*x^9 + 22226933020446*(f*x)^m*m^2*x^11 + 11238474936150*(f*x)^m*x^13 + (f*x)^m*m^11*x + 96745*(f*x)^m*m^9*x^3 + 380801190*(f*x)^m*m^7*x^5 + 158293212990*(f*x)^m*m^5*x^7 + 7587607623090*(f*x)^m*m^3*x^9 + 28336045738770*(f*x)^m*m*x^11 + 143*(f*x)^m*m^10*x + 3514005*(f*x)^m*m^8*x^3 + 5825106210*(f*x)^m*m^6*x^5 + 1059628145070*(f*x)^m*m^4*x^7 + 18930738943710*(f*x)^m*m^2*x^9 + 13281834015450*(f*x)^m*x^11 + 9075*(f*x)^m*m^9*x + 82295598*(f*x)^m*m^7*x^3 + 60431072570*(f*x)^m*m^5*x^5 + 4558015784025*(f*x)^m*m^3*x^7 + 24503570194950*(f*x)^m*m*x^9 + 336765*(f*x)^m*m^8*x + 1298935638*(f*x)^m*m^6*x^3 + 420404849150*(f*x)^m*m^4*x^5 + 11703493287585*(f*x)^m*m^2*x^7 + 11595251918250*(f*x)^m*x^9 + 8103018*(f*x)^m*m^7*x + 14014513810*(f*x)^m*m^5*x^3 + 1889780020755*(f*x)^m*m^3*x^5 + 15515657331075*(f*x)^m*m*x^7 + 132426294*(f*x)^m*m^6*x + 102468500970*(f*x)^m*m^4*x^3 + 5087634488145*(f*x)^m*m^2*x^5 + 7454090518875*(f*x)^m*x^7 + 1495875590*(f*x)^m*m^5*x + 490955350391*(f*x)^m*m^3*x^3 + 7041864340665*(f*x)^m*m*x^5 + 11641582810*(f*x)^m*m^4*x + 1434440867211*(f*x)^m*m^2*x^3 + 3478575575475*(f*x)^m*x^5 + 60936676581*(f*x)^m*m^3*x + 2192684754645*(f*x)^m*m*x^3 + 203363952363*(f*x)^m*m^2*x + 1159525191825*(f*x)^m*x^3 + 387182170935*(f*x)^m*m*x + 316234143225*(f*x)^m*x)/(m^12 + 144*m^11 + 9218*m^10 + 345840*m^9 + 8439783*m^8 + 140529312*m^7 + 1628301884*m^6 + 13137458400*m^5 + 72578259391*m^4 + 264300628944*m^3 + 590546123298*m^2 + 703416314160*m + 316234143225)","B",0
66,1,61,0,0.338811," ","integrate(x^5*(x^2+1)*(x^4+2*x^2+1)^5,x, algorithm=""giac"")","\frac{1}{28} \, x^{28} + \frac{11}{26} \, x^{26} + \frac{55}{24} \, x^{24} + \frac{15}{2} \, x^{22} + \frac{33}{2} \, x^{20} + \frac{77}{3} \, x^{18} + \frac{231}{8} \, x^{16} + \frac{165}{7} \, x^{14} + \frac{55}{4} \, x^{12} + \frac{11}{2} \, x^{10} + \frac{11}{8} \, x^{8} + \frac{1}{6} \, x^{6}"," ",0,"1/28*x^28 + 11/26*x^26 + 55/24*x^24 + 15/2*x^22 + 33/2*x^20 + 77/3*x^18 + 231/8*x^16 + 165/7*x^14 + 55/4*x^12 + 11/2*x^10 + 11/8*x^8 + 1/6*x^6","B",0
67,1,61,0,0.413768," ","integrate(x^4*(x^2+1)*(x^4+2*x^2+1)^5,x, algorithm=""giac"")","\frac{1}{27} \, x^{27} + \frac{11}{25} \, x^{25} + \frac{55}{23} \, x^{23} + \frac{55}{7} \, x^{21} + \frac{330}{19} \, x^{19} + \frac{462}{17} \, x^{17} + \frac{154}{5} \, x^{15} + \frac{330}{13} \, x^{13} + 15 \, x^{11} + \frac{55}{9} \, x^{9} + \frac{11}{7} \, x^{7} + \frac{1}{5} \, x^{5}"," ",0,"1/27*x^27 + 11/25*x^25 + 55/23*x^23 + 55/7*x^21 + 330/19*x^19 + 462/17*x^17 + 154/5*x^15 + 330/13*x^13 + 15*x^11 + 55/9*x^9 + 11/7*x^7 + 1/5*x^5","A",0
68,1,61,0,0.362286," ","integrate(x^3*(x^2+1)*(x^4+2*x^2+1)^5,x, algorithm=""giac"")","\frac{1}{26} \, x^{26} + \frac{11}{24} \, x^{24} + \frac{5}{2} \, x^{22} + \frac{33}{4} \, x^{20} + \frac{55}{3} \, x^{18} + \frac{231}{8} \, x^{16} + 33 \, x^{14} + \frac{55}{2} \, x^{12} + \frac{33}{2} \, x^{10} + \frac{55}{8} \, x^{8} + \frac{11}{6} \, x^{6} + \frac{1}{4} \, x^{4}"," ",0,"1/26*x^26 + 11/24*x^24 + 5/2*x^22 + 33/4*x^20 + 55/3*x^18 + 231/8*x^16 + 33*x^14 + 55/2*x^12 + 33/2*x^10 + 55/8*x^8 + 11/6*x^6 + 1/4*x^4","B",0
69,1,61,0,0.304204," ","integrate(x^2*(x^2+1)*(x^4+2*x^2+1)^5,x, algorithm=""giac"")","\frac{1}{25} \, x^{25} + \frac{11}{23} \, x^{23} + \frac{55}{21} \, x^{21} + \frac{165}{19} \, x^{19} + \frac{330}{17} \, x^{17} + \frac{154}{5} \, x^{15} + \frac{462}{13} \, x^{13} + 30 \, x^{11} + \frac{55}{3} \, x^{9} + \frac{55}{7} \, x^{7} + \frac{11}{5} \, x^{5} + \frac{1}{3} \, x^{3}"," ",0,"1/25*x^25 + 11/23*x^23 + 55/21*x^21 + 165/19*x^19 + 330/17*x^17 + 154/5*x^15 + 462/13*x^13 + 30*x^11 + 55/3*x^9 + 55/7*x^7 + 11/5*x^5 + 1/3*x^3","A",0
70,1,76,0,0.314286," ","integrate(x*(x^2+1)*(x^4+2*x^2+1)^5,x, algorithm=""giac"")","\frac{1}{24} \, {\left(x^{4} + 2 \, x^{2}\right)}^{6} + \frac{1}{4} \, {\left(x^{4} + 2 \, x^{2}\right)}^{5} + \frac{5}{8} \, {\left(x^{4} + 2 \, x^{2}\right)}^{4} + \frac{1}{4} \, x^{4} + \frac{5}{6} \, {\left(x^{4} + 2 \, x^{2}\right)}^{3} + \frac{5}{8} \, {\left(x^{4} + 2 \, x^{2}\right)}^{2} + \frac{1}{2} \, x^{2}"," ",0,"1/24*(x^4 + 2*x^2)^6 + 1/4*(x^4 + 2*x^2)^5 + 5/8*(x^4 + 2*x^2)^4 + 1/4*x^4 + 5/6*(x^4 + 2*x^2)^3 + 5/8*(x^4 + 2*x^2)^2 + 1/2*x^2","B",0
71,1,57,0,0.273639," ","integrate((x^2+1)*(x^4+2*x^2+1)^5,x, algorithm=""giac"")","\frac{1}{23} \, x^{23} + \frac{11}{21} \, x^{21} + \frac{55}{19} \, x^{19} + \frac{165}{17} \, x^{17} + 22 \, x^{15} + \frac{462}{13} \, x^{13} + 42 \, x^{11} + \frac{110}{3} \, x^{9} + \frac{165}{7} \, x^{7} + 11 \, x^{5} + \frac{11}{3} \, x^{3} + x"," ",0,"1/23*x^23 + 11/21*x^21 + 55/19*x^19 + 165/17*x^17 + 22*x^15 + 462/13*x^13 + 42*x^11 + 110/3*x^9 + 165/7*x^7 + 11*x^5 + 11/3*x^3 + x","A",0
72,1,62,0,0.230012," ","integrate((x^2+1)*(x^4+2*x^2+1)^5/x,x, algorithm=""giac"")","\frac{1}{22} \, x^{22} + \frac{11}{20} \, x^{20} + \frac{55}{18} \, x^{18} + \frac{165}{16} \, x^{16} + \frac{165}{7} \, x^{14} + \frac{77}{2} \, x^{12} + \frac{231}{5} \, x^{10} + \frac{165}{4} \, x^{8} + \frac{55}{2} \, x^{6} + \frac{55}{4} \, x^{4} + \frac{11}{2} \, x^{2} + \frac{1}{2} \, \log\left(x^{2}\right)"," ",0,"1/22*x^22 + 11/20*x^20 + 55/18*x^18 + 165/16*x^16 + 165/7*x^14 + 77/2*x^12 + 231/5*x^10 + 165/4*x^8 + 55/2*x^6 + 55/4*x^4 + 11/2*x^2 + 1/2*log(x^2)","A",0
73,1,59,0,0.296994," ","integrate((x^2+1)*(x^4+2*x^2+1)^5/x^2,x, algorithm=""giac"")","\frac{1}{21} \, x^{21} + \frac{11}{19} \, x^{19} + \frac{55}{17} \, x^{17} + 11 \, x^{15} + \frac{330}{13} \, x^{13} + 42 \, x^{11} + \frac{154}{3} \, x^{9} + \frac{330}{7} \, x^{7} + 33 \, x^{5} + \frac{55}{3} \, x^{3} + 11 \, x - \frac{1}{x}"," ",0,"1/21*x^21 + 11/19*x^19 + 55/17*x^17 + 11*x^15 + 330/13*x^13 + 42*x^11 + 154/3*x^9 + 330/7*x^7 + 33*x^5 + 55/3*x^3 + 11*x - 1/x","A",0
74,1,69,0,0.356778," ","integrate((x^2+1)*(x^4+2*x^2+1)^5/x^3,x, algorithm=""giac"")","\frac{1}{20} \, x^{20} + \frac{11}{18} \, x^{18} + \frac{55}{16} \, x^{16} + \frac{165}{14} \, x^{14} + \frac{55}{2} \, x^{12} + \frac{231}{5} \, x^{10} + \frac{231}{4} \, x^{8} + 55 \, x^{6} + \frac{165}{4} \, x^{4} + \frac{55}{2} \, x^{2} - \frac{11 \, x^{2} + 1}{2 \, x^{2}} + \frac{11}{2} \, \log\left(x^{2}\right)"," ",0,"1/20*x^20 + 11/18*x^18 + 55/16*x^16 + 165/14*x^14 + 55/2*x^12 + 231/5*x^10 + 231/4*x^8 + 55*x^6 + 165/4*x^4 + 55/2*x^2 - 1/2*(11*x^2 + 1)/x^2 + 11/2*log(x^2)","A",0
75,1,101,0,0.430016," ","integrate(x^2*(e*x^2+d)/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{{\left(a b d \mathrm{sgn}\left(b x^{2} + a\right) - a^{2} e \mathrm{sgn}\left(b x^{2} + a\right)\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} + \frac{b^{2} x^{3} e \mathrm{sgn}\left(b x^{2} + a\right) + 3 \, b^{2} d x \mathrm{sgn}\left(b x^{2} + a\right) - 3 \, a b x e \mathrm{sgn}\left(b x^{2} + a\right)}{3 \, b^{3}}"," ",0,"-(a*b*d*sgn(b*x^2 + a) - a^2*e*sgn(b*x^2 + a))*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) + 1/3*(b^2*x^3*e*sgn(b*x^2 + a) + 3*b^2*d*x*sgn(b*x^2 + a) - 3*a*b*x*e*sgn(b*x^2 + a))/b^3","A",0
76,1,42,0,0.383432," ","integrate(x*(e*x^2+d)/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{x^{2} e}{b} + \frac{{\left(b d - a e\right)} \log\left({\left| b x^{2} + a \right|}\right)}{b^{2}}\right)} \mathrm{sgn}\left(b x^{2} + a\right)"," ",0,"1/2*(x^2*e/b + (b*d - a*e)*log(abs(b*x^2 + a))/b^2)*sgn(b*x^2 + a)","A",0
77,1,59,0,0.264538," ","integrate((e*x^2+d)/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{x e \mathrm{sgn}\left(b x^{2} + a\right)}{b} + \frac{{\left(b d \mathrm{sgn}\left(b x^{2} + a\right) - a e \mathrm{sgn}\left(b x^{2} + a\right)\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b}"," ",0,"x*e*sgn(b*x^2 + a)/b + (b*d*sgn(b*x^2 + a) - a*e*sgn(b*x^2 + a))*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b)","A",0
78,1,61,0,0.381439," ","integrate((e*x^2+d)/x/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{d \log\left(x^{2}\right) \mathrm{sgn}\left(b x^{2} + a\right)}{2 \, a} - \frac{{\left(b d \mathrm{sgn}\left(b x^{2} + a\right) - a e \mathrm{sgn}\left(b x^{2} + a\right)\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a b}"," ",0,"1/2*d*log(x^2)*sgn(b*x^2 + a)/a - 1/2*(b*d*sgn(b*x^2 + a) - a*e*sgn(b*x^2 + a))*log(abs(b*x^2 + a))/(a*b)","A",0
79,1,62,0,0.342746," ","integrate((e*x^2+d)/x^2/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{{\left(b d \mathrm{sgn}\left(b x^{2} + a\right) - a e \mathrm{sgn}\left(b x^{2} + a\right)\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a} - \frac{d \mathrm{sgn}\left(b x^{2} + a\right)}{a x}"," ",0,"-(b*d*sgn(b*x^2 + a) - a*e*sgn(b*x^2 + a))*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a) - d*sgn(b*x^2 + a)/(a*x)","A",0
80,1,131,0,0.386281," ","integrate((e*x^2+d)/x^3/((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{{\left(b d \mathrm{sgn}\left(b x^{2} + a\right) - a e \mathrm{sgn}\left(b x^{2} + a\right)\right)} \log\left(x^{2}\right)}{2 \, a^{2}} + \frac{{\left(b^{2} d \mathrm{sgn}\left(b x^{2} + a\right) - a b e \mathrm{sgn}\left(b x^{2} + a\right)\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{2} b} + \frac{b d x^{2} \mathrm{sgn}\left(b x^{2} + a\right) - a x^{2} e \mathrm{sgn}\left(b x^{2} + a\right) - a d \mathrm{sgn}\left(b x^{2} + a\right)}{2 \, a^{2} x^{2}}"," ",0,"-1/2*(b*d*sgn(b*x^2 + a) - a*e*sgn(b*x^2 + a))*log(x^2)/a^2 + 1/2*(b^2*d*sgn(b*x^2 + a) - a*b*e*sgn(b*x^2 + a))*log(abs(b*x^2 + a))/(a^2*b) + 1/2*(b*d*x^2*sgn(b*x^2 + a) - a*x^2*e*sgn(b*x^2 + a) - a*d*sgn(b*x^2 + a))/(a^2*x^2)","A",0
81,0,0,0,0.000000," ","integrate(x^2*(e*x^2+d)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
82,1,40,0,0.507462," ","integrate(x*(e*x^2+d)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","-\frac{2 \, b x^{2} e + b d + a e}{4 \, {\left(b x^{2} + a\right)}^{2} b^{2} \mathrm{sgn}\left(b x^{2} + a\right)}"," ",0,"-1/4*(2*b*x^2*e + b*d + a*e)/((b*x^2 + a)^2*b^2*sgn(b*x^2 + a))","A",0
83,0,0,0,0.000000," ","integrate((e*x^2+d)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
84,1,96,0,0.527900," ","integrate((e*x^2+d)/x/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","-\frac{d \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{3} \mathrm{sgn}\left(b x^{2} + a\right)} + \frac{d \log\left({\left| x \right|}\right)}{a^{3} \mathrm{sgn}\left(b x^{2} + a\right)} + \frac{2 \, a b^{2} d x^{2} + 3 \, a^{2} b d - a^{3} e}{4 \, {\left(b x^{2} + a\right)}^{2} a^{3} b \mathrm{sgn}\left(b x^{2} + a\right)}"," ",0,"-1/2*d*log(abs(b*x^2 + a))/(a^3*sgn(b*x^2 + a)) + d*log(abs(x))/(a^3*sgn(b*x^2 + a)) + 1/4*(2*a*b^2*d*x^2 + 3*a^2*b*d - a^3*e)/((b*x^2 + a)^2*a^3*b*sgn(b*x^2 + a))","A",0
85,0,0,0,0.000000," ","integrate((e*x^2+d)/x^2/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
86,1,144,0,0.403311," ","integrate((e*x^2+d)/x^3/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","-\frac{{\left(3 \, b d - a e\right)} \log\left({\left| x \right|}\right)}{a^{4} \mathrm{sgn}\left(b x^{2} + a\right)} + \frac{{\left(3 \, b^{2} d - a b e\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{4} b \mathrm{sgn}\left(b x^{2} + a\right)} - \frac{2 \, {\left(3 \, a b^{2} d - a^{2} b e\right)} x^{4} + 2 \, a^{3} d + 3 \, {\left(3 \, a^{2} b d - a^{3} e\right)} x^{2}}{4 \, {\left(b x^{2} + a\right)}^{2} a^{4} x^{2} \mathrm{sgn}\left(b x^{2} + a\right)}"," ",0,"-(3*b*d - a*e)*log(abs(x))/(a^4*sgn(b*x^2 + a)) + 1/2*(3*b^2*d - a*b*e)*log(abs(b*x^2 + a))/(a^4*b*sgn(b*x^2 + a)) - 1/4*(2*(3*a*b^2*d - a^2*b*e)*x^4 + 2*a^3*d + 3*(3*a^2*b*d - a^3*e)*x^2)/((b*x^2 + a)^2*a^4*x^2*sgn(b*x^2 + a))","A",0
87,1,2213,0,0.686980," ","integrate((f*x)^m*(e*x^2+d)*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""giac"")","\frac{\left(f x\right)^{m} b^{5} m^{6} x^{13} e \mathrm{sgn}\left(b x^{2} + a\right) + 36 \, \left(f x\right)^{m} b^{5} m^{5} x^{13} e \mathrm{sgn}\left(b x^{2} + a\right) + \left(f x\right)^{m} b^{5} d m^{6} x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, \left(f x\right)^{m} a b^{4} m^{6} x^{11} e \mathrm{sgn}\left(b x^{2} + a\right) + 505 \, \left(f x\right)^{m} b^{5} m^{4} x^{13} e \mathrm{sgn}\left(b x^{2} + a\right) + 38 \, \left(f x\right)^{m} b^{5} d m^{5} x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + 190 \, \left(f x\right)^{m} a b^{4} m^{5} x^{11} e \mathrm{sgn}\left(b x^{2} + a\right) + 3480 \, \left(f x\right)^{m} b^{5} m^{3} x^{13} e \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, \left(f x\right)^{m} a b^{4} d m^{6} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + 555 \, \left(f x\right)^{m} b^{5} d m^{4} x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + 10 \, \left(f x\right)^{m} a^{2} b^{3} m^{6} x^{9} e \mathrm{sgn}\left(b x^{2} + a\right) + 2775 \, \left(f x\right)^{m} a b^{4} m^{4} x^{11} e \mathrm{sgn}\left(b x^{2} + a\right) + 12139 \, \left(f x\right)^{m} b^{5} m^{2} x^{13} e \mathrm{sgn}\left(b x^{2} + a\right) + 200 \, \left(f x\right)^{m} a b^{4} d m^{5} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + 3940 \, \left(f x\right)^{m} b^{5} d m^{3} x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + 400 \, \left(f x\right)^{m} a^{2} b^{3} m^{5} x^{9} e \mathrm{sgn}\left(b x^{2} + a\right) + 19700 \, \left(f x\right)^{m} a b^{4} m^{3} x^{11} e \mathrm{sgn}\left(b x^{2} + a\right) + 19524 \, \left(f x\right)^{m} b^{5} m x^{13} e \mathrm{sgn}\left(b x^{2} + a\right) + 10 \, \left(f x\right)^{m} a^{2} b^{3} d m^{6} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 3065 \, \left(f x\right)^{m} a b^{4} d m^{4} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + 14039 \, \left(f x\right)^{m} b^{5} d m^{2} x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + 10 \, \left(f x\right)^{m} a^{3} b^{2} m^{6} x^{7} e \mathrm{sgn}\left(b x^{2} + a\right) + 6130 \, \left(f x\right)^{m} a^{2} b^{3} m^{4} x^{9} e \mathrm{sgn}\left(b x^{2} + a\right) + 70195 \, \left(f x\right)^{m} a b^{4} m^{2} x^{11} e \mathrm{sgn}\left(b x^{2} + a\right) + 10395 \, \left(f x\right)^{m} b^{5} x^{13} e \mathrm{sgn}\left(b x^{2} + a\right) + 420 \, \left(f x\right)^{m} a^{2} b^{3} d m^{5} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 22640 \, \left(f x\right)^{m} a b^{4} d m^{3} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + 22902 \, \left(f x\right)^{m} b^{5} d m x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + 420 \, \left(f x\right)^{m} a^{3} b^{2} m^{5} x^{7} e \mathrm{sgn}\left(b x^{2} + a\right) + 45280 \, \left(f x\right)^{m} a^{2} b^{3} m^{3} x^{9} e \mathrm{sgn}\left(b x^{2} + a\right) + 114510 \, \left(f x\right)^{m} a b^{4} m x^{11} e \mathrm{sgn}\left(b x^{2} + a\right) + 10 \, \left(f x\right)^{m} a^{3} b^{2} d m^{6} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 6790 \, \left(f x\right)^{m} a^{2} b^{3} d m^{4} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 83135 \, \left(f x\right)^{m} a b^{4} d m^{2} x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + 12285 \, \left(f x\right)^{m} b^{5} d x^{11} \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, \left(f x\right)^{m} a^{4} b m^{6} x^{5} e \mathrm{sgn}\left(b x^{2} + a\right) + 6790 \, \left(f x\right)^{m} a^{3} b^{2} m^{4} x^{7} e \mathrm{sgn}\left(b x^{2} + a\right) + 166270 \, \left(f x\right)^{m} a^{2} b^{3} m^{2} x^{9} e \mathrm{sgn}\left(b x^{2} + a\right) + 61425 \, \left(f x\right)^{m} a b^{4} x^{11} e \mathrm{sgn}\left(b x^{2} + a\right) + 440 \, \left(f x\right)^{m} a^{3} b^{2} d m^{5} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 52920 \, \left(f x\right)^{m} a^{2} b^{3} d m^{3} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 138440 \, \left(f x\right)^{m} a b^{4} d m x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + 220 \, \left(f x\right)^{m} a^{4} b m^{5} x^{5} e \mathrm{sgn}\left(b x^{2} + a\right) + 52920 \, \left(f x\right)^{m} a^{3} b^{2} m^{3} x^{7} e \mathrm{sgn}\left(b x^{2} + a\right) + 276880 \, \left(f x\right)^{m} a^{2} b^{3} m x^{9} e \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, \left(f x\right)^{m} a^{4} b d m^{6} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 7530 \, \left(f x\right)^{m} a^{3} b^{2} d m^{4} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 203350 \, \left(f x\right)^{m} a^{2} b^{3} d m^{2} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 75075 \, \left(f x\right)^{m} a b^{4} d x^{9} \mathrm{sgn}\left(b x^{2} + a\right) + \left(f x\right)^{m} a^{5} m^{6} x^{3} e \mathrm{sgn}\left(b x^{2} + a\right) + 3765 \, \left(f x\right)^{m} a^{4} b m^{4} x^{5} e \mathrm{sgn}\left(b x^{2} + a\right) + 203350 \, \left(f x\right)^{m} a^{3} b^{2} m^{2} x^{7} e \mathrm{sgn}\left(b x^{2} + a\right) + 150150 \, \left(f x\right)^{m} a^{2} b^{3} x^{9} e \mathrm{sgn}\left(b x^{2} + a\right) + 230 \, \left(f x\right)^{m} a^{4} b d m^{5} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 62800 \, \left(f x\right)^{m} a^{3} b^{2} d m^{3} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 349860 \, \left(f x\right)^{m} a^{2} b^{3} d m x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 46 \, \left(f x\right)^{m} a^{5} m^{5} x^{3} e \mathrm{sgn}\left(b x^{2} + a\right) + 31400 \, \left(f x\right)^{m} a^{4} b m^{3} x^{5} e \mathrm{sgn}\left(b x^{2} + a\right) + 349860 \, \left(f x\right)^{m} a^{3} b^{2} m x^{7} e \mathrm{sgn}\left(b x^{2} + a\right) + \left(f x\right)^{m} a^{5} d m^{6} x \mathrm{sgn}\left(b x^{2} + a\right) + 4175 \, \left(f x\right)^{m} a^{4} b d m^{4} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 259790 \, \left(f x\right)^{m} a^{3} b^{2} d m^{2} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 193050 \, \left(f x\right)^{m} a^{2} b^{3} d x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 835 \, \left(f x\right)^{m} a^{5} m^{4} x^{3} e \mathrm{sgn}\left(b x^{2} + a\right) + 129895 \, \left(f x\right)^{m} a^{4} b m^{2} x^{5} e \mathrm{sgn}\left(b x^{2} + a\right) + 193050 \, \left(f x\right)^{m} a^{3} b^{2} x^{7} e \mathrm{sgn}\left(b x^{2} + a\right) + 48 \, \left(f x\right)^{m} a^{5} d m^{5} x \mathrm{sgn}\left(b x^{2} + a\right) + 37700 \, \left(f x\right)^{m} a^{4} b d m^{3} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 474360 \, \left(f x\right)^{m} a^{3} b^{2} d m x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 7540 \, \left(f x\right)^{m} a^{5} m^{3} x^{3} e \mathrm{sgn}\left(b x^{2} + a\right) + 237180 \, \left(f x\right)^{m} a^{4} b m x^{5} e \mathrm{sgn}\left(b x^{2} + a\right) + 925 \, \left(f x\right)^{m} a^{5} d m^{4} x \mathrm{sgn}\left(b x^{2} + a\right) + 173795 \, \left(f x\right)^{m} a^{4} b d m^{2} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 270270 \, \left(f x\right)^{m} a^{3} b^{2} d x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 34759 \, \left(f x\right)^{m} a^{5} m^{2} x^{3} e \mathrm{sgn}\left(b x^{2} + a\right) + 135135 \, \left(f x\right)^{m} a^{4} b x^{5} e \mathrm{sgn}\left(b x^{2} + a\right) + 9120 \, \left(f x\right)^{m} a^{5} d m^{3} x \mathrm{sgn}\left(b x^{2} + a\right) + 365270 \, \left(f x\right)^{m} a^{4} b d m x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 73054 \, \left(f x\right)^{m} a^{5} m x^{3} e \mathrm{sgn}\left(b x^{2} + a\right) + 48259 \, \left(f x\right)^{m} a^{5} d m^{2} x \mathrm{sgn}\left(b x^{2} + a\right) + 225225 \, \left(f x\right)^{m} a^{4} b d x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 45045 \, \left(f x\right)^{m} a^{5} x^{3} e \mathrm{sgn}\left(b x^{2} + a\right) + 129072 \, \left(f x\right)^{m} a^{5} d m x \mathrm{sgn}\left(b x^{2} + a\right) + 135135 \, \left(f x\right)^{m} a^{5} d x \mathrm{sgn}\left(b x^{2} + a\right)}{m^{7} + 49 \, m^{6} + 973 \, m^{5} + 10045 \, m^{4} + 57379 \, m^{3} + 177331 \, m^{2} + 264207 \, m + 135135}"," ",0,"((f*x)^m*b^5*m^6*x^13*e*sgn(b*x^2 + a) + 36*(f*x)^m*b^5*m^5*x^13*e*sgn(b*x^2 + a) + (f*x)^m*b^5*d*m^6*x^11*sgn(b*x^2 + a) + 5*(f*x)^m*a*b^4*m^6*x^11*e*sgn(b*x^2 + a) + 505*(f*x)^m*b^5*m^4*x^13*e*sgn(b*x^2 + a) + 38*(f*x)^m*b^5*d*m^5*x^11*sgn(b*x^2 + a) + 190*(f*x)^m*a*b^4*m^5*x^11*e*sgn(b*x^2 + a) + 3480*(f*x)^m*b^5*m^3*x^13*e*sgn(b*x^2 + a) + 5*(f*x)^m*a*b^4*d*m^6*x^9*sgn(b*x^2 + a) + 555*(f*x)^m*b^5*d*m^4*x^11*sgn(b*x^2 + a) + 10*(f*x)^m*a^2*b^3*m^6*x^9*e*sgn(b*x^2 + a) + 2775*(f*x)^m*a*b^4*m^4*x^11*e*sgn(b*x^2 + a) + 12139*(f*x)^m*b^5*m^2*x^13*e*sgn(b*x^2 + a) + 200*(f*x)^m*a*b^4*d*m^5*x^9*sgn(b*x^2 + a) + 3940*(f*x)^m*b^5*d*m^3*x^11*sgn(b*x^2 + a) + 400*(f*x)^m*a^2*b^3*m^5*x^9*e*sgn(b*x^2 + a) + 19700*(f*x)^m*a*b^4*m^3*x^11*e*sgn(b*x^2 + a) + 19524*(f*x)^m*b^5*m*x^13*e*sgn(b*x^2 + a) + 10*(f*x)^m*a^2*b^3*d*m^6*x^7*sgn(b*x^2 + a) + 3065*(f*x)^m*a*b^4*d*m^4*x^9*sgn(b*x^2 + a) + 14039*(f*x)^m*b^5*d*m^2*x^11*sgn(b*x^2 + a) + 10*(f*x)^m*a^3*b^2*m^6*x^7*e*sgn(b*x^2 + a) + 6130*(f*x)^m*a^2*b^3*m^4*x^9*e*sgn(b*x^2 + a) + 70195*(f*x)^m*a*b^4*m^2*x^11*e*sgn(b*x^2 + a) + 10395*(f*x)^m*b^5*x^13*e*sgn(b*x^2 + a) + 420*(f*x)^m*a^2*b^3*d*m^5*x^7*sgn(b*x^2 + a) + 22640*(f*x)^m*a*b^4*d*m^3*x^9*sgn(b*x^2 + a) + 22902*(f*x)^m*b^5*d*m*x^11*sgn(b*x^2 + a) + 420*(f*x)^m*a^3*b^2*m^5*x^7*e*sgn(b*x^2 + a) + 45280*(f*x)^m*a^2*b^3*m^3*x^9*e*sgn(b*x^2 + a) + 114510*(f*x)^m*a*b^4*m*x^11*e*sgn(b*x^2 + a) + 10*(f*x)^m*a^3*b^2*d*m^6*x^5*sgn(b*x^2 + a) + 6790*(f*x)^m*a^2*b^3*d*m^4*x^7*sgn(b*x^2 + a) + 83135*(f*x)^m*a*b^4*d*m^2*x^9*sgn(b*x^2 + a) + 12285*(f*x)^m*b^5*d*x^11*sgn(b*x^2 + a) + 5*(f*x)^m*a^4*b*m^6*x^5*e*sgn(b*x^2 + a) + 6790*(f*x)^m*a^3*b^2*m^4*x^7*e*sgn(b*x^2 + a) + 166270*(f*x)^m*a^2*b^3*m^2*x^9*e*sgn(b*x^2 + a) + 61425*(f*x)^m*a*b^4*x^11*e*sgn(b*x^2 + a) + 440*(f*x)^m*a^3*b^2*d*m^5*x^5*sgn(b*x^2 + a) + 52920*(f*x)^m*a^2*b^3*d*m^3*x^7*sgn(b*x^2 + a) + 138440*(f*x)^m*a*b^4*d*m*x^9*sgn(b*x^2 + a) + 220*(f*x)^m*a^4*b*m^5*x^5*e*sgn(b*x^2 + a) + 52920*(f*x)^m*a^3*b^2*m^3*x^7*e*sgn(b*x^2 + a) + 276880*(f*x)^m*a^2*b^3*m*x^9*e*sgn(b*x^2 + a) + 5*(f*x)^m*a^4*b*d*m^6*x^3*sgn(b*x^2 + a) + 7530*(f*x)^m*a^3*b^2*d*m^4*x^5*sgn(b*x^2 + a) + 203350*(f*x)^m*a^2*b^3*d*m^2*x^7*sgn(b*x^2 + a) + 75075*(f*x)^m*a*b^4*d*x^9*sgn(b*x^2 + a) + (f*x)^m*a^5*m^6*x^3*e*sgn(b*x^2 + a) + 3765*(f*x)^m*a^4*b*m^4*x^5*e*sgn(b*x^2 + a) + 203350*(f*x)^m*a^3*b^2*m^2*x^7*e*sgn(b*x^2 + a) + 150150*(f*x)^m*a^2*b^3*x^9*e*sgn(b*x^2 + a) + 230*(f*x)^m*a^4*b*d*m^5*x^3*sgn(b*x^2 + a) + 62800*(f*x)^m*a^3*b^2*d*m^3*x^5*sgn(b*x^2 + a) + 349860*(f*x)^m*a^2*b^3*d*m*x^7*sgn(b*x^2 + a) + 46*(f*x)^m*a^5*m^5*x^3*e*sgn(b*x^2 + a) + 31400*(f*x)^m*a^4*b*m^3*x^5*e*sgn(b*x^2 + a) + 349860*(f*x)^m*a^3*b^2*m*x^7*e*sgn(b*x^2 + a) + (f*x)^m*a^5*d*m^6*x*sgn(b*x^2 + a) + 4175*(f*x)^m*a^4*b*d*m^4*x^3*sgn(b*x^2 + a) + 259790*(f*x)^m*a^3*b^2*d*m^2*x^5*sgn(b*x^2 + a) + 193050*(f*x)^m*a^2*b^3*d*x^7*sgn(b*x^2 + a) + 835*(f*x)^m*a^5*m^4*x^3*e*sgn(b*x^2 + a) + 129895*(f*x)^m*a^4*b*m^2*x^5*e*sgn(b*x^2 + a) + 193050*(f*x)^m*a^3*b^2*x^7*e*sgn(b*x^2 + a) + 48*(f*x)^m*a^5*d*m^5*x*sgn(b*x^2 + a) + 37700*(f*x)^m*a^4*b*d*m^3*x^3*sgn(b*x^2 + a) + 474360*(f*x)^m*a^3*b^2*d*m*x^5*sgn(b*x^2 + a) + 7540*(f*x)^m*a^5*m^3*x^3*e*sgn(b*x^2 + a) + 237180*(f*x)^m*a^4*b*m*x^5*e*sgn(b*x^2 + a) + 925*(f*x)^m*a^5*d*m^4*x*sgn(b*x^2 + a) + 173795*(f*x)^m*a^4*b*d*m^2*x^3*sgn(b*x^2 + a) + 270270*(f*x)^m*a^3*b^2*d*x^5*sgn(b*x^2 + a) + 34759*(f*x)^m*a^5*m^2*x^3*e*sgn(b*x^2 + a) + 135135*(f*x)^m*a^4*b*x^5*e*sgn(b*x^2 + a) + 9120*(f*x)^m*a^5*d*m^3*x*sgn(b*x^2 + a) + 365270*(f*x)^m*a^4*b*d*m*x^3*sgn(b*x^2 + a) + 73054*(f*x)^m*a^5*m*x^3*e*sgn(b*x^2 + a) + 48259*(f*x)^m*a^5*d*m^2*x*sgn(b*x^2 + a) + 225225*(f*x)^m*a^4*b*d*x^3*sgn(b*x^2 + a) + 45045*(f*x)^m*a^5*x^3*e*sgn(b*x^2 + a) + 129072*(f*x)^m*a^5*d*m*x*sgn(b*x^2 + a) + 135135*(f*x)^m*a^5*d*x*sgn(b*x^2 + a))/(m^7 + 49*m^6 + 973*m^5 + 10045*m^4 + 57379*m^3 + 177331*m^2 + 264207*m + 135135)","B",0
88,1,1013,0,0.524308," ","integrate((f*x)^m*(e*x^2+d)*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{\left(f x\right)^{m} b^{3} m^{4} x^{9} e \mathrm{sgn}\left(b x^{2} + a\right) + 16 \, \left(f x\right)^{m} b^{3} m^{3} x^{9} e \mathrm{sgn}\left(b x^{2} + a\right) + \left(f x\right)^{m} b^{3} d m^{4} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 3 \, \left(f x\right)^{m} a b^{2} m^{4} x^{7} e \mathrm{sgn}\left(b x^{2} + a\right) + 86 \, \left(f x\right)^{m} b^{3} m^{2} x^{9} e \mathrm{sgn}\left(b x^{2} + a\right) + 18 \, \left(f x\right)^{m} b^{3} d m^{3} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 54 \, \left(f x\right)^{m} a b^{2} m^{3} x^{7} e \mathrm{sgn}\left(b x^{2} + a\right) + 176 \, \left(f x\right)^{m} b^{3} m x^{9} e \mathrm{sgn}\left(b x^{2} + a\right) + 3 \, \left(f x\right)^{m} a b^{2} d m^{4} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 104 \, \left(f x\right)^{m} b^{3} d m^{2} x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 3 \, \left(f x\right)^{m} a^{2} b m^{4} x^{5} e \mathrm{sgn}\left(b x^{2} + a\right) + 312 \, \left(f x\right)^{m} a b^{2} m^{2} x^{7} e \mathrm{sgn}\left(b x^{2} + a\right) + 105 \, \left(f x\right)^{m} b^{3} x^{9} e \mathrm{sgn}\left(b x^{2} + a\right) + 60 \, \left(f x\right)^{m} a b^{2} d m^{3} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 222 \, \left(f x\right)^{m} b^{3} d m x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + 60 \, \left(f x\right)^{m} a^{2} b m^{3} x^{5} e \mathrm{sgn}\left(b x^{2} + a\right) + 666 \, \left(f x\right)^{m} a b^{2} m x^{7} e \mathrm{sgn}\left(b x^{2} + a\right) + 3 \, \left(f x\right)^{m} a^{2} b d m^{4} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 390 \, \left(f x\right)^{m} a b^{2} d m^{2} x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 135 \, \left(f x\right)^{m} b^{3} d x^{7} \mathrm{sgn}\left(b x^{2} + a\right) + \left(f x\right)^{m} a^{3} m^{4} x^{3} e \mathrm{sgn}\left(b x^{2} + a\right) + 390 \, \left(f x\right)^{m} a^{2} b m^{2} x^{5} e \mathrm{sgn}\left(b x^{2} + a\right) + 405 \, \left(f x\right)^{m} a b^{2} x^{7} e \mathrm{sgn}\left(b x^{2} + a\right) + 66 \, \left(f x\right)^{m} a^{2} b d m^{3} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 900 \, \left(f x\right)^{m} a b^{2} d m x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 22 \, \left(f x\right)^{m} a^{3} m^{3} x^{3} e \mathrm{sgn}\left(b x^{2} + a\right) + 900 \, \left(f x\right)^{m} a^{2} b m x^{5} e \mathrm{sgn}\left(b x^{2} + a\right) + \left(f x\right)^{m} a^{3} d m^{4} x \mathrm{sgn}\left(b x^{2} + a\right) + 492 \, \left(f x\right)^{m} a^{2} b d m^{2} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 567 \, \left(f x\right)^{m} a b^{2} d x^{5} \mathrm{sgn}\left(b x^{2} + a\right) + 164 \, \left(f x\right)^{m} a^{3} m^{2} x^{3} e \mathrm{sgn}\left(b x^{2} + a\right) + 567 \, \left(f x\right)^{m} a^{2} b x^{5} e \mathrm{sgn}\left(b x^{2} + a\right) + 24 \, \left(f x\right)^{m} a^{3} d m^{3} x \mathrm{sgn}\left(b x^{2} + a\right) + 1374 \, \left(f x\right)^{m} a^{2} b d m x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 458 \, \left(f x\right)^{m} a^{3} m x^{3} e \mathrm{sgn}\left(b x^{2} + a\right) + 206 \, \left(f x\right)^{m} a^{3} d m^{2} x \mathrm{sgn}\left(b x^{2} + a\right) + 945 \, \left(f x\right)^{m} a^{2} b d x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 315 \, \left(f x\right)^{m} a^{3} x^{3} e \mathrm{sgn}\left(b x^{2} + a\right) + 744 \, \left(f x\right)^{m} a^{3} d m x \mathrm{sgn}\left(b x^{2} + a\right) + 945 \, \left(f x\right)^{m} a^{3} d x \mathrm{sgn}\left(b x^{2} + a\right)}{m^{5} + 25 \, m^{4} + 230 \, m^{3} + 950 \, m^{2} + 1689 \, m + 945}"," ",0,"((f*x)^m*b^3*m^4*x^9*e*sgn(b*x^2 + a) + 16*(f*x)^m*b^3*m^3*x^9*e*sgn(b*x^2 + a) + (f*x)^m*b^3*d*m^4*x^7*sgn(b*x^2 + a) + 3*(f*x)^m*a*b^2*m^4*x^7*e*sgn(b*x^2 + a) + 86*(f*x)^m*b^3*m^2*x^9*e*sgn(b*x^2 + a) + 18*(f*x)^m*b^3*d*m^3*x^7*sgn(b*x^2 + a) + 54*(f*x)^m*a*b^2*m^3*x^7*e*sgn(b*x^2 + a) + 176*(f*x)^m*b^3*m*x^9*e*sgn(b*x^2 + a) + 3*(f*x)^m*a*b^2*d*m^4*x^5*sgn(b*x^2 + a) + 104*(f*x)^m*b^3*d*m^2*x^7*sgn(b*x^2 + a) + 3*(f*x)^m*a^2*b*m^4*x^5*e*sgn(b*x^2 + a) + 312*(f*x)^m*a*b^2*m^2*x^7*e*sgn(b*x^2 + a) + 105*(f*x)^m*b^3*x^9*e*sgn(b*x^2 + a) + 60*(f*x)^m*a*b^2*d*m^3*x^5*sgn(b*x^2 + a) + 222*(f*x)^m*b^3*d*m*x^7*sgn(b*x^2 + a) + 60*(f*x)^m*a^2*b*m^3*x^5*e*sgn(b*x^2 + a) + 666*(f*x)^m*a*b^2*m*x^7*e*sgn(b*x^2 + a) + 3*(f*x)^m*a^2*b*d*m^4*x^3*sgn(b*x^2 + a) + 390*(f*x)^m*a*b^2*d*m^2*x^5*sgn(b*x^2 + a) + 135*(f*x)^m*b^3*d*x^7*sgn(b*x^2 + a) + (f*x)^m*a^3*m^4*x^3*e*sgn(b*x^2 + a) + 390*(f*x)^m*a^2*b*m^2*x^5*e*sgn(b*x^2 + a) + 405*(f*x)^m*a*b^2*x^7*e*sgn(b*x^2 + a) + 66*(f*x)^m*a^2*b*d*m^3*x^3*sgn(b*x^2 + a) + 900*(f*x)^m*a*b^2*d*m*x^5*sgn(b*x^2 + a) + 22*(f*x)^m*a^3*m^3*x^3*e*sgn(b*x^2 + a) + 900*(f*x)^m*a^2*b*m*x^5*e*sgn(b*x^2 + a) + (f*x)^m*a^3*d*m^4*x*sgn(b*x^2 + a) + 492*(f*x)^m*a^2*b*d*m^2*x^3*sgn(b*x^2 + a) + 567*(f*x)^m*a*b^2*d*x^5*sgn(b*x^2 + a) + 164*(f*x)^m*a^3*m^2*x^3*e*sgn(b*x^2 + a) + 567*(f*x)^m*a^2*b*x^5*e*sgn(b*x^2 + a) + 24*(f*x)^m*a^3*d*m^3*x*sgn(b*x^2 + a) + 1374*(f*x)^m*a^2*b*d*m*x^3*sgn(b*x^2 + a) + 458*(f*x)^m*a^3*m*x^3*e*sgn(b*x^2 + a) + 206*(f*x)^m*a^3*d*m^2*x*sgn(b*x^2 + a) + 945*(f*x)^m*a^2*b*d*x^3*sgn(b*x^2 + a) + 315*(f*x)^m*a^3*x^3*e*sgn(b*x^2 + a) + 744*(f*x)^m*a^3*d*m*x*sgn(b*x^2 + a) + 945*(f*x)^m*a^3*d*x*sgn(b*x^2 + a))/(m^5 + 25*m^4 + 230*m^3 + 950*m^2 + 1689*m + 945)","B",0
89,1,269,0,0.321860," ","integrate((f*x)^m*(e*x^2+d)*(b^2*x^4+2*a*b*x^2+a^2)^(1/2),x, algorithm=""giac"")","\frac{\left(f x\right)^{m} b m^{2} x^{5} e \mathrm{sgn}\left(b x^{2} + a\right) + 4 \, \left(f x\right)^{m} b m x^{5} e \mathrm{sgn}\left(b x^{2} + a\right) + \left(f x\right)^{m} b d m^{2} x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + \left(f x\right)^{m} a m^{2} x^{3} e \mathrm{sgn}\left(b x^{2} + a\right) + 3 \, \left(f x\right)^{m} b x^{5} e \mathrm{sgn}\left(b x^{2} + a\right) + 6 \, \left(f x\right)^{m} b d m x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 6 \, \left(f x\right)^{m} a m x^{3} e \mathrm{sgn}\left(b x^{2} + a\right) + \left(f x\right)^{m} a d m^{2} x \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, \left(f x\right)^{m} b d x^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, \left(f x\right)^{m} a x^{3} e \mathrm{sgn}\left(b x^{2} + a\right) + 8 \, \left(f x\right)^{m} a d m x \mathrm{sgn}\left(b x^{2} + a\right) + 15 \, \left(f x\right)^{m} a d x \mathrm{sgn}\left(b x^{2} + a\right)}{m^{3} + 9 \, m^{2} + 23 \, m + 15}"," ",0,"((f*x)^m*b*m^2*x^5*e*sgn(b*x^2 + a) + 4*(f*x)^m*b*m*x^5*e*sgn(b*x^2 + a) + (f*x)^m*b*d*m^2*x^3*sgn(b*x^2 + a) + (f*x)^m*a*m^2*x^3*e*sgn(b*x^2 + a) + 3*(f*x)^m*b*x^5*e*sgn(b*x^2 + a) + 6*(f*x)^m*b*d*m*x^3*sgn(b*x^2 + a) + 6*(f*x)^m*a*m*x^3*e*sgn(b*x^2 + a) + (f*x)^m*a*d*m^2*x*sgn(b*x^2 + a) + 5*(f*x)^m*b*d*x^3*sgn(b*x^2 + a) + 5*(f*x)^m*a*x^3*e*sgn(b*x^2 + a) + 8*(f*x)^m*a*d*m*x*sgn(b*x^2 + a) + 15*(f*x)^m*a*d*x*sgn(b*x^2 + a))/(m^3 + 9*m^2 + 23*m + 15)","B",0
90,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)/(b^2*x^4+2*a*b*x^2+a^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)} \left(f x\right)^{m}}{\sqrt{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}}\,{d x}"," ",0,"integrate((e*x^2 + d)*(f*x)^m/sqrt(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
91,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)} \left(f x\right)^{m}}{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x^2 + d)*(f*x)^m/(b^2*x^4 + 2*a*b*x^2 + a^2)^(3/2), x)","F",0
92,1,32,0,0.289245," ","integrate(x*(b*x^2+a)*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""giac"")","\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p + 1}}{4 \, b {\left(p + 1\right)}}"," ",0,"1/4*(b^2*x^4 + 2*a*b*x^2 + a^2)^(p + 1)/(b*(p + 1))","A",0
93,1,196,0,0.426535," ","integrate(x^3*(b*x^2+a)*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""giac"")","\frac{2 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} b^{3} p x^{6} + 2 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} b^{3} x^{6} + 4 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a b^{2} p x^{4} + 3 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a b^{2} x^{4} + 2 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a^{2} b p x^{2} - {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a^{3}}{4 \, {\left(2 \, b^{2} p^{2} + 5 \, b^{2} p + 3 \, b^{2}\right)}}"," ",0,"1/4*(2*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*b^3*p*x^6 + 2*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*b^3*x^6 + 4*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*a*b^2*p*x^4 + 3*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*a*b^2*x^4 + 2*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*a^2*b*p*x^2 - (b^2*x^4 + 2*a*b*x^2 + a^2)^p*a^3)/(2*b^2*p^2 + 5*b^2*p + 3*b^2)","B",0
94,1,331,0,0.384889," ","integrate(x^5*(b*x^2+a)*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""giac"")","\frac{2 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} b^{4} p^{2} x^{8} + 5 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} b^{4} p x^{8} + 4 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a b^{3} p^{2} x^{6} + 3 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} b^{4} x^{8} + 8 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a b^{3} p x^{6} + 2 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a^{2} b^{2} p^{2} x^{4} + 4 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a b^{3} x^{6} + {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a^{2} b^{2} p x^{4} - 2 \, {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a^{3} b p x^{2} + {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p} a^{4}}{4 \, {\left(2 \, b^{3} p^{3} + 9 \, b^{3} p^{2} + 13 \, b^{3} p + 6 \, b^{3}\right)}}"," ",0,"1/4*(2*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*b^4*p^2*x^8 + 5*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*b^4*p*x^8 + 4*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*a*b^3*p^2*x^6 + 3*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*b^4*x^8 + 8*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*a*b^3*p*x^6 + 2*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*a^2*b^2*p^2*x^4 + 4*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*a*b^3*x^6 + (b^2*x^4 + 2*a*b*x^2 + a^2)^p*a^2*b^2*p*x^4 - 2*(b^2*x^4 + 2*a*b*x^2 + a^2)^p*a^3*b*p*x^2 + (b^2*x^4 + 2*a*b*x^2 + a^2)^p*a^4)/(2*b^3*p^3 + 9*b^3*p^2 + 13*b^3*p + 6*b^3)","B",0
95,1,193,0,0.337980," ","integrate(x^3*(B*x^2+A)*(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{18} \, B c^{3} x^{18} + \frac{3}{16} \, B b c^{2} x^{16} + \frac{1}{16} \, A c^{3} x^{16} + \frac{3}{14} \, B b^{2} c x^{14} + \frac{3}{14} \, B a c^{2} x^{14} + \frac{3}{14} \, A b c^{2} x^{14} + \frac{1}{12} \, B b^{3} x^{12} + \frac{1}{2} \, B a b c x^{12} + \frac{1}{4} \, A b^{2} c x^{12} + \frac{1}{4} \, A a c^{2} x^{12} + \frac{3}{10} \, B a b^{2} x^{10} + \frac{1}{10} \, A b^{3} x^{10} + \frac{3}{10} \, B a^{2} c x^{10} + \frac{3}{5} \, A a b c x^{10} + \frac{3}{8} \, B a^{2} b x^{8} + \frac{3}{8} \, A a b^{2} x^{8} + \frac{3}{8} \, A a^{2} c x^{8} + \frac{1}{6} \, B a^{3} x^{6} + \frac{1}{2} \, A a^{2} b x^{6} + \frac{1}{4} \, A a^{3} x^{4}"," ",0,"1/18*B*c^3*x^18 + 3/16*B*b*c^2*x^16 + 1/16*A*c^3*x^16 + 3/14*B*b^2*c*x^14 + 3/14*B*a*c^2*x^14 + 3/14*A*b*c^2*x^14 + 1/12*B*b^3*x^12 + 1/2*B*a*b*c*x^12 + 1/4*A*b^2*c*x^12 + 1/4*A*a*c^2*x^12 + 3/10*B*a*b^2*x^10 + 1/10*A*b^3*x^10 + 3/10*B*a^2*c*x^10 + 3/5*A*a*b*c*x^10 + 3/8*B*a^2*b*x^8 + 3/8*A*a*b^2*x^8 + 3/8*A*a^2*c*x^8 + 1/6*B*a^3*x^6 + 1/2*A*a^2*b*x^6 + 1/4*A*a^3*x^4","A",0
96,1,193,0,0.270458," ","integrate(x^2*(B*x^2+A)*(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{17} \, B c^{3} x^{17} + \frac{1}{5} \, B b c^{2} x^{15} + \frac{1}{15} \, A c^{3} x^{15} + \frac{3}{13} \, B b^{2} c x^{13} + \frac{3}{13} \, B a c^{2} x^{13} + \frac{3}{13} \, A b c^{2} x^{13} + \frac{1}{11} \, B b^{3} x^{11} + \frac{6}{11} \, B a b c x^{11} + \frac{3}{11} \, A b^{2} c x^{11} + \frac{3}{11} \, A a c^{2} x^{11} + \frac{1}{3} \, B a b^{2} x^{9} + \frac{1}{9} \, A b^{3} x^{9} + \frac{1}{3} \, B a^{2} c x^{9} + \frac{2}{3} \, A a b c x^{9} + \frac{3}{7} \, B a^{2} b x^{7} + \frac{3}{7} \, A a b^{2} x^{7} + \frac{3}{7} \, A a^{2} c x^{7} + \frac{1}{5} \, B a^{3} x^{5} + \frac{3}{5} \, A a^{2} b x^{5} + \frac{1}{3} \, A a^{3} x^{3}"," ",0,"1/17*B*c^3*x^17 + 1/5*B*b*c^2*x^15 + 1/15*A*c^3*x^15 + 3/13*B*b^2*c*x^13 + 3/13*B*a*c^2*x^13 + 3/13*A*b*c^2*x^13 + 1/11*B*b^3*x^11 + 6/11*B*a*b*c*x^11 + 3/11*A*b^2*c*x^11 + 3/11*A*a*c^2*x^11 + 1/3*B*a*b^2*x^9 + 1/9*A*b^3*x^9 + 1/3*B*a^2*c*x^9 + 2/3*A*a*b*c*x^9 + 3/7*B*a^2*b*x^7 + 3/7*A*a*b^2*x^7 + 3/7*A*a^2*c*x^7 + 1/5*B*a^3*x^5 + 3/5*A*a^2*b*x^5 + 1/3*A*a^3*x^3","A",0
97,1,193,0,0.286753," ","integrate(x*(B*x^2+A)*(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{16} \, B c^{3} x^{16} + \frac{3}{14} \, B b c^{2} x^{14} + \frac{1}{14} \, A c^{3} x^{14} + \frac{1}{4} \, B b^{2} c x^{12} + \frac{1}{4} \, B a c^{2} x^{12} + \frac{1}{4} \, A b c^{2} x^{12} + \frac{1}{10} \, B b^{3} x^{10} + \frac{3}{5} \, B a b c x^{10} + \frac{3}{10} \, A b^{2} c x^{10} + \frac{3}{10} \, A a c^{2} x^{10} + \frac{3}{8} \, B a b^{2} x^{8} + \frac{1}{8} \, A b^{3} x^{8} + \frac{3}{8} \, B a^{2} c x^{8} + \frac{3}{4} \, A a b c x^{8} + \frac{1}{2} \, B a^{2} b x^{6} + \frac{1}{2} \, A a b^{2} x^{6} + \frac{1}{2} \, A a^{2} c x^{6} + \frac{1}{4} \, B a^{3} x^{4} + \frac{3}{4} \, A a^{2} b x^{4} + \frac{1}{2} \, A a^{3} x^{2}"," ",0,"1/16*B*c^3*x^16 + 3/14*B*b*c^2*x^14 + 1/14*A*c^3*x^14 + 1/4*B*b^2*c*x^12 + 1/4*B*a*c^2*x^12 + 1/4*A*b*c^2*x^12 + 1/10*B*b^3*x^10 + 3/5*B*a*b*c*x^10 + 3/10*A*b^2*c*x^10 + 3/10*A*a*c^2*x^10 + 3/8*B*a*b^2*x^8 + 1/8*A*b^3*x^8 + 3/8*B*a^2*c*x^8 + 3/4*A*a*b*c*x^8 + 1/2*B*a^2*b*x^6 + 1/2*A*a*b^2*x^6 + 1/2*A*a^2*c*x^6 + 1/4*B*a^3*x^4 + 3/4*A*a^2*b*x^4 + 1/2*A*a^3*x^2","A",0
98,1,189,0,0.264225," ","integrate((B*x^2+A)*(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{15} \, B c^{3} x^{15} + \frac{3}{13} \, B b c^{2} x^{13} + \frac{1}{13} \, A c^{3} x^{13} + \frac{3}{11} \, B b^{2} c x^{11} + \frac{3}{11} \, B a c^{2} x^{11} + \frac{3}{11} \, A b c^{2} x^{11} + \frac{1}{9} \, B b^{3} x^{9} + \frac{2}{3} \, B a b c x^{9} + \frac{1}{3} \, A b^{2} c x^{9} + \frac{1}{3} \, A a c^{2} x^{9} + \frac{3}{7} \, B a b^{2} x^{7} + \frac{1}{7} \, A b^{3} x^{7} + \frac{3}{7} \, B a^{2} c x^{7} + \frac{6}{7} \, A a b c x^{7} + \frac{3}{5} \, B a^{2} b x^{5} + \frac{3}{5} \, A a b^{2} x^{5} + \frac{3}{5} \, A a^{2} c x^{5} + \frac{1}{3} \, B a^{3} x^{3} + A a^{2} b x^{3} + A a^{3} x"," ",0,"1/15*B*c^3*x^15 + 3/13*B*b*c^2*x^13 + 1/13*A*c^3*x^13 + 3/11*B*b^2*c*x^11 + 3/11*B*a*c^2*x^11 + 3/11*A*b*c^2*x^11 + 1/9*B*b^3*x^9 + 2/3*B*a*b*c*x^9 + 1/3*A*b^2*c*x^9 + 1/3*A*a*c^2*x^9 + 3/7*B*a*b^2*x^7 + 1/7*A*b^3*x^7 + 3/7*B*a^2*c*x^7 + 6/7*A*a*b*c*x^7 + 3/5*B*a^2*b*x^5 + 3/5*A*a*b^2*x^5 + 3/5*A*a^2*c*x^5 + 1/3*B*a^3*x^3 + A*a^2*b*x^3 + A*a^3*x","A",0
99,1,193,0,0.335418," ","integrate((B*x^2+A)*(c*x^4+b*x^2+a)^3/x,x, algorithm=""giac"")","\frac{1}{14} \, B c^{3} x^{14} + \frac{1}{4} \, B b c^{2} x^{12} + \frac{1}{12} \, A c^{3} x^{12} + \frac{3}{10} \, B b^{2} c x^{10} + \frac{3}{10} \, B a c^{2} x^{10} + \frac{3}{10} \, A b c^{2} x^{10} + \frac{1}{8} \, B b^{3} x^{8} + \frac{3}{4} \, B a b c x^{8} + \frac{3}{8} \, A b^{2} c x^{8} + \frac{3}{8} \, A a c^{2} x^{8} + \frac{1}{2} \, B a b^{2} x^{6} + \frac{1}{6} \, A b^{3} x^{6} + \frac{1}{2} \, B a^{2} c x^{6} + A a b c x^{6} + \frac{3}{4} \, B a^{2} b x^{4} + \frac{3}{4} \, A a b^{2} x^{4} + \frac{3}{4} \, A a^{2} c x^{4} + \frac{1}{2} \, B a^{3} x^{2} + \frac{3}{2} \, A a^{2} b x^{2} + \frac{1}{2} \, A a^{3} \log\left(x^{2}\right)"," ",0,"1/14*B*c^3*x^14 + 1/4*B*b*c^2*x^12 + 1/12*A*c^3*x^12 + 3/10*B*b^2*c*x^10 + 3/10*B*a*c^2*x^10 + 3/10*A*b*c^2*x^10 + 1/8*B*b^3*x^8 + 3/4*B*a*b*c*x^8 + 3/8*A*b^2*c*x^8 + 3/8*A*a*c^2*x^8 + 1/2*B*a*b^2*x^6 + 1/6*A*b^3*x^6 + 1/2*B*a^2*c*x^6 + A*a*b*c*x^6 + 3/4*B*a^2*b*x^4 + 3/4*A*a*b^2*x^4 + 3/4*A*a^2*c*x^4 + 1/2*B*a^3*x^2 + 3/2*A*a^2*b*x^2 + 1/2*A*a^3*log(x^2)","A",0
100,1,185,0,0.306125," ","integrate((B*x^2+A)*(c*x^4+b*x^2+a)^3/x^2,x, algorithm=""giac"")","\frac{1}{13} \, B c^{3} x^{13} + \frac{3}{11} \, B b c^{2} x^{11} + \frac{1}{11} \, A c^{3} x^{11} + \frac{1}{3} \, B b^{2} c x^{9} + \frac{1}{3} \, B a c^{2} x^{9} + \frac{1}{3} \, A b c^{2} x^{9} + \frac{1}{7} \, B b^{3} x^{7} + \frac{6}{7} \, B a b c x^{7} + \frac{3}{7} \, A b^{2} c x^{7} + \frac{3}{7} \, A a c^{2} x^{7} + \frac{3}{5} \, B a b^{2} x^{5} + \frac{1}{5} \, A b^{3} x^{5} + \frac{3}{5} \, B a^{2} c x^{5} + \frac{6}{5} \, A a b c x^{5} + B a^{2} b x^{3} + A a b^{2} x^{3} + A a^{2} c x^{3} + B a^{3} x + 3 \, A a^{2} b x - \frac{A a^{3}}{x}"," ",0,"1/13*B*c^3*x^13 + 3/11*B*b*c^2*x^11 + 1/11*A*c^3*x^11 + 1/3*B*b^2*c*x^9 + 1/3*B*a*c^2*x^9 + 1/3*A*b*c^2*x^9 + 1/7*B*b^3*x^7 + 6/7*B*a*b*c*x^7 + 3/7*A*b^2*c*x^7 + 3/7*A*a*c^2*x^7 + 3/5*B*a*b^2*x^5 + 1/5*A*b^3*x^5 + 3/5*B*a^2*c*x^5 + 6/5*A*a*b*c*x^5 + B*a^2*b*x^3 + A*a*b^2*x^3 + A*a^2*c*x^3 + B*a^3*x + 3*A*a^2*b*x - A*a^3/x","A",0
101,1,212,0,0.404478," ","integrate((B*x^2+A)*(c*x^4+b*x^2+a)^3/x^3,x, algorithm=""giac"")","\frac{1}{12} \, B c^{3} x^{12} + \frac{3}{10} \, B b c^{2} x^{10} + \frac{1}{10} \, A c^{3} x^{10} + \frac{3}{8} \, B b^{2} c x^{8} + \frac{3}{8} \, B a c^{2} x^{8} + \frac{3}{8} \, A b c^{2} x^{8} + \frac{1}{6} \, B b^{3} x^{6} + B a b c x^{6} + \frac{1}{2} \, A b^{2} c x^{6} + \frac{1}{2} \, A a c^{2} x^{6} + \frac{3}{4} \, B a b^{2} x^{4} + \frac{1}{4} \, A b^{3} x^{4} + \frac{3}{4} \, B a^{2} c x^{4} + \frac{3}{2} \, A a b c x^{4} + \frac{3}{2} \, B a^{2} b x^{2} + \frac{3}{2} \, A a b^{2} x^{2} + \frac{3}{2} \, A a^{2} c x^{2} + \frac{1}{2} \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \log\left(x^{2}\right) - \frac{B a^{3} x^{2} + 3 \, A a^{2} b x^{2} + A a^{3}}{2 \, x^{2}}"," ",0,"1/12*B*c^3*x^12 + 3/10*B*b*c^2*x^10 + 1/10*A*c^3*x^10 + 3/8*B*b^2*c*x^8 + 3/8*B*a*c^2*x^8 + 3/8*A*b*c^2*x^8 + 1/6*B*b^3*x^6 + B*a*b*c*x^6 + 1/2*A*b^2*c*x^6 + 1/2*A*a*c^2*x^6 + 3/4*B*a*b^2*x^4 + 1/4*A*b^3*x^4 + 3/4*B*a^2*c*x^4 + 3/2*A*a*b*c*x^4 + 3/2*B*a^2*b*x^2 + 3/2*A*a*b^2*x^2 + 3/2*A*a^2*c*x^2 + 1/2*(B*a^3 + 3*A*a^2*b)*log(x^2) - 1/2*(B*a^3*x^2 + 3*A*a^2*b*x^2 + A*a^3)/x^2","A",0
102,1,126,0,1.872702," ","integrate(x^5*(B*x^2+A)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{B c x^{4} - 2 \, B b x^{2} + 2 \, A c x^{2}}{4 \, c^{2}} + \frac{{\left(B b^{2} - B a c - A b c\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, c^{3}} - \frac{{\left(B b^{3} - 3 \, B a b c - A b^{2} c + 2 \, A a c^{2}\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*(B*c*x^4 - 2*B*b*x^2 + 2*A*c*x^2)/c^2 + 1/4*(B*b^2 - B*a*c - A*b*c)*log(c*x^4 + b*x^2 + a)/c^3 - 1/2*(B*b^3 - 3*B*a*b*c - A*b^2*c + 2*A*a*c^2)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^3)","A",0
103,1,91,0,1.812442," ","integrate(x^3*(B*x^2+A)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{B x^{2}}{2 \, c} - \frac{{\left(B b - A c\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, c^{2}} + \frac{{\left(B b^{2} - 2 \, B a c - A b c\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*B*x^2/c - 1/4*(B*b - A*c)*log(c*x^4 + b*x^2 + a)/c^2 + 1/2*(B*b^2 - 2*B*a*c - A*b*c)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^2)","A",0
104,1,67,0,1.714634," ","integrate(x*(B*x^2+A)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{B \log\left(c x^{4} + b x^{2} + a\right)}{4 \, c} - \frac{{\left(B b - 2 \, A c\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} c}"," ",0,"1/4*B*log(c*x^4 + b*x^2 + a)/c - 1/2*(B*b - 2*A*c)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c)","A",0
105,1,78,0,1.609560," ","integrate((B*x^2+A)/x/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{A \log\left(c x^{4} + b x^{2} + a\right)}{4 \, a} + \frac{A \log\left(x^{2}\right)}{2 \, a} + \frac{{\left(2 \, B a - A b\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, \sqrt{-b^{2} + 4 \, a c} a}"," ",0,"-1/4*A*log(c*x^4 + b*x^2 + a)/a + 1/2*A*log(x^2)/a + 1/2*(2*B*a - A*b)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a)","A",0
106,1,124,0,1.874049," ","integrate((B*x^2+A)/x^3/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(B a - A b\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, a^{2}} + \frac{{\left(B a - A b\right)} \log\left(x^{2}\right)}{2 \, a^{2}} - \frac{{\left(B a b - A b^{2} + 2 \, A a c\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 a x^{2} - A b x^{2} + A a}{2 \, a^{2} x^{2}}"," ",0,"-1/4*(B*a - A*b)*log(c*x^4 + b*x^2 + a)/a^2 + 1/2*(B*a - A*b)*log(x^2)/a^2 - 1/2*(B*a*b - A*b^2 + 2*A*a*c)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*a^2) - 1/2*(B*a*x^2 - A*b*x^2 + A*a)/(a^2*x^2)","A",0
107,1,4391,0,3.789122," ","integrate(x^4*(B*x^2+A)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\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)} B 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)} B {\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)} B\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^{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)} B 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)} B {\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)} B\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{B c^{2} x^{3} - 3 \, B b c x + 3 \, A c^{2} x}{3 \, c^{3}}"," ",0,"-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)*B*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)*B*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)*B)*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^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)*B*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)*B*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)*B)*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*(B*c^2*x^3 - 3*B*b*c*x + 3*A*c^2*x)/c^3","B",0
108,1,3179,0,3.498091," ","integrate(x^2*(B*x^2+A)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{B x}{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)} 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^{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)} 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^{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)} 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^{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)} 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^{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,"B*x/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)*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^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)*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^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)*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^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)*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^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
109,1,1400,0,2.416475," ","integrate((B*x^2+A)/(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^{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)} B\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)} B\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,"1/4*((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)*B)*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)*B)*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
110,1,2805,0,3.568037," ","integrate((B*x^2+A)/x^2/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\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 a^{2} + 2 \, {\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} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 32 \, a^{3} b 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}\right)} A {\left| a \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, a^{2} b^{4} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 16 \, a^{3} b^{2} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 32 \, a^{4} c^{3} + 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}\right)} B {\left| a \right|} + {\left(2 \, a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2}\right)} A - 2 \, {\left(2 \, a^{3} b^{3} c^{2} - 8 \, a^{4} b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2}\right)} B\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} - 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| a \right|} {\left| c \right|}} + \frac{{\left({\left(2 \, b^{4} c^{2} - 16 \, a b^{2} c^{3} + 32 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} A a^{2} - 2 \, {\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} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 32 \, a^{3} b 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}\right)} A {\left| a \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c + 2 \, a^{2} b^{4} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 16 \, a^{3} b^{2} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 32 \, a^{4} c^{3} - 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}\right)} B {\left| a \right|} + {\left(2 \, a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2}\right)} A - 2 \, {\left(2 \, a^{3} b^{3} c^{2} - 8 \, a^{4} b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2}\right)} B\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} - 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| a \right|} {\left| c \right|}}"," ",0,"-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*a^2 + 2*(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 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 32*a^3*b*c^3 + 2*(b^2 - 4*a*c)*a*b^3*c - 8*(b^2 - 4*a*c)*a^2*b*c^2)*A*abs(a) - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - 2*a^2*b^4*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 16*a^3*b^2*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 - 32*a^4*c^3 + 2*(b^2 - 4*a*c)*a^2*b^2*c - 8*(b^2 - 4*a*c)*a^3*c^2)*B*abs(a) + (2*a^2*b^4*c^2 - 8*a^3*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2*c^2)*A - 2*(2*a^3*b^3*c^2 - 8*a^4*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 - 2*(b^2 - 4*a*c)*a^3*b*c^2)*B)*arctan(2*sqrt(1/2)*x/sqrt((a*b + sqrt(a^2*b^2 - 4*a^3*c))/(a*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(a)*abs(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)*A*a^2 - 2*(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 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 32*a^3*b*c^3 - 2*(b^2 - 4*a*c)*a*b^3*c + 8*(b^2 - 4*a*c)*a^2*b*c^2)*A*abs(a) + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c + 2*a^2*b^4*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 16*a^3*b^2*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 32*a^4*c^3 - 2*(b^2 - 4*a*c)*a^2*b^2*c + 8*(b^2 - 4*a*c)*a^3*c^2)*B*abs(a) + (2*a^2*b^4*c^2 - 8*a^3*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2*c^2)*A - 2*(2*a^3*b^3*c^2 - 8*a^4*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 - 2*(b^2 - 4*a*c)*a^3*b*c^2)*B)*arctan(2*sqrt(1/2)*x/sqrt((a*b - sqrt(a^2*b^2 - 4*a^3*c))/(a*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(a)*abs(c))","B",0
111,1,2870,0,3.346184," ","integrate((B*x^2+A)/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)} A - {\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)} B\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)} A - {\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)} B\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 a x^{2} - 3 \, A b x^{2} + A a}{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)*A - (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)*B)*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)*A - (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)*B)*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*a*x^2 - 3*A*b*x^2 + A*a)/(a^2*x^3)","B",0
112,1,239,0,1.649185," ","integrate(x^7*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{B x^{2}}{2 \, c^{2}} + \frac{{\left(2 \, B b^{4} - 12 \, B a b^{2} c - A b^{3} c + 12 \, B a^{2} c^{2} + 6 \, A a b c^{2}\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 b^{3} x^{4} - 8 \, B a b c x^{4} - A b^{2} c x^{4} + 4 \, A a c^{2} x^{4} + A b^{3} x^{2} - 4 \, B a^{2} c x^{2} - 2 \, A a b c x^{2} - 2 \, B a^{2} b + A a b^{2}}{4 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}} - \frac{{\left(2 \, B b - A c\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, c^{3}}"," ",0,"1/2*B*x^2/c^2 + 1/2*(2*B*b^4 - 12*B*a*b^2*c - A*b^3*c + 12*B*a^2*c^2 + 6*A*a*b*c^2)*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*b^3*x^4 - 8*B*a*b*c*x^4 - A*b^2*c*x^4 + 4*A*a*c^2*x^4 + A*b^3*x^2 - 4*B*a^2*c*x^2 - 2*A*a*b*c*x^2 - 2*B*a^2*b + A*a*b^2)/((c*x^4 + b*x^2 + a)*(b^2*c^2 - 4*a*c^3)) - 1/4*(2*B*b - A*c)*log(c*x^4 + b*x^2 + a)/c^3","A",0
113,1,194,0,1.617436," ","integrate(x^5*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(B b^{3} - 6 \, B a b c + 4 \, A a c^{2}\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{B \log\left(c x^{4} + b x^{2} + a\right)}{4 \, c^{2}} - \frac{B b^{2} c x^{4} - 4 \, B a c^{2} x^{4} - B b^{3} x^{2} + 2 \, B a b c x^{2} + 2 \, A b^{2} c x^{2} - 4 \, A a c^{2} x^{2} - B a b^{2} + 2 \, A a b c}{4 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}"," ",0,"-1/2*(B*b^3 - 6*B*a*b*c + 4*A*a*c^2)*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*B*log(c*x^4 + b*x^2 + a)/c^2 - 1/4*(B*b^2*c*x^4 - 4*B*a*c^2*x^4 - B*b^3*x^2 + 2*B*a*b*c*x^2 + 2*A*b^2*c*x^2 - 4*A*a*c^2*x^2 - B*a*b^2 + 2*A*a*b*c)/((c*x^4 + b*x^2 + a)*(b^2*c^2 - 4*a*c^3))","A",0
114,1,120,0,1.723340," ","integrate(x^3*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, B a - A b\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{B b^{2} x^{2} - 2 \, B a c x^{2} - A b c x^{2} + B 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)}}"," ",0,"-(2*B*a - A*b)*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*(B*b^2*x^2 - 2*B*a*c*x^2 - A*b*c*x^2 + B*a*b - 2*A*a*c)/((c*x^4 + b*x^2 + a)*(b^2*c - 4*a*c^2))","A",0
115,1,102,0,1.366571," ","integrate(x*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(B b - 2 \, A c\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{B b x^{2} - 2 \, A c x^{2} + 2 \, B a - A b}{2 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"(B*b - 2*A*c)*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*(B*b*x^2 - 2*A*c*x^2 + 2*B*a - A*b)/((c*x^4 + b*x^2 + a)*(b^2 - 4*a*c))","A",0
116,1,201,0,1.710197," ","integrate((B*x^2+A)/x/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(A b^{3} + 4 \, B a^{2} c - 6 \, A a b c\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{A \log\left(c x^{4} + b x^{2} + a\right)}{4 \, a^{2}} + \frac{A \log\left(x^{2}\right)}{2 \, a^{2}} + \frac{A b^{2} c x^{4} - 4 \, A a c^{2} x^{4} + A b^{3} x^{2} - 4 \, B a^{2} c x^{2} - 2 \, A a b c x^{2} - 2 \, B a^{2} b + 3 \, A a b^{2} - 8 \, A a^{2} c}{4 \, {\left(c x^{4} + b x^{2} + a\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}}"," ",0,"-1/2*(A*b^3 + 4*B*a^2*c - 6*A*a*b*c)*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*A*log(c*x^4 + b*x^2 + a)/a^2 + 1/2*A*log(x^2)/a^2 + 1/4*(A*b^2*c*x^4 - 4*A*a*c^2*x^4 + A*b^3*x^2 - 4*B*a^2*c*x^2 - 2*A*a*b*c*x^2 - 2*B*a^2*b + 3*A*a*b^2 - 8*A*a^2*c)/((c*x^4 + b*x^2 + a)*(a^2*b^2 - 4*a^3*c))","A",0
117,1,250,0,1.647297," ","integrate((B*x^2+A)/x^3/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(B a b^{3} - 2 \, A b^{4} - 6 \, B a^{2} b c + 12 \, A a b^{2} c - 12 \, A a^{2} c^{2}\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{B a b c x^{4} - 2 \, A b^{2} c x^{4} + 6 \, A a c^{2} x^{4} + B a b^{2} x^{2} - 2 \, A b^{3} x^{2} - 2 \, B a^{2} c x^{2} + 7 \, A a b c x^{2} - A a b^{2} + 4 \, A a^{2} c}{2 \, {\left(c x^{6} + b x^{4} + a x^{2}\right)} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)}} - \frac{{\left(B a - 2 \, A b\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, a^{3}} + \frac{{\left(B a - 2 \, A b\right)} \log\left(x^{2}\right)}{2 \, a^{3}}"," ",0,"-1/2*(B*a*b^3 - 2*A*b^4 - 6*B*a^2*b*c + 12*A*a*b^2*c - 12*A*a^2*c^2)*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*(B*a*b*c*x^4 - 2*A*b^2*c*x^4 + 6*A*a*c^2*x^4 + B*a*b^2*x^2 - 2*A*b^3*x^2 - 2*B*a^2*c*x^2 + 7*A*a*b*c*x^2 - A*a*b^2 + 4*A*a^2*c)/((c*x^6 + b*x^4 + a*x^2)*(a^2*b^2 - 4*a^3*c)) - 1/4*(B*a - 2*A*b)*log(c*x^4 + b*x^2 + a)/a^3 + 1/2*(B*a - 2*A*b)*log(x^2)/a^3","A",0
118,1,5681,0,6.490158," ","integrate(x^6*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{B x}{c^{2}} + \frac{B b^{3} x^{3} - 3 \, B a b c x^{3} - A b^{2} c x^{3} + 2 \, A a c^{2} x^{3} + B a b^{2} x - 2 \, B a^{2} c x - A a b c x}{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^{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} A - {\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} B + 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)} A {\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)} B {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} - {\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)} A + {\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)} B\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^{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} A - {\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} B - 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)} A {\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)} B {\left| -b^{2} c^{2} + 4 \, a c^{3} \right|} - {\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)} A + {\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)} B\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,"B*x/c^2 + 1/2*(B*b^3*x^3 - 3*B*a*b*c*x^3 - A*b^2*c*x^3 + 2*A*a*c^2*x^3 + B*a*b^2*x - 2*B*a^2*c*x - A*a*b*c*x)/((c*x^4 + b*x^2 + a)*(b^2*c^2 - 4*a*c^3)) + 1/16*((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*A - (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*B + 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)*A*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)*B*abs(-b^2*c^2 + 4*a*c^3) - (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)*A + (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)*B)*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^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*A - (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*B - 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)*A*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)*B*abs(-b^2*c^2 + 4*a*c^3) - (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)*A + (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)*B)*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
119,1,4538,0,6.288251," ","integrate(x^4*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{B b^{2} x^{3} - 2 \, B a c x^{3} - A b c x^{3} + B a b x - 2 \, A a c x}{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} B - 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)} B {\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)} B\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} B + 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)} B {\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)} B\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*(B*b^2*x^3 - 2*B*a*c*x^3 - A*b*c*x^3 + B*a*b*x - 2*A*a*c*x)/((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*B - 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)*B*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)*B)*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*B + 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)*B*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)*B)*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
120,1,3776,0,4.776611," ","integrate(x^2*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{B b x^{3} - 2 \, A c x^{3} + 2 \, B a x - A b x}{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} B - 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)} B {\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)} 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(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} B + 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)} B {\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)} 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|}}"," ",0,"1/2*(B*b*x^3 - 2*A*c*x^3 + 2*B*a*x - A*b*x)/((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*B - 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)*B*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)*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*(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*B + 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)*B*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)*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))","B",0
121,1,4426,0,5.964570," ","integrate((B*x^2+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{2 \, B a c x^{3} - A b c x^{3} + B a b x - A b^{2} x + 2 \, A a c x}{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} B + 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)} B {\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)} B\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} B - 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)} B {\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)} B\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|}}"," ",0,"-1/2*(2*B*a*c*x^3 - A*b*c*x^3 + B*a*b*x - A*b^2*x + 2*A*a*c*x)/((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*B + 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)*B*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)*B)*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*B - 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)*B*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)*B)*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))","B",0
122,1,5408,0,6.160081," ","integrate((B*x^2+A)/x^2/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{B a b c x^{4} - 3 \, A b^{2} c x^{4} + 10 \, A a c^{2} x^{4} + B a b^{2} x^{2} - 3 \, A b^{3} x^{2} - 2 \, B a^{2} c x^{2} + 11 \, A a b c x^{2} - 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(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} A - {\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} B + 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)} A {\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)} B {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} + {\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)} A - {\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)} B\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} A - {\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} B - 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)} A {\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)} B {\left| a^{2} b^{2} - 4 \, a^{3} c \right|} + {\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)} A - {\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)} B\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*(B*a*b*c*x^4 - 3*A*b^2*c*x^4 + 10*A*a*c^2*x^4 + B*a*b^2*x^2 - 3*A*b^3*x^2 - 2*B*a^2*c*x^2 + 11*A*a*b*c*x^2 - 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*((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*A - (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*B + 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)*A*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)*B*abs(a^2*b^2 - 4*a^3*c) + (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)*A - (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)*B)*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*A - (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*B - 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)*A*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)*B*abs(a^2*b^2 - 4*a^3*c) + (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)*A - (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)*B)*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
123,1,6327,0,8.150477," ","integrate((B*x^2+A)/x^4/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","-\frac{B a b^{2} c x^{3} - A b^{3} c x^{3} - 2 \, B a^{2} c^{2} x^{3} + 3 \, A a b c^{2} x^{3} + B a b^{3} x - A b^{4} x - 3 \, B a^{2} b c x + 4 \, A a b^{2} c x - 2 \, A a^{2} c^{2} x}{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} A - {\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} B + 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)} A {\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)} B {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} + {\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)} A - {\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)} B\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} A - {\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} B - 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)} A {\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)} B {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} + {\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)} A - {\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)} B\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{3 \, B a x^{2} - 6 \, A b x^{2} + A a}{3 \, a^{3} x^{3}}"," ",0,"-1/2*(B*a*b^2*c*x^3 - A*b^3*c*x^3 - 2*B*a^2*c^2*x^3 + 3*A*a*b*c^2*x^3 + B*a*b^3*x - A*b^4*x - 3*B*a^2*b*c*x + 4*A*a*b^2*c*x - 2*A*a^2*c^2*x)/((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*A - (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*B + 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)*A*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)*B*abs(a^3*b^2 - 4*a^4*c) + (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)*A - (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)*B)*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*A - (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*B - 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)*A*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)*B*abs(a^3*b^2 - 4*a^4*c) + (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)*A - (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)*B)*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*(3*B*a*x^2 - 6*A*b*x^2 + A*a)/(a^3*x^3)","B",0
124,1,598,0,5.883130," ","integrate(x^11*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(3 \, B b^{6} - 30 \, B a b^{4} c - A b^{5} c + 90 \, B a^{2} b^{2} c^{2} + 10 \, A a b^{3} c^{2} - 60 \, B a^{3} c^{3} - 30 \, A a^{2} b c^{3}\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{B x^{2}}{2 \, c^{3}} + \frac{9 \, B b^{5} c^{2} x^{8} - 72 \, B a b^{3} c^{3} x^{8} - 3 \, A b^{4} c^{3} x^{8} + 144 \, B a^{2} b c^{4} x^{8} + 24 \, A a b^{2} c^{4} x^{8} - 48 \, A a^{2} c^{5} x^{8} + 6 \, B b^{6} c x^{6} - 48 \, B a b^{4} c^{2} x^{6} + 2 \, A b^{5} c^{2} x^{6} + 84 \, B a^{2} b^{2} c^{3} x^{6} - 12 \, A a b^{3} c^{3} x^{6} + 72 \, B a^{3} c^{4} x^{6} + 4 \, A a^{2} b c^{4} x^{6} - B b^{7} x^{4} + 14 \, B a b^{5} c x^{4} + 3 \, A b^{6} c x^{4} - 82 \, B a^{2} b^{3} c^{2} x^{4} - 20 \, A a b^{4} c^{2} x^{4} + 204 \, B a^{3} b c^{3} x^{4} + 22 \, A a^{2} b^{2} c^{3} x^{4} - 32 \, A a^{3} c^{4} x^{4} - 2 \, B a b^{6} x^{2} + 8 \, B a^{2} b^{4} c x^{2} + 6 \, A a b^{5} c x^{2} + 4 \, B a^{3} b^{2} c^{2} x^{2} - 40 \, A a^{2} b^{3} c^{2} x^{2} + 56 \, B a^{4} c^{3} x^{2} + 28 \, A a^{3} b c^{3} x^{2} - B a^{2} b^{5} + 3 \, A a^{2} b^{4} c + 28 \, B a^{4} b c^{2} - 18 \, A a^{3} b^{2} c^{2}}{8 \, {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{2}} - \frac{{\left(3 \, B b - A c\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, c^{4}}"," ",0,"1/2*(3*B*b^6 - 30*B*a*b^4*c - A*b^5*c + 90*B*a^2*b^2*c^2 + 10*A*a*b^3*c^2 - 60*B*a^3*c^3 - 30*A*a^2*b*c^3)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*sqrt(-b^2 + 4*a*c)) + 1/2*B*x^2/c^3 + 1/8*(9*B*b^5*c^2*x^8 - 72*B*a*b^3*c^3*x^8 - 3*A*b^4*c^3*x^8 + 144*B*a^2*b*c^4*x^8 + 24*A*a*b^2*c^4*x^8 - 48*A*a^2*c^5*x^8 + 6*B*b^6*c*x^6 - 48*B*a*b^4*c^2*x^6 + 2*A*b^5*c^2*x^6 + 84*B*a^2*b^2*c^3*x^6 - 12*A*a*b^3*c^3*x^6 + 72*B*a^3*c^4*x^6 + 4*A*a^2*b*c^4*x^6 - B*b^7*x^4 + 14*B*a*b^5*c*x^4 + 3*A*b^6*c*x^4 - 82*B*a^2*b^3*c^2*x^4 - 20*A*a*b^4*c^2*x^4 + 204*B*a^3*b*c^3*x^4 + 22*A*a^2*b^2*c^3*x^4 - 32*A*a^3*c^4*x^4 - 2*B*a*b^6*x^2 + 8*B*a^2*b^4*c*x^2 + 6*A*a*b^5*c*x^2 + 4*B*a^3*b^2*c^2*x^2 - 40*A*a^2*b^3*c^2*x^2 + 56*B*a^4*c^3*x^2 + 28*A*a^3*b*c^3*x^2 - B*a^2*b^5 + 3*A*a^2*b^4*c + 28*B*a^4*b*c^2 - 18*A*a^3*b^2*c^2)/((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*(c*x^4 + b*x^2 + a)^2) - 1/4*(3*B*b - A*c)*log(c*x^4 + b*x^2 + a)/c^4","A",0
125,1,466,0,6.310751," ","integrate(x^9*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","-\frac{{\left(B b^{5} - 10 \, B a b^{3} c + 30 \, B a^{2} b c^{2} - 12 \, A a^{2} c^{3}\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{B \log\left(c x^{4} + b x^{2} + a\right)}{4 \, c^{3}} - \frac{3 \, B b^{4} c^{2} x^{8} - 24 \, B a b^{2} c^{3} x^{8} + 48 \, B a^{2} c^{4} x^{8} - 2 \, B b^{5} c x^{6} + 12 \, B a b^{3} c^{2} x^{6} + 4 \, A b^{4} c^{2} x^{6} - 4 \, B a^{2} b c^{3} x^{6} - 32 \, A a b^{2} c^{3} x^{6} + 40 \, A a^{2} c^{4} x^{6} - 3 \, B b^{6} x^{4} + 20 \, B a b^{4} c x^{4} + 2 \, A b^{5} c x^{4} - 22 \, B a^{2} b^{2} c^{2} x^{4} - 16 \, A a b^{3} c^{2} x^{4} + 32 \, B a^{3} c^{3} x^{4} - 4 \, A a^{2} b c^{3} x^{4} - 6 \, B a b^{5} x^{2} + 40 \, B a^{2} b^{3} c x^{2} + 4 \, A a b^{4} c x^{2} - 28 \, B a^{3} b c^{2} x^{2} - 40 \, A a^{2} b^{2} c^{2} x^{2} + 24 \, A a^{3} c^{3} x^{2} - 3 \, B a^{2} b^{4} + 18 \, B a^{3} b^{2} c + 2 \, A a^{2} b^{3} c - 20 \, A a^{3} b c^{2}}{8 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{2}}"," ",0,"-1/2*(B*b^5 - 10*B*a*b^3*c + 30*B*a^2*b*c^2 - 12*A*a^2*c^3)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt(-b^2 + 4*a*c)) + 1/4*B*log(c*x^4 + b*x^2 + a)/c^3 - 1/8*(3*B*b^4*c^2*x^8 - 24*B*a*b^2*c^3*x^8 + 48*B*a^2*c^4*x^8 - 2*B*b^5*c*x^6 + 12*B*a*b^3*c^2*x^6 + 4*A*b^4*c^2*x^6 - 4*B*a^2*b*c^3*x^6 - 32*A*a*b^2*c^3*x^6 + 40*A*a^2*c^4*x^6 - 3*B*b^6*x^4 + 20*B*a*b^4*c*x^4 + 2*A*b^5*c*x^4 - 22*B*a^2*b^2*c^2*x^4 - 16*A*a*b^3*c^2*x^4 + 32*B*a^3*c^3*x^4 - 4*A*a^2*b*c^3*x^4 - 6*B*a*b^5*x^2 + 40*B*a^2*b^3*c*x^2 + 4*A*a*b^4*c*x^2 - 28*B*a^3*b*c^2*x^2 - 40*A*a^2*b^2*c^2*x^2 + 24*A*a^3*c^3*x^2 - 3*B*a^2*b^4 + 18*B*a^3*b^2*c + 2*A*a^2*b^3*c - 20*A*a^3*b*c^2)/((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*(c*x^4 + b*x^2 + a)^2)","A",0
126,1,318,0,6.462959," ","integrate(x^7*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{3 \, {\left(2 \, B a^{2} - A a b\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, B b^{4} c x^{6} - 16 \, B a b^{2} c^{2} x^{6} + 20 \, B a^{2} c^{3} x^{6} + 6 \, A a b c^{3} x^{6} + B b^{5} x^{4} - 8 \, B a b^{3} c x^{4} + A b^{4} c x^{4} - 2 \, B a^{2} b c^{2} x^{4} + A a b^{2} c^{2} x^{4} + 16 \, A a^{2} c^{3} x^{4} + 2 \, B a b^{4} x^{2} - 20 \, B a^{2} b^{2} c x^{2} + 2 \, A a b^{3} c x^{2} + 12 \, B a^{3} c^{2} x^{2} + 10 \, A a^{2} b c^{2} x^{2} + B a^{2} b^{3} - 10 \, B a^{3} b c + A a^{2} b^{2} c + 8 \, A a^{3} c^{2}}{4 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{2}}"," ",0,"3*(2*B*a^2 - A*a*b)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) - 1/4*(2*B*b^4*c*x^6 - 16*B*a*b^2*c^2*x^6 + 20*B*a^2*c^3*x^6 + 6*A*a*b*c^3*x^6 + B*b^5*x^4 - 8*B*a*b^3*c*x^4 + A*b^4*c*x^4 - 2*B*a^2*b*c^2*x^4 + A*a*b^2*c^2*x^4 + 16*A*a^2*c^3*x^4 + 2*B*a*b^4*x^2 - 20*B*a^2*b^2*c*x^2 + 2*A*a*b^3*c*x^2 + 12*B*a^3*c^2*x^2 + 10*A*a^2*b*c^2*x^2 + B*a^2*b^3 - 10*B*a^3*b*c + A*a^2*b^2*c + 8*A*a^3*c^2)/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*(c*x^4 + b*x^2 + a)^2)","B",0
127,1,268,0,6.587332," ","integrate(x^5*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","-\frac{{\left(3 \, B a b - A b^{2} - 2 \, A a c\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{6 \, B a b c^{2} x^{6} - 2 \, A b^{2} c^{2} x^{6} - 4 \, A a c^{3} x^{6} + B b^{4} x^{4} + B a b^{2} c x^{4} - 3 \, A b^{3} c x^{4} + 16 \, B a^{2} c^{2} x^{4} - 6 \, A a b c^{2} x^{4} + 2 \, B a b^{3} x^{2} + 10 \, B a^{2} b c x^{2} - 10 \, A a b^{2} c x^{2} + 4 \, A a^{2} c^{2} x^{2} + B a^{2} b^{2} + 8 \, B a^{3} c - 6 \, A a^{2} b c}{4 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{2}}"," ",0,"-(3*B*a*b - A*b^2 - 2*A*a*c)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) - 1/4*(6*B*a*b*c^2*x^6 - 2*A*b^2*c^2*x^6 - 4*A*a*c^3*x^6 + B*b^4*x^4 + B*a*b^2*c*x^4 - 3*A*b^3*c*x^4 + 16*B*a^2*c^2*x^4 - 6*A*a*b*c^2*x^4 + 2*B*a*b^3*x^2 + 10*B*a^2*b*c*x^2 - 10*A*a*b^2*c*x^2 + 4*A*a^2*c^2*x^2 + B*a^2*b^2 + 8*B*a^3*c - 6*A*a^2*b*c)/((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*(c*x^4 + b*x^2 + a)^2)","A",0
128,1,228,0,6.056926," ","integrate(x^3*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(B b^{2} + 2 \, B a c - 3 \, A b c\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{2 \, B b^{2} c x^{6} + 4 \, B a c^{2} x^{6} - 6 \, A b c^{2} x^{6} + 3 \, B b^{3} x^{4} + 6 \, B a b c x^{4} - 9 \, A b^{2} c x^{4} + 10 \, B a b^{2} x^{2} - 2 \, A b^{3} x^{2} - 4 \, B a^{2} c x^{2} - 10 \, A a b c x^{2} + 6 \, B a^{2} b - A a b^{2} - 8 \, A a^{2} c}{4 \, {\left(c x^{4} + b x^{2} + a\right)}^{2} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)}}"," ",0,"(B*b^2 + 2*B*a*c - 3*A*b*c)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) + 1/4*(2*B*b^2*c*x^6 + 4*B*a*c^2*x^6 - 6*A*b*c^2*x^6 + 3*B*b^3*x^4 + 6*B*a*b*c*x^4 - 9*A*b^2*c*x^4 + 10*B*a*b^2*x^2 - 2*A*b^3*x^2 - 4*B*a^2*c*x^2 - 10*A*a*b*c*x^2 + 6*B*a^2*b - A*a*b^2 - 8*A*a^2*c)/((c*x^4 + b*x^2 + a)^2*(b^4 - 8*a*b^2*c + 16*a^2*c^2))","A",0
129,1,208,0,5.569765," ","integrate(x*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(B b c - 2 \, A c^{2}\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{6 \, B b c^{2} x^{6} - 12 \, A c^{3} x^{6} + 9 \, B b^{2} c x^{4} - 18 \, A b c^{2} x^{4} + 2 \, B b^{3} x^{2} + 10 \, B a b c x^{2} - 4 \, A b^{2} c x^{2} - 20 \, A a c^{2} x^{2} + B a b^{2} + A b^{3} + 8 \, B a^{2} c - 10 \, A a b c}{4 \, {\left(c x^{4} + b x^{2} + a\right)}^{2} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)}}"," ",0,"-3*(B*b*c - 2*A*c^2)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) - 1/4*(6*B*b*c^2*x^6 - 12*A*c^3*x^6 + 9*B*b^2*c*x^4 - 18*A*b*c^2*x^4 + 2*B*b^3*x^2 + 10*B*a*b*c*x^2 - 4*A*b^2*c*x^2 - 20*A*a*c^2*x^2 + B*a*b^2 + A*b^3 + 8*B*a^2*c - 10*A*a*b*c)/((c*x^4 + b*x^2 + a)^2*(b^4 - 8*a*b^2*c + 16*a^2*c^2))","A",0
130,1,421,0,6.444904," ","integrate((B*x^2+A)/x/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","-\frac{{\left(A b^{5} - 10 \, A a b^{3} c - 12 \, B a^{3} c^{2} + 30 \, A a^{2} b c^{2}\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{A \log\left(c x^{4} + b x^{2} + a\right)}{4 \, a^{3}} + \frac{A \log\left(x^{2}\right)}{2 \, a^{3}} + \frac{3 \, A b^{4} c^{2} x^{8} - 24 \, A a b^{2} c^{3} x^{8} + 48 \, A a^{2} c^{4} x^{8} + 6 \, A b^{5} c x^{6} - 44 \, A a b^{3} c^{2} x^{6} + 24 \, B a^{3} c^{3} x^{6} + 68 \, A a^{2} b c^{3} x^{6} + 3 \, A b^{6} x^{4} - 10 \, A a b^{4} c x^{4} + 36 \, B a^{3} b c^{2} x^{4} - 58 \, A a^{2} b^{2} c^{2} x^{4} + 128 \, A a^{3} c^{3} x^{4} + 10 \, A a b^{5} x^{2} + 8 \, B a^{3} b^{2} c x^{2} - 72 \, A a^{2} b^{3} c x^{2} + 40 \, B a^{4} c^{2} x^{2} + 92 \, A a^{3} b c^{2} x^{2} - 2 \, B a^{3} b^{3} + 9 \, A a^{2} b^{4} + 20 \, B a^{4} b c - 66 \, A a^{3} b^{2} c + 96 \, A a^{4} c^{2}}{8 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{2}}"," ",0,"-1/2*(A*b^5 - 10*A*a*b^3*c - 12*B*a^3*c^2 + 30*A*a^2*b*c^2)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt(-b^2 + 4*a*c)) - 1/4*A*log(c*x^4 + b*x^2 + a)/a^3 + 1/2*A*log(x^2)/a^3 + 1/8*(3*A*b^4*c^2*x^8 - 24*A*a*b^2*c^3*x^8 + 48*A*a^2*c^4*x^8 + 6*A*b^5*c*x^6 - 44*A*a*b^3*c^2*x^6 + 24*B*a^3*c^3*x^6 + 68*A*a^2*b*c^3*x^6 + 3*A*b^6*x^4 - 10*A*a*b^4*c*x^4 + 36*B*a^3*b*c^2*x^4 - 58*A*a^2*b^2*c^2*x^4 + 128*A*a^3*c^3*x^4 + 10*A*a*b^5*x^2 + 8*B*a^3*b^2*c*x^2 - 72*A*a^2*b^3*c*x^2 + 40*B*a^4*c^2*x^2 + 92*A*a^3*b*c^2*x^2 - 2*B*a^3*b^3 + 9*A*a^2*b^4 + 20*B*a^4*b*c - 66*A*a^3*b^2*c + 96*A*a^4*c^2)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*(c*x^4 + b*x^2 + a)^2)","A",0
131,1,648,0,6.371436," ","integrate((B*x^2+A)/x^3/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","-\frac{{\left(B a b^{5} - 3 \, A b^{6} - 10 \, B a^{2} b^{3} c + 30 \, A a b^{4} c + 30 \, B a^{3} b c^{2} - 90 \, A a^{2} b^{2} c^{2} + 60 \, A a^{3} c^{3}\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{3 \, B a b^{4} c^{2} x^{8} - 9 \, A b^{5} c^{2} x^{8} - 24 \, B a^{2} b^{2} c^{3} x^{8} + 72 \, A a b^{3} c^{3} x^{8} + 48 \, B a^{3} c^{4} x^{8} - 144 \, A a^{2} b c^{4} x^{8} + 6 \, B a b^{5} c x^{6} - 18 \, A b^{6} c x^{6} - 44 \, B a^{2} b^{3} c^{2} x^{6} + 136 \, A a b^{4} c^{2} x^{6} + 68 \, B a^{3} b c^{3} x^{6} - 236 \, A a^{2} b^{2} c^{3} x^{6} - 56 \, A a^{3} c^{4} x^{6} + 3 \, B a b^{6} x^{4} - 9 \, A b^{7} x^{4} - 10 \, B a^{2} b^{4} c x^{4} + 38 \, A a b^{5} c x^{4} - 58 \, B a^{3} b^{2} c^{2} x^{4} + 110 \, A a^{2} b^{3} c^{2} x^{4} + 128 \, B a^{4} c^{3} x^{4} - 436 \, A a^{3} b c^{3} x^{4} + 10 \, B a^{2} b^{5} x^{2} - 26 \, A a b^{6} x^{2} - 72 \, B a^{3} b^{3} c x^{2} + 192 \, A a^{2} b^{4} c x^{2} + 92 \, B a^{4} b c^{2} x^{2} - 316 \, A a^{3} b^{2} c^{2} x^{2} - 72 \, A a^{4} c^{3} x^{2} + 9 \, B a^{3} b^{4} - 19 \, A a^{2} b^{5} - 66 \, B a^{4} b^{2} c + 144 \, A a^{3} b^{3} c + 96 \, B a^{5} c^{2} - 260 \, A a^{4} b c^{2}}{8 \, {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{2}} - \frac{{\left(B a - 3 \, A b\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, a^{4}} + \frac{{\left(B a - 3 \, A b\right)} \log\left(x^{2}\right)}{2 \, a^{4}} - \frac{B a x^{2} - 3 \, A b x^{2} + A a}{2 \, a^{4} x^{2}}"," ",0,"-1/2*(B*a*b^5 - 3*A*b^6 - 10*B*a^2*b^3*c + 30*A*a*b^4*c + 30*B*a^3*b*c^2 - 90*A*a^2*b^2*c^2 + 60*A*a^3*c^3)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*sqrt(-b^2 + 4*a*c)) + 1/8*(3*B*a*b^4*c^2*x^8 - 9*A*b^5*c^2*x^8 - 24*B*a^2*b^2*c^3*x^8 + 72*A*a*b^3*c^3*x^8 + 48*B*a^3*c^4*x^8 - 144*A*a^2*b*c^4*x^8 + 6*B*a*b^5*c*x^6 - 18*A*b^6*c*x^6 - 44*B*a^2*b^3*c^2*x^6 + 136*A*a*b^4*c^2*x^6 + 68*B*a^3*b*c^3*x^6 - 236*A*a^2*b^2*c^3*x^6 - 56*A*a^3*c^4*x^6 + 3*B*a*b^6*x^4 - 9*A*b^7*x^4 - 10*B*a^2*b^4*c*x^4 + 38*A*a*b^5*c*x^4 - 58*B*a^3*b^2*c^2*x^4 + 110*A*a^2*b^3*c^2*x^4 + 128*B*a^4*c^3*x^4 - 436*A*a^3*b*c^3*x^4 + 10*B*a^2*b^5*x^2 - 26*A*a*b^6*x^2 - 72*B*a^3*b^3*c*x^2 + 192*A*a^2*b^4*c*x^2 + 92*B*a^4*b*c^2*x^2 - 316*A*a^3*b^2*c^2*x^2 - 72*A*a^4*c^3*x^2 + 9*B*a^3*b^4 - 19*A*a^2*b^5 - 66*B*a^4*b^2*c + 144*A*a^3*b^3*c + 96*B*a^5*c^2 - 260*A*a^4*b*c^2)/((a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*(c*x^4 + b*x^2 + a)^2) - 1/4*(B*a - 3*A*b)*log(c*x^4 + b*x^2 + a)/a^4 + 1/2*(B*a - 3*A*b)*log(x^2)/a^4 - 1/2*(B*a*x^2 - 3*A*b*x^2 + A*a)/(a^4*x^2)","A",0
132,1,3987,0,8.280235," ","integrate(x^8*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left({\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 12 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 2 \, b^{6} c^{2} - 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 24 \, a b^{4} c^{3} - 2 \, b^{5} c^{3} + 320 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 160 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 288 \, a^{2} b^{2} c^{4} + 112 \, a b^{3} c^{4} - 80 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 640 \, a^{3} c^{5} - 416 \, 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 - 56 \, \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} + 208 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 104 \, \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} - 52 \, \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^{4} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} - 160 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4} - 104 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} A + 3 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 2 \, b^{7} c + 80 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 24 \, \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} + 32 \, a b^{5} c^{2} - 2 \, b^{6} c^{2} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 12 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 160 \, a^{2} b^{3} c^{3} + 28 \, a b^{4} c^{3} + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 256 \, a^{3} b c^{4} - 192 \, a^{2} b^{2} c^{4} + 448 \, a^{3} c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} - 14 \, \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 + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 20 \, \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} - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c - 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} - 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 112 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4} + \sqrt{{\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)}^{2} - 4 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}}\right)}{32 \, {\left(b^{8} c^{2} - 16 \, a b^{6} c^{3} - 2 \, b^{7} c^{3} + 96 \, a^{2} b^{4} c^{4} + 24 \, a b^{5} c^{4} + b^{6} c^{4} - 256 \, a^{3} b^{2} c^{5} - 96 \, a^{2} b^{3} c^{5} - 12 \, a b^{4} c^{5} + 256 \, a^{4} c^{6} + 128 \, a^{3} b c^{6} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} {\left| c \right|}} + \frac{{\left({\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 12 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 2 \, b^{6} c^{2} - 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 24 \, a b^{4} c^{3} + 2 \, b^{5} c^{3} + 320 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 160 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 288 \, a^{2} b^{2} c^{4} - 112 \, a b^{3} c^{4} - 80 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 640 \, a^{3} c^{5} + 416 \, 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 + 56 \, \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} - 208 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 104 \, \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} + 52 \, \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^{4} c^{2} - 32 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} + 160 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4} + 104 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} A + 3 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 2 \, b^{7} c + 80 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 24 \, \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} - 32 \, a b^{5} c^{2} + 2 \, b^{6} c^{2} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 12 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 160 \, a^{2} b^{3} c^{3} - 28 \, a b^{4} c^{3} + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 256 \, a^{3} b c^{4} + 192 \, a^{2} b^{2} c^{4} - 448 \, a^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} + 14 \, \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 - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 20 \, \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} + 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} + 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 112 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4} - \sqrt{{\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)}^{2} - 4 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}}\right)}{32 \, {\left(b^{8} c^{2} - 16 \, a b^{6} c^{3} - 2 \, b^{7} c^{3} + 96 \, a^{2} b^{4} c^{4} + 24 \, a b^{5} c^{4} + b^{6} c^{4} - 256 \, a^{3} b^{2} c^{5} - 96 \, a^{2} b^{3} c^{5} - 12 \, a b^{4} c^{5} + 256 \, a^{4} c^{6} + 128 \, a^{3} b c^{6} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} {\left| c \right|}} - \frac{5 \, B b^{4} c x^{7} - 37 \, B a b^{2} c^{2} x^{7} - A b^{3} c^{2} x^{7} + 44 \, B a^{2} c^{3} x^{7} + 16 \, A a b c^{3} x^{7} + 3 \, B b^{5} x^{5} - 20 \, B a b^{3} c x^{5} + A b^{4} c x^{5} - 4 \, B a^{2} b c^{2} x^{5} + 5 \, A a b^{2} c^{2} x^{5} + 36 \, A a^{2} c^{3} x^{5} + 6 \, B a b^{4} x^{3} - 49 \, B a^{2} b^{2} c x^{3} + 2 \, A a b^{3} c x^{3} + 28 \, B a^{3} c^{2} x^{3} + 28 \, A a^{2} b c^{2} x^{3} + 3 \, B a^{2} b^{3} x - 24 \, B a^{3} b c x + A a^{2} b^{2} c x + 20 \, A a^{3} c^{2} x}{8 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{2}}"," ",0,"1/32*((sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 12*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 2*b^6*c^2 - 144*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 24*a*b^4*c^3 - 2*b^5*c^3 + 320*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 160*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 + 288*a^2*b^2*c^4 + 112*a*b^3*c^4 - 80*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 640*a^3*c^5 - 416*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 - 56*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 + 208*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 104*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 - 52*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^4*c^2 + 32*(b^2 - 4*a*c)*a*b^2*c^3 + 2*(b^2 - 4*a*c)*b^3*c^3 - 160*(b^2 - 4*a*c)*a^2*c^4 - 104*(b^2 - 4*a*c)*a*b*c^4)*A + 3*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c - 2*b^7*c + 80*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + 24*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 + 32*a*b^5*c^2 - 2*b^6*c^2 - 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 12*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 160*a^2*b^3*c^3 + 28*a*b^4*c^3 + 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 256*a^3*b*c^4 - 192*a^2*b^2*c^4 + 448*a^3*c^5 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 - 14*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 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 20*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 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + 56*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^5*c - 24*(b^2 - 4*a*c)*a*b^3*c^2 + 2*(b^2 - 4*a*c)*b^4*c^2 + 64*(b^2 - 4*a*c)*a^2*b*c^3 - 20*(b^2 - 4*a*c)*a*b^2*c^3 + 112*(b^2 - 4*a*c)*a^2*c^4)*B)*arctan(2*sqrt(1/2)*x/sqrt((b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4 + sqrt((b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)^2 - 4*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))/((b^8*c^2 - 16*a*b^6*c^3 - 2*b^7*c^3 + 96*a^2*b^4*c^4 + 24*a*b^5*c^4 + b^6*c^4 - 256*a^3*b^2*c^5 - 96*a^2*b^3*c^5 - 12*a*b^4*c^5 + 256*a^4*c^6 + 128*a^3*b*c^6 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*abs(c)) + 1/32*((sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 12*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 2*b^6*c^2 - 144*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 24*a*b^4*c^3 + 2*b^5*c^3 + 320*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 160*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 288*a^2*b^2*c^4 - 112*a*b^3*c^4 - 80*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^5 + 640*a^3*c^5 + 416*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 + 56*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 - 208*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 104*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 + 52*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^4*c^2 - 32*(b^2 - 4*a*c)*a*b^2*c^3 - 2*(b^2 - 4*a*c)*b^3*c^3 + 160*(b^2 - 4*a*c)*a^2*c^4 + 104*(b^2 - 4*a*c)*a*b*c^4)*A + 3*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 2*b^7*c + 80*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + 24*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 - 32*a*b^5*c^2 + 2*b^6*c^2 - 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 12*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 160*a^2*b^3*c^3 - 28*a*b^4*c^3 + 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 256*a^3*b*c^4 + 192*a^2*b^2*c^4 - 448*a^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 + 14*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 - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 20*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 + 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 56*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^5*c + 24*(b^2 - 4*a*c)*a*b^3*c^2 - 2*(b^2 - 4*a*c)*b^4*c^2 - 64*(b^2 - 4*a*c)*a^2*b*c^3 + 20*(b^2 - 4*a*c)*a*b^2*c^3 - 112*(b^2 - 4*a*c)*a^2*c^4)*B)*arctan(2*sqrt(1/2)*x/sqrt((b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4 - sqrt((b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)^2 - 4*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))/((b^8*c^2 - 16*a*b^6*c^3 - 2*b^7*c^3 + 96*a^2*b^4*c^4 + 24*a*b^5*c^4 + b^6*c^4 - 256*a^3*b^2*c^5 - 96*a^2*b^3*c^5 - 12*a*b^4*c^5 + 256*a^4*c^6 + 128*a^3*b*c^6 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*abs(c)) - 1/8*(5*B*b^4*c*x^7 - 37*B*a*b^2*c^2*x^7 - A*b^3*c^2*x^7 + 44*B*a^2*c^3*x^7 + 16*A*a*b*c^3*x^7 + 3*B*b^5*x^5 - 20*B*a*b^3*c*x^5 + A*b^4*c*x^5 - 4*B*a^2*b*c^2*x^5 + 5*A*a*b^2*c^2*x^5 + 36*A*a^2*c^3*x^5 + 6*B*a*b^4*x^3 - 49*B*a^2*b^2*c*x^3 + 2*A*a*b^3*c*x^3 + 28*B*a^3*c^2*x^3 + 28*A*a^2*b*c^2*x^3 + 3*B*a^2*b^3*x - 24*B*a^3*b*c*x + A*a^2*b^2*c*x + 20*A*a^3*c^2*x)/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*(c*x^4 + b*x^2 + a)^2)","B",0
133,1,7578,0,11.662335," ","integrate(x^6*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(3 \, {\left(2 \, b^{4} c^{3} - 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 + 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)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}^{2} A + {\left(2 \, b^{5} c^{2} - 40 \, a b^{3} c^{3} + 128 \, 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} + 20 \, \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 - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 32 \, \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} + 16 \, \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} + 32 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}^{2} B - 24 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{3} - 12 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{4} - 2 \, a b^{7} c^{4} + 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{5} + 24 \, a^{2} b^{5} c^{5} - 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} - 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{6} - 96 \, a^{3} b^{3} c^{6} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{7} + 128 \, a^{4} b c^{7} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{4} - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{5} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{6}\right)} A {\left| b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3} \right|} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{8} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{3} - 2 \, a b^{8} c^{3} - 192 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{4} - 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{4} - 16 \, a^{2} b^{6} c^{4} + 896 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{5} + 288 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 12 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} + 384 \, a^{3} b^{4} c^{5} - 1280 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{6} - 640 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} - 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} - 1792 \, a^{4} b^{2} c^{6} + 320 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{7} + 2560 \, a^{5} c^{7} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{6} c^{3} + 24 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{4} - 288 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{5} + 640 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{6}\right)} B {\left| b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3} \right|} - 3 \, {\left(2 \, b^{12} c^{5} - 8 \, a b^{10} c^{6} - 192 \, a^{2} b^{8} c^{7} + 1792 \, a^{3} b^{6} c^{8} - 5632 \, a^{4} b^{4} c^{9} + 6144 \, a^{5} b^{2} c^{10} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{12} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{10} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{11} c^{4} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{8} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{10} c^{5} - 896 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{6} - 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c^{6} + 2816 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{7} + 1024 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{7} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{7} - 3072 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{8} - 1536 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{8} - 512 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{8} + 768 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{9} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{10} c^{5} + 192 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{6} c^{7} - 1024 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{8} + 1536 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{9}\right)} A - {\left(2 \, b^{13} c^{4} - 68 \, a b^{11} c^{5} + 688 \, a^{2} b^{9} c^{6} - 2688 \, a^{3} b^{7} c^{7} + 2048 \, a^{4} b^{5} c^{8} + 11264 \, a^{5} b^{3} c^{9} - 20480 \, a^{6} b c^{10} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{13} c^{2} + 34 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{11} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{12} c^{3} - 344 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{9} c^{4} - 60 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{10} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{11} c^{4} + 1344 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c^{5} + 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{8} c^{5} + 30 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{9} c^{5} - 1024 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{6} - 896 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{6} - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c^{6} - 5632 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{7} - 1536 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{7} + 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{7} + 10240 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{8} + 5120 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{8} + 768 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{8} - 2560 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{9} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{11} c^{4} + 60 \, {\left(b^{2} - 4 \, a c\right)} a b^{9} c^{5} - 448 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{7} c^{6} + 896 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{5} c^{7} + 1536 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{3} c^{8} - 5120 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{9}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3} + \sqrt{{\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)}^{2} - 4 \, {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)}}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}}}\right)}{64 \, {\left(a b^{10} c^{3} - 20 \, a^{2} b^{8} c^{4} - 2 \, a b^{9} c^{4} + 160 \, a^{3} b^{6} c^{5} + 32 \, a^{2} b^{7} c^{5} + a b^{8} c^{5} - 640 \, a^{4} b^{4} c^{6} - 192 \, a^{3} b^{5} c^{6} - 16 \, a^{2} b^{6} c^{6} + 1280 \, a^{5} b^{2} c^{7} + 512 \, a^{4} b^{3} c^{7} + 96 \, a^{3} b^{4} c^{7} - 1024 \, a^{6} c^{8} - 512 \, a^{5} b c^{8} - 256 \, a^{4} b^{2} c^{8} + 256 \, a^{5} c^{9}\right)} {\left| b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3} \right|} {\left| c \right|}} - \frac{{\left(3 \, {\left(2 \, b^{4} c^{3} - 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 + 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)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}^{2} A + {\left(2 \, b^{5} c^{2} - 40 \, a b^{3} c^{3} + 128 \, 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} + 20 \, \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 - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 32 \, \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} + 16 \, \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} + 32 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}^{2} B + 24 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{3} - 12 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{4} + 2 \, a b^{7} c^{4} + 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{5} - 24 \, a^{2} b^{5} c^{5} - 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} - 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{6} + 96 \, a^{3} b^{3} c^{6} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{7} - 128 \, a^{4} b c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{4} + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{5} - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{6}\right)} A {\left| b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3} \right|} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{8} c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{3} + 2 \, a b^{8} c^{3} - 192 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{4} - 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{4} + 16 \, a^{2} b^{6} c^{4} + 896 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{5} + 288 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 12 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} - 384 \, a^{3} b^{4} c^{5} - 1280 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{6} - 640 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} - 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} + 1792 \, a^{4} b^{2} c^{6} + 320 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{7} - 2560 \, a^{5} c^{7} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{6} c^{3} - 24 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{4} + 288 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{5} - 640 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{6}\right)} B {\left| b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3} \right|} - 3 \, {\left(2 \, b^{12} c^{5} - 8 \, a b^{10} c^{6} - 192 \, a^{2} b^{8} c^{7} + 1792 \, a^{3} b^{6} c^{8} - 5632 \, a^{4} b^{4} c^{9} + 6144 \, a^{5} b^{2} c^{10} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{12} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{10} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{11} c^{4} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{8} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{10} c^{5} - 896 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{6} - 192 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c^{6} + 2816 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{7} + 1024 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{7} + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{7} - 3072 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{8} - 1536 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{8} - 512 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{8} + 768 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{9} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{10} c^{5} + 192 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{6} c^{7} - 1024 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{8} + 1536 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{9}\right)} A - {\left(2 \, b^{13} c^{4} - 68 \, a b^{11} c^{5} + 688 \, a^{2} b^{9} c^{6} - 2688 \, a^{3} b^{7} c^{7} + 2048 \, a^{4} b^{5} c^{8} + 11264 \, a^{5} b^{3} c^{9} - 20480 \, a^{6} b c^{10} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{13} c^{2} + 34 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{11} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{12} c^{3} - 344 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{9} c^{4} - 60 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{10} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{11} c^{4} + 1344 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c^{5} + 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{8} c^{5} + 30 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{9} c^{5} - 1024 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{6} - 896 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{6} - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c^{6} - 5632 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{7} - 1536 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{7} + 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{7} + 10240 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{8} + 5120 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{8} + 768 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{8} - 2560 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{9} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{11} c^{4} + 60 \, {\left(b^{2} - 4 \, a c\right)} a b^{9} c^{5} - 448 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{7} c^{6} + 896 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{5} c^{7} + 1536 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{3} c^{8} - 5120 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{9}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3} - \sqrt{{\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)}^{2} - 4 \, {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)}}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}}}\right)}{64 \, {\left(a b^{10} c^{3} - 20 \, a^{2} b^{8} c^{4} - 2 \, a b^{9} c^{4} + 160 \, a^{3} b^{6} c^{5} + 32 \, a^{2} b^{7} c^{5} + a b^{8} c^{5} - 640 \, a^{4} b^{4} c^{6} - 192 \, a^{3} b^{5} c^{6} - 16 \, a^{2} b^{6} c^{6} + 1280 \, a^{5} b^{2} c^{7} + 512 \, a^{4} b^{3} c^{7} + 96 \, a^{3} b^{4} c^{7} - 1024 \, a^{6} c^{8} - 512 \, a^{5} b c^{8} - 256 \, a^{4} b^{2} c^{8} + 256 \, a^{5} c^{9}\right)} {\left| b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3} \right|} {\left| c \right|}} + \frac{B b^{3} c x^{7} - 16 \, B a b c^{2} x^{7} + 3 \, A b^{2} c^{2} x^{7} + 12 \, A a c^{3} x^{7} - B b^{4} x^{5} - 5 \, B a b^{2} c x^{5} + 5 \, A b^{3} c x^{5} - 36 \, B a^{2} c^{2} x^{5} + 16 \, A a b c^{2} x^{5} - 2 \, B a b^{3} x^{3} - 28 \, B a^{2} b c x^{3} + 19 \, A a b^{2} c x^{3} - 4 \, A a^{2} c^{2} x^{3} - B a^{2} b^{2} x - 20 \, B a^{3} c x + 12 \, A a^{2} b c x}{8 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{2}}"," ",0,"1/64*(3*(2*b^4*c^3 - 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 + 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)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)^2*A + (2*b^5*c^2 - 40*a*b^3*c^3 + 128*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 + 20*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 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 32*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 + 16*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 + 32*(b^2 - 4*a*c)*a*b*c^3)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)^2*B - 24*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^3 - 12*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^4 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^4 - 2*a*b^7*c^4 + 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^5 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^5 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^5 + 24*a^2*b^5*c^5 - 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^6 - 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^6 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^6 - 96*a^3*b^3*c^6 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^7 + 128*a^4*b*c^7 + 2*(b^2 - 4*a*c)*a*b^5*c^4 - 16*(b^2 - 4*a*c)*a^2*b^3*c^5 + 32*(b^2 - 4*a*c)*a^3*b*c^6)*A*abs(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3) + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^8*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^3 - 2*a*b^8*c^3 - 192*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^4 - 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^4 - 16*a^2*b^6*c^4 + 896*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^5 + 288*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^5 + 12*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^5 + 384*a^3*b^4*c^5 - 1280*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*c^6 - 640*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^6 - 144*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^6 - 1792*a^4*b^2*c^6 + 320*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^7 + 2560*a^5*c^7 + 2*(b^2 - 4*a*c)*a*b^6*c^3 + 24*(b^2 - 4*a*c)*a^2*b^4*c^4 - 288*(b^2 - 4*a*c)*a^3*b^2*c^5 + 640*(b^2 - 4*a*c)*a^4*c^6)*B*abs(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3) - 3*(2*b^12*c^5 - 8*a*b^10*c^6 - 192*a^2*b^8*c^7 + 1792*a^3*b^6*c^8 - 5632*a^4*b^4*c^9 + 6144*a^5*b^2*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^12*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^10*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^11*c^4 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^8*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^10*c^5 - 896*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^6 - 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c^6 + 2816*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^7 + 1024*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^7 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^7 - 3072*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^8 - 1536*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^8 - 512*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^8 + 768*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^9 - 2*(b^2 - 4*a*c)*b^10*c^5 + 192*(b^2 - 4*a*c)*a^2*b^6*c^7 - 1024*(b^2 - 4*a*c)*a^3*b^4*c^8 + 1536*(b^2 - 4*a*c)*a^4*b^2*c^9)*A - (2*b^13*c^4 - 68*a*b^11*c^5 + 688*a^2*b^9*c^6 - 2688*a^3*b^7*c^7 + 2048*a^4*b^5*c^8 + 11264*a^5*b^3*c^9 - 20480*a^6*b*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^13*c^2 + 34*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^11*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^12*c^3 - 344*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^9*c^4 - 60*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^10*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^11*c^4 + 1344*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c^5 + 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^8*c^5 + 30*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^9*c^5 - 1024*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^6 - 896*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^6 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c^6 - 5632*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^7 - 1536*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^7 + 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^7 + 10240*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^8 + 5120*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^8 + 768*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^8 - 2560*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^9 - 2*(b^2 - 4*a*c)*b^11*c^4 + 60*(b^2 - 4*a*c)*a*b^9*c^5 - 448*(b^2 - 4*a*c)*a^2*b^7*c^6 + 896*(b^2 - 4*a*c)*a^3*b^5*c^7 + 1536*(b^2 - 4*a*c)*a^4*b^3*c^8 - 5120*(b^2 - 4*a*c)*a^5*b*c^9)*B)*arctan(2*sqrt(1/2)*x/sqrt((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3 + sqrt((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)^2 - 4*(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)))/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)))/((a*b^10*c^3 - 20*a^2*b^8*c^4 - 2*a*b^9*c^4 + 160*a^3*b^6*c^5 + 32*a^2*b^7*c^5 + a*b^8*c^5 - 640*a^4*b^4*c^6 - 192*a^3*b^5*c^6 - 16*a^2*b^6*c^6 + 1280*a^5*b^2*c^7 + 512*a^4*b^3*c^7 + 96*a^3*b^4*c^7 - 1024*a^6*c^8 - 512*a^5*b*c^8 - 256*a^4*b^2*c^8 + 256*a^5*c^9)*abs(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*abs(c)) - 1/64*(3*(2*b^4*c^3 - 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 + 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)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)^2*A + (2*b^5*c^2 - 40*a*b^3*c^3 + 128*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 + 20*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 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 32*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 + 16*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 + 32*(b^2 - 4*a*c)*a*b*c^3)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)^2*B + 24*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^3 - 12*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^4 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^4 + 2*a*b^7*c^4 + 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^5 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^5 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^5 - 24*a^2*b^5*c^5 - 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^6 - 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^6 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^6 + 96*a^3*b^3*c^6 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^7 - 128*a^4*b*c^7 - 2*(b^2 - 4*a*c)*a*b^5*c^4 + 16*(b^2 - 4*a*c)*a^2*b^3*c^5 - 32*(b^2 - 4*a*c)*a^3*b*c^6)*A*abs(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3) - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^8*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^3 + 2*a*b^8*c^3 - 192*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^4 - 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^4 + 16*a^2*b^6*c^4 + 896*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^5 + 288*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^5 + 12*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^5 - 384*a^3*b^4*c^5 - 1280*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*c^6 - 640*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^6 - 144*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^6 + 1792*a^4*b^2*c^6 + 320*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^7 - 2560*a^5*c^7 - 2*(b^2 - 4*a*c)*a*b^6*c^3 - 24*(b^2 - 4*a*c)*a^2*b^4*c^4 + 288*(b^2 - 4*a*c)*a^3*b^2*c^5 - 640*(b^2 - 4*a*c)*a^4*c^6)*B*abs(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3) - 3*(2*b^12*c^5 - 8*a*b^10*c^6 - 192*a^2*b^8*c^7 + 1792*a^3*b^6*c^8 - 5632*a^4*b^4*c^9 + 6144*a^5*b^2*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^12*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^10*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^11*c^4 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^8*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^10*c^5 - 896*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^6 - 192*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c^6 + 2816*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^7 + 1024*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^7 + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^7 - 3072*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^8 - 1536*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^8 - 512*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^8 + 768*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^9 - 2*(b^2 - 4*a*c)*b^10*c^5 + 192*(b^2 - 4*a*c)*a^2*b^6*c^7 - 1024*(b^2 - 4*a*c)*a^3*b^4*c^8 + 1536*(b^2 - 4*a*c)*a^4*b^2*c^9)*A - (2*b^13*c^4 - 68*a*b^11*c^5 + 688*a^2*b^9*c^6 - 2688*a^3*b^7*c^7 + 2048*a^4*b^5*c^8 + 11264*a^5*b^3*c^9 - 20480*a^6*b*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^13*c^2 + 34*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^11*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^12*c^3 - 344*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^9*c^4 - 60*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^10*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^11*c^4 + 1344*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c^5 + 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^8*c^5 + 30*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^9*c^5 - 1024*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^6 - 896*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^6 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c^6 - 5632*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^7 - 1536*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^7 + 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^7 + 10240*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^8 + 5120*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^8 + 768*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^8 - 2560*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^9 - 2*(b^2 - 4*a*c)*b^11*c^4 + 60*(b^2 - 4*a*c)*a*b^9*c^5 - 448*(b^2 - 4*a*c)*a^2*b^7*c^6 + 896*(b^2 - 4*a*c)*a^3*b^5*c^7 + 1536*(b^2 - 4*a*c)*a^4*b^3*c^8 - 5120*(b^2 - 4*a*c)*a^5*b*c^9)*B)*arctan(2*sqrt(1/2)*x/sqrt((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3 - sqrt((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)^2 - 4*(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)))/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)))/((a*b^10*c^3 - 20*a^2*b^8*c^4 - 2*a*b^9*c^4 + 160*a^3*b^6*c^5 + 32*a^2*b^7*c^5 + a*b^8*c^5 - 640*a^4*b^4*c^6 - 192*a^3*b^5*c^6 - 16*a^2*b^6*c^6 + 1280*a^5*b^2*c^7 + 512*a^4*b^3*c^7 + 96*a^3*b^4*c^7 - 1024*a^6*c^8 - 512*a^5*b*c^8 - 256*a^4*b^2*c^8 + 256*a^5*c^9)*abs(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*abs(c)) + 1/8*(B*b^3*c*x^7 - 16*B*a*b*c^2*x^7 + 3*A*b^2*c^2*x^7 + 12*A*a*c^3*x^7 - B*b^4*x^5 - 5*B*a*b^2*c*x^5 + 5*A*b^3*c*x^5 - 36*B*a^2*c^2*x^5 + 16*A*a*b*c^2*x^5 - 2*B*a*b^3*x^3 - 28*B*a^2*b*c*x^3 + 19*A*a*b^2*c*x^3 - 4*A*a^2*c^2*x^3 - B*a^2*b^2*x - 20*B*a^3*c*x + 12*A*a^2*b*c*x)/((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*(c*x^4 + b*x^2 + a)^2)","B",0
134,1,3162,0,8.260873," ","integrate(x^4*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{3 \, {\left({\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} - 4 \, \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 - 16 \, \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} b^{4} c^{2} + 8 \, a b^{4} c^{2} + 2 \, b^{5} c^{2} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 32 \, a^{2} b^{2} c^{3} + 16 \, a b^{3} c^{3} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 128 \, a^{3} c^{4} - 96 \, 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 + 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 24 \, \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} - 12 \, \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 - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} - 24 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} A - 2 \, {\left(2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 16 \, \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 \, a b^{5} c + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 16 \, \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} + 32 \, a^{2} b^{3} c^{2} + 6 \, a b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 64 \, a^{3} b c^{3} - 16 \, a^{2} b^{2} c^{3} - 32 \, 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} + 8 \, \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 + 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} - 3 \, \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} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2} - 6 \, {\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\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + \sqrt{{\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)}^{2} - 4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}\right)}{32 \, {\left(a b^{8} - 16 \, a^{2} b^{6} c - 2 \, a b^{7} c + 96 \, a^{3} b^{4} c^{2} + 24 \, a^{2} b^{5} c^{2} + a b^{6} c^{2} - 256 \, a^{4} b^{2} c^{3} - 96 \, a^{3} b^{3} c^{3} - 12 \, a^{2} b^{4} c^{3} + 256 \, a^{5} c^{4} + 128 \, a^{4} b c^{4} + 48 \, a^{3} b^{2} c^{4} - 64 \, a^{4} c^{5}\right)} {\left| c \right|}} + \frac{3 \, {\left({\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} - 4 \, \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 - 16 \, \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} b^{4} c^{2} - 8 \, a b^{4} c^{2} - 2 \, b^{5} c^{2} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 32 \, a^{2} b^{2} c^{3} - 16 \, a b^{3} c^{3} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 128 \, a^{3} c^{4} + 96 \, 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 - 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 24 \, \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} + 12 \, \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 + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3} + 24 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} A - 2 \, {\left(2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 16 \, \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 \, a b^{5} c + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 16 \, \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} - 32 \, a^{2} b^{3} c^{2} - 6 \, a b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 64 \, a^{3} b c^{3} + 16 \, a^{2} b^{2} c^{3} + 32 \, 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} - 8 \, \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 - 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} + 3 \, \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} - 4 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2} + 6 \, {\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\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} - \sqrt{{\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)}^{2} - 4 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}\right)}{32 \, {\left(a b^{8} - 16 \, a^{2} b^{6} c - 2 \, a b^{7} c + 96 \, a^{3} b^{4} c^{2} + 24 \, a^{2} b^{5} c^{2} + a b^{6} c^{2} - 256 \, a^{4} b^{2} c^{3} - 96 \, a^{3} b^{3} c^{3} - 12 \, a^{2} b^{4} c^{3} + 256 \, a^{5} c^{4} + 128 \, a^{4} b c^{4} + 48 \, a^{3} b^{2} c^{4} - 64 \, a^{4} c^{5}\right)} {\left| c \right|}} + \frac{3 \, B b^{2} c x^{7} + 12 \, B a c^{2} x^{7} - 12 \, A b c^{2} x^{7} + 5 \, B b^{3} x^{5} + 16 \, B a b c x^{5} - 19 \, A b^{2} c x^{5} + 4 \, A a c^{2} x^{5} + 19 \, B a b^{2} x^{3} - 5 \, A b^{3} x^{3} - 4 \, B a^{2} c x^{3} - 16 \, A a b c x^{3} + 12 \, B a^{2} b x - 3 \, A a b^{2} x - 12 \, A a^{2} c x}{8 \, {\left(c x^{4} + b x^{2} + a\right)}^{2} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)}}"," ",0,"3/32*((sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 - 4*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 - 16*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)*b^4*c^2 + 8*a*b^4*c^2 + 2*b^5*c^2 + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 32*a^2*b^2*c^3 + 16*a*b^3*c^3 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 128*a^3*c^4 - 96*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 + 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 24*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 - 12*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 - 2*(b^2 - 4*a*c)*b^3*c^2 - 32*(b^2 - 4*a*c)*a^2*c^3 - 24*(b^2 - 4*a*c)*a*b*c^3)*A - 2*(2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5 - 16*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*a*b^5*c + 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + 16*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 + 32*a^2*b^3*c^2 + 6*a*b^4*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 64*a^3*b*c^3 - 16*a^2*b^2*c^3 - 32*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 + 8*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 + 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 - 3*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 + 4*(b^2 - 4*a*c)*a*b^3*c - 16*(b^2 - 4*a*c)*a^2*b*c^2 - 6*(b^2 - 4*a*c)*a*b^2*c^2 - 8*(b^2 - 4*a*c)*a^2*c^3)*B)*arctan(2*sqrt(1/2)*x/sqrt((b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + sqrt((b^5 - 8*a*b^3*c + 16*a^2*b*c^2)^2 - 4*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/((a*b^8 - 16*a^2*b^6*c - 2*a*b^7*c + 96*a^3*b^4*c^2 + 24*a^2*b^5*c^2 + a*b^6*c^2 - 256*a^4*b^2*c^3 - 96*a^3*b^3*c^3 - 12*a^2*b^4*c^3 + 256*a^5*c^4 + 128*a^4*b*c^4 + 48*a^3*b^2*c^4 - 64*a^4*c^5)*abs(c)) + 3/32*((sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 - 4*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 - 16*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)*b^4*c^2 - 8*a*b^4*c^2 - 2*b^5*c^2 + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 32*a^2*b^2*c^3 - 16*a*b^3*c^3 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 + 128*a^3*c^4 + 96*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 - 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 24*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 + 12*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 + 2*(b^2 - 4*a*c)*b^3*c^2 + 32*(b^2 - 4*a*c)*a^2*c^3 + 24*(b^2 - 4*a*c)*a*b*c^3)*A - 2*(2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5 - 16*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*a*b^5*c + 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + 16*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 - 32*a^2*b^3*c^2 - 6*a*b^4*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 64*a^3*b*c^3 + 16*a^2*b^2*c^3 + 32*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 - 8*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 - 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 + 3*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 - 4*(b^2 - 4*a*c)*a*b^3*c + 16*(b^2 - 4*a*c)*a^2*b*c^2 + 6*(b^2 - 4*a*c)*a*b^2*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3)*B)*arctan(2*sqrt(1/2)*x/sqrt((b^5 - 8*a*b^3*c + 16*a^2*b*c^2 - sqrt((b^5 - 8*a*b^3*c + 16*a^2*b*c^2)^2 - 4*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/((a*b^8 - 16*a^2*b^6*c - 2*a*b^7*c + 96*a^3*b^4*c^2 + 24*a^2*b^5*c^2 + a*b^6*c^2 - 256*a^4*b^2*c^3 - 96*a^3*b^3*c^3 - 12*a^2*b^4*c^3 + 256*a^5*c^4 + 128*a^4*b*c^4 + 48*a^3*b^2*c^4 - 64*a^4*c^5)*abs(c)) + 1/8*(3*B*b^2*c*x^7 + 12*B*a*c^2*x^7 - 12*A*b*c^2*x^7 + 5*B*b^3*x^5 + 16*B*a*b*c*x^5 - 19*A*b^2*c*x^5 + 4*A*a*c^2*x^5 + 19*B*a*b^2*x^3 - 5*A*b^3*x^3 - 4*B*a^2*c*x^3 - 16*A*a*b*c*x^3 + 12*B*a^2*b*x - 3*A*a*b^2*x - 12*A*a^2*c*x)/((c*x^4 + b*x^2 + a)^2*(b^4 - 8*a*b^2*c + 16*a^2*c^2))","B",0
135,1,7267,0,11.773192," ","integrate(x^2*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left({\left(2 \, b^{4} c^{2} + 32 \, a b^{2} c^{3} - 160 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 40 \, \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} - 20 \, \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} - 40 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)}^{2} A - 12 \, {\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)}^{2} B + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{9} - 28 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{8} c - 2 \, a b^{9} c + 240 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} + 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{2} + 56 \, a^{2} b^{7} c^{2} - 832 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 288 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} - 480 \, a^{3} b^{5} c^{3} + 1024 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} + 512 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} + 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} + 1664 \, a^{4} b^{3} c^{4} - 256 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} - 2048 \, a^{5} b c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{7} c - 48 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} + 288 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} - 512 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} A {\left| a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} \right|} + 6 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{8} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c - 2 \, a^{2} b^{8} c + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} + 16 \, a^{3} b^{6} c^{2} + 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 256 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{4} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} - 256 \, a^{5} b^{2} c^{4} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{5} + 512 \, a^{6} c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{6} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{2} - 32 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{3} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{5} c^{4}\right)} B {\left| a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} \right|} + {\left(2 \, a^{2} b^{12} c^{2} - 136 \, a^{3} b^{10} c^{3} + 1856 \, a^{4} b^{8} c^{4} - 10496 \, a^{5} b^{6} c^{5} + 27136 \, a^{6} b^{4} c^{6} - 26624 \, a^{7} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{12} + 68 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{10} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{11} c - 928 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c^{2} - 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{9} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{10} c^{2} + 5248 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{3} + 1344 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{3} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{8} c^{3} - 13568 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{4} - 5120 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{4} - 672 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{4} + 13312 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} + 6656 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{5} + 2560 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{5} - 3328 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{10} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{8} c^{3} - 1344 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{6} c^{4} + 5120 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c^{5} - 6656 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{6}\right)} A + 6 \, {\left(6 \, a^{3} b^{11} c^{2} - 88 \, a^{4} b^{9} c^{3} + 448 \, a^{5} b^{7} c^{4} - 768 \, a^{6} b^{5} c^{5} - 512 \, a^{7} b^{3} c^{6} + 2048 \, a^{8} b c^{7} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{11} + 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{9} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{10} c - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{9} c^{2} + 384 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} 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^{6} c^{3} + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{3} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{4} - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{4} - 1024 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{5} - 512 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{6} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{9} c^{2} + 64 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{7} c^{3} - 192 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{5} c^{4} + 512 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{6}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + \sqrt{{\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)}^{2} - 4 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)}}}{a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}}}}\right)}{64 \, {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c - 2 \, a^{3} b^{9} c + 160 \, a^{5} b^{6} c^{2} + 32 \, a^{4} b^{7} c^{2} + a^{3} b^{8} c^{2} - 640 \, a^{6} b^{4} c^{3} - 192 \, a^{5} b^{5} c^{3} - 16 \, a^{4} b^{6} c^{3} + 1280 \, a^{7} b^{2} c^{4} + 512 \, a^{6} b^{3} c^{4} + 96 \, a^{5} b^{4} c^{4} - 1024 \, a^{8} c^{5} - 512 \, a^{7} b c^{5} - 256 \, a^{6} b^{2} c^{5} + 256 \, a^{7} c^{6}\right)} {\left| a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} \right|} {\left| c \right|}} - \frac{{\left({\left(2 \, b^{4} c^{2} + 32 \, a b^{2} c^{3} - 160 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 40 \, \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} - 20 \, \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} - 40 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)}^{2} A - 12 \, {\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^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)}^{2} B - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{9} - 28 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{8} c + 2 \, a b^{9} c + 240 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} + 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{2} - 56 \, a^{2} b^{7} c^{2} - 832 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 288 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} + 480 \, a^{3} b^{5} c^{3} + 1024 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} + 512 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} + 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 1664 \, a^{4} b^{3} c^{4} - 256 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} + 2048 \, a^{5} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{7} c + 48 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} - 288 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} + 512 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} A {\left| a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} \right|} - 6 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{8} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c + 2 \, a^{2} b^{8} c + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} - 16 \, a^{3} b^{6} c^{2} + 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 256 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{4} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} + 256 \, a^{5} b^{2} c^{4} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{5} - 512 \, a^{6} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{6} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{2} + 32 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{3} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{5} c^{4}\right)} B {\left| a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} \right|} + {\left(2 \, a^{2} b^{12} c^{2} - 136 \, a^{3} b^{10} c^{3} + 1856 \, a^{4} b^{8} c^{4} - 10496 \, a^{5} b^{6} c^{5} + 27136 \, a^{6} b^{4} c^{6} - 26624 \, a^{7} b^{2} c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{12} + 68 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{10} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{11} c - 928 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c^{2} - 128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{9} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{10} c^{2} + 5248 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{3} + 1344 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{3} + 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{8} c^{3} - 13568 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{4} - 5120 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{4} - 672 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{4} + 13312 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} + 6656 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{5} + 2560 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{5} - 3328 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{10} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{8} c^{3} - 1344 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{6} c^{4} + 5120 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c^{5} - 6656 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{6}\right)} A + 6 \, {\left(6 \, a^{3} b^{11} c^{2} - 88 \, a^{4} b^{9} c^{3} + 448 \, a^{5} b^{7} c^{4} - 768 \, a^{6} b^{5} c^{5} - 512 \, a^{7} b^{3} c^{6} + 2048 \, a^{8} b c^{7} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{11} + 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{9} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{10} c - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} c^{2} - 64 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{9} c^{2} + 384 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} 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^{6} c^{3} + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{3} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{4} - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{4} - 1024 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{5} - 512 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} + 256 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{6} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{9} c^{2} + 64 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{7} c^{3} - 192 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{5} c^{4} + 512 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{6}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} - \sqrt{{\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)}^{2} - 4 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)}}}{a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}}}}\right)}{64 \, {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c - 2 \, a^{3} b^{9} c + 160 \, a^{5} b^{6} c^{2} + 32 \, a^{4} b^{7} c^{2} + a^{3} b^{8} c^{2} - 640 \, a^{6} b^{4} c^{3} - 192 \, a^{5} b^{5} c^{3} - 16 \, a^{4} b^{6} c^{3} + 1280 \, a^{7} b^{2} c^{4} + 512 \, a^{6} b^{3} c^{4} + 96 \, a^{5} b^{4} c^{4} - 1024 \, a^{8} c^{5} - 512 \, a^{7} b c^{5} - 256 \, a^{6} b^{2} c^{5} + 256 \, a^{7} c^{6}\right)} {\left| a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} \right|} {\left| c \right|}} - \frac{12 \, B a b c^{2} x^{7} - A b^{2} c^{2} x^{7} - 20 \, A a c^{3} x^{7} + 19 \, B a b^{2} c x^{5} - 2 \, A b^{3} c x^{5} - 4 \, B a^{2} c^{2} x^{5} - 28 \, A a b c^{2} x^{5} + 5 \, B a b^{3} x^{3} - A b^{4} x^{3} + 16 \, B a^{2} b c x^{3} - 5 \, A a b^{2} c x^{3} - 36 \, A a^{2} c^{2} x^{3} + 3 \, B a^{2} b^{2} x + A a b^{3} x + 12 \, B a^{3} c x - 16 \, A a^{2} b c x}{8 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{2}}"," ",0,"1/64*((2*b^4*c^2 + 32*a*b^2*c^3 - 160*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 40*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 - 20*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 - 40*(b^2 - 4*a*c)*a*c^3)*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)^2*A - 12*(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^4 - 8*a^2*b^2*c + 16*a^3*c^2)^2*B + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^9 - 28*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^8*c - 2*a*b^9*c + 240*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^2 + 56*a^2*b^7*c^2 - 832*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 288*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 - 480*a^3*b^5*c^3 + 1024*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 + 512*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + 144*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 + 1664*a^4*b^3*c^4 - 256*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 - 2048*a^5*b*c^5 + 2*(b^2 - 4*a*c)*a*b^7*c - 48*(b^2 - 4*a*c)*a^2*b^5*c^2 + 288*(b^2 - 4*a*c)*a^3*b^3*c^3 - 512*(b^2 - 4*a*c)*a^4*b*c^4)*A*abs(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2) + 6*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^8 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c - 2*a^2*b^8*c + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 + 16*a^3*b^6*c^2 + 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 + 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 256*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*c^4 - 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 256*a^5*b^2*c^4 + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*c^5 + 512*a^6*c^5 + 2*(b^2 - 4*a*c)*a^2*b^6*c - 8*(b^2 - 4*a*c)*a^3*b^4*c^2 - 32*(b^2 - 4*a*c)*a^4*b^2*c^3 + 128*(b^2 - 4*a*c)*a^5*c^4)*B*abs(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2) + (2*a^2*b^12*c^2 - 136*a^3*b^10*c^3 + 1856*a^4*b^8*c^4 - 10496*a^5*b^6*c^5 + 27136*a^6*b^4*c^6 - 26624*a^7*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^12 + 68*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^10*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^11*c - 928*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c^2 - 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^9*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^10*c^2 + 5248*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^3 + 1344*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^3 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^8*c^3 - 13568*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^4 - 5120*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^4 - 672*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^4 + 13312*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 + 6656*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^5 + 2560*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^5 - 3328*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^6 - 2*(b^2 - 4*a*c)*a^2*b^10*c^2 + 128*(b^2 - 4*a*c)*a^3*b^8*c^3 - 1344*(b^2 - 4*a*c)*a^4*b^6*c^4 + 5120*(b^2 - 4*a*c)*a^5*b^4*c^5 - 6656*(b^2 - 4*a*c)*a^6*b^2*c^6)*A + 6*(6*a^3*b^11*c^2 - 88*a^4*b^9*c^3 + 448*a^5*b^7*c^4 - 768*a^6*b^5*c^5 - 512*a^7*b^3*c^6 + 2048*a^8*b*c^7 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^11 + 44*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^9*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^10*c - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^7*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^9*c^2 + 384*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*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^6*c^3 + 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^3 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^4 - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^4 - 1024*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b*c^5 - 512*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b*c^6 - 6*(b^2 - 4*a*c)*a^3*b^9*c^2 + 64*(b^2 - 4*a*c)*a^4*b^7*c^3 - 192*(b^2 - 4*a*c)*a^5*b^5*c^4 + 512*(b^2 - 4*a*c)*a^7*b*c^6)*B)*arctan(2*sqrt(1/2)*x/sqrt((a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + sqrt((a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)^2 - 4*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)))/(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)))/((a^3*b^10 - 20*a^4*b^8*c - 2*a^3*b^9*c + 160*a^5*b^6*c^2 + 32*a^4*b^7*c^2 + a^3*b^8*c^2 - 640*a^6*b^4*c^3 - 192*a^5*b^5*c^3 - 16*a^4*b^6*c^3 + 1280*a^7*b^2*c^4 + 512*a^6*b^3*c^4 + 96*a^5*b^4*c^4 - 1024*a^8*c^5 - 512*a^7*b*c^5 - 256*a^6*b^2*c^5 + 256*a^7*c^6)*abs(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*abs(c)) - 1/64*((2*b^4*c^2 + 32*a*b^2*c^3 - 160*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 40*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 - 20*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 - 40*(b^2 - 4*a*c)*a*c^3)*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)^2*A - 12*(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^4 - 8*a^2*b^2*c + 16*a^3*c^2)^2*B - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^9 - 28*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^8*c + 2*a*b^9*c + 240*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^2 - 56*a^2*b^7*c^2 - 832*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 288*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 + 480*a^3*b^5*c^3 + 1024*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 + 512*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + 144*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 1664*a^4*b^3*c^4 - 256*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 + 2048*a^5*b*c^5 - 2*(b^2 - 4*a*c)*a*b^7*c + 48*(b^2 - 4*a*c)*a^2*b^5*c^2 - 288*(b^2 - 4*a*c)*a^3*b^3*c^3 + 512*(b^2 - 4*a*c)*a^4*b*c^4)*A*abs(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2) - 6*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^8 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c + 2*a^2*b^8*c + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 - 16*a^3*b^6*c^2 + 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 + 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 256*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*c^4 - 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + 256*a^5*b^2*c^4 + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*c^5 - 512*a^6*c^5 - 2*(b^2 - 4*a*c)*a^2*b^6*c + 8*(b^2 - 4*a*c)*a^3*b^4*c^2 + 32*(b^2 - 4*a*c)*a^4*b^2*c^3 - 128*(b^2 - 4*a*c)*a^5*c^4)*B*abs(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2) + (2*a^2*b^12*c^2 - 136*a^3*b^10*c^3 + 1856*a^4*b^8*c^4 - 10496*a^5*b^6*c^5 + 27136*a^6*b^4*c^6 - 26624*a^7*b^2*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^12 + 68*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^10*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^11*c - 928*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c^2 - 128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^9*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^10*c^2 + 5248*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^3 + 1344*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^3 + 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^8*c^3 - 13568*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^4 - 5120*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^4 - 672*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^4 + 13312*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 + 6656*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^5 + 2560*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^5 - 3328*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^6 - 2*(b^2 - 4*a*c)*a^2*b^10*c^2 + 128*(b^2 - 4*a*c)*a^3*b^8*c^3 - 1344*(b^2 - 4*a*c)*a^4*b^6*c^4 + 5120*(b^2 - 4*a*c)*a^5*b^4*c^5 - 6656*(b^2 - 4*a*c)*a^6*b^2*c^6)*A + 6*(6*a^3*b^11*c^2 - 88*a^4*b^9*c^3 + 448*a^5*b^7*c^4 - 768*a^6*b^5*c^5 - 512*a^7*b^3*c^6 + 2048*a^8*b*c^7 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^11 + 44*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^9*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^10*c - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^7*c^2 - 64*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^9*c^2 + 384*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*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^6*c^3 + 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^3 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^4 - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^4 - 1024*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b*c^5 - 512*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 + 256*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^6 - 6*(b^2 - 4*a*c)*a^3*b^9*c^2 + 64*(b^2 - 4*a*c)*a^4*b^7*c^3 - 192*(b^2 - 4*a*c)*a^5*b^5*c^4 + 512*(b^2 - 4*a*c)*a^7*b*c^6)*B)*arctan(2*sqrt(1/2)*x/sqrt((a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 - sqrt((a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)^2 - 4*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)))/(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)))/((a^3*b^10 - 20*a^4*b^8*c - 2*a^3*b^9*c + 160*a^5*b^6*c^2 + 32*a^4*b^7*c^2 + a^3*b^8*c^2 - 640*a^6*b^4*c^3 - 192*a^5*b^5*c^3 - 16*a^4*b^6*c^3 + 1280*a^7*b^2*c^4 + 512*a^6*b^3*c^4 + 96*a^5*b^4*c^4 - 1024*a^8*c^5 - 512*a^7*b*c^5 - 256*a^6*b^2*c^5 + 256*a^7*c^6)*abs(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*abs(c)) - 1/8*(12*B*a*b*c^2*x^7 - A*b^2*c^2*x^7 - 20*A*a*c^3*x^7 + 19*B*a*b^2*c*x^5 - 2*A*b^3*c*x^5 - 4*B*a^2*c^2*x^5 - 28*A*a*b*c^2*x^5 + 5*B*a*b^3*x^3 - A*b^4*x^3 + 16*B*a^2*b*c*x^3 - 5*A*a*b^2*c*x^3 - 36*A*a^2*c^2*x^3 + 3*B*a^2*b^2*x + A*a*b^3*x + 12*B*a^3*c*x - 16*A*a^2*b*c*x)/((a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*(c*x^4 + b*x^2 + a)^2)","B",0
136,1,4609,0,8.536994," ","integrate((B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(3 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} - 17 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c - 2 \, b^{8} c + 116 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 26 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 34 \, a b^{6} c^{2} + 2 \, b^{7} c^{2} - 368 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 13 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 232 \, a^{2} b^{4} c^{3} - 30 \, a b^{5} c^{3} + 448 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 224 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 736 \, a^{3} b^{2} c^{4} + 176 \, a^{2} b^{3} c^{4} - 112 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} - 896 \, a^{4} c^{5} - 352 \, a^{3} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} + 15 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c - 26 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} + 22 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} - 224 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} - 88 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} A + {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, a b^{7} c + 144 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 40 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 48 \, a^{2} b^{5} c^{2} + 2 \, a b^{6} c^{2} - 256 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 288 \, a^{3} b^{3} c^{3} - 44 \, a^{2} b^{4} c^{3} + 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 512 \, a^{4} b c^{4} + 64 \, a^{3} b^{2} c^{4} + 320 \, a^{4} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} - 36 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} - 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} - 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} + 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c - 40 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3} + 36 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} + 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2} + \sqrt{{\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)}^{2} - 4 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)}}}{a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}}}}\right)}{32 \, {\left(a^{3} b^{8} - 16 \, a^{4} b^{6} c - 2 \, a^{3} b^{7} c + 96 \, a^{5} b^{4} c^{2} + 24 \, a^{4} b^{5} c^{2} + a^{3} b^{6} c^{2} - 256 \, a^{6} b^{2} c^{3} - 96 \, a^{5} b^{3} c^{3} - 12 \, a^{4} b^{4} c^{3} + 256 \, a^{7} c^{4} + 128 \, a^{6} b c^{4} + 48 \, a^{5} b^{2} c^{4} - 64 \, a^{6} c^{5}\right)} {\left| c \right|}} + \frac{{\left(3 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} - 17 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c + 2 \, b^{8} c + 116 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + 26 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} - 34 \, a b^{6} c^{2} - 2 \, b^{7} c^{2} - 368 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 13 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 232 \, a^{2} b^{4} c^{3} + 30 \, a b^{5} c^{3} + 448 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} + 224 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 736 \, a^{3} b^{2} c^{4} - 176 \, a^{2} b^{3} c^{4} - 112 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 896 \, a^{4} c^{5} + 352 \, a^{3} b c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} - 15 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 176 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 88 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 44 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c + 26 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 22 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{3} + 224 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4} + 88 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4}\right)} A + {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c + 2 \, a b^{7} c + 144 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 40 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 48 \, a^{2} b^{5} c^{2} - 2 \, a b^{6} c^{2} - 256 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{3} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 288 \, a^{3} b^{3} c^{3} + 44 \, a^{2} b^{4} c^{3} + 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 512 \, a^{4} b c^{4} - 64 \, a^{3} b^{2} c^{4} - 320 \, a^{4} c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} - 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c + 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} + 36 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 160 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} + 80 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c + 40 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 128 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3} - 36 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 80 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} B\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2} - \sqrt{{\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)}^{2} - 4 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)}}}{a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}}}}\right)}{32 \, {\left(a^{3} b^{8} - 16 \, a^{4} b^{6} c - 2 \, a^{3} b^{7} c + 96 \, a^{5} b^{4} c^{2} + 24 \, a^{4} b^{5} c^{2} + a^{3} b^{6} c^{2} - 256 \, a^{6} b^{2} c^{3} - 96 \, a^{5} b^{3} c^{3} - 12 \, a^{4} b^{4} c^{3} + 256 \, a^{7} c^{4} + 128 \, a^{6} b c^{4} + 48 \, a^{5} b^{2} c^{4} - 64 \, a^{6} c^{5}\right)} {\left| c \right|}} + \frac{B a b^{2} c^{2} x^{7} + 3 \, A b^{3} c^{2} x^{7} + 20 \, B a^{2} c^{3} x^{7} - 24 \, A a b c^{3} x^{7} + 2 \, B a b^{3} c x^{5} + 6 \, A b^{4} c x^{5} + 28 \, B a^{2} b c^{2} x^{5} - 49 \, A a b^{2} c^{2} x^{5} + 28 \, A a^{2} c^{3} x^{5} + B a b^{4} x^{3} + 3 \, A b^{5} x^{3} + 5 \, B a^{2} b^{2} c x^{3} - 20 \, A a b^{3} c x^{3} + 36 \, B a^{3} c^{2} x^{3} - 4 \, A a^{2} b c^{2} x^{3} - B a^{2} b^{3} x + 5 \, A a b^{4} x + 16 \, B a^{3} b c x - 37 \, A a^{2} b^{2} c x + 44 \, A a^{3} c^{2} x}{8 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} {\left(c x^{4} + b x^{2} + a\right)}^{2}}"," ",0,"1/32*(3*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8 - 17*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c - 2*b^8*c + 116*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + 26*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^2 + 34*a*b^6*c^2 + 2*b^7*c^2 - 368*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 13*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 232*a^2*b^4*c^3 - 30*a*b^5*c^3 + 448*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^4 + 224*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + 736*a^3*b^2*c^4 + 176*a^2*b^3*c^4 - 112*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^5 - 896*a^4*c^5 - 352*a^3*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 + 15*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c - 88*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 + 88*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 11*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 44*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 2*(b^2 - 4*a*c)*b^6*c - 26*(b^2 - 4*a*c)*a*b^4*c^2 - 2*(b^2 - 4*a*c)*b^5*c^2 + 128*(b^2 - 4*a*c)*a^2*b^2*c^3 + 22*(b^2 - 4*a*c)*a*b^3*c^3 - 224*(b^2 - 4*a*c)*a^3*c^4 - 88*(b^2 - 4*a*c)*a^2*b*c^4)*A + (sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7 - 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c - 2*a*b^7*c + 144*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + 40*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 + 48*a^2*b^5*c^2 + 2*a*b^6*c^2 - 256*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 - 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 20*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 288*a^3*b^3*c^3 - 44*a^2*b^4*c^3 + 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 512*a^4*b*c^4 + 64*a^3*b^2*c^4 + 320*a^4*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 - 36*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 - 160*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^3 - 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 + 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 + 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 2*(b^2 - 4*a*c)*a*b^5*c - 40*(b^2 - 4*a*c)*a^2*b^3*c^2 - 2*(b^2 - 4*a*c)*a*b^4*c^2 + 128*(b^2 - 4*a*c)*a^3*b*c^3 + 36*(b^2 - 4*a*c)*a^2*b^2*c^3 + 80*(b^2 - 4*a*c)*a^3*c^4)*B)*arctan(2*sqrt(1/2)*x/sqrt((a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2 + sqrt((a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)^2 - 4*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)))/(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)))/((a^3*b^8 - 16*a^4*b^6*c - 2*a^3*b^7*c + 96*a^5*b^4*c^2 + 24*a^4*b^5*c^2 + a^3*b^6*c^2 - 256*a^6*b^2*c^3 - 96*a^5*b^3*c^3 - 12*a^4*b^4*c^3 + 256*a^7*c^4 + 128*a^6*b*c^4 + 48*a^5*b^2*c^4 - 64*a^6*c^5)*abs(c)) + 1/32*(3*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8 - 17*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c + 2*b^8*c + 116*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + 26*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^2 - 34*a*b^6*c^2 - 2*b^7*c^2 - 368*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 13*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 232*a^2*b^4*c^3 + 30*a*b^5*c^3 + 448*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^4 + 224*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 736*a^3*b^2*c^4 - 176*a^2*b^3*c^4 - 112*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^5 + 896*a^4*c^5 + 352*a^3*b*c^5 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 - 15*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 88*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 176*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 88*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 11*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 44*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^6*c + 26*(b^2 - 4*a*c)*a*b^4*c^2 + 2*(b^2 - 4*a*c)*b^5*c^2 - 128*(b^2 - 4*a*c)*a^2*b^2*c^3 - 22*(b^2 - 4*a*c)*a*b^3*c^3 + 224*(b^2 - 4*a*c)*a^3*c^4 + 88*(b^2 - 4*a*c)*a^2*b*c^4)*A + (sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7 - 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c + 2*a*b^7*c + 144*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + 40*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 - 48*a^2*b^5*c^2 - 2*a*b^6*c^2 - 256*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^3 - 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 - 20*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 + 288*a^3*b^3*c^3 + 44*a^2*b^4*c^3 + 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 - 512*a^4*b*c^4 - 64*a^3*b^2*c^4 - 320*a^4*c^5 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6 - 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c + 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 + 36*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 160*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^3 + 80*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 - 2*(b^2 - 4*a*c)*a*b^5*c + 40*(b^2 - 4*a*c)*a^2*b^3*c^2 + 2*(b^2 - 4*a*c)*a*b^4*c^2 - 128*(b^2 - 4*a*c)*a^3*b*c^3 - 36*(b^2 - 4*a*c)*a^2*b^2*c^3 - 80*(b^2 - 4*a*c)*a^3*c^4)*B)*arctan(2*sqrt(1/2)*x/sqrt((a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2 - sqrt((a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)^2 - 4*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)))/(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)))/((a^3*b^8 - 16*a^4*b^6*c - 2*a^3*b^7*c + 96*a^5*b^4*c^2 + 24*a^4*b^5*c^2 + a^3*b^6*c^2 - 256*a^6*b^2*c^3 - 96*a^5*b^3*c^3 - 12*a^4*b^4*c^3 + 256*a^7*c^4 + 128*a^6*b*c^4 + 48*a^5*b^2*c^4 - 64*a^6*c^5)*abs(c)) + 1/8*(B*a*b^2*c^2*x^7 + 3*A*b^3*c^2*x^7 + 20*B*a^2*c^3*x^7 - 24*A*a*b*c^3*x^7 + 2*B*a*b^3*c*x^5 + 6*A*b^4*c*x^5 + 28*B*a^2*b*c^2*x^5 - 49*A*a*b^2*c^2*x^5 + 28*A*a^2*c^3*x^5 + B*a*b^4*x^3 + 3*A*b^5*x^3 + 5*B*a^2*b^2*c*x^3 - 20*A*a*b^3*c*x^3 + 36*B*a^3*c^2*x^3 - 4*A*a^2*b*c^2*x^3 - B*a^2*b^3*x + 5*A*a*b^4*x + 16*B*a^3*b*c*x - 37*A*a^2*b^2*c*x + 44*A*a^3*c^2*x)/((a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*(c*x^4 + b*x^2 + a)^2)","B",0
137,1,19,0,0.305044," ","integrate(x*(4*x^2-7)/(x^4-5*x^2+4),x, algorithm=""giac"")","\frac{1}{2} \, \log\left({\left| x^{2} - 1 \right|}\right) + \frac{3}{2} \, \log\left({\left| x^{2} - 4 \right|}\right)"," ",0,"1/2*log(abs(x^2 - 1)) + 3/2*log(abs(x^2 - 4))","A",0
138,1,19,0,0.283206," ","integrate((4*x^3-7*x)/(x^4-5*x^2+4),x, algorithm=""giac"")","\frac{1}{2} \, \log\left({\left| x^{2} - 1 \right|}\right) + \frac{3}{2} \, \log\left({\left| x^{2} - 4 \right|}\right)"," ",0,"1/2*log(abs(x^2 - 1)) + 3/2*log(abs(x^2 - 4))","A",0
139,1,30,0,0.282084," ","integrate(x*(x^2+2)/(x^4+x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + 1\right)}\right) + \frac{1}{4} \, \log\left(x^{4} + x^{2} + 1\right)"," ",0,"1/2*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 + 1)) + 1/4*log(x^4 + x^2 + 1)","A",0
140,1,30,0,0.371825," ","integrate((x^3+2*x)/(x^4+x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + 1\right)}\right) + \frac{1}{4} \, \log\left(x^{4} + x^{2} + 1\right)"," ",0,"1/2*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 + 1)) + 1/4*log(x^4 + x^2 + 1)","A",0
141,1,38,0,0.944478," ","integrate((2*x^3+11*x)/(x^4+2*x^2+3)^2,x, algorithm=""giac"")","\frac{9}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x^{2} + 1\right)}\right) + \frac{9 \, x^{2} + 5}{8 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}}"," ",0,"9/16*sqrt(2)*arctan(1/2*sqrt(2)*(x^2 + 1)) + 1/8*(9*x^2 + 5)/(x^4 + 2*x^2 + 3)","A",0
142,1,102,0,0.464542," ","integrate(x^5*(3*x^2+2)*(x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","\frac{1}{1280} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, x^{2} + 5\right)} x^{2} - 127\right)} x^{2} + 2635\right)} x^{2} - 33429\right)} + \frac{1}{192} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, {\left(4 \, {\left(6 \, x^{2} + 5\right)} x^{2} - 89\right)} x^{2} + 1095\right)} - \frac{21229}{512} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5\right)"," ",0,"1/1280*sqrt(x^4 + 5*x^2 + 3)*(2*(4*(6*(8*x^2 + 5)*x^2 - 127)*x^2 + 2635)*x^2 - 33429) + 1/192*sqrt(x^4 + 5*x^2 + 3)*(2*(4*(6*x^2 + 5)*x^2 - 89)*x^2 + 1095) - 21229/512*log(2*x^2 - 2*sqrt(x^4 + 5*x^2 + 3) + 5)","A",0
143,1,88,0,0.362850," ","integrate(x^3*(3*x^2+2)*(x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","\frac{1}{128} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, {\left(4 \, {\left(6 \, x^{2} + 5\right)} x^{2} - 89\right)} x^{2} + 1095\right)} + \frac{1}{24} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, {\left(4 \, x^{2} + 5\right)} x^{2} - 51\right)} + \frac{3367}{256} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5\right)"," ",0,"1/128*sqrt(x^4 + 5*x^2 + 3)*(2*(4*(6*x^2 + 5)*x^2 - 89)*x^2 + 1095) + 1/24*sqrt(x^4 + 5*x^2 + 3)*(2*(4*x^2 + 5)*x^2 - 51) + 3367/256*log(2*x^2 - 2*sqrt(x^4 + 5*x^2 + 3) + 5)","A",0
144,1,74,0,0.342453," ","integrate(x*(3*x^2+2)*(x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","\frac{1}{16} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, {\left(4 \, x^{2} + 5\right)} x^{2} - 51\right)} + \frac{1}{4} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, x^{2} + 5\right)} - \frac{143}{32} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5\right)"," ",0,"1/16*sqrt(x^4 + 5*x^2 + 3)*(2*(4*x^2 + 5)*x^2 - 51) + 1/4*sqrt(x^4 + 5*x^2 + 3)*(2*x^2 + 5) - 143/32*log(2*x^2 - 2*sqrt(x^4 + 5*x^2 + 3) + 5)","A",0
145,1,98,0,0.477583," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x,x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(6 \, x^{2} + 23\right)} + \sqrt{3} \log\left(\frac{x^{2} + \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}{x^{2} - \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}\right) - \frac{1}{16} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5\right)"," ",0,"1/8*sqrt(x^4 + 5*x^2 + 3)*(6*x^2 + 23) + sqrt(3)*log((x^2 + sqrt(3) - sqrt(x^4 + 5*x^2 + 3))/(x^2 - sqrt(3) - sqrt(x^4 + 5*x^2 + 3))) - 1/16*log(2*x^2 - 2*sqrt(x^4 + 5*x^2 + 3) + 5)","A",0
146,1,138,0,0.514704," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^3,x, algorithm=""giac"")","\frac{7}{3} \, \sqrt{3} \log\left(\frac{x^{2} + \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}{x^{2} - \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}\right) + \frac{3}{2} \, \sqrt{x^{4} + 5 \, x^{2} + 3} + \frac{5 \, x^{2} - 5 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 6}{{\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{2} - 3} - \frac{19}{4} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5\right)"," ",0,"7/3*sqrt(3)*log((x^2 + sqrt(3) - sqrt(x^4 + 5*x^2 + 3))/(x^2 - sqrt(3) - sqrt(x^4 + 5*x^2 + 3))) + 3/2*sqrt(x^4 + 5*x^2 + 3) + (5*x^2 - 5*sqrt(x^4 + 5*x^2 + 3) + 6)/((x^2 - sqrt(x^4 + 5*x^2 + 3))^2 - 3) - 19/4*log(2*x^2 - 2*sqrt(x^4 + 5*x^2 + 3) + 5)","A",0
147,1,169,0,0.572116," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^5,x, algorithm=""giac"")","\frac{77}{72} \, \sqrt{3} \log\left(\frac{x^{2} + \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}{x^{2} - \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}\right) + \frac{127 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{3} + 228 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{2} - 159 \, x^{2} + 159 \, \sqrt{x^{4} + 5 \, x^{2} + 3} - 324}{12 \, {\left({\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{2} - 3\right)}^{2}} - \frac{3}{2} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5\right)"," ",0,"77/72*sqrt(3)*log((x^2 + sqrt(3) - sqrt(x^4 + 5*x^2 + 3))/(x^2 - sqrt(3) - sqrt(x^4 + 5*x^2 + 3))) + 1/12*(127*(x^2 - sqrt(x^4 + 5*x^2 + 3))^3 + 228*(x^2 - sqrt(x^4 + 5*x^2 + 3))^2 - 159*x^2 + 159*sqrt(x^4 + 5*x^2 + 3) - 324)/((x^2 - sqrt(x^4 + 5*x^2 + 3))^2 - 3)^2 - 3/2*log(2*x^2 - 2*sqrt(x^4 + 5*x^2 + 3) + 5)","B",0
148,1,189,0,0.532213," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^7,x, algorithm=""giac"")","-\frac{13}{108} \, \sqrt{3} \log\left(\frac{x^{2} + \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}{x^{2} - \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}\right) + \frac{67 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{5} + 306 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{4} + 430 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{3} + 90 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{2} - 63 \, x^{2} + 63 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 108}{18 \, {\left({\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{2} - 3\right)}^{3}}"," ",0,"-13/108*sqrt(3)*log((x^2 + sqrt(3) - sqrt(x^4 + 5*x^2 + 3))/(x^2 - sqrt(3) - sqrt(x^4 + 5*x^2 + 3))) + 1/18*(67*(x^2 - sqrt(x^4 + 5*x^2 + 3))^5 + 306*(x^2 - sqrt(x^4 + 5*x^2 + 3))^4 + 430*(x^2 - sqrt(x^4 + 5*x^2 + 3))^3 + 90*(x^2 - sqrt(x^4 + 5*x^2 + 3))^2 - 63*x^2 + 63*sqrt(x^4 + 5*x^2 + 3) + 108)/((x^2 - sqrt(x^4 + 5*x^2 + 3))^2 - 3)^3","B",0
149,1,233,0,0.457212," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^9,x, algorithm=""giac"")","\frac{871}{10368} \, \sqrt{3} \log\left(\frac{x^{2} + \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}{x^{2} - \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}\right) - \frac{871 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{7} - 5184 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{6} - 57389 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{5} - 165888 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{4} - 204807 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{3} - 93312 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{2} - 2403 \, x^{2} + 2403 \, \sqrt{x^{4} + 5 \, x^{2} + 3} - 5184}{1728 \, {\left({\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{2} - 3\right)}^{4}}"," ",0,"871/10368*sqrt(3)*log((x^2 + sqrt(3) - sqrt(x^4 + 5*x^2 + 3))/(x^2 - sqrt(3) - sqrt(x^4 + 5*x^2 + 3))) - 1/1728*(871*(x^2 - sqrt(x^4 + 5*x^2 + 3))^7 - 5184*(x^2 - sqrt(x^4 + 5*x^2 + 3))^6 - 57389*(x^2 - sqrt(x^4 + 5*x^2 + 3))^5 - 165888*(x^2 - sqrt(x^4 + 5*x^2 + 3))^4 - 204807*(x^2 - sqrt(x^4 + 5*x^2 + 3))^3 - 93312*(x^2 - sqrt(x^4 + 5*x^2 + 3))^2 - 2403*x^2 + 2403*sqrt(x^4 + 5*x^2 + 3) - 5184)/((x^2 - sqrt(x^4 + 5*x^2 + 3))^2 - 3)^4","B",0
150,1,255,0,0.563102," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^11,x, algorithm=""giac"")","-\frac{2093}{31104} \, \sqrt{3} \log\left(\frac{x^{2} + \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}{x^{2} - \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}\right) + \frac{10465 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{9} - 42830 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{7} + 1270080 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{6} + 7060800 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{5} + 15310080 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{4} + 16095870 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{3} + 7568640 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{2} + 1096335 \, x^{2} - 1096335 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 202176}{25920 \, {\left({\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{2} - 3\right)}^{5}}"," ",0,"-2093/31104*sqrt(3)*log((x^2 + sqrt(3) - sqrt(x^4 + 5*x^2 + 3))/(x^2 - sqrt(3) - sqrt(x^4 + 5*x^2 + 3))) + 1/25920*(10465*(x^2 - sqrt(x^4 + 5*x^2 + 3))^9 - 42830*(x^2 - sqrt(x^4 + 5*x^2 + 3))^7 + 1270080*(x^2 - sqrt(x^4 + 5*x^2 + 3))^6 + 7060800*(x^2 - sqrt(x^4 + 5*x^2 + 3))^5 + 15310080*(x^2 - sqrt(x^4 + 5*x^2 + 3))^4 + 16095870*(x^2 - sqrt(x^4 + 5*x^2 + 3))^3 + 7568640*(x^2 - sqrt(x^4 + 5*x^2 + 3))^2 + 1096335*x^2 - 1096335*sqrt(x^4 + 5*x^2 + 3) + 202176)/((x^2 - sqrt(x^4 + 5*x^2 + 3))^2 - 3)^5","B",0
151,0,0,0,0.000000," ","integrate(x^4*(3*x^2+2)*(x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(3 \, x^{2} + 2\right)} x^{4}\,{d x}"," ",0,"integrate(sqrt(x^4 + 5*x^2 + 3)*(3*x^2 + 2)*x^4, x)","F",0
152,0,0,0,0.000000," ","integrate(x^2*(3*x^2+2)*(x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(3 \, x^{2} + 2\right)} x^{2}\,{d x}"," ",0,"integrate(sqrt(x^4 + 5*x^2 + 3)*(3*x^2 + 2)*x^2, x)","F",0
153,0,0,0,0.000000," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","\int \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(3 \, x^{2} + 2\right)}\,{d x}"," ",0,"integrate(sqrt(x^4 + 5*x^2 + 3)*(3*x^2 + 2), x)","F",0
154,0,0,0,0.000000," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 5 \, x^{2} + 3} {\left(3 \, x^{2} + 2\right)}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(x^4 + 5*x^2 + 3)*(3*x^2 + 2)/x^2, x)","F",0
155,0,0,0,0.000000," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{x^{4} + 5 \, x^{2} + 3} {\left(3 \, x^{2} + 2\right)}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(x^4 + 5*x^2 + 3)*(3*x^2 + 2)/x^4, x)","F",0
156,1,207,0,0.540517," ","integrate(x^5*(3*x^2+2)*(x^4+5*x^2+3)^(3/2),x, algorithm=""giac"")","\frac{1}{71680} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(12 \, x^{2} + 5\right)} x^{2} - 203\right)} x^{2} + 7635\right)} x^{2} - 76083\right)} x^{2} + 1627215\right)} x^{2} - 20756241\right)} + \frac{17}{3072} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, x^{2} + 1\right)} x^{2} - 33\right)} x^{2} + 321\right)} x^{2} - 6837\right)} x^{2} + 87147\right)} + \frac{19}{3840} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, x^{2} + 5\right)} x^{2} - 127\right)} x^{2} + 2635\right)} x^{2} - 33429\right)} + \frac{1}{64} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, {\left(4 \, {\left(6 \, x^{2} + 5\right)} x^{2} - 89\right)} x^{2} + 1095\right)} + \frac{368927}{4096} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5\right)"," ",0,"1/71680*sqrt(x^4 + 5*x^2 + 3)*(2*(4*(2*(8*(10*(12*x^2 + 5)*x^2 - 203)*x^2 + 7635)*x^2 - 76083)*x^2 + 1627215)*x^2 - 20756241) + 17/3072*sqrt(x^4 + 5*x^2 + 3)*(2*(4*(2*(8*(2*x^2 + 1)*x^2 - 33)*x^2 + 321)*x^2 - 6837)*x^2 + 87147) + 19/3840*sqrt(x^4 + 5*x^2 + 3)*(2*(4*(6*(8*x^2 + 5)*x^2 - 127)*x^2 + 2635)*x^2 - 33429) + 1/64*sqrt(x^4 + 5*x^2 + 3)*(2*(4*(6*x^2 + 5)*x^2 - 89)*x^2 + 1095) + 368927/4096*log(2*x^2 - 2*sqrt(x^4 + 5*x^2 + 3) + 5)","A",0
157,1,179,0,0.587316," ","integrate(x^3*(3*x^2+2)*(x^4+5*x^2+3)^(3/2),x, algorithm=""giac"")","\frac{1}{1024} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, x^{2} + 1\right)} x^{2} - 33\right)} x^{2} + 321\right)} x^{2} - 6837\right)} x^{2} + 87147\right)} + \frac{17}{3840} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, x^{2} + 5\right)} x^{2} - 127\right)} x^{2} + 2635\right)} x^{2} - 33429\right)} + \frac{19}{384} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, {\left(4 \, {\left(6 \, x^{2} + 5\right)} x^{2} - 89\right)} x^{2} + 1095\right)} + \frac{1}{8} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, {\left(4 \, x^{2} + 5\right)} x^{2} - 51\right)} - \frac{62361}{2048} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5\right)"," ",0,"1/1024*sqrt(x^4 + 5*x^2 + 3)*(2*(4*(2*(8*(2*x^2 + 1)*x^2 - 33)*x^2 + 321)*x^2 - 6837)*x^2 + 87147) + 17/3840*sqrt(x^4 + 5*x^2 + 3)*(2*(4*(6*(8*x^2 + 5)*x^2 - 127)*x^2 + 2635)*x^2 - 33429) + 19/384*sqrt(x^4 + 5*x^2 + 3)*(2*(4*(6*x^2 + 5)*x^2 - 89)*x^2 + 1095) + 1/8*sqrt(x^4 + 5*x^2 + 3)*(2*(4*x^2 + 5)*x^2 - 51) - 62361/2048*log(2*x^2 - 2*sqrt(x^4 + 5*x^2 + 3) + 5)","B",0
158,1,151,0,0.452302," ","integrate(x*(3*x^2+2)*(x^4+5*x^2+3)^(3/2),x, algorithm=""giac"")","\frac{1}{1280} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, x^{2} + 5\right)} x^{2} - 127\right)} x^{2} + 2635\right)} x^{2} - 33429\right)} + \frac{17}{384} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, {\left(4 \, {\left(6 \, x^{2} + 5\right)} x^{2} - 89\right)} x^{2} + 1095\right)} + \frac{19}{48} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, {\left(4 \, x^{2} + 5\right)} x^{2} - 51\right)} + \frac{3}{4} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, x^{2} + 5\right)} + \frac{5577}{512} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5\right)"," ",0,"1/1280*sqrt(x^4 + 5*x^2 + 3)*(2*(4*(6*(8*x^2 + 5)*x^2 - 127)*x^2 + 2635)*x^2 - 33429) + 17/384*sqrt(x^4 + 5*x^2 + 3)*(2*(4*(6*x^2 + 5)*x^2 - 89)*x^2 + 1095) + 19/48*sqrt(x^4 + 5*x^2 + 3)*(2*(4*x^2 + 5)*x^2 - 51) + 3/4*sqrt(x^4 + 5*x^2 + 3)*(2*x^2 + 5) + 5577/512*log(2*x^2 - 2*sqrt(x^4 + 5*x^2 + 3) + 5)","A",0
159,1,113,0,0.498471," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x,x, algorithm=""giac"")","\frac{1}{384} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, {\left(4 \, {\left(18 \, x^{2} + 151\right)} x^{2} + 1325\right)} x^{2} + 2061\right)} + 3 \, \sqrt{3} \log\left(\frac{x^{2} + \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}{x^{2} - \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}\right) - \frac{2401}{256} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5\right)"," ",0,"1/384*sqrt(x^4 + 5*x^2 + 3)*(2*(4*(18*x^2 + 151)*x^2 + 1325)*x^2 + 2061) + 3*sqrt(3)*log((x^2 + sqrt(3) - sqrt(x^4 + 5*x^2 + 3))/(x^2 - sqrt(3) - sqrt(x^4 + 5*x^2 + 3))) - 2401/256*log(2*x^2 - 2*sqrt(x^4 + 5*x^2 + 3) + 5)","A",0
160,1,153,0,0.558714," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x^3,x, algorithm=""giac"")","\frac{1}{16} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, {\left(4 \, x^{2} + 39\right)} x^{2} + 271\right)} + 12 \, \sqrt{3} \log\left(\frac{x^{2} + \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}{x^{2} - \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}\right) + \frac{3 \, {\left(5 \, x^{2} - 5 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 6\right)}}{{\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{2} - 3} - \frac{609}{32} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5\right)"," ",0,"1/16*sqrt(x^4 + 5*x^2 + 3)*(2*(4*x^2 + 39)*x^2 + 271) + 12*sqrt(3)*log((x^2 + sqrt(3) - sqrt(x^4 + 5*x^2 + 3))/(x^2 - sqrt(3) - sqrt(x^4 + 5*x^2 + 3))) + 3*(5*x^2 - 5*sqrt(x^4 + 5*x^2 + 3) + 6)/((x^2 - sqrt(x^4 + 5*x^2 + 3))^2 - 3) - 609/32*log(2*x^2 - 2*sqrt(x^4 + 5*x^2 + 3) + 5)","A",0
161,1,190,0,0.654338," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x^5,x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(6 \, x^{2} + 83\right)} + \frac{127}{8} \, \sqrt{3} \log\left(\frac{x^{2} + \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}{x^{2} - \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}\right) + \frac{227 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{3} + 348 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{2} - 459 \, x^{2} + 459 \, \sqrt{x^{4} + 5 \, x^{2} + 3} - 684}{4 \, {\left({\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{2} - 3\right)}^{2}} - \frac{453}{16} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5\right)"," ",0,"1/8*sqrt(x^4 + 5*x^2 + 3)*(6*x^2 + 83) + 127/8*sqrt(3)*log((x^2 + sqrt(3) - sqrt(x^4 + 5*x^2 + 3))/(x^2 - sqrt(3) - sqrt(x^4 + 5*x^2 + 3))) + 1/4*(227*(x^2 - sqrt(x^4 + 5*x^2 + 3))^3 + 348*(x^2 - sqrt(x^4 + 5*x^2 + 3))^2 - 459*x^2 + 459*sqrt(x^4 + 5*x^2 + 3) - 684)/((x^2 - sqrt(x^4 + 5*x^2 + 3))^2 - 3)^2 - 453/16*log(2*x^2 - 2*sqrt(x^4 + 5*x^2 + 3) + 5)","A",0
162,1,227,0,0.681388," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x^7,x, algorithm=""giac"")","\frac{527}{72} \, \sqrt{3} \log\left(\frac{x^{2} + \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}{x^{2} - \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}\right) + \frac{3}{2} \, \sqrt{x^{4} + 5 \, x^{2} + 3} + \frac{829 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{5} + 1824 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{4} - 2200 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{3} - 5292 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{2} + 2799 \, x^{2} - 2799 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5724}{12 \, {\left({\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{2} - 3\right)}^{3}} - \frac{49}{4} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5\right)"," ",0,"527/72*sqrt(3)*log((x^2 + sqrt(3) - sqrt(x^4 + 5*x^2 + 3))/(x^2 - sqrt(3) - sqrt(x^4 + 5*x^2 + 3))) + 3/2*sqrt(x^4 + 5*x^2 + 3) + 1/12*(829*(x^2 - sqrt(x^4 + 5*x^2 + 3))^5 + 1824*(x^2 - sqrt(x^4 + 5*x^2 + 3))^4 - 2200*(x^2 - sqrt(x^4 + 5*x^2 + 3))^3 - 5292*(x^2 - sqrt(x^4 + 5*x^2 + 3))^2 + 2799*x^2 - 2799*sqrt(x^4 + 5*x^2 + 3) + 5724)/((x^2 - sqrt(x^4 + 5*x^2 + 3))^2 - 3)^3 - 49/4*log(2*x^2 - 2*sqrt(x^4 + 5*x^2 + 3) + 5)","B",0
163,0,0,0,0.000000," ","integrate(x^4*(3*x^2+2)*(x^4+5*x^2+3)^(3/2),x, algorithm=""giac"")","\int {\left(x^{4} + 5 \, x^{2} + 3\right)}^{\frac{3}{2}} {\left(3 \, x^{2} + 2\right)} x^{4}\,{d x}"," ",0,"integrate((x^4 + 5*x^2 + 3)^(3/2)*(3*x^2 + 2)*x^4, x)","F",0
164,0,0,0,0.000000," ","integrate(x^2*(3*x^2+2)*(x^4+5*x^2+3)^(3/2),x, algorithm=""giac"")","\int {\left(x^{4} + 5 \, x^{2} + 3\right)}^{\frac{3}{2}} {\left(3 \, x^{2} + 2\right)} x^{2}\,{d x}"," ",0,"integrate((x^4 + 5*x^2 + 3)^(3/2)*(3*x^2 + 2)*x^2, x)","F",0
165,0,0,0,0.000000," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(3/2),x, algorithm=""giac"")","\int {\left(x^{4} + 5 \, x^{2} + 3\right)}^{\frac{3}{2}} {\left(3 \, x^{2} + 2\right)}\,{d x}"," ",0,"integrate((x^4 + 5*x^2 + 3)^(3/2)*(3*x^2 + 2), x)","F",0
166,0,0,0,0.000000," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x^2,x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 5 \, x^{2} + 3\right)}^{\frac{3}{2}} {\left(3 \, x^{2} + 2\right)}}{x^{2}}\,{d x}"," ",0,"integrate((x^4 + 5*x^2 + 3)^(3/2)*(3*x^2 + 2)/x^2, x)","F",0
167,0,0,0,0.000000," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x^4,x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 5 \, x^{2} + 3\right)}^{\frac{3}{2}} {\left(3 \, x^{2} + 2\right)}}{x^{4}}\,{d x}"," ",0,"integrate((x^4 + 5*x^2 + 3)^(3/2)*(3*x^2 + 2)/x^4, x)","F",0
168,0,0,0,0.000000," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x^6,x, algorithm=""giac"")","\int \frac{{\left(x^{4} + 5 \, x^{2} + 3\right)}^{\frac{3}{2}} {\left(3 \, x^{2} + 2\right)}}{x^{6}}\,{d x}"," ",0,"integrate((x^4 + 5*x^2 + 3)^(3/2)*(3*x^2 + 2)/x^6, x)","F",0
169,1,138,0,0.544325," ","integrate(x^5*(B*x^2+A)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{48} \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, {\left(\frac{4 \, B x^{2}}{c} - \frac{5 \, B b c - 6 \, A c^{2}}{c^{3}}\right)} x^{2} + \frac{15 \, B b^{2} - 16 \, B a c - 18 \, A b c}{c^{3}}\right)} + \frac{{\left(5 \, B b^{3} - 12 \, B a b c - 6 \, A b^{2} c + 8 \, A a c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{32 \, c^{\frac{7}{2}}}"," ",0,"1/48*sqrt(c*x^4 + b*x^2 + a)*(2*(4*B*x^2/c - (5*B*b*c - 6*A*c^2)/c^3)*x^2 + (15*B*b^2 - 16*B*a*c - 18*A*b*c)/c^3) + 1/32*(5*B*b^3 - 12*B*a*b*c - 6*A*b^2*c + 8*A*a*c^2)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(7/2)","A",0
170,1,98,0,0.449234," ","integrate(x^3*(B*x^2+A)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{c x^{4} + b x^{2} + a} {\left(\frac{2 \, B x^{2}}{c} - \frac{3 \, B b - 4 \, A c}{c^{2}}\right)} - \frac{{\left(3 \, B b^{2} - 4 \, B a c - 4 \, A b c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{5}{2}}}"," ",0,"1/8*sqrt(c*x^4 + b*x^2 + a)*(2*B*x^2/c - (3*B*b - 4*A*c)/c^2) - 1/16*(3*B*b^2 - 4*B*a*c - 4*A*b*c)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(5/2)","A",0
171,1,69,0,0.461351," ","integrate(x*(B*x^2+A)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{c x^{4} + b x^{2} + a} B}{2 \, c} + \frac{{\left(B b - 2 \, A c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} \sqrt{c} - b \right|}\right)}{4 \, c^{\frac{3}{2}}}"," ",0,"1/2*sqrt(c*x^4 + b*x^2 + a)*B/c + 1/4*(B*b - 2*A*c)*log(abs(-2*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*sqrt(c) - b))/c^(3/2)","A",0
172,-2,0,0,0.000000," ","integrate((B*x^2+A)/x/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
173,1,124,0,0.537719," ","integrate((B*x^2+A)/x^3/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{{\left(2 \, B a - A b\right)} \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{2 \, \sqrt{-a} a} + \frac{{\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} A b + 2 \, A a \sqrt{c}}{2 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)} a}"," ",0,"1/2*(2*B*a - A*b)*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a) + 1/2*((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*A*b + 2*A*a*sqrt(c))/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)*a)","A",0
174,1,339,0,0.515570," ","integrate((B*x^2+A)/x^5/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{{\left(4 \, B a b - 3 \, A b^{2} + 4 \, A a c\right)} \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{8 \, \sqrt{-a} a^{2}} + \frac{4 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} B a b - 3 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} A b^{2} + 4 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} A a c + 8 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} B a^{2} \sqrt{c} - 4 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} B a^{2} b + 5 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} A a b^{2} + 4 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} A a^{2} c - 8 \, B a^{3} \sqrt{c} + 8 \, A a^{2} b \sqrt{c}}{8 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)}^{2} a^{2}}"," ",0,"-1/8*(4*B*a*b - 3*A*b^2 + 4*A*a*c)*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^2) + 1/8*(4*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*B*a*b - 3*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*A*b^2 + 4*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*A*a*c + 8*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2*B*a^2*sqrt(c) - 4*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*B*a^2*b + 5*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*A*a*b^2 + 4*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*A*a^2*c - 8*B*a^3*sqrt(c) + 8*A*a^2*b*sqrt(c))/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)^2*a^2)","B",0
175,1,571,0,0.639358," ","integrate((B*x^2+A)/x^7/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{{\left(6 \, B a b^{2} - 5 \, A b^{3} - 8 \, B a^{2} c + 12 \, A a b c\right)} \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{16 \, \sqrt{-a} a^{3}} - \frac{18 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} B a b^{2} - 15 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} A b^{3} - 24 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} B a^{2} c + 36 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{5} A a b c - 48 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} B a^{2} b^{2} + 40 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} A a b^{3} - 96 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{3} A a^{2} b c - 48 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} B a^{3} b \sqrt{c} - 96 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} A a^{3} c^{\frac{3}{2}} + 30 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} B a^{3} b^{2} - 33 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} A a^{2} b^{3} + 24 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} B a^{4} c - 36 \, {\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} A a^{3} b c + 48 \, B a^{4} b \sqrt{c} - 48 \, A a^{3} b^{2} \sqrt{c} + 32 \, A a^{4} c^{\frac{3}{2}}}{48 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)}^{3} a^{3}}"," ",0,"1/16*(6*B*a*b^2 - 5*A*b^3 - 8*B*a^2*c + 12*A*a*b*c)*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^3) - 1/48*(18*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*B*a*b^2 - 15*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*A*b^3 - 24*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*B*a^2*c + 36*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^5*A*a*b*c - 48*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*B*a^2*b^2 + 40*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*A*a*b^3 - 96*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^3*A*a^2*b*c - 48*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2*B*a^3*b*sqrt(c) - 96*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2*A*a^3*c^(3/2) + 30*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*B*a^3*b^2 - 33*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*A*a^2*b^3 + 24*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*B*a^4*c - 36*(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*A*a^3*b*c + 48*B*a^4*b*sqrt(c) - 48*A*a^3*b^2*sqrt(c) + 32*A*a^4*c^(3/2))/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)^3*a^3)","B",0
176,0,0,0,0.000000," ","integrate(x^4*(B*x^2+A)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} x^{4}}{\sqrt{c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate((B*x^2 + A)*x^4/sqrt(c*x^4 + b*x^2 + a), x)","F",0
177,0,0,0,0.000000," ","integrate(x^2*(B*x^2+A)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} x^{2}}{\sqrt{c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate((B*x^2 + A)*x^2/sqrt(c*x^4 + b*x^2 + a), x)","F",0
178,0,0,0,0.000000," ","integrate((B*x^2+A)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{B x^{2} + A}{\sqrt{c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate((B*x^2 + A)/sqrt(c*x^4 + b*x^2 + a), x)","F",0
179,0,0,0,0.000000," ","integrate((B*x^2+A)/x^2/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{B x^{2} + A}{\sqrt{c x^{4} + b x^{2} + a} x^{2}}\,{d x}"," ",0,"integrate((B*x^2 + A)/(sqrt(c*x^4 + b*x^2 + a)*x^2), x)","F",0
180,0,0,0,0.000000," ","integrate((B*x^2+A)/x^4/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{B x^{2} + A}{\sqrt{c x^{4} + b x^{2} + a} x^{4}}\,{d x}"," ",0,"integrate((B*x^2 + A)/(sqrt(c*x^4 + b*x^2 + a)*x^4), x)","F",0
181,1,60,0,0.369932," ","integrate(x^7*(3*x^2+2)/(x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","\frac{1}{384} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, {\left(4 \, {\left(18 \, x^{2} - 89\right)} x^{2} + 1901\right)} x^{2} - 24243\right)} - \frac{32801}{256} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5\right)"," ",0,"1/384*sqrt(x^4 + 5*x^2 + 3)*(2*(4*(18*x^2 - 89)*x^2 + 1901)*x^2 - 24243) - 32801/256*log(2*x^2 - 2*sqrt(x^4 + 5*x^2 + 3) + 5)","A",0
182,1,53,0,0.344068," ","integrate(x^5*(3*x^2+2)/(x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","\frac{1}{16} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(2 \, {\left(4 \, x^{2} - 21\right)} x^{2} + 267\right)} + \frac{1083}{32} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5\right)"," ",0,"1/16*sqrt(x^4 + 5*x^2 + 3)*(2*(4*x^2 - 21)*x^2 + 267) + 1083/32*log(2*x^2 - 2*sqrt(x^4 + 5*x^2 + 3) + 5)","A",0
183,1,46,0,0.347958," ","integrate(x^3*(3*x^2+2)/(x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(6 \, x^{2} - 37\right)} - \frac{149}{16} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5\right)"," ",0,"1/8*sqrt(x^4 + 5*x^2 + 3)*(6*x^2 - 37) - 149/16*log(2*x^2 - 2*sqrt(x^4 + 5*x^2 + 3) + 5)","A",0
184,1,39,0,0.467665," ","integrate(x*(3*x^2+2)/(x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","\frac{3}{2} \, \sqrt{x^{4} + 5 \, x^{2} + 3} + \frac{11}{4} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5\right)"," ",0,"3/2*sqrt(x^4 + 5*x^2 + 3) + 11/4*log(2*x^2 - 2*sqrt(x^4 + 5*x^2 + 3) + 5)","A",0
185,1,78,0,0.434604," ","integrate((3*x^2+2)/x/(x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \log\left(\frac{x^{2} + \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}{x^{2} - \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}\right) - \frac{3}{2} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5\right)"," ",0,"1/3*sqrt(3)*log((x^2 + sqrt(3) - sqrt(x^4 + 5*x^2 + 3))/(x^2 - sqrt(3) - sqrt(x^4 + 5*x^2 + 3))) - 3/2*log(2*x^2 - 2*sqrt(x^4 + 5*x^2 + 3) + 5)","A",0
186,1,101,0,0.385777," ","integrate((3*x^2+2)/x^3/(x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, \sqrt{3} \log\left(\frac{x^{2} + \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}{x^{2} - \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}\right) + \frac{5 \, x^{2} - 5 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 6}{3 \, {\left({\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{2} - 3\right)}}"," ",0,"2/9*sqrt(3)*log((x^2 + sqrt(3) - sqrt(x^4 + 5*x^2 + 3))/(x^2 - sqrt(3) - sqrt(x^4 + 5*x^2 + 3))) + 1/3*(5*x^2 - 5*sqrt(x^4 + 5*x^2 + 3) + 6)/((x^2 - sqrt(x^4 + 5*x^2 + 3))^2 - 3)","B",0
187,1,145,0,0.520663," ","integrate((3*x^2+2)/x^5/(x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{3} \log\left(\frac{x^{2} + \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}{x^{2} - \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}\right) + \frac{9 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{3} + 36 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{2} + 47 \, x^{2} - 47 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 12}{12 \, {\left({\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{2} - 3\right)}^{2}}"," ",0,"-1/8*sqrt(3)*log((x^2 + sqrt(3) - sqrt(x^4 + 5*x^2 + 3))/(x^2 - sqrt(3) - sqrt(x^4 + 5*x^2 + 3))) + 1/12*(9*(x^2 - sqrt(x^4 + 5*x^2 + 3))^3 + 36*(x^2 - sqrt(x^4 + 5*x^2 + 3))^2 + 47*x^2 - 47*sqrt(x^4 + 5*x^2 + 3) + 12)/((x^2 - sqrt(x^4 + 5*x^2 + 3))^2 - 3)^2","B",0
188,1,167,0,0.507016," ","integrate((3*x^2+2)/x^7/(x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","\frac{61}{648} \, \sqrt{3} \log\left(\frac{x^{2} + \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}{x^{2} - \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}\right) - \frac{61 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{5} - 920 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{3} - 2052 \, {\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{2} - 1449 \, x^{2} + 1449 \, \sqrt{x^{4} + 5 \, x^{2} + 3} - 108}{108 \, {\left({\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{2} - 3\right)}^{3}}"," ",0,"61/648*sqrt(3)*log((x^2 + sqrt(3) - sqrt(x^4 + 5*x^2 + 3))/(x^2 - sqrt(3) - sqrt(x^4 + 5*x^2 + 3))) - 1/108*(61*(x^2 - sqrt(x^4 + 5*x^2 + 3))^5 - 920*(x^2 - sqrt(x^4 + 5*x^2 + 3))^3 - 2052*(x^2 - sqrt(x^4 + 5*x^2 + 3))^2 - 1449*x^2 + 1449*sqrt(x^4 + 5*x^2 + 3) - 108)/((x^2 - sqrt(x^4 + 5*x^2 + 3))^2 - 3)^3","B",0
189,0,0,0,0.000000," ","integrate(x^4*(3*x^2+2)/(x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{2} + 2\right)} x^{4}}{\sqrt{x^{4} + 5 \, x^{2} + 3}}\,{d x}"," ",0,"integrate((3*x^2 + 2)*x^4/sqrt(x^4 + 5*x^2 + 3), x)","F",0
190,0,0,0,0.000000," ","integrate(x^2*(3*x^2+2)/(x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{2} + 2\right)} x^{2}}{\sqrt{x^{4} + 5 \, x^{2} + 3}}\,{d x}"," ",0,"integrate((3*x^2 + 2)*x^2/sqrt(x^4 + 5*x^2 + 3), x)","F",0
191,0,0,0,0.000000," ","integrate((3*x^2+2)/(x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{3 \, x^{2} + 2}{\sqrt{x^{4} + 5 \, x^{2} + 3}}\,{d x}"," ",0,"integrate((3*x^2 + 2)/sqrt(x^4 + 5*x^2 + 3), x)","F",0
192,0,0,0,0.000000," ","integrate((3*x^2+2)/x^2/(x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{3 \, x^{2} + 2}{\sqrt{x^{4} + 5 \, x^{2} + 3} x^{2}}\,{d x}"," ",0,"integrate((3*x^2 + 2)/(sqrt(x^4 + 5*x^2 + 3)*x^2), x)","F",0
193,0,0,0,0.000000," ","integrate((3*x^2+2)/x^4/(x^4+5*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{3 \, x^{2} + 2}{\sqrt{x^{4} + 5 \, x^{2} + 3} x^{4}}\,{d x}"," ",0,"integrate((3*x^2 + 2)/(sqrt(x^4 + 5*x^2 + 3)*x^4), x)","F",0
194,1,52,0,0.383003," ","integrate(x^5*(3*x^2+2)/(x^4+5*x^2+3)^(3/2),x, algorithm=""giac"")","\frac{{\left(39 \, x^{2} + 599\right)} x^{2} + 399}{26 \, \sqrt{x^{4} + 5 \, x^{2} + 3}} + \frac{41}{4} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5\right)"," ",0,"1/26*((39*x^2 + 599)*x^2 + 399)/sqrt(x^4 + 5*x^2 + 3) + 41/4*log(2*x^2 - 2*sqrt(x^4 + 5*x^2 + 3) + 5)","A",0
195,1,46,0,0.512217," ","integrate(x^3*(3*x^2+2)/(x^4+5*x^2+3)^(3/2),x, algorithm=""giac"")","-\frac{47 \, x^{2} + 33}{13 \, \sqrt{x^{4} + 5 \, x^{2} + 3}} - \frac{3}{2} \, \log\left(2 \, x^{2} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 5\right)"," ",0,"-1/13*(47*x^2 + 33)/sqrt(x^4 + 5*x^2 + 3) - 3/2*log(2*x^2 - 2*sqrt(x^4 + 5*x^2 + 3) + 5)","A",0
196,1,21,0,0.363368," ","integrate(x*(3*x^2+2)/(x^4+5*x^2+3)^(3/2),x, algorithm=""giac"")","\frac{11 \, x^{2} + 8}{13 \, \sqrt{x^{4} + 5 \, x^{2} + 3}}"," ",0,"1/13*(11*x^2 + 8)/sqrt(x^4 + 5*x^2 + 3)","A",0
197,1,78,0,0.556038," ","integrate((3*x^2+2)/x/(x^4+5*x^2+3)^(3/2),x, algorithm=""giac"")","-\frac{1}{9} \, \sqrt{3} \log\left(-x^{2} + \sqrt{3} + \sqrt{x^{4} + 5 \, x^{2} + 3}\right) + \frac{1}{9} \, \sqrt{3} \log\left(-x^{2} - \sqrt{3} + \sqrt{x^{4} + 5 \, x^{2} + 3}\right) - \frac{8 \, x^{2} + 7}{39 \, \sqrt{x^{4} + 5 \, x^{2} + 3}}"," ",0,"-1/9*sqrt(3)*log(-x^2 + sqrt(3) + sqrt(x^4 + 5*x^2 + 3)) + 1/9*sqrt(3)*log(-x^2 - sqrt(3) + sqrt(x^4 + 5*x^2 + 3)) - 1/39*(8*x^2 + 7)/sqrt(x^4 + 5*x^2 + 3)","A",0
198,1,122,0,0.492451," ","integrate((3*x^2+2)/x^3/(x^4+5*x^2+3)^(3/2),x, algorithm=""giac"")","-\frac{1}{9} \, \sqrt{3} \log\left(\frac{x^{2} + \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}{x^{2} - \sqrt{3} - \sqrt{x^{4} + 5 \, x^{2} + 3}}\right) + \frac{7 \, x^{2} + 11}{117 \, \sqrt{x^{4} + 5 \, x^{2} + 3}} + \frac{5 \, x^{2} - 5 \, \sqrt{x^{4} + 5 \, x^{2} + 3} + 6}{9 \, {\left({\left(x^{2} - \sqrt{x^{4} + 5 \, x^{2} + 3}\right)}^{2} - 3\right)}}"," ",0,"-1/9*sqrt(3)*log((x^2 + sqrt(3) - sqrt(x^4 + 5*x^2 + 3))/(x^2 - sqrt(3) - sqrt(x^4 + 5*x^2 + 3))) + 1/117*(7*x^2 + 11)/sqrt(x^4 + 5*x^2 + 3) + 1/9*(5*x^2 - 5*sqrt(x^4 + 5*x^2 + 3) + 6)/((x^2 - sqrt(x^4 + 5*x^2 + 3))^2 - 3)","A",0
199,0,0,0,0.000000," ","integrate(x^4*(3*x^2+2)/(x^4+5*x^2+3)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{2} + 2\right)} x^{4}}{{\left(x^{4} + 5 \, x^{2} + 3\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((3*x^2 + 2)*x^4/(x^4 + 5*x^2 + 3)^(3/2), x)","F",0
200,0,0,0,0.000000," ","integrate(x^2*(3*x^2+2)/(x^4+5*x^2+3)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(3 \, x^{2} + 2\right)} x^{2}}{{\left(x^{4} + 5 \, x^{2} + 3\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((3*x^2 + 2)*x^2/(x^4 + 5*x^2 + 3)^(3/2), x)","F",0
201,0,0,0,0.000000," ","integrate((3*x^2+2)/(x^4+5*x^2+3)^(3/2),x, algorithm=""giac"")","\int \frac{3 \, x^{2} + 2}{{\left(x^{4} + 5 \, x^{2} + 3\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((3*x^2 + 2)/(x^4 + 5*x^2 + 3)^(3/2), x)","F",0
202,0,0,0,0.000000," ","integrate((3*x^2+2)/x^2/(x^4+5*x^2+3)^(3/2),x, algorithm=""giac"")","\int \frac{3 \, x^{2} + 2}{{\left(x^{4} + 5 \, x^{2} + 3\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate((3*x^2 + 2)/((x^4 + 5*x^2 + 3)^(3/2)*x^2), x)","F",0
203,0,0,0,0.000000," ","integrate((3*x^2+2)/x^4/(x^4+5*x^2+3)^(3/2),x, algorithm=""giac"")","\int \frac{3 \, x^{2} + 2}{{\left(x^{4} + 5 \, x^{2} + 3\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate((3*x^2 + 2)/((x^4 + 5*x^2 + 3)^(3/2)*x^4), x)","F",0
204,0,0,0,0.000000," ","integrate((f*x)^(3/2)*(e*x^2+d)*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{4} + b x^{2} + a} {\left(e x^{2} + d\right)} \left(f x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2 + a)*(e*x^2 + d)*(f*x)^(3/2), x)","F",0
205,0,0,0,0.000000," ","integrate((f*x)^(1/2)*(e*x^2+d)*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{4} + b x^{2} + a} {\left(e x^{2} + d\right)} \sqrt{f x}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2 + a)*(e*x^2 + d)*sqrt(f*x), x)","F",0
206,0,0,0,0.000000," ","integrate((e*x^2+d)*(c*x^4+b*x^2+a)^(1/2)/(f*x)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + b x^{2} + a} {\left(e x^{2} + d\right)}}{\sqrt{f x}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2 + a)*(e*x^2 + d)/sqrt(f*x), x)","F",0
207,0,0,0,0.000000," ","integrate((e*x^2+d)*(c*x^4+b*x^2+a)^(1/2)/(f*x)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{4} + b x^{2} + a} {\left(e x^{2} + d\right)}}{\left(f x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2 + a)*(e*x^2 + d)/(f*x)^(3/2), x)","F",0
208,0,0,0,0.000000," ","integrate((f*x)^(3/2)*(e*x^2+d)*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}} {\left(e x^{2} + d\right)} \left(f x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^(3/2)*(e*x^2 + d)*(f*x)^(3/2), x)","F",0
209,0,0,0,0.000000," ","integrate((f*x)^(1/2)*(e*x^2+d)*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}} {\left(e x^{2} + d\right)} \sqrt{f x}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^(3/2)*(e*x^2 + d)*sqrt(f*x), x)","F",0
210,0,0,0,0.000000," ","integrate((e*x^2+d)*(c*x^4+b*x^2+a)^(3/2)/(f*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}} {\left(e x^{2} + d\right)}}{\sqrt{f x}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^(3/2)*(e*x^2 + d)/sqrt(f*x), x)","F",0
211,0,0,0,0.000000," ","integrate((e*x^2+d)*(c*x^4+b*x^2+a)^(3/2)/(f*x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}} {\left(e x^{2} + d\right)}}{\left(f x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^(3/2)*(e*x^2 + d)/(f*x)^(3/2), x)","F",0
212,0,0,0,0.000000," ","integrate((f*x)^(3/2)*(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)} \left(f x\right)^{\frac{3}{2}}}{\sqrt{c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)*(f*x)^(3/2)/sqrt(c*x^4 + b*x^2 + a), x)","F",0
213,0,0,0,0.000000," ","integrate((f*x)^(1/2)*(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)} \sqrt{f x}}{\sqrt{c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)*sqrt(f*x)/sqrt(c*x^4 + b*x^2 + a), x)","F",0
214,0,0,0,0.000000," ","integrate((e*x^2+d)/(f*x)^(1/2)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d}{\sqrt{c x^{4} + b x^{2} + a} \sqrt{f x}}\,{d x}"," ",0,"integrate((e*x^2 + d)/(sqrt(c*x^4 + b*x^2 + a)*sqrt(f*x)), x)","F",0
215,0,0,0,0.000000," ","integrate((e*x^2+d)/(f*x)^(3/2)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d}{\sqrt{c x^{4} + b x^{2} + a} \left(f x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x^2 + d)/(sqrt(c*x^4 + b*x^2 + a)*(f*x)^(3/2)), x)","F",0
216,0,0,0,0.000000," ","integrate((f*x)^(3/2)*(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)} \left(f x\right)^{\frac{3}{2}}}{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x^2 + d)*(f*x)^(3/2)/(c*x^4 + b*x^2 + a)^(3/2), x)","F",0
217,0,0,0,0.000000," ","integrate((f*x)^(1/2)*(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)} \sqrt{f x}}{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x^2 + d)*sqrt(f*x)/(c*x^4 + b*x^2 + a)^(3/2), x)","F",0
218,0,0,0,0.000000," ","integrate((e*x^2+d)/(f*x)^(1/2)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d}{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}} \sqrt{f x}}\,{d x}"," ",0,"integrate((e*x^2 + d)/((c*x^4 + b*x^2 + a)^(3/2)*sqrt(f*x)), x)","F",0
219,0,0,0,0.000000," ","integrate((e*x^2+d)/(f*x)^(3/2)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{e x^{2} + d}{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}} \left(f x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x^2 + d)/((c*x^4 + b*x^2 + a)^(3/2)*(f*x)^(3/2)), x)","F",0
220,1,2816,0,0.750380," ","integrate((f*x)^m*(e*x^2+d)*(c*x^4+b*x^2+a)^3,x, algorithm=""giac"")","\frac{\left(f x\right)^{m} c^{3} m^{7} x^{15} e + 49 \, \left(f x\right)^{m} c^{3} m^{6} x^{15} e + \left(f x\right)^{m} c^{3} d m^{7} x^{13} + 3 \, \left(f x\right)^{m} b c^{2} m^{7} x^{13} e + 973 \, \left(f x\right)^{m} c^{3} m^{5} x^{15} e + 51 \, \left(f x\right)^{m} c^{3} d m^{6} x^{13} + 153 \, \left(f x\right)^{m} b c^{2} m^{6} x^{13} e + 10045 \, \left(f x\right)^{m} c^{3} m^{4} x^{15} e + 3 \, \left(f x\right)^{m} b c^{2} d m^{7} x^{11} + 1045 \, \left(f x\right)^{m} c^{3} d m^{5} x^{13} + 3 \, \left(f x\right)^{m} b^{2} c m^{7} x^{11} e + 3 \, \left(f x\right)^{m} a c^{2} m^{7} x^{11} e + 3135 \, \left(f x\right)^{m} b c^{2} m^{5} x^{13} e + 57379 \, \left(f x\right)^{m} c^{3} m^{3} x^{15} e + 159 \, \left(f x\right)^{m} b c^{2} d m^{6} x^{11} + 11055 \, \left(f x\right)^{m} c^{3} d m^{4} x^{13} + 159 \, \left(f x\right)^{m} b^{2} c m^{6} x^{11} e + 159 \, \left(f x\right)^{m} a c^{2} m^{6} x^{11} e + 33165 \, \left(f x\right)^{m} b c^{2} m^{4} x^{13} e + 177331 \, \left(f x\right)^{m} c^{3} m^{2} x^{15} e + 3 \, \left(f x\right)^{m} b^{2} c d m^{7} x^{9} + 3 \, \left(f x\right)^{m} a c^{2} d m^{7} x^{9} + 3375 \, \left(f x\right)^{m} b c^{2} d m^{5} x^{11} + 64339 \, \left(f x\right)^{m} c^{3} d m^{3} x^{13} + \left(f x\right)^{m} b^{3} m^{7} x^{9} e + 6 \, \left(f x\right)^{m} a b c m^{7} x^{9} e + 3375 \, \left(f x\right)^{m} b^{2} c m^{5} x^{11} e + 3375 \, \left(f x\right)^{m} a c^{2} m^{5} x^{11} e + 193017 \, \left(f x\right)^{m} b c^{2} m^{3} x^{13} e + 264207 \, \left(f x\right)^{m} c^{3} m x^{15} e + 165 \, \left(f x\right)^{m} b^{2} c d m^{6} x^{9} + 165 \, \left(f x\right)^{m} a c^{2} d m^{6} x^{9} + 36795 \, \left(f x\right)^{m} b c^{2} d m^{4} x^{11} + 201609 \, \left(f x\right)^{m} c^{3} d m^{2} x^{13} + 55 \, \left(f x\right)^{m} b^{3} m^{6} x^{9} e + 330 \, \left(f x\right)^{m} a b c m^{6} x^{9} e + 36795 \, \left(f x\right)^{m} b^{2} c m^{4} x^{11} e + 36795 \, \left(f x\right)^{m} a c^{2} m^{4} x^{11} e + 604827 \, \left(f x\right)^{m} b c^{2} m^{2} x^{13} e + 135135 \, \left(f x\right)^{m} c^{3} x^{15} e + \left(f x\right)^{m} b^{3} d m^{7} x^{7} + 6 \, \left(f x\right)^{m} a b c d m^{7} x^{7} + 3639 \, \left(f x\right)^{m} b^{2} c d m^{5} x^{9} + 3639 \, \left(f x\right)^{m} a c^{2} d m^{5} x^{9} + 219417 \, \left(f x\right)^{m} b c^{2} d m^{3} x^{11} + 303255 \, \left(f x\right)^{m} c^{3} d m x^{13} + 3 \, \left(f x\right)^{m} a b^{2} m^{7} x^{7} e + 3 \, \left(f x\right)^{m} a^{2} c m^{7} x^{7} e + 1213 \, \left(f x\right)^{m} b^{3} m^{5} x^{9} e + 7278 \, \left(f x\right)^{m} a b c m^{5} x^{9} e + 219417 \, \left(f x\right)^{m} b^{2} c m^{3} x^{11} e + 219417 \, \left(f x\right)^{m} a c^{2} m^{3} x^{11} e + 909765 \, \left(f x\right)^{m} b c^{2} m x^{13} e + 57 \, \left(f x\right)^{m} b^{3} d m^{6} x^{7} + 342 \, \left(f x\right)^{m} a b c d m^{6} x^{7} + 41169 \, \left(f x\right)^{m} b^{2} c d m^{4} x^{9} + 41169 \, \left(f x\right)^{m} a c^{2} d m^{4} x^{9} + 700461 \, \left(f x\right)^{m} b c^{2} d m^{2} x^{11} + 155925 \, \left(f x\right)^{m} c^{3} d x^{13} + 171 \, \left(f x\right)^{m} a b^{2} m^{6} x^{7} e + 171 \, \left(f x\right)^{m} a^{2} c m^{6} x^{7} e + 13723 \, \left(f x\right)^{m} b^{3} m^{4} x^{9} e + 82338 \, \left(f x\right)^{m} a b c m^{4} x^{9} e + 700461 \, \left(f x\right)^{m} b^{2} c m^{2} x^{11} e + 700461 \, \left(f x\right)^{m} a c^{2} m^{2} x^{11} e + 467775 \, \left(f x\right)^{m} b c^{2} x^{13} e + 3 \, \left(f x\right)^{m} a b^{2} d m^{7} x^{5} + 3 \, \left(f x\right)^{m} a^{2} c d m^{7} x^{5} + 1309 \, \left(f x\right)^{m} b^{3} d m^{5} x^{7} + 7854 \, \left(f x\right)^{m} a b c d m^{5} x^{7} + 253641 \, \left(f x\right)^{m} b^{2} c d m^{3} x^{9} + 253641 \, \left(f x\right)^{m} a c^{2} d m^{3} x^{9} + 1067445 \, \left(f x\right)^{m} b c^{2} d m x^{11} + 3 \, \left(f x\right)^{m} a^{2} b m^{7} x^{5} e + 3927 \, \left(f x\right)^{m} a b^{2} m^{5} x^{7} e + 3927 \, \left(f x\right)^{m} a^{2} c m^{5} x^{7} e + 84547 \, \left(f x\right)^{m} b^{3} m^{3} x^{9} e + 507282 \, \left(f x\right)^{m} a b c m^{3} x^{9} e + 1067445 \, \left(f x\right)^{m} b^{2} c m x^{11} e + 1067445 \, \left(f x\right)^{m} a c^{2} m x^{11} e + 177 \, \left(f x\right)^{m} a b^{2} d m^{6} x^{5} + 177 \, \left(f x\right)^{m} a^{2} c d m^{6} x^{5} + 15477 \, \left(f x\right)^{m} b^{3} d m^{4} x^{7} + 92862 \, \left(f x\right)^{m} a b c d m^{4} x^{7} + 831279 \, \left(f x\right)^{m} b^{2} c d m^{2} x^{9} + 831279 \, \left(f x\right)^{m} a c^{2} d m^{2} x^{9} + 552825 \, \left(f x\right)^{m} b c^{2} d x^{11} + 177 \, \left(f x\right)^{m} a^{2} b m^{6} x^{5} e + 46431 \, \left(f x\right)^{m} a b^{2} m^{4} x^{7} e + 46431 \, \left(f x\right)^{m} a^{2} c m^{4} x^{7} e + 277093 \, \left(f x\right)^{m} b^{3} m^{2} x^{9} e + 1662558 \, \left(f x\right)^{m} a b c m^{2} x^{9} e + 552825 \, \left(f x\right)^{m} b^{2} c x^{11} e + 552825 \, \left(f x\right)^{m} a c^{2} x^{11} e + 3 \, \left(f x\right)^{m} a^{2} b d m^{7} x^{3} + 4239 \, \left(f x\right)^{m} a b^{2} d m^{5} x^{5} + 4239 \, \left(f x\right)^{m} a^{2} c d m^{5} x^{5} + 99715 \, \left(f x\right)^{m} b^{3} d m^{3} x^{7} + 598290 \, \left(f x\right)^{m} a b c d m^{3} x^{7} + 1291005 \, \left(f x\right)^{m} b^{2} c d m x^{9} + 1291005 \, \left(f x\right)^{m} a c^{2} d m x^{9} + \left(f x\right)^{m} a^{3} m^{7} x^{3} e + 4239 \, \left(f x\right)^{m} a^{2} b m^{5} x^{5} e + 299145 \, \left(f x\right)^{m} a b^{2} m^{3} x^{7} e + 299145 \, \left(f x\right)^{m} a^{2} c m^{3} x^{7} e + 430335 \, \left(f x\right)^{m} b^{3} m x^{9} e + 2582010 \, \left(f x\right)^{m} a b c m x^{9} e + 183 \, \left(f x\right)^{m} a^{2} b d m^{6} x^{3} + 52725 \, \left(f x\right)^{m} a b^{2} d m^{4} x^{5} + 52725 \, \left(f x\right)^{m} a^{2} c d m^{4} x^{5} + 340011 \, \left(f x\right)^{m} b^{3} d m^{2} x^{7} + 2040066 \, \left(f x\right)^{m} a b c d m^{2} x^{7} + 675675 \, \left(f x\right)^{m} b^{2} c d x^{9} + 675675 \, \left(f x\right)^{m} a c^{2} d x^{9} + 61 \, \left(f x\right)^{m} a^{3} m^{6} x^{3} e + 52725 \, \left(f x\right)^{m} a^{2} b m^{4} x^{5} e + 1020033 \, \left(f x\right)^{m} a b^{2} m^{2} x^{7} e + 1020033 \, \left(f x\right)^{m} a^{2} c m^{2} x^{7} e + 225225 \, \left(f x\right)^{m} b^{3} x^{9} e + 1351350 \, \left(f x\right)^{m} a b c x^{9} e + \left(f x\right)^{m} a^{3} d m^{7} x + 4575 \, \left(f x\right)^{m} a^{2} b d m^{5} x^{3} + 360537 \, \left(f x\right)^{m} a b^{2} d m^{3} x^{5} + 360537 \, \left(f x\right)^{m} a^{2} c d m^{3} x^{5} + 544095 \, \left(f x\right)^{m} b^{3} d m x^{7} + 3264570 \, \left(f x\right)^{m} a b c d m x^{7} + 1525 \, \left(f x\right)^{m} a^{3} m^{5} x^{3} e + 360537 \, \left(f x\right)^{m} a^{2} b m^{3} x^{5} e + 1632285 \, \left(f x\right)^{m} a b^{2} m x^{7} e + 1632285 \, \left(f x\right)^{m} a^{2} c m x^{7} e + 63 \, \left(f x\right)^{m} a^{3} d m^{6} x + 60195 \, \left(f x\right)^{m} a^{2} b d m^{4} x^{3} + 1311363 \, \left(f x\right)^{m} a b^{2} d m^{2} x^{5} + 1311363 \, \left(f x\right)^{m} a^{2} c d m^{2} x^{5} + 289575 \, \left(f x\right)^{m} b^{3} d x^{7} + 1737450 \, \left(f x\right)^{m} a b c d x^{7} + 20065 \, \left(f x\right)^{m} a^{3} m^{4} x^{3} e + 1311363 \, \left(f x\right)^{m} a^{2} b m^{2} x^{5} e + 868725 \, \left(f x\right)^{m} a b^{2} x^{7} e + 868725 \, \left(f x\right)^{m} a^{2} c x^{7} e + 1645 \, \left(f x\right)^{m} a^{3} d m^{5} x + 443577 \, \left(f x\right)^{m} a^{2} b d m^{3} x^{3} + 2215701 \, \left(f x\right)^{m} a b^{2} d m x^{5} + 2215701 \, \left(f x\right)^{m} a^{2} c d m x^{5} + 147859 \, \left(f x\right)^{m} a^{3} m^{3} x^{3} e + 2215701 \, \left(f x\right)^{m} a^{2} b m x^{5} e + 22995 \, \left(f x\right)^{m} a^{3} d m^{4} x + 1783317 \, \left(f x\right)^{m} a^{2} b d m^{2} x^{3} + 1216215 \, \left(f x\right)^{m} a b^{2} d x^{5} + 1216215 \, \left(f x\right)^{m} a^{2} c d x^{5} + 594439 \, \left(f x\right)^{m} a^{3} m^{2} x^{3} e + 1216215 \, \left(f x\right)^{m} a^{2} b x^{5} e + 185059 \, \left(f x\right)^{m} a^{3} d m^{3} x + 3422565 \, \left(f x\right)^{m} a^{2} b d m x^{3} + 1140855 \, \left(f x\right)^{m} a^{3} m x^{3} e + 852957 \, \left(f x\right)^{m} a^{3} d m^{2} x + 2027025 \, \left(f x\right)^{m} a^{2} b d x^{3} + 675675 \, \left(f x\right)^{m} a^{3} x^{3} e + 2071215 \, \left(f x\right)^{m} a^{3} d m x + 2027025 \, \left(f x\right)^{m} a^{3} d x}{m^{8} + 64 \, m^{7} + 1708 \, m^{6} + 24640 \, m^{5} + 208054 \, m^{4} + 1038016 \, m^{3} + 2924172 \, m^{2} + 4098240 \, m + 2027025}"," ",0,"((f*x)^m*c^3*m^7*x^15*e + 49*(f*x)^m*c^3*m^6*x^15*e + (f*x)^m*c^3*d*m^7*x^13 + 3*(f*x)^m*b*c^2*m^7*x^13*e + 973*(f*x)^m*c^3*m^5*x^15*e + 51*(f*x)^m*c^3*d*m^6*x^13 + 153*(f*x)^m*b*c^2*m^6*x^13*e + 10045*(f*x)^m*c^3*m^4*x^15*e + 3*(f*x)^m*b*c^2*d*m^7*x^11 + 1045*(f*x)^m*c^3*d*m^5*x^13 + 3*(f*x)^m*b^2*c*m^7*x^11*e + 3*(f*x)^m*a*c^2*m^7*x^11*e + 3135*(f*x)^m*b*c^2*m^5*x^13*e + 57379*(f*x)^m*c^3*m^3*x^15*e + 159*(f*x)^m*b*c^2*d*m^6*x^11 + 11055*(f*x)^m*c^3*d*m^4*x^13 + 159*(f*x)^m*b^2*c*m^6*x^11*e + 159*(f*x)^m*a*c^2*m^6*x^11*e + 33165*(f*x)^m*b*c^2*m^4*x^13*e + 177331*(f*x)^m*c^3*m^2*x^15*e + 3*(f*x)^m*b^2*c*d*m^7*x^9 + 3*(f*x)^m*a*c^2*d*m^7*x^9 + 3375*(f*x)^m*b*c^2*d*m^5*x^11 + 64339*(f*x)^m*c^3*d*m^3*x^13 + (f*x)^m*b^3*m^7*x^9*e + 6*(f*x)^m*a*b*c*m^7*x^9*e + 3375*(f*x)^m*b^2*c*m^5*x^11*e + 3375*(f*x)^m*a*c^2*m^5*x^11*e + 193017*(f*x)^m*b*c^2*m^3*x^13*e + 264207*(f*x)^m*c^3*m*x^15*e + 165*(f*x)^m*b^2*c*d*m^6*x^9 + 165*(f*x)^m*a*c^2*d*m^6*x^9 + 36795*(f*x)^m*b*c^2*d*m^4*x^11 + 201609*(f*x)^m*c^3*d*m^2*x^13 + 55*(f*x)^m*b^3*m^6*x^9*e + 330*(f*x)^m*a*b*c*m^6*x^9*e + 36795*(f*x)^m*b^2*c*m^4*x^11*e + 36795*(f*x)^m*a*c^2*m^4*x^11*e + 604827*(f*x)^m*b*c^2*m^2*x^13*e + 135135*(f*x)^m*c^3*x^15*e + (f*x)^m*b^3*d*m^7*x^7 + 6*(f*x)^m*a*b*c*d*m^7*x^7 + 3639*(f*x)^m*b^2*c*d*m^5*x^9 + 3639*(f*x)^m*a*c^2*d*m^5*x^9 + 219417*(f*x)^m*b*c^2*d*m^3*x^11 + 303255*(f*x)^m*c^3*d*m*x^13 + 3*(f*x)^m*a*b^2*m^7*x^7*e + 3*(f*x)^m*a^2*c*m^7*x^7*e + 1213*(f*x)^m*b^3*m^5*x^9*e + 7278*(f*x)^m*a*b*c*m^5*x^9*e + 219417*(f*x)^m*b^2*c*m^3*x^11*e + 219417*(f*x)^m*a*c^2*m^3*x^11*e + 909765*(f*x)^m*b*c^2*m*x^13*e + 57*(f*x)^m*b^3*d*m^6*x^7 + 342*(f*x)^m*a*b*c*d*m^6*x^7 + 41169*(f*x)^m*b^2*c*d*m^4*x^9 + 41169*(f*x)^m*a*c^2*d*m^4*x^9 + 700461*(f*x)^m*b*c^2*d*m^2*x^11 + 155925*(f*x)^m*c^3*d*x^13 + 171*(f*x)^m*a*b^2*m^6*x^7*e + 171*(f*x)^m*a^2*c*m^6*x^7*e + 13723*(f*x)^m*b^3*m^4*x^9*e + 82338*(f*x)^m*a*b*c*m^4*x^9*e + 700461*(f*x)^m*b^2*c*m^2*x^11*e + 700461*(f*x)^m*a*c^2*m^2*x^11*e + 467775*(f*x)^m*b*c^2*x^13*e + 3*(f*x)^m*a*b^2*d*m^7*x^5 + 3*(f*x)^m*a^2*c*d*m^7*x^5 + 1309*(f*x)^m*b^3*d*m^5*x^7 + 7854*(f*x)^m*a*b*c*d*m^5*x^7 + 253641*(f*x)^m*b^2*c*d*m^3*x^9 + 253641*(f*x)^m*a*c^2*d*m^3*x^9 + 1067445*(f*x)^m*b*c^2*d*m*x^11 + 3*(f*x)^m*a^2*b*m^7*x^5*e + 3927*(f*x)^m*a*b^2*m^5*x^7*e + 3927*(f*x)^m*a^2*c*m^5*x^7*e + 84547*(f*x)^m*b^3*m^3*x^9*e + 507282*(f*x)^m*a*b*c*m^3*x^9*e + 1067445*(f*x)^m*b^2*c*m*x^11*e + 1067445*(f*x)^m*a*c^2*m*x^11*e + 177*(f*x)^m*a*b^2*d*m^6*x^5 + 177*(f*x)^m*a^2*c*d*m^6*x^5 + 15477*(f*x)^m*b^3*d*m^4*x^7 + 92862*(f*x)^m*a*b*c*d*m^4*x^7 + 831279*(f*x)^m*b^2*c*d*m^2*x^9 + 831279*(f*x)^m*a*c^2*d*m^2*x^9 + 552825*(f*x)^m*b*c^2*d*x^11 + 177*(f*x)^m*a^2*b*m^6*x^5*e + 46431*(f*x)^m*a*b^2*m^4*x^7*e + 46431*(f*x)^m*a^2*c*m^4*x^7*e + 277093*(f*x)^m*b^3*m^2*x^9*e + 1662558*(f*x)^m*a*b*c*m^2*x^9*e + 552825*(f*x)^m*b^2*c*x^11*e + 552825*(f*x)^m*a*c^2*x^11*e + 3*(f*x)^m*a^2*b*d*m^7*x^3 + 4239*(f*x)^m*a*b^2*d*m^5*x^5 + 4239*(f*x)^m*a^2*c*d*m^5*x^5 + 99715*(f*x)^m*b^3*d*m^3*x^7 + 598290*(f*x)^m*a*b*c*d*m^3*x^7 + 1291005*(f*x)^m*b^2*c*d*m*x^9 + 1291005*(f*x)^m*a*c^2*d*m*x^9 + (f*x)^m*a^3*m^7*x^3*e + 4239*(f*x)^m*a^2*b*m^5*x^5*e + 299145*(f*x)^m*a*b^2*m^3*x^7*e + 299145*(f*x)^m*a^2*c*m^3*x^7*e + 430335*(f*x)^m*b^3*m*x^9*e + 2582010*(f*x)^m*a*b*c*m*x^9*e + 183*(f*x)^m*a^2*b*d*m^6*x^3 + 52725*(f*x)^m*a*b^2*d*m^4*x^5 + 52725*(f*x)^m*a^2*c*d*m^4*x^5 + 340011*(f*x)^m*b^3*d*m^2*x^7 + 2040066*(f*x)^m*a*b*c*d*m^2*x^7 + 675675*(f*x)^m*b^2*c*d*x^9 + 675675*(f*x)^m*a*c^2*d*x^9 + 61*(f*x)^m*a^3*m^6*x^3*e + 52725*(f*x)^m*a^2*b*m^4*x^5*e + 1020033*(f*x)^m*a*b^2*m^2*x^7*e + 1020033*(f*x)^m*a^2*c*m^2*x^7*e + 225225*(f*x)^m*b^3*x^9*e + 1351350*(f*x)^m*a*b*c*x^9*e + (f*x)^m*a^3*d*m^7*x + 4575*(f*x)^m*a^2*b*d*m^5*x^3 + 360537*(f*x)^m*a*b^2*d*m^3*x^5 + 360537*(f*x)^m*a^2*c*d*m^3*x^5 + 544095*(f*x)^m*b^3*d*m*x^7 + 3264570*(f*x)^m*a*b*c*d*m*x^7 + 1525*(f*x)^m*a^3*m^5*x^3*e + 360537*(f*x)^m*a^2*b*m^3*x^5*e + 1632285*(f*x)^m*a*b^2*m*x^7*e + 1632285*(f*x)^m*a^2*c*m*x^7*e + 63*(f*x)^m*a^3*d*m^6*x + 60195*(f*x)^m*a^2*b*d*m^4*x^3 + 1311363*(f*x)^m*a*b^2*d*m^2*x^5 + 1311363*(f*x)^m*a^2*c*d*m^2*x^5 + 289575*(f*x)^m*b^3*d*x^7 + 1737450*(f*x)^m*a*b*c*d*x^7 + 20065*(f*x)^m*a^3*m^4*x^3*e + 1311363*(f*x)^m*a^2*b*m^2*x^5*e + 868725*(f*x)^m*a*b^2*x^7*e + 868725*(f*x)^m*a^2*c*x^7*e + 1645*(f*x)^m*a^3*d*m^5*x + 443577*(f*x)^m*a^2*b*d*m^3*x^3 + 2215701*(f*x)^m*a*b^2*d*m*x^5 + 2215701*(f*x)^m*a^2*c*d*m*x^5 + 147859*(f*x)^m*a^3*m^3*x^3*e + 2215701*(f*x)^m*a^2*b*m*x^5*e + 22995*(f*x)^m*a^3*d*m^4*x + 1783317*(f*x)^m*a^2*b*d*m^2*x^3 + 1216215*(f*x)^m*a*b^2*d*x^5 + 1216215*(f*x)^m*a^2*c*d*x^5 + 594439*(f*x)^m*a^3*m^2*x^3*e + 1216215*(f*x)^m*a^2*b*x^5*e + 185059*(f*x)^m*a^3*d*m^3*x + 3422565*(f*x)^m*a^2*b*d*m*x^3 + 1140855*(f*x)^m*a^3*m*x^3*e + 852957*(f*x)^m*a^3*d*m^2*x + 2027025*(f*x)^m*a^2*b*d*x^3 + 675675*(f*x)^m*a^3*x^3*e + 2071215*(f*x)^m*a^3*d*m*x + 2027025*(f*x)^m*a^3*d*x)/(m^8 + 64*m^7 + 1708*m^6 + 24640*m^5 + 208054*m^4 + 1038016*m^3 + 2924172*m^2 + 4098240*m + 2027025)","B",0
221,1,1178,0,0.398151," ","integrate((f*x)^m*(e*x^2+d)*(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\frac{\left(f x\right)^{m} c^{2} m^{5} x^{11} e + 25 \, \left(f x\right)^{m} c^{2} m^{4} x^{11} e + \left(f x\right)^{m} c^{2} d m^{5} x^{9} + 2 \, \left(f x\right)^{m} b c m^{5} x^{9} e + 230 \, \left(f x\right)^{m} c^{2} m^{3} x^{11} e + 27 \, \left(f x\right)^{m} c^{2} d m^{4} x^{9} + 54 \, \left(f x\right)^{m} b c m^{4} x^{9} e + 950 \, \left(f x\right)^{m} c^{2} m^{2} x^{11} e + 2 \, \left(f x\right)^{m} b c d m^{5} x^{7} + 262 \, \left(f x\right)^{m} c^{2} d m^{3} x^{9} + \left(f x\right)^{m} b^{2} m^{5} x^{7} e + 2 \, \left(f x\right)^{m} a c m^{5} x^{7} e + 524 \, \left(f x\right)^{m} b c m^{3} x^{9} e + 1689 \, \left(f x\right)^{m} c^{2} m x^{11} e + 58 \, \left(f x\right)^{m} b c d m^{4} x^{7} + 1122 \, \left(f x\right)^{m} c^{2} d m^{2} x^{9} + 29 \, \left(f x\right)^{m} b^{2} m^{4} x^{7} e + 58 \, \left(f x\right)^{m} a c m^{4} x^{7} e + 2244 \, \left(f x\right)^{m} b c m^{2} x^{9} e + 945 \, \left(f x\right)^{m} c^{2} x^{11} e + \left(f x\right)^{m} b^{2} d m^{5} x^{5} + 2 \, \left(f x\right)^{m} a c d m^{5} x^{5} + 604 \, \left(f x\right)^{m} b c d m^{3} x^{7} + 2041 \, \left(f x\right)^{m} c^{2} d m x^{9} + 2 \, \left(f x\right)^{m} a b m^{5} x^{5} e + 302 \, \left(f x\right)^{m} b^{2} m^{3} x^{7} e + 604 \, \left(f x\right)^{m} a c m^{3} x^{7} e + 4082 \, \left(f x\right)^{m} b c m x^{9} e + 31 \, \left(f x\right)^{m} b^{2} d m^{4} x^{5} + 62 \, \left(f x\right)^{m} a c d m^{4} x^{5} + 2732 \, \left(f x\right)^{m} b c d m^{2} x^{7} + 1155 \, \left(f x\right)^{m} c^{2} d x^{9} + 62 \, \left(f x\right)^{m} a b m^{4} x^{5} e + 1366 \, \left(f x\right)^{m} b^{2} m^{2} x^{7} e + 2732 \, \left(f x\right)^{m} a c m^{2} x^{7} e + 2310 \, \left(f x\right)^{m} b c x^{9} e + 2 \, \left(f x\right)^{m} a b d m^{5} x^{3} + 350 \, \left(f x\right)^{m} b^{2} d m^{3} x^{5} + 700 \, \left(f x\right)^{m} a c d m^{3} x^{5} + 5154 \, \left(f x\right)^{m} b c d m x^{7} + \left(f x\right)^{m} a^{2} m^{5} x^{3} e + 700 \, \left(f x\right)^{m} a b m^{3} x^{5} e + 2577 \, \left(f x\right)^{m} b^{2} m x^{7} e + 5154 \, \left(f x\right)^{m} a c m x^{7} e + 66 \, \left(f x\right)^{m} a b d m^{4} x^{3} + 1730 \, \left(f x\right)^{m} b^{2} d m^{2} x^{5} + 3460 \, \left(f x\right)^{m} a c d m^{2} x^{5} + 2970 \, \left(f x\right)^{m} b c d x^{7} + 33 \, \left(f x\right)^{m} a^{2} m^{4} x^{3} e + 3460 \, \left(f x\right)^{m} a b m^{2} x^{5} e + 1485 \, \left(f x\right)^{m} b^{2} x^{7} e + 2970 \, \left(f x\right)^{m} a c x^{7} e + \left(f x\right)^{m} a^{2} d m^{5} x + 812 \, \left(f x\right)^{m} a b d m^{3} x^{3} + 3489 \, \left(f x\right)^{m} b^{2} d m x^{5} + 6978 \, \left(f x\right)^{m} a c d m x^{5} + 406 \, \left(f x\right)^{m} a^{2} m^{3} x^{3} e + 6978 \, \left(f x\right)^{m} a b m x^{5} e + 35 \, \left(f x\right)^{m} a^{2} d m^{4} x + 4524 \, \left(f x\right)^{m} a b d m^{2} x^{3} + 2079 \, \left(f x\right)^{m} b^{2} d x^{5} + 4158 \, \left(f x\right)^{m} a c d x^{5} + 2262 \, \left(f x\right)^{m} a^{2} m^{2} x^{3} e + 4158 \, \left(f x\right)^{m} a b x^{5} e + 470 \, \left(f x\right)^{m} a^{2} d m^{3} x + 10706 \, \left(f x\right)^{m} a b d m x^{3} + 5353 \, \left(f x\right)^{m} a^{2} m x^{3} e + 3010 \, \left(f x\right)^{m} a^{2} d m^{2} x + 6930 \, \left(f x\right)^{m} a b d x^{3} + 3465 \, \left(f x\right)^{m} a^{2} x^{3} e + 9129 \, \left(f x\right)^{m} a^{2} d m x + 10395 \, \left(f x\right)^{m} a^{2} d x}{m^{6} + 36 \, m^{5} + 505 \, m^{4} + 3480 \, m^{3} + 12139 \, m^{2} + 19524 \, m + 10395}"," ",0,"((f*x)^m*c^2*m^5*x^11*e + 25*(f*x)^m*c^2*m^4*x^11*e + (f*x)^m*c^2*d*m^5*x^9 + 2*(f*x)^m*b*c*m^5*x^9*e + 230*(f*x)^m*c^2*m^3*x^11*e + 27*(f*x)^m*c^2*d*m^4*x^9 + 54*(f*x)^m*b*c*m^4*x^9*e + 950*(f*x)^m*c^2*m^2*x^11*e + 2*(f*x)^m*b*c*d*m^5*x^7 + 262*(f*x)^m*c^2*d*m^3*x^9 + (f*x)^m*b^2*m^5*x^7*e + 2*(f*x)^m*a*c*m^5*x^7*e + 524*(f*x)^m*b*c*m^3*x^9*e + 1689*(f*x)^m*c^2*m*x^11*e + 58*(f*x)^m*b*c*d*m^4*x^7 + 1122*(f*x)^m*c^2*d*m^2*x^9 + 29*(f*x)^m*b^2*m^4*x^7*e + 58*(f*x)^m*a*c*m^4*x^7*e + 2244*(f*x)^m*b*c*m^2*x^9*e + 945*(f*x)^m*c^2*x^11*e + (f*x)^m*b^2*d*m^5*x^5 + 2*(f*x)^m*a*c*d*m^5*x^5 + 604*(f*x)^m*b*c*d*m^3*x^7 + 2041*(f*x)^m*c^2*d*m*x^9 + 2*(f*x)^m*a*b*m^5*x^5*e + 302*(f*x)^m*b^2*m^3*x^7*e + 604*(f*x)^m*a*c*m^3*x^7*e + 4082*(f*x)^m*b*c*m*x^9*e + 31*(f*x)^m*b^2*d*m^4*x^5 + 62*(f*x)^m*a*c*d*m^4*x^5 + 2732*(f*x)^m*b*c*d*m^2*x^7 + 1155*(f*x)^m*c^2*d*x^9 + 62*(f*x)^m*a*b*m^4*x^5*e + 1366*(f*x)^m*b^2*m^2*x^7*e + 2732*(f*x)^m*a*c*m^2*x^7*e + 2310*(f*x)^m*b*c*x^9*e + 2*(f*x)^m*a*b*d*m^5*x^3 + 350*(f*x)^m*b^2*d*m^3*x^5 + 700*(f*x)^m*a*c*d*m^3*x^5 + 5154*(f*x)^m*b*c*d*m*x^7 + (f*x)^m*a^2*m^5*x^3*e + 700*(f*x)^m*a*b*m^3*x^5*e + 2577*(f*x)^m*b^2*m*x^7*e + 5154*(f*x)^m*a*c*m*x^7*e + 66*(f*x)^m*a*b*d*m^4*x^3 + 1730*(f*x)^m*b^2*d*m^2*x^5 + 3460*(f*x)^m*a*c*d*m^2*x^5 + 2970*(f*x)^m*b*c*d*x^7 + 33*(f*x)^m*a^2*m^4*x^3*e + 3460*(f*x)^m*a*b*m^2*x^5*e + 1485*(f*x)^m*b^2*x^7*e + 2970*(f*x)^m*a*c*x^7*e + (f*x)^m*a^2*d*m^5*x + 812*(f*x)^m*a*b*d*m^3*x^3 + 3489*(f*x)^m*b^2*d*m*x^5 + 6978*(f*x)^m*a*c*d*m*x^5 + 406*(f*x)^m*a^2*m^3*x^3*e + 6978*(f*x)^m*a*b*m*x^5*e + 35*(f*x)^m*a^2*d*m^4*x + 4524*(f*x)^m*a*b*d*m^2*x^3 + 2079*(f*x)^m*b^2*d*x^5 + 4158*(f*x)^m*a*c*d*x^5 + 2262*(f*x)^m*a^2*m^2*x^3*e + 4158*(f*x)^m*a*b*x^5*e + 470*(f*x)^m*a^2*d*m^3*x + 10706*(f*x)^m*a*b*d*m*x^3 + 5353*(f*x)^m*a^2*m*x^3*e + 3010*(f*x)^m*a^2*d*m^2*x + 6930*(f*x)^m*a*b*d*x^3 + 3465*(f*x)^m*a^2*x^3*e + 9129*(f*x)^m*a^2*d*m*x + 10395*(f*x)^m*a^2*d*x)/(m^6 + 36*m^5 + 505*m^4 + 3480*m^3 + 12139*m^2 + 19524*m + 10395)","B",0
222,1,350,0,0.419001," ","integrate((f*x)^m*(e*x^2+d)*(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{\left(f x\right)^{m} c m^{3} x^{7} e + 9 \, \left(f x\right)^{m} c m^{2} x^{7} e + \left(f x\right)^{m} c d m^{3} x^{5} + \left(f x\right)^{m} b m^{3} x^{5} e + 23 \, \left(f x\right)^{m} c m x^{7} e + 11 \, \left(f x\right)^{m} c d m^{2} x^{5} + 11 \, \left(f x\right)^{m} b m^{2} x^{5} e + 15 \, \left(f x\right)^{m} c x^{7} e + \left(f x\right)^{m} b d m^{3} x^{3} + 31 \, \left(f x\right)^{m} c d m x^{5} + \left(f x\right)^{m} a m^{3} x^{3} e + 31 \, \left(f x\right)^{m} b m x^{5} e + 13 \, \left(f x\right)^{m} b d m^{2} x^{3} + 21 \, \left(f x\right)^{m} c d x^{5} + 13 \, \left(f x\right)^{m} a m^{2} x^{3} e + 21 \, \left(f x\right)^{m} b x^{5} e + \left(f x\right)^{m} a d m^{3} x + 47 \, \left(f x\right)^{m} b d m x^{3} + 47 \, \left(f x\right)^{m} a m x^{3} e + 15 \, \left(f x\right)^{m} a d m^{2} x + 35 \, \left(f x\right)^{m} b d x^{3} + 35 \, \left(f x\right)^{m} a x^{3} e + 71 \, \left(f x\right)^{m} a d m x + 105 \, \left(f x\right)^{m} a d x}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105}"," ",0,"((f*x)^m*c*m^3*x^7*e + 9*(f*x)^m*c*m^2*x^7*e + (f*x)^m*c*d*m^3*x^5 + (f*x)^m*b*m^3*x^5*e + 23*(f*x)^m*c*m*x^7*e + 11*(f*x)^m*c*d*m^2*x^5 + 11*(f*x)^m*b*m^2*x^5*e + 15*(f*x)^m*c*x^7*e + (f*x)^m*b*d*m^3*x^3 + 31*(f*x)^m*c*d*m*x^5 + (f*x)^m*a*m^3*x^3*e + 31*(f*x)^m*b*m*x^5*e + 13*(f*x)^m*b*d*m^2*x^3 + 21*(f*x)^m*c*d*x^5 + 13*(f*x)^m*a*m^2*x^3*e + 21*(f*x)^m*b*x^5*e + (f*x)^m*a*d*m^3*x + 47*(f*x)^m*b*d*m*x^3 + 47*(f*x)^m*a*m*x^3*e + 15*(f*x)^m*a*d*m^2*x + 35*(f*x)^m*b*d*x^3 + 35*(f*x)^m*a*x^3*e + 71*(f*x)^m*a*d*m*x + 105*(f*x)^m*a*d*x)/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105)","B",0
223,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)} \left(f x\right)^{m}}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate((e*x^2 + d)*(f*x)^m/(c*x^4 + b*x^2 + a), x)","F",0
224,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)} \left(f x\right)^{m}}{{\left(c x^{4} + b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*x^2 + d)*(f*x)^m/(c*x^4 + b*x^2 + a)^2, x)","F",0
225,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}} {\left(e x^{2} + d\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate((c*x^4 + b*x^2 + a)^(3/2)*(e*x^2 + d)*(f*x)^m, x)","F",0
226,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{4} + b x^{2} + a} {\left(e x^{2} + d\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate(sqrt(c*x^4 + b*x^2 + a)*(e*x^2 + d)*(f*x)^m, x)","F",0
227,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)} \left(f x\right)^{m}}{\sqrt{c x^{4} + b x^{2} + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)*(f*x)^m/sqrt(c*x^4 + b*x^2 + a), x)","F",0
228,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)} \left(f x\right)^{m}}{{\left(c x^{4} + b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x^2 + d)*(f*x)^m/(c*x^4 + b*x^2 + a)^(3/2), x)","F",0
229,1,121,0,0.308612," ","integrate(x^9/(e*x^2+d)/(c*x^4+a),x, algorithm=""giac"")","\frac{d^{4} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c d^{2} e^{3} + a e^{5}\right)}} - \frac{a^{2} e \log\left(c x^{4} + a\right)}{4 \, {\left(c^{3} d^{2} + a c^{2} e^{2}\right)}} + \frac{a^{2} d \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{2 \, {\left(c^{2} d^{2} + a c e^{2}\right)} \sqrt{a c}} + \frac{{\left(c x^{4} e - 2 \, c d x^{2}\right)} e^{\left(-2\right)}}{4 \, c^{2}}"," ",0,"1/2*d^4*log(abs(x^2*e + d))/(c*d^2*e^3 + a*e^5) - 1/4*a^2*e*log(c*x^4 + a)/(c^3*d^2 + a*c^2*e^2) + 1/2*a^2*d*arctan(c*x^2/sqrt(a*c))/((c^2*d^2 + a*c*e^2)*sqrt(a*c)) + 1/4*(c*x^4*e - 2*c*d*x^2)*e^(-2)/c^2","A",0
230,1,105,0,0.307493," ","integrate(x^7/(e*x^2+d)/(c*x^4+a),x, algorithm=""giac"")","-\frac{d^{3} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c d^{2} e^{2} + a e^{4}\right)}} - \frac{a^{2} \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right) e}{2 \, {\left(c^{2} d^{2} + a c e^{2}\right)} \sqrt{a c}} + \frac{x^{2} e^{\left(-1\right)}}{2 \, c} - \frac{a d \log\left(c x^{4} + a\right)}{4 \, {\left(c^{2} d^{2} + a c e^{2}\right)}}"," ",0,"-1/2*d^3*log(abs(x^2*e + d))/(c*d^2*e^2 + a*e^4) - 1/2*a^2*arctan(c*x^2/sqrt(a*c))*e/((c^2*d^2 + a*c*e^2)*sqrt(a*c)) + 1/2*x^2*e^(-1)/c - 1/4*a*d*log(c*x^4 + a)/(c^2*d^2 + a*c*e^2)","A",0
231,1,90,0,0.355848," ","integrate(x^5/(e*x^2+d)/(c*x^4+a),x, algorithm=""giac"")","\frac{a e \log\left(c x^{4} + a\right)}{4 \, {\left(c^{2} d^{2} + a c e^{2}\right)}} + \frac{d^{2} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c d^{2} e + a e^{3}\right)}} - \frac{a d \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{2 \, {\left(c d^{2} + a e^{2}\right)} \sqrt{a c}}"," ",0,"1/4*a*e*log(c*x^4 + a)/(c^2*d^2 + a*c*e^2) + 1/2*d^2*log(abs(x^2*e + d))/(c*d^2*e + a*e^3) - 1/2*a*d*arctan(c*x^2/sqrt(a*c))/((c*d^2 + a*e^2)*sqrt(a*c))","A",0
232,1,86,0,0.392820," ","integrate(x^3/(e*x^2+d)/(c*x^4+a),x, algorithm=""giac"")","-\frac{d e \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c d^{2} e + a e^{3}\right)}} + \frac{a \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right) e}{2 \, {\left(c d^{2} + a e^{2}\right)} \sqrt{a c}} + \frac{d \log\left(c x^{4} + a\right)}{4 \, {\left(c d^{2} + a e^{2}\right)}}"," ",0,"-1/2*d*e*log(abs(x^2*e + d))/(c*d^2*e + a*e^3) + 1/2*a*arctan(c*x^2/sqrt(a*c))*e/((c*d^2 + a*e^2)*sqrt(a*c)) + 1/4*d*log(c*x^4 + a)/(c*d^2 + a*e^2)","A",0
233,1,85,0,0.354308," ","integrate(x/(e*x^2+d)/(c*x^4+a),x, algorithm=""giac"")","\frac{c d \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{2 \, {\left(c d^{2} + a e^{2}\right)} \sqrt{a c}} - \frac{e \log\left(c x^{4} + a\right)}{4 \, {\left(c d^{2} + a e^{2}\right)}} + \frac{e^{2} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c d^{2} e + a e^{3}\right)}}"," ",0,"1/2*c*d*arctan(c*x^2/sqrt(a*c))/((c*d^2 + a*e^2)*sqrt(a*c)) - 1/4*e*log(c*x^4 + a)/(c*d^2 + a*e^2) + 1/2*e^2*log(abs(x^2*e + d))/(c*d^2*e + a*e^3)","A",0
234,1,102,0,0.288703," ","integrate(1/x/(e*x^2+d)/(c*x^4+a),x, algorithm=""giac"")","-\frac{c d \log\left(c x^{4} + a\right)}{4 \, {\left(a c d^{2} + a^{2} e^{2}\right)}} - \frac{c \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right) e}{2 \, {\left(c d^{2} + a e^{2}\right)} \sqrt{a c}} - \frac{e^{3} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c d^{3} e + a d e^{3}\right)}} + \frac{\log\left(x^{2}\right)}{2 \, a d}"," ",0,"-1/4*c*d*log(c*x^4 + a)/(a*c*d^2 + a^2*e^2) - 1/2*c*arctan(c*x^2/sqrt(a*c))*e/((c*d^2 + a*e^2)*sqrt(a*c)) - 1/2*e^3*log(abs(x^2*e + d))/(c*d^3*e + a*d*e^3) + 1/2*log(x^2)/(a*d)","A",0
235,1,132,0,0.301830," ","integrate(1/x^3/(e*x^2+d)/(c*x^4+a),x, algorithm=""giac"")","-\frac{c^{2} d \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{2 \, {\left(a c d^{2} + a^{2} e^{2}\right)} \sqrt{a c}} + \frac{c e \log\left(c x^{4} + a\right)}{4 \, {\left(a c d^{2} + a^{2} e^{2}\right)}} + \frac{e^{4} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c d^{4} e + a d^{2} e^{3}\right)}} - \frac{e \log\left(x^{2}\right)}{2 \, a d^{2}} + \frac{x^{2} e - d}{2 \, a d^{2} x^{2}}"," ",0,"-1/2*c^2*d*arctan(c*x^2/sqrt(a*c))/((a*c*d^2 + a^2*e^2)*sqrt(a*c)) + 1/4*c*e*log(c*x^4 + a)/(a*c*d^2 + a^2*e^2) + 1/2*e^4*log(abs(x^2*e + d))/(c*d^4*e + a*d^2*e^3) - 1/2*e*log(x^2)/(a*d^2) + 1/2*(x^2*e - d)/(a*d^2*x^2)","A",0
236,1,168,0,0.342177," ","integrate(1/x^5/(e*x^2+d)/(c*x^4+a),x, algorithm=""giac"")","\frac{c^{2} d \log\left(c x^{4} + a\right)}{4 \, {\left(a^{2} c d^{2} + a^{3} e^{2}\right)}} + \frac{c^{2} \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right) e}{2 \, {\left(a c d^{2} + a^{2} e^{2}\right)} \sqrt{a c}} - \frac{e^{5} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c d^{5} e + a d^{3} e^{3}\right)}} - \frac{{\left(c d^{2} - a e^{2}\right)} \log\left(x^{2}\right)}{2 \, a^{2} d^{3}} + \frac{3 \, c d^{2} x^{4} - 3 \, a x^{4} e^{2} + 2 \, a d x^{2} e - a d^{2}}{4 \, a^{2} d^{3} x^{4}}"," ",0,"1/4*c^2*d*log(c*x^4 + a)/(a^2*c*d^2 + a^3*e^2) + 1/2*c^2*arctan(c*x^2/sqrt(a*c))*e/((a*c*d^2 + a^2*e^2)*sqrt(a*c)) - 1/2*e^5*log(abs(x^2*e + d))/(c*d^5*e + a*d^3*e^3) - 1/2*(c*d^2 - a*e^2)*log(x^2)/(a^2*d^3) + 1/4*(3*c*d^2*x^4 - 3*a*x^4*e^2 + 2*a*d*x^2*e - a*d^2)/(a^2*d^3*x^4)","A",0
237,1,363,0,0.541472," ","integrate(x^8/(e*x^2+d)/(c*x^4+a),x, algorithm=""giac"")","\frac{d^{\frac{7}{2}} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{1}{2}\right)}}{c d^{2} e^{2} + a e^{4}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d - \left(a c^{3}\right)^{\frac{3}{4}} a e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} c^{5} d^{2} + \sqrt{2} a c^{4} e^{2}\right)}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d - \left(a c^{3}\right)^{\frac{3}{4}} a e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} c^{5} d^{2} + \sqrt{2} a c^{4} e^{2}\right)}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d + \left(a c^{3}\right)^{\frac{3}{4}} a e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{4 \, {\left(\sqrt{2} c^{5} d^{2} + \sqrt{2} a c^{4} e^{2}\right)}} - \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d + \left(a c^{3}\right)^{\frac{3}{4}} a e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{4 \, {\left(\sqrt{2} c^{5} d^{2} + \sqrt{2} a c^{4} e^{2}\right)}} + \frac{{\left(c^{2} x^{3} e^{2} - 3 \, c^{2} d x e\right)} e^{\left(-3\right)}}{3 \, c^{3}}"," ",0,"d^(7/2)*arctan(x*e^(1/2)/sqrt(d))*e^(-1/2)/(c*d^2*e^2 + a*e^4) + 1/2*((a*c^3)^(1/4)*a*c^2*d - (a*c^3)^(3/4)*a*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*c^5*d^2 + sqrt(2)*a*c^4*e^2) + 1/2*((a*c^3)^(1/4)*a*c^2*d - (a*c^3)^(3/4)*a*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*c^5*d^2 + sqrt(2)*a*c^4*e^2) + 1/4*((a*c^3)^(1/4)*a*c^2*d + (a*c^3)^(3/4)*a*e)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*c^5*d^2 + sqrt(2)*a*c^4*e^2) - 1/4*((a*c^3)^(1/4)*a*c^2*d + (a*c^3)^(3/4)*a*e)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*c^5*d^2 + sqrt(2)*a*c^4*e^2) + 1/3*(c^2*x^3*e^2 - 3*c^2*d*x*e)*e^(-3)/c^3","A",0
238,1,333,0,0.444087," ","integrate(x^6/(e*x^2+d)/(c*x^4+a),x, algorithm=""giac"")","-\frac{d^{\frac{5}{2}} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{1}{2}\right)}}{c d^{2} e + a e^{3}} - \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} a c e + \left(a c^{3}\right)^{\frac{3}{4}} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} c^{4} d^{2} + \sqrt{2} a c^{3} e^{2}\right)}} - \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} a c e + \left(a c^{3}\right)^{\frac{3}{4}} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} c^{4} d^{2} + \sqrt{2} a c^{3} e^{2}\right)}} + \frac{x e^{\left(-1\right)}}{c} - \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} a c e - \left(a c^{3}\right)^{\frac{3}{4}} d\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{4 \, {\left(\sqrt{2} c^{4} d^{2} + \sqrt{2} a c^{3} e^{2}\right)}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} a c e - \left(a c^{3}\right)^{\frac{3}{4}} d\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{4 \, {\left(\sqrt{2} c^{4} d^{2} + \sqrt{2} a c^{3} e^{2}\right)}}"," ",0,"-d^(5/2)*arctan(x*e^(1/2)/sqrt(d))*e^(-1/2)/(c*d^2*e + a*e^3) - 1/2*((a*c^3)^(1/4)*a*c*e + (a*c^3)^(3/4)*d)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*c^4*d^2 + sqrt(2)*a*c^3*e^2) - 1/2*((a*c^3)^(1/4)*a*c*e + (a*c^3)^(3/4)*d)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*c^4*d^2 + sqrt(2)*a*c^3*e^2) + x*e^(-1)/c - 1/4*((a*c^3)^(1/4)*a*c*e - (a*c^3)^(3/4)*d)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*c^4*d^2 + sqrt(2)*a*c^3*e^2) + 1/4*((a*c^3)^(1/4)*a*c*e - (a*c^3)^(3/4)*d)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*c^4*d^2 + sqrt(2)*a*c^3*e^2)","A",0
239,1,327,0,0.434466," ","integrate(x^4/(e*x^2+d)/(c*x^4+a),x, algorithm=""giac"")","\frac{d^{\frac{3}{2}} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{1}{2}\right)}}{c d^{2} + a e^{2}} - \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d - \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} c^{4} d^{2} + \sqrt{2} a c^{3} e^{2}\right)}} - \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d - \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} c^{4} d^{2} + \sqrt{2} a c^{3} e^{2}\right)}} - \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d + \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{4 \, {\left(\sqrt{2} c^{4} d^{2} + \sqrt{2} a c^{3} e^{2}\right)}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d + \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{4 \, {\left(\sqrt{2} c^{4} d^{2} + \sqrt{2} a c^{3} e^{2}\right)}}"," ",0,"d^(3/2)*arctan(x*e^(1/2)/sqrt(d))*e^(-1/2)/(c*d^2 + a*e^2) - 1/2*((a*c^3)^(1/4)*c^2*d - (a*c^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*c^4*d^2 + sqrt(2)*a*c^3*e^2) - 1/2*((a*c^3)^(1/4)*c^2*d - (a*c^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*c^4*d^2 + sqrt(2)*a*c^3*e^2) - 1/4*((a*c^3)^(1/4)*c^2*d + (a*c^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*c^4*d^2 + sqrt(2)*a*c^3*e^2) + 1/4*((a*c^3)^(1/4)*c^2*d + (a*c^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*c^4*d^2 + sqrt(2)*a*c^3*e^2)","A",0
240,1,336,0,0.376863," ","integrate(x^2/(e*x^2+d)/(c*x^4+a),x, algorithm=""giac"")","-\frac{\sqrt{d} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\frac{1}{2}}}{c d^{2} + a e^{2}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} a c e + \left(a c^{3}\right)^{\frac{3}{4}} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a c^{3} d^{2} + \sqrt{2} a^{2} c^{2} e^{2}\right)}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} a c e + \left(a c^{3}\right)^{\frac{3}{4}} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a c^{3} d^{2} + \sqrt{2} a^{2} c^{2} e^{2}\right)}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} a c e - \left(a c^{3}\right)^{\frac{3}{4}} d\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{4 \, {\left(\sqrt{2} a c^{3} d^{2} + \sqrt{2} a^{2} c^{2} e^{2}\right)}} - \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} a c e - \left(a c^{3}\right)^{\frac{3}{4}} d\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{4 \, {\left(\sqrt{2} a c^{3} d^{2} + \sqrt{2} a^{2} c^{2} e^{2}\right)}}"," ",0,"-sqrt(d)*arctan(x*e^(1/2)/sqrt(d))*e^(1/2)/(c*d^2 + a*e^2) + 1/2*((a*c^3)^(1/4)*a*c*e + (a*c^3)^(3/4)*d)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a*c^3*d^2 + sqrt(2)*a^2*c^2*e^2) + 1/2*((a*c^3)^(1/4)*a*c*e + (a*c^3)^(3/4)*d)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a*c^3*d^2 + sqrt(2)*a^2*c^2*e^2) + 1/4*((a*c^3)^(1/4)*a*c*e - (a*c^3)^(3/4)*d)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a*c^3*d^2 + sqrt(2)*a^2*c^2*e^2) - 1/4*((a*c^3)^(1/4)*a*c*e - (a*c^3)^(3/4)*d)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a*c^3*d^2 + sqrt(2)*a^2*c^2*e^2)","A",0
241,1,339,0,0.415816," ","integrate(1/(e*x^2+d)/(c*x^4+a),x, algorithm=""giac"")","\frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d - \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a c^{3} d^{2} + \sqrt{2} a^{2} c^{2} e^{2}\right)}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d - \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a c^{3} d^{2} + \sqrt{2} a^{2} c^{2} e^{2}\right)}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d + \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{4 \, {\left(\sqrt{2} a c^{3} d^{2} + \sqrt{2} a^{2} c^{2} e^{2}\right)}} - \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d + \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{4 \, {\left(\sqrt{2} a c^{3} d^{2} + \sqrt{2} a^{2} c^{2} e^{2}\right)}} + \frac{\arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\frac{3}{2}}}{{\left(c d^{2} + a e^{2}\right)} \sqrt{d}}"," ",0,"1/2*((a*c^3)^(1/4)*c^2*d - (a*c^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a*c^3*d^2 + sqrt(2)*a^2*c^2*e^2) + 1/2*((a*c^3)^(1/4)*c^2*d - (a*c^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a*c^3*d^2 + sqrt(2)*a^2*c^2*e^2) + 1/4*((a*c^3)^(1/4)*c^2*d + (a*c^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a*c^3*d^2 + sqrt(2)*a^2*c^2*e^2) - 1/4*((a*c^3)^(1/4)*c^2*d + (a*c^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a*c^3*d^2 + sqrt(2)*a^2*c^2*e^2) + arctan(x*e^(1/2)/sqrt(d))*e^(3/2)/((c*d^2 + a*e^2)*sqrt(d))","A",0
242,1,348,0,0.397528," ","integrate(1/x^2/(e*x^2+d)/(c*x^4+a),x, algorithm=""giac"")","-\frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} a c e + \left(a c^{3}\right)^{\frac{3}{4}} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a^{2} c^{2} d^{2} + \sqrt{2} a^{3} c e^{2}\right)}} - \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} a c e + \left(a c^{3}\right)^{\frac{3}{4}} d\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a^{2} c^{2} d^{2} + \sqrt{2} a^{3} c e^{2}\right)}} - \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} a c e - \left(a c^{3}\right)^{\frac{3}{4}} d\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{4 \, {\left(\sqrt{2} a^{2} c^{2} d^{2} + \sqrt{2} a^{3} c e^{2}\right)}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} a c e - \left(a c^{3}\right)^{\frac{3}{4}} d\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{4 \, {\left(\sqrt{2} a^{2} c^{2} d^{2} + \sqrt{2} a^{3} c e^{2}\right)}} - \frac{\arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\frac{5}{2}}}{{\left(c d^{3} + a d e^{2}\right)} \sqrt{d}} - \frac{1}{a d x}"," ",0,"-1/2*((a*c^3)^(1/4)*a*c*e + (a*c^3)^(3/4)*d)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^2*c^2*d^2 + sqrt(2)*a^3*c*e^2) - 1/2*((a*c^3)^(1/4)*a*c*e + (a*c^3)^(3/4)*d)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^2*c^2*d^2 + sqrt(2)*a^3*c*e^2) - 1/4*((a*c^3)^(1/4)*a*c*e - (a*c^3)^(3/4)*d)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a^2*c^2*d^2 + sqrt(2)*a^3*c*e^2) + 1/4*((a*c^3)^(1/4)*a*c*e - (a*c^3)^(3/4)*d)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a^2*c^2*d^2 + sqrt(2)*a^3*c*e^2) - arctan(x*e^(1/2)/sqrt(d))*e^(5/2)/((c*d^3 + a*d*e^2)*sqrt(d)) - 1/(a*d*x)","A",0
243,1,364,0,0.395107," ","integrate(1/x^4/(e*x^2+d)/(c*x^4+a),x, algorithm=""giac"")","-\frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d - \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a^{2} c^{2} d^{2} + \sqrt{2} a^{3} c e^{2}\right)}} - \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d - \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{2 \, {\left(\sqrt{2} a^{2} c^{2} d^{2} + \sqrt{2} a^{3} c e^{2}\right)}} - \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d + \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{4 \, {\left(\sqrt{2} a^{2} c^{2} d^{2} + \sqrt{2} a^{3} c e^{2}\right)}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{2} d + \left(a c^{3}\right)^{\frac{3}{4}} e\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{4 \, {\left(\sqrt{2} a^{2} c^{2} d^{2} + \sqrt{2} a^{3} c e^{2}\right)}} + \frac{\arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\frac{7}{2}}}{{\left(c d^{4} + a d^{2} e^{2}\right)} \sqrt{d}} + \frac{3 \, x^{2} e - d}{3 \, a d^{2} x^{3}}"," ",0,"-1/2*((a*c^3)^(1/4)*c^2*d - (a*c^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^2*c^2*d^2 + sqrt(2)*a^3*c*e^2) - 1/2*((a*c^3)^(1/4)*c^2*d - (a*c^3)^(3/4)*e)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^2*c^2*d^2 + sqrt(2)*a^3*c*e^2) - 1/4*((a*c^3)^(1/4)*c^2*d + (a*c^3)^(3/4)*e)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a^2*c^2*d^2 + sqrt(2)*a^3*c*e^2) + 1/4*((a*c^3)^(1/4)*c^2*d + (a*c^3)^(3/4)*e)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a^2*c^2*d^2 + sqrt(2)*a^3*c*e^2) + arctan(x*e^(1/2)/sqrt(d))*e^(7/2)/((c*d^4 + a*d^2*e^2)*sqrt(d)) + 1/3*(3*x^2*e - d)/(a*d^2*x^3)","A",0
244,1,251,0,0.363543," ","integrate(x^9/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{d^{4} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)}} + \frac{{\left(2 \, a c d^{2} e + a^{2} e^{3}\right)} \log\left(c x^{4} + a\right)}{4 \, {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)}} - \frac{{\left(3 \, a c d^{3} + a^{2} d e^{2}\right)} \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{4 \, {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} \sqrt{a c}} - \frac{2 \, a c d^{2} x^{4} e - a c d^{3} x^{2} + a^{2} x^{4} e^{3} - a^{2} d x^{2} e^{2} + a^{2} d^{2} e}{4 \, {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} {\left(c x^{4} + a\right)}}"," ",0,"1/2*d^4*log(abs(x^2*e + d))/(c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5) + 1/4*(2*a*c*d^2*e + a^2*e^3)*log(c*x^4 + a)/(c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4) - 1/4*(3*a*c*d^3 + a^2*d*e^2)*arctan(c*x^2/sqrt(a*c))/((c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*sqrt(a*c)) - 1/4*(2*a*c*d^2*x^4*e - a*c*d^3*x^2 + a^2*x^4*e^3 - a^2*d*x^2*e^2 + a^2*d^2*e)/((c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*(c*x^4 + a))","A",0
245,1,223,0,0.351220," ","integrate(x^7/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{d^{3} e \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)}} + \frac{d^{3} \log\left(c x^{4} + a\right)}{4 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)}} + \frac{{\left(3 \, a c d^{2} e + a^{2} e^{3}\right)} \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{4 \, {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} \sqrt{a c}} - \frac{c^{2} d^{3} x^{4} + a c d^{2} x^{2} e + a^{2} x^{2} e^{3} - a^{2} d e^{2}}{4 \, {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} {\left(c x^{4} + a\right)}}"," ",0,"-1/2*d^3*e*log(abs(x^2*e + d))/(c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5) + 1/4*d^3*log(c*x^4 + a)/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4) + 1/4*(3*a*c*d^2*e + a^2*e^3)*arctan(c*x^2/sqrt(a*c))/((c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*sqrt(a*c)) - 1/4*(c^2*d^3*x^4 + a*c*d^2*x^2*e + a^2*x^2*e^3 - a^2*d*e^2)/((c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*(c*x^4 + a))","A",0
246,1,220,0,0.331461," ","integrate(x^5/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{d^{2} e \log\left(c x^{4} + a\right)}{4 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)}} + \frac{d^{2} e^{2} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)}} + \frac{{\left(c d^{3} - a d e^{2}\right)} \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{4 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{a c}} + \frac{c^{2} d^{2} x^{4} e - c^{2} d^{3} x^{2} - a c d x^{2} e^{2} - a^{2} e^{3}}{4 \, {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} {\left(c x^{4} + a\right)}}"," ",0,"-1/4*d^2*e*log(c*x^4 + a)/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4) + 1/2*d^2*e^2*log(abs(x^2*e + d))/(c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5) + 1/4*(c*d^3 - a*d*e^2)*arctan(c*x^2/sqrt(a*c))/((c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(a*c)) + 1/4*(c^2*d^2*x^4*e - c^2*d^3*x^2 - a*c*d*x^2*e^2 - a^2*e^3)/((c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*(c*x^4 + a))","A",0
247,1,188,0,0.281111," ","integrate(x^3/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{d e^{2} \log\left(c x^{4} + a\right)}{4 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)}} - \frac{d e^{3} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)}} - \frac{{\left(c d^{2} e - a e^{3}\right)} \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{4 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{a c}} - \frac{c d^{3} - {\left(c d^{2} e + a e^{3}\right)} x^{2} + a d e^{2}}{4 \, {\left(c x^{4} + a\right)} {\left(c d^{2} + a e^{2}\right)}^{2}}"," ",0,"1/4*d*e^2*log(c*x^4 + a)/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4) - 1/2*d*e^3*log(abs(x^2*e + d))/(c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5) - 1/4*(c*d^2*e - a*e^3)*arctan(c*x^2/sqrt(a*c))/((c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(a*c)) - 1/4*(c*d^3 - (c*d^2*e + a*e^3)*x^2 + a*d*e^2)/((c*x^4 + a)*(c*d^2 + a*e^2)^2)","A",0
248,1,199,0,0.383392," ","integrate(x/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{e^{3} \log\left(c x^{4} + a\right)}{4 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)}} + \frac{e^{4} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)}} + \frac{{\left(c^{2} d^{3} + 3 \, a c d e^{2}\right)} \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{4 \, {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{a c}} + \frac{a c d^{2} e + {\left(c^{2} d^{3} + a c d e^{2}\right)} x^{2} + a^{2} e^{3}}{4 \, {\left(c x^{4} + a\right)} {\left(c d^{2} + a e^{2}\right)}^{2} a}"," ",0,"-1/4*e^3*log(c*x^4 + a)/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4) + 1/2*e^4*log(abs(x^2*e + d))/(c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5) + 1/4*(c^2*d^3 + 3*a*c*d*e^2)*arctan(c*x^2/sqrt(a*c))/((a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(a*c)) + 1/4*(a*c*d^2*e + (c^2*d^3 + a*c*d*e^2)*x^2 + a^2*e^3)/((c*x^4 + a)*(c*d^2 + a*e^2)^2*a)","A",0
249,1,279,0,0.368415," ","integrate(1/x/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{{\left(c^{2} d^{3} + 2 \, a c d e^{2}\right)} \log\left(c x^{4} + a\right)}{4 \, {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)}} - \frac{e^{5} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c^{2} d^{5} e + 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)}} - \frac{{\left(c^{2} d^{2} e + 3 \, a c e^{3}\right)} \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{4 \, {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{a c}} + \frac{c^{3} d^{3} x^{4} + 2 \, a c^{2} d x^{4} e^{2} - a c^{2} d^{2} x^{2} e + 2 \, a c^{2} d^{3} - a^{2} c x^{2} e^{3} + 3 \, a^{2} c d e^{2}}{4 \, {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} {\left(c x^{4} + a\right)}} + \frac{\log\left(x^{2}\right)}{2 \, a^{2} d}"," ",0,"-1/4*(c^2*d^3 + 2*a*c*d*e^2)*log(c*x^4 + a)/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4) - 1/2*e^5*log(abs(x^2*e + d))/(c^2*d^5*e + 2*a*c*d^3*e^3 + a^2*d*e^5) - 1/4*(c^2*d^2*e + 3*a*c*e^3)*arctan(c*x^2/sqrt(a*c))/((a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(a*c)) + 1/4*(c^3*d^3*x^4 + 2*a*c^2*d*x^4*e^2 - a*c^2*d^2*x^2*e + 2*a*c^2*d^3 - a^2*c*x^2*e^3 + 3*a^2*c*d*e^2)/((a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*(c*x^4 + a)) + 1/2*log(x^2)/(a^2*d)","A",0
250,1,344,0,0.352701," ","integrate(1/x^3/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{{\left(c^{2} d^{2} e + 2 \, a c e^{3}\right)} \log\left(c x^{4} + a\right)}{4 \, {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)}} + \frac{e^{6} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c^{2} d^{6} e + 2 \, a c d^{4} e^{3} + a^{2} d^{2} e^{5}\right)}} - \frac{{\left(3 \, c^{3} d^{3} + 5 \, a c^{2} d e^{2}\right)} \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{4 \, {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \sqrt{a c}} - \frac{9 \, c^{3} d^{5} x^{4} + 15 \, a c^{2} d^{3} x^{4} e^{2} - 2 \, a^{2} c x^{6} e^{5} + 3 \, a c^{2} d^{4} x^{2} e + 6 \, a^{2} c d x^{4} e^{4} + 6 \, a c^{2} d^{5} + 3 \, a^{2} c d^{2} x^{2} e^{3} + 12 \, a^{2} c d^{3} e^{2} - 2 \, a^{3} x^{2} e^{5} + 6 \, a^{3} d e^{4}}{12 \, {\left(a^{2} c^{2} d^{6} + 2 \, a^{3} c d^{4} e^{2} + a^{4} d^{2} e^{4}\right)} {\left(c x^{6} + a x^{2}\right)}} - \frac{e \log\left(x^{2}\right)}{2 \, a^{2} d^{2}}"," ",0,"1/4*(c^2*d^2*e + 2*a*c*e^3)*log(c*x^4 + a)/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4) + 1/2*e^6*log(abs(x^2*e + d))/(c^2*d^6*e + 2*a*c*d^4*e^3 + a^2*d^2*e^5) - 1/4*(3*c^3*d^3 + 5*a*c^2*d*e^2)*arctan(c*x^2/sqrt(a*c))/((a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*sqrt(a*c)) - 1/12*(9*c^3*d^5*x^4 + 15*a*c^2*d^3*x^4*e^2 - 2*a^2*c*x^6*e^5 + 3*a*c^2*d^4*x^2*e + 6*a^2*c*d*x^4*e^4 + 6*a*c^2*d^5 + 3*a^2*c*d^2*x^2*e^3 + 12*a^2*c*d^3*e^2 - 2*a^3*x^2*e^5 + 6*a^3*d*e^4)/((a^2*c^2*d^6 + 2*a^3*c*d^4*e^2 + a^4*d^2*e^4)*(c*x^6 + a*x^2)) - 1/2*e*log(x^2)/(a^2*d^2)","A",0
251,1,350,0,0.367420," ","integrate(1/x^5/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{{\left(2 \, c^{3} d^{3} + 3 \, a c^{2} d e^{2}\right)} \log\left(c x^{4} + a\right)}{4 \, {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)}} - \frac{e^{7} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c^{2} d^{7} e + 2 \, a c d^{5} e^{3} + a^{2} d^{3} e^{5}\right)}} + \frac{{\left(3 \, c^{3} d^{2} e + 5 \, a c^{2} e^{3}\right)} \arctan\left(\frac{c x^{2}}{\sqrt{a c}}\right)}{4 \, {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \sqrt{a c}} - \frac{2 \, c^{4} d^{3} x^{4} + 3 \, a c^{3} d x^{4} e^{2} - a c^{3} d^{2} x^{2} e + 3 \, a c^{3} d^{3} - a^{2} c^{2} x^{2} e^{3} + 4 \, a^{2} c^{2} d e^{2}}{4 \, {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} {\left(c x^{4} + a\right)}} - \frac{{\left(2 \, c d^{2} - a e^{2}\right)} \log\left(x^{2}\right)}{2 \, a^{3} d^{3}} + \frac{6 \, c d^{2} x^{4} - 3 \, a x^{4} e^{2} + 2 \, a d x^{2} e - a d^{2}}{4 \, a^{3} d^{3} x^{4}}"," ",0,"1/4*(2*c^3*d^3 + 3*a*c^2*d*e^2)*log(c*x^4 + a)/(a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4) - 1/2*e^7*log(abs(x^2*e + d))/(c^2*d^7*e + 2*a*c*d^5*e^3 + a^2*d^3*e^5) + 1/4*(3*c^3*d^2*e + 5*a*c^2*e^3)*arctan(c*x^2/sqrt(a*c))/((a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*sqrt(a*c)) - 1/4*(2*c^4*d^3*x^4 + 3*a*c^3*d*x^4*e^2 - a*c^3*d^2*x^2*e + 3*a*c^3*d^3 - a^2*c^2*x^2*e^3 + 4*a^2*c^2*d*e^2)/((a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*(c*x^4 + a)) - 1/2*(2*c*d^2 - a*e^2)*log(x^2)/(a^3*d^3) + 1/4*(6*c*d^2*x^4 - 3*a*x^4*e^2 + 2*a*d*x^2*e - a*d^2)/(a^3*d^3*x^4)","A",0
252,1,581,0,0.572691," ","integrate(x^8/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{d^{\frac{7}{2}} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{1}{2}\right)}}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}} - \frac{{\left(5 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} + \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} - 7 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e - 3 \, \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} c^{6} d^{4} + 2 \, \sqrt{2} a c^{5} d^{2} e^{2} + \sqrt{2} a^{2} c^{4} e^{4}\right)}} - \frac{{\left(5 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} + \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} - 7 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e - 3 \, \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} c^{6} d^{4} + 2 \, \sqrt{2} a c^{5} d^{2} e^{2} + \sqrt{2} a^{2} c^{4} e^{4}\right)}} - \frac{{\left(5 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} + \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} + 7 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e + 3 \, \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{16 \, {\left(\sqrt{2} c^{6} d^{4} + 2 \, \sqrt{2} a c^{5} d^{2} e^{2} + \sqrt{2} a^{2} c^{4} e^{4}\right)}} + \frac{{\left(5 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} + \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} + 7 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e + 3 \, \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{16 \, {\left(\sqrt{2} c^{6} d^{4} + 2 \, \sqrt{2} a c^{5} d^{2} e^{2} + \sqrt{2} a^{2} c^{4} e^{4}\right)}} - \frac{a x^{3} e - a d x}{4 \, {\left(c x^{4} + a\right)} {\left(c^{2} d^{2} + a c e^{2}\right)}}"," ",0,"d^(7/2)*arctan(x*e^(1/2)/sqrt(d))*e^(-1/2)/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4) - 1/8*(5*(a*c^3)^(1/4)*c^3*d^3 + (a*c^3)^(1/4)*a*c^2*d*e^2 - 7*(a*c^3)^(3/4)*c*d^2*e - 3*(a*c^3)^(3/4)*a*e^3)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*c^6*d^4 + 2*sqrt(2)*a*c^5*d^2*e^2 + sqrt(2)*a^2*c^4*e^4) - 1/8*(5*(a*c^3)^(1/4)*c^3*d^3 + (a*c^3)^(1/4)*a*c^2*d*e^2 - 7*(a*c^3)^(3/4)*c*d^2*e - 3*(a*c^3)^(3/4)*a*e^3)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*c^6*d^4 + 2*sqrt(2)*a*c^5*d^2*e^2 + sqrt(2)*a^2*c^4*e^4) - 1/16*(5*(a*c^3)^(1/4)*c^3*d^3 + (a*c^3)^(1/4)*a*c^2*d*e^2 + 7*(a*c^3)^(3/4)*c*d^2*e + 3*(a*c^3)^(3/4)*a*e^3)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*c^6*d^4 + 2*sqrt(2)*a*c^5*d^2*e^2 + sqrt(2)*a^2*c^4*e^4) + 1/16*(5*(a*c^3)^(1/4)*c^3*d^3 + (a*c^3)^(1/4)*a*c^2*d*e^2 + 7*(a*c^3)^(3/4)*c*d^2*e + 3*(a*c^3)^(3/4)*a*e^3)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*c^6*d^4 + 2*sqrt(2)*a*c^5*d^2*e^2 + sqrt(2)*a^2*c^4*e^4) - 1/4*(a*x^3*e - a*d*x)/((c*x^4 + a)*(c^2*d^2 + a*c*e^2))","A",0
253,1,595,0,0.587253," ","integrate(x^6/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{d^{\frac{5}{2}} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\frac{1}{2}}}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}} + \frac{{\left(5 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e + 3 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} + \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c e^{3} - \left(a c^{3}\right)^{\frac{3}{4}} a d e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a c^{5} d^{4} + 2 \, \sqrt{2} a^{2} c^{4} d^{2} e^{2} + \sqrt{2} a^{3} c^{3} e^{4}\right)}} + \frac{{\left(5 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e + 3 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} + \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c e^{3} - \left(a c^{3}\right)^{\frac{3}{4}} a d e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a c^{5} d^{4} + 2 \, \sqrt{2} a^{2} c^{4} d^{2} e^{2} + \sqrt{2} a^{3} c^{3} e^{4}\right)}} + \frac{{\left(5 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e - 3 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} + \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c e^{3} + \left(a c^{3}\right)^{\frac{3}{4}} a d e^{2}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{16 \, {\left(\sqrt{2} a c^{5} d^{4} + 2 \, \sqrt{2} a^{2} c^{4} d^{2} e^{2} + \sqrt{2} a^{3} c^{3} e^{4}\right)}} - \frac{{\left(5 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e - 3 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} + \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c e^{3} + \left(a c^{3}\right)^{\frac{3}{4}} a d e^{2}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{16 \, {\left(\sqrt{2} a c^{5} d^{4} + 2 \, \sqrt{2} a^{2} c^{4} d^{2} e^{2} + \sqrt{2} a^{3} c^{3} e^{4}\right)}} - \frac{c d x^{3} + a x e}{4 \, {\left(c x^{4} + a\right)} {\left(c^{2} d^{2} + a c e^{2}\right)}}"," ",0,"-d^(5/2)*arctan(x*e^(1/2)/sqrt(d))*e^(1/2)/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4) + 1/8*(5*(a*c^3)^(1/4)*a*c^2*d^2*e + 3*(a*c^3)^(3/4)*c*d^3 + (a*c^3)^(1/4)*a^2*c*e^3 - (a*c^3)^(3/4)*a*d*e^2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a*c^5*d^4 + 2*sqrt(2)*a^2*c^4*d^2*e^2 + sqrt(2)*a^3*c^3*e^4) + 1/8*(5*(a*c^3)^(1/4)*a*c^2*d^2*e + 3*(a*c^3)^(3/4)*c*d^3 + (a*c^3)^(1/4)*a^2*c*e^3 - (a*c^3)^(3/4)*a*d*e^2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a*c^5*d^4 + 2*sqrt(2)*a^2*c^4*d^2*e^2 + sqrt(2)*a^3*c^3*e^4) + 1/16*(5*(a*c^3)^(1/4)*a*c^2*d^2*e - 3*(a*c^3)^(3/4)*c*d^3 + (a*c^3)^(1/4)*a^2*c*e^3 + (a*c^3)^(3/4)*a*d*e^2)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a*c^5*d^4 + 2*sqrt(2)*a^2*c^4*d^2*e^2 + sqrt(2)*a^3*c^3*e^4) - 1/16*(5*(a*c^3)^(1/4)*a*c^2*d^2*e - 3*(a*c^3)^(3/4)*c*d^3 + (a*c^3)^(1/4)*a^2*c*e^3 + (a*c^3)^(3/4)*a*d*e^2)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a*c^5*d^4 + 2*sqrt(2)*a^2*c^4*d^2*e^2 + sqrt(2)*a^3*c^3*e^4) - 1/4*(c*d*x^3 + a*x*e)/((c*x^4 + a)*(c^2*d^2 + a*c*e^2))","A",0
254,1,586,0,0.466400," ","integrate(x^4/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{d^{\frac{3}{2}} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\frac{3}{2}}}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} - 3 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} - 3 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e + \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a c^{5} d^{4} + 2 \, \sqrt{2} a^{2} c^{4} d^{2} e^{2} + \sqrt{2} a^{3} c^{3} e^{4}\right)}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} - 3 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} - 3 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e + \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a c^{5} d^{4} + 2 \, \sqrt{2} a^{2} c^{4} d^{2} e^{2} + \sqrt{2} a^{3} c^{3} e^{4}\right)}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} - 3 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} + 3 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e - \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{16 \, {\left(\sqrt{2} a c^{5} d^{4} + 2 \, \sqrt{2} a^{2} c^{4} d^{2} e^{2} + \sqrt{2} a^{3} c^{3} e^{4}\right)}} - \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} - 3 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} + 3 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e - \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{16 \, {\left(\sqrt{2} a c^{5} d^{4} + 2 \, \sqrt{2} a^{2} c^{4} d^{2} e^{2} + \sqrt{2} a^{3} c^{3} e^{4}\right)}} + \frac{x^{3} e - d x}{4 \, {\left(c x^{4} + a\right)} {\left(c d^{2} + a e^{2}\right)}}"," ",0,"d^(3/2)*arctan(x*e^(1/2)/sqrt(d))*e^(3/2)/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4) + 1/8*((a*c^3)^(1/4)*c^3*d^3 - 3*(a*c^3)^(1/4)*a*c^2*d*e^2 - 3*(a*c^3)^(3/4)*c*d^2*e + (a*c^3)^(3/4)*a*e^3)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a*c^5*d^4 + 2*sqrt(2)*a^2*c^4*d^2*e^2 + sqrt(2)*a^3*c^3*e^4) + 1/8*((a*c^3)^(1/4)*c^3*d^3 - 3*(a*c^3)^(1/4)*a*c^2*d*e^2 - 3*(a*c^3)^(3/4)*c*d^2*e + (a*c^3)^(3/4)*a*e^3)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a*c^5*d^4 + 2*sqrt(2)*a^2*c^4*d^2*e^2 + sqrt(2)*a^3*c^3*e^4) + 1/16*((a*c^3)^(1/4)*c^3*d^3 - 3*(a*c^3)^(1/4)*a*c^2*d*e^2 + 3*(a*c^3)^(3/4)*c*d^2*e - (a*c^3)^(3/4)*a*e^3)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a*c^5*d^4 + 2*sqrt(2)*a^2*c^4*d^2*e^2 + sqrt(2)*a^3*c^3*e^4) - 1/16*((a*c^3)^(1/4)*c^3*d^3 - 3*(a*c^3)^(1/4)*a*c^2*d*e^2 + 3*(a*c^3)^(3/4)*c*d^2*e - (a*c^3)^(3/4)*a*e^3)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a*c^5*d^4 + 2*sqrt(2)*a^2*c^4*d^2*e^2 + sqrt(2)*a^3*c^3*e^4) + 1/4*(x^3*e - d*x)/((c*x^4 + a)*(c*d^2 + a*e^2))","A",0
255,1,603,0,0.502054," ","integrate(x^2/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{d} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\frac{5}{2}}}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}} - \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e - \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} - 3 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c e^{3} - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} a d e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{2} c^{4} d^{4} + 2 \, \sqrt{2} a^{3} c^{3} d^{2} e^{2} + \sqrt{2} a^{4} c^{2} e^{4}\right)}} - \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e - \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} - 3 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c e^{3} - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} a d e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{2} c^{4} d^{4} + 2 \, \sqrt{2} a^{3} c^{3} d^{2} e^{2} + \sqrt{2} a^{4} c^{2} e^{4}\right)}} - \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e + \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} - 3 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c e^{3} + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} a d e^{2}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{16 \, {\left(\sqrt{2} a^{2} c^{4} d^{4} + 2 \, \sqrt{2} a^{3} c^{3} d^{2} e^{2} + \sqrt{2} a^{4} c^{2} e^{4}\right)}} + \frac{{\left(\left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e + \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} - 3 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c e^{3} + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} a d e^{2}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{16 \, {\left(\sqrt{2} a^{2} c^{4} d^{4} + 2 \, \sqrt{2} a^{3} c^{3} d^{2} e^{2} + \sqrt{2} a^{4} c^{2} e^{4}\right)}} + \frac{c d x^{3} + a x e}{4 \, {\left(c x^{4} + a\right)} {\left(a c d^{2} + a^{2} e^{2}\right)}}"," ",0,"-sqrt(d)*arctan(x*e^(1/2)/sqrt(d))*e^(5/2)/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4) - 1/8*((a*c^3)^(1/4)*a*c^2*d^2*e - (a*c^3)^(3/4)*c*d^3 - 3*(a*c^3)^(1/4)*a^2*c*e^3 - 5*(a*c^3)^(3/4)*a*d*e^2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^2*c^4*d^4 + 2*sqrt(2)*a^3*c^3*d^2*e^2 + sqrt(2)*a^4*c^2*e^4) - 1/8*((a*c^3)^(1/4)*a*c^2*d^2*e - (a*c^3)^(3/4)*c*d^3 - 3*(a*c^3)^(1/4)*a^2*c*e^3 - 5*(a*c^3)^(3/4)*a*d*e^2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^2*c^4*d^4 + 2*sqrt(2)*a^3*c^3*d^2*e^2 + sqrt(2)*a^4*c^2*e^4) - 1/16*((a*c^3)^(1/4)*a*c^2*d^2*e + (a*c^3)^(3/4)*c*d^3 - 3*(a*c^3)^(1/4)*a^2*c*e^3 + 5*(a*c^3)^(3/4)*a*d*e^2)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a^2*c^4*d^4 + 2*sqrt(2)*a^3*c^3*d^2*e^2 + sqrt(2)*a^4*c^2*e^4) + 1/16*((a*c^3)^(1/4)*a*c^2*d^2*e + (a*c^3)^(3/4)*c*d^3 - 3*(a*c^3)^(1/4)*a^2*c*e^3 + 5*(a*c^3)^(3/4)*a*d*e^2)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a^2*c^4*d^4 + 2*sqrt(2)*a^3*c^3*d^2*e^2 + sqrt(2)*a^4*c^2*e^4) + 1/4*(c*d*x^3 + a*x*e)/((c*x^4 + a)*(a*c*d^2 + a^2*e^2))","A",0
256,1,603,0,0.466028," ","integrate(1/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""giac"")","\frac{{\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} + 7 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} - \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{2} c^{4} d^{4} + 2 \, \sqrt{2} a^{3} c^{3} d^{2} e^{2} + \sqrt{2} a^{4} c^{2} e^{4}\right)}} + \frac{{\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} + 7 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} - \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{2} c^{4} d^{4} + 2 \, \sqrt{2} a^{3} c^{3} d^{2} e^{2} + \sqrt{2} a^{4} c^{2} e^{4}\right)}} + \frac{{\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} + 7 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} + \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{16 \, {\left(\sqrt{2} a^{2} c^{4} d^{4} + 2 \, \sqrt{2} a^{3} c^{3} d^{2} e^{2} + \sqrt{2} a^{4} c^{2} e^{4}\right)}} - \frac{{\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} + 7 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} + \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{16 \, {\left(\sqrt{2} a^{2} c^{4} d^{4} + 2 \, \sqrt{2} a^{3} c^{3} d^{2} e^{2} + \sqrt{2} a^{4} c^{2} e^{4}\right)}} + \frac{\arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\frac{7}{2}}}{{\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{d}} - \frac{c x^{3} e - c d x}{4 \, {\left(c x^{4} + a\right)} {\left(a c d^{2} + a^{2} e^{2}\right)}}"," ",0,"1/8*(3*(a*c^3)^(1/4)*c^3*d^3 + 7*(a*c^3)^(1/4)*a*c^2*d*e^2 - (a*c^3)^(3/4)*c*d^2*e - 5*(a*c^3)^(3/4)*a*e^3)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^2*c^4*d^4 + 2*sqrt(2)*a^3*c^3*d^2*e^2 + sqrt(2)*a^4*c^2*e^4) + 1/8*(3*(a*c^3)^(1/4)*c^3*d^3 + 7*(a*c^3)^(1/4)*a*c^2*d*e^2 - (a*c^3)^(3/4)*c*d^2*e - 5*(a*c^3)^(3/4)*a*e^3)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^2*c^4*d^4 + 2*sqrt(2)*a^3*c^3*d^2*e^2 + sqrt(2)*a^4*c^2*e^4) + 1/16*(3*(a*c^3)^(1/4)*c^3*d^3 + 7*(a*c^3)^(1/4)*a*c^2*d*e^2 + (a*c^3)^(3/4)*c*d^2*e + 5*(a*c^3)^(3/4)*a*e^3)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a^2*c^4*d^4 + 2*sqrt(2)*a^3*c^3*d^2*e^2 + sqrt(2)*a^4*c^2*e^4) - 1/16*(3*(a*c^3)^(1/4)*c^3*d^3 + 7*(a*c^3)^(1/4)*a*c^2*d*e^2 + (a*c^3)^(3/4)*c*d^2*e + 5*(a*c^3)^(3/4)*a*e^3)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a^2*c^4*d^4 + 2*sqrt(2)*a^3*c^3*d^2*e^2 + sqrt(2)*a^4*c^2*e^4) + arctan(x*e^(1/2)/sqrt(d))*e^(7/2)/((c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(d)) - 1/4*(c*x^3*e - c*d*x)/((c*x^4 + a)*(a*c*d^2 + a^2*e^2))","A",0
257,1,639,0,0.451792," ","integrate(1/x^2/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{{\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} + 7 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c e^{3} + 9 \, \left(a c^{3}\right)^{\frac{3}{4}} a d e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{3} c^{3} d^{4} + 2 \, \sqrt{2} a^{4} c^{2} d^{2} e^{2} + \sqrt{2} a^{5} c e^{4}\right)}} - \frac{{\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} + 7 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c e^{3} + 9 \, \left(a c^{3}\right)^{\frac{3}{4}} a d e^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{3} c^{3} d^{4} + 2 \, \sqrt{2} a^{4} c^{2} d^{2} e^{2} + \sqrt{2} a^{5} c e^{4}\right)}} - \frac{{\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} + 7 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c e^{3} - 9 \, \left(a c^{3}\right)^{\frac{3}{4}} a d e^{2}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{16 \, {\left(\sqrt{2} a^{3} c^{3} d^{4} + 2 \, \sqrt{2} a^{4} c^{2} d^{2} e^{2} + \sqrt{2} a^{5} c e^{4}\right)}} + \frac{{\left(3 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d^{2} e - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{3} + 7 \, \left(a c^{3}\right)^{\frac{1}{4}} a^{2} c e^{3} - 9 \, \left(a c^{3}\right)^{\frac{3}{4}} a d e^{2}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{16 \, {\left(\sqrt{2} a^{3} c^{3} d^{4} + 2 \, \sqrt{2} a^{4} c^{2} d^{2} e^{2} + \sqrt{2} a^{5} c e^{4}\right)}} - \frac{\arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\frac{9}{2}}}{{\left(c^{2} d^{5} + 2 \, a c d^{3} e^{2} + a^{2} d e^{4}\right)} \sqrt{d}} - \frac{5 \, c^{2} d^{2} x^{4} + 4 \, a c x^{4} e^{2} + a c d x^{2} e + 4 \, a c d^{2} + 4 \, a^{2} e^{2}}{4 \, {\left(a^{2} c d^{3} + a^{3} d e^{2}\right)} {\left(c x^{5} + a x\right)}}"," ",0,"-1/8*(3*(a*c^3)^(1/4)*a*c^2*d^2*e + 5*(a*c^3)^(3/4)*c*d^3 + 7*(a*c^3)^(1/4)*a^2*c*e^3 + 9*(a*c^3)^(3/4)*a*d*e^2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^3*c^3*d^4 + 2*sqrt(2)*a^4*c^2*d^2*e^2 + sqrt(2)*a^5*c*e^4) - 1/8*(3*(a*c^3)^(1/4)*a*c^2*d^2*e + 5*(a*c^3)^(3/4)*c*d^3 + 7*(a*c^3)^(1/4)*a^2*c*e^3 + 9*(a*c^3)^(3/4)*a*d*e^2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^3*c^3*d^4 + 2*sqrt(2)*a^4*c^2*d^2*e^2 + sqrt(2)*a^5*c*e^4) - 1/16*(3*(a*c^3)^(1/4)*a*c^2*d^2*e - 5*(a*c^3)^(3/4)*c*d^3 + 7*(a*c^3)^(1/4)*a^2*c*e^3 - 9*(a*c^3)^(3/4)*a*d*e^2)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a^3*c^3*d^4 + 2*sqrt(2)*a^4*c^2*d^2*e^2 + sqrt(2)*a^5*c*e^4) + 1/16*(3*(a*c^3)^(1/4)*a*c^2*d^2*e - 5*(a*c^3)^(3/4)*c*d^3 + 7*(a*c^3)^(1/4)*a^2*c*e^3 - 9*(a*c^3)^(3/4)*a*d*e^2)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a^3*c^3*d^4 + 2*sqrt(2)*a^4*c^2*d^2*e^2 + sqrt(2)*a^5*c*e^4) - arctan(x*e^(1/2)/sqrt(d))*e^(9/2)/((c^2*d^5 + 2*a*c*d^3*e^2 + a^2*d*e^4)*sqrt(d)) - 1/4*(5*c^2*d^2*x^4 + 4*a*c*x^4*e^2 + a*c*d*x^2*e + 4*a*c*d^2 + 4*a^2*e^2)/((a^2*c*d^3 + a^3*d*e^2)*(c*x^5 + a*x))","A",0
258,1,628,0,0.497139," ","integrate(1/x^4/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""giac"")","-\frac{{\left(7 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} + 11 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e - 9 \, \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x + \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{3} c^{3} d^{4} + 2 \, \sqrt{2} a^{4} c^{2} d^{2} e^{2} + \sqrt{2} a^{5} c e^{4}\right)}} - \frac{{\left(7 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} + 11 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} - 5 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e - 9 \, \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, x - \sqrt{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}}{2 \, \left(\frac{a}{c}\right)^{\frac{1}{4}}}\right)}{8 \, {\left(\sqrt{2} a^{3} c^{3} d^{4} + 2 \, \sqrt{2} a^{4} c^{2} d^{2} e^{2} + \sqrt{2} a^{5} c e^{4}\right)}} - \frac{{\left(7 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} + 11 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e + 9 \, \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \log\left(x^{2} + \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{16 \, {\left(\sqrt{2} a^{3} c^{3} d^{4} + 2 \, \sqrt{2} a^{4} c^{2} d^{2} e^{2} + \sqrt{2} a^{5} c e^{4}\right)}} + \frac{{\left(7 \, \left(a c^{3}\right)^{\frac{1}{4}} c^{3} d^{3} + 11 \, \left(a c^{3}\right)^{\frac{1}{4}} a c^{2} d e^{2} + 5 \, \left(a c^{3}\right)^{\frac{3}{4}} c d^{2} e + 9 \, \left(a c^{3}\right)^{\frac{3}{4}} a e^{3}\right)} \log\left(x^{2} - \sqrt{2} x \left(\frac{a}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{a}{c}}\right)}{16 \, {\left(\sqrt{2} a^{3} c^{3} d^{4} + 2 \, \sqrt{2} a^{4} c^{2} d^{2} e^{2} + \sqrt{2} a^{5} c e^{4}\right)}} + \frac{\arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\frac{11}{2}}}{{\left(c^{2} d^{6} + 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4}\right)} \sqrt{d}} + \frac{c^{2} x^{3} e - c^{2} d x}{4 \, {\left(a^{2} c d^{2} + a^{3} e^{2}\right)} {\left(c x^{4} + a\right)}} + \frac{3 \, x^{2} e - d}{3 \, a^{2} d^{2} x^{3}}"," ",0,"-1/8*(7*(a*c^3)^(1/4)*c^3*d^3 + 11*(a*c^3)^(1/4)*a*c^2*d*e^2 - 5*(a*c^3)^(3/4)*c*d^2*e - 9*(a*c^3)^(3/4)*a*e^3)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^3*c^3*d^4 + 2*sqrt(2)*a^4*c^2*d^2*e^2 + sqrt(2)*a^5*c*e^4) - 1/8*(7*(a*c^3)^(1/4)*c^3*d^3 + 11*(a*c^3)^(1/4)*a*c^2*d*e^2 - 5*(a*c^3)^(3/4)*c*d^2*e - 9*(a*c^3)^(3/4)*a*e^3)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)*(a/c)^(1/4))/(a/c)^(1/4))/(sqrt(2)*a^3*c^3*d^4 + 2*sqrt(2)*a^4*c^2*d^2*e^2 + sqrt(2)*a^5*c*e^4) - 1/16*(7*(a*c^3)^(1/4)*c^3*d^3 + 11*(a*c^3)^(1/4)*a*c^2*d*e^2 + 5*(a*c^3)^(3/4)*c*d^2*e + 9*(a*c^3)^(3/4)*a*e^3)*log(x^2 + sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a^3*c^3*d^4 + 2*sqrt(2)*a^4*c^2*d^2*e^2 + sqrt(2)*a^5*c*e^4) + 1/16*(7*(a*c^3)^(1/4)*c^3*d^3 + 11*(a*c^3)^(1/4)*a*c^2*d*e^2 + 5*(a*c^3)^(3/4)*c*d^2*e + 9*(a*c^3)^(3/4)*a*e^3)*log(x^2 - sqrt(2)*x*(a/c)^(1/4) + sqrt(a/c))/(sqrt(2)*a^3*c^3*d^4 + 2*sqrt(2)*a^4*c^2*d^2*e^2 + sqrt(2)*a^5*c*e^4) + arctan(x*e^(1/2)/sqrt(d))*e^(11/2)/((c^2*d^6 + 2*a*c*d^4*e^2 + a^2*d^2*e^4)*sqrt(d)) + 1/4*(c^2*x^3*e - c^2*d*x)/((a^2*c*d^2 + a^3*e^2)*(c*x^4 + a)) + 1/3*(3*x^2*e - d)/(a^2*d^2*x^3)","A",0
259,0,0,0,0.000000," ","integrate(x^2/(x^2+1)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{x^{4} + 1} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate(x^2/(sqrt(x^4 + 1)*(x^2 + 1)), x)","F",0
260,0,0,0,0.000000," ","integrate(x^2/(-x^2+1)/(x^4+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2}}{\sqrt{x^{4} + 1} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate(-x^2/(sqrt(x^4 + 1)*(x^2 - 1)), x)","F",0
261,0,0,0,0.000000," ","integrate(x^2/(x^2+1)/(-x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{-x^{4} + 1} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate(x^2/(sqrt(-x^4 + 1)*(x^2 + 1)), x)","F",0
262,0,0,0,0.000000," ","integrate(x^2/(-x^2+1)/(-x^4+1)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2}}{\sqrt{-x^{4} + 1} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate(-x^2/(sqrt(-x^4 + 1)*(x^2 - 1)), x)","F",0
263,0,0,0,0.000000," ","integrate(x^2/(x^2+1)/(x^4-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{x^{4} - 1} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate(x^2/(sqrt(x^4 - 1)*(x^2 + 1)), x)","F",0
264,0,0,0,0.000000," ","integrate(x^2/(-x^2+1)/(x^4-1)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2}}{\sqrt{x^{4} - 1} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate(-x^2/(sqrt(x^4 - 1)*(x^2 - 1)), x)","F",0
265,0,0,0,0.000000," ","integrate(x^2/(x^2+1)/(-x^4-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{-x^{4} - 1} {\left(x^{2} + 1\right)}}\,{d x}"," ",0,"integrate(x^2/(sqrt(-x^4 - 1)*(x^2 + 1)), x)","F",0
266,0,0,0,0.000000," ","integrate(x^2/(-x^2+1)/(-x^4-1)^(1/2),x, algorithm=""giac"")","\int -\frac{x^{2}}{\sqrt{-x^{4} - 1} {\left(x^{2} - 1\right)}}\,{d x}"," ",0,"integrate(-x^2/(sqrt(-x^4 - 1)*(x^2 - 1)), x)","F",0
267,1,156,0,0.376216," ","integrate(x^2*(d*x^2+c)^(1/2)*((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{48} \, {\left(2 \, {\left(4 \, b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{b c d^{3} \mathrm{sgn}\left(b x^{2} + a\right) + 6 \, a d^{4} \mathrm{sgn}\left(b x^{2} + a\right)}{d^{4}}\right)} x^{2} - \frac{3 \, {\left(b c^{2} d^{2} \mathrm{sgn}\left(b x^{2} + a\right) - 2 \, a c d^{3} \mathrm{sgn}\left(b x^{2} + a\right)\right)}}{d^{4}}\right)} \sqrt{d x^{2} + c} x - \frac{{\left(b c^{3} \mathrm{sgn}\left(b x^{2} + a\right) - 2 \, a c^{2} d \mathrm{sgn}\left(b x^{2} + a\right)\right)} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right)}{16 \, d^{\frac{5}{2}}}"," ",0,"1/48*(2*(4*b*x^2*sgn(b*x^2 + a) + (b*c*d^3*sgn(b*x^2 + a) + 6*a*d^4*sgn(b*x^2 + a))/d^4)*x^2 - 3*(b*c^2*d^2*sgn(b*x^2 + a) - 2*a*c*d^3*sgn(b*x^2 + a))/d^4)*sqrt(d*x^2 + c)*x - 1/16*(b*c^3*sgn(b*x^2 + a) - 2*a*c^2*d*sgn(b*x^2 + a))*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))/d^(5/2)","A",0
268,1,68,0,0.336323," ","integrate(x*(d*x^2+c)^(1/2)*((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{3 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b \mathrm{sgn}\left(b x^{2} + a\right) - 5 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b c \mathrm{sgn}\left(b x^{2} + a\right) + 5 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a d \mathrm{sgn}\left(b x^{2} + a\right)}{15 \, d^{2}}"," ",0,"1/15*(3*(d*x^2 + c)^(5/2)*b*sgn(b*x^2 + a) - 5*(d*x^2 + c)^(3/2)*b*c*sgn(b*x^2 + a) + 5*(d*x^2 + c)^(3/2)*a*d*sgn(b*x^2 + a))/d^2","A",0
269,1,109,0,0.460611," ","integrate((d*x^2+c)^(1/2)*((b*x^2+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(2 \, b x^{2} \mathrm{sgn}\left(b x^{2} + a\right) + \frac{b c d \mathrm{sgn}\left(b x^{2} + a\right) + 4 \, a d^{2} \mathrm{sgn}\left(b x^{2} + a\right)}{d^{2}}\right)} \sqrt{d x^{2} + c} x + \frac{{\left(b c^{2} \mathrm{sgn}\left(b x^{2} + a\right) - 4 \, a c d \mathrm{sgn}\left(b x^{2} + a\right)\right)} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right)}{8 \, d^{\frac{3}{2}}}"," ",0,"1/8*(2*b*x^2*sgn(b*x^2 + a) + (b*c*d*sgn(b*x^2 + a) + 4*a*d^2*sgn(b*x^2 + a))/d^2)*sqrt(d*x^2 + c)*x + 1/8*(b*c^2*sgn(b*x^2 + a) - 4*a*c*d*sgn(b*x^2 + a))*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))/d^(3/2)","A",0
270,1,84,0,0.445062," ","integrate((d*x^2+c)^(1/2)*((b*x^2+a)^2)^(1/2)/x,x, algorithm=""giac"")","\frac{a c \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right) \mathrm{sgn}\left(b x^{2} + a\right)}{\sqrt{-c}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b d^{2} \mathrm{sgn}\left(b x^{2} + a\right) + 3 \, \sqrt{d x^{2} + c} a d^{3} \mathrm{sgn}\left(b x^{2} + a\right)}{3 \, d^{3}}"," ",0,"a*c*arctan(sqrt(d*x^2 + c)/sqrt(-c))*sgn(b*x^2 + a)/sqrt(-c) + 1/3*((d*x^2 + c)^(3/2)*b*d^2*sgn(b*x^2 + a) + 3*sqrt(d*x^2 + c)*a*d^3*sgn(b*x^2 + a))/d^3","A",0
271,1,116,0,0.471092," ","integrate((d*x^2+c)^(1/2)*((b*x^2+a)^2)^(1/2)/x^2,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{d x^{2} + c} b x \mathrm{sgn}\left(b x^{2} + a\right) + \frac{2 \, a c \sqrt{d} \mathrm{sgn}\left(b x^{2} + a\right)}{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c} - \frac{{\left(b c \sqrt{d} \mathrm{sgn}\left(b x^{2} + a\right) + 2 \, a d^{\frac{3}{2}} \mathrm{sgn}\left(b x^{2} + a\right)\right)} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right)}{4 \, d}"," ",0,"1/2*sqrt(d*x^2 + c)*b*x*sgn(b*x^2 + a) + 2*a*c*sqrt(d)*sgn(b*x^2 + a)/((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c) - 1/4*(b*c*sqrt(d)*sgn(b*x^2 + a) + 2*a*d^(3/2)*sgn(b*x^2 + a))*log((sqrt(d)*x - sqrt(d*x^2 + c))^2)/d","A",0
272,1,100,0,0.442988," ","integrate((d*x^2+c)^(1/2)*((b*x^2+a)^2)^(1/2)/x^3,x, algorithm=""giac"")","\frac{2 \, \sqrt{d x^{2} + c} b d \mathrm{sgn}\left(b x^{2} + a\right) + \frac{{\left(2 \, b c d \mathrm{sgn}\left(b x^{2} + a\right) + a d^{2} \mathrm{sgn}\left(b x^{2} + a\right)\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} - \frac{\sqrt{d x^{2} + c} a d \mathrm{sgn}\left(b x^{2} + a\right)}{x^{2}}}{2 \, d}"," ",0,"1/2*(2*sqrt(d*x^2 + c)*b*d*sgn(b*x^2 + a) + (2*b*c*d*sgn(b*x^2 + a) + a*d^2*sgn(b*x^2 + a))*arctan(sqrt(d*x^2 + c)/sqrt(-c))/sqrt(-c) - sqrt(d*x^2 + c)*a*d*sgn(b*x^2 + a)/x^2)/d","A",0
273,1,79,0,0.267010," ","integrate(x^3*(e*x^2+d)^2*(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{1}{12} \, c x^{12} e^{2} + \frac{1}{5} \, c d x^{10} e + \frac{1}{10} \, b x^{10} e^{2} + \frac{1}{8} \, c d^{2} x^{8} + \frac{1}{4} \, b d x^{8} e + \frac{1}{8} \, a x^{8} e^{2} + \frac{1}{6} \, b d^{2} x^{6} + \frac{1}{3} \, a d x^{6} e + \frac{1}{4} \, a d^{2} x^{4}"," ",0,"1/12*c*x^12*e^2 + 1/5*c*d*x^10*e + 1/10*b*x^10*e^2 + 1/8*c*d^2*x^8 + 1/4*b*d*x^8*e + 1/8*a*x^8*e^2 + 1/6*b*d^2*x^6 + 1/3*a*d*x^6*e + 1/4*a*d^2*x^4","A",0
274,1,79,0,0.388162," ","integrate(x^2*(e*x^2+d)^2*(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{1}{11} \, c x^{11} e^{2} + \frac{2}{9} \, c d x^{9} e + \frac{1}{9} \, b x^{9} e^{2} + \frac{1}{7} \, c d^{2} x^{7} + \frac{2}{7} \, b d x^{7} e + \frac{1}{7} \, a x^{7} e^{2} + \frac{1}{5} \, b d^{2} x^{5} + \frac{2}{5} \, a d x^{5} e + \frac{1}{3} \, a d^{2} x^{3}"," ",0,"1/11*c*x^11*e^2 + 2/9*c*d*x^9*e + 1/9*b*x^9*e^2 + 1/7*c*d^2*x^7 + 2/7*b*d*x^7*e + 1/7*a*x^7*e^2 + 1/5*b*d^2*x^5 + 2/5*a*d*x^5*e + 1/3*a*d^2*x^3","A",0
275,1,79,0,0.268627," ","integrate(x*(e*x^2+d)^2*(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{1}{10} \, c x^{10} e^{2} + \frac{1}{4} \, c d x^{8} e + \frac{1}{8} \, b x^{8} e^{2} + \frac{1}{6} \, c d^{2} x^{6} + \frac{1}{3} \, b d x^{6} e + \frac{1}{6} \, a x^{6} e^{2} + \frac{1}{4} \, b d^{2} x^{4} + \frac{1}{2} \, a d x^{4} e + \frac{1}{2} \, a d^{2} x^{2}"," ",0,"1/10*c*x^10*e^2 + 1/4*c*d*x^8*e + 1/8*b*x^8*e^2 + 1/6*c*d^2*x^6 + 1/3*b*d*x^6*e + 1/6*a*x^6*e^2 + 1/4*b*d^2*x^4 + 1/2*a*d*x^4*e + 1/2*a*d^2*x^2","A",0
276,1,76,0,0.353976," ","integrate((e*x^2+d)^2*(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{1}{9} \, c x^{9} e^{2} + \frac{2}{7} \, c d x^{7} e + \frac{1}{7} \, b x^{7} e^{2} + \frac{1}{5} \, c d^{2} x^{5} + \frac{2}{5} \, b d x^{5} e + \frac{1}{5} \, a x^{5} e^{2} + \frac{1}{3} \, b d^{2} x^{3} + \frac{2}{3} \, a d x^{3} e + a d^{2} x"," ",0,"1/9*c*x^9*e^2 + 2/7*c*d*x^7*e + 1/7*b*x^7*e^2 + 1/5*c*d^2*x^5 + 2/5*b*d*x^5*e + 1/5*a*x^5*e^2 + 1/3*b*d^2*x^3 + 2/3*a*d*x^3*e + a*d^2*x","A",0
277,1,79,0,0.262828," ","integrate((e*x^2+d)^2*(c*x^4+b*x^2+a)/x,x, algorithm=""giac"")","\frac{1}{8} \, c x^{8} e^{2} + \frac{1}{3} \, c d x^{6} e + \frac{1}{6} \, b x^{6} e^{2} + \frac{1}{4} \, c d^{2} x^{4} + \frac{1}{2} \, b d x^{4} e + \frac{1}{4} \, a x^{4} e^{2} + \frac{1}{2} \, b d^{2} x^{2} + a d x^{2} e + \frac{1}{2} \, a d^{2} \log\left(x^{2}\right)"," ",0,"1/8*c*x^8*e^2 + 1/3*c*d*x^6*e + 1/6*b*x^6*e^2 + 1/4*c*d^2*x^4 + 1/2*b*d*x^4*e + 1/4*a*x^4*e^2 + 1/2*b*d^2*x^2 + a*d*x^2*e + 1/2*a*d^2*log(x^2)","A",0
278,1,74,0,0.360568," ","integrate((e*x^2+d)^2*(c*x^4+b*x^2+a)/x^2,x, algorithm=""giac"")","\frac{1}{7} \, c x^{7} e^{2} + \frac{2}{5} \, c d x^{5} e + \frac{1}{5} \, b x^{5} e^{2} + \frac{1}{3} \, c d^{2} x^{3} + \frac{2}{3} \, b d x^{3} e + \frac{1}{3} \, a x^{3} e^{2} + b d^{2} x + 2 \, a d x e - \frac{a d^{2}}{x}"," ",0,"1/7*c*x^7*e^2 + 2/5*c*d*x^5*e + 1/5*b*x^5*e^2 + 1/3*c*d^2*x^3 + 2/3*b*d*x^3*e + 1/3*a*x^3*e^2 + b*d^2*x + 2*a*d*x*e - a*d^2/x","A",0
279,1,97,0,0.379489," ","integrate((e*x^2+d)^2*(c*x^4+b*x^2+a)/x^3,x, algorithm=""giac"")","\frac{1}{6} \, c x^{6} e^{2} + \frac{1}{2} \, c d x^{4} e + \frac{1}{4} \, b x^{4} e^{2} + \frac{1}{2} \, c d^{2} x^{2} + b d x^{2} e + \frac{1}{2} \, a x^{2} e^{2} + \frac{1}{2} \, {\left(b d^{2} + 2 \, a d e\right)} \log\left(x^{2}\right) - \frac{b d^{2} x^{2} + 2 \, a d x^{2} e + a d^{2}}{2 \, x^{2}}"," ",0,"1/6*c*x^6*e^2 + 1/2*c*d*x^4*e + 1/4*b*x^4*e^2 + 1/2*c*d^2*x^2 + b*d*x^2*e + 1/2*a*x^2*e^2 + 1/2*(b*d^2 + 2*a*d*e)*log(x^2) - 1/2*(b*d^2*x^2 + 2*a*d*x^2*e + a*d^2)/x^2","A",0
280,1,160,0,0.320771," ","integrate(x^6*(c*x^4+b*x^2+a)/(e*x^2+d)^2,x, algorithm=""giac"")","\frac{{\left(9 \, c d^{4} - 7 \, b d^{3} e + 5 \, a d^{2} e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{11}{2}\right)}}{2 \, \sqrt{d}} + \frac{1}{105} \, {\left(15 \, c x^{7} e^{12} - 42 \, c d x^{5} e^{11} + 21 \, b x^{5} e^{12} + 105 \, c d^{2} x^{3} e^{10} - 70 \, b d x^{3} e^{11} - 420 \, c d^{3} x e^{9} + 35 \, a x^{3} e^{12} + 315 \, b d^{2} x e^{10} - 210 \, a d x e^{11}\right)} e^{\left(-14\right)} - \frac{{\left(c d^{4} x - b d^{3} x e + a d^{2} x e^{2}\right)} e^{\left(-5\right)}}{2 \, {\left(x^{2} e + d\right)}}"," ",0,"1/2*(9*c*d^4 - 7*b*d^3*e + 5*a*d^2*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-11/2)/sqrt(d) + 1/105*(15*c*x^7*e^12 - 42*c*d*x^5*e^11 + 21*b*x^5*e^12 + 105*c*d^2*x^3*e^10 - 70*b*d*x^3*e^11 - 420*c*d^3*x*e^9 + 35*a*x^3*e^12 + 315*b*d^2*x*e^10 - 210*a*d*x*e^11)*e^(-14) - 1/2*(c*d^4*x - b*d^3*x*e + a*d^2*x*e^2)*e^(-5)/(x^2*e + d)","A",0
281,1,125,0,0.277108," ","integrate(x^4*(c*x^4+b*x^2+a)/(e*x^2+d)^2,x, algorithm=""giac"")","-\frac{{\left(7 \, c d^{3} - 5 \, b d^{2} e + 3 \, a d e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{9}{2}\right)}}{2 \, \sqrt{d}} + \frac{1}{15} \, {\left(3 \, c x^{5} e^{8} - 10 \, c d x^{3} e^{7} + 5 \, b x^{3} e^{8} + 45 \, c d^{2} x e^{6} - 30 \, b d x e^{7} + 15 \, a x e^{8}\right)} e^{\left(-10\right)} + \frac{{\left(c d^{3} x - b d^{2} x e + a d x e^{2}\right)} e^{\left(-4\right)}}{2 \, {\left(x^{2} e + d\right)}}"," ",0,"-1/2*(7*c*d^3 - 5*b*d^2*e + 3*a*d*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-9/2)/sqrt(d) + 1/15*(3*c*x^5*e^8 - 10*c*d*x^3*e^7 + 5*b*x^3*e^8 + 45*c*d^2*x*e^6 - 30*b*d*x*e^7 + 15*a*x*e^8)*e^(-10) + 1/2*(c*d^3*x - b*d^2*x*e + a*d*x*e^2)*e^(-4)/(x^2*e + d)","A",0
282,1,91,0,0.335365," ","integrate(x^2*(c*x^4+b*x^2+a)/(e*x^2+d)^2,x, algorithm=""giac"")","\frac{{\left(5 \, c d^{2} - 3 \, b d e + a e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{7}{2}\right)}}{2 \, \sqrt{d}} + \frac{1}{3} \, {\left(c x^{3} e^{4} - 6 \, c d x e^{3} + 3 \, b x e^{4}\right)} e^{\left(-6\right)} - \frac{{\left(c d^{2} x - b d x e + a x e^{2}\right)} e^{\left(-3\right)}}{2 \, {\left(x^{2} e + d\right)}}"," ",0,"1/2*(5*c*d^2 - 3*b*d*e + a*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-7/2)/sqrt(d) + 1/3*(c*x^3*e^4 - 6*c*d*x*e^3 + 3*b*x*e^4)*e^(-6) - 1/2*(c*d^2*x - b*d*x*e + a*x*e^2)*e^(-3)/(x^2*e + d)","A",0
283,1,75,0,0.405500," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^2,x, algorithm=""giac"")","c x e^{\left(-2\right)} - \frac{{\left(3 \, c d^{2} - b d e - a e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{5}{2}\right)}}{2 \, d^{\frac{3}{2}}} + \frac{{\left(c d^{2} x - b d x e + a x e^{2}\right)} e^{\left(-2\right)}}{2 \, {\left(x^{2} e + d\right)} d}"," ",0,"c*x*e^(-2) - 1/2*(3*c*d^2 - b*d*e - a*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-5/2)/d^(3/2) + 1/2*(c*d^2*x - b*d*x*e + a*x*e^2)*e^(-2)/((x^2*e + d)*d)","A",0
284,1,83,0,0.293431," ","integrate((c*x^4+b*x^2+a)/x^2/(e*x^2+d)^2,x, algorithm=""giac"")","\frac{{\left(c d^{2} + b d e - 3 \, a e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{3}{2}\right)}}{2 \, d^{\frac{5}{2}}} - \frac{{\left(c d^{2} x^{2} - b d x^{2} e + 3 \, a x^{2} e^{2} + 2 \, a d e\right)} e^{\left(-1\right)}}{2 \, {\left(x^{3} e + d x\right)} d^{2}}"," ",0,"1/2*(c*d^2 + b*d*e - 3*a*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-3/2)/d^(5/2) - 1/2*(c*d^2*x^2 - b*d*x^2*e + 3*a*x^2*e^2 + 2*a*d*e)*e^(-1)/((x^3*e + d*x)*d^2)","A",0
285,1,94,0,0.260823," ","integrate((c*x^4+b*x^2+a)/x^4/(e*x^2+d)^2,x, algorithm=""giac"")","\frac{{\left(c d^{2} - 3 \, b d e + 5 \, a e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{1}{2}\right)}}{2 \, d^{\frac{7}{2}}} + \frac{c d^{2} x - b d x e + a x e^{2}}{2 \, {\left(x^{2} e + d\right)} d^{3}} - \frac{3 \, b d x^{2} - 6 \, a x^{2} e + a d}{3 \, d^{3} x^{3}}"," ",0,"1/2*(c*d^2 - 3*b*d*e + 5*a*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-1/2)/d^(7/2) + 1/2*(c*d^2*x - b*d*x*e + a*x*e^2)/((x^2*e + d)*d^3) - 1/3*(3*b*d*x^2 - 6*a*x^2*e + a*d)/(d^3*x^3)","A",0
286,1,131,0,0.327232," ","integrate((c*x^4+b*x^2+a)/x^6/(e*x^2+d)^2,x, algorithm=""giac"")","-\frac{{\left(3 \, c d^{2} e - 5 \, b d e^{2} + 7 \, a e^{3}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{1}{2}\right)}}{2 \, d^{\frac{9}{2}}} - \frac{c d^{2} x e - b d x e^{2} + a x e^{3}}{2 \, {\left(x^{2} e + d\right)} d^{4}} - \frac{15 \, c d^{2} x^{4} - 30 \, b d x^{4} e + 45 \, a x^{4} e^{2} + 5 \, b d^{2} x^{2} - 10 \, a d x^{2} e + 3 \, a d^{2}}{15 \, d^{4} x^{5}}"," ",0,"-1/2*(3*c*d^2*e - 5*b*d*e^2 + 7*a*e^3)*arctan(x*e^(1/2)/sqrt(d))*e^(-1/2)/d^(9/2) - 1/2*(c*d^2*x*e - b*d*x*e^2 + a*x*e^3)/((x^2*e + d)*d^4) - 1/15*(15*c*d^2*x^4 - 30*b*d*x^4*e + 45*a*x^4*e^2 + 5*b*d^2*x^2 - 10*a*d*x^2*e + 3*a*d^2)/(d^4*x^5)","A",0
287,1,164,0,0.416973," ","integrate((c*x^4+b*x^2+a)/x^8/(e*x^2+d)^2,x, algorithm=""giac"")","\frac{{\left(5 \, c d^{2} e^{2} - 7 \, b d e^{3} + 9 \, a e^{4}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{1}{2}\right)}}{2 \, d^{\frac{11}{2}}} + \frac{c d^{2} x e^{2} - b d x e^{3} + a x e^{4}}{2 \, {\left(x^{2} e + d\right)} d^{5}} + \frac{210 \, c d^{2} x^{6} e - 315 \, b d x^{6} e^{2} - 35 \, c d^{3} x^{4} + 420 \, a x^{6} e^{3} + 70 \, b d^{2} x^{4} e - 105 \, a d x^{4} e^{2} - 21 \, b d^{3} x^{2} + 42 \, a d^{2} x^{2} e - 15 \, a d^{3}}{105 \, d^{5} x^{7}}"," ",0,"1/2*(5*c*d^2*e^2 - 7*b*d*e^3 + 9*a*e^4)*arctan(x*e^(1/2)/sqrt(d))*e^(-1/2)/d^(11/2) + 1/2*(c*d^2*x*e^2 - b*d*x*e^3 + a*x*e^4)/((x^2*e + d)*d^5) + 1/105*(210*c*d^2*x^6*e - 315*b*d*x^6*e^2 - 35*c*d^3*x^4 + 420*a*x^6*e^3 + 70*b*d^2*x^4*e - 105*a*d*x^4*e^2 - 21*b*d^3*x^2 + 42*a*d^2*x^2*e - 15*a*d^3)/(d^5*x^7)","A",0
288,1,160,0,0.358754," ","integrate(x^6*(c*x^4+b*x^2+a)/(e*x^2+d)^3,x, algorithm=""giac"")","-\frac{{\left(63 \, c d^{3} - 35 \, b d^{2} e + 15 \, a d e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{11}{2}\right)}}{8 \, \sqrt{d}} + \frac{1}{15} \, {\left(3 \, c x^{5} e^{12} - 15 \, c d x^{3} e^{11} + 5 \, b x^{3} e^{12} + 90 \, c d^{2} x e^{10} - 45 \, b d x e^{11} + 15 \, a x e^{12}\right)} e^{\left(-15\right)} + \frac{{\left(17 \, c d^{3} x^{3} e - 13 \, b d^{2} x^{3} e^{2} + 15 \, c d^{4} x + 9 \, a d x^{3} e^{3} - 11 \, b d^{3} x e + 7 \, a d^{2} x e^{2}\right)} e^{\left(-5\right)}}{8 \, {\left(x^{2} e + d\right)}^{2}}"," ",0,"-1/8*(63*c*d^3 - 35*b*d^2*e + 15*a*d*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-11/2)/sqrt(d) + 1/15*(3*c*x^5*e^12 - 15*c*d*x^3*e^11 + 5*b*x^3*e^12 + 90*c*d^2*x*e^10 - 45*b*d*x*e^11 + 15*a*x*e^12)*e^(-15) + 1/8*(17*c*d^3*x^3*e - 13*b*d^2*x^3*e^2 + 15*c*d^4*x + 9*a*d*x^3*e^3 - 11*b*d^3*x*e + 7*a*d^2*x*e^2)*e^(-5)/(x^2*e + d)^2","A",0
289,1,125,0,0.470813," ","integrate(x^4*(c*x^4+b*x^2+a)/(e*x^2+d)^3,x, algorithm=""giac"")","\frac{{\left(35 \, c d^{2} - 15 \, b d e + 3 \, a e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{9}{2}\right)}}{8 \, \sqrt{d}} + \frac{1}{3} \, {\left(c x^{3} e^{6} - 9 \, c d x e^{5} + 3 \, b x e^{6}\right)} e^{\left(-9\right)} - \frac{{\left(13 \, c d^{2} x^{3} e - 9 \, b d x^{3} e^{2} + 11 \, c d^{3} x + 5 \, a x^{3} e^{3} - 7 \, b d^{2} x e + 3 \, a d x e^{2}\right)} e^{\left(-4\right)}}{8 \, {\left(x^{2} e + d\right)}^{2}}"," ",0,"1/8*(35*c*d^2 - 15*b*d*e + 3*a*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-9/2)/sqrt(d) + 1/3*(c*x^3*e^6 - 9*c*d*x*e^5 + 3*b*x*e^6)*e^(-9) - 1/8*(13*c*d^2*x^3*e - 9*b*d*x^3*e^2 + 11*c*d^3*x + 5*a*x^3*e^3 - 7*b*d^2*x*e + 3*a*d*x*e^2)*e^(-4)/(x^2*e + d)^2","A",0
290,1,107,0,0.262847," ","integrate(x^2*(c*x^4+b*x^2+a)/(e*x^2+d)^3,x, algorithm=""giac"")","c x e^{\left(-3\right)} - \frac{{\left(15 \, c d^{2} - 3 \, b d e - a e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{7}{2}\right)}}{8 \, d^{\frac{3}{2}}} + \frac{{\left(9 \, c d^{2} x^{3} e - 5 \, b d x^{3} e^{2} + 7 \, c d^{3} x + a x^{3} e^{3} - 3 \, b d^{2} x e - a d x e^{2}\right)} e^{\left(-3\right)}}{8 \, {\left(x^{2} e + d\right)}^{2} d}"," ",0,"c*x*e^(-3) - 1/8*(15*c*d^2 - 3*b*d*e - a*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-7/2)/d^(3/2) + 1/8*(9*c*d^2*x^3*e - 5*b*d*x^3*e^2 + 7*c*d^3*x + a*x^3*e^3 - 3*b*d^2*x*e - a*d*x*e^2)*e^(-3)/((x^2*e + d)^2*d)","A",0
291,1,101,0,0.311637," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^3,x, algorithm=""giac"")","\frac{{\left(3 \, c d^{2} + b d e + 3 \, a e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{5}{2}\right)}}{8 \, d^{\frac{5}{2}}} - \frac{{\left(5 \, c d^{2} x^{3} e - b d x^{3} e^{2} + 3 \, c d^{3} x - 3 \, a x^{3} e^{3} + b d^{2} x e - 5 \, a d x e^{2}\right)} e^{\left(-2\right)}}{8 \, {\left(x^{2} e + d\right)}^{2} d^{2}}"," ",0,"1/8*(3*c*d^2 + b*d*e + 3*a*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-5/2)/d^(5/2) - 1/8*(5*c*d^2*x^3*e - b*d*x^3*e^2 + 3*c*d^3*x - 3*a*x^3*e^3 + b*d^2*x*e - 5*a*d*x*e^2)*e^(-2)/((x^2*e + d)^2*d^2)","A",0
292,1,110,0,0.316222," ","integrate((c*x^4+b*x^2+a)/x^2/(e*x^2+d)^3,x, algorithm=""giac"")","\frac{{\left(c d^{2} + 3 \, b d e - 15 \, a e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{3}{2}\right)}}{8 \, d^{\frac{7}{2}}} - \frac{a}{d^{3} x} + \frac{{\left(c d^{2} x^{3} e + 3 \, b d x^{3} e^{2} - c d^{3} x - 7 \, a x^{3} e^{3} + 5 \, b d^{2} x e - 9 \, a d x e^{2}\right)} e^{\left(-1\right)}}{8 \, {\left(x^{2} e + d\right)}^{2} d^{3}}"," ",0,"1/8*(c*d^2 + 3*b*d*e - 15*a*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-3/2)/d^(7/2) - a/(d^3*x) + 1/8*(c*d^2*x^3*e + 3*b*d*x^3*e^2 - c*d^3*x - 7*a*x^3*e^3 + 5*b*d^2*x*e - 9*a*d*x*e^2)*e^(-1)/((x^2*e + d)^2*d^3)","A",0
293,1,128,0,0.340400," ","integrate((c*x^4+b*x^2+a)/x^4/(e*x^2+d)^3,x, algorithm=""giac"")","\frac{{\left(3 \, c d^{2} - 15 \, b d e + 35 \, a e^{2}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{1}{2}\right)}}{8 \, d^{\frac{9}{2}}} + \frac{3 \, c d^{2} x^{3} e - 7 \, b d x^{3} e^{2} + 5 \, c d^{3} x + 11 \, a x^{3} e^{3} - 9 \, b d^{2} x e + 13 \, a d x e^{2}}{8 \, {\left(x^{2} e + d\right)}^{2} d^{4}} - \frac{3 \, b d x^{2} - 9 \, a x^{2} e + a d}{3 \, d^{4} x^{3}}"," ",0,"1/8*(3*c*d^2 - 15*b*d*e + 35*a*e^2)*arctan(x*e^(1/2)/sqrt(d))*e^(-1/2)/d^(9/2) + 1/8*(3*c*d^2*x^3*e - 7*b*d*x^3*e^2 + 5*c*d^3*x + 11*a*x^3*e^3 - 9*b*d^2*x*e + 13*a*d*x*e^2)/((x^2*e + d)^2*d^4) - 1/3*(3*b*d*x^2 - 9*a*x^2*e + a*d)/(d^4*x^3)","A",0
294,1,164,0,0.347312," ","integrate((c*x^4+b*x^2+a)/x^6/(e*x^2+d)^3,x, algorithm=""giac"")","-\frac{{\left(15 \, c d^{2} e - 35 \, b d e^{2} + 63 \, a e^{3}\right)} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{1}{2}\right)}}{8 \, d^{\frac{11}{2}}} - \frac{7 \, c d^{2} x^{3} e^{2} - 11 \, b d x^{3} e^{3} + 9 \, c d^{3} x e + 15 \, a x^{3} e^{4} - 13 \, b d^{2} x e^{2} + 17 \, a d x e^{3}}{8 \, {\left(x^{2} e + d\right)}^{2} d^{5}} - \frac{15 \, c d^{2} x^{4} - 45 \, b d x^{4} e + 90 \, a x^{4} e^{2} + 5 \, b d^{2} x^{2} - 15 \, a d x^{2} e + 3 \, a d^{2}}{15 \, d^{5} x^{5}}"," ",0,"-1/8*(15*c*d^2*e - 35*b*d*e^2 + 63*a*e^3)*arctan(x*e^(1/2)/sqrt(d))*e^(-1/2)/d^(11/2) - 1/8*(7*c*d^2*x^3*e^2 - 11*b*d*x^3*e^3 + 9*c*d^3*x*e + 15*a*x^3*e^4 - 13*b*d^2*x*e^2 + 17*a*d*x*e^3)/((x^2*e + d)^2*d^5) - 1/15*(15*c*d^2*x^4 - 45*b*d*x^4*e + 90*a*x^4*e^2 + 5*b*d^2*x^2 - 15*a*d*x^2*e + 3*a*d^2)/(d^5*x^5)","A",0
295,1,236,0,1.728467," ","integrate(x^9/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{d^{4} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c d^{2} e^{3} - b d e^{4} + a e^{5}\right)}} - \frac{{\left(b^{3} d - 2 \, a b c d - a b^{2} e + a^{2} c e\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(c^{4} d^{2} - b c^{3} d e + a c^{3} e^{2}\right)}} + \frac{{\left(b^{4} d - 4 \, a b^{2} c d + 2 \, a^{2} c^{2} d - a b^{3} e + 3 \, a^{2} b c e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(c^{4} d^{2} - b c^{3} d e + a c^{3} e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{{\left(c x^{4} e - 2 \, c d x^{2} - 2 \, b x^{2} e\right)} e^{\left(-2\right)}}{4 \, c^{2}}"," ",0,"1/2*d^4*log(abs(x^2*e + d))/(c*d^2*e^3 - b*d*e^4 + a*e^5) - 1/4*(b^3*d - 2*a*b*c*d - a*b^2*e + a^2*c*e)*log(c*x^4 + b*x^2 + a)/(c^4*d^2 - b*c^3*d*e + a*c^3*e^2) + 1/2*(b^4*d - 4*a*b^2*c*d + 2*a^2*c^2*d - a*b^3*e + 3*a^2*b*c*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((c^4*d^2 - b*c^3*d*e + a*c^3*e^2)*sqrt(-b^2 + 4*a*c)) + 1/4*(c*x^4*e - 2*c*d*x^2 - 2*b*x^2*e)*e^(-2)/c^2","A",0
296,1,194,0,2.185341," ","integrate(x^7/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{d^{3} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c d^{2} e^{2} - b d e^{3} + a e^{4}\right)}} + \frac{x^{2} e^{\left(-1\right)}}{2 \, c} + \frac{{\left(b^{2} d - a c d - a b e\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(c^{3} d^{2} - b c^{2} d e + a c^{2} e^{2}\right)}} - \frac{{\left(b^{3} d - 3 \, a b c d - 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 \, {\left(c^{3} d^{2} - b c^{2} d e + a c^{2} e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}}"," ",0,"-1/2*d^3*log(abs(x^2*e + d))/(c*d^2*e^2 - b*d*e^3 + a*e^4) + 1/2*x^2*e^(-1)/c + 1/4*(b^2*d - a*c*d - a*b*e)*log(c*x^4 + b*x^2 + a)/(c^3*d^2 - b*c^2*d*e + a*c^2*e^2) - 1/2*(b^3*d - 3*a*b*c*d - a*b^2*e + 2*a^2*c*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((c^3*d^2 - b*c^2*d*e + a*c^2*e^2)*sqrt(-b^2 + 4*a*c))","A",0
297,1,157,0,1.843176," ","integrate(x^5/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{d^{2} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c d^{2} e - b d e^{2} + a e^{3}\right)}} - \frac{{\left(b d - a e\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)}} + \frac{{\left(b^{2} d - 2 \, a c d - a b e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}}"," ",0,"1/2*d^2*log(abs(x^2*e + d))/(c*d^2*e - b*d*e^2 + a*e^3) - 1/4*(b*d - a*e)*log(c*x^4 + b*x^2 + a)/(c^2*d^2 - b*c*d*e + a*c*e^2) + 1/2*(b^2*d - 2*a*c*d - a*b*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((c^2*d^2 - b*c*d*e + a*c*e^2)*sqrt(-b^2 + 4*a*c))","A",0
298,1,133,0,1.719795," ","integrate(x^3/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{d e \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c d^{2} e - b d e^{2} + a e^{3}\right)}} + \frac{d \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(c d^{2} - b d e + a e^{2}\right)}} - \frac{{\left(b d - 2 \, a e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}}"," ",0,"-1/2*d*e*log(abs(x^2*e + d))/(c*d^2*e - b*d*e^2 + a*e^3) + 1/4*d*log(c*x^4 + b*x^2 + a)/(c*d^2 - b*d*e + a*e^2) - 1/2*(b*d - 2*a*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((c*d^2 - b*d*e + a*e^2)*sqrt(-b^2 + 4*a*c))","A",0
299,1,134,0,1.907529," ","integrate(x/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{e \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(c d^{2} - b d e + a e^{2}\right)}} + \frac{e^{2} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c d^{2} e - b d e^{2} + a e^{3}\right)}} + \frac{{\left(2 \, c d - b e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}}"," ",0,"-1/4*e*log(c*x^4 + b*x^2 + a)/(c*d^2 - b*d*e + a*e^2) + 1/2*e^2*log(abs(x^2*e + d))/(c*d^2*e - b*d*e^2 + a*e^3) + 1/2*(2*c*d - b*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((c*d^2 - b*d*e + a*e^2)*sqrt(-b^2 + 4*a*c))","A",0
300,1,172,0,1.916888," ","integrate(1/x/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(c d - b e\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(a c d^{2} - a b d e + a^{2} e^{2}\right)}} - \frac{e^{3} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c d^{3} e - b d^{2} e^{2} + a d e^{3}\right)}} - \frac{{\left(b c d - b^{2} e + 2 \, a c e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{\log\left(x^{2}\right)}{2 \, a d}"," ",0,"-1/4*(c*d - b*e)*log(c*x^4 + b*x^2 + a)/(a*c*d^2 - a*b*d*e + a^2*e^2) - 1/2*e^3*log(abs(x^2*e + d))/(c*d^3*e - b*d^2*e^2 + a*d*e^3) - 1/2*(b*c*d - b^2*e + 2*a*c*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((a*c*d^2 - a*b*d*e + a^2*e^2)*sqrt(-b^2 + 4*a*c)) + 1/2*log(x^2)/(a*d)","A",0
301,1,237,0,1.962470," ","integrate(1/x^3/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{{\left(b c d - b^{2} e + a c e\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2}\right)}} + \frac{e^{4} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c d^{4} e - b d^{3} e^{2} + a d^{2} e^{3}\right)}} + \frac{{\left(b^{2} c d - 2 \, a c^{2} d - b^{3} e + 3 \, a b c e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{{\left(b d + a e\right)} \log\left(x^{2}\right)}{2 \, a^{2} d^{2}} + \frac{b d x^{2} + a x^{2} e - a d}{2 \, a^{2} d^{2} x^{2}}"," ",0,"1/4*(b*c*d - b^2*e + a*c*e)*log(c*x^4 + b*x^2 + a)/(a^2*c*d^2 - a^2*b*d*e + a^3*e^2) + 1/2*e^4*log(abs(x^2*e + d))/(c*d^4*e - b*d^3*e^2 + a*d^2*e^3) + 1/2*(b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*sqrt(-b^2 + 4*a*c)) - 1/2*(b*d + a*e)*log(x^2)/(a^2*d^2) + 1/2*(b*d*x^2 + a*x^2*e - a*d)/(a^2*d^2*x^2)","A",0
302,1,332,0,1.461879," ","integrate(1/x^5/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(b^{2} c d - a c^{2} d - b^{3} e + 2 \, a b c e\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(a^{3} c d^{2} - a^{3} b d e + a^{4} e^{2}\right)}} - \frac{e^{5} \log\left({\left| x^{2} e + d \right|}\right)}{2 \, {\left(c d^{5} e - b d^{4} e^{2} + a d^{3} e^{3}\right)}} - \frac{{\left(b^{3} c d - 3 \, a b c^{2} d - b^{4} e + 4 \, a b^{2} c e - 2 \, a^{2} c^{2} e\right)} \arctan\left(\frac{2 \, c x^{2} + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{2 \, {\left(a^{3} c d^{2} - a^{3} b d e + a^{4} e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{{\left(b^{2} d^{2} - a c d^{2} + a b d e + a^{2} e^{2}\right)} \log\left(x^{2}\right)}{2 \, a^{3} d^{3}} - \frac{3 \, b^{2} d^{2} x^{4} - 3 \, a c d^{2} x^{4} + 3 \, a b d x^{4} e + 3 \, a^{2} x^{4} e^{2} - 2 \, a b d^{2} x^{2} - 2 \, a^{2} d x^{2} e + a^{2} d^{2}}{4 \, a^{3} d^{3} x^{4}}"," ",0,"-1/4*(b^2*c*d - a*c^2*d - b^3*e + 2*a*b*c*e)*log(c*x^4 + b*x^2 + a)/(a^3*c*d^2 - a^3*b*d*e + a^4*e^2) - 1/2*e^5*log(abs(x^2*e + d))/(c*d^5*e - b*d^4*e^2 + a*d^3*e^3) - 1/2*(b^3*c*d - 3*a*b*c^2*d - b^4*e + 4*a*b^2*c*e - 2*a^2*c^2*e)*arctan((2*c*x^2 + b)/sqrt(-b^2 + 4*a*c))/((a^3*c*d^2 - a^3*b*d*e + a^4*e^2)*sqrt(-b^2 + 4*a*c)) + 1/2*(b^2*d^2 - a*c*d^2 + a*b*d*e + a^2*e^2)*log(x^2)/(a^3*d^3) - 1/4*(3*b^2*d^2*x^4 - 3*a*c*d^2*x^4 + 3*a*b*d*x^4*e + 3*a^2*x^4*e^2 - 2*a*b*d^2*x^2 - 2*a^2*d*x^2*e + a^2*d^2)/(a^3*d^3*x^4)","A",0
303,1,12506,0,12.649136," ","integrate(x^8/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{d^{\frac{7}{2}} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{1}{2}\right)}}{c d^{2} e^{2} - b d e^{3} + a e^{4}} + \frac{{\left({\left(2 \, b^{7} c^{8} - 16 \, a b^{5} c^{9} + 36 \, a^{2} b^{3} c^{10} - 16 \, 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} + 8 \, \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} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{8} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{8} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{9} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{9} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{9} - 2 \, \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} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{9} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{10}\right)} d^{5} - {\left(4 \, b^{8} c^{7} - 30 \, a b^{6} c^{8} + 58 \, a^{2} b^{4} c^{9} - 8 \, a^{3} b^{2} c^{10} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{5} + 15 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{6} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} - 29 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{7} - 14 \, \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} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{8} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{8} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{9} - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{7} + 14 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{9}\right)} d^{4} e - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{4} - 9 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{5} + 2 \, a b^{6} c^{5} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} + 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{6} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{6} - 18 \, a^{2} b^{4} c^{6} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{7} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{7} - 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{7} + 48 \, a^{3} b^{2} c^{7} + 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{8} - 32 \, a^{4} c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{5} + 10 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{6} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{7}\right)} d^{3} {\left| -c^{3} d^{2} + b c^{2} d e - a c^{2} e^{2} \right|} + {\left(2 \, b^{9} c^{6} - 8 \, a b^{7} c^{7} - 24 \, a^{2} b^{5} c^{8} + 104 \, a^{3} b^{3} c^{9} - 32 \, a^{4} b c^{10} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{9} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} - 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{7} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{7} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{8} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{8} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{8} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{9} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{7} c^{6} + 24 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{8} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{9}\right)} d^{3} e^{2} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{4} + 2 \, a b^{7} c^{4} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{5} - 16 \, a^{2} b^{5} c^{5} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{6} + 32 \, a^{3} b^{3} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{5}\right)} d^{2} {\left| -c^{3} d^{2} + b c^{2} d e - a c^{2} e^{2} \right|} e - {\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)} {\left(c^{3} d^{2} - b c^{2} d e + a c^{2} e^{2}\right)}^{2} d - {\left(6 \, a b^{8} c^{6} - 42 \, a^{2} b^{6} c^{7} + 68 \, a^{3} b^{4} c^{8} + 16 \, a^{4} b^{2} c^{9} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{8} c^{4} + 21 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{5} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{5} - 34 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{6} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{6} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{7} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{7} + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{7} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{8} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{6} c^{6} + 18 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{7} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{8}\right)} d^{2} e^{3} - 2 \, {\left(2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{3} - 17 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} + 4 \, a^{2} b^{6} c^{4} + 40 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{5} + 18 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} - 34 \, a^{3} b^{4} c^{5} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{6} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} - 9 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} + 80 \, a^{4} b^{2} c^{6} + 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{7} - 32 \, a^{5} c^{7} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{4} + 18 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{5} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{6}\right)} d {\left| -c^{3} d^{2} + b c^{2} d e - a c^{2} e^{2} \right|} e^{2} + {\left(2 \, a b^{6} c^{2} - 18 \, a^{2} b^{4} c^{3} + 48 \, a^{3} b^{2} c^{4} - 32 \, a^{4} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 10 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} {\left(c^{3} d^{2} - b c^{2} d e + a c^{2} e^{2}\right)}^{2} e + {\left(6 \, a^{2} b^{7} c^{6} - 44 \, a^{3} b^{5} c^{7} + 84 \, a^{4} b^{3} c^{8} - 16 \, a^{5} b c^{9} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c^{4} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{5} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{5} - 42 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{6} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{6} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{7} + 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} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{7} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{8} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{6} + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{7} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{8}\right)} d e^{4} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{3} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{4} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{4} + 2 \, a^{3} b^{5} c^{4} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{5} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{5} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} - 16 \, a^{4} b^{3} c^{5} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} + 32 \, a^{5} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{5}\right)} {\left| -c^{3} d^{2} + b c^{2} d e - a c^{2} e^{2} \right|} e^{3} - {\left(2 \, a^{3} b^{6} c^{6} - 14 \, a^{4} b^{4} c^{7} + 24 \, 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} + 7 \, \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} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{6} - 6 \, \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} + 3 \, \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} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{7}\right)} e^{5}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c^{3} d^{2} - b^{2} c^{2} d e + a b c^{2} e^{2} + \sqrt{{\left(b c^{3} d^{2} - b^{2} c^{2} d e + a b c^{2} e^{2}\right)}^{2} - 4 \, {\left(a c^{3} d^{2} - a b c^{2} d e + a^{2} c^{2} e^{2}\right)} {\left(c^{4} d^{2} - b c^{3} d e + a c^{3} e^{2}\right)}}}{c^{4} d^{2} - b c^{3} d e + a c^{3} e^{2}}}}\right)}{8 \, {\left({\left(a b^{4} c^{7} - 8 \, a^{2} b^{2} c^{8} - 2 \, a b^{3} c^{8} + 16 \, a^{3} c^{9} + 8 \, a^{2} b c^{9} + a b^{2} c^{9} - 4 \, a^{2} c^{10}\right)} d^{4} {\left| -c^{3} d^{2} + b c^{2} d e - a c^{2} e^{2} \right|} {\left| c \right|} - 2 \, {\left(a b^{5} c^{6} - 8 \, a^{2} b^{3} c^{7} - 2 \, a b^{4} c^{7} + 16 \, a^{3} b c^{8} + 8 \, a^{2} b^{2} c^{8} + a b^{3} c^{8} - 4 \, a^{2} b c^{9}\right)} d^{3} {\left| -c^{3} d^{2} + b c^{2} d e - a c^{2} e^{2} \right|} {\left| c \right|} e + {\left(a b^{6} c^{5} - 6 \, a^{2} b^{4} c^{6} - 2 \, a b^{5} c^{6} + 4 \, a^{2} b^{3} c^{7} + a b^{4} c^{7} + 32 \, a^{4} c^{8} + 16 \, a^{3} b c^{8} - 2 \, a^{2} b^{2} c^{8} - 8 \, a^{3} c^{9}\right)} d^{2} {\left| -c^{3} d^{2} + b c^{2} d e - a c^{2} e^{2} \right|} {\left| c \right|} e^{2} - 2 \, {\left(a^{2} b^{5} c^{5} - 8 \, a^{3} b^{3} c^{6} - 2 \, a^{2} b^{4} c^{6} + 16 \, a^{4} b c^{7} + 8 \, a^{3} b^{2} c^{7} + a^{2} b^{3} c^{7} - 4 \, a^{3} b c^{8}\right)} d {\left| -c^{3} d^{2} + b c^{2} d e - a c^{2} e^{2} \right|} {\left| c \right|} e^{3} + {\left(a^{3} b^{4} c^{5} - 8 \, a^{4} b^{2} c^{6} - 2 \, a^{3} b^{3} c^{6} + 16 \, a^{5} c^{7} + 8 \, a^{4} b c^{7} + a^{3} b^{2} c^{7} - 4 \, a^{4} c^{8}\right)} {\left| -c^{3} d^{2} + b c^{2} d e - a c^{2} e^{2} \right|} {\left| c \right|} e^{4}\right)}} - \frac{{\left({\left(2 \, b^{7} c^{8} - 16 \, a b^{5} c^{9} + 36 \, a^{2} b^{3} c^{10} - 16 \, 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} + 8 \, \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} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{8} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{8} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{9} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{9} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{9} - 2 \, \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} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{9} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{10}\right)} d^{5} - {\left(4 \, b^{8} c^{7} - 30 \, a b^{6} c^{8} + 58 \, a^{2} b^{4} c^{9} - 8 \, a^{3} b^{2} c^{10} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{5} + 15 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{6} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} - 29 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{7} - 14 \, \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} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{8} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{8} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{9} - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{6} c^{7} + 14 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{8} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{9}\right)} d^{4} e + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{4} - 9 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{5} - 2 \, a b^{6} c^{5} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} + 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{6} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{6} + 18 \, a^{2} b^{4} c^{6} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{7} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{7} - 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{7} - 48 \, a^{3} b^{2} c^{7} + 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{8} + 32 \, a^{4} c^{8} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{5} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{6} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{7}\right)} d^{3} {\left| -c^{3} d^{2} + b c^{2} d e - a c^{2} e^{2} \right|} + {\left(2 \, b^{9} c^{6} - 8 \, a b^{7} c^{7} - 24 \, a^{2} b^{5} c^{8} + 104 \, a^{3} b^{3} c^{9} - 32 \, a^{4} b c^{10} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{9} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{8} c^{5} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{6} - 52 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{7} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{7} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{8} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{8} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{8} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{9} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{7} c^{6} + 24 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{8} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{9}\right)} d^{3} e^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{4} - 2 \, a b^{7} c^{4} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{5} + 16 \, a^{2} b^{5} c^{5} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{6} - 32 \, a^{3} b^{3} c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{5}\right)} d^{2} {\left| -c^{3} d^{2} + b c^{2} d e - a c^{2} e^{2} \right|} e - {\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)} {\left(c^{3} d^{2} - b c^{2} d e + a c^{2} e^{2}\right)}^{2} d - {\left(6 \, a b^{8} c^{6} - 42 \, a^{2} b^{6} c^{7} + 68 \, a^{3} b^{4} c^{8} + 16 \, a^{4} b^{2} c^{9} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{8} c^{4} + 21 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{5} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{5} - 34 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{6} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{6} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{7} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{7} + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{7} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{8} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{6} c^{6} + 18 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{7} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{8}\right)} d^{2} e^{3} + 2 \, {\left(2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{3} - 17 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{4} - 4 \, a^{2} b^{6} c^{4} + 40 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{5} + 18 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{5} + 34 \, a^{3} b^{4} c^{5} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{6} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} - 9 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{6} - 80 \, a^{4} b^{2} c^{6} + 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{7} + 32 \, a^{5} c^{7} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{4} - 18 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{5} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{6}\right)} d {\left| -c^{3} d^{2} + b c^{2} d e - a c^{2} e^{2} \right|} e^{2} + {\left(2 \, a b^{6} c^{2} - 18 \, a^{2} b^{4} c^{3} + 48 \, a^{3} b^{2} c^{4} - 32 \, a^{4} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{2} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{3} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 10 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} {\left(c^{3} d^{2} - b c^{2} d e + a c^{2} e^{2}\right)}^{2} e + {\left(6 \, a^{2} b^{7} c^{6} - 44 \, a^{3} b^{5} c^{7} + 84 \, a^{4} b^{3} c^{8} - 16 \, a^{5} b c^{9} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c^{4} + 22 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{5} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{5} - 42 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{6} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{6} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{7} + 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} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{7} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{8} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{6} + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{7} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{8}\right)} d e^{4} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{3} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{4} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{4} - 2 \, a^{3} b^{5} c^{4} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{5} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{5} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{5} + 16 \, a^{4} b^{3} c^{5} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{6} - 32 \, a^{5} b c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{5}\right)} {\left| -c^{3} d^{2} + b c^{2} d e - a c^{2} e^{2} \right|} e^{3} - {\left(2 \, a^{3} b^{6} c^{6} - 14 \, a^{4} b^{4} c^{7} + 24 \, 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} + 7 \, \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} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{6} - 6 \, \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} + 3 \, \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} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{7}\right)} e^{5}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c^{3} d^{2} - b^{2} c^{2} d e + a b c^{2} e^{2} - \sqrt{{\left(b c^{3} d^{2} - b^{2} c^{2} d e + a b c^{2} e^{2}\right)}^{2} - 4 \, {\left(a c^{3} d^{2} - a b c^{2} d e + a^{2} c^{2} e^{2}\right)} {\left(c^{4} d^{2} - b c^{3} d e + a c^{3} e^{2}\right)}}}{c^{4} d^{2} - b c^{3} d e + a c^{3} e^{2}}}}\right)}{8 \, {\left({\left(a b^{4} c^{7} - 8 \, a^{2} b^{2} c^{8} - 2 \, a b^{3} c^{8} + 16 \, a^{3} c^{9} + 8 \, a^{2} b c^{9} + a b^{2} c^{9} - 4 \, a^{2} c^{10}\right)} d^{4} {\left| -c^{3} d^{2} + b c^{2} d e - a c^{2} e^{2} \right|} {\left| c \right|} - 2 \, {\left(a b^{5} c^{6} - 8 \, a^{2} b^{3} c^{7} - 2 \, a b^{4} c^{7} + 16 \, a^{3} b c^{8} + 8 \, a^{2} b^{2} c^{8} + a b^{3} c^{8} - 4 \, a^{2} b c^{9}\right)} d^{3} {\left| -c^{3} d^{2} + b c^{2} d e - a c^{2} e^{2} \right|} {\left| c \right|} e + {\left(a b^{6} c^{5} - 6 \, a^{2} b^{4} c^{6} - 2 \, a b^{5} c^{6} + 4 \, a^{2} b^{3} c^{7} + a b^{4} c^{7} + 32 \, a^{4} c^{8} + 16 \, a^{3} b c^{8} - 2 \, a^{2} b^{2} c^{8} - 8 \, a^{3} c^{9}\right)} d^{2} {\left| -c^{3} d^{2} + b c^{2} d e - a c^{2} e^{2} \right|} {\left| c \right|} e^{2} - 2 \, {\left(a^{2} b^{5} c^{5} - 8 \, a^{3} b^{3} c^{6} - 2 \, a^{2} b^{4} c^{6} + 16 \, a^{4} b c^{7} + 8 \, a^{3} b^{2} c^{7} + a^{2} b^{3} c^{7} - 4 \, a^{3} b c^{8}\right)} d {\left| -c^{3} d^{2} + b c^{2} d e - a c^{2} e^{2} \right|} {\left| c \right|} e^{3} + {\left(a^{3} b^{4} c^{5} - 8 \, a^{4} b^{2} c^{6} - 2 \, a^{3} b^{3} c^{6} + 16 \, a^{5} c^{7} + 8 \, a^{4} b c^{7} + a^{3} b^{2} c^{7} - 4 \, a^{4} c^{8}\right)} {\left| -c^{3} d^{2} + b c^{2} d e - a c^{2} e^{2} \right|} {\left| c \right|} e^{4}\right)}} + \frac{{\left(c^{2} x^{3} e^{2} - 3 \, c^{2} d x e - 3 \, b c x e^{2}\right)} e^{\left(-3\right)}}{3 \, c^{3}}"," ",0,"d^(7/2)*arctan(x*e^(1/2)/sqrt(d))*e^(-1/2)/(c*d^2*e^2 - b*d*e^3 + a*e^4) + 1/8*((2*b^7*c^8 - 16*a*b^5*c^9 + 36*a^2*b^3*c^10 - 16*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 + 8*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 - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^8 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^9 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^9 - 2*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 + 8*(b^2 - 4*a*c)*a*b^3*c^9 - 4*(b^2 - 4*a*c)*a^2*b*c^10)*d^5 - (4*b^8*c^7 - 30*a*b^6*c^8 + 58*a^2*b^4*c^9 - 8*a^3*b^2*c^10 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^5 + 15*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^6 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^6 - 29*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 - 14*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 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^8 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 - 4*(b^2 - 4*a*c)*b^6*c^7 + 14*(b^2 - 4*a*c)*a*b^4*c^8 - 2*(b^2 - 4*a*c)*a^2*b^2*c^9)*d^4*e - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^4 - 9*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^5 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^5 + 2*a*b^6*c^5 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^6 + 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^6 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^6 - 18*a^2*b^4*c^6 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^7 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^7 - 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^7 + 48*a^3*b^2*c^7 + 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^8 - 32*a^4*c^8 - 2*(b^2 - 4*a*c)*a*b^4*c^5 + 10*(b^2 - 4*a*c)*a^2*b^2*c^6 - 8*(b^2 - 4*a*c)*a^3*c^7)*d^3*abs(-c^3*d^2 + b*c^2*d*e - a*c^2*e^2) + (2*b^9*c^6 - 8*a*b^7*c^7 - 24*a^2*b^5*c^8 + 104*a^3*b^3*c^9 - 32*a^4*b*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^9*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^8*c^5 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^6 - 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^7 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^8 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^8 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^9 - 2*(b^2 - 4*a*c)*b^7*c^6 + 24*(b^2 - 4*a*c)*a^2*b^3*c^8 - 8*(b^2 - 4*a*c)*a^3*b*c^9)*d^3*e^2 + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^3 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^4 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^4 + 2*a*b^7*c^4 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^5 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^5 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^5 - 16*a^2*b^5*c^5 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^6 + 32*a^3*b^3*c^6 - 2*(b^2 - 4*a*c)*a*b^5*c^4 + 8*(b^2 - 4*a*c)*a^2*b^3*c^5)*d^2*abs(-c^3*d^2 + b*c^2*d*e - a*c^2*e^2)*e - (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^3*d^2 - b*c^2*d*e + a*c^2*e^2)^2*d - (6*a*b^8*c^6 - 42*a^2*b^6*c^7 + 68*a^3*b^4*c^8 + 16*a^4*b^2*c^9 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^8*c^4 + 21*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^5 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^5 - 34*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^6 - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^6 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^7 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^7 + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^8 - 6*(b^2 - 4*a*c)*a*b^6*c^6 + 18*(b^2 - 4*a*c)*a^2*b^4*c^7 + 4*(b^2 - 4*a*c)*a^3*b^2*c^8)*d^2*e^3 - 2*(2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^3 - 17*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^4 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^4 + 4*a^2*b^6*c^4 + 40*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^5 + 18*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^5 + 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^5 - 34*a^3*b^4*c^5 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*c^6 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^6 - 9*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^6 + 80*a^4*b^2*c^6 + 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^7 - 32*a^5*c^7 - 4*(b^2 - 4*a*c)*a^2*b^4*c^4 + 18*(b^2 - 4*a*c)*a^3*b^2*c^5 - 8*(b^2 - 4*a*c)*a^4*c^6)*d*abs(-c^3*d^2 + b*c^2*d*e - a*c^2*e^2)*e^2 + (2*a*b^6*c^2 - 18*a^2*b^4*c^3 + 48*a^3*b^2*c^4 - 32*a^4*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6 + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^3 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 - 2*(b^2 - 4*a*c)*a*b^4*c^2 + 10*(b^2 - 4*a*c)*a^2*b^2*c^3 - 8*(b^2 - 4*a*c)*a^3*c^4)*(c^3*d^2 - b*c^2*d*e + a*c^2*e^2)^2*e + (6*a^2*b^7*c^6 - 44*a^3*b^5*c^7 + 84*a^4*b^3*c^8 - 16*a^5*b*c^9 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c^4 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^5 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^5 - 42*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^6 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^6 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^7 + 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 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^7 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^8 - 6*(b^2 - 4*a*c)*a^2*b^5*c^6 + 20*(b^2 - 4*a*c)*a^3*b^3*c^7 - 4*(b^2 - 4*a*c)*a^4*b*c^8)*d*e^4 + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^3 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^4 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^4 + 2*a^3*b^5*c^4 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^5 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^5 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^5 - 16*a^4*b^3*c^5 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^6 + 32*a^5*b*c^6 - 2*(b^2 - 4*a*c)*a^3*b^3*c^4 + 8*(b^2 - 4*a*c)*a^4*b*c^5)*abs(-c^3*d^2 + b*c^2*d*e - a*c^2*e^2)*e^3 - (2*a^3*b^6*c^6 - 14*a^4*b^4*c^7 + 24*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 + 7*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 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^6 - 6*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 + 3*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 + 6*(b^2 - 4*a*c)*a^4*b^2*c^7)*e^5)*arctan(2*sqrt(1/2)*x/sqrt((b*c^3*d^2 - b^2*c^2*d*e + a*b*c^2*e^2 + sqrt((b*c^3*d^2 - b^2*c^2*d*e + a*b*c^2*e^2)^2 - 4*(a*c^3*d^2 - a*b*c^2*d*e + a^2*c^2*e^2)*(c^4*d^2 - b*c^3*d*e + a*c^3*e^2)))/(c^4*d^2 - b*c^3*d*e + a*c^3*e^2)))/((a*b^4*c^7 - 8*a^2*b^2*c^8 - 2*a*b^3*c^8 + 16*a^3*c^9 + 8*a^2*b*c^9 + a*b^2*c^9 - 4*a^2*c^10)*d^4*abs(-c^3*d^2 + b*c^2*d*e - a*c^2*e^2)*abs(c) - 2*(a*b^5*c^6 - 8*a^2*b^3*c^7 - 2*a*b^4*c^7 + 16*a^3*b*c^8 + 8*a^2*b^2*c^8 + a*b^3*c^8 - 4*a^2*b*c^9)*d^3*abs(-c^3*d^2 + b*c^2*d*e - a*c^2*e^2)*abs(c)*e + (a*b^6*c^5 - 6*a^2*b^4*c^6 - 2*a*b^5*c^6 + 4*a^2*b^3*c^7 + a*b^4*c^7 + 32*a^4*c^8 + 16*a^3*b*c^8 - 2*a^2*b^2*c^8 - 8*a^3*c^9)*d^2*abs(-c^3*d^2 + b*c^2*d*e - a*c^2*e^2)*abs(c)*e^2 - 2*(a^2*b^5*c^5 - 8*a^3*b^3*c^6 - 2*a^2*b^4*c^6 + 16*a^4*b*c^7 + 8*a^3*b^2*c^7 + a^2*b^3*c^7 - 4*a^3*b*c^8)*d*abs(-c^3*d^2 + b*c^2*d*e - a*c^2*e^2)*abs(c)*e^3 + (a^3*b^4*c^5 - 8*a^4*b^2*c^6 - 2*a^3*b^3*c^6 + 16*a^5*c^7 + 8*a^4*b*c^7 + a^3*b^2*c^7 - 4*a^4*c^8)*abs(-c^3*d^2 + b*c^2*d*e - a*c^2*e^2)*abs(c)*e^4) - 1/8*((2*b^7*c^8 - 16*a*b^5*c^9 + 36*a^2*b^3*c^10 - 16*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 + 8*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 - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^8 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^9 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^9 - 2*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 + 8*(b^2 - 4*a*c)*a*b^3*c^9 - 4*(b^2 - 4*a*c)*a^2*b*c^10)*d^5 - (4*b^8*c^7 - 30*a*b^6*c^8 + 58*a^2*b^4*c^9 - 8*a^3*b^2*c^10 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^5 + 15*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^6 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^6 - 29*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 - 14*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 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^8 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^9 - 4*(b^2 - 4*a*c)*b^6*c^7 + 14*(b^2 - 4*a*c)*a*b^4*c^8 - 2*(b^2 - 4*a*c)*a^2*b^2*c^9)*d^4*e + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^4 - 9*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^5 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^5 - 2*a*b^6*c^5 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^6 + 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^6 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^6 + 18*a^2*b^4*c^6 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^7 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^7 - 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^7 - 48*a^3*b^2*c^7 + 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^8 + 32*a^4*c^8 + 2*(b^2 - 4*a*c)*a*b^4*c^5 - 10*(b^2 - 4*a*c)*a^2*b^2*c^6 + 8*(b^2 - 4*a*c)*a^3*c^7)*d^3*abs(-c^3*d^2 + b*c^2*d*e - a*c^2*e^2) + (2*b^9*c^6 - 8*a*b^7*c^7 - 24*a^2*b^5*c^8 + 104*a^3*b^3*c^9 - 32*a^4*b*c^10 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^9*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^8*c^5 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^6 - 52*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^7 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^8 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^8 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^8 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^9 - 2*(b^2 - 4*a*c)*b^7*c^6 + 24*(b^2 - 4*a*c)*a^2*b^3*c^8 - 8*(b^2 - 4*a*c)*a^3*b*c^9)*d^3*e^2 - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^3 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^4 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^4 - 2*a*b^7*c^4 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^5 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^5 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^5 + 16*a^2*b^5*c^5 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^6 - 32*a^3*b^3*c^6 + 2*(b^2 - 4*a*c)*a*b^5*c^4 - 8*(b^2 - 4*a*c)*a^2*b^3*c^5)*d^2*abs(-c^3*d^2 + b*c^2*d*e - a*c^2*e^2)*e - (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^3*d^2 - b*c^2*d*e + a*c^2*e^2)^2*d - (6*a*b^8*c^6 - 42*a^2*b^6*c^7 + 68*a^3*b^4*c^8 + 16*a^4*b^2*c^9 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^8*c^4 + 21*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^5 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^5 - 34*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^6 - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^6 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^7 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^7 + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^7 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^8 - 6*(b^2 - 4*a*c)*a*b^6*c^6 + 18*(b^2 - 4*a*c)*a^2*b^4*c^7 + 4*(b^2 - 4*a*c)*a^3*b^2*c^8)*d^2*e^3 + 2*(2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^3 - 17*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^4 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^4 - 4*a^2*b^6*c^4 + 40*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^5 + 18*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^5 + 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^5 + 34*a^3*b^4*c^5 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*c^6 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^6 - 9*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^6 - 80*a^4*b^2*c^6 + 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^7 + 32*a^5*c^7 + 4*(b^2 - 4*a*c)*a^2*b^4*c^4 - 18*(b^2 - 4*a*c)*a^3*b^2*c^5 + 8*(b^2 - 4*a*c)*a^4*c^6)*d*abs(-c^3*d^2 + b*c^2*d*e - a*c^2*e^2)*e^2 + (2*a*b^6*c^2 - 18*a^2*b^4*c^3 + 48*a^3*b^2*c^4 - 32*a^4*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6 + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^2 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^3 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 - 2*(b^2 - 4*a*c)*a*b^4*c^2 + 10*(b^2 - 4*a*c)*a^2*b^2*c^3 - 8*(b^2 - 4*a*c)*a^3*c^4)*(c^3*d^2 - b*c^2*d*e + a*c^2*e^2)^2*e + (6*a^2*b^7*c^6 - 44*a^3*b^5*c^7 + 84*a^4*b^3*c^8 - 16*a^5*b*c^9 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c^4 + 22*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^5 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^5 - 42*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^6 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^6 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^7 + 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 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^7 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^8 - 6*(b^2 - 4*a*c)*a^2*b^5*c^6 + 20*(b^2 - 4*a*c)*a^3*b^3*c^7 - 4*(b^2 - 4*a*c)*a^4*b*c^8)*d*e^4 - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^3 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^4 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^4 - 2*a^3*b^5*c^4 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^5 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^5 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^5 + 16*a^4*b^3*c^5 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^6 - 32*a^5*b*c^6 + 2*(b^2 - 4*a*c)*a^3*b^3*c^4 - 8*(b^2 - 4*a*c)*a^4*b*c^5)*abs(-c^3*d^2 + b*c^2*d*e - a*c^2*e^2)*e^3 - (2*a^3*b^6*c^6 - 14*a^4*b^4*c^7 + 24*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 + 7*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 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^6 - 6*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 + 3*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 + 6*(b^2 - 4*a*c)*a^4*b^2*c^7)*e^5)*arctan(2*sqrt(1/2)*x/sqrt((b*c^3*d^2 - b^2*c^2*d*e + a*b*c^2*e^2 - sqrt((b*c^3*d^2 - b^2*c^2*d*e + a*b*c^2*e^2)^2 - 4*(a*c^3*d^2 - a*b*c^2*d*e + a^2*c^2*e^2)*(c^4*d^2 - b*c^3*d*e + a*c^3*e^2)))/(c^4*d^2 - b*c^3*d*e + a*c^3*e^2)))/((a*b^4*c^7 - 8*a^2*b^2*c^8 - 2*a*b^3*c^8 + 16*a^3*c^9 + 8*a^2*b*c^9 + a*b^2*c^9 - 4*a^2*c^10)*d^4*abs(-c^3*d^2 + b*c^2*d*e - a*c^2*e^2)*abs(c) - 2*(a*b^5*c^6 - 8*a^2*b^3*c^7 - 2*a*b^4*c^7 + 16*a^3*b*c^8 + 8*a^2*b^2*c^8 + a*b^3*c^8 - 4*a^2*b*c^9)*d^3*abs(-c^3*d^2 + b*c^2*d*e - a*c^2*e^2)*abs(c)*e + (a*b^6*c^5 - 6*a^2*b^4*c^6 - 2*a*b^5*c^6 + 4*a^2*b^3*c^7 + a*b^4*c^7 + 32*a^4*c^8 + 16*a^3*b*c^8 - 2*a^2*b^2*c^8 - 8*a^3*c^9)*d^2*abs(-c^3*d^2 + b*c^2*d*e - a*c^2*e^2)*abs(c)*e^2 - 2*(a^2*b^5*c^5 - 8*a^3*b^3*c^6 - 2*a^2*b^4*c^6 + 16*a^4*b*c^7 + 8*a^3*b^2*c^7 + a^2*b^3*c^7 - 4*a^3*b*c^8)*d*abs(-c^3*d^2 + b*c^2*d*e - a*c^2*e^2)*abs(c)*e^3 + (a^3*b^4*c^5 - 8*a^4*b^2*c^6 - 2*a^3*b^3*c^6 + 16*a^5*c^7 + 8*a^4*b*c^7 + a^3*b^2*c^7 - 4*a^4*c^8)*abs(-c^3*d^2 + b*c^2*d*e - a*c^2*e^2)*abs(c)*e^4) + 1/3*(c^2*x^3*e^2 - 3*c^2*d*x*e - 3*b*c*x*e^2)*e^(-3)/c^3","B",0
304,1,11030,0,13.868447," ","integrate(x^6/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{d^{\frac{5}{2}} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{1}{2}\right)}}{c d^{2} e - b d e^{2} + a e^{3}} - \frac{{\left({\left(2 \, b^{6} c^{6} - 14 \, a b^{4} c^{7} + 24 \, 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} + 7 \, \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} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 6 \, \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} + 3 \, \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} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{7}\right)} d^{5} - {\left(4 \, b^{7} c^{5} - 26 \, a b^{5} c^{6} + 36 \, a^{2} b^{3} c^{7} + 16 \, a^{3} b c^{8} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{3} + 13 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{4} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} - 10 \, \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} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{6} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{7} - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{5} + 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{6} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{7}\right)} d^{4} e - 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)} d^{3} {\left| -c^{2} d^{2} + b c d e - a c e^{2} \right|} + {\left(2 \, b^{8} c^{4} - 6 \, a b^{6} c^{5} - 28 \, a^{2} b^{4} c^{6} + 80 \, 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} + 3 \, \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} + 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} + 2 \, \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} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} - 20 \, \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} a b^{4} c^{5} + 10 \, \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} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{5} + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{6}\right)} d^{3} e^{2} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} - 7 \, \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} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} + 6 \, \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} - 14 \, 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} - 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} + 16 \, 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} + 6 \, {\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)} d^{2} {\left| -c^{2} d^{2} + b c d e - a c e^{2} \right|} e - {\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)} {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)}^{2} d - {\left(6 \, a b^{7} c^{4} - 36 \, a^{2} b^{5} c^{5} + 40 \, a^{3} b^{3} c^{6} + 32 \, a^{4} b c^{7} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{2} + 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} 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^{6} c^{3} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} 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^{5} c^{4} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{4} + 12 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{5} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{6}\right)} d^{2} e^{3} - 4 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} + 2 \, a^{2} b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} - 16 \, a^{3} b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} + 32 \, a^{4} b c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{4}\right)} d {\left| -c^{2} d^{2} + b c d e - a c e^{2} \right|} e^{2} + {\left(2 \, a b^{5} c^{2} - 16 \, a^{2} b^{3} c^{3} + 32 \, a^{3} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)}^{2} e + {\left(6 \, a^{2} b^{6} c^{4} - 38 \, a^{3} b^{4} c^{5} + 56 \, a^{4} b^{2} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} + 19 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} - 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} - 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{4} + 14 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{5}\right)} d e^{4} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} + 2 \, a^{3} b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} - 16 \, a^{4} b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{5} + 32 \, a^{5} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{4}\right)} {\left| -c^{2} d^{2} + b c d e - a c e^{2} \right|} e^{3} - {\left(2 \, a^{3} b^{5} c^{4} - 12 \, a^{4} b^{3} c^{5} + 16 \, a^{5} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{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^{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} + 2 \, \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^{3} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{5}\right)} e^{5}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c^{2} d^{2} - b^{2} c d e + a b c e^{2} + \sqrt{{\left(b c^{2} d^{2} - b^{2} c d e + a b c e^{2}\right)}^{2} - 4 \, {\left(a c^{2} d^{2} - a b c d e + a^{2} c e^{2}\right)} {\left(c^{3} d^{2} - b c^{2} d e + a c^{2} e^{2}\right)}}}{c^{3} d^{2} - b c^{2} d e + a c^{2} e^{2}}}}\right)}{8 \, {\left({\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)} d^{4} {\left| -c^{2} d^{2} + b c d e - a c e^{2} \right|} {\left| c \right|} - 2 \, {\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} - 2 \, a b^{4} c^{5} + 16 \, a^{3} b c^{6} + 8 \, a^{2} b^{2} c^{6} + a b^{3} c^{6} - 4 \, a^{2} b c^{7}\right)} d^{3} {\left| -c^{2} d^{2} + b c d e - a c e^{2} \right|} {\left| c \right|} e + {\left(a b^{6} c^{3} - 6 \, a^{2} b^{4} c^{4} - 2 \, a b^{5} c^{4} + 4 \, a^{2} b^{3} c^{5} + a b^{4} c^{5} + 32 \, a^{4} c^{6} + 16 \, a^{3} b c^{6} - 2 \, a^{2} b^{2} c^{6} - 8 \, a^{3} c^{7}\right)} d^{2} {\left| -c^{2} d^{2} + b c d e - a c e^{2} \right|} {\left| c \right|} e^{2} - 2 \, {\left(a^{2} b^{5} c^{3} - 8 \, a^{3} b^{3} c^{4} - 2 \, a^{2} b^{4} c^{4} + 16 \, a^{4} b c^{5} + 8 \, a^{3} b^{2} c^{5} + a^{2} b^{3} c^{5} - 4 \, a^{3} b c^{6}\right)} d {\left| -c^{2} d^{2} + b c d e - a c e^{2} \right|} {\left| c \right|} e^{3} + {\left(a^{3} b^{4} c^{3} - 8 \, a^{4} b^{2} c^{4} - 2 \, a^{3} b^{3} c^{4} + 16 \, a^{5} c^{5} + 8 \, a^{4} b c^{5} + a^{3} b^{2} c^{5} - 4 \, a^{4} c^{6}\right)} {\left| -c^{2} d^{2} + b c d e - a c e^{2} \right|} {\left| c \right|} e^{4}\right)}} + \frac{{\left({\left(2 \, b^{6} c^{6} - 14 \, a b^{4} c^{7} + 24 \, 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} + 7 \, \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} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} - 6 \, \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} + 3 \, \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} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{7}\right)} d^{5} - {\left(4 \, b^{7} c^{5} - 26 \, a b^{5} c^{6} + 36 \, a^{2} b^{3} c^{7} + 16 \, a^{3} b c^{8} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} c^{3} + 13 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{4} - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} - 10 \, \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} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{6} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{6} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{7} - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{5} + 10 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{6} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{7}\right)} d^{4} e + 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)} d^{3} {\left| -c^{2} d^{2} + b c d e - a c e^{2} \right|} + {\left(2 \, b^{8} c^{4} - 6 \, a b^{6} c^{5} - 28 \, a^{2} b^{4} c^{6} + 80 \, 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} + 3 \, \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} + 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} + 2 \, \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} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} - 20 \, \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} a b^{4} c^{5} + 10 \, \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} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{5} + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{6}\right)} d^{3} e^{2} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c^{2} - 7 \, \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} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} + 6 \, \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} + 14 \, 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} - 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{5} - 16 \, 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} - 6 \, {\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)} d^{2} {\left| -c^{2} d^{2} + b c d e - a c e^{2} \right|} e - {\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)} {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)}^{2} d - {\left(6 \, a b^{7} c^{4} - 36 \, a^{2} b^{5} c^{5} + 40 \, a^{3} b^{3} c^{6} + 32 \, a^{4} b c^{7} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} c^{2} + 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} 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^{6} c^{3} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} 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^{5} c^{4} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{5} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{6} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c^{4} + 12 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{5} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{6}\right)} d^{2} e^{3} + 4 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} - 2 \, a^{2} b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} + 16 \, a^{3} b^{3} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} - 32 \, a^{4} b c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{4}\right)} d {\left| -c^{2} d^{2} + b c d e - a c e^{2} \right|} e^{2} + {\left(2 \, a b^{5} c^{2} - 16 \, a^{2} b^{3} c^{3} + 32 \, a^{3} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)}^{2} e + {\left(6 \, a^{2} b^{6} c^{4} - 38 \, a^{3} b^{4} c^{5} + 56 \, a^{4} b^{2} c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} + 19 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} - 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} - 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{4} + 14 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{5}\right)} d e^{4} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 2 \, a^{3} b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} + 16 \, a^{4} b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{5} - 32 \, a^{5} c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{4}\right)} {\left| -c^{2} d^{2} + b c d e - a c e^{2} \right|} e^{3} - {\left(2 \, a^{3} b^{5} c^{4} - 12 \, a^{4} b^{3} c^{5} + 16 \, a^{5} b c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{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^{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} + 2 \, \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^{3} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{5}\right)} e^{5}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c^{2} d^{2} - b^{2} c d e + a b c e^{2} - \sqrt{{\left(b c^{2} d^{2} - b^{2} c d e + a b c e^{2}\right)}^{2} - 4 \, {\left(a c^{2} d^{2} - a b c d e + a^{2} c e^{2}\right)} {\left(c^{3} d^{2} - b c^{2} d e + a c^{2} e^{2}\right)}}}{c^{3} d^{2} - b c^{2} d e + a c^{2} e^{2}}}}\right)}{8 \, {\left({\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)} d^{4} {\left| -c^{2} d^{2} + b c d e - a c e^{2} \right|} {\left| c \right|} - 2 \, {\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} - 2 \, a b^{4} c^{5} + 16 \, a^{3} b c^{6} + 8 \, a^{2} b^{2} c^{6} + a b^{3} c^{6} - 4 \, a^{2} b c^{7}\right)} d^{3} {\left| -c^{2} d^{2} + b c d e - a c e^{2} \right|} {\left| c \right|} e + {\left(a b^{6} c^{3} - 6 \, a^{2} b^{4} c^{4} - 2 \, a b^{5} c^{4} + 4 \, a^{2} b^{3} c^{5} + a b^{4} c^{5} + 32 \, a^{4} c^{6} + 16 \, a^{3} b c^{6} - 2 \, a^{2} b^{2} c^{6} - 8 \, a^{3} c^{7}\right)} d^{2} {\left| -c^{2} d^{2} + b c d e - a c e^{2} \right|} {\left| c \right|} e^{2} - 2 \, {\left(a^{2} b^{5} c^{3} - 8 \, a^{3} b^{3} c^{4} - 2 \, a^{2} b^{4} c^{4} + 16 \, a^{4} b c^{5} + 8 \, a^{3} b^{2} c^{5} + a^{2} b^{3} c^{5} - 4 \, a^{3} b c^{6}\right)} d {\left| -c^{2} d^{2} + b c d e - a c e^{2} \right|} {\left| c \right|} e^{3} + {\left(a^{3} b^{4} c^{3} - 8 \, a^{4} b^{2} c^{4} - 2 \, a^{3} b^{3} c^{4} + 16 \, a^{5} c^{5} + 8 \, a^{4} b c^{5} + a^{3} b^{2} c^{5} - 4 \, a^{4} c^{6}\right)} {\left| -c^{2} d^{2} + b c d e - a c e^{2} \right|} {\left| c \right|} e^{4}\right)}} + \frac{x e^{\left(-1\right)}}{c}"," ",0,"-d^(5/2)*arctan(x*e^(1/2)/sqrt(d))*e^(-1/2)/(c*d^2*e - b*d*e^2 + a*e^3) - 1/8*((2*b^6*c^6 - 14*a*b^4*c^7 + 24*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 + 7*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 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 6*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 + 3*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 + 6*(b^2 - 4*a*c)*a*b^2*c^7)*d^5 - (4*b^7*c^5 - 26*a*b^5*c^6 + 36*a^2*b^3*c^7 + 16*a^3*b*c^8 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7*c^3 + 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c^4 - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 - 10*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 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^6 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 - 4*(b^2 - 4*a*c)*b^5*c^5 + 10*(b^2 - 4*a*c)*a*b^3*c^6 + 4*(b^2 - 4*a*c)*a^2*b*c^7)*d^4*e - 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)*d^3*abs(-c^2*d^2 + b*c*d*e - a*c*e^2) + (2*b^8*c^4 - 6*a*b^6*c^5 - 28*a^2*b^4*c^6 + 80*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 + 3*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 + 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 + 2*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 - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 - 20*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)*a*b^4*c^5 + 10*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 - 2*(b^2 - 4*a*c)*a*b^4*c^5 + 20*(b^2 - 4*a*c)*a^2*b^2*c^6)*d^3*e^2 + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c^2 - 7*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 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 + 6*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 - 14*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 - 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 + 16*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 + 6*(b^2 - 4*a*c)*a^2*b^2*c^4 + 8*(b^2 - 4*a*c)*a^3*c^5)*d^2*abs(-c^2*d^2 + b*c*d*e - a*c*e^2)*e - (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*d^2 - b*c*d*e + a*c*e^2)^2*d - (6*a*b^7*c^4 - 36*a^2*b^5*c^5 + 40*a^3*b^3*c^6 + 32*a^4*b*c^7 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7*c^2 + 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*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^6*c^3 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*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^5*c^4 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 6*(b^2 - 4*a*c)*a*b^5*c^4 + 12*(b^2 - 4*a*c)*a^2*b^3*c^5 + 8*(b^2 - 4*a*c)*a^3*b*c^6)*d^2*e^3 - 4*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 + 2*a^2*b^5*c^3 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 - 16*a^3*b^3*c^4 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 + 32*a^4*b*c^5 - 2*(b^2 - 4*a*c)*a^2*b^3*c^3 + 8*(b^2 - 4*a*c)*a^3*b*c^4)*d*abs(-c^2*d^2 + b*c*d*e - a*c*e^2)*e^2 + (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)*(c^2*d^2 - b*c*d*e + a*c*e^2)^2*e + (6*a^2*b^6*c^4 - 38*a^3*b^4*c^5 + 56*a^4*b^2*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 + 19*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 - 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 - 6*(b^2 - 4*a*c)*a^2*b^4*c^4 + 14*(b^2 - 4*a*c)*a^3*b^2*c^5)*d*e^4 + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 + 2*a^3*b^4*c^3 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*c^4 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 - 16*a^4*b^2*c^4 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^5 + 32*a^5*c^5 - 2*(b^2 - 4*a*c)*a^3*b^2*c^3 + 8*(b^2 - 4*a*c)*a^4*c^4)*abs(-c^2*d^2 + b*c*d*e - a*c*e^2)*e^3 - (2*a^3*b^5*c^4 - 12*a^4*b^3*c^5 + 16*a^5*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^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^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 + 2*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^3*b^3*c^4 + 4*(b^2 - 4*a*c)*a^4*b*c^5)*e^5)*arctan(2*sqrt(1/2)*x/sqrt((b*c^2*d^2 - b^2*c*d*e + a*b*c*e^2 + sqrt((b*c^2*d^2 - b^2*c*d*e + a*b*c*e^2)^2 - 4*(a*c^2*d^2 - a*b*c*d*e + a^2*c*e^2)*(c^3*d^2 - b*c^2*d*e + a*c^2*e^2)))/(c^3*d^2 - b*c^2*d*e + a*c^2*e^2)))/((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)*d^4*abs(-c^2*d^2 + b*c*d*e - a*c*e^2)*abs(c) - 2*(a*b^5*c^4 - 8*a^2*b^3*c^5 - 2*a*b^4*c^5 + 16*a^3*b*c^6 + 8*a^2*b^2*c^6 + a*b^3*c^6 - 4*a^2*b*c^7)*d^3*abs(-c^2*d^2 + b*c*d*e - a*c*e^2)*abs(c)*e + (a*b^6*c^3 - 6*a^2*b^4*c^4 - 2*a*b^5*c^4 + 4*a^2*b^3*c^5 + a*b^4*c^5 + 32*a^4*c^6 + 16*a^3*b*c^6 - 2*a^2*b^2*c^6 - 8*a^3*c^7)*d^2*abs(-c^2*d^2 + b*c*d*e - a*c*e^2)*abs(c)*e^2 - 2*(a^2*b^5*c^3 - 8*a^3*b^3*c^4 - 2*a^2*b^4*c^4 + 16*a^4*b*c^5 + 8*a^3*b^2*c^5 + a^2*b^3*c^5 - 4*a^3*b*c^6)*d*abs(-c^2*d^2 + b*c*d*e - a*c*e^2)*abs(c)*e^3 + (a^3*b^4*c^3 - 8*a^4*b^2*c^4 - 2*a^3*b^3*c^4 + 16*a^5*c^5 + 8*a^4*b*c^5 + a^3*b^2*c^5 - 4*a^4*c^6)*abs(-c^2*d^2 + b*c*d*e - a*c*e^2)*abs(c)*e^4) + 1/8*((2*b^6*c^6 - 14*a*b^4*c^7 + 24*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 + 7*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 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 - 6*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 + 3*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 + 6*(b^2 - 4*a*c)*a*b^2*c^7)*d^5 - (4*b^7*c^5 - 26*a*b^5*c^6 + 36*a^2*b^3*c^7 + 16*a^3*b*c^8 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7*c^3 + 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c^4 - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 - 10*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 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^6 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^6 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^7 - 4*(b^2 - 4*a*c)*b^5*c^5 + 10*(b^2 - 4*a*c)*a*b^3*c^6 + 4*(b^2 - 4*a*c)*a^2*b*c^7)*d^4*e + 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)*d^3*abs(-c^2*d^2 + b*c*d*e - a*c*e^2) + (2*b^8*c^4 - 6*a*b^6*c^5 - 28*a^2*b^4*c^6 + 80*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 + 3*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 + 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 + 2*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 - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 - 20*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)*a*b^4*c^5 + 10*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 - 2*(b^2 - 4*a*c)*a*b^4*c^5 + 20*(b^2 - 4*a*c)*a^2*b^2*c^6)*d^3*e^2 - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c^2 - 7*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 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 + 6*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 + 14*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 - 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^5 - 16*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 - 6*(b^2 - 4*a*c)*a^2*b^2*c^4 - 8*(b^2 - 4*a*c)*a^3*c^5)*d^2*abs(-c^2*d^2 + b*c*d*e - a*c*e^2)*e - (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*d^2 - b*c*d*e + a*c*e^2)^2*d - (6*a*b^7*c^4 - 36*a^2*b^5*c^5 + 40*a^3*b^3*c^6 + 32*a^4*b*c^7 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7*c^2 + 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*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^6*c^3 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*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^5*c^4 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^5 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^6 - 6*(b^2 - 4*a*c)*a*b^5*c^4 + 12*(b^2 - 4*a*c)*a^2*b^3*c^5 + 8*(b^2 - 4*a*c)*a^3*b*c^6)*d^2*e^3 + 4*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 - 2*a^2*b^5*c^3 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 + 16*a^3*b^3*c^4 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 - 32*a^4*b*c^5 + 2*(b^2 - 4*a*c)*a^2*b^3*c^3 - 8*(b^2 - 4*a*c)*a^3*b*c^4)*d*abs(-c^2*d^2 + b*c*d*e - a*c*e^2)*e^2 + (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)*(c^2*d^2 - b*c*d*e + a*c*e^2)^2*e + (6*a^2*b^6*c^4 - 38*a^3*b^4*c^5 + 56*a^4*b^2*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 + 19*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 - 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 - 6*(b^2 - 4*a*c)*a^2*b^4*c^4 + 14*(b^2 - 4*a*c)*a^3*b^2*c^5)*d*e^4 - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 - 2*a^3*b^4*c^3 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*c^4 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 + 16*a^4*b^2*c^4 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^5 - 32*a^5*c^5 + 2*(b^2 - 4*a*c)*a^3*b^2*c^3 - 8*(b^2 - 4*a*c)*a^4*c^4)*abs(-c^2*d^2 + b*c*d*e - a*c*e^2)*e^3 - (2*a^3*b^5*c^4 - 12*a^4*b^3*c^5 + 16*a^5*b*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^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^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 + 2*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^3*b^3*c^4 + 4*(b^2 - 4*a*c)*a^4*b*c^5)*e^5)*arctan(2*sqrt(1/2)*x/sqrt((b*c^2*d^2 - b^2*c*d*e + a*b*c*e^2 - sqrt((b*c^2*d^2 - b^2*c*d*e + a*b*c*e^2)^2 - 4*(a*c^2*d^2 - a*b*c*d*e + a^2*c*e^2)*(c^3*d^2 - b*c^2*d*e + a*c^2*e^2)))/(c^3*d^2 - b*c^2*d*e + a*c^2*e^2)))/((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)*d^4*abs(-c^2*d^2 + b*c*d*e - a*c*e^2)*abs(c) - 2*(a*b^5*c^4 - 8*a^2*b^3*c^5 - 2*a*b^4*c^5 + 16*a^3*b*c^6 + 8*a^2*b^2*c^6 + a*b^3*c^6 - 4*a^2*b*c^7)*d^3*abs(-c^2*d^2 + b*c*d*e - a*c*e^2)*abs(c)*e + (a*b^6*c^3 - 6*a^2*b^4*c^4 - 2*a*b^5*c^4 + 4*a^2*b^3*c^5 + a*b^4*c^5 + 32*a^4*c^6 + 16*a^3*b*c^6 - 2*a^2*b^2*c^6 - 8*a^3*c^7)*d^2*abs(-c^2*d^2 + b*c*d*e - a*c*e^2)*abs(c)*e^2 - 2*(a^2*b^5*c^3 - 8*a^3*b^3*c^4 - 2*a^2*b^4*c^4 + 16*a^4*b*c^5 + 8*a^3*b^2*c^5 + a^2*b^3*c^5 - 4*a^3*b*c^6)*d*abs(-c^2*d^2 + b*c*d*e - a*c*e^2)*abs(c)*e^3 + (a^3*b^4*c^3 - 8*a^4*b^2*c^4 - 2*a^3*b^3*c^4 + 16*a^5*c^5 + 8*a^4*b*c^5 + a^3*b^2*c^5 - 4*a^4*c^6)*abs(-c^2*d^2 + b*c*d*e - a*c*e^2)*abs(c)*e^4) + x*e^(-1)/c","B",0
305,1,8658,0,11.235550," ","integrate(x^4/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{d^{\frac{3}{2}} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\left(-\frac{1}{2}\right)}}{c d^{2} - b d e + a e^{2}} + \frac{{\left({\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)} d^{5} - {\left(4 \, b^{6} c^{3} - 22 \, a b^{4} c^{4} + 24 \, a^{2} b^{2} c^{5} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 12 \, \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} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4}\right)} d^{4} e - 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)} d^{3} {\left| c d^{2} - b d e + a e^{2} \right|} + {\left(2 \, b^{7} c^{2} - 4 \, a b^{5} c^{3} - 24 \, a^{2} b^{3} c^{4} + 32 \, 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} + 2 \, \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 + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 4 \, \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} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 8 \, \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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} - 4 \, {\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)} d^{3} e^{2} + 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^{2} {\left| c d^{2} - b d e + a e^{2} \right|} e - {\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)} {\left(c d^{2} - b d e + a e^{2}\right)}^{2} d - {\left(6 \, a b^{6} c^{2} - 28 \, a^{2} b^{4} c^{3} + 16 \, a^{3} b^{2} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} + 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 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} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 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} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3}\right)} d^{2} e^{3} - 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)} d {\left| c d^{2} - b d e + a e^{2} \right|} e^{2} + {\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)} {\left(c d^{2} - b d e + a e^{2}\right)}^{2} e + {\left(6 \, a^{2} b^{5} c^{2} - 28 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} + 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{2} - 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} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3}\right)} d e^{4} - {\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)} e^{5}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c d^{2} - b^{2} d e + a b e^{2} + \sqrt{{\left(b c d^{2} - b^{2} d e + a b e^{2}\right)}^{2} - 4 \, {\left(a c d^{2} - a b d e + a^{2} e^{2}\right)} {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)}}}{c^{2} d^{2} - b c d e + a c e^{2}}}}\right)}{8 \, {\left({\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)} d^{4} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} - 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}\right)} d^{3} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e + {\left(a b^{6} c - 6 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 4 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} + 32 \, a^{4} c^{4} + 16 \, a^{3} b c^{4} - 2 \, a^{2} b^{2} c^{4} - 8 \, a^{3} c^{5}\right)} d^{2} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{2} - 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} - 2 \, a^{2} b^{4} c^{2} + 16 \, a^{4} b c^{3} + 8 \, a^{3} b^{2} c^{3} + a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4}\right)} d {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{3} + {\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| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{4}\right)}} - \frac{{\left({\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)} d^{5} - {\left(4 \, b^{6} c^{3} - 22 \, a b^{4} c^{4} + 24 \, a^{2} b^{2} c^{5} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 12 \, \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} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4}\right)} d^{4} e + 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)} d^{3} {\left| c d^{2} - b d e + a e^{2} \right|} + {\left(2 \, b^{7} c^{2} - 4 \, a b^{5} c^{3} - 24 \, a^{2} b^{3} c^{4} + 32 \, 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} + 2 \, \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 + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 4 \, \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} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 8 \, \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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c^{2} - 4 \, {\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)} d^{3} e^{2} - 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^{2} {\left| c d^{2} - b d e + a e^{2} \right|} e - {\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)} {\left(c d^{2} - b d e + a e^{2}\right)}^{2} d - {\left(6 \, a b^{6} c^{2} - 28 \, a^{2} b^{4} c^{3} + 16 \, a^{3} b^{2} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} + 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 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} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + 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} - 6 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3}\right)} d^{2} e^{3} + 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)} d {\left| c d^{2} - b d e + a e^{2} \right|} e^{2} + {\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)} {\left(c d^{2} - b d e + a e^{2}\right)}^{2} e + {\left(6 \, a^{2} b^{5} c^{2} - 28 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} + 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{2} - 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} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{3}\right)} d e^{4} - {\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)} e^{5}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c d^{2} - b^{2} d e + a b e^{2} - \sqrt{{\left(b c d^{2} - b^{2} d e + a b e^{2}\right)}^{2} - 4 \, {\left(a c d^{2} - a b d e + a^{2} e^{2}\right)} {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)}}}{c^{2} d^{2} - b c d e + a c e^{2}}}}\right)}{8 \, {\left({\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)} d^{4} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} - 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}\right)} d^{3} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e + {\left(a b^{6} c - 6 \, a^{2} b^{4} c^{2} - 2 \, a b^{5} c^{2} + 4 \, a^{2} b^{3} c^{3} + a b^{4} c^{3} + 32 \, a^{4} c^{4} + 16 \, a^{3} b c^{4} - 2 \, a^{2} b^{2} c^{4} - 8 \, a^{3} c^{5}\right)} d^{2} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{2} - 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} - 2 \, a^{2} b^{4} c^{2} + 16 \, a^{4} b c^{3} + 8 \, a^{3} b^{2} c^{3} + a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4}\right)} d {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{3} + {\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| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{4}\right)}}"," ",0,"d^(3/2)*arctan(x*e^(1/2)/sqrt(d))*e^(-1/2)/(c*d^2 - b*d*e + a*e^2) + 1/8*((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)*d^5 - (4*b^6*c^3 - 22*a*b^4*c^4 + 24*a^2*b^2*c^5 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c + 11*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 12*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 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 4*(b^2 - 4*a*c)*b^4*c^3 + 6*(b^2 - 4*a*c)*a*b^2*c^4)*d^4*e - 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)*d^3*abs(c*d^2 - b*d*e + a*e^2) + (2*b^7*c^2 - 4*a*b^5*c^3 - 24*a^2*b^3*c^4 + 32*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 + 2*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 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + 4*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 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 8*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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 - 4*(b^2 - 4*a*c)*a*b^3*c^3 + 8*(b^2 - 4*a*c)*a^2*b*c^4)*d^3*e^2 + 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^2*abs(c*d^2 - b*d*e + a*e^2)*e - (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*d^2 - b*d*e + a*e^2)^2*d - (6*a*b^6*c^2 - 28*a^2*b^4*c^3 + 16*a^3*b^2*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6 + 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 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 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 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 - 6*(b^2 - 4*a*c)*a*b^4*c^2 + 4*(b^2 - 4*a*c)*a^2*b^2*c^3)*d^2*e^3 - 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)*d*abs(c*d^2 - b*d*e + a*e^2)*e^2 + (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)*(c*d^2 - b*d*e + a*e^2)^2*e + (6*a^2*b^5*c^2 - 28*a^3*b^3*c^3 + 16*a^4*b*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5 + 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^2 - 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 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 6*(b^2 - 4*a*c)*a^2*b^3*c^2 + 4*(b^2 - 4*a*c)*a^3*b*c^3)*d*e^4 - (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)*e^5)*arctan(2*sqrt(1/2)*x/sqrt((b*c*d^2 - b^2*d*e + a*b*e^2 + sqrt((b*c*d^2 - b^2*d*e + a*b*e^2)^2 - 4*(a*c*d^2 - a*b*d*e + a^2*e^2)*(c^2*d^2 - b*c*d*e + a*c*e^2)))/(c^2*d^2 - b*c*d*e + a*c*e^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)*d^4*abs(c*d^2 - b*d*e + a*e^2)*abs(c) - 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)*d^3*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e + (a*b^6*c - 6*a^2*b^4*c^2 - 2*a*b^5*c^2 + 4*a^2*b^3*c^3 + a*b^4*c^3 + 32*a^4*c^4 + 16*a^3*b*c^4 - 2*a^2*b^2*c^4 - 8*a^3*c^5)*d^2*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e^2 - 2*(a^2*b^5*c - 8*a^3*b^3*c^2 - 2*a^2*b^4*c^2 + 16*a^4*b*c^3 + 8*a^3*b^2*c^3 + a^2*b^3*c^3 - 4*a^3*b*c^4)*d*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e^3 + (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(c*d^2 - b*d*e + a*e^2)*abs(c)*e^4) - 1/8*((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)*d^5 - (4*b^6*c^3 - 22*a*b^4*c^4 + 24*a^2*b^2*c^5 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 11*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 12*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 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 4*(b^2 - 4*a*c)*b^4*c^3 + 6*(b^2 - 4*a*c)*a*b^2*c^4)*d^4*e + 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)*d^3*abs(c*d^2 - b*d*e + a*e^2) + (2*b^7*c^2 - 4*a*b^5*c^3 - 24*a^2*b^3*c^4 + 32*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 + 2*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 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + 4*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 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 8*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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 2*(b^2 - 4*a*c)*b^5*c^2 - 4*(b^2 - 4*a*c)*a*b^3*c^3 + 8*(b^2 - 4*a*c)*a^2*b*c^4)*d^3*e^2 - 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^2*abs(c*d^2 - b*d*e + a*e^2)*e - (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*d^2 - b*d*e + a*e^2)^2*d - (6*a*b^6*c^2 - 28*a^2*b^4*c^3 + 16*a^3*b^2*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6 + 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 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 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + 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 - 6*(b^2 - 4*a*c)*a*b^4*c^2 + 4*(b^2 - 4*a*c)*a^2*b^2*c^3)*d^2*e^3 + 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)*d*abs(c*d^2 - b*d*e + a*e^2)*e^2 + (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)*(c*d^2 - b*d*e + a*e^2)^2*e + (6*a^2*b^5*c^2 - 28*a^3*b^3*c^3 + 16*a^4*b*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5 + 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^2 - 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 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 6*(b^2 - 4*a*c)*a^2*b^3*c^2 + 4*(b^2 - 4*a*c)*a^3*b*c^3)*d*e^4 - (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)*e^5)*arctan(2*sqrt(1/2)*x/sqrt((b*c*d^2 - b^2*d*e + a*b*e^2 - sqrt((b*c*d^2 - b^2*d*e + a*b*e^2)^2 - 4*(a*c*d^2 - a*b*d*e + a^2*e^2)*(c^2*d^2 - b*c*d*e + a*c*e^2)))/(c^2*d^2 - b*c*d*e + a*c*e^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)*d^4*abs(c*d^2 - b*d*e + a*e^2)*abs(c) - 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)*d^3*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e + (a*b^6*c - 6*a^2*b^4*c^2 - 2*a*b^5*c^2 + 4*a^2*b^3*c^3 + a*b^4*c^3 + 32*a^4*c^4 + 16*a^3*b*c^4 - 2*a^2*b^2*c^4 - 8*a^3*c^5)*d^2*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e^2 - 2*(a^2*b^5*c - 8*a^3*b^3*c^2 - 2*a^2*b^4*c^2 + 16*a^4*b*c^3 + 8*a^3*b^2*c^3 + a^2*b^3*c^3 - 4*a^3*b*c^4)*d*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e^3 + (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(c*d^2 - b*d*e + a*e^2)*abs(c)*e^4)","B",0
306,1,6921,0,8.452916," ","integrate(x^2/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{\sqrt{d} \arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\frac{1}{2}}}{c d^{2} - b d e + a e^{2}} - \frac{{\left({\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)} d^{5} - 2 \, {\left(2 \, b^{5} c^{3} - 6 \, 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} b^{5} c + 3 \, \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} + 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} b^{3} 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)} b^{3} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} d^{4} e + {\left(2 \, b^{6} c^{2} + 4 \, a b^{4} c^{3} - 48 \, 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} - 2 \, \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} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 6 \, \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} - 12 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3}\right)} d^{3} e^{2} - 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)} d^{2} {\left| c d^{2} - b d e + a e^{2} \right|} e - {\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)} {\left(c d^{2} - b d e + a e^{2}\right)}^{2} d - 4 \, {\left(2 \, a b^{5} c^{2} - 6 \, a^{2} b^{3} c^{3} - 8 \, 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} + 3 \, \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 + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 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} - \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} a^{2} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} d^{2} e^{3} + 2 \, {\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} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 32 \, a^{3} b 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}\right)} d {\left| c d^{2} - b d e + a e^{2} \right|} e^{2} + 5 \, {\left(2 \, a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2}\right)} d e^{4} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - 2 \, a^{2} b^{4} c + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{2} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 16 \, a^{3} b^{2} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 32 \, a^{4} c^{3} + 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}\right)} {\left| c d^{2} - b d e + a e^{2} \right|} e^{3} - 2 \, {\left(2 \, a^{3} b^{3} c^{2} - 8 \, a^{4} b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2}\right)} e^{5}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c d^{2} - b^{2} d e + a b e^{2} + \sqrt{{\left(b c d^{2} - b^{2} d e + a b e^{2}\right)}^{2} - 4 \, {\left(a c d^{2} - a b d e + a^{2} e^{2}\right)} {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)}}}{c^{2} d^{2} - b c d e + a c e^{2}}}}\right)}{8 \, {\left({\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)} d^{4} {\left| c d^{2} - b d e + a e^{2} \right|} {\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}\right)} d^{3} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e + {\left(a b^{6} - 6 \, a^{2} b^{4} c - 2 \, a b^{5} c + 4 \, a^{2} b^{3} c^{2} + a b^{4} c^{2} + 32 \, a^{4} c^{3} + 16 \, a^{3} b c^{3} - 2 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d^{2} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{2} - 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c - 2 \, a^{2} b^{4} c + 16 \, a^{4} b c^{2} + 8 \, a^{3} b^{2} c^{2} + a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{3} + {\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 d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{4}\right)}} + \frac{{\left({\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)} d^{5} - 2 \, {\left(2 \, b^{5} c^{3} - 6 \, 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} b^{5} c + 3 \, \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} + 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} b^{3} 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)} b^{3} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} d^{4} e + {\left(2 \, b^{6} c^{2} + 4 \, a b^{4} c^{3} - 48 \, 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} - 2 \, \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} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 6 \, \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} - 12 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3}\right)} d^{3} e^{2} + 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)} d^{2} {\left| c d^{2} - b d e + a e^{2} \right|} e - {\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)} {\left(c d^{2} - b d e + a e^{2}\right)}^{2} d - 4 \, {\left(2 \, a b^{5} c^{2} - 6 \, a^{2} b^{3} c^{3} - 8 \, 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} + 3 \, \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 + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 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} - \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} a^{2} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} d^{2} e^{3} - 2 \, {\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} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 32 \, a^{3} b 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}\right)} d {\left| c d^{2} - b d e + a e^{2} \right|} e^{2} + 5 \, {\left(2 \, a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2}\right)} d e^{4} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c + 2 \, a^{2} b^{4} c + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{2} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 16 \, a^{3} b^{2} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 32 \, a^{4} c^{3} - 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}\right)} {\left| c d^{2} - b d e + a e^{2} \right|} e^{3} - 2 \, {\left(2 \, a^{3} b^{3} c^{2} - 8 \, a^{4} b c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2}\right)} e^{5}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c d^{2} - b^{2} d e + a b e^{2} - \sqrt{{\left(b c d^{2} - b^{2} d e + a b e^{2}\right)}^{2} - 4 \, {\left(a c d^{2} - a b d e + a^{2} e^{2}\right)} {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)}}}{c^{2} d^{2} - b c d e + a c e^{2}}}}\right)}{8 \, {\left({\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)} d^{4} {\left| c d^{2} - b d e + a e^{2} \right|} {\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}\right)} d^{3} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e + {\left(a b^{6} - 6 \, a^{2} b^{4} c - 2 \, a b^{5} c + 4 \, a^{2} b^{3} c^{2} + a b^{4} c^{2} + 32 \, a^{4} c^{3} + 16 \, a^{3} b c^{3} - 2 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d^{2} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{2} - 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c - 2 \, a^{2} b^{4} c + 16 \, a^{4} b c^{2} + 8 \, a^{3} b^{2} c^{2} + a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{3} + {\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 d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{4}\right)}}"," ",0,"-sqrt(d)*arctan(x*e^(1/2)/sqrt(d))*e^(1/2)/(c*d^2 - b*d*e + a*e^2) - 1/8*((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)*d^5 - 2*(2*b^5*c^3 - 6*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)*b^5*c + 3*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 + 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)*b^3*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)*b^3*c^3 - 2*(b^2 - 4*a*c)*a*b*c^4)*d^4*e + (2*b^6*c^2 + 4*a*b^4*c^3 - 48*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 - 2*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 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 6*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 - 12*(b^2 - 4*a*c)*a*b^2*c^3)*d^3*e^2 - 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)*d^2*abs(c*d^2 - b*d*e + a*e^2)*e - (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)*(c*d^2 - b*d*e + a*e^2)^2*d - 4*(2*a*b^5*c^2 - 6*a^2*b^3*c^3 - 8*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 + 3*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 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + 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 - 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)*a^2*b*c^3 - 2*(b^2 - 4*a*c)*a*b^3*c^2 - 2*(b^2 - 4*a*c)*a^2*b*c^3)*d^2*e^3 + 2*(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 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 32*a^3*b*c^3 + 2*(b^2 - 4*a*c)*a*b^3*c - 8*(b^2 - 4*a*c)*a^2*b*c^2)*d*abs(c*d^2 - b*d*e + a*e^2)*e^2 + 5*(2*a^2*b^4*c^2 - 8*a^3*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2*c^2)*d*e^4 - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - 2*a^2*b^4*c + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^2 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 16*a^3*b^2*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 - 32*a^4*c^3 + 2*(b^2 - 4*a*c)*a^2*b^2*c - 8*(b^2 - 4*a*c)*a^3*c^2)*abs(c*d^2 - b*d*e + a*e^2)*e^3 - 2*(2*a^3*b^3*c^2 - 8*a^4*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 - 2*(b^2 - 4*a*c)*a^3*b*c^2)*e^5)*arctan(2*sqrt(1/2)*x/sqrt((b*c*d^2 - b^2*d*e + a*b*e^2 + sqrt((b*c*d^2 - b^2*d*e + a*b*e^2)^2 - 4*(a*c*d^2 - a*b*d*e + a^2*e^2)*(c^2*d^2 - b*c*d*e + a*c*e^2)))/(c^2*d^2 - b*c*d*e + a*c*e^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)*d^4*abs(c*d^2 - b*d*e + a*e^2)*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)*d^3*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e + (a*b^6 - 6*a^2*b^4*c - 2*a*b^5*c + 4*a^2*b^3*c^2 + a*b^4*c^2 + 32*a^4*c^3 + 16*a^3*b*c^3 - 2*a^2*b^2*c^3 - 8*a^3*c^4)*d^2*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e^2 - 2*(a^2*b^5 - 8*a^3*b^3*c - 2*a^2*b^4*c + 16*a^4*b*c^2 + 8*a^3*b^2*c^2 + a^2*b^3*c^2 - 4*a^3*b*c^3)*d*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e^3 + (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*d^2 - b*d*e + a*e^2)*abs(c)*e^4) + 1/8*((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)*d^5 - 2*(2*b^5*c^3 - 6*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)*b^5*c + 3*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 + 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)*b^3*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)*b^3*c^3 - 2*(b^2 - 4*a*c)*a*b*c^4)*d^4*e + (2*b^6*c^2 + 4*a*b^4*c^3 - 48*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 - 2*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 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 6*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 - 12*(b^2 - 4*a*c)*a*b^2*c^3)*d^3*e^2 + 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)*d^2*abs(c*d^2 - b*d*e + a*e^2)*e - (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)*(c*d^2 - b*d*e + a*e^2)^2*d - 4*(2*a*b^5*c^2 - 6*a^2*b^3*c^3 - 8*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 + 3*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 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + 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 - 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)*a^2*b*c^3 - 2*(b^2 - 4*a*c)*a*b^3*c^2 - 2*(b^2 - 4*a*c)*a^2*b*c^3)*d^2*e^3 - 2*(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 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 32*a^3*b*c^3 - 2*(b^2 - 4*a*c)*a*b^3*c + 8*(b^2 - 4*a*c)*a^2*b*c^2)*d*abs(c*d^2 - b*d*e + a*e^2)*e^2 + 5*(2*a^2*b^4*c^2 - 8*a^3*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2*c^2)*d*e^4 + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c + 2*a^2*b^4*c + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^2 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 16*a^3*b^2*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 32*a^4*c^3 - 2*(b^2 - 4*a*c)*a^2*b^2*c + 8*(b^2 - 4*a*c)*a^3*c^2)*abs(c*d^2 - b*d*e + a*e^2)*e^3 - 2*(2*a^3*b^3*c^2 - 8*a^4*b*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 - 2*(b^2 - 4*a*c)*a^3*b*c^2)*e^5)*arctan(2*sqrt(1/2)*x/sqrt((b*c*d^2 - b^2*d*e + a*b*e^2 - sqrt((b*c*d^2 - b^2*d*e + a*b*e^2)^2 - 4*(a*c*d^2 - a*b*d*e + a^2*e^2)*(c^2*d^2 - b*c*d*e + a*c*e^2)))/(c^2*d^2 - b*c*d*e + a*c*e^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)*d^4*abs(c*d^2 - b*d*e + a*e^2)*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)*d^3*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e + (a*b^6 - 6*a^2*b^4*c - 2*a*b^5*c + 4*a^2*b^3*c^2 + a*b^4*c^2 + 32*a^4*c^3 + 16*a^3*b*c^3 - 2*a^2*b^2*c^3 - 8*a^3*c^4)*d^2*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e^2 - 2*(a^2*b^5 - 8*a^3*b^3*c - 2*a^2*b^4*c + 16*a^4*b*c^2 + 8*a^3*b^2*c^2 + a^2*b^3*c^2 - 4*a^3*b*c^3)*d*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e^3 + (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*d^2 - b*d*e + a*e^2)*abs(c)*e^4)","B",0
307,1,7650,0,9.134422," ","integrate(1/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{{\left(2 \, {\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)} d^{5} - 5 \, {\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)} d^{4} e + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} - 2 \, b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{4} + 16 \, a b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a c^{5} - 32 \, a^{2} c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} d^{3} {\left| c d^{2} - b d e + a e^{2} \right|} + 4 \, {\left(2 \, b^{5} c^{3} - 6 \, 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} b^{5} c + 3 \, \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} + 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} b^{3} 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)} b^{3} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} d^{3} e^{2} - 4 \, {\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)} d^{2} {\left| c d^{2} - b d e + a e^{2} \right|} e - {\left(2 \, b^{6} c^{2} + 4 \, a b^{4} c^{3} - 48 \, 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} - 2 \, \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} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 6 \, \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} - 12 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3}\right)} d^{2} e^{3} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} - 7 \, \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 + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 6 \, \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} + 14 \, 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} - 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)} b^{4} c - 6 \, {\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)} d {\left| c d^{2} - b d e + a e^{2} \right|} e^{2} - {\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)} {\left(c d^{2} - b d e + a e^{2}\right)}^{2} e + 2 \, {\left(2 \, a b^{5} c^{2} - 6 \, a^{2} b^{3} c^{3} - 8 \, 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} + 3 \, \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 + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 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} - \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} a^{2} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} d e^{4} - 2 \, {\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} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 32 \, a^{3} b 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}\right)} {\left| c d^{2} - b d e + a e^{2} \right|} e^{3} - {\left(2 \, a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2}\right)} e^{5}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c d^{2} - b^{2} d e + a b e^{2} + \sqrt{{\left(b c d^{2} - b^{2} d e + a b e^{2}\right)}^{2} - 4 \, {\left(a c d^{2} - a b d e + a^{2} e^{2}\right)} {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)}}}{c^{2} d^{2} - b c d e + a c e^{2}}}}\right)}{8 \, {\left({\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)} d^{4} {\left| c d^{2} - b d e + a e^{2} \right|} {\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}\right)} d^{3} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e + {\left(a b^{6} - 6 \, a^{2} b^{4} c - 2 \, a b^{5} c + 4 \, a^{2} b^{3} c^{2} + a b^{4} c^{2} + 32 \, a^{4} c^{3} + 16 \, a^{3} b c^{3} - 2 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d^{2} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{2} - 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c - 2 \, a^{2} b^{4} c + 16 \, a^{4} b c^{2} + 8 \, a^{3} b^{2} c^{2} + a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{3} + {\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 d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{4}\right)}} - \frac{{\left(2 \, {\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)} d^{5} - 5 \, {\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)} d^{4} e - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} + 2 \, b^{4} c^{3} + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{4} - 16 \, a b^{2} c^{4} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a c^{5} + 32 \, a^{2} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{4}\right)} d^{3} {\left| c d^{2} - b d e + a e^{2} \right|} + 4 \, {\left(2 \, b^{5} c^{3} - 6 \, 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} b^{5} c + 3 \, \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} + 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} b^{3} 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)} b^{3} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} d^{3} e^{2} + 4 \, {\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)} d^{2} {\left| c d^{2} - b d e + a e^{2} \right|} e - {\left(2 \, b^{6} c^{2} + 4 \, a b^{4} c^{3} - 48 \, 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} - 2 \, \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} + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 6 \, \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} - 12 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3}\right)} d^{2} e^{3} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} - 7 \, \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 + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 6 \, \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} - 14 \, 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} - 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)} b^{4} c + 6 \, {\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)} d {\left| c d^{2} - b d e + a e^{2} \right|} e^{2} - {\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)} {\left(c d^{2} - b d e + a e^{2}\right)}^{2} e + 2 \, {\left(2 \, a b^{5} c^{2} - 6 \, a^{2} b^{3} c^{3} - 8 \, 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} + 3 \, \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 + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} + 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} - \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} a^{2} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} d e^{4} + 2 \, {\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} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 32 \, a^{3} b 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}\right)} {\left| c d^{2} - b d e + a e^{2} \right|} e^{3} - {\left(2 \, a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2}\right)} e^{5}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{b c d^{2} - b^{2} d e + a b e^{2} - \sqrt{{\left(b c d^{2} - b^{2} d e + a b e^{2}\right)}^{2} - 4 \, {\left(a c d^{2} - a b d e + a^{2} e^{2}\right)} {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)}}}{c^{2} d^{2} - b c d e + a c e^{2}}}}\right)}{8 \, {\left({\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)} d^{4} {\left| c d^{2} - b d e + a e^{2} \right|} {\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}\right)} d^{3} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e + {\left(a b^{6} - 6 \, a^{2} b^{4} c - 2 \, a b^{5} c + 4 \, a^{2} b^{3} c^{2} + a b^{4} c^{2} + 32 \, a^{4} c^{3} + 16 \, a^{3} b c^{3} - 2 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d^{2} {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{2} - 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c - 2 \, a^{2} b^{4} c + 16 \, a^{4} b c^{2} + 8 \, a^{3} b^{2} c^{2} + a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d {\left| c d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{3} + {\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 d^{2} - b d e + a e^{2} \right|} {\left| c \right|} e^{4}\right)}} + \frac{\arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\frac{3}{2}}}{{\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{d}}"," ",0,"1/8*(2*(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)*d^5 - 5*(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)*d^4*e + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^3 - 2*b^4*c^3 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^2*c^4 + 16*a*b^2*c^4 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*c^5 - 32*a^2*c^5 + 2*(b^2 - 4*a*c)*b^2*c^3 - 8*(b^2 - 4*a*c)*a*c^4)*d^3*abs(c*d^2 - b*d*e + a*e^2) + 4*(2*b^5*c^3 - 6*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)*b^5*c + 3*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 + 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)*b^3*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)*b^3*c^3 - 2*(b^2 - 4*a*c)*a*b*c^4)*d^3*e^2 - 4*(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)*d^2*abs(c*d^2 - b*d*e + a*e^2)*e - (2*b^6*c^2 + 4*a*b^4*c^3 - 48*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 - 2*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 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 6*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 - 12*(b^2 - 4*a*c)*a*b^2*c^3)*d^2*e^3 + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 - 7*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 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 6*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 + 14*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 - 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)*b^4*c - 6*(b^2 - 4*a*c)*a*b^2*c^2 - 8*(b^2 - 4*a*c)*a^2*c^3)*d*abs(c*d^2 - b*d*e + a*e^2)*e^2 - (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)*(c*d^2 - b*d*e + a*e^2)^2*e + 2*(2*a*b^5*c^2 - 6*a^2*b^3*c^3 - 8*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 + 3*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 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + 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 - 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)*a^2*b*c^3 - 2*(b^2 - 4*a*c)*a*b^3*c^2 - 2*(b^2 - 4*a*c)*a^2*b*c^3)*d*e^4 - 2*(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 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 32*a^3*b*c^3 + 2*(b^2 - 4*a*c)*a*b^3*c - 8*(b^2 - 4*a*c)*a^2*b*c^2)*abs(c*d^2 - b*d*e + a*e^2)*e^3 - (2*a^2*b^4*c^2 - 8*a^3*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2*c^2)*e^5)*arctan(2*sqrt(1/2)*x/sqrt((b*c*d^2 - b^2*d*e + a*b*e^2 + sqrt((b*c*d^2 - b^2*d*e + a*b*e^2)^2 - 4*(a*c*d^2 - a*b*d*e + a^2*e^2)*(c^2*d^2 - b*c*d*e + a*c*e^2)))/(c^2*d^2 - b*c*d*e + a*c*e^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)*d^4*abs(c*d^2 - b*d*e + a*e^2)*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)*d^3*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e + (a*b^6 - 6*a^2*b^4*c - 2*a*b^5*c + 4*a^2*b^3*c^2 + a*b^4*c^2 + 32*a^4*c^3 + 16*a^3*b*c^3 - 2*a^2*b^2*c^3 - 8*a^3*c^4)*d^2*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e^2 - 2*(a^2*b^5 - 8*a^3*b^3*c - 2*a^2*b^4*c + 16*a^4*b*c^2 + 8*a^3*b^2*c^2 + a^2*b^3*c^2 - 4*a^3*b*c^3)*d*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e^3 + (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*d^2 - b*d*e + a*e^2)*abs(c)*e^4) - 1/8*(2*(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)*d^5 - 5*(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)*d^4*e - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^3 + 2*b^4*c^3 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^2*c^4 - 16*a*b^2*c^4 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*c^5 + 32*a^2*c^5 - 2*(b^2 - 4*a*c)*b^2*c^3 + 8*(b^2 - 4*a*c)*a*c^4)*d^3*abs(c*d^2 - b*d*e + a*e^2) + 4*(2*b^5*c^3 - 6*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)*b^5*c + 3*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 + 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)*b^3*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)*b^3*c^3 - 2*(b^2 - 4*a*c)*a*b*c^4)*d^3*e^2 + 4*(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)*d^2*abs(c*d^2 - b*d*e + a*e^2)*e - (2*b^6*c^2 + 4*a*b^4*c^3 - 48*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 - 2*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 + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 6*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 - 12*(b^2 - 4*a*c)*a*b^2*c^3)*d^2*e^3 - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 - 7*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 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 6*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 - 14*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 - 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)*b^4*c + 6*(b^2 - 4*a*c)*a*b^2*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3)*d*abs(c*d^2 - b*d*e + a*e^2)*e^2 - (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)*(c*d^2 - b*d*e + a*e^2)^2*e + 2*(2*a*b^5*c^2 - 6*a^2*b^3*c^3 - 8*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 + 3*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 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 + 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 - 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)*a^2*b*c^3 - 2*(b^2 - 4*a*c)*a*b^3*c^2 - 2*(b^2 - 4*a*c)*a^2*b*c^3)*d*e^4 + 2*(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 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 32*a^3*b*c^3 - 2*(b^2 - 4*a*c)*a*b^3*c + 8*(b^2 - 4*a*c)*a^2*b*c^2)*abs(c*d^2 - b*d*e + a*e^2)*e^3 - (2*a^2*b^4*c^2 - 8*a^3*b^2*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2*c^2)*e^5)*arctan(2*sqrt(1/2)*x/sqrt((b*c*d^2 - b^2*d*e + a*b*e^2 - sqrt((b*c*d^2 - b^2*d*e + a*b*e^2)^2 - 4*(a*c*d^2 - a*b*d*e + a^2*e^2)*(c^2*d^2 - b*c*d*e + a*c*e^2)))/(c^2*d^2 - b*c*d*e + a*c*e^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)*d^4*abs(c*d^2 - b*d*e + a*e^2)*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)*d^3*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e + (a*b^6 - 6*a^2*b^4*c - 2*a*b^5*c + 4*a^2*b^3*c^2 + a*b^4*c^2 + 32*a^4*c^3 + 16*a^3*b*c^3 - 2*a^2*b^2*c^3 - 8*a^3*c^4)*d^2*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e^2 - 2*(a^2*b^5 - 8*a^3*b^3*c - 2*a^2*b^4*c + 16*a^4*b*c^2 + 8*a^3*b^2*c^2 + a^2*b^3*c^2 - 4*a^3*b*c^3)*d*abs(c*d^2 - b*d*e + a*e^2)*abs(c)*e^3 + (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*d^2 - b*d*e + a*e^2)*abs(c)*e^4) + arctan(x*e^(1/2)/sqrt(d))*e^(3/2)/((c*d^2 - b*d*e + a*e^2)*sqrt(d))","B",0
308,1,10058,0,12.817503," ","integrate(1/x^2/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left({\left(2 \, a^{2} b^{4} c^{5} - 8 \, a^{3} b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{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} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{5}\right)} d^{5} - {\left(6 \, a^{2} b^{5} c^{4} - 28 \, a^{3} b^{3} c^{5} + 16 \, a^{4} b c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{5}\right)} d^{4} 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)} d^{3} {\left| a c d^{2} - a b d e + a^{2} e^{2} \right|} + {\left(6 \, a^{2} b^{6} c^{3} - 28 \, a^{3} b^{4} c^{4} + 16 \, a^{4} b^{2} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c + 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{3} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{4}\right)} d^{3} e^{2} - 2 \, {\left(2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 17 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} - 4 \, a b^{6} c^{2} + 40 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} + 18 \, \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} + 34 \, a^{2} b^{4} c^{3} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 9 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 80 \, a^{3} b^{2} c^{4} + 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} + 32 \, a^{4} c^{5} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} - 18 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} d^{2} {\left| a c d^{2} - a b d e + a^{2} e^{2} \right|} e + {\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)} {\left(a c d^{2} - a b d e + a^{2} e^{2}\right)}^{2} d - {\left(2 \, a^{2} b^{7} c^{2} - 4 \, a^{3} b^{5} c^{3} - 24 \, a^{4} b^{3} c^{4} + 32 \, 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} + 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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} + 4 \, \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} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} - 8 \, \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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} + 4 \, \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} - 4 \, {\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)} d^{2} e^{3} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 8 \, \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 + 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 8 \, \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} + 16 \, a^{2} b^{5} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 32 \, a^{3} b^{3} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2}\right)} d {\left| a c d^{2} - a b d e + a^{2} e^{2} \right|} e^{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)} {\left(a c d^{2} - a b d e + a^{2} e^{2}\right)}^{2} e + {\left(4 \, a^{3} b^{6} c^{2} - 22 \, a^{4} b^{4} c^{3} + 24 \, a^{5} b^{2} 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} + 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} 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^{5} c - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{2} - 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} - 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} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{2} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{3}\right)} d e^{4} - 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 c d^{2} - a b d e + a^{2} e^{2} \right|} e^{3} - {\left(2 \, a^{4} b^{5} c^{2} - 12 \, a^{5} b^{3} c^{3} + 16 \, a^{6} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} + 6 \, \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^{4} b^{4} c - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{2} - 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^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{3} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{3}\right)} e^{5}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b c d^{2} - a b^{2} d e + a^{2} b e^{2} + \sqrt{{\left(a b c d^{2} - a b^{2} d e + a^{2} b e^{2}\right)}^{2} - 4 \, {\left(a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2}\right)} {\left(a c^{2} d^{2} - a b c d e + a^{2} c e^{2}\right)}}}{a c^{2} d^{2} - a b c d e + a^{2} c e^{2}}}}\right)}{8 \, {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} - 2 \, a^{3} b^{3} c^{3} + 16 \, a^{5} c^{4} + 8 \, a^{4} b c^{4} + a^{3} b^{2} c^{4} - 4 \, a^{4} c^{5}\right)} d^{4} {\left| a c d^{2} - a b d e + a^{2} e^{2} \right|} {\left| c \right|} - 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} - 2 \, a^{3} b^{4} c^{2} + 16 \, a^{5} b c^{3} + 8 \, a^{4} b^{2} c^{3} + a^{3} b^{3} c^{3} - 4 \, a^{4} b c^{4}\right)} d^{3} {\left| a c d^{2} - a b d e + a^{2} e^{2} \right|} {\left| c \right|} e + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c - 2 \, a^{3} b^{5} c + 4 \, a^{4} b^{3} c^{2} + a^{3} b^{4} c^{2} + 32 \, a^{6} c^{3} + 16 \, a^{5} b c^{3} - 2 \, a^{4} b^{2} c^{3} - 8 \, a^{5} c^{4}\right)} d^{2} {\left| a c d^{2} - a b d e + a^{2} e^{2} \right|} {\left| c \right|} e^{2} - 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c - 2 \, a^{4} b^{4} c + 16 \, a^{6} b c^{2} + 8 \, a^{5} b^{2} c^{2} + a^{4} b^{3} c^{2} - 4 \, a^{5} b c^{3}\right)} d {\left| a c d^{2} - a b d e + a^{2} e^{2} \right|} {\left| c \right|} e^{3} + {\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 c d^{2} - a b d e + a^{2} e^{2} \right|} {\left| c \right|} e^{4}\right)}} + \frac{{\left({\left(2 \, a^{2} b^{4} c^{5} - 8 \, a^{3} b^{2} c^{6} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{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} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{5}\right)} d^{5} - {\left(6 \, a^{2} b^{5} c^{4} - 28 \, a^{3} b^{3} c^{5} + 16 \, a^{4} b c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} + 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{4} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{5}\right)} d^{4} 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)} d^{3} {\left| a c d^{2} - a b d e + a^{2} e^{2} \right|} + {\left(6 \, a^{2} b^{6} c^{3} - 28 \, a^{3} b^{4} c^{4} + 16 \, a^{4} b^{2} c^{5} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c + 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{4} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{4} c^{3} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c^{4}\right)} d^{3} e^{2} + 2 \, {\left(2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{6} c - 17 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + 4 \, a b^{6} c^{2} + 40 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{3} + 18 \, \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} - 34 \, a^{2} b^{4} c^{3} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} - 9 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 80 \, a^{3} b^{2} c^{4} + 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{5} - 32 \, a^{4} c^{5} - 4 \, {\left(b^{2} - 4 \, a c\right)} a b^{4} c^{2} + 18 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{4}\right)} d^{2} {\left| a c d^{2} - a b d e + a^{2} e^{2} \right|} e + {\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)} {\left(a c d^{2} - a b d e + a^{2} e^{2}\right)}^{2} d - {\left(2 \, a^{2} b^{7} c^{2} - 4 \, a^{3} b^{5} c^{3} - 24 \, a^{4} b^{3} c^{4} + 32 \, 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} + 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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c + 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{2} + 4 \, \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} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} - 8 \, \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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{3} + 4 \, \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} - 4 \, {\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)} d^{2} e^{3} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{7} - 8 \, \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 + 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{2} + 8 \, \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} - 16 \, a^{2} b^{5} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} + 32 \, a^{3} b^{3} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{5} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} c^{2}\right)} d {\left| a c d^{2} - a b d e + a^{2} e^{2} \right|} e^{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)} {\left(a c d^{2} - a b d e + a^{2} e^{2}\right)}^{2} e + {\left(4 \, a^{3} b^{6} c^{2} - 22 \, a^{4} b^{4} c^{3} + 24 \, a^{5} b^{2} 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} + 11 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} 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^{5} c - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{2} - 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} - 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} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{2} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{3}\right)} d e^{4} + 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 c d^{2} - a b d e + a^{2} e^{2} \right|} e^{3} - {\left(2 \, a^{4} b^{5} c^{2} - 12 \, a^{5} b^{3} c^{3} + 16 \, a^{6} b c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} + 6 \, \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^{4} b^{4} c - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{2} - 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^{2} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{3} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{3}\right)} e^{5}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a b c d^{2} - a b^{2} d e + a^{2} b e^{2} - \sqrt{{\left(a b c d^{2} - a b^{2} d e + a^{2} b e^{2}\right)}^{2} - 4 \, {\left(a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2}\right)} {\left(a c^{2} d^{2} - a b c d e + a^{2} c e^{2}\right)}}}{a c^{2} d^{2} - a b c d e + a^{2} c e^{2}}}}\right)}{8 \, {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} - 2 \, a^{3} b^{3} c^{3} + 16 \, a^{5} c^{4} + 8 \, a^{4} b c^{4} + a^{3} b^{2} c^{4} - 4 \, a^{4} c^{5}\right)} d^{4} {\left| a c d^{2} - a b d e + a^{2} e^{2} \right|} {\left| c \right|} - 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} - 2 \, a^{3} b^{4} c^{2} + 16 \, a^{5} b c^{3} + 8 \, a^{4} b^{2} c^{3} + a^{3} b^{3} c^{3} - 4 \, a^{4} b c^{4}\right)} d^{3} {\left| a c d^{2} - a b d e + a^{2} e^{2} \right|} {\left| c \right|} e + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c - 2 \, a^{3} b^{5} c + 4 \, a^{4} b^{3} c^{2} + a^{3} b^{4} c^{2} + 32 \, a^{6} c^{3} + 16 \, a^{5} b c^{3} - 2 \, a^{4} b^{2} c^{3} - 8 \, a^{5} c^{4}\right)} d^{2} {\left| a c d^{2} - a b d e + a^{2} e^{2} \right|} {\left| c \right|} e^{2} - 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c - 2 \, a^{4} b^{4} c + 16 \, a^{6} b c^{2} + 8 \, a^{5} b^{2} c^{2} + a^{4} b^{3} c^{2} - 4 \, a^{5} b c^{3}\right)} d {\left| a c d^{2} - a b d e + a^{2} e^{2} \right|} {\left| c \right|} e^{3} + {\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 c d^{2} - a b d e + a^{2} e^{2} \right|} {\left| c \right|} e^{4}\right)}} - \frac{\arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\frac{5}{2}}}{{\left(c d^{3} - b d^{2} e + a d e^{2}\right)} \sqrt{d}} - \frac{1}{a d x}"," ",0,"-1/8*((2*a^2*b^4*c^5 - 8*a^3*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^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 - 2*(b^2 - 4*a*c)*a^2*b^2*c^5)*d^5 - (6*a^2*b^5*c^4 - 28*a^3*b^3*c^5 + 16*a^4*b*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 + 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 - 6*(b^2 - 4*a*c)*a^2*b^3*c^4 + 4*(b^2 - 4*a*c)*a^3*b*c^5)*d^4*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)*d^3*abs(a*c*d^2 - a*b*d*e + a^2*e^2) + (6*a^2*b^6*c^3 - 28*a^3*b^4*c^4 + 16*a^4*b^2*c^5 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c + 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 - 6*(b^2 - 4*a*c)*a^2*b^4*c^3 + 4*(b^2 - 4*a*c)*a^3*b^2*c^4)*d^3*e^2 - 2*(2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^6*c - 17*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 - 4*a*b^6*c^2 + 40*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 + 18*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 + 34*a^2*b^4*c^3 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*c^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 - 9*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 80*a^3*b^2*c^4 + 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^5 + 32*a^4*c^5 + 4*(b^2 - 4*a*c)*a*b^4*c^2 - 18*(b^2 - 4*a*c)*a^2*b^2*c^3 + 8*(b^2 - 4*a*c)*a^3*c^4)*d^2*abs(a*c*d^2 - a*b*d*e + a^2*e^2)*e + (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*d^2 - a*b*d*e + a^2*e^2)^2*d - (2*a^2*b^7*c^2 - 4*a^3*b^5*c^3 - 24*a^4*b^3*c^4 + 32*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 + 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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 + 4*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 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 - 8*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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 + 4*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 - 4*(b^2 - 4*a*c)*a^3*b^3*c^3 + 8*(b^2 - 4*a*c)*a^4*b*c^4)*d^2*e^3 + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^7 - 8*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 + 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + 8*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 + 16*a^2*b^5*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 32*a^3*b^3*c^3 + 2*(b^2 - 4*a*c)*a*b^5*c - 8*(b^2 - 4*a*c)*a^2*b^3*c^2)*d*abs(a*c*d^2 - a*b*d*e + a^2*e^2)*e^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)*(a*c*d^2 - a*b*d*e + a^2*e^2)^2*e + (4*a^3*b^6*c^2 - 22*a^4*b^4*c^3 + 24*a^5*b^2*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 + 11*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*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^5*c - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^2 - 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 - 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 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 - 4*(b^2 - 4*a*c)*a^3*b^4*c^2 + 6*(b^2 - 4*a*c)*a^4*b^2*c^3)*d*e^4 - 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*c*d^2 - a*b*d*e + a^2*e^2)*e^3 - (2*a^4*b^5*c^2 - 12*a^5*b^3*c^3 + 16*a^6*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5 + 6*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^4*b^4*c - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^2 - 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^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 - 2*(b^2 - 4*a*c)*a^4*b^3*c^2 + 4*(b^2 - 4*a*c)*a^5*b*c^3)*e^5)*arctan(2*sqrt(1/2)*x/sqrt((a*b*c*d^2 - a*b^2*d*e + a^2*b*e^2 + sqrt((a*b*c*d^2 - a*b^2*d*e + a^2*b*e^2)^2 - 4*(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*(a*c^2*d^2 - a*b*c*d*e + a^2*c*e^2)))/(a*c^2*d^2 - a*b*c*d*e + a^2*c*e^2)))/((a^3*b^4*c^2 - 8*a^4*b^2*c^3 - 2*a^3*b^3*c^3 + 16*a^5*c^4 + 8*a^4*b*c^4 + a^3*b^2*c^4 - 4*a^4*c^5)*d^4*abs(a*c*d^2 - a*b*d*e + a^2*e^2)*abs(c) - 2*(a^3*b^5*c - 8*a^4*b^3*c^2 - 2*a^3*b^4*c^2 + 16*a^5*b*c^3 + 8*a^4*b^2*c^3 + a^3*b^3*c^3 - 4*a^4*b*c^4)*d^3*abs(a*c*d^2 - a*b*d*e + a^2*e^2)*abs(c)*e + (a^3*b^6 - 6*a^4*b^4*c - 2*a^3*b^5*c + 4*a^4*b^3*c^2 + a^3*b^4*c^2 + 32*a^6*c^3 + 16*a^5*b*c^3 - 2*a^4*b^2*c^3 - 8*a^5*c^4)*d^2*abs(a*c*d^2 - a*b*d*e + a^2*e^2)*abs(c)*e^2 - 2*(a^4*b^5 - 8*a^5*b^3*c - 2*a^4*b^4*c + 16*a^6*b*c^2 + 8*a^5*b^2*c^2 + a^4*b^3*c^2 - 4*a^5*b*c^3)*d*abs(a*c*d^2 - a*b*d*e + a^2*e^2)*abs(c)*e^3 + (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*c*d^2 - a*b*d*e + a^2*e^2)*abs(c)*e^4) + 1/8*((2*a^2*b^4*c^5 - 8*a^3*b^2*c^6 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^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 - 2*(b^2 - 4*a*c)*a^2*b^2*c^5)*d^5 - (6*a^2*b^5*c^4 - 28*a^3*b^3*c^5 + 16*a^4*b*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 + 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^4 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^5 - 6*(b^2 - 4*a*c)*a^2*b^3*c^4 + 4*(b^2 - 4*a*c)*a^3*b*c^5)*d^4*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)*d^3*abs(a*c*d^2 - a*b*d*e + a^2*e^2) + (6*a^2*b^6*c^3 - 28*a^3*b^4*c^4 + 16*a^4*b^2*c^5 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c + 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^2 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^4 - 6*(b^2 - 4*a*c)*a^2*b^4*c^3 + 4*(b^2 - 4*a*c)*a^3*b^2*c^4)*d^3*e^2 + 2*(2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^6*c - 17*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 + 4*a*b^6*c^2 + 40*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^3 + 18*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 - 34*a^2*b^4*c^3 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*c^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 - 9*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + 80*a^3*b^2*c^4 + 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^5 - 32*a^4*c^5 - 4*(b^2 - 4*a*c)*a*b^4*c^2 + 18*(b^2 - 4*a*c)*a^2*b^2*c^3 - 8*(b^2 - 4*a*c)*a^3*c^4)*d^2*abs(a*c*d^2 - a*b*d*e + a^2*e^2)*e + (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*d^2 - a*b*d*e + a^2*e^2)^2*d - (2*a^2*b^7*c^2 - 4*a^3*b^5*c^3 - 24*a^4*b^3*c^4 + 32*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 + 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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c + 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^2 + 4*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 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 - 8*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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^3 + 4*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 - 4*(b^2 - 4*a*c)*a^3*b^3*c^3 + 8*(b^2 - 4*a*c)*a^4*b*c^4)*d^2*e^3 - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^7 - 8*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 + 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^2 + 8*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 - 16*a^2*b^5*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 + 32*a^3*b^3*c^3 - 2*(b^2 - 4*a*c)*a*b^5*c + 8*(b^2 - 4*a*c)*a^2*b^3*c^2)*d*abs(a*c*d^2 - a*b*d*e + a^2*e^2)*e^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)*(a*c*d^2 - a*b*d*e + a^2*e^2)^2*e + (4*a^3*b^6*c^2 - 22*a^4*b^4*c^3 + 24*a^5*b^2*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 + 11*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*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^5*c - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^2 - 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 - 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 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^3 - 4*(b^2 - 4*a*c)*a^3*b^4*c^2 + 6*(b^2 - 4*a*c)*a^4*b^2*c^3)*d*e^4 + 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*c*d^2 - a*b*d*e + a^2*e^2)*e^3 - (2*a^4*b^5*c^2 - 12*a^5*b^3*c^3 + 16*a^6*b*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5 + 6*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^4*b^4*c - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^2 - 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^2 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^3 - 2*(b^2 - 4*a*c)*a^4*b^3*c^2 + 4*(b^2 - 4*a*c)*a^5*b*c^3)*e^5)*arctan(2*sqrt(1/2)*x/sqrt((a*b*c*d^2 - a*b^2*d*e + a^2*b*e^2 - sqrt((a*b*c*d^2 - a*b^2*d*e + a^2*b*e^2)^2 - 4*(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*(a*c^2*d^2 - a*b*c*d*e + a^2*c*e^2)))/(a*c^2*d^2 - a*b*c*d*e + a^2*c*e^2)))/((a^3*b^4*c^2 - 8*a^4*b^2*c^3 - 2*a^3*b^3*c^3 + 16*a^5*c^4 + 8*a^4*b*c^4 + a^3*b^2*c^4 - 4*a^4*c^5)*d^4*abs(a*c*d^2 - a*b*d*e + a^2*e^2)*abs(c) - 2*(a^3*b^5*c - 8*a^4*b^3*c^2 - 2*a^3*b^4*c^2 + 16*a^5*b*c^3 + 8*a^4*b^2*c^3 + a^3*b^3*c^3 - 4*a^4*b*c^4)*d^3*abs(a*c*d^2 - a*b*d*e + a^2*e^2)*abs(c)*e + (a^3*b^6 - 6*a^4*b^4*c - 2*a^3*b^5*c + 4*a^4*b^3*c^2 + a^3*b^4*c^2 + 32*a^6*c^3 + 16*a^5*b*c^3 - 2*a^4*b^2*c^3 - 8*a^5*c^4)*d^2*abs(a*c*d^2 - a*b*d*e + a^2*e^2)*abs(c)*e^2 - 2*(a^4*b^5 - 8*a^5*b^3*c - 2*a^4*b^4*c + 16*a^6*b*c^2 + 8*a^5*b^2*c^2 + a^4*b^3*c^2 - 4*a^5*b*c^3)*d*abs(a*c*d^2 - a*b*d*e + a^2*e^2)*abs(c)*e^3 + (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*c*d^2 - a*b*d*e + a^2*e^2)*abs(c)*e^4) - arctan(x*e^(1/2)/sqrt(d))*e^(5/2)/((c*d^3 - b*d^2*e + a*d*e^2)*sqrt(d)) - 1/(a*d*x)","B",0
309,1,12268,0,11.999734," ","integrate(1/x^4/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{{\left({\left(2 \, a^{4} b^{5} c^{5} - 12 \, a^{5} b^{3} c^{6} + 16 \, a^{6} b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{5} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} 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^{4} b^{3} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{3} c^{5} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{6}\right)} d^{5} - {\left(6 \, a^{4} b^{6} c^{4} - 38 \, a^{5} b^{4} c^{5} + 56 \, a^{6} 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^{6} c^{2} + 19 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{3} - 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{4} - 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{4} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{4} c^{4} + 14 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{2} c^{5}\right)} d^{4} e + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} - 9 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} - 2 \, a^{2} b^{6} c^{3} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} + 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} + 18 \, 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} - 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} - 48 \, 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^{2} b^{4} c^{3} - 10 \, {\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)} d^{3} {\left| a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2} \right|} + {\left(6 \, a^{4} b^{7} c^{3} - 36 \, a^{5} b^{5} c^{4} + 40 \, a^{6} b^{3} c^{5} + 32 \, a^{7} b c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c + 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{3} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{3} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{3} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{4} - 8 \, \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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{5} c^{3} + 12 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{3} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b c^{5}\right)} d^{3} e^{2} - 2 \, {\left(2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c - 19 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} - 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} - 4 \, a^{2} b^{7} c^{2} + 56 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} + 22 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} + 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} + 38 \, a^{3} b^{5} c^{3} - 48 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} - 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} - 11 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} - 112 \, a^{4} b^{3} c^{4} + 12 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} + 96 \, a^{5} b c^{5} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} - 22 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} + 24 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} d^{2} {\left| a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2} \right|} e + {\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)} {\left(a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2}\right)}^{2} d - {\left(2 \, a^{4} b^{8} c^{2} - 6 \, a^{5} b^{6} c^{3} - 28 \, a^{6} b^{4} c^{4} + 80 \, a^{7} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c + 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{2} + 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} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{2} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{3} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{6} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c^{3} + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{4}\right)} d^{2} e^{3} + 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{8} - 9 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c - 2 \, a^{2} b^{8} c + 23 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{2} + 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} + 18 \, a^{3} b^{6} c^{2} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 46 \, a^{4} b^{4} c^{3} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{4} - 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} + 3 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} + 16 \, a^{5} b^{2} c^{4} + 4 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{5} + 32 \, a^{6} c^{5} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{6} c - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{2} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{5} c^{4}\right)} d {\left| a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2} \right|} e^{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)} {\left(a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2}\right)}^{2} e + {\left(4 \, a^{5} b^{7} c^{2} - 26 \, a^{6} b^{5} c^{3} + 36 \, a^{7} b^{3} c^{4} + 16 \, a^{8} b c^{5} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} + 13 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{2} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{2} - 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} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b 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^{3} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{4} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{5} c^{2} + 10 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{3} c^{3} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{4}\right)} d e^{4} - 2 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c - 2 \, a^{3} b^{7} c + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{2} + 12 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} + 20 \, a^{4} b^{5} c^{2} - 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{3} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} - 6 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 64 \, a^{5} b^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} + 64 \, a^{6} b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{5} c - 12 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{3} c^{2} + 16 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{3}\right)} {\left| a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2} \right|} e^{3} - {\left(2 \, a^{6} b^{6} c^{2} - 14 \, a^{7} b^{4} c^{3} + 24 \, 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} + 7 \, \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 - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{2} c^{2} - 6 \, \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} + 3 \, \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} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{2} c^{3}\right)} e^{5}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{2} b c d^{2} - a^{2} b^{2} d e + a^{3} b e^{2} + \sqrt{{\left(a^{2} b c d^{2} - a^{2} b^{2} d e + a^{3} b e^{2}\right)}^{2} - 4 \, {\left(a^{3} c d^{2} - a^{3} b d e + a^{4} e^{2}\right)} {\left(a^{2} c^{2} d^{2} - a^{2} b c d e + a^{3} c e^{2}\right)}}}{a^{2} c^{2} d^{2} - a^{2} b c d e + a^{3} c e^{2}}}}\right)}{8 \, {\left({\left(a^{5} b^{4} c^{2} - 8 \, a^{6} b^{2} c^{3} - 2 \, a^{5} b^{3} c^{3} + 16 \, a^{7} c^{4} + 8 \, a^{6} b c^{4} + a^{5} b^{2} c^{4} - 4 \, a^{6} c^{5}\right)} d^{4} {\left| a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2} \right|} {\left| c \right|} - 2 \, {\left(a^{5} b^{5} c - 8 \, a^{6} b^{3} c^{2} - 2 \, a^{5} b^{4} c^{2} + 16 \, a^{7} b c^{3} + 8 \, a^{6} b^{2} c^{3} + a^{5} b^{3} c^{3} - 4 \, a^{6} b c^{4}\right)} d^{3} {\left| a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2} \right|} {\left| c \right|} e + {\left(a^{5} b^{6} - 6 \, a^{6} b^{4} c - 2 \, a^{5} b^{5} c + 4 \, a^{6} b^{3} c^{2} + a^{5} b^{4} c^{2} + 32 \, a^{8} c^{3} + 16 \, a^{7} b c^{3} - 2 \, a^{6} b^{2} c^{3} - 8 \, a^{7} c^{4}\right)} d^{2} {\left| a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2} \right|} {\left| c \right|} e^{2} - 2 \, {\left(a^{6} b^{5} - 8 \, a^{7} b^{3} c - 2 \, a^{6} b^{4} c + 16 \, a^{8} b c^{2} + 8 \, a^{7} b^{2} c^{2} + a^{6} b^{3} c^{2} - 4 \, a^{7} b c^{3}\right)} d {\left| a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2} \right|} {\left| c \right|} e^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c - 2 \, a^{7} b^{3} c + 16 \, a^{9} c^{2} + 8 \, a^{8} b c^{2} + a^{7} b^{2} c^{2} - 4 \, a^{8} c^{3}\right)} {\left| a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2} \right|} {\left| c \right|} e^{4}\right)}} - \frac{{\left({\left(2 \, a^{4} b^{5} c^{5} - 12 \, a^{5} b^{3} c^{6} + 16 \, a^{6} b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{4} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{4} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{5} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} 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^{4} b^{3} c^{5} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{3} c^{5} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{6}\right)} d^{5} - {\left(6 \, a^{4} b^{6} c^{4} - 38 \, a^{5} b^{4} c^{5} + 56 \, a^{6} 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^{6} c^{2} + 19 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{3} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{3} - 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{4} - 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{4} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{4} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{4} c^{4} + 14 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{2} c^{5}\right)} d^{4} e - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} - 9 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} + 2 \, a^{2} b^{6} c^{3} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} + 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} c^{4} - 18 \, 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} - 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c^{5} + 48 \, 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^{2} b^{4} c^{3} + 10 \, {\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)} d^{3} {\left| a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2} \right|} + {\left(6 \, a^{4} b^{7} c^{3} - 36 \, a^{5} b^{5} c^{4} + 40 \, a^{6} b^{3} c^{5} + 32 \, a^{7} b c^{6} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c + 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{3} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{3} - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{3} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{4} - 8 \, \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 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{4} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{5} c^{3} + 12 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{3} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b c^{5}\right)} d^{3} e^{2} + 2 \, {\left(2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c - 19 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} - 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} + 4 \, a^{2} b^{7} c^{2} + 56 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} + 22 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} + 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{5} c^{3} - 38 \, a^{3} b^{5} c^{3} - 48 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} - 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} - 11 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} c^{4} + 112 \, a^{4} b^{3} c^{4} + 12 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c^{5} - 96 \, a^{5} b c^{5} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{5} c^{2} + 22 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} c^{3} - 24 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c^{4}\right)} d^{2} {\left| a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2} \right|} e + {\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)} {\left(a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2}\right)}^{2} d - {\left(2 \, a^{4} b^{8} c^{2} - 6 \, a^{5} b^{6} c^{3} - 28 \, a^{6} b^{4} c^{4} + 80 \, a^{7} b^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} + 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c + 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{2} + 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} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c^{2} - 40 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{3} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{6} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{4} c^{3} + 20 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{2} c^{4}\right)} d^{2} e^{3} - 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{8} - 9 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{7} c + 2 \, a^{2} b^{8} c + 23 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{2} + 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{6} c^{2} - 18 \, a^{3} b^{6} c^{2} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} - 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{4} c^{3} + 46 \, a^{4} b^{4} c^{3} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{4} - 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} + 3 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{2} c^{4} - 16 \, a^{5} b^{2} c^{4} + 4 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} c^{5} - 32 \, a^{6} c^{5} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{6} c + 10 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{4} c^{2} - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{5} c^{4}\right)} d {\left| a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2} \right|} e^{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)} {\left(a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2}\right)}^{2} e + {\left(4 \, a^{5} b^{7} c^{2} - 26 \, a^{6} b^{5} c^{3} + 36 \, a^{7} b^{3} c^{4} + 16 \, a^{8} b c^{5} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} + 13 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c - 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{2} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{2} - 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} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b 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^{3} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{3} + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{4} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{5} c^{2} + 10 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{3} c^{3} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{4}\right)} d e^{4} + 2 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c + 2 \, a^{3} b^{7} c + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{2} + 12 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{5} c^{2} - 20 \, a^{4} b^{5} c^{2} - 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{3} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{3} - 6 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{3} c^{3} + 64 \, a^{5} b^{3} c^{3} + 8 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b c^{4} - 64 \, a^{6} b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{5} c + 12 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{3} c^{2} - 16 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c^{3}\right)} {\left| a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2} \right|} e^{3} - {\left(2 \, a^{6} b^{6} c^{2} - 14 \, a^{7} b^{4} c^{3} + 24 \, 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} + 7 \, \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 - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{2} c^{2} - 6 \, \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} + 3 \, \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} + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{2} c^{3}\right)} e^{5}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} x}{\sqrt{\frac{a^{2} b c d^{2} - a^{2} b^{2} d e + a^{3} b e^{2} - \sqrt{{\left(a^{2} b c d^{2} - a^{2} b^{2} d e + a^{3} b e^{2}\right)}^{2} - 4 \, {\left(a^{3} c d^{2} - a^{3} b d e + a^{4} e^{2}\right)} {\left(a^{2} c^{2} d^{2} - a^{2} b c d e + a^{3} c e^{2}\right)}}}{a^{2} c^{2} d^{2} - a^{2} b c d e + a^{3} c e^{2}}}}\right)}{8 \, {\left({\left(a^{5} b^{4} c^{2} - 8 \, a^{6} b^{2} c^{3} - 2 \, a^{5} b^{3} c^{3} + 16 \, a^{7} c^{4} + 8 \, a^{6} b c^{4} + a^{5} b^{2} c^{4} - 4 \, a^{6} c^{5}\right)} d^{4} {\left| a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2} \right|} {\left| c \right|} - 2 \, {\left(a^{5} b^{5} c - 8 \, a^{6} b^{3} c^{2} - 2 \, a^{5} b^{4} c^{2} + 16 \, a^{7} b c^{3} + 8 \, a^{6} b^{2} c^{3} + a^{5} b^{3} c^{3} - 4 \, a^{6} b c^{4}\right)} d^{3} {\left| a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2} \right|} {\left| c \right|} e + {\left(a^{5} b^{6} - 6 \, a^{6} b^{4} c - 2 \, a^{5} b^{5} c + 4 \, a^{6} b^{3} c^{2} + a^{5} b^{4} c^{2} + 32 \, a^{8} c^{3} + 16 \, a^{7} b c^{3} - 2 \, a^{6} b^{2} c^{3} - 8 \, a^{7} c^{4}\right)} d^{2} {\left| a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2} \right|} {\left| c \right|} e^{2} - 2 \, {\left(a^{6} b^{5} - 8 \, a^{7} b^{3} c - 2 \, a^{6} b^{4} c + 16 \, a^{8} b c^{2} + 8 \, a^{7} b^{2} c^{2} + a^{6} b^{3} c^{2} - 4 \, a^{7} b c^{3}\right)} d {\left| a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2} \right|} {\left| c \right|} e^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c - 2 \, a^{7} b^{3} c + 16 \, a^{9} c^{2} + 8 \, a^{8} b c^{2} + a^{7} b^{2} c^{2} - 4 \, a^{8} c^{3}\right)} {\left| a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2} \right|} {\left| c \right|} e^{4}\right)}} + \frac{\arctan\left(\frac{x e^{\frac{1}{2}}}{\sqrt{d}}\right) e^{\frac{7}{2}}}{{\left(c d^{4} - b d^{3} e + a d^{2} e^{2}\right)} \sqrt{d}} + \frac{3 \, b d x^{2} + 3 \, a x^{2} e - a d}{3 \, a^{2} d^{2} x^{3}}"," ",0,"1/8*((2*a^4*b^5*c^5 - 12*a^5*b^3*c^6 + 16*a^6*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^5 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*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^4*b^3*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^6 - 2*(b^2 - 4*a*c)*a^4*b^3*c^5 + 4*(b^2 - 4*a*c)*a^5*b*c^6)*d^5 - (6*a^4*b^6*c^4 - 38*a^5*b^4*c^5 + 56*a^6*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^6*c^2 + 19*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^3 - 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^4 - 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^4 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^5 - 6*(b^2 - 4*a*c)*a^4*b^4*c^4 + 14*(b^2 - 4*a*c)*a^5*b^2*c^5)*d^4*e + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 - 9*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 - 2*a^2*b^6*c^3 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 + 18*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 - 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 - 48*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^2*b^4*c^3 - 10*(b^2 - 4*a*c)*a^3*b^2*c^4 + 8*(b^2 - 4*a*c)*a^4*c^5)*d^3*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2) + (6*a^4*b^7*c^3 - 36*a^5*b^5*c^4 + 40*a^6*b^3*c^5 + 32*a^7*b*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c + 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^3 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^3 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^3 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b*c^4 - 8*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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^5 - 6*(b^2 - 4*a*c)*a^4*b^5*c^3 + 12*(b^2 - 4*a*c)*a^5*b^3*c^4 + 8*(b^2 - 4*a*c)*a^6*b*c^5)*d^3*e^2 - 2*(2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c - 19*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 - 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 - 4*a^2*b^7*c^2 + 56*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 + 22*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 + 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 + 38*a^3*b^5*c^3 - 48*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 - 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 11*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 - 112*a^4*b^3*c^4 + 12*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 + 96*a^5*b*c^5 + 4*(b^2 - 4*a*c)*a^2*b^5*c^2 - 22*(b^2 - 4*a*c)*a^3*b^3*c^3 + 24*(b^2 - 4*a*c)*a^4*b*c^4)*d^2*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*e + (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^2*c*d^2 - a^2*b*d*e + a^3*e^2)^2*d - (2*a^4*b^8*c^2 - 6*a^5*b^6*c^3 - 28*a^6*b^4*c^4 + 80*a^7*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^8 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c + 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^2 - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^3 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^3 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^4 - 2*(b^2 - 4*a*c)*a^4*b^6*c^2 - 2*(b^2 - 4*a*c)*a^5*b^4*c^3 + 20*(b^2 - 4*a*c)*a^6*b^2*c^4)*d^2*e^3 + 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^8 - 9*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c - 2*a^2*b^8*c + 23*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^2 + 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 + 18*a^3*b^6*c^2 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 46*a^4*b^4*c^3 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*c^4 - 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 + 3*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + 16*a^5*b^2*c^4 + 4*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*c^5 + 32*a^6*c^5 + 2*(b^2 - 4*a*c)*a^2*b^6*c - 10*(b^2 - 4*a*c)*a^3*b^4*c^2 + 6*(b^2 - 4*a*c)*a^4*b^2*c^3 + 8*(b^2 - 4*a*c)*a^5*c^4)*d*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*e^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)*(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)^2*e + (4*a^5*b^7*c^2 - 26*a^6*b^5*c^3 + 36*a^7*b^3*c^4 + 16*a^8*b*c^5 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^7 + 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^2 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 - 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 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b*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^3 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b*c^4 - 4*(b^2 - 4*a*c)*a^5*b^5*c^2 + 10*(b^2 - 4*a*c)*a^6*b^3*c^3 + 4*(b^2 - 4*a*c)*a^7*b*c^4)*d*e^4 - 2*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^7 - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c - 2*a^3*b^7*c + 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^2 + 12*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + 20*a^4*b^5*c^2 - 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^3 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 - 6*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 64*a^5*b^3*c^3 + 8*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 + 64*a^6*b*c^4 + 2*(b^2 - 4*a*c)*a^3*b^5*c - 12*(b^2 - 4*a*c)*a^4*b^3*c^2 + 16*(b^2 - 4*a*c)*a^5*b*c^3)*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*e^3 - (2*a^6*b^6*c^2 - 14*a^7*b^4*c^3 + 24*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 + 7*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 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^2*c^2 - 6*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 + 3*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 + 6*(b^2 - 4*a*c)*a^7*b^2*c^3)*e^5)*arctan(2*sqrt(1/2)*x/sqrt((a^2*b*c*d^2 - a^2*b^2*d*e + a^3*b*e^2 + sqrt((a^2*b*c*d^2 - a^2*b^2*d*e + a^3*b*e^2)^2 - 4*(a^3*c*d^2 - a^3*b*d*e + a^4*e^2)*(a^2*c^2*d^2 - a^2*b*c*d*e + a^3*c*e^2)))/(a^2*c^2*d^2 - a^2*b*c*d*e + a^3*c*e^2)))/((a^5*b^4*c^2 - 8*a^6*b^2*c^3 - 2*a^5*b^3*c^3 + 16*a^7*c^4 + 8*a^6*b*c^4 + a^5*b^2*c^4 - 4*a^6*c^5)*d^4*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*abs(c) - 2*(a^5*b^5*c - 8*a^6*b^3*c^2 - 2*a^5*b^4*c^2 + 16*a^7*b*c^3 + 8*a^6*b^2*c^3 + a^5*b^3*c^3 - 4*a^6*b*c^4)*d^3*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*abs(c)*e + (a^5*b^6 - 6*a^6*b^4*c - 2*a^5*b^5*c + 4*a^6*b^3*c^2 + a^5*b^4*c^2 + 32*a^8*c^3 + 16*a^7*b*c^3 - 2*a^6*b^2*c^3 - 8*a^7*c^4)*d^2*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*abs(c)*e^2 - 2*(a^6*b^5 - 8*a^7*b^3*c - 2*a^6*b^4*c + 16*a^8*b*c^2 + 8*a^7*b^2*c^2 + a^6*b^3*c^2 - 4*a^7*b*c^3)*d*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*abs(c)*e^3 + (a^7*b^4 - 8*a^8*b^2*c - 2*a^7*b^3*c + 16*a^9*c^2 + 8*a^8*b*c^2 + a^7*b^2*c^2 - 4*a^8*c^3)*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*abs(c)*e^4) - 1/8*((2*a^4*b^5*c^5 - 12*a^5*b^3*c^6 + 16*a^6*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^4 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^4 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^5 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*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^4*b^3*c^5 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^6 - 2*(b^2 - 4*a*c)*a^4*b^3*c^5 + 4*(b^2 - 4*a*c)*a^5*b*c^6)*d^5 - (6*a^4*b^6*c^4 - 38*a^5*b^4*c^5 + 56*a^6*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^6*c^2 + 19*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^3 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^3 - 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^4 - 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^4 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^4 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^5 - 6*(b^2 - 4*a*c)*a^4*b^4*c^4 + 14*(b^2 - 4*a*c)*a^5*b^2*c^5)*d^4*e - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 - 9*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 + 2*a^2*b^6*c^3 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 + 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^4*c^4 - 18*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 - 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c^5 + 48*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^2*b^4*c^3 + 10*(b^2 - 4*a*c)*a^3*b^2*c^4 - 8*(b^2 - 4*a*c)*a^4*c^5)*d^3*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2) + (6*a^4*b^7*c^3 - 36*a^5*b^5*c^4 + 40*a^6*b^3*c^5 + 32*a^7*b*c^6 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c + 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^3 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^3 - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^3 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^4 - 8*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*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^4 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^5 - 6*(b^2 - 4*a*c)*a^4*b^5*c^3 + 12*(b^2 - 4*a*c)*a^5*b^3*c^4 + 8*(b^2 - 4*a*c)*a^6*b*c^5)*d^3*e^2 + 2*(2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c - 19*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 - 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 + 4*a^2*b^7*c^2 + 56*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 + 22*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 + 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^5*c^3 - 38*a^3*b^5*c^3 - 48*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 - 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 11*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^3*c^4 + 112*a^4*b^3*c^4 + 12*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b*c^5 - 96*a^5*b*c^5 - 4*(b^2 - 4*a*c)*a^2*b^5*c^2 + 22*(b^2 - 4*a*c)*a^3*b^3*c^3 - 24*(b^2 - 4*a*c)*a^4*b*c^4)*d^2*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*e + (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^2*c*d^2 - a^2*b*d*e + a^3*e^2)^2*d - (2*a^4*b^8*c^2 - 6*a^5*b^6*c^3 - 28*a^6*b^4*c^4 + 80*a^7*b^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^8 + 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c + 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 + 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 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c^2 - 40*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^3 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^3 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^4 - 2*(b^2 - 4*a*c)*a^4*b^6*c^2 - 2*(b^2 - 4*a*c)*a^5*b^4*c^3 + 20*(b^2 - 4*a*c)*a^6*b^2*c^4)*d^2*e^3 - 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^8 - 9*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^7*c + 2*a^2*b^8*c + 23*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^2 + 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^6*c^2 - 18*a^3*b^6*c^2 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 - 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^4*c^3 + 46*a^4*b^4*c^3 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*c^4 - 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 + 3*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^2*c^4 - 16*a^5*b^2*c^4 + 4*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*c^5 - 32*a^6*c^5 - 2*(b^2 - 4*a*c)*a^2*b^6*c + 10*(b^2 - 4*a*c)*a^3*b^4*c^2 - 6*(b^2 - 4*a*c)*a^4*b^2*c^3 - 8*(b^2 - 4*a*c)*a^5*c^4)*d*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*e^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)*(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)^2*e + (4*a^5*b^7*c^2 - 26*a^6*b^5*c^3 + 36*a^7*b^3*c^4 + 16*a^8*b*c^5 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^7 + 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c - 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^2 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^2 - 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 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b*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^3 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^3 + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^4 - 4*(b^2 - 4*a*c)*a^5*b^5*c^2 + 10*(b^2 - 4*a*c)*a^6*b^3*c^3 + 4*(b^2 - 4*a*c)*a^7*b*c^4)*d*e^4 + 2*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^7 - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c + 2*a^3*b^7*c + 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^2 + 12*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^5*c^2 - 20*a^4*b^5*c^2 - 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^3 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^3 - 6*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^3*c^3 + 64*a^5*b^3*c^3 + 8*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b*c^4 - 64*a^6*b*c^4 - 2*(b^2 - 4*a*c)*a^3*b^5*c + 12*(b^2 - 4*a*c)*a^4*b^3*c^2 - 16*(b^2 - 4*a*c)*a^5*b*c^3)*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*e^3 - (2*a^6*b^6*c^2 - 14*a^7*b^4*c^3 + 24*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 + 7*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 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^2*c^2 - 6*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 + 3*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 + 6*(b^2 - 4*a*c)*a^7*b^2*c^3)*e^5)*arctan(2*sqrt(1/2)*x/sqrt((a^2*b*c*d^2 - a^2*b^2*d*e + a^3*b*e^2 - sqrt((a^2*b*c*d^2 - a^2*b^2*d*e + a^3*b*e^2)^2 - 4*(a^3*c*d^2 - a^3*b*d*e + a^4*e^2)*(a^2*c^2*d^2 - a^2*b*c*d*e + a^3*c*e^2)))/(a^2*c^2*d^2 - a^2*b*c*d*e + a^3*c*e^2)))/((a^5*b^4*c^2 - 8*a^6*b^2*c^3 - 2*a^5*b^3*c^3 + 16*a^7*c^4 + 8*a^6*b*c^4 + a^5*b^2*c^4 - 4*a^6*c^5)*d^4*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*abs(c) - 2*(a^5*b^5*c - 8*a^6*b^3*c^2 - 2*a^5*b^4*c^2 + 16*a^7*b*c^3 + 8*a^6*b^2*c^3 + a^5*b^3*c^3 - 4*a^6*b*c^4)*d^3*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*abs(c)*e + (a^5*b^6 - 6*a^6*b^4*c - 2*a^5*b^5*c + 4*a^6*b^3*c^2 + a^5*b^4*c^2 + 32*a^8*c^3 + 16*a^7*b*c^3 - 2*a^6*b^2*c^3 - 8*a^7*c^4)*d^2*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*abs(c)*e^2 - 2*(a^6*b^5 - 8*a^7*b^3*c - 2*a^6*b^4*c + 16*a^8*b*c^2 + 8*a^7*b^2*c^2 + a^6*b^3*c^2 - 4*a^7*b*c^3)*d*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*abs(c)*e^3 + (a^7*b^4 - 8*a^8*b^2*c - 2*a^7*b^3*c + 16*a^9*c^2 + 8*a^8*b*c^2 + a^7*b^2*c^2 - 4*a^8*c^3)*abs(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*abs(c)*e^4) + arctan(x*e^(1/2)/sqrt(d))*e^(7/2)/((c*d^4 - b*d^3*e + a*d^2*e^2)*sqrt(d)) + 1/3*(3*b*d*x^2 + 3*a*x^2*e - a*d)/(a^2*d^2*x^3)","B",0
310,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(c*x^4+b*x^2+a)/(f*x)^(1/2),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
311,-2,0,0,0.000000," ","integrate(x^5*(c*x^4+b*x^2+a)^(1/2)/(e*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
312,-2,0,0,0.000000," ","integrate(x^3*(c*x^4+b*x^2+a)^(1/2)/(e*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
313,-2,0,0,0.000000," ","integrate(x*(c*x^4+b*x^2+a)^(1/2)/(e*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
314,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(1/2)/x/(e*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
315,1,216,0,0.523434," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^3/(e*x^2+d),x, algorithm=""giac"")","\frac{{\left(c d^{2} - b d e + a e^{2}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{\sqrt{-c d^{2} + b d e - a e^{2}} d^{2}} + \frac{{\left(b d - 2 \, a e\right)} \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{2 \, \sqrt{-a} d^{2}} + \frac{{\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} b + 2 \, a \sqrt{c}}{2 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)} d}"," ",0,"(c*d^2 - b*d*e + a*e^2)*arctan(-((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/(sqrt(-c*d^2 + b*d*e - a*e^2)*d^2) + 1/2*(b*d - 2*a*e)*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/(sqrt(-a)*d^2) + 1/2*((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*b + 2*a*sqrt(c))/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)*d)","A",0
316,0,0,0,0.000000," ","integrate(x^4*(2*x^4+2*x^2+1)^(1/2)/(2*x^2+3),x, algorithm=""giac"")","\int \frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1} x^{4}}{2 \, x^{2} + 3}\,{d x}"," ",0,"integrate(sqrt(2*x^4 + 2*x^2 + 1)*x^4/(2*x^2 + 3), x)","F",0
317,0,0,0,0.000000," ","integrate(x^2*(2*x^4+2*x^2+1)^(1/2)/(2*x^2+3),x, algorithm=""giac"")","\int \frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1} x^{2}}{2 \, x^{2} + 3}\,{d x}"," ",0,"integrate(sqrt(2*x^4 + 2*x^2 + 1)*x^2/(2*x^2 + 3), x)","F",0
318,0,0,0,0.000000," ","integrate((2*x^4+2*x^2+1)^(1/2)/(2*x^2+3),x, algorithm=""giac"")","\int \frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1}}{2 \, x^{2} + 3}\,{d x}"," ",0,"integrate(sqrt(2*x^4 + 2*x^2 + 1)/(2*x^2 + 3), x)","F",0
319,0,0,0,0.000000," ","integrate((2*x^4+2*x^2+1)^(1/2)/x^2/(2*x^2+3),x, algorithm=""giac"")","\int \frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1}}{{\left(2 \, x^{2} + 3\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(2*x^4 + 2*x^2 + 1)/((2*x^2 + 3)*x^2), x)","F",0
320,0,0,0,0.000000," ","integrate((2*x^4+2*x^2+1)^(1/2)/x^4/(2*x^2+3),x, algorithm=""giac"")","\int \frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1}}{{\left(2 \, x^{2} + 3\right)} x^{4}}\,{d x}"," ",0,"integrate(sqrt(2*x^4 + 2*x^2 + 1)/((2*x^2 + 3)*x^4), x)","F",0
321,0,0,0,0.000000," ","integrate((2*x^4+2*x^2+1)^(1/2)/x^6/(2*x^2+3),x, algorithm=""giac"")","\int \frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1}}{{\left(2 \, x^{2} + 3\right)} x^{6}}\,{d x}"," ",0,"integrate(sqrt(2*x^4 + 2*x^2 + 1)/((2*x^2 + 3)*x^6), x)","F",0
322,-2,0,0,0.000000," ","integrate(x^5*(c*x^4+b*x^2+a)^(3/2)/(e*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
323,-2,0,0,0.000000," ","integrate(x^3*(c*x^4+b*x^2+a)^(3/2)/(e*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
324,-2,0,0,0.000000," ","integrate(x*(c*x^4+b*x^2+a)^(3/2)/(e*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
325,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(3/2)/x/(e*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
326,-2,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^3/(e*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
327,0,0,0,0.000000," ","integrate(x^2*(2*x^4+2*x^2+1)^(3/2)/(-2*x^2+3),x, algorithm=""giac"")","\int -\frac{{\left(2 \, x^{4} + 2 \, x^{2} + 1\right)}^{\frac{3}{2}} x^{2}}{2 \, x^{2} - 3}\,{d x}"," ",0,"integrate(-(2*x^4 + 2*x^2 + 1)^(3/2)*x^2/(2*x^2 - 3), x)","F",0
328,0,0,0,0.000000," ","integrate((2*x^4+2*x^2+1)^(3/2)/(-2*x^2+3),x, algorithm=""giac"")","\int -\frac{{\left(2 \, x^{4} + 2 \, x^{2} + 1\right)}^{\frac{3}{2}}}{2 \, x^{2} - 3}\,{d x}"," ",0,"integrate(-(2*x^4 + 2*x^2 + 1)^(3/2)/(2*x^2 - 3), x)","F",0
329,0,0,0,0.000000," ","integrate((2*x^4+2*x^2+1)^(3/2)/x^2/(-2*x^2+3),x, algorithm=""giac"")","\int -\frac{{\left(2 \, x^{4} + 2 \, x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(2 \, x^{2} - 3\right)} x^{2}}\,{d x}"," ",0,"integrate(-(2*x^4 + 2*x^2 + 1)^(3/2)/((2*x^2 - 3)*x^2), x)","F",0
330,0,0,0,0.000000," ","integrate((2*x^4+2*x^2+1)^(3/2)/x^4/(-2*x^2+3),x, algorithm=""giac"")","\int -\frac{{\left(2 \, x^{4} + 2 \, x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(2 \, x^{2} - 3\right)} x^{4}}\,{d x}"," ",0,"integrate(-(2*x^4 + 2*x^2 + 1)^(3/2)/((2*x^2 - 3)*x^4), x)","F",0
331,0,0,0,0.000000," ","integrate((2*x^4+2*x^2+1)^(3/2)/x^6/(-2*x^2+3),x, algorithm=""giac"")","\int -\frac{{\left(2 \, x^{4} + 2 \, x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(2 \, x^{2} - 3\right)} x^{6}}\,{d x}"," ",0,"integrate(-(2*x^4 + 2*x^2 + 1)^(3/2)/((2*x^2 - 3)*x^6), x)","F",0
332,-2,0,0,0.000000," ","integrate(x^5/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
333,-2,0,0,0.000000," ","integrate(x^3/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
334,1,75,0,0.485527," ","integrate(x/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{\arctan\left(-\frac{{\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{\sqrt{-c d^{2} + b d e - a e^{2}}}"," ",0,"arctan(-((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/sqrt(-c*d^2 + b*d*e - a*e^2)","A",0
335,-2,0,0,0.000000," ","integrate(1/x/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
336,1,208,0,0.487706," ","integrate(1/x^3/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{\arctan\left(-\frac{{\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right) e^{2}}{\sqrt{-c d^{2} + b d e - a e^{2}} d^{2}} - \frac{{\left(b d + 2 \, a e\right)} \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{2 \, \sqrt{-a} a d^{2}} + \frac{{\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} b + 2 \, a \sqrt{c}}{2 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)} a d}"," ",0,"arctan(-((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))*e^2/(sqrt(-c*d^2 + b*d*e - a*e^2)*d^2) - 1/2*(b*d + 2*a*e)*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a*d^2) + 1/2*((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*b + 2*a*sqrt(c))/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)*a*d)","A",0
337,0,0,0,0.000000," ","integrate(x^4/(2*x^2+3)/(2*x^4+2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1} {\left(2 \, x^{2} + 3\right)}}\,{d x}"," ",0,"integrate(x^4/(sqrt(2*x^4 + 2*x^2 + 1)*(2*x^2 + 3)), x)","F",0
338,0,0,0,0.000000," ","integrate(x^2/(2*x^2+3)/(2*x^4+2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1} {\left(2 \, x^{2} + 3\right)}}\,{d x}"," ",0,"integrate(x^2/(sqrt(2*x^4 + 2*x^2 + 1)*(2*x^2 + 3)), x)","F",0
339,0,0,0,0.000000," ","integrate(1/(2*x^2+3)/(2*x^4+2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1} {\left(2 \, x^{2} + 3\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(2*x^4 + 2*x^2 + 1)*(2*x^2 + 3)), x)","F",0
340,0,0,0,0.000000," ","integrate(1/x^2/(2*x^2+3)/(2*x^4+2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1} {\left(2 \, x^{2} + 3\right)} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(2*x^4 + 2*x^2 + 1)*(2*x^2 + 3)*x^2), x)","F",0
341,0,0,0,0.000000," ","integrate(1/x^4/(2*x^2+3)/(2*x^4+2*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1} {\left(2 \, x^{2} + 3\right)} x^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(2*x^4 + 2*x^2 + 1)*(2*x^2 + 3)*x^4), x)","F",0
342,-2,0,0,0.000000," ","integrate(x^7/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
343,1,458,0,0.719814," ","integrate(x^5/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{d^{2} \arctan\left(-\frac{{\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{{\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} - \frac{\frac{{\left(b^{2} c d^{3} - 2 \, a c^{2} d^{3} - b^{3} d^{2} e + a b c d^{2} e + 2 \, a b^{2} d e^{2} - 2 \, a^{2} c d e^{2} - a^{2} b e^{3}\right)} x^{2}}{b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} - 2 \, b^{3} c d^{3} e + 8 \, a b c^{2} d^{3} e + b^{4} d^{2} e^{2} - 2 \, a b^{2} c d^{2} e^{2} - 8 \, a^{2} c^{2} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 8 \, a^{2} b c d e^{3} + a^{2} b^{2} e^{4} - 4 \, a^{3} c e^{4}} + \frac{a b c d^{3} - a b^{2} d^{2} e - 2 \, a^{2} c d^{2} e + 3 \, a^{2} b d e^{2} - 2 \, a^{3} e^{3}}{b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} - 2 \, b^{3} c d^{3} e + 8 \, a b c^{2} d^{3} e + b^{4} d^{2} e^{2} - 2 \, a b^{2} c d^{2} e^{2} - 8 \, a^{2} c^{2} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 8 \, a^{2} b c d e^{3} + a^{2} b^{2} e^{4} - 4 \, a^{3} c e^{4}}}{\sqrt{c x^{4} + b x^{2} + a}}"," ",0,"d^2*arctan(-((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c*d^2 - b*d*e + a*e^2)*sqrt(-c*d^2 + b*d*e - a*e^2)) - ((b^2*c*d^3 - 2*a*c^2*d^3 - b^3*d^2*e + a*b*c*d^2*e + 2*a*b^2*d*e^2 - 2*a^2*c*d*e^2 - a^2*b*e^3)*x^2/(b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2 - 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4) + (a*b*c*d^3 - a*b^2*d^2*e - 2*a^2*c*d^2*e + 3*a^2*b*d*e^2 - 2*a^3*e^3)/(b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2 - 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4))/sqrt(c*x^4 + b*x^2 + a)","B",0
344,1,441,0,0.641464," ","integrate(x^3/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{d \arctan\left(-\frac{{\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right) e}{{\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} + \frac{\frac{{\left(b c^{2} d^{3} - b^{2} c d^{2} e - 2 \, a c^{2} d^{2} e + 3 \, a b c d e^{2} - 2 \, a^{2} c e^{3}\right)} x^{2}}{b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} - 2 \, b^{3} c d^{3} e + 8 \, a b c^{2} d^{3} e + b^{4} d^{2} e^{2} - 2 \, a b^{2} c d^{2} e^{2} - 8 \, a^{2} c^{2} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 8 \, a^{2} b c d e^{3} + a^{2} b^{2} e^{4} - 4 \, a^{3} c e^{4}} + \frac{2 \, a c^{2} d^{3} - 3 \, a b c d^{2} e + a b^{2} d e^{2} + 2 \, a^{2} c d e^{2} - a^{2} b e^{3}}{b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} - 2 \, b^{3} c d^{3} e + 8 \, a b c^{2} d^{3} e + b^{4} d^{2} e^{2} - 2 \, a b^{2} c d^{2} e^{2} - 8 \, a^{2} c^{2} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 8 \, a^{2} b c d e^{3} + a^{2} b^{2} e^{4} - 4 \, a^{3} c e^{4}}}{\sqrt{c x^{4} + b x^{2} + a}}"," ",0,"-d*arctan(-((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))*e/((c*d^2 - b*d*e + a*e^2)*sqrt(-c*d^2 + b*d*e - a*e^2)) + ((b*c^2*d^3 - b^2*c*d^2*e - 2*a*c^2*d^2*e + 3*a*b*c*d*e^2 - 2*a^2*c*e^3)*x^2/(b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2 - 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4) + (2*a*c^2*d^3 - 3*a*b*c*d^2*e + a*b^2*d*e^2 + 2*a^2*c*d*e^2 - a^2*b*e^3)/(b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2 - 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4))/sqrt(c*x^4 + b*x^2 + a)","B",0
345,1,454,0,0.618183," ","integrate(x/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{\frac{{\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + b^{2} c d e^{2} + 2 \, a c^{2} d e^{2} - a b c e^{3}\right)} x^{2}}{b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} - 2 \, b^{3} c d^{3} e + 8 \, a b c^{2} d^{3} e + b^{4} d^{2} e^{2} - 2 \, a b^{2} c d^{2} e^{2} - 8 \, a^{2} c^{2} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 8 \, a^{2} b c d e^{3} + a^{2} b^{2} e^{4} - 4 \, a^{3} c e^{4}} + \frac{b c^{2} d^{3} - 2 \, b^{2} c d^{2} e + 2 \, a c^{2} d^{2} e + b^{3} d e^{2} - a b c d e^{2} - a b^{2} e^{3} + 2 \, a^{2} c e^{3}}{b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} - 2 \, b^{3} c d^{3} e + 8 \, a b c^{2} d^{3} e + b^{4} d^{2} e^{2} - 2 \, a b^{2} c d^{2} e^{2} - 8 \, a^{2} c^{2} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 8 \, a^{2} b c d e^{3} + a^{2} b^{2} e^{4} - 4 \, a^{3} c e^{4}}}{\sqrt{c x^{4} + b x^{2} + a}} + \frac{\arctan\left(-\frac{{\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right) e^{2}}{{\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}}"," ",0,"-((2*c^3*d^3 - 3*b*c^2*d^2*e + b^2*c*d*e^2 + 2*a*c^2*d*e^2 - a*b*c*e^3)*x^2/(b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2 - 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4) + (b*c^2*d^3 - 2*b^2*c*d^2*e + 2*a*c^2*d^2*e + b^3*d*e^2 - a*b*c*d*e^2 - a*b^2*e^3 + 2*a^2*c*e^3)/(b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2 - 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4))/sqrt(c*x^4 + b*x^2 + a) + arctan(-((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))*e^2/((c*d^2 - b*d*e + a*e^2)*sqrt(-c*d^2 + b*d*e - a*e^2))","B",0
346,-2,0,0,0.000000," ","integrate(1/x/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
347,1,762,0,2.736492," ","integrate(1/x^3/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{\frac{{\left(a^{2} b^{2} c^{3} d^{3} - 2 \, a^{3} c^{4} d^{3} - 2 \, a^{2} b^{3} c^{2} d^{2} e + 5 \, a^{3} b c^{3} d^{2} e + a^{2} b^{4} c d e^{2} - 2 \, a^{3} b^{2} c^{2} d e^{2} - 2 \, a^{4} c^{3} d e^{2} - a^{3} b^{3} c e^{3} + 3 \, a^{4} b c^{2} e^{3}\right)} x^{2}}{a^{4} b^{2} c^{2} d^{4} - 4 \, a^{5} c^{3} d^{4} - 2 \, a^{4} b^{3} c d^{3} e + 8 \, a^{5} b c^{2} d^{3} e + a^{4} b^{4} d^{2} e^{2} - 2 \, a^{5} b^{2} c d^{2} e^{2} - 8 \, a^{6} c^{2} d^{2} e^{2} - 2 \, a^{5} b^{3} d e^{3} + 8 \, a^{6} b c d e^{3} + a^{6} b^{2} e^{4} - 4 \, a^{7} c e^{4}} + \frac{a^{2} b^{3} c^{2} d^{3} - 3 \, a^{3} b c^{3} d^{3} - 2 \, a^{2} b^{4} c d^{2} e + 7 \, a^{3} b^{2} c^{2} d^{2} e - 2 \, a^{4} c^{3} d^{2} e + a^{2} b^{5} d e^{2} - 3 \, a^{3} b^{3} c d e^{2} - a^{4} b c^{2} d e^{2} - a^{3} b^{4} e^{3} + 4 \, a^{4} b^{2} c e^{3} - 2 \, a^{5} c^{2} e^{3}}{a^{4} b^{2} c^{2} d^{4} - 4 \, a^{5} c^{3} d^{4} - 2 \, a^{4} b^{3} c d^{3} e + 8 \, a^{5} b c^{2} d^{3} e + a^{4} b^{4} d^{2} e^{2} - 2 \, a^{5} b^{2} c d^{2} e^{2} - 8 \, a^{6} c^{2} d^{2} e^{2} - 2 \, a^{5} b^{3} d e^{3} + 8 \, a^{6} b c d e^{3} + a^{6} b^{2} e^{4} - 4 \, a^{7} c e^{4}}}{\sqrt{c x^{4} + b x^{2} + a}} + \frac{\arctan\left(-\frac{{\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right) e^{4}}{{\left(c d^{4} - b d^{3} e + a d^{2} e^{2}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} - \frac{{\left(3 \, b d + 2 \, a e\right)} \arctan\left(-\frac{\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}}{\sqrt{-a}}\right)}{2 \, \sqrt{-a} a^{2} d^{2}} + \frac{{\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)} b + 2 \, a \sqrt{c}}{2 \, {\left({\left(\sqrt{c} x^{2} - \sqrt{c x^{4} + b x^{2} + a}\right)}^{2} - a\right)} a^{2} d}"," ",0,"-((a^2*b^2*c^3*d^3 - 2*a^3*c^4*d^3 - 2*a^2*b^3*c^2*d^2*e + 5*a^3*b*c^3*d^2*e + a^2*b^4*c*d*e^2 - 2*a^3*b^2*c^2*d*e^2 - 2*a^4*c^3*d*e^2 - a^3*b^3*c*e^3 + 3*a^4*b*c^2*e^3)*x^2/(a^4*b^2*c^2*d^4 - 4*a^5*c^3*d^4 - 2*a^4*b^3*c*d^3*e + 8*a^5*b*c^2*d^3*e + a^4*b^4*d^2*e^2 - 2*a^5*b^2*c*d^2*e^2 - 8*a^6*c^2*d^2*e^2 - 2*a^5*b^3*d*e^3 + 8*a^6*b*c*d*e^3 + a^6*b^2*e^4 - 4*a^7*c*e^4) + (a^2*b^3*c^2*d^3 - 3*a^3*b*c^3*d^3 - 2*a^2*b^4*c*d^2*e + 7*a^3*b^2*c^2*d^2*e - 2*a^4*c^3*d^2*e + a^2*b^5*d*e^2 - 3*a^3*b^3*c*d*e^2 - a^4*b*c^2*d*e^2 - a^3*b^4*e^3 + 4*a^4*b^2*c*e^3 - 2*a^5*c^2*e^3)/(a^4*b^2*c^2*d^4 - 4*a^5*c^3*d^4 - 2*a^4*b^3*c*d^3*e + 8*a^5*b*c^2*d^3*e + a^4*b^4*d^2*e^2 - 2*a^5*b^2*c*d^2*e^2 - 8*a^6*c^2*d^2*e^2 - 2*a^5*b^3*d*e^3 + 8*a^6*b*c*d*e^3 + a^6*b^2*e^4 - 4*a^7*c*e^4))/sqrt(c*x^4 + b*x^2 + a) + arctan(-((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))*e^4/((c*d^4 - b*d^3*e + a*d^2*e^2)*sqrt(-c*d^2 + b*d*e - a*e^2)) - 1/2*(3*b*d + 2*a*e)*arctan(-(sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))/sqrt(-a))/(sqrt(-a)*a^2*d^2) + 1/2*((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))*b + 2*a*sqrt(c))/(((sqrt(c)*x^2 - sqrt(c*x^4 + b*x^2 + a))^2 - a)*a^2*d)","B",0
348,0,0,0,0.000000," ","integrate(x^8/(2*x^2+3)/(2*x^4+2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{x^{8}}{{\left(2 \, x^{4} + 2 \, x^{2} + 1\right)}^{\frac{3}{2}} {\left(2 \, x^{2} + 3\right)}}\,{d x}"," ",0,"integrate(x^8/((2*x^4 + 2*x^2 + 1)^(3/2)*(2*x^2 + 3)), x)","F",0
349,0,0,0,0.000000," ","integrate(x^6/(2*x^2+3)/(2*x^4+2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(2 \, x^{4} + 2 \, x^{2} + 1\right)}^{\frac{3}{2}} {\left(2 \, x^{2} + 3\right)}}\,{d x}"," ",0,"integrate(x^6/((2*x^4 + 2*x^2 + 1)^(3/2)*(2*x^2 + 3)), x)","F",0
350,0,0,0,0.000000," ","integrate(x^4/(2*x^2+3)/(2*x^4+2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(2 \, x^{4} + 2 \, x^{2} + 1\right)}^{\frac{3}{2}} {\left(2 \, x^{2} + 3\right)}}\,{d x}"," ",0,"integrate(x^4/((2*x^4 + 2*x^2 + 1)^(3/2)*(2*x^2 + 3)), x)","F",0
351,0,0,0,0.000000," ","integrate(x^2/(2*x^2+3)/(2*x^4+2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(2 \, x^{4} + 2 \, x^{2} + 1\right)}^{\frac{3}{2}} {\left(2 \, x^{2} + 3\right)}}\,{d x}"," ",0,"integrate(x^2/((2*x^4 + 2*x^2 + 1)^(3/2)*(2*x^2 + 3)), x)","F",0
352,0,0,0,0.000000," ","integrate(1/(2*x^2+3)/(2*x^4+2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(2 \, x^{4} + 2 \, x^{2} + 1\right)}^{\frac{3}{2}} {\left(2 \, x^{2} + 3\right)}}\,{d x}"," ",0,"integrate(1/((2*x^4 + 2*x^2 + 1)^(3/2)*(2*x^2 + 3)), x)","F",0
353,0,0,0,0.000000," ","integrate(1/x^2/(2*x^2+3)/(2*x^4+2*x^2+1)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(2 \, x^{4} + 2 \, x^{2} + 1\right)}^{\frac{3}{2}} {\left(2 \, x^{2} + 3\right)} x^{2}}\,{d x}"," ",0,"integrate(1/((2*x^4 + 2*x^2 + 1)^(3/2)*(2*x^2 + 3)*x^2), x)","F",0
354,1,928,0,0.650181," ","integrate(x^7*(e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left({\left({\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d e - {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} e^{2}\right)} c^{2} + 2 \, {\left(b^{3} c^{4} - 3 \, a b c^{5}\right)} d^{2} - {\left(3 \, b^{4} c^{3} - 11 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d e - 2 \, {\left({\left(b^{2} c^{3} - a c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} - {\left(b^{3} c^{2} - a b c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d e + {\left(a b^{2} c^{2} - a^{2} c^{3}\right)} \sqrt{b^{2} - 4 \, a c} e^{2}\right)} {\left| c \right|} + {\left(b^{5} c^{2} - 4 \, a b^{3} c^{3} + 2 \, a^{2} b c^{4}\right)} e^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{2} e + d}}{\sqrt{-\frac{{\left(2 \, c^{6} d e^{12} - b c^{5} e^{13} + \sqrt{-4 \, {\left(c^{6} d^{2} e^{12} - b c^{5} d e^{13} + a c^{5} e^{14}\right)} c^{6} e^{12} + {\left(2 \, c^{6} d e^{12} - b c^{5} e^{13}\right)}^{2}}\right)} e^{\left(-12\right)}}{c^{6}}}}\right)}{{\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{4} d + {\left(b^{2} c^{3} - 4 \, a c^{4} - \sqrt{b^{2} - 4 \, a c} b c^{3}\right)} e\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{2}} + \frac{{\left({\left({\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d e - {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} e^{2}\right)} c^{2} + 2 \, {\left(b^{3} c^{4} - 3 \, a b c^{5}\right)} d^{2} - {\left(3 \, b^{4} c^{3} - 11 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d e + 2 \, {\left({\left(b^{2} c^{3} - a c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} - {\left(b^{3} c^{2} - a b c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d e + {\left(a b^{2} c^{2} - a^{2} c^{3}\right)} \sqrt{b^{2} - 4 \, a c} e^{2}\right)} {\left| c \right|} + {\left(b^{5} c^{2} - 4 \, a b^{3} c^{3} + 2 \, a^{2} b c^{4}\right)} e^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{2} e + d}}{\sqrt{-\frac{{\left(2 \, c^{6} d e^{12} - b c^{5} e^{13} - \sqrt{-4 \, {\left(c^{6} d^{2} e^{12} - b c^{5} d e^{13} + a c^{5} e^{14}\right)} c^{6} e^{12} + {\left(2 \, c^{6} d e^{12} - b c^{5} e^{13}\right)}^{2}}\right)} e^{\left(-12\right)}}{c^{6}}}}\right)}{{\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{4} d - {\left(b^{2} c^{3} - 4 \, a c^{4} + \sqrt{b^{2} - 4 \, a c} b c^{3}\right)} e\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{2}} + \frac{{\left(3 \, {\left(x^{2} e + d\right)}^{\frac{5}{2}} c^{4} e^{8} - 5 \, {\left(x^{2} e + d\right)}^{\frac{3}{2}} c^{4} d e^{8} - 5 \, {\left(x^{2} e + d\right)}^{\frac{3}{2}} b c^{3} e^{9} + 15 \, \sqrt{x^{2} e + d} b^{2} c^{2} e^{10} - 15 \, \sqrt{x^{2} e + d} a c^{3} e^{10}\right)} e^{\left(-10\right)}}{15 \, c^{5}}"," ",0,"-(((b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d*e - (b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*e^2)*c^2 + 2*(b^3*c^4 - 3*a*b*c^5)*d^2 - (3*b^4*c^3 - 11*a*b^2*c^4 + 4*a^2*c^5)*d*e - 2*((b^2*c^3 - a*c^4)*sqrt(b^2 - 4*a*c)*d^2 - (b^3*c^2 - a*b*c^3)*sqrt(b^2 - 4*a*c)*d*e + (a*b^2*c^2 - a^2*c^3)*sqrt(b^2 - 4*a*c)*e^2)*abs(c) + (b^5*c^2 - 4*a*b^3*c^3 + 2*a^2*b*c^4)*e^2)*arctan(2*sqrt(1/2)*sqrt(x^2*e + d)/sqrt(-(2*c^6*d*e^12 - b*c^5*e^13 + sqrt(-4*(c^6*d^2*e^12 - b*c^5*d*e^13 + a*c^5*e^14)*c^6*e^12 + (2*c^6*d*e^12 - b*c^5*e^13)^2))*e^(-12)/c^6))/((2*sqrt(b^2 - 4*a*c)*c^4*d + (b^2*c^3 - 4*a*c^4 - sqrt(b^2 - 4*a*c)*b*c^3)*e)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*c^2) + (((b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d*e - (b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*e^2)*c^2 + 2*(b^3*c^4 - 3*a*b*c^5)*d^2 - (3*b^4*c^3 - 11*a*b^2*c^4 + 4*a^2*c^5)*d*e + 2*((b^2*c^3 - a*c^4)*sqrt(b^2 - 4*a*c)*d^2 - (b^3*c^2 - a*b*c^3)*sqrt(b^2 - 4*a*c)*d*e + (a*b^2*c^2 - a^2*c^3)*sqrt(b^2 - 4*a*c)*e^2)*abs(c) + (b^5*c^2 - 4*a*b^3*c^3 + 2*a^2*b*c^4)*e^2)*arctan(2*sqrt(1/2)*sqrt(x^2*e + d)/sqrt(-(2*c^6*d*e^12 - b*c^5*e^13 - sqrt(-4*(c^6*d^2*e^12 - b*c^5*d*e^13 + a*c^5*e^14)*c^6*e^12 + (2*c^6*d*e^12 - b*c^5*e^13)^2))*e^(-12)/c^6))/((2*sqrt(b^2 - 4*a*c)*c^4*d - (b^2*c^3 - 4*a*c^4 + sqrt(b^2 - 4*a*c)*b*c^3)*e)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*c^2) + 1/15*(3*(x^2*e + d)^(5/2)*c^4*e^8 - 5*(x^2*e + d)^(3/2)*c^4*d*e^8 - 5*(x^2*e + d)^(3/2)*b*c^3*e^9 + 15*sqrt(x^2*e + d)*b^2*c^2*e^10 - 15*sqrt(x^2*e + d)*a*c^3*e^10)*e^(-10)/c^5","B",0
355,1,745,0,0.819475," ","integrate(x^5*(e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{{\left({\left(x^{2} e + d\right)}^{\frac{3}{2}} c^{2} e^{2} - 3 \, \sqrt{x^{2} e + d} b c e^{3}\right)} e^{\left(-3\right)}}{3 \, c^{3}} + \frac{{\left({\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d e - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{2}\right)} c^{2} + 2 \, {\left(b^{2} c^{4} - 2 \, a c^{5}\right)} d^{2} - {\left(3 \, b^{3} c^{3} - 8 \, a b c^{4}\right)} d e - 2 \, {\left(\sqrt{b^{2} - 4 \, a c} b c^{3} d^{2} - \sqrt{b^{2} - 4 \, a c} b^{2} c^{2} d e + \sqrt{b^{2} - 4 \, a c} a b c^{2} e^{2}\right)} {\left| c \right|} + {\left(b^{4} c^{2} - 3 \, a b^{2} c^{3}\right)} e^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{2} e + d}}{\sqrt{-\frac{{\left(2 \, c^{4} d e^{4} - b c^{3} e^{5} + \sqrt{-4 \, {\left(c^{4} d^{2} e^{4} - b c^{3} d e^{5} + a c^{3} e^{6}\right)} c^{4} e^{4} + {\left(2 \, c^{4} d e^{4} - b c^{3} e^{5}\right)}^{2}}\right)} e^{\left(-4\right)}}{c^{4}}}}\right)}{{\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{3} d + {\left(b^{2} c^{2} - 4 \, a c^{3} - \sqrt{b^{2} - 4 \, a c} b c^{2}\right)} e\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{2}} - \frac{{\left({\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d e - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{2}\right)} c^{2} + 2 \, {\left(b^{2} c^{4} - 2 \, a c^{5}\right)} d^{2} - {\left(3 \, b^{3} c^{3} - 8 \, a b c^{4}\right)} d e + 2 \, {\left(\sqrt{b^{2} - 4 \, a c} b c^{3} d^{2} - \sqrt{b^{2} - 4 \, a c} b^{2} c^{2} d e + \sqrt{b^{2} - 4 \, a c} a b c^{2} e^{2}\right)} {\left| c \right|} + {\left(b^{4} c^{2} - 3 \, a b^{2} c^{3}\right)} e^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{2} e + d}}{\sqrt{-\frac{{\left(2 \, c^{4} d e^{4} - b c^{3} e^{5} - \sqrt{-4 \, {\left(c^{4} d^{2} e^{4} - b c^{3} d e^{5} + a c^{3} e^{6}\right)} c^{4} e^{4} + {\left(2 \, c^{4} d e^{4} - b c^{3} e^{5}\right)}^{2}}\right)} e^{\left(-4\right)}}{c^{4}}}}\right)}{{\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{3} d - {\left(b^{2} c^{2} - 4 \, a c^{3} + \sqrt{b^{2} - 4 \, a c} b c^{2}\right)} e\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{2}}"," ",0,"1/3*((x^2*e + d)^(3/2)*c^2*e^2 - 3*sqrt(x^2*e + d)*b*c*e^3)*e^(-3)/c^3 + (((b^3*c - 4*a*b*c^2)*d*e - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e^2)*c^2 + 2*(b^2*c^4 - 2*a*c^5)*d^2 - (3*b^3*c^3 - 8*a*b*c^4)*d*e - 2*(sqrt(b^2 - 4*a*c)*b*c^3*d^2 - sqrt(b^2 - 4*a*c)*b^2*c^2*d*e + sqrt(b^2 - 4*a*c)*a*b*c^2*e^2)*abs(c) + (b^4*c^2 - 3*a*b^2*c^3)*e^2)*arctan(2*sqrt(1/2)*sqrt(x^2*e + d)/sqrt(-(2*c^4*d*e^4 - b*c^3*e^5 + sqrt(-4*(c^4*d^2*e^4 - b*c^3*d*e^5 + a*c^3*e^6)*c^4*e^4 + (2*c^4*d*e^4 - b*c^3*e^5)^2))*e^(-4)/c^4))/((2*sqrt(b^2 - 4*a*c)*c^3*d + (b^2*c^2 - 4*a*c^3 - sqrt(b^2 - 4*a*c)*b*c^2)*e)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*c^2) - (((b^3*c - 4*a*b*c^2)*d*e - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e^2)*c^2 + 2*(b^2*c^4 - 2*a*c^5)*d^2 - (3*b^3*c^3 - 8*a*b*c^4)*d*e + 2*(sqrt(b^2 - 4*a*c)*b*c^3*d^2 - sqrt(b^2 - 4*a*c)*b^2*c^2*d*e + sqrt(b^2 - 4*a*c)*a*b*c^2*e^2)*abs(c) + (b^4*c^2 - 3*a*b^2*c^3)*e^2)*arctan(2*sqrt(1/2)*sqrt(x^2*e + d)/sqrt(-(2*c^4*d*e^4 - b*c^3*e^5 - sqrt(-4*(c^4*d^2*e^4 - b*c^3*d*e^5 + a*c^3*e^6)*c^4*e^4 + (2*c^4*d*e^4 - b*c^3*e^5)^2))*e^(-4)/c^4))/((2*sqrt(b^2 - 4*a*c)*c^3*d - (b^2*c^2 - 4*a*c^3 + sqrt(b^2 - 4*a*c)*b*c^2)*e)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*c^2)","B",0
356,1,619,0,0.781773," ","integrate(x^3*(e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{\sqrt{x^{2} e + d}}{c} - \frac{{\left(2 \, b c^{4} d^{2} + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d e - {\left(b^{3} - 4 \, a b c\right)} e^{2}\right)} c^{2} - {\left(3 \, b^{2} c^{3} - 4 \, a c^{4}\right)} d e - 2 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{3} d^{2} - \sqrt{b^{2} - 4 \, a c} b c^{2} d e + \sqrt{b^{2} - 4 \, a c} a c^{2} e^{2}\right)} {\left| c \right|} + {\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} e^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{2} e + d}}{\sqrt{-\frac{2 \, c^{2} d - b c e + \sqrt{-4 \, {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} c^{2} + {\left(2 \, c^{2} d - b c e\right)}^{2}}}{c^{2}}}}\right)}{{\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{2} d - {\left(b^{2} c - 4 \, a c^{2} + \sqrt{b^{2} - 4 \, a c} b c\right)} e\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{2}} + \frac{{\left(2 \, b c^{4} d^{2} + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d e - {\left(b^{3} - 4 \, a b c\right)} e^{2}\right)} c^{2} - {\left(3 \, b^{2} c^{3} - 4 \, a c^{4}\right)} d e + 2 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{3} d^{2} - \sqrt{b^{2} - 4 \, a c} b c^{2} d e + \sqrt{b^{2} - 4 \, a c} a c^{2} e^{2}\right)} {\left| c \right|} + {\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} e^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{2} e + d}}{\sqrt{-\frac{2 \, c^{2} d - b c e - \sqrt{-4 \, {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} c^{2} + {\left(2 \, c^{2} d - b c e\right)}^{2}}}{c^{2}}}}\right)}{{\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{2} d + {\left(b^{2} c - 4 \, a c^{2} - \sqrt{b^{2} - 4 \, a c} b c\right)} e\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{2}}"," ",0,"sqrt(x^2*e + d)/c - (2*b*c^4*d^2 + ((b^2*c - 4*a*c^2)*d*e - (b^3 - 4*a*b*c)*e^2)*c^2 - (3*b^2*c^3 - 4*a*c^4)*d*e - 2*(sqrt(b^2 - 4*a*c)*c^3*d^2 - sqrt(b^2 - 4*a*c)*b*c^2*d*e + sqrt(b^2 - 4*a*c)*a*c^2*e^2)*abs(c) + (b^3*c^2 - 2*a*b*c^3)*e^2)*arctan(2*sqrt(1/2)*sqrt(x^2*e + d)/sqrt(-(2*c^2*d - b*c*e + sqrt(-4*(c^2*d^2 - b*c*d*e + a*c*e^2)*c^2 + (2*c^2*d - b*c*e)^2))/c^2))/((2*sqrt(b^2 - 4*a*c)*c^2*d - (b^2*c - 4*a*c^2 + sqrt(b^2 - 4*a*c)*b*c)*e)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*c^2) + (2*b*c^4*d^2 + ((b^2*c - 4*a*c^2)*d*e - (b^3 - 4*a*b*c)*e^2)*c^2 - (3*b^2*c^3 - 4*a*c^4)*d*e + 2*(sqrt(b^2 - 4*a*c)*c^3*d^2 - sqrt(b^2 - 4*a*c)*b*c^2*d*e + sqrt(b^2 - 4*a*c)*a*c^2*e^2)*abs(c) + (b^3*c^2 - 2*a*b*c^3)*e^2)*arctan(2*sqrt(1/2)*sqrt(x^2*e + d)/sqrt(-(2*c^2*d - b*c*e - sqrt(-4*(c^2*d^2 - b*c*d*e + a*c*e^2)*c^2 + (2*c^2*d - b*c*e)^2))/c^2))/((2*sqrt(b^2 - 4*a*c)*c^2*d + (b^2*c - 4*a*c^2 - sqrt(b^2 - 4*a*c)*b*c)*e)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*c^2)","B",0
357,1,228,0,0.554846," ","integrate(x*(e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{\sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{2} e + d}}{\sqrt{-\frac{2 \, c d - b e + \sqrt{{\left(2 \, c d - b e\right)}^{2} - 4 \, {\left(c d^{2} - b d e + a e^{2}\right)} c}}{c}}}\right)}{2 \, \sqrt{b^{2} - 4 \, a c} {\left| c \right|}} + \frac{\sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{2} e + d}}{\sqrt{-\frac{2 \, c d - b e - \sqrt{{\left(2 \, c d - b e\right)}^{2} - 4 \, {\left(c d^{2} - b d e + a e^{2}\right)} c}}{c}}}\right)}{2 \, \sqrt{b^{2} - 4 \, a c} {\left| c \right|}}"," ",0,"-1/2*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*arctan(2*sqrt(1/2)*sqrt(x^2*e + d)/sqrt(-(2*c*d - b*e + sqrt((2*c*d - b*e)^2 - 4*(c*d^2 - b*d*e + a*e^2)*c))/c))/(sqrt(b^2 - 4*a*c)*abs(c)) + 1/2*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*arctan(2*sqrt(1/2)*sqrt(x^2*e + d)/sqrt(-(2*c*d - b*e - sqrt((2*c*d - b*e)^2 - 4*(c*d^2 - b*d*e + a*e^2)*c))/c))/(sqrt(b^2 - 4*a*c)*abs(c))","A",0
358,1,717,0,0.675384," ","integrate((e*x^2+d)^(1/2)/x/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{d \arctan\left(\frac{\sqrt{x^{2} e + d}}{\sqrt{-d}}\right)}{a \sqrt{-d}} - \frac{{\left(\sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(b^{2} - 4 \, a c\right)} a^{2} d e - 2 \, {\left(\sqrt{b^{2} - 4 \, a c} a c d^{2} - \sqrt{b^{2} - 4 \, a c} a b d e + \sqrt{b^{2} - 4 \, a c} a^{2} e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| a \right|} - {\left(2 \, a^{2} b c d^{2} + 2 \, a^{3} b e^{2} - {\left(a^{2} b^{2} + 4 \, a^{3} c\right)} d e\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{2} e + d}}{\sqrt{-\frac{2 \, a c d - a b e + \sqrt{-4 \, {\left(a c d^{2} - a b d e + a^{2} e^{2}\right)} a c + {\left(2 \, a c d - a b e\right)}^{2}}}{a c}}}\right)}{8 \, {\left(\sqrt{b^{2} - 4 \, a c} a^{2} c d^{2} - \sqrt{b^{2} - 4 \, a c} a^{2} b d e + \sqrt{b^{2} - 4 \, a c} a^{3} e^{2}\right)} {\left| a \right|} {\left| c \right|}} + \frac{{\left(\sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(b^{2} - 4 \, a c\right)} a^{2} d e + 2 \, {\left(\sqrt{b^{2} - 4 \, a c} a c d^{2} - \sqrt{b^{2} - 4 \, a c} a b d e + \sqrt{b^{2} - 4 \, a c} a^{2} e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| a \right|} - {\left(2 \, a^{2} b c d^{2} + 2 \, a^{3} b e^{2} - {\left(a^{2} b^{2} + 4 \, a^{3} c\right)} d e\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{2} e + d}}{\sqrt{-\frac{2 \, a c d - a b e - \sqrt{-4 \, {\left(a c d^{2} - a b d e + a^{2} e^{2}\right)} a c + {\left(2 \, a c d - a b e\right)}^{2}}}{a c}}}\right)}{8 \, {\left(\sqrt{b^{2} - 4 \, a c} a^{2} c d^{2} - \sqrt{b^{2} - 4 \, a c} a^{2} b d e + \sqrt{b^{2} - 4 \, a c} a^{3} e^{2}\right)} {\left| a \right|} {\left| c \right|}}"," ",0,"d*arctan(sqrt(x^2*e + d)/sqrt(-d))/(a*sqrt(-d)) - 1/8*(sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*(b^2 - 4*a*c)*a^2*d*e - 2*(sqrt(b^2 - 4*a*c)*a*c*d^2 - sqrt(b^2 - 4*a*c)*a*b*d*e + sqrt(b^2 - 4*a*c)*a^2*e^2)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(a) - (2*a^2*b*c*d^2 + 2*a^3*b*e^2 - (a^2*b^2 + 4*a^3*c)*d*e)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x^2*e + d)/sqrt(-(2*a*c*d - a*b*e + sqrt(-4*(a*c*d^2 - a*b*d*e + a^2*e^2)*a*c + (2*a*c*d - a*b*e)^2))/(a*c)))/((sqrt(b^2 - 4*a*c)*a^2*c*d^2 - sqrt(b^2 - 4*a*c)*a^2*b*d*e + sqrt(b^2 - 4*a*c)*a^3*e^2)*abs(a)*abs(c)) + 1/8*(sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*(b^2 - 4*a*c)*a^2*d*e + 2*(sqrt(b^2 - 4*a*c)*a*c*d^2 - sqrt(b^2 - 4*a*c)*a*b*d*e + sqrt(b^2 - 4*a*c)*a^2*e^2)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(a) - (2*a^2*b*c*d^2 + 2*a^3*b*e^2 - (a^2*b^2 + 4*a^3*c)*d*e)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x^2*e + d)/sqrt(-(2*a*c*d - a*b*e - sqrt(-4*(a*c*d^2 - a*b*d*e + a^2*e^2)*a*c + (2*a*c*d - a*b*e)^2))/(a*c)))/((sqrt(b^2 - 4*a*c)*a^2*c*d^2 - sqrt(b^2 - 4*a*c)*a^2*b*d*e + sqrt(b^2 - 4*a*c)*a^3*e^2)*abs(a)*abs(c))","B",0
359,-2,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)/x^3/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueDone","F(-2)",0
360,1,1055,0,0.904627," ","integrate((e*x^2+d)^(1/2)/x^5/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(\sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d e - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{2}\right)} a^{2} - 2 \, {\left({\left(a b^{2} c - a^{2} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} - {\left(a b^{3} - a^{2} b c\right)} \sqrt{b^{2} - 4 \, a c} d e + {\left(a^{2} b^{2} - a^{3} c\right)} \sqrt{b^{2} - 4 \, a c} e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| a \right|} - \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(2 \, {\left(a^{2} b^{3} c - 3 \, a^{3} b c^{2}\right)} d^{2} - {\left(a^{2} b^{4} - a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d e + {\left(a^{3} b^{3} - 2 \, a^{4} b c\right)} e^{2}\right)}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{2} e + d}}{\sqrt{-\frac{2 \, a^{3} c d - a^{3} b e + \sqrt{-4 \, {\left(a^{3} c d^{2} - a^{3} b d e + a^{4} e^{2}\right)} a^{3} c + {\left(2 \, a^{3} c d - a^{3} b e\right)}^{2}}}{a^{3} c}}}\right)}{8 \, {\left(\sqrt{b^{2} - 4 \, a c} a^{4} c d^{2} - \sqrt{b^{2} - 4 \, a c} a^{4} b d e + \sqrt{b^{2} - 4 \, a c} a^{5} e^{2}\right)} {\left| a \right|} {\left| c \right|}} + \frac{{\left(\sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d e - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{2}\right)} a^{2} + 2 \, {\left({\left(a b^{2} c - a^{2} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} - {\left(a b^{3} - a^{2} b c\right)} \sqrt{b^{2} - 4 \, a c} d e + {\left(a^{2} b^{2} - a^{3} c\right)} \sqrt{b^{2} - 4 \, a c} e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| a \right|} - \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(2 \, {\left(a^{2} b^{3} c - 3 \, a^{3} b c^{2}\right)} d^{2} - {\left(a^{2} b^{4} - a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d e + {\left(a^{3} b^{3} - 2 \, a^{4} b c\right)} e^{2}\right)}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{2} e + d}}{\sqrt{-\frac{2 \, a^{3} c d - a^{3} b e - \sqrt{-4 \, {\left(a^{3} c d^{2} - a^{3} b d e + a^{4} e^{2}\right)} a^{3} c + {\left(2 \, a^{3} c d - a^{3} b e\right)}^{2}}}{a^{3} c}}}\right)}{8 \, {\left(\sqrt{b^{2} - 4 \, a c} a^{4} c d^{2} - \sqrt{b^{2} - 4 \, a c} a^{4} b d e + \sqrt{b^{2} - 4 \, a c} a^{5} e^{2}\right)} {\left| a \right|} {\left| c \right|}} + \frac{{\left(8 \, b^{2} d^{2} - 8 \, a c d^{2} - 4 \, a b d e - a^{2} e^{2}\right)} \arctan\left(\frac{\sqrt{x^{2} e + d}}{\sqrt{-d}}\right)}{8 \, a^{3} \sqrt{-d} d} + \frac{{\left(4 \, {\left(x^{2} e + d\right)}^{\frac{3}{2}} b d e - 4 \, \sqrt{x^{2} e + d} b d^{2} e - {\left(x^{2} e + d\right)}^{\frac{3}{2}} a e^{2} - \sqrt{x^{2} e + d} a d e^{2}\right)} e^{\left(-2\right)}}{8 \, a^{2} d x^{4}}"," ",0,"-1/8*(sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d*e - (a*b^3 - 4*a^2*b*c)*e^2)*a^2 - 2*((a*b^2*c - a^2*c^2)*sqrt(b^2 - 4*a*c)*d^2 - (a*b^3 - a^2*b*c)*sqrt(b^2 - 4*a*c)*d*e + (a^2*b^2 - a^3*c)*sqrt(b^2 - 4*a*c)*e^2)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(a) - sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*(2*(a^2*b^3*c - 3*a^3*b*c^2)*d^2 - (a^2*b^4 - a^3*b^2*c - 4*a^4*c^2)*d*e + (a^3*b^3 - 2*a^4*b*c)*e^2))*arctan(2*sqrt(1/2)*sqrt(x^2*e + d)/sqrt(-(2*a^3*c*d - a^3*b*e + sqrt(-4*(a^3*c*d^2 - a^3*b*d*e + a^4*e^2)*a^3*c + (2*a^3*c*d - a^3*b*e)^2))/(a^3*c)))/((sqrt(b^2 - 4*a*c)*a^4*c*d^2 - sqrt(b^2 - 4*a*c)*a^4*b*d*e + sqrt(b^2 - 4*a*c)*a^5*e^2)*abs(a)*abs(c)) + 1/8*(sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d*e - (a*b^3 - 4*a^2*b*c)*e^2)*a^2 + 2*((a*b^2*c - a^2*c^2)*sqrt(b^2 - 4*a*c)*d^2 - (a*b^3 - a^2*b*c)*sqrt(b^2 - 4*a*c)*d*e + (a^2*b^2 - a^3*c)*sqrt(b^2 - 4*a*c)*e^2)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(a) - sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*(2*(a^2*b^3*c - 3*a^3*b*c^2)*d^2 - (a^2*b^4 - a^3*b^2*c - 4*a^4*c^2)*d*e + (a^3*b^3 - 2*a^4*b*c)*e^2))*arctan(2*sqrt(1/2)*sqrt(x^2*e + d)/sqrt(-(2*a^3*c*d - a^3*b*e - sqrt(-4*(a^3*c*d^2 - a^3*b*d*e + a^4*e^2)*a^3*c + (2*a^3*c*d - a^3*b*e)^2))/(a^3*c)))/((sqrt(b^2 - 4*a*c)*a^4*c*d^2 - sqrt(b^2 - 4*a*c)*a^4*b*d*e + sqrt(b^2 - 4*a*c)*a^5*e^2)*abs(a)*abs(c)) + 1/8*(8*b^2*d^2 - 8*a*c*d^2 - 4*a*b*d*e - a^2*e^2)*arctan(sqrt(x^2*e + d)/sqrt(-d))/(a^3*sqrt(-d)*d) + 1/8*(4*(x^2*e + d)^(3/2)*b*d*e - 4*sqrt(x^2*e + d)*b*d^2*e - (x^2*e + d)^(3/2)*a*e^2 - sqrt(x^2*e + d)*a*d*e^2)*e^(-2)/(a^2*d*x^4)","B",0
361,1,53,0,2.038015," ","integrate(x^4*(e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(c d - 2 \, b e\right)} e^{\left(-\frac{1}{2}\right)} \log\left({\left(x e^{\frac{1}{2}} - \sqrt{x^{2} e + d}\right)}^{2}\right)}{4 \, c^{2}} + \frac{\sqrt{x^{2} e + d} x}{2 \, c}"," ",0,"-1/4*(c*d - 2*b*e)*e^(-1/2)*log((x*e^(1/2) - sqrt(x^2*e + d))^2)/c^2 + 1/2*sqrt(x^2*e + d)*x/c","A",0
362,1,27,0,1.831984," ","integrate(x^2*(e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{e^{\frac{1}{2}} \log\left({\left(x e^{\frac{1}{2}} - \sqrt{x^{2} e + d}\right)}^{2}\right)}{2 \, c}"," ",0,"-1/2*e^(1/2)*log((x*e^(1/2) - sqrt(x^2*e + d))^2)/c","A",0
363,-2,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,c]=[44,93,-37]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,c]=[-72,-7,6]Evaluation time: 0.44Unable to divide, perhaps due to rounding error%%%{18446744069414584320,[4,7,8,2,3,14,2]%%%}+%%%{-2147483648,[3,8,10,8,3,10,1]%%%}+%%%{-12884901888,[3,8,10,7,2,12,2]%%%}+%%%{463856467968,[3,8,10,6,1,14,3]%%%}+%%%{1924145348608,[3,8,10,5,0,16,4]%%%}+%%%{536870912,[3,8,9,8,5,10,0]%%%}+%%%{20401094656,[3,8,9,7,4,12,1]%%%}+%%%{-150323855360,[3,8,9,6,3,14,2]%%%}+%%%{-3135326126080,[3,8,9,5,2,16,3]%%%}+%%%{-4672924418048,[3,8,9,4,1,18,4]%%%}+%%%{6047313952768,[3,8,9,3,0,20,5]%%%}+%%%{-4294967296,[3,8,8,7,6,12,0]%%%}+%%%{-42412802048,[3,8,8,6,5,14,1]%%%}+%%%{1046898278400,[3,8,8,5,4,16,2]%%%}+%%%{6210522710016,[3,8,8,4,3,18,3]%%%}+%%%{-1786706395136,[3,8,8,3,2,20,4]%%%}+%%%{-11544872091648,[3,8,8,2,1,22,5]%%%}+%%%{4398046511104,[3,8,8,1,0,24,6]%%%}+%%%{12750684160,[3,8,7,6,7,14,0]%%%}+%%%{-23890755584,[3,8,7,5,6,16,1]%%%}+%%%{-2103460233216,[3,8,7,4,5,18,2]%%%}+%%%{-3324304687104,[3,8,7,3,4,20,3]%%%}+%%%{9758165696512,[3,8,7,2,3,22,4]%%%}+%%%{1649267441664,[3,8,7,1,2,24,5]%%%}+%%%{-4398046511104,[3,8,7,0,1,26,6]%%%}+%%%{-17985175552,[3,8,6,5,8,16,0]%%%}+%%%{161866579968,[3,8,6,4,7,18,1]%%%}+%%%{1586990415872,[3,8,6,3,6,20,2]%%%}+%%%{-1795296329728,[3,8,6,2,5,22,3]%%%}+%%%{-4123168604160,[3,8,6,1,4,24,4]%%%}+%%%{3848290697216,[3,8,6,0,3,26,5]%%%}+%%%{12213813248,[3,8,5,4,9,18,0]%%%}+%%%{-171798691840,[3,8,5,3,8,20,1]%%%}+%%%{-212600881152,[3,8,5,2,7,22,2]%%%}+%%%{1477468749824,[3,8,5,1,6,24,3]%%%}+%%%{-1099511627776,[3,8,5,0,5,26,4]%%%}+%%%{-3221225472,[3,8,4,3,10,20,0]%%%}+%%%{57982058496,[3,8,4,2,9,22,1]%%%}+%%%{-154618822656,[3,8,4,1,8,24,2]%%%}+%%%{103079215104,[3,8,4,0,7,26,3]%%%}+%%%{1048576,[3,6,10,4,2,4,0]%%%}+%%%{8388608,[3,6,10,3,1,6,1]%%%}+%%%{16777216,[3,6,10,2,0,8,2]%%%}+%%%{-5242880,[3,6,9,3,3,6,0]%%%}+%%%{-29360128,[3,6,9,2,2,8,1]%%%}+%%%{-33554432,[3,6,9,1,1,10,2]%%%}+%%%{9699328,[3,6,8,2,4,8,0]%%%}+%%%{33554432,[3,6,8,1,3,10,1]%%%}+%%%{16777216,[3,6,8,0,2,12,2]%%%}+%%%{-7864320,[3,6,7,1,5,10,0]%%%}+%%%{-12582912,[3,6,7,0,4,12,1]%%%}+%%%{2359296,[3,6,6,0,6,12,0]%%%}+%%%{536870912,[2,7,10,6,2,8,1]%%%}+%%%{6710886400,[2,7,10,5,1,10,2]%%%}+%%%{18253611008,[2,7,10,4,0,12,3]%%%}+%%%{-134217728,[2,7,9,6,4,8,0]%%%}+%%%{-5502926848,[2,7,9,5,3,10,1]%%%}+%%%{-36909875200,[2,7,9,4,2,12,2]%%%}+%%%{-42949672960,[2,7,9,3,1,14,3]%%%}+%%%{42949672960,[2,7,9,2,0,16,4]%%%}+%%%{956301312,[2,7,8,5,5,10,0]%%%}+%%%{18656264192,[2,7,8,4,4,12,1]%%%}+%%%{64961380352,[2,7,8,3,3,14,2]%%%}+%%%{-8589934592,[2,7,8,2,2,16,3]%%%}+%%%{-85899345920,[2,7,8,1,1,18,4]%%%}+%%%{-2642411520,[2,7,7,4,6,12,0]%%%}+%%%{-27783069696,[2,7,7,3,5,14,1]%%%}+%%%{-33957085184,[2,7,7,2,4,16,2]%%%}+%%%{73014444032,[2,7,7,1,3,18,3]%%%}+%%%{42949672960,[2,7,7,0,2,20,4]%%%}+%%%{3556769792,[2,7,6,3,7,14,0]%%%}+%%%{17716740096,[2,7,6,2,6,16,1]%%%}+%%%{-12884901888,[2,7,6,1,5,18,2]%%%}+%%%{-39728447488,[2,7,6,0,4,20,3]%%%}+%%%{-2340421632,[2,7,5,2,8,16,0]%%%}+%%%{-2415919104,[2,7,5,1,7,18,1]%%%}+%%%{12079595520,[2,7,5,0,6,20,2]%%%}+%%%{603979776,[2,7,4,1,9,18,0]%%%}+%%%{-1207959552,[2,7,4,0,8,20,1]%%%}+%%%{2147483648,[1,8,10,9,3,10,1]%%%}+%%%{38654705664,[1,8,10,8,2,12,2]%%%}+%%%{51539607552,[1,8,10,7,1,14,3]%%%}+%%%{-274877906944,[1,8,10,6,0,16,4]%%%}+%%%{-536870912,[1,8,9,9,5,10,0]%%%}+%%%{-26843545600,[1,8,9,8,4,12,1]%%%}+%%%{-188978561024,[1,8,9,7,3,14,2]%%%}+%%%{146028888064,[1,8,9,6,2,16,3]%%%}+%%%{962072674304,[1,8,9,5,1,18,4]%%%}+%%%{-549755813888,[1,8,9,4,0,20,5]%%%}+%%%{4294967296,[1,8,8,8,6,12,0]%%%}+%%%{95026151424,[1,8,8,7,5,14,1]%%%}+%%%{239444426752,[1,8,8,6,4,16,2]%%%}+%%%{-858993459200,[1,8,8,5,3,18,3]%%%}+%%%{-618475290624,[1,8,8,4,2,20,4]%%%}+%%%{1099511627776,[1,8,8,3,1,22,5]%%%}+%%%{-12750684160,[1,8,7,7,7,14,0]%%%}+%%%{-136633647104,[1,8,7,6,6,16,1]%%%}+%%%{62277025792,[1,8,7,5,5,18,2]%%%}+%%%{936302870528,[1,8,7,4,4,20,3]%%%}+%%%{-549755813888,[1,8,7,3,3,22,4]%%%}+%%%{-549755813888,[1,8,7,2,2,24,5]%%%}+%%%{17985175552,[1,8,6,6,8,16,0]%%%}+%%%{71940702208,[1,8,6,5,7,18,1]%%%}+%%%{-267361714176,[1,8,6,4,6,20,2]%%%}+%%%{-137438953472,[1,8,6,3,5,22,3]%%%}+%%%{481036337152,[1,8,6,2,4,24,4]%%%}+%%%{-12213813248,[1,8,5,5,9,18,0]%%%}+%%%{7247757312,[1,8,5,4,8,20,1]%%%}+%%%{103079215104,[1,8,5,3,7,22,2]%%%}+%%%{-137438953472,[1,8,5,2,6,24,3]%%%}+%%%{3221225472,[1,8,4,4,10,20,0]%%%}+%%%{-12884901888,[1,8,4,3,9,22,1]%%%}+%%%{12884901888,[1,8,4,2,8,24,2]%%%}+%%%{-1048576,[1,6,10,5,2,4,0]%%%}+%%%{-8388608,[1,6,10,4,1,6,1]%%%}+%%%{-16777216,[1,6,10,3,0,8,2]%%%}+%%%{8388608,[1,6,9,4,3,6,0]%%%}+%%%{62914560,[1,6,9,3,2,8,1]%%%}+%%%{150994944,[1,6,9,2,1,10,2]%%%}+%%%{134217728,[1,6,9,1,0,12,3]%%%}+%%%{-26476544,[1,6,8,3,4,8,0]%%%}+%%%{-163577856,[1,6,8,2,3,10,1]%%%}+%%%{-301989888,[1,6,8,1,2,12,2]%%%}+%%%{-134217728,[1,6,8,0,1,14,3]%%%}+%%%{41156608,[1,6,7,2,5,10,0]%%%}+%%%{178257920,[1,6,7,1,4,12,1]%%%}+%%%{167772160,[1,6,7,0,3,14,2]%%%}+%%%{-31457280,[1,6,6,1,6,12,0]%%%}+%%%{-69206016,[1,6,6,0,5,14,1]%%%}+%%%{9437184,[1,6,5,0,7,14,0]%%%}+%%%{-402653184,[0,7,10,7,2,8,1]%%%}+%%%{-5637144576,[0,7,10,6,1,10,2]%%%}+%%%{-16106127360,[0,7,10,5,0,12,3]%%%}+%%%{100663296,[0,7,9,7,4,8,0]%%%}+%%%{4160749568,[0,7,9,6,3,10,1]%%%}+%%%{30198988800,[0,7,9,5,2,12,2]%%%}+%%%{28991029248,[0,7,9,4,1,14,3]%%%}+%%%{-68719476736,[0,7,9,3,0,16,4]%%%}+%%%{-687865856,[0,7,8,6,5,10,0]%%%}+%%%{-13925089280,[0,7,8,5,4,12,1]%%%}+%%%{-48184164352,[0,7,8,4,3,14,2]%%%}+%%%{49392123904,[0,7,8,3,2,16,3]%%%}+%%%{120259084288,[0,7,8,2,1,18,4]%%%}+%%%{-68719476736,[0,7,8,1,0,20,5]%%%}+%%%{1845493760,[0,7,7,5,6,12,0]%%%}+%%%{19964887040,[0,7,7,4,5,14,1]%%%}+%%%{11542724608,[0,7,7,3,4,16,2]%%%}+%%%{-113816633344,[0,7,7,2,3,18,3]%%%}+%%%{8589934592,[0,7,7,1,2,20,4]%%%}+%%%{68719476736,[0,7,7,0,1,22,5]%%%}+%%%{-2432696320,[0,7,6,4,7,14,0]%%%}+%%%{-11207180288,[0,7,6,3,6,16,1]%%%}+%%%{28185722880,[0,7,6,2,5,18,2]%%%}+%%%{34359738368,[0,7,6,1,4,20,3]%%%}+%%%{-60129542144,[0,7,6,0,3,22,4]%%%}+%%%{1577058304,[0,7,5,3,8,16,0]%%%}+%%%{-201326592,[0,7,5,2,7,18,1]%%%}+%%%{-14495514624,[0,7,5,1,6,20,2]%%%}+%%%{17179869184,[0,7,5,0,5,22,3]%%%}+%%%{-402653184,[0,7,4,2,9,18,0]%%%}+%%%{1610612736,[0,7,4,1,8,20,1]%%%}+%%%{-1610612736,[0,7,4,0,7,22,2]%%%} / %%%{-1024,[0,3,4,2,1,2,0]%%%}+%%%{-4096,[0,3,4,1,0,4,1]%%%}+%%%{2560,[0,3,3,1,2,4,0]%%%}+%%%{4096,[0,3,3,0,1,6,1]%%%}+%%%{-1536,[0,3,2,0,3,6,0]%%%} Error: Bad Argument Value","F(-2)",0
364,-1,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)/x^2/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
365,-1,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)/x^4/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
366,-1,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)/x^6/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
367,1,857,0,1.246010," ","integrate(x^3*(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(2 \, b c^{5} d^{3} - {\left(5 \, b^{2} c^{4} - 8 \, a c^{5}\right)} d^{2} e + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{3}\right)} c^{2} + 2 \, {\left(2 \, b^{3} c^{3} - 5 \, a b c^{4}\right)} d e^{2} - 2 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{4} d^{3} - 2 \, \sqrt{b^{2} - 4 \, a c} b c^{3} d^{2} e - \sqrt{b^{2} - 4 \, a c} a b c^{2} e^{3} + {\left(b^{2} c^{2} + a c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d e^{2}\right)} {\left| c \right|} - {\left(b^{4} c^{2} - 3 \, a b^{2} c^{3}\right)} e^{3}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{2} e + d}}{\sqrt{-\frac{2 \, c^{4} d - b c^{3} e + \sqrt{-4 \, {\left(c^{4} d^{2} - b c^{3} d e + a c^{3} e^{2}\right)} c^{4} + {\left(2 \, c^{4} d - b c^{3} e\right)}^{2}}}{c^{4}}}}\right)}{{\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{3} d - {\left(b^{2} c^{2} - 4 \, a c^{3} + \sqrt{b^{2} - 4 \, a c} b c^{2}\right)} e\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{2}} + \frac{{\left(2 \, b c^{5} d^{3} - {\left(5 \, b^{2} c^{4} - 8 \, a c^{5}\right)} d^{2} e + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{3}\right)} c^{2} + 2 \, {\left(2 \, b^{3} c^{3} - 5 \, a b c^{4}\right)} d e^{2} + 2 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{4} d^{3} - 2 \, \sqrt{b^{2} - 4 \, a c} b c^{3} d^{2} e - \sqrt{b^{2} - 4 \, a c} a b c^{2} e^{3} + {\left(b^{2} c^{2} + a c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d e^{2}\right)} {\left| c \right|} - {\left(b^{4} c^{2} - 3 \, a b^{2} c^{3}\right)} e^{3}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{2} e + d}}{\sqrt{-\frac{2 \, c^{4} d - b c^{3} e - \sqrt{-4 \, {\left(c^{4} d^{2} - b c^{3} d e + a c^{3} e^{2}\right)} c^{4} + {\left(2 \, c^{4} d - b c^{3} e\right)}^{2}}}{c^{4}}}}\right)}{{\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{3} d + {\left(b^{2} c^{2} - 4 \, a c^{3} - \sqrt{b^{2} - 4 \, a c} b c^{2}\right)} e\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{2}} + \frac{{\left(x^{2} e + d\right)}^{\frac{3}{2}} c^{2} + 3 \, \sqrt{x^{2} e + d} c^{2} d - 3 \, \sqrt{x^{2} e + d} b c e}{3 \, c^{3}}"," ",0,"-(2*b*c^5*d^3 - (5*b^2*c^4 - 8*a*c^5)*d^2*e + ((b^2*c^2 - 4*a*c^3)*d^2*e - 2*(b^3*c - 4*a*b*c^2)*d*e^2 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e^3)*c^2 + 2*(2*b^3*c^3 - 5*a*b*c^4)*d*e^2 - 2*(sqrt(b^2 - 4*a*c)*c^4*d^3 - 2*sqrt(b^2 - 4*a*c)*b*c^3*d^2*e - sqrt(b^2 - 4*a*c)*a*b*c^2*e^3 + (b^2*c^2 + a*c^3)*sqrt(b^2 - 4*a*c)*d*e^2)*abs(c) - (b^4*c^2 - 3*a*b^2*c^3)*e^3)*arctan(2*sqrt(1/2)*sqrt(x^2*e + d)/sqrt(-(2*c^4*d - b*c^3*e + sqrt(-4*(c^4*d^2 - b*c^3*d*e + a*c^3*e^2)*c^4 + (2*c^4*d - b*c^3*e)^2))/c^4))/((2*sqrt(b^2 - 4*a*c)*c^3*d - (b^2*c^2 - 4*a*c^3 + sqrt(b^2 - 4*a*c)*b*c^2)*e)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*c^2) + (2*b*c^5*d^3 - (5*b^2*c^4 - 8*a*c^5)*d^2*e + ((b^2*c^2 - 4*a*c^3)*d^2*e - 2*(b^3*c - 4*a*b*c^2)*d*e^2 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e^3)*c^2 + 2*(2*b^3*c^3 - 5*a*b*c^4)*d*e^2 + 2*(sqrt(b^2 - 4*a*c)*c^4*d^3 - 2*sqrt(b^2 - 4*a*c)*b*c^3*d^2*e - sqrt(b^2 - 4*a*c)*a*b*c^2*e^3 + (b^2*c^2 + a*c^3)*sqrt(b^2 - 4*a*c)*d*e^2)*abs(c) - (b^4*c^2 - 3*a*b^2*c^3)*e^3)*arctan(2*sqrt(1/2)*sqrt(x^2*e + d)/sqrt(-(2*c^4*d - b*c^3*e - sqrt(-4*(c^4*d^2 - b*c^3*d*e + a*c^3*e^2)*c^4 + (2*c^4*d - b*c^3*e)^2))/c^4))/((2*sqrt(b^2 - 4*a*c)*c^3*d + (b^2*c^2 - 4*a*c^3 - sqrt(b^2 - 4*a*c)*b*c^2)*e)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*c^2) + 1/3*((x^2*e + d)^(3/2)*c^2 + 3*sqrt(x^2*e + d)*c^2*d - 3*sqrt(x^2*e + d)*b*c*e)/c^3","B",0
368,1,649,0,1.088760," ","integrate(x*(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{\sqrt{x^{2} e + d} e}{c} + \frac{{\left(4 \, c^{5} d^{3} - 6 \, b c^{4} d^{2} e - {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 4 \, a b c\right)} e^{3}\right)} c^{2} + 4 \, {\left(b^{2} c^{3} - a c^{4}\right)} d e^{2} + 2 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{3} d^{2} e - \sqrt{b^{2} - 4 \, a c} b c^{2} d e^{2} + \sqrt{b^{2} - 4 \, a c} a c^{2} e^{3}\right)} {\left| c \right|} - {\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} e^{3}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{2} e + d}}{\sqrt{-\frac{2 \, c^{2} d - b c e + \sqrt{-4 \, {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} c^{2} + {\left(2 \, c^{2} d - b c e\right)}^{2}}}{c^{2}}}}\right)}{{\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{2} d - {\left(b^{2} c - 4 \, a c^{2} + \sqrt{b^{2} - 4 \, a c} b c\right)} e\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{2}} - \frac{{\left(4 \, c^{5} d^{3} - 6 \, b c^{4} d^{2} e - {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 4 \, a b c\right)} e^{3}\right)} c^{2} + 4 \, {\left(b^{2} c^{3} - a c^{4}\right)} d e^{2} - 2 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{3} d^{2} e - \sqrt{b^{2} - 4 \, a c} b c^{2} d e^{2} + \sqrt{b^{2} - 4 \, a c} a c^{2} e^{3}\right)} {\left| c \right|} - {\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} e^{3}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{2} e + d}}{\sqrt{-\frac{2 \, c^{2} d - b c e - \sqrt{-4 \, {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} c^{2} + {\left(2 \, c^{2} d - b c e\right)}^{2}}}{c^{2}}}}\right)}{{\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{2} d + {\left(b^{2} c - 4 \, a c^{2} - \sqrt{b^{2} - 4 \, a c} b c\right)} e\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{2}}"," ",0,"sqrt(x^2*e + d)*e/c + (4*c^5*d^3 - 6*b*c^4*d^2*e - (2*(b^2*c - 4*a*c^2)*d*e^2 - (b^3 - 4*a*b*c)*e^3)*c^2 + 4*(b^2*c^3 - a*c^4)*d*e^2 + 2*(sqrt(b^2 - 4*a*c)*c^3*d^2*e - sqrt(b^2 - 4*a*c)*b*c^2*d*e^2 + sqrt(b^2 - 4*a*c)*a*c^2*e^3)*abs(c) - (b^3*c^2 - 2*a*b*c^3)*e^3)*arctan(2*sqrt(1/2)*sqrt(x^2*e + d)/sqrt(-(2*c^2*d - b*c*e + sqrt(-4*(c^2*d^2 - b*c*d*e + a*c*e^2)*c^2 + (2*c^2*d - b*c*e)^2))/c^2))/((2*sqrt(b^2 - 4*a*c)*c^2*d - (b^2*c - 4*a*c^2 + sqrt(b^2 - 4*a*c)*b*c)*e)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*c^2) - (4*c^5*d^3 - 6*b*c^4*d^2*e - (2*(b^2*c - 4*a*c^2)*d*e^2 - (b^3 - 4*a*b*c)*e^3)*c^2 + 4*(b^2*c^3 - a*c^4)*d*e^2 - 2*(sqrt(b^2 - 4*a*c)*c^3*d^2*e - sqrt(b^2 - 4*a*c)*b*c^2*d*e^2 + sqrt(b^2 - 4*a*c)*a*c^2*e^3)*abs(c) - (b^3*c^2 - 2*a*b*c^3)*e^3)*arctan(2*sqrt(1/2)*sqrt(x^2*e + d)/sqrt(-(2*c^2*d - b*c*e - sqrt(-4*(c^2*d^2 - b*c*d*e + a*c*e^2)*c^2 + (2*c^2*d - b*c*e)^2))/c^2))/((2*sqrt(b^2 - 4*a*c)*c^2*d + (b^2*c - 4*a*c^2 - sqrt(b^2 - 4*a*c)*b*c)*e)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*c^2)","B",0
369,1,827,0,1.023804," ","integrate((e*x^2+d)^(3/2)/x/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{d^{2} \arctan\left(\frac{\sqrt{x^{2} e + d}}{\sqrt{-d}}\right)}{a \sqrt{-d}} - \frac{{\left({\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e - {\left(a b^{2} - 4 \, a^{2} c\right)} e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} a^{2} - 2 \, {\left(\sqrt{b^{2} - 4 \, a c} a c^{2} d^{3} - \sqrt{b^{2} - 4 \, a c} a b c d^{2} e + \sqrt{b^{2} - 4 \, a c} a^{2} c d e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| a \right|} - {\left(2 \, a^{2} b c^{2} d^{3} + 6 \, a^{3} b c d e^{2} - a^{3} b^{2} e^{3} - {\left(a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} d^{2} e\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{2} e + d}}{\sqrt{-\frac{2 \, a c d - a b e + \sqrt{-4 \, {\left(a c d^{2} - a b d e + a^{2} e^{2}\right)} a c + {\left(2 \, a c d - a b e\right)}^{2}}}{a c}}}\right)}{8 \, {\left(\sqrt{b^{2} - 4 \, a c} a^{2} c^{2} d^{2} - \sqrt{b^{2} - 4 \, a c} a^{2} b c d e + \sqrt{b^{2} - 4 \, a c} a^{3} c e^{2}\right)} {\left| a \right|} {\left| c \right|}} + \frac{{\left({\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e - {\left(a b^{2} - 4 \, a^{2} c\right)} e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} a^{2} + 2 \, {\left(\sqrt{b^{2} - 4 \, a c} a c^{2} d^{3} - \sqrt{b^{2} - 4 \, a c} a b c d^{2} e + \sqrt{b^{2} - 4 \, a c} a^{2} c d e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| a \right|} - {\left(2 \, a^{2} b c^{2} d^{3} + 6 \, a^{3} b c d e^{2} - a^{3} b^{2} e^{3} - {\left(a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} d^{2} e\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{2} e + d}}{\sqrt{-\frac{2 \, a c d - a b e - \sqrt{-4 \, {\left(a c d^{2} - a b d e + a^{2} e^{2}\right)} a c + {\left(2 \, a c d - a b e\right)}^{2}}}{a c}}}\right)}{8 \, {\left(\sqrt{b^{2} - 4 \, a c} a^{2} c^{2} d^{2} - \sqrt{b^{2} - 4 \, a c} a^{2} b c d e + \sqrt{b^{2} - 4 \, a c} a^{3} c e^{2}\right)} {\left| a \right|} {\left| c \right|}}"," ",0,"d^2*arctan(sqrt(x^2*e + d)/sqrt(-d))/(a*sqrt(-d)) - 1/8*(((b^2*c - 4*a*c^2)*d^2*e - (a*b^2 - 4*a^2*c)*e^3)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*a^2 - 2*(sqrt(b^2 - 4*a*c)*a*c^2*d^3 - sqrt(b^2 - 4*a*c)*a*b*c*d^2*e + sqrt(b^2 - 4*a*c)*a^2*c*d*e^2)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(a) - (2*a^2*b*c^2*d^3 + 6*a^3*b*c*d*e^2 - a^3*b^2*e^3 - (a^2*b^2*c + 8*a^3*c^2)*d^2*e)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x^2*e + d)/sqrt(-(2*a*c*d - a*b*e + sqrt(-4*(a*c*d^2 - a*b*d*e + a^2*e^2)*a*c + (2*a*c*d - a*b*e)^2))/(a*c)))/((sqrt(b^2 - 4*a*c)*a^2*c^2*d^2 - sqrt(b^2 - 4*a*c)*a^2*b*c*d*e + sqrt(b^2 - 4*a*c)*a^3*c*e^2)*abs(a)*abs(c)) + 1/8*(((b^2*c - 4*a*c^2)*d^2*e - (a*b^2 - 4*a^2*c)*e^3)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*a^2 + 2*(sqrt(b^2 - 4*a*c)*a*c^2*d^3 - sqrt(b^2 - 4*a*c)*a*b*c*d^2*e + sqrt(b^2 - 4*a*c)*a^2*c*d*e^2)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(a) - (2*a^2*b*c^2*d^3 + 6*a^3*b*c*d*e^2 - a^3*b^2*e^3 - (a^2*b^2*c + 8*a^3*c^2)*d^2*e)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x^2*e + d)/sqrt(-(2*a*c*d - a*b*e - sqrt(-4*(a*c*d^2 - a*b*d*e + a^2*e^2)*a*c + (2*a*c*d - a*b*e)^2))/(a*c)))/((sqrt(b^2 - 4*a*c)*a^2*c^2*d^2 - sqrt(b^2 - 4*a*c)*a^2*b*c*d*e + sqrt(b^2 - 4*a*c)*a^3*c*e^2)*abs(a)*abs(c))","B",0
370,1,433,0,0.724810," ","integrate((e*x^2+d)^(3/2)/x^3/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(2 \, b d^{2} - 3 \, a d e\right)} \arctan\left(\frac{\sqrt{x^{2} e + d}}{\sqrt{-d}}\right)}{2 \, a^{2} \sqrt{-d}} - \frac{\sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left({\left(b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} b\right)} d - {\left(a b + \sqrt{b^{2} - 4 \, a c} a\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{2} e + d}}{\sqrt{-\frac{2 \, a^{2} c d - a^{2} b e + \sqrt{-4 \, {\left(a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2}\right)} a^{2} c + {\left(2 \, a^{2} c d - a^{2} b e\right)}^{2}}}{a^{2} c}}}\right)}{4 \, \sqrt{b^{2} - 4 \, a c} a^{2} {\left| c \right|}} + \frac{\sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left({\left(b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} b\right)} d - {\left(a b - \sqrt{b^{2} - 4 \, a c} a\right)} e\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x^{2} e + d}}{\sqrt{-\frac{2 \, a^{2} c d - a^{2} b e - \sqrt{-4 \, {\left(a^{2} c d^{2} - a^{2} b d e + a^{3} e^{2}\right)} a^{2} c + {\left(2 \, a^{2} c d - a^{2} b e\right)}^{2}}}{a^{2} c}}}\right)}{4 \, \sqrt{b^{2} - 4 \, a c} a^{2} {\left| c \right|}} - \frac{\sqrt{x^{2} e + d} d}{2 \, a x^{2}}"," ",0,"-1/2*(2*b*d^2 - 3*a*d*e)*arctan(sqrt(x^2*e + d)/sqrt(-d))/(a^2*sqrt(-d)) - 1/4*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*((b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*b)*d - (a*b + sqrt(b^2 - 4*a*c)*a)*e)*arctan(2*sqrt(1/2)*sqrt(x^2*e + d)/sqrt(-(2*a^2*c*d - a^2*b*e + sqrt(-4*(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*a^2*c + (2*a^2*c*d - a^2*b*e)^2))/(a^2*c)))/(sqrt(b^2 - 4*a*c)*a^2*abs(c)) + 1/4*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*((b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*b)*d - (a*b - sqrt(b^2 - 4*a*c)*a)*e)*arctan(2*sqrt(1/2)*sqrt(x^2*e + d)/sqrt(-(2*a^2*c*d - a^2*b*e - sqrt(-4*(a^2*c*d^2 - a^2*b*d*e + a^3*e^2)*a^2*c + (2*a^2*c*d - a^2*b*e)^2))/(a^2*c)))/(sqrt(b^2 - 4*a*c)*a^2*abs(c)) - 1/2*sqrt(x^2*e + d)*d/(a*x^2)","A",0
371,1,104,0,1.868582," ","integrate(x^4*(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{x^{2} e + d} {\left(\frac{2 \, x^{2} e}{c} + \frac{{\left(5 \, c^{5} d e^{2} - 4 \, b c^{4} e^{3}\right)} e^{\left(-2\right)}}{c^{6}}\right)} x - \frac{{\left(3 \, c^{2} d^{2} - 12 \, b c d e + 8 \, b^{2} e^{2} - 8 \, a c e^{2}\right)} e^{\left(-\frac{1}{2}\right)} \log\left({\left(x e^{\frac{1}{2}} - \sqrt{x^{2} e + d}\right)}^{2}\right)}{16 \, c^{3}}"," ",0,"1/8*sqrt(x^2*e + d)*(2*x^2*e/c + (5*c^5*d*e^2 - 4*b*c^4*e^3)*e^(-2)/c^6)*x - 1/16*(3*c^2*d^2 - 12*b*c*d*e + 8*b^2*e^2 - 8*a*c*e^2)*e^(-1/2)*log((x*e^(1/2) - sqrt(x^2*e + d))^2)/c^3","A",0
372,1,58,0,1.974800," ","integrate(x^2*(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{\sqrt{x^{2} e + d} x e}{2 \, c} - \frac{{\left(3 \, c d e - 2 \, b e^{2}\right)} e^{\left(-\frac{1}{2}\right)} \log\left({\left(x e^{\frac{1}{2}} - \sqrt{x^{2} e + d}\right)}^{2}\right)}{4 \, c^{2}}"," ",0,"1/2*sqrt(x^2*e + d)*x*e/c - 1/4*(3*c*d*e - 2*b*e^2)*e^(-1/2)*log((x*e^(1/2) - sqrt(x^2*e + d))^2)/c^2","A",0
373,1,27,0,1.967544," ","integrate((e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{e^{\frac{3}{2}} \log\left({\left(x e^{\frac{1}{2}} - \sqrt{x^{2} e + d}\right)}^{2}\right)}{2 \, c}"," ",0,"-1/2*e^(3/2)*log((x*e^(1/2) - sqrt(x^2*e + d))^2)/c","A",0
374,-1,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)/x^2/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
375,-1,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)/x^4/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
376,1,4637,0,4.484135," ","integrate(x^5*(-x^2+1)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(2 \, b^{6} c^{4} - 14 \, a b^{4} c^{5} + 6 \, b^{5} c^{5} + 24 \, a^{2} b^{2} c^{6} - 40 \, a b^{3} c^{6} + 4 \, b^{4} c^{6} + 64 \, a^{2} b c^{7} - 24 \, a b^{2} c^{7} + 32 \, a^{2} c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 26 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 13 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + 43 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 19 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{6} + 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b c^{6} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{6} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a c^{7} - 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} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{5} + 16 \, {\left(b^{2} - 4 \, a c\right)} a b c^{6} - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{6} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{7} - {\left(2 \, b^{6} c^{2} - 18 \, a b^{4} c^{3} + 2 \, b^{5} c^{3} + 48 \, a^{2} b^{2} c^{4} - 16 \, a b^{3} c^{4} - 32 \, a^{3} c^{5} + 32 \, a^{2} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{6} + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 33 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b 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} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} c^{2} - 2 \, {\left(\sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} - 8 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 6 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 3 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} + 2 \, a b^{5} c^{3} + 2 \, b^{6} c^{3} + 16 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 8 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 11 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 16 \, a^{2} b^{3} c^{4} + 7 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} - 16 \, a b^{4} c^{4} + 2 \, b^{5} c^{4} - 4 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + 32 \, a^{3} b c^{5} - 28 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} + 32 \, a^{2} b^{2} c^{5} + 5 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} - 16 \, a b^{3} c^{5} - 20 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \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)} a b^{3} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4} - 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)} {\left| c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{-x^{2} + 1}}{\sqrt{-\frac{b c^{3} + 2 \, c^{4} + \sqrt{-4 \, {\left(a c^{3} + b c^{3} + c^{4}\right)} c^{4} + {\left(b c^{3} + 2 \, c^{4}\right)}^{2}}}{c^{4}}}}\right)}{8 \, {\left(a b^{4} c^{4} + b^{5} c^{4} - 8 \, a^{2} b^{2} c^{5} - 6 \, a b^{3} c^{5} + 3 \, b^{4} c^{5} + 16 \, a^{3} c^{6} + 8 \, a^{2} b c^{6} - 11 \, a b^{2} c^{6} + 7 \, b^{3} c^{6} - 4 \, a^{2} c^{7} - 28 \, a b c^{7} + 5 \, b^{2} c^{7} - 20 \, a c^{8}\right)} c^{2}} + \frac{{\left(2 \, b^{6} c^{4} - 14 \, a b^{4} c^{5} + 6 \, b^{5} c^{5} + 24 \, a^{2} b^{2} c^{6} - 40 \, a b^{3} c^{6} + 4 \, b^{4} c^{6} + 64 \, a^{2} b c^{7} - 24 \, a b^{2} c^{7} + 32 \, a^{2} c^{8} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} + 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 12 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} + 26 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} - 13 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} - 32 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} + 43 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 19 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{6} + 48 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b c^{6} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{6} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a c^{7} - 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} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{5} + 16 \, {\left(b^{2} - 4 \, a c\right)} a b c^{6} - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{6} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{7} - {\left(2 \, b^{6} c^{2} - 18 \, a b^{4} c^{3} + 2 \, b^{5} c^{3} + 48 \, a^{2} b^{2} c^{4} - 16 \, a b^{3} c^{4} - 32 \, a^{3} c^{5} + 32 \, a^{2} b c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{6} + 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 18 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 24 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 33 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{3} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b 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} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4}\right)} c^{2} + 2 \, {\left(\sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c^{2} + \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{6} c^{2} - 8 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{3} - 6 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{3} + 3 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{3} - 2 \, a b^{5} c^{3} - 2 \, b^{6} c^{3} + 16 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{4} + 8 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{4} - 11 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{4} + 16 \, a^{2} b^{3} c^{4} + 7 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{4} + 16 \, a b^{4} c^{4} - 2 \, b^{5} c^{4} - 4 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{5} - 32 \, a^{3} b c^{5} - 28 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{5} - 32 \, a^{2} b^{2} c^{5} + 5 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{5} + 16 \, a b^{3} c^{5} - 20 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \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)} a b^{3} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{4} + 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)} {\left| c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{-x^{2} + 1}}{\sqrt{-\frac{b c^{3} + 2 \, c^{4} - \sqrt{-4 \, {\left(a c^{3} + b c^{3} + c^{4}\right)} c^{4} + {\left(b c^{3} + 2 \, c^{4}\right)}^{2}}}{c^{4}}}}\right)}{8 \, {\left(a b^{4} c^{4} + b^{5} c^{4} - 8 \, a^{2} b^{2} c^{5} - 6 \, a b^{3} c^{5} + 3 \, b^{4} c^{5} + 16 \, a^{3} c^{6} + 8 \, a^{2} b c^{6} - 11 \, a b^{2} c^{6} + 7 \, b^{3} c^{6} - 4 \, a^{2} c^{7} - 28 \, a b c^{7} + 5 \, b^{2} c^{7} - 20 \, a c^{8}\right)} c^{2}} - \frac{{\left(-x^{2} + 1\right)}^{\frac{3}{2}} c^{2} + 3 \, \sqrt{-x^{2} + 1} b c}{3 \, c^{3}}"," ",0,"-1/8*(2*b^6*c^4 - 14*a*b^4*c^5 + 6*b^5*c^5 + 24*a^2*b^2*c^6 - 40*a*b^3*c^6 + 4*b^4*c^6 + 64*a^2*b*c^7 - 24*a*b^2*c^7 + 32*a^2*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^6*c^2 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^5*c^3 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + 26*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^4*c^4 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 + 43*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 - 19*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^3*c^5 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*c^6 + 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b*c^6 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^2*c^6 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*c^7 - 2*(b^2 - 4*a*c)*b^4*c^4 + 6*(b^2 - 4*a*c)*a*b^2*c^5 - 6*(b^2 - 4*a*c)*b^3*c^5 + 16*(b^2 - 4*a*c)*a*b*c^6 - 4*(b^2 - 4*a*c)*b^2*c^6 + 8*(b^2 - 4*a*c)*a*c^7 - (2*b^6*c^2 - 18*a*b^4*c^3 + 2*b^5*c^3 + 48*a^2*b^2*c^4 - 16*a*b^3*c^4 - 32*a^3*c^5 + 32*a^2*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^6 + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^5*c - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 33*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^3*c^3 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - 2*(b^2 - 4*a*c)*b^4*c^2 + 10*(b^2 - 4*a*c)*a*b^2*c^3 - 2*(b^2 - 4*a*c)*b^3*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4 + 8*(b^2 - 4*a*c)*a*b*c^4)*c^2 - 2*(sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 + sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^6*c^2 - 8*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 6*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 3*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^5*c^3 + 2*a*b^5*c^3 + 2*b^6*c^3 + 16*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 8*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 11*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - 16*a^2*b^3*c^4 + 7*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^4*c^4 - 16*a*b^4*c^4 + 2*b^5*c^4 - 4*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 + 32*a^3*b*c^5 - 28*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 + 32*a^2*b^2*c^5 + 5*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^3*c^5 - 16*a*b^3*c^5 - 20*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b*c^6 + 32*a^2*b*c^6 - 2*(b^2 - 4*a*c)*a*b^3*c^3 - 2*(b^2 - 4*a*c)*b^4*c^3 + 8*(b^2 - 4*a*c)*a^2*b*c^4 + 8*(b^2 - 4*a*c)*a*b^2*c^4 - 2*(b^2 - 4*a*c)*b^3*c^4 + 8*(b^2 - 4*a*c)*a*b*c^5)*abs(c))*arctan(2*sqrt(1/2)*sqrt(-x^2 + 1)/sqrt(-(b*c^3 + 2*c^4 + sqrt(-4*(a*c^3 + b*c^3 + c^4)*c^4 + (b*c^3 + 2*c^4)^2))/c^4))/((a*b^4*c^4 + b^5*c^4 - 8*a^2*b^2*c^5 - 6*a*b^3*c^5 + 3*b^4*c^5 + 16*a^3*c^6 + 8*a^2*b*c^6 - 11*a*b^2*c^6 + 7*b^3*c^6 - 4*a^2*c^7 - 28*a*b*c^7 + 5*b^2*c^7 - 20*a*c^8)*c^2) + 1/8*(2*b^6*c^4 - 14*a*b^4*c^5 + 6*b^5*c^5 + 24*a^2*b^2*c^6 - 40*a*b^3*c^6 + 4*b^4*c^6 + 64*a^2*b*c^7 - 24*a*b^2*c^7 + 32*a^2*c^8 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^6*c^2 + 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^5*c^3 - 12*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 + 26*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 - 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^4*c^4 - 32*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 + 43*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 - 19*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^3*c^5 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*c^6 + 48*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b*c^6 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^2*c^6 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*c^7 - 2*(b^2 - 4*a*c)*b^4*c^4 + 6*(b^2 - 4*a*c)*a*b^2*c^5 - 6*(b^2 - 4*a*c)*b^3*c^5 + 16*(b^2 - 4*a*c)*a*b*c^6 - 4*(b^2 - 4*a*c)*b^2*c^6 + 8*(b^2 - 4*a*c)*a*c^7 - (2*b^6*c^2 - 18*a*b^4*c^3 + 2*b^5*c^3 + 48*a^2*b^2*c^4 - 16*a*b^3*c^4 - 32*a^3*c^5 + 32*a^2*b*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^6 + 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^5*c - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 18*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 - 24*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 33*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^3*c^3 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b*c^4 - 2*(b^2 - 4*a*c)*b^4*c^2 + 10*(b^2 - 4*a*c)*a*b^2*c^3 - 2*(b^2 - 4*a*c)*b^3*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4 + 8*(b^2 - 4*a*c)*a*b*c^4)*c^2 + 2*(sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^5*c^2 + sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^6*c^2 - 8*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^3 - 6*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^3 + 3*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^5*c^3 - 2*a*b^5*c^3 - 2*b^6*c^3 + 16*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^4 + 8*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^4 - 11*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^4 + 16*a^2*b^3*c^4 + 7*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^4*c^4 + 16*a*b^4*c^4 - 2*b^5*c^4 - 4*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^5 - 32*a^3*b*c^5 - 28*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^5 - 32*a^2*b^2*c^5 + 5*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^3*c^5 + 16*a*b^3*c^5 - 20*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b*c^6 - 32*a^2*b*c^6 + 2*(b^2 - 4*a*c)*a*b^3*c^3 + 2*(b^2 - 4*a*c)*b^4*c^3 - 8*(b^2 - 4*a*c)*a^2*b*c^4 - 8*(b^2 - 4*a*c)*a*b^2*c^4 + 2*(b^2 - 4*a*c)*b^3*c^4 - 8*(b^2 - 4*a*c)*a*b*c^5)*abs(c))*arctan(2*sqrt(1/2)*sqrt(-x^2 + 1)/sqrt(-(b*c^3 + 2*c^4 - sqrt(-4*(a*c^3 + b*c^3 + c^4)*c^4 + (b*c^3 + 2*c^4)^2))/c^4))/((a*b^4*c^4 + b^5*c^4 - 8*a^2*b^2*c^5 - 6*a*b^3*c^5 + 3*b^4*c^5 + 16*a^3*c^6 + 8*a^2*b*c^6 - 11*a*b^2*c^6 + 7*b^3*c^6 - 4*a^2*c^7 - 28*a*b*c^7 + 5*b^2*c^7 - 20*a*c^8)*c^2) - 1/3*((-x^2 + 1)^(3/2)*c^2 + 3*sqrt(-x^2 + 1)*b*c)/c^3","B",0
377,1,4060,0,4.104032," ","integrate(x^3*(-x^2+1)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{\sqrt{-x^{2} + 1}}{c} + \frac{{\left(2 \, b^{5} c^{4} - 12 \, a b^{3} c^{5} + 6 \, b^{4} c^{5} + 16 \, a^{2} b c^{6} - 32 \, a b^{2} c^{6} + 4 \, b^{3} c^{6} + 32 \, a^{2} c^{7} - 16 \, a b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 13 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 26 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 19 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a c^{6} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{5} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{6} - 4 \, {\left(b^{2} - 4 \, a c\right)} b c^{6} - {\left(2 \, b^{5} c^{2} - 16 \, a b^{3} c^{3} + 2 \, b^{4} c^{3} + 32 \, a^{2} b c^{4} - 16 \, a b^{2} c^{4} + 32 \, a^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a 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} - 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} - 2 \, {\left(\sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 6 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 3 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} + 2 \, a b^{4} c^{3} + 2 \, b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 8 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 11 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 16 \, a^{2} b^{2} c^{4} + 7 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} - 16 \, a b^{3} c^{4} + 2 \, b^{4} c^{4} - 4 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 32 \, a^{3} c^{5} - 28 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b c^{5} + 32 \, a^{2} b c^{5} + 5 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} - 16 \, a b^{2} c^{5} - 20 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a c^{6} + 32 \, a^{2} c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{4} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{5}\right)} {\left| c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{-x^{2} + 1}}{\sqrt{-\frac{b c + 2 \, c^{2} + \sqrt{-4 \, {\left(a c + b c + c^{2}\right)} c^{2} + {\left(b c + 2 \, c^{2}\right)}^{2}}}{c^{2}}}}\right)}{8 \, {\left(a b^{4} c^{3} + b^{5} c^{3} - 8 \, a^{2} b^{2} c^{4} - 6 \, a b^{3} c^{4} + 3 \, b^{4} c^{4} + 16 \, a^{3} c^{5} + 8 \, a^{2} b c^{5} - 11 \, a b^{2} c^{5} + 7 \, b^{3} c^{5} - 4 \, a^{2} c^{6} - 28 \, a b c^{6} + 5 \, b^{2} c^{6} - 20 \, a c^{7}\right)} c^{2}} - \frac{{\left(2 \, b^{5} c^{4} - 12 \, a b^{3} c^{5} + 6 \, b^{4} c^{5} + 16 \, a^{2} b c^{6} - 32 \, a b^{2} c^{6} + 4 \, b^{3} c^{6} + 32 \, a^{2} c^{7} - 16 \, a b c^{7} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} - 13 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} + 26 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 19 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a c^{6} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b c^{6} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{4} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b c^{5} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{5} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{6} - 4 \, {\left(b^{2} - 4 \, a c\right)} b c^{6} - {\left(2 \, b^{5} c^{2} - 16 \, a b^{3} c^{3} + 2 \, b^{4} c^{3} + 32 \, a^{2} b c^{4} - 16 \, a b^{2} c^{4} + 32 \, a^{2} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c - 3 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 7 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{3} + 28 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{3} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a 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} - 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} + 2 \, {\left(\sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 8 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 6 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 3 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{3} - 2 \, a b^{4} c^{3} - 2 \, b^{5} c^{3} + 16 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{4} + 8 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 11 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{4} + 16 \, a^{2} b^{2} c^{4} + 7 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{4} + 16 \, a b^{3} c^{4} - 2 \, b^{4} c^{4} - 4 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{5} - 32 \, a^{3} c^{5} - 28 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b c^{5} - 32 \, a^{2} b c^{5} + 5 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{5} + 16 \, a b^{2} c^{5} - 20 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a c^{6} - 32 \, a^{2} c^{6} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{4} - 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{5}\right)} {\left| c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{-x^{2} + 1}}{\sqrt{-\frac{b c + 2 \, c^{2} - \sqrt{-4 \, {\left(a c + b c + c^{2}\right)} c^{2} + {\left(b c + 2 \, c^{2}\right)}^{2}}}{c^{2}}}}\right)}{8 \, {\left(a b^{4} c^{3} + b^{5} c^{3} - 8 \, a^{2} b^{2} c^{4} - 6 \, a b^{3} c^{4} + 3 \, b^{4} c^{4} + 16 \, a^{3} c^{5} + 8 \, a^{2} b c^{5} - 11 \, a b^{2} c^{5} + 7 \, b^{3} c^{5} - 4 \, a^{2} c^{6} - 28 \, a b c^{6} + 5 \, b^{2} c^{6} - 20 \, a c^{7}\right)} c^{2}}"," ",0,"sqrt(-x^2 + 1)/c + 1/8*(2*b^5*c^4 - 12*a*b^3*c^5 + 6*b^4*c^5 + 16*a^2*b*c^6 - 32*a*b^2*c^6 + 4*b^3*c^6 + 32*a^2*c^7 - 16*a*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^3*c^4 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*c^5 + 26*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 19*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^2*c^5 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*c^6 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b*c^6 - 2*(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*a*b*c^5 - 6*(b^2 - 4*a*c)*b^2*c^5 + 8*(b^2 - 4*a*c)*a*c^6 - 4*(b^2 - 4*a*c)*b*c^6 - (2*b^5*c^2 - 16*a*b^3*c^3 + 2*b^4*c^3 + 32*a^2*b*c^4 - 16*a*b^2*c^4 + 32*a^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^5 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^4*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^2*c^3 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*c^4 - 2*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^2*c^3 + 8*(b^2 - 4*a*c)*a*c^4)*c^2 - 2*(sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 8*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 6*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 3*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^4*c^3 + 2*a*b^4*c^3 + 2*b^5*c^3 + 16*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 8*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 11*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 16*a^2*b^2*c^4 + 7*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^3*c^4 - 16*a*b^3*c^4 + 2*b^4*c^4 - 4*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*c^5 + 32*a^3*c^5 - 28*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b*c^5 + 32*a^2*b*c^5 + 5*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^2*c^5 - 16*a*b^2*c^5 - 20*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*c^6 + 32*a^2*c^6 - 2*(b^2 - 4*a*c)*a*b^2*c^3 - 2*(b^2 - 4*a*c)*b^3*c^3 + 8*(b^2 - 4*a*c)*a^2*c^4 + 8*(b^2 - 4*a*c)*a*b*c^4 - 2*(b^2 - 4*a*c)*b^2*c^4 + 8*(b^2 - 4*a*c)*a*c^5)*abs(c))*arctan(2*sqrt(1/2)*sqrt(-x^2 + 1)/sqrt(-(b*c + 2*c^2 + sqrt(-4*(a*c + b*c + c^2)*c^2 + (b*c + 2*c^2)^2))/c^2))/((a*b^4*c^3 + b^5*c^3 - 8*a^2*b^2*c^4 - 6*a*b^3*c^4 + 3*b^4*c^4 + 16*a^3*c^5 + 8*a^2*b*c^5 - 11*a*b^2*c^5 + 7*b^3*c^5 - 4*a^2*c^6 - 28*a*b*c^6 + 5*b^2*c^6 - 20*a*c^7)*c^2) - 1/8*(2*b^5*c^4 - 12*a*b^3*c^5 + 6*b^4*c^5 + 16*a^2*b*c^6 - 32*a*b^2*c^6 + 4*b^3*c^6 + 32*a^2*c^7 - 16*a*b*c^7 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 - 13*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^3*c^4 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*c^5 + 26*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 19*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^2*c^5 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*c^6 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b*c^6 - 2*(b^2 - 4*a*c)*b^3*c^4 + 4*(b^2 - 4*a*c)*a*b*c^5 - 6*(b^2 - 4*a*c)*b^2*c^5 + 8*(b^2 - 4*a*c)*a*c^6 - 4*(b^2 - 4*a*c)*b*c^6 - (2*b^5*c^2 - 16*a*b^3*c^3 + 2*b^4*c^3 + 32*a^2*b*c^4 - 16*a*b^2*c^4 + 32*a^2*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^5 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^3*c - 3*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^4*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 7*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*c^3 + 28*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^2*c^3 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*c^4 - 2*(b^2 - 4*a*c)*b^3*c^2 + 8*(b^2 - 4*a*c)*a*b*c^3 - 2*(b^2 - 4*a*c)*b^2*c^3 + 8*(b^2 - 4*a*c)*a*c^4)*c^2 + 2*(sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 8*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 6*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 3*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^4*c^3 - 2*a*b^4*c^3 - 2*b^5*c^3 + 16*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^3*c^4 + 8*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 11*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^4 + 16*a^2*b^2*c^4 + 7*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^3*c^4 + 16*a*b^3*c^4 - 2*b^4*c^4 - 4*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*c^5 - 32*a^3*c^5 - 28*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b*c^5 - 32*a^2*b*c^5 + 5*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^2*c^5 + 16*a*b^2*c^5 - 20*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*c^6 - 32*a^2*c^6 + 2*(b^2 - 4*a*c)*a*b^2*c^3 + 2*(b^2 - 4*a*c)*b^3*c^3 - 8*(b^2 - 4*a*c)*a^2*c^4 - 8*(b^2 - 4*a*c)*a*b*c^4 + 2*(b^2 - 4*a*c)*b^2*c^4 - 8*(b^2 - 4*a*c)*a*c^5)*abs(c))*arctan(2*sqrt(1/2)*sqrt(-x^2 + 1)/sqrt(-(b*c + 2*c^2 - sqrt(-4*(a*c + b*c + c^2)*c^2 + (b*c + 2*c^2)^2))/c^2))/((a*b^4*c^3 + b^5*c^3 - 8*a^2*b^2*c^4 - 6*a*b^3*c^4 + 3*b^4*c^4 + 16*a^3*c^5 + 8*a^2*b*c^5 - 11*a*b^2*c^5 + 7*b^3*c^5 - 4*a^2*c^6 - 28*a*b*c^6 + 5*b^2*c^6 - 20*a*c^7)*c^2)","B",0
378,1,591,0,4.241655," ","integrate(x*(-x^2+1)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(2 \, b^{2} c^{2} - 8 \, a c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b c - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{-x^{2} + 1}}{\sqrt{-\frac{b + 2 \, c + \sqrt{{\left(b + 2 \, c\right)}^{2} - 4 \, {\left(a + b + c\right)} c}}{c}}}\right)}{2 \, {\left(b^{4} - 8 \, a b^{2} c + 2 \, b^{3} c + 16 \, a^{2} c^{2} - 8 \, a b c^{2} + 5 \, b^{2} c^{2} - 20 \, a c^{3}\right)} {\left| c \right|}} + \frac{{\left(2 \, b^{2} c^{2} - 8 \, a c^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b c - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} c^{2}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{-x^{2} + 1}}{\sqrt{-\frac{b + 2 \, c - \sqrt{{\left(b + 2 \, c\right)}^{2} - 4 \, {\left(a + b + c\right)} c}}{c}}}\right)}{2 \, {\left(b^{4} - 8 \, a b^{2} c + 2 \, b^{3} c + 16 \, a^{2} c^{2} - 8 \, a b c^{2} + 5 \, b^{2} c^{2} - 20 \, a c^{3}\right)} {\left| c \right|}}"," ",0,"-1/2*(2*b^2*c^2 - 8*a*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b*c - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*c^2 - 2*(b^2 - 4*a*c)*c^2)*arctan(2*sqrt(1/2)*sqrt(-x^2 + 1)/sqrt(-(b + 2*c + sqrt((b + 2*c)^2 - 4*(a + b + c)*c))/c))/((b^4 - 8*a*b^2*c + 2*b^3*c + 16*a^2*c^2 - 8*a*b*c^2 + 5*b^2*c^2 - 20*a*c^3)*abs(c)) + 1/2*(2*b^2*c^2 - 8*a*c^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b*c - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*c^2 - 2*(b^2 - 4*a*c)*c^2)*arctan(2*sqrt(1/2)*sqrt(-x^2 + 1)/sqrt(-(b + 2*c - sqrt((b + 2*c)^2 - 4*(a + b + c)*c))/c))/((b^4 - 8*a*b^2*c + 2*b^3*c + 16*a^2*c^2 - 8*a*b*c^2 + 5*b^2*c^2 - 20*a*c^3)*abs(c))","B",0
379,1,3639,0,3.674436," ","integrate((-x^2+1)^(1/2)/x/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{\log\left(\sqrt{-x^{2} + 1} + 1\right)}{2 \, a} + \frac{\log\left(-\sqrt{-x^{2} + 1} + 1\right)}{2 \, a} + \frac{{\left(4 \, a^{3} b^{3} c^{2} + 2 \, a^{2} b^{4} c^{2} - 16 \, a^{4} b c^{3} + 4 \, a^{2} b^{3} c^{3} - 32 \, a^{4} c^{4} - 16 \, a^{3} b c^{4} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{4} b c - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{2} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} + {\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 - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \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^{2} + 2 \, {\left(\sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} + \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 8 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - 6 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c + 3 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, a^{2} b^{4} c - 2 \, a b^{5} c + 16 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{2} + 8 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 11 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 16 \, a^{3} b^{2} c^{2} + 7 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \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 - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 32 \, a^{4} c^{3} - 28 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 32 \, a^{3} b c^{3} + 5 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 16 \, a^{2} b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \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^{2} b^{2} c + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} {\left| a \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{-x^{2} + 1}}{\sqrt{-\frac{a b + 2 \, a c + \sqrt{-4 \, {\left(a^{2} + a b + a c\right)} a c + {\left(a b + 2 \, a c\right)}^{2}}}{a c}}}\right)}{8 \, {\left(a^{3} b^{4} + a^{2} b^{5} - 8 \, a^{4} b^{2} c - 6 \, a^{3} b^{3} c + 3 \, a^{2} b^{4} c + 16 \, a^{5} c^{2} + 8 \, a^{4} b c^{2} - 11 \, a^{3} b^{2} c^{2} + 7 \, a^{2} b^{3} c^{2} - 4 \, a^{4} c^{3} - 28 \, a^{3} b c^{3} + 5 \, a^{2} b^{2} c^{3} - 20 \, a^{3} c^{4}\right)} {\left| a \right|} {\left| c \right|}} - \frac{{\left(4 \, a^{3} b^{3} c^{2} + 2 \, a^{2} b^{4} c^{2} - 16 \, a^{4} b c^{3} + 4 \, a^{2} b^{3} c^{3} - 32 \, a^{4} c^{4} - 16 \, a^{3} b c^{4} - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{3} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{4} b c - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c + 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{2} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 9 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} + {\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 - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{4} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 16 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \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^{2} - 2 \, {\left(\sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{4} + \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{5} - 8 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{2} c - 6 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c + 3 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, a^{2} b^{4} c + 2 \, a b^{5} c + 16 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{4} c^{2} + 8 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{2} - 11 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 16 \, a^{3} b^{2} c^{2} + 7 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \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 - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 32 \, a^{4} c^{3} - 28 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 32 \, a^{3} b c^{3} + 5 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 16 \, a^{2} b^{2} c^{3} - 20 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \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^{2} b^{2} c - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} {\left| a \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{-x^{2} + 1}}{\sqrt{-\frac{a b + 2 \, a c - \sqrt{-4 \, {\left(a^{2} + a b + a c\right)} a c + {\left(a b + 2 \, a c\right)}^{2}}}{a c}}}\right)}{8 \, {\left(a^{3} b^{4} + a^{2} b^{5} - 8 \, a^{4} b^{2} c - 6 \, a^{3} b^{3} c + 3 \, a^{2} b^{4} c + 16 \, a^{5} c^{2} + 8 \, a^{4} b c^{2} - 11 \, a^{3} b^{2} c^{2} + 7 \, a^{2} b^{3} c^{2} - 4 \, a^{4} c^{3} - 28 \, a^{3} b c^{3} + 5 \, a^{2} b^{2} c^{3} - 20 \, a^{3} c^{4}\right)} {\left| a \right|} {\left| c \right|}}"," ",0,"-1/2*log(sqrt(-x^2 + 1) + 1)/a + 1/2*log(-sqrt(-x^2 + 1) + 1)/a + 1/8*(4*a^3*b^3*c^2 + 2*a^2*b^4*c^2 - 16*a^4*b*c^3 + 4*a^2*b^3*c^3 - 32*a^4*c^4 - 16*a^3*b*c^4 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^3*b^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*b^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^4*b*c - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^4*c^2 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 - 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 4*(b^2 - 4*a*c)*a^3*b*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2*c^2 - 8*(b^2 - 4*a*c)*a^3*c^3 - 4*(b^2 - 4*a*c)*a^2*b*c^3 + (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 - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^3*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + 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^2 + 2*(sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*b^4 + sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^5 - 8*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c - 6*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c + 3*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 2*a^2*b^4*c - 2*a*b^5*c + 16*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^4*c^2 + 8*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 - 11*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 16*a^3*b^2*c^2 + 7*sqrt(2)*sqrt(-b*c - 2*c^2 + 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 - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 - 32*a^4*c^3 - 28*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 32*a^3*b*c^3 + 5*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + 16*a^2*b^2*c^3 - 20*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 32*a^3*c^4 + 2*(b^2 - 4*a*c)*a^2*b^2*c + 2*(b^2 - 4*a*c)*a*b^3*c - 8*(b^2 - 4*a*c)*a^3*c^2 - 8*(b^2 - 4*a*c)*a^2*b*c^2 + 2*(b^2 - 4*a*c)*a*b^2*c^2 - 8*(b^2 - 4*a*c)*a^2*c^3)*abs(a))*arctan(2*sqrt(1/2)*sqrt(-x^2 + 1)/sqrt(-(a*b + 2*a*c + sqrt(-4*(a^2 + a*b + a*c)*a*c + (a*b + 2*a*c)^2))/(a*c)))/((a^3*b^4 + a^2*b^5 - 8*a^4*b^2*c - 6*a^3*b^3*c + 3*a^2*b^4*c + 16*a^5*c^2 + 8*a^4*b*c^2 - 11*a^3*b^2*c^2 + 7*a^2*b^3*c^2 - 4*a^4*c^3 - 28*a^3*b*c^3 + 5*a^2*b^2*c^3 - 20*a^3*c^4)*abs(a)*abs(c)) - 1/8*(4*a^3*b^3*c^2 + 2*a^2*b^4*c^2 - 16*a^4*b*c^3 + 4*a^2*b^3*c^3 - 32*a^4*c^4 - 16*a^3*b*c^4 - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^3*b^3 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*b^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^4*b*c - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c + 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^4*c^2 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 - 9*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 4*(b^2 - 4*a*c)*a^3*b*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2*c^2 - 8*(b^2 - 4*a*c)*a^3*c^3 - 4*(b^2 - 4*a*c)*a^2*b*c^3 + (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 - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^4 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^3*c - 16*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - 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^2 - 2*(sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*b^4 + sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^5 - 8*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^3*b^2*c - 6*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c + 3*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*a^2*b^4*c + 2*a*b^5*c + 16*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^4*c^2 + 8*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^2 - 11*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 16*a^3*b^2*c^2 + 7*sqrt(2)*sqrt(-b*c - 2*c^2 - 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 - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 32*a^4*c^3 - 28*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 32*a^3*b*c^3 + 5*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 16*a^2*b^2*c^3 - 20*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 + 32*a^3*c^4 - 2*(b^2 - 4*a*c)*a^2*b^2*c - 2*(b^2 - 4*a*c)*a*b^3*c + 8*(b^2 - 4*a*c)*a^3*c^2 + 8*(b^2 - 4*a*c)*a^2*b*c^2 - 2*(b^2 - 4*a*c)*a*b^2*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3)*abs(a))*arctan(2*sqrt(1/2)*sqrt(-x^2 + 1)/sqrt(-(a*b + 2*a*c - sqrt(-4*(a^2 + a*b + a*c)*a*c + (a*b + 2*a*c)^2))/(a*c)))/((a^3*b^4 + a^2*b^5 - 8*a^4*b^2*c - 6*a^3*b^3*c + 3*a^2*b^4*c + 16*a^5*c^2 + 8*a^4*b*c^2 - 11*a^3*b^2*c^2 + 7*a^2*b^3*c^2 - 4*a^4*c^3 - 28*a^3*b*c^3 + 5*a^2*b^2*c^3 - 20*a^3*c^4)*abs(a)*abs(c))","B",0
380,1,1675,0,7.120008," ","integrate((-x^2+1)^(1/2)/x^3/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(\sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{5} - 8 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{4} c + 2 \, b^{5} c + 16 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 8 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 5 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} - 16 \, a b^{3} c^{2} + 2 \, b^{4} c^{2} - 20 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} + 32 \, a^{2} b c^{3} - 12 \, a b^{2} c^{3} + 16 \, a^{2} c^{4} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{4} + 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{3} c - 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} + 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a b c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} - \sqrt{b^{2} - 4 \, a c} c} a c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{-x^{2} + 1}}{\sqrt{-\frac{a^{2} b + 2 \, a^{2} c + \sqrt{-4 \, {\left(a^{3} + a^{2} b + a^{2} c\right)} a^{2} c + {\left(a^{2} b + 2 \, a^{2} c\right)}^{2}}}{a^{2} c}}}\right)}{4 \, {\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} + 5 \, a^{2} b^{2} c^{2} - 20 \, a^{3} c^{3}\right)} {\left| c \right|}} - \frac{{\left(\sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{5} - 8 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 2 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 2 \, b^{5} c + 16 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 8 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} + 5 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 16 \, a b^{3} c^{2} - 2 \, b^{4} c^{2} - 20 \, \sqrt{2} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 32 \, a^{2} b c^{3} + 12 \, a b^{2} c^{3} - 16 \, a^{2} c^{4} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{4} - 6 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{3} c + 8 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{2} - 4 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a b c^{2} + 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} b^{2} c^{2} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{-b c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} c} a c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c^{2} - 4 \, {\left(b^{2} - 4 \, a c\right)} a c^{3}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{-x^{2} + 1}}{\sqrt{-\frac{a^{2} b + 2 \, a^{2} c - \sqrt{-4 \, {\left(a^{3} + a^{2} b + a^{2} c\right)} a^{2} c + {\left(a^{2} b + 2 \, a^{2} c\right)}^{2}}}{a^{2} c}}}\right)}{4 \, {\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} + 5 \, a^{2} b^{2} c^{2} - 20 \, a^{3} c^{3}\right)} {\left| c \right|}} + \frac{{\left(a + 2 \, b\right)} \log\left(\sqrt{-x^{2} + 1} + 1\right)}{4 \, a^{2}} - \frac{{\left(a + 2 \, b\right)} \log\left(-\sqrt{-x^{2} + 1} + 1\right)}{4 \, a^{2}} - \frac{\sqrt{-x^{2} + 1}}{2 \, a x^{2}}"," ",0,"-1/4*(sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^5 - 8*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^4*c + 2*b^5*c + 16*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 8*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 5*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 - 16*a*b^3*c^2 + 2*b^4*c^2 - 20*sqrt(2)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 + 32*a^2*b*c^3 - 12*a*b^2*c^3 + 16*a^2*c^4 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^4 + 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b^2*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^3*c - 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a^2*c^2 + 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*b*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*b^2*c^2 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 - sqrt(b^2 - 4*a*c)*c)*a*c^3 - 2*(b^2 - 4*a*c)*b^3*c + 8*(b^2 - 4*a*c)*a*b*c^2 - 2*(b^2 - 4*a*c)*b^2*c^2 + 4*(b^2 - 4*a*c)*a*c^3)*arctan(2*sqrt(1/2)*sqrt(-x^2 + 1)/sqrt(-(a^2*b + 2*a^2*c + sqrt(-4*(a^3 + a^2*b + a^2*c)*a^2*c + (a^2*b + 2*a^2*c)^2))/(a^2*c)))/((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 + 5*a^2*b^2*c^2 - 20*a^3*c^3)*abs(c)) - 1/4*(sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^5 - 8*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 2*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^4*c - 2*b^5*c + 16*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 8*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 + 5*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 16*a*b^3*c^2 - 2*b^4*c^2 - 20*sqrt(2)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 32*a^2*b*c^3 + 12*a*b^2*c^3 - 16*a^2*c^4 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^4 - 6*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b^2*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^3*c + 8*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a^2*c^2 - 4*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*b*c^2 + 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*b^2*c^2 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(-b*c - 2*c^2 + sqrt(b^2 - 4*a*c)*c)*a*c^3 + 2*(b^2 - 4*a*c)*b^3*c - 8*(b^2 - 4*a*c)*a*b*c^2 + 2*(b^2 - 4*a*c)*b^2*c^2 - 4*(b^2 - 4*a*c)*a*c^3)*arctan(2*sqrt(1/2)*sqrt(-x^2 + 1)/sqrt(-(a^2*b + 2*a^2*c - sqrt(-4*(a^3 + a^2*b + a^2*c)*a^2*c + (a^2*b + 2*a^2*c)^2))/(a^2*c)))/((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 + 5*a^2*b^2*c^2 - 20*a^3*c^3)*abs(c)) + 1/4*(a + 2*b)*log(sqrt(-x^2 + 1) + 1)/a^2 - 1/4*(a + 2*b)*log(-sqrt(-x^2 + 1) + 1)/a^2 - 1/2*sqrt(-x^2 + 1)/(a*x^2)","B",0
381,1,1710,0,6.686054," ","integrate(x^4*(-x^2+1)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{{\left(3 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{2} b^{3} + 2 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a b^{4} - 2 \, a^{2} b^{4} - \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} b^{5} + 2 \, a b^{5} - 12 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{3} b c - 8 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{2} b^{2} c + 12 \, a^{3} b^{2} c + 8 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a b^{3} c - 16 \, a^{2} b^{3} c - 16 \, a^{4} c^{2} - 16 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{2} b c^{2} + 32 \, a^{3} b c^{2} - 3 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} - 2 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a b^{3} + \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} b^{4} + 6 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{3} c + 4 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} b c - 6 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a b^{2} c + 8 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c\right)} {\left| a \right|} \arctan\left(-\frac{\sqrt{2} {\left(\frac{x}{\sqrt{-x^{2} + 1} - 1} - \frac{\sqrt{-x^{2} + 1} - 1}{x}\right)}}{2 \, \sqrt{\frac{2 \, a c^{2} + b c^{2} + \sqrt{-4 \, {\left(a c^{2} + b c^{2} + c^{3}\right)} a c^{2} + {\left(2 \, a c^{2} + b c^{2}\right)}^{2}}}{a c^{2}}}}\right)}{4 \, {\left(3 \, a^{4} b^{2} c^{2} + 2 \, a^{3} b^{3} c^{2} - a^{2} b^{4} c^{2} - 12 \, a^{5} c^{3} - 8 \, a^{4} b c^{3} + 8 \, a^{3} b^{2} c^{3} - 16 \, a^{4} c^{4}\right)}} + \frac{{\left(3 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{2} b^{3} + 2 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a b^{4} + 2 \, a^{2} b^{4} - \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} b^{5} - 2 \, a b^{5} - 12 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{3} b c - 8 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{2} b^{2} c - 12 \, a^{3} b^{2} c + 8 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a b^{3} c + 16 \, a^{2} b^{3} c + 16 \, a^{4} c^{2} - 16 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{2} b c^{2} - 32 \, a^{3} b c^{2} + 3 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} + 2 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a b^{3} - \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} b^{4} - 6 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{3} c - 4 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} b c + 6 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a b^{2} c - 8 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c\right)} {\left| a \right|} \arctan\left(-\frac{\sqrt{2} {\left(\frac{x}{\sqrt{-x^{2} + 1} - 1} - \frac{\sqrt{-x^{2} + 1} - 1}{x}\right)}}{2 \, \sqrt{\frac{2 \, a c^{2} + b c^{2} - \sqrt{-4 \, {\left(a c^{2} + b c^{2} + c^{3}\right)} a c^{2} + {\left(2 \, a c^{2} + b c^{2}\right)}^{2}}}{a c^{2}}}}\right)}{4 \, {\left(3 \, a^{4} b^{2} c^{2} + 2 \, a^{3} b^{3} c^{2} - a^{2} b^{4} c^{2} - 12 \, a^{5} c^{3} - 8 \, a^{4} b c^{3} + 8 \, a^{3} b^{2} c^{3} - 16 \, a^{4} c^{4}\right)}} + \frac{\sqrt{-x^{2} + 1} x}{2 \, c} + \frac{{\left(\pi \mathrm{sgn}\left(x\right) + 2 \, \arctan\left(-\frac{x {\left(\frac{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - 1\right)}}{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}\right)\right)} {\left(2 \, b + c\right)}}{4 \, c^{2}}"," ",0,"1/4*(3*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^2*b^3 + 2*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a*b^4 - 2*a^2*b^4 - sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*b^5 + 2*a*b^5 - 12*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^3*b*c - 8*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^2*b^2*c + 12*a^3*b^2*c + 8*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a*b^3*c - 16*a^2*b^3*c - 16*a^4*c^2 - 16*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^2*b*c^2 + 32*a^3*b*c^2 - 3*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*b^2 - 2*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a*b^3 + sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*b^4 + 6*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^3*c + 4*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*b*c - 6*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a*b^2*c + 8*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*c^2 + 2*(b^2 - 4*a*c)*a^2*b^2 - 2*(b^2 - 4*a*c)*a*b^3 - 4*(b^2 - 4*a*c)*a^3*c + 8*(b^2 - 4*a*c)*a^2*b*c)*abs(a)*arctan(-1/2*sqrt(2)*(x/(sqrt(-x^2 + 1) - 1) - (sqrt(-x^2 + 1) - 1)/x)/sqrt((2*a*c^2 + b*c^2 + sqrt(-4*(a*c^2 + b*c^2 + c^3)*a*c^2 + (2*a*c^2 + b*c^2)^2))/(a*c^2)))/(3*a^4*b^2*c^2 + 2*a^3*b^3*c^2 - a^2*b^4*c^2 - 12*a^5*c^3 - 8*a^4*b*c^3 + 8*a^3*b^2*c^3 - 16*a^4*c^4) + 1/4*(3*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^2*b^3 + 2*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a*b^4 + 2*a^2*b^4 - sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*b^5 - 2*a*b^5 - 12*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^3*b*c - 8*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^2*b^2*c - 12*a^3*b^2*c + 8*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a*b^3*c + 16*a^2*b^3*c + 16*a^4*c^2 - 16*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^2*b*c^2 - 32*a^3*b*c^2 + 3*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*b^2 + 2*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a*b^3 - sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*b^4 - 6*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^3*c - 4*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*b*c + 6*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a*b^2*c - 8*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2 + 2*(b^2 - 4*a*c)*a*b^3 + 4*(b^2 - 4*a*c)*a^3*c - 8*(b^2 - 4*a*c)*a^2*b*c)*abs(a)*arctan(-1/2*sqrt(2)*(x/(sqrt(-x^2 + 1) - 1) - (sqrt(-x^2 + 1) - 1)/x)/sqrt((2*a*c^2 + b*c^2 - sqrt(-4*(a*c^2 + b*c^2 + c^3)*a*c^2 + (2*a*c^2 + b*c^2)^2))/(a*c^2)))/(3*a^4*b^2*c^2 + 2*a^3*b^3*c^2 - a^2*b^4*c^2 - 12*a^5*c^3 - 8*a^4*b*c^3 + 8*a^3*b^2*c^3 - 16*a^4*c^4) + 1/2*sqrt(-x^2 + 1)*x/c + 1/4*(pi*sgn(x) + 2*arctan(-1/2*x*((sqrt(-x^2 + 1) - 1)^2/x^2 - 1)/(sqrt(-x^2 + 1) - 1)))*(2*b + c)/c^2","B",0
382,1,3580,0,4.734329," ","integrate(x^2*(-x^2+1)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{\pi \mathrm{sgn}\left(x\right) + 2 \, \arctan\left(-\frac{x {\left(\frac{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - 1\right)}}{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}\right)}{2 \, c} + \frac{{\left({\left(2 \, a^{2} b^{4} - 16 \, a^{3} b^{2} c + 32 \, a^{4} c^{2} + 3 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} + 2 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a b^{3} - \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} b^{4} - 12 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{3} c - 8 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} b c + 8 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a b^{2} c - 16 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c\right)} c^{2} {\left| a \right|} - 2 \, {\left(3 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{3} b^{2} c + 5 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{2} b^{3} c + \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a b^{4} c + 2 \, a^{2} b^{4} c - \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} b^{5} c + 2 \, a b^{5} c - 12 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{4} c^{2} - 20 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{3} b c^{2} + 3 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{2} b^{2} c^{2} - 16 \, a^{3} b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a b^{3} c^{2} - 16 \, a^{2} b^{3} c^{2} - \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} b^{4} c^{2} + 2 \, a b^{4} c^{2} - 28 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{3} c^{3} + 32 \, a^{4} c^{3} - 24 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{2} b c^{3} + 32 \, a^{3} b c^{3} + 8 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a b^{2} c^{3} - 16 \, a^{2} b^{2} c^{3} - 16 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{2} c^{4} + 32 \, a^{3} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} {\left| a \right|} {\left| c \right|} + {\left(4 \, a^{3} b^{3} c^{2} + 2 \, a^{2} b^{4} c^{2} - 16 \, a^{4} b c^{3} + 4 \, a^{2} b^{3} c^{3} - 32 \, a^{4} c^{4} - 16 \, a^{3} b c^{4} + 6 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{3} b c^{2} + 7 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} c^{2} - \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} b^{4} c^{2} + 12 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{3} c^{3} + 22 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} b c^{3} + 4 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} b^{3} c^{3} + 16 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} c^{4} + 8 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a b c^{4} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} {\left| a \right|}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\frac{x}{\sqrt{-x^{2} + 1} - 1} - \frac{\sqrt{-x^{2} + 1} - 1}{x}\right)}}{2 \, \sqrt{\frac{2 \, a c + b c + \sqrt{-4 \, {\left(a c + b c + c^{2}\right)} a c + {\left(2 \, a c + b c\right)}^{2}}}{a c}}}\right)}{8 \, {\left(3 \, a^{5} b^{2} c^{2} + 5 \, a^{4} b^{3} c^{2} + a^{3} b^{4} c^{2} - a^{2} b^{5} c^{2} - 12 \, a^{6} c^{3} - 20 \, a^{5} b c^{3} + 3 \, a^{4} b^{2} c^{3} + 10 \, a^{3} b^{3} c^{3} - a^{2} b^{4} c^{3} - 28 \, a^{5} c^{4} - 24 \, a^{4} b c^{4} + 8 \, a^{3} b^{2} c^{4} - 16 \, a^{4} c^{5}\right)} {\left| c \right|}} - \frac{{\left({\left(2 \, a^{2} b^{4} - 16 \, a^{3} b^{2} c + 32 \, a^{4} c^{2} + 3 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} + 2 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a b^{3} - \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} b^{4} - 12 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{3} c - 8 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} b c + 8 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a b^{2} c - 16 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c\right)} c^{2} {\left| a \right|} + 2 \, {\left(3 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{3} b^{2} c + 5 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{2} b^{3} c + \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a b^{4} c - 2 \, a^{2} b^{4} c - \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} b^{5} c - 2 \, a b^{5} c - 12 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{4} c^{2} - 20 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{3} b c^{2} + 3 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{2} b^{2} c^{2} + 16 \, a^{3} b^{2} c^{2} + 10 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a b^{3} c^{2} + 16 \, a^{2} b^{3} c^{2} - \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} b^{4} c^{2} - 2 \, a b^{4} c^{2} - 28 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{3} c^{3} - 32 \, a^{4} c^{3} - 24 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{2} b c^{3} - 32 \, a^{3} b c^{3} + 8 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a b^{2} c^{3} + 16 \, a^{2} b^{2} c^{3} - 16 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{2} c^{4} - 32 \, a^{3} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{3}\right)} {\left| a \right|} {\left| c \right|} + {\left(4 \, a^{3} b^{3} c^{2} + 2 \, a^{2} b^{4} c^{2} - 16 \, a^{4} b c^{3} + 4 \, a^{2} b^{3} c^{3} - 32 \, a^{4} c^{4} - 16 \, a^{3} b c^{4} + 6 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{3} b c^{2} + 7 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} b^{2} c^{2} - \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} b^{4} c^{2} + 12 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{3} c^{3} + 22 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} b c^{3} + 4 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a b^{2} c^{3} - 2 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} b^{3} c^{3} + 16 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} c^{4} + 8 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a b c^{4} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{2} c^{2} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3}\right)} {\left| a \right|}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\frac{x}{\sqrt{-x^{2} + 1} - 1} - \frac{\sqrt{-x^{2} + 1} - 1}{x}\right)}}{2 \, \sqrt{\frac{2 \, a c + b c - \sqrt{-4 \, {\left(a c + b c + c^{2}\right)} a c + {\left(2 \, a c + b c\right)}^{2}}}{a c}}}\right)}{8 \, {\left(3 \, a^{5} b^{2} c^{2} + 5 \, a^{4} b^{3} c^{2} + a^{3} b^{4} c^{2} - a^{2} b^{5} c^{2} - 12 \, a^{6} c^{3} - 20 \, a^{5} b c^{3} + 3 \, a^{4} b^{2} c^{3} + 10 \, a^{3} b^{3} c^{3} - a^{2} b^{4} c^{3} - 28 \, a^{5} c^{4} - 24 \, a^{4} b c^{4} + 8 \, a^{3} b^{2} c^{4} - 16 \, a^{4} c^{5}\right)} {\left| c \right|}}"," ",0,"-1/2*(pi*sgn(x) + 2*arctan(-1/2*x*((sqrt(-x^2 + 1) - 1)^2/x^2 - 1)/(sqrt(-x^2 + 1) - 1)))/c + 1/8*((2*a^2*b^4 - 16*a^3*b^2*c + 32*a^4*c^2 + 3*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*b^2 + 2*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a*b^3 - sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*b^4 - 12*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^3*c - 8*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*b*c + 8*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a*b^2*c - 16*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2 + 8*(b^2 - 4*a*c)*a^3*c)*c^2*abs(a) - 2*(3*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^3*b^2*c + 5*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^2*b^3*c + sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a*b^4*c + 2*a^2*b^4*c - sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*b^5*c + 2*a*b^5*c - 12*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^4*c^2 - 20*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^3*b*c^2 + 3*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^2*b^2*c^2 - 16*a^3*b^2*c^2 + 10*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a*b^3*c^2 - 16*a^2*b^3*c^2 - sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*b^4*c^2 + 2*a*b^4*c^2 - 28*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^3*c^3 + 32*a^4*c^3 - 24*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^2*b*c^3 + 32*a^3*b*c^3 + 8*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a*b^2*c^3 - 16*a^2*b^2*c^3 - 16*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^2*c^4 + 32*a^3*c^4 - 2*(b^2 - 4*a*c)*a^2*b^2*c - 2*(b^2 - 4*a*c)*a*b^3*c + 8*(b^2 - 4*a*c)*a^3*c^2 + 8*(b^2 - 4*a*c)*a^2*b*c^2 - 2*(b^2 - 4*a*c)*a*b^2*c^2 + 8*(b^2 - 4*a*c)*a^2*c^3)*abs(a)*abs(c) + (4*a^3*b^3*c^2 + 2*a^2*b^4*c^2 - 16*a^4*b*c^3 + 4*a^2*b^3*c^3 - 32*a^4*c^4 - 16*a^3*b*c^4 + 6*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^3*b*c^2 + 7*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*b^2*c^2 - sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*b^4*c^2 + 12*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^3*c^3 + 22*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*b*c^3 + 4*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a*b^2*c^3 - 2*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*b^3*c^3 + 16*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*c^4 + 8*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a*b*c^4 - 4*(b^2 - 4*a*c)*a^3*b*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2*c^2 - 8*(b^2 - 4*a*c)*a^3*c^3 - 4*(b^2 - 4*a*c)*a^2*b*c^3)*abs(a))*arctan(-1/2*sqrt(2)*(x/(sqrt(-x^2 + 1) - 1) - (sqrt(-x^2 + 1) - 1)/x)/sqrt((2*a*c + b*c + sqrt(-4*(a*c + b*c + c^2)*a*c + (2*a*c + b*c)^2))/(a*c)))/((3*a^5*b^2*c^2 + 5*a^4*b^3*c^2 + a^3*b^4*c^2 - a^2*b^5*c^2 - 12*a^6*c^3 - 20*a^5*b*c^3 + 3*a^4*b^2*c^3 + 10*a^3*b^3*c^3 - a^2*b^4*c^3 - 28*a^5*c^4 - 24*a^4*b*c^4 + 8*a^3*b^2*c^4 - 16*a^4*c^5)*abs(c)) - 1/8*((2*a^2*b^4 - 16*a^3*b^2*c + 32*a^4*c^2 + 3*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*b^2 + 2*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a*b^3 - sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*b^4 - 12*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^3*c - 8*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*b*c + 8*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a*b^2*c - 16*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2 + 8*(b^2 - 4*a*c)*a^3*c)*c^2*abs(a) + 2*(3*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^3*b^2*c + 5*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^2*b^3*c + sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a*b^4*c - 2*a^2*b^4*c - sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*b^5*c - 2*a*b^5*c - 12*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^4*c^2 - 20*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^3*b*c^2 + 3*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^2*b^2*c^2 + 16*a^3*b^2*c^2 + 10*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a*b^3*c^2 + 16*a^2*b^3*c^2 - sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*b^4*c^2 - 2*a*b^4*c^2 - 28*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^3*c^3 - 32*a^4*c^3 - 24*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^2*b*c^3 - 32*a^3*b*c^3 + 8*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a*b^2*c^3 + 16*a^2*b^2*c^3 - 16*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^2*c^4 - 32*a^3*c^4 + 2*(b^2 - 4*a*c)*a^2*b^2*c + 2*(b^2 - 4*a*c)*a*b^3*c - 8*(b^2 - 4*a*c)*a^3*c^2 - 8*(b^2 - 4*a*c)*a^2*b*c^2 + 2*(b^2 - 4*a*c)*a*b^2*c^2 - 8*(b^2 - 4*a*c)*a^2*c^3)*abs(a)*abs(c) + (4*a^3*b^3*c^2 + 2*a^2*b^4*c^2 - 16*a^4*b*c^3 + 4*a^2*b^3*c^3 - 32*a^4*c^4 - 16*a^3*b*c^4 + 6*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^3*b*c^2 + 7*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*b^2*c^2 - sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*b^4*c^2 + 12*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^3*c^3 + 22*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*b*c^3 + 4*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a*b^2*c^3 - 2*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*b^3*c^3 + 16*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*c^4 + 8*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a*b*c^4 - 4*(b^2 - 4*a*c)*a^3*b*c^2 - 2*(b^2 - 4*a*c)*a^2*b^2*c^2 - 8*(b^2 - 4*a*c)*a^3*c^3 - 4*(b^2 - 4*a*c)*a^2*b*c^3)*abs(a))*arctan(-1/2*sqrt(2)*(x/(sqrt(-x^2 + 1) - 1) - (sqrt(-x^2 + 1) - 1)/x)/sqrt((2*a*c + b*c - sqrt(-4*(a*c + b*c + c^2)*a*c + (2*a*c + b*c)^2))/(a*c)))/((3*a^5*b^2*c^2 + 5*a^4*b^3*c^2 + a^3*b^4*c^2 - a^2*b^5*c^2 - 12*a^6*c^3 - 20*a^5*b*c^3 + 3*a^4*b^2*c^3 + 10*a^3*b^3*c^3 - a^2*b^4*c^3 - 28*a^5*c^4 - 24*a^4*b*c^4 + 8*a^3*b^2*c^4 - 16*a^4*c^5)*abs(c))","B",0
383,1,641,0,5.121614," ","integrate((-x^2+1)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(2 \, a^{2} b^{2} - 8 \, a^{3} c + 3 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} + 2 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a b - \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} b^{2} + 4 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a c - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2}\right)} {\left| a \right|} \arctan\left(-\frac{\sqrt{2} {\left(\frac{x}{\sqrt{-x^{2} + 1} - 1} - \frac{\sqrt{-x^{2} + 1} - 1}{x}\right)}}{2 \, \sqrt{\frac{2 \, a + b + \sqrt{{\left(2 \, a + b\right)}^{2} - 4 \, {\left(a + b + c\right)} a}}{a}}}\right)}{2 \, {\left(3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - a^{2} b^{4} - 12 \, a^{5} c - 8 \, a^{4} b c + 8 \, a^{3} b^{2} c - 16 \, a^{4} c^{2}\right)}} + \frac{{\left(2 \, a^{2} b^{2} - 8 \, a^{3} c + 3 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} + 2 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a b - \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} b^{2} + 4 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a c - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2}\right)} {\left| a \right|} \arctan\left(-\frac{\sqrt{2} {\left(\frac{x}{\sqrt{-x^{2} + 1} - 1} - \frac{\sqrt{-x^{2} + 1} - 1}{x}\right)}}{2 \, \sqrt{\frac{2 \, a + b - \sqrt{{\left(2 \, a + b\right)}^{2} - 4 \, {\left(a + b + c\right)} a}}{a}}}\right)}{2 \, {\left(3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - a^{2} b^{4} - 12 \, a^{5} c - 8 \, a^{4} b c + 8 \, a^{3} b^{2} c - 16 \, a^{4} c^{2}\right)}}"," ",0,"-1/2*(2*a^2*b^2 - 8*a^3*c + 3*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2 + 2*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a*b - sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*b^2 + 4*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a*c - 2*(b^2 - 4*a*c)*a^2)*abs(a)*arctan(-1/2*sqrt(2)*(x/(sqrt(-x^2 + 1) - 1) - (sqrt(-x^2 + 1) - 1)/x)/sqrt((2*a + b + sqrt((2*a + b)^2 - 4*(a + b + c)*a))/a))/(3*a^4*b^2 + 2*a^3*b^3 - a^2*b^4 - 12*a^5*c - 8*a^4*b*c + 8*a^3*b^2*c - 16*a^4*c^2) + 1/2*(2*a^2*b^2 - 8*a^3*c + 3*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2 + 2*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a*b - sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*b^2 + 4*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a*c - 2*(b^2 - 4*a*c)*a^2)*abs(a)*arctan(-1/2*sqrt(2)*(x/(sqrt(-x^2 + 1) - 1) - (sqrt(-x^2 + 1) - 1)/x)/sqrt((2*a + b - sqrt((2*a + b)^2 - 4*(a + b + c)*a))/a))/(3*a^4*b^2 + 2*a^3*b^3 - a^2*b^4 - 12*a^5*c - 8*a^4*b*c + 8*a^3*b^2*c - 16*a^4*c^2)","B",0
384,1,3965,0,5.037433," ","integrate((-x^2+1)^(1/2)/x^2/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\frac{{\left(4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} + 2 \, a^{4} b^{5} - 16 \, a^{7} b c - 32 \, a^{6} b^{2} c - 12 \, a^{5} b^{3} c + 32 \, a^{7} c^{2} + 16 \, a^{6} b c^{2} + 6 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{6} b + 13 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{5} b^{2} + 7 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{4} b^{3} - \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{3} b^{4} - \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} b^{5} - 12 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{6} c - 6 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{5} b c + 12 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{4} b^{2} c + 6 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{3} b^{3} c - 16 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{5} c^{2} - 8 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{4} b c^{2} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{6} c + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c - {\left(2 \, a^{3} b^{4} + 2 \, a^{2} b^{5} - 16 \, a^{4} b^{2} c - 16 \, a^{3} b^{3} c + 32 \, a^{5} c^{2} + 32 \, a^{4} b c^{2} + 3 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{3} b^{2} + 5 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} b^{3} + \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a b^{4} - \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} b^{5} - 12 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{4} c - 20 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{3} b c + 8 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a b^{3} c - 16 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{3} c^{2} - 16 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c\right)} a^{2} + 2 \, {\left(3 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{5} b^{2} + 5 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{4} b^{3} + \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{3} b^{4} - 2 \, a^{4} b^{4} - \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{2} b^{5} - 2 \, a^{3} b^{5} - 12 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{6} c - 20 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{5} b c + 3 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{4} b^{2} c + 16 \, a^{5} b^{2} c + 10 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{3} b^{3} c + 16 \, a^{4} b^{3} c - \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{2} b^{4} c - 2 \, a^{3} b^{4} c - 28 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{5} c^{2} - 32 \, a^{6} c^{2} - 24 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{4} b c^{2} - 32 \, a^{5} b c^{2} + 8 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{3} b^{2} c^{2} + 16 \, a^{4} b^{2} c^{2} - 16 \, \sqrt{2} \sqrt{2 \, a^{2} + a b - \sqrt{b^{2} - 4 \, a c} a} a^{4} c^{3} - 32 \, a^{5} c^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{5} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c + 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c - 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{2}\right)} {\left| a \right|}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\frac{x}{\sqrt{-x^{2} + 1} - 1} - \frac{\sqrt{-x^{2} + 1} - 1}{x}\right)}}{2 \, \sqrt{\frac{2 \, a^{2} + a b + \sqrt{-4 \, {\left(a^{2} + a b + a c\right)} a^{2} + {\left(2 \, a^{2} + a b\right)}^{2}}}{a^{2}}}}\right)}{8 \, {\left(3 \, a^{8} b^{2} + 5 \, a^{7} b^{3} + a^{6} b^{4} - a^{5} b^{5} - 12 \, a^{9} c - 20 \, a^{8} b c + 3 \, a^{7} b^{2} c + 10 \, a^{6} b^{3} c - a^{5} b^{4} c - 28 \, a^{8} c^{2} - 24 \, a^{7} b c^{2} + 8 \, a^{6} b^{2} c^{2} - 16 \, a^{7} c^{3}\right)}} - \frac{{\left(4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} + 2 \, a^{4} b^{5} - 16 \, a^{7} b c - 32 \, a^{6} b^{2} c - 12 \, a^{5} b^{3} c + 32 \, a^{7} c^{2} + 16 \, a^{6} b c^{2} + 6 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{6} b + 13 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{5} b^{2} + 7 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{4} b^{3} - \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{3} b^{4} - \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} b^{5} - 12 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{6} c - 6 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{5} b c + 12 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{4} b^{2} c + 6 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{3} b^{3} c - 16 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{5} c^{2} - 8 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{4} b c^{2} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b - 6 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{6} c + 4 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b c - {\left(2 \, a^{3} b^{4} + 2 \, a^{2} b^{5} - 16 \, a^{4} b^{2} c - 16 \, a^{3} b^{3} c + 32 \, a^{5} c^{2} + 32 \, a^{4} b c^{2} + 3 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{3} b^{2} + 5 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} b^{3} + \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a b^{4} - \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} b^{5} - 12 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{4} c - 20 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{3} b c + 8 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a b^{3} c - 16 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{3} c^{2} - 16 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} \sqrt{b^{2} - 4 \, a c} a^{2} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b c\right)} a^{2} - 2 \, {\left(3 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{5} b^{2} + 5 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{4} b^{3} + \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{3} b^{4} + 2 \, a^{4} b^{4} - \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{2} b^{5} + 2 \, a^{3} b^{5} - 12 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{6} c - 20 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{5} b c + 3 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{4} b^{2} c - 16 \, a^{5} b^{2} c + 10 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{3} b^{3} c - 16 \, a^{4} b^{3} c - \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{2} b^{4} c + 2 \, a^{3} b^{4} c - 28 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{5} c^{2} + 32 \, a^{6} c^{2} - 24 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{4} b c^{2} + 32 \, a^{5} b c^{2} + 8 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{3} b^{2} c^{2} - 16 \, a^{4} b^{2} c^{2} - 16 \, \sqrt{2} \sqrt{2 \, a^{2} + a b + \sqrt{b^{2} - 4 \, a c} a} a^{4} c^{3} + 32 \, a^{5} c^{3} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{3} + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{5} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b c - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{2} c + 8 \, {\left(b^{2} - 4 \, a c\right)} a^{4} c^{2}\right)} {\left| a \right|}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\frac{x}{\sqrt{-x^{2} + 1} - 1} - \frac{\sqrt{-x^{2} + 1} - 1}{x}\right)}}{2 \, \sqrt{\frac{2 \, a^{2} + a b - \sqrt{-4 \, {\left(a^{2} + a b + a c\right)} a^{2} + {\left(2 \, a^{2} + a b\right)}^{2}}}{a^{2}}}}\right)}{8 \, {\left(3 \, a^{8} b^{2} + 5 \, a^{7} b^{3} + a^{6} b^{4} - a^{5} b^{5} - 12 \, a^{9} c - 20 \, a^{8} b c + 3 \, a^{7} b^{2} c + 10 \, a^{6} b^{3} c - a^{5} b^{4} c - 28 \, a^{8} c^{2} - 24 \, a^{7} b c^{2} + 8 \, a^{6} b^{2} c^{2} - 16 \, a^{7} c^{3}\right)}} + \frac{\frac{x}{\sqrt{-x^{2} + 1} - 1} - \frac{\sqrt{-x^{2} + 1} - 1}{x}}{2 \, a}"," ",0,"1/8*(4*a^6*b^3 + 6*a^5*b^4 + 2*a^4*b^5 - 16*a^7*b*c - 32*a^6*b^2*c - 12*a^5*b^3*c + 32*a^7*c^2 + 16*a^6*b*c^2 + 6*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^6*b + 13*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^5*b^2 + 7*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^4*b^3 - sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^3*b^4 - sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*b^5 - 12*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^6*c - 6*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^5*b*c + 12*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^4*b^2*c + 6*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^3*b^3*c - 16*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^5*c^2 - 8*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^4*b*c^2 - 4*(b^2 - 4*a*c)*a^6*b - 6*(b^2 - 4*a*c)*a^5*b^2 - 2*(b^2 - 4*a*c)*a^4*b^3 + 8*(b^2 - 4*a*c)*a^6*c + 4*(b^2 - 4*a*c)*a^5*b*c - (2*a^3*b^4 + 2*a^2*b^5 - 16*a^4*b^2*c - 16*a^3*b^3*c + 32*a^5*c^2 + 32*a^4*b*c^2 + 3*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^3*b^2 + 5*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*b^3 + sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a*b^4 - sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*b^5 - 12*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^4*c - 20*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^3*b*c + 8*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a*b^3*c - 16*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^3*c^2 - 16*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*b*c^2 - 2*(b^2 - 4*a*c)*a^3*b^2 - 2*(b^2 - 4*a*c)*a^2*b^3 + 8*(b^2 - 4*a*c)*a^4*c + 8*(b^2 - 4*a*c)*a^3*b*c)*a^2 + 2*(3*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^5*b^2 + 5*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^4*b^3 + sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^3*b^4 - 2*a^4*b^4 - sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^2*b^5 - 2*a^3*b^5 - 12*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^6*c - 20*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^5*b*c + 3*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^4*b^2*c + 16*a^5*b^2*c + 10*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^3*b^3*c + 16*a^4*b^3*c - sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^2*b^4*c - 2*a^3*b^4*c - 28*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^5*c^2 - 32*a^6*c^2 - 24*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^4*b*c^2 - 32*a^5*b*c^2 + 8*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^3*b^2*c^2 + 16*a^4*b^2*c^2 - 16*sqrt(2)*sqrt(2*a^2 + a*b - sqrt(b^2 - 4*a*c)*a)*a^4*c^3 - 32*a^5*c^3 + 2*(b^2 - 4*a*c)*a^4*b^2 + 2*(b^2 - 4*a*c)*a^3*b^3 - 8*(b^2 - 4*a*c)*a^5*c - 8*(b^2 - 4*a*c)*a^4*b*c + 2*(b^2 - 4*a*c)*a^3*b^2*c - 8*(b^2 - 4*a*c)*a^4*c^2)*abs(a))*arctan(-1/2*sqrt(2)*(x/(sqrt(-x^2 + 1) - 1) - (sqrt(-x^2 + 1) - 1)/x)/sqrt((2*a^2 + a*b + sqrt(-4*(a^2 + a*b + a*c)*a^2 + (2*a^2 + a*b)^2))/a^2))/(3*a^8*b^2 + 5*a^7*b^3 + a^6*b^4 - a^5*b^5 - 12*a^9*c - 20*a^8*b*c + 3*a^7*b^2*c + 10*a^6*b^3*c - a^5*b^4*c - 28*a^8*c^2 - 24*a^7*b*c^2 + 8*a^6*b^2*c^2 - 16*a^7*c^3) - 1/8*(4*a^6*b^3 + 6*a^5*b^4 + 2*a^4*b^5 - 16*a^7*b*c - 32*a^6*b^2*c - 12*a^5*b^3*c + 32*a^7*c^2 + 16*a^6*b*c^2 + 6*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^6*b + 13*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^5*b^2 + 7*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^4*b^3 - sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^3*b^4 - sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*b^5 - 12*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^6*c - 6*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^5*b*c + 12*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^4*b^2*c + 6*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^3*b^3*c - 16*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^5*c^2 - 8*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^4*b*c^2 - 4*(b^2 - 4*a*c)*a^6*b - 6*(b^2 - 4*a*c)*a^5*b^2 - 2*(b^2 - 4*a*c)*a^4*b^3 + 8*(b^2 - 4*a*c)*a^6*c + 4*(b^2 - 4*a*c)*a^5*b*c - (2*a^3*b^4 + 2*a^2*b^5 - 16*a^4*b^2*c - 16*a^3*b^3*c + 32*a^5*c^2 + 32*a^4*b*c^2 + 3*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^3*b^2 + 5*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*b^3 + sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a*b^4 - sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*b^5 - 12*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^4*c - 20*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^3*b*c + 8*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a*b^3*c - 16*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^3*c^2 - 16*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*sqrt(b^2 - 4*a*c)*a^2*b*c^2 - 2*(b^2 - 4*a*c)*a^3*b^2 - 2*(b^2 - 4*a*c)*a^2*b^3 + 8*(b^2 - 4*a*c)*a^4*c + 8*(b^2 - 4*a*c)*a^3*b*c)*a^2 - 2*(3*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^5*b^2 + 5*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^4*b^3 + sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^3*b^4 + 2*a^4*b^4 - sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^2*b^5 + 2*a^3*b^5 - 12*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^6*c - 20*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^5*b*c + 3*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^4*b^2*c - 16*a^5*b^2*c + 10*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^3*b^3*c - 16*a^4*b^3*c - sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^2*b^4*c + 2*a^3*b^4*c - 28*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^5*c^2 + 32*a^6*c^2 - 24*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^4*b*c^2 + 32*a^5*b*c^2 + 8*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^3*b^2*c^2 - 16*a^4*b^2*c^2 - 16*sqrt(2)*sqrt(2*a^2 + a*b + sqrt(b^2 - 4*a*c)*a)*a^4*c^3 + 32*a^5*c^3 - 2*(b^2 - 4*a*c)*a^4*b^2 - 2*(b^2 - 4*a*c)*a^3*b^3 + 8*(b^2 - 4*a*c)*a^5*c + 8*(b^2 - 4*a*c)*a^4*b*c - 2*(b^2 - 4*a*c)*a^3*b^2*c + 8*(b^2 - 4*a*c)*a^4*c^2)*abs(a))*arctan(-1/2*sqrt(2)*(x/(sqrt(-x^2 + 1) - 1) - (sqrt(-x^2 + 1) - 1)/x)/sqrt((2*a^2 + a*b - sqrt(-4*(a^2 + a*b + a*c)*a^2 + (2*a^2 + a*b)^2))/a^2))/(3*a^8*b^2 + 5*a^7*b^3 + a^6*b^4 - a^5*b^5 - 12*a^9*c - 20*a^8*b*c + 3*a^7*b^2*c + 10*a^6*b^3*c - a^5*b^4*c - 28*a^8*c^2 - 24*a^7*b*c^2 + 8*a^6*b^2*c^2 - 16*a^7*c^3) + 1/2*(x/(sqrt(-x^2 + 1) - 1) - (sqrt(-x^2 + 1) - 1)/x)/a","B",0
385,1,209,0,0.718072," ","integrate(x^2*(-x^2+1)^(1/2)/(x^4+x^2-1),x, algorithm=""giac"")","-\frac{1}{2} \, \pi \mathrm{sgn}\left(x\right) - \frac{1}{5} \, \sqrt{5 \, \sqrt{5} + 10} \arctan\left(-\frac{\frac{x}{\sqrt{-x^{2} + 1} - 1} - \frac{\sqrt{-x^{2} + 1} - 1}{x}}{\sqrt{2 \, \sqrt{5} + 2}}\right) - \frac{1}{10} \, \sqrt{5 \, \sqrt{5} - 10} \log\left({\left| \sqrt{2 \, \sqrt{5} - 2} - \frac{x}{\sqrt{-x^{2} + 1} - 1} + \frac{\sqrt{-x^{2} + 1} - 1}{x} \right|}\right) + \frac{1}{10} \, \sqrt{5 \, \sqrt{5} - 10} \log\left({\left| -\sqrt{2 \, \sqrt{5} - 2} - \frac{x}{\sqrt{-x^{2} + 1} - 1} + \frac{\sqrt{-x^{2} + 1} - 1}{x} \right|}\right) - \arctan\left(-\frac{x {\left(\frac{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - 1\right)}}{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}\right)"," ",0,"-1/2*pi*sgn(x) - 1/5*sqrt(5*sqrt(5) + 10)*arctan(-(x/(sqrt(-x^2 + 1) - 1) - (sqrt(-x^2 + 1) - 1)/x)/sqrt(2*sqrt(5) + 2)) - 1/10*sqrt(5*sqrt(5) - 10)*log(abs(sqrt(2*sqrt(5) - 2) - x/(sqrt(-x^2 + 1) - 1) + (sqrt(-x^2 + 1) - 1)/x)) + 1/10*sqrt(5*sqrt(5) - 10)*log(abs(-sqrt(2*sqrt(5) - 2) - x/(sqrt(-x^2 + 1) - 1) + (sqrt(-x^2 + 1) - 1)/x)) - arctan(-1/2*x*((sqrt(-x^2 + 1) - 1)^2/x^2 - 1)/(sqrt(-x^2 + 1) - 1))","B",0
386,1,105,0,2.026659," ","integrate(x^8/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{x^{2} e + d} {\left(\frac{2 \, x^{2} e^{\left(-1\right)}}{c} - \frac{{\left(3 \, c^{5} d e + 4 \, b c^{4} e^{2}\right)} e^{\left(-3\right)}}{c^{6}}\right)} x - \frac{{\left(3 \, c^{2} d^{2} + 4 \, b c d e + 8 \, b^{2} e^{2} - 8 \, a c e^{2}\right)} e^{\left(-\frac{5}{2}\right)} \log\left({\left(x e^{\frac{1}{2}} - \sqrt{x^{2} e + d}\right)}^{2}\right)}{16 \, c^{3}}"," ",0,"1/8*sqrt(x^2*e + d)*(2*x^2*e^(-1)/c - (3*c^5*d*e + 4*b*c^4*e^2)*e^(-3)/c^6)*x - 1/16*(3*c^2*d^2 + 4*b*c*d*e + 8*b^2*e^2 - 8*a*c*e^2)*e^(-5/2)*log((x*e^(1/2) - sqrt(x^2*e + d))^2)/c^3","A",0
387,1,55,0,2.140094," ","integrate(x^6/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{x^{2} e + d} x e^{\left(-1\right)}}{2 \, c} + \frac{{\left(c d + 2 \, b e\right)} e^{\left(-\frac{3}{2}\right)} \log\left({\left(x e^{\frac{1}{2}} - \sqrt{x^{2} e + d}\right)}^{2}\right)}{4 \, c^{2}}"," ",0,"1/2*sqrt(x^2*e + d)*x*e^(-1)/c + 1/4*(c*d + 2*b*e)*e^(-3/2)*log((x*e^(1/2) - sqrt(x^2*e + d))^2)/c^2","A",0
388,1,27,0,2.049456," ","integrate(x^4/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x, algorithm=""giac"")","-\frac{e^{\left(-\frac{1}{2}\right)} \log\left({\left(x e^{\frac{1}{2}} - \sqrt{x^{2} e + d}\right)}^{2}\right)}{2 \, c}"," ",0,"-1/2*e^(-1/2)*log((x*e^(1/2) - sqrt(x^2*e + d))^2)/c","A",0
389,-2,0,0,0.000000," ","integrate(x^2/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,c]=[44,93,-37]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,c]=[-72,-7,6]Evaluation time: 0.44Unable to divide, perhaps due to rounding error%%%{18446744069414584320,[4,7,8,2,3,14,2]%%%}+%%%{-2147483648,[3,8,10,8,3,10,1]%%%}+%%%{-12884901888,[3,8,10,7,2,12,2]%%%}+%%%{463856467968,[3,8,10,6,1,14,3]%%%}+%%%{1924145348608,[3,8,10,5,0,16,4]%%%}+%%%{536870912,[3,8,9,8,5,10,0]%%%}+%%%{20401094656,[3,8,9,7,4,12,1]%%%}+%%%{-150323855360,[3,8,9,6,3,14,2]%%%}+%%%{-3135326126080,[3,8,9,5,2,16,3]%%%}+%%%{-4672924418048,[3,8,9,4,1,18,4]%%%}+%%%{6047313952768,[3,8,9,3,0,20,5]%%%}+%%%{-4294967296,[3,8,8,7,6,12,0]%%%}+%%%{-42412802048,[3,8,8,6,5,14,1]%%%}+%%%{1046898278400,[3,8,8,5,4,16,2]%%%}+%%%{6210522710016,[3,8,8,4,3,18,3]%%%}+%%%{-1786706395136,[3,8,8,3,2,20,4]%%%}+%%%{-11544872091648,[3,8,8,2,1,22,5]%%%}+%%%{4398046511104,[3,8,8,1,0,24,6]%%%}+%%%{12750684160,[3,8,7,6,7,14,0]%%%}+%%%{-23890755584,[3,8,7,5,6,16,1]%%%}+%%%{-2103460233216,[3,8,7,4,5,18,2]%%%}+%%%{-3324304687104,[3,8,7,3,4,20,3]%%%}+%%%{9758165696512,[3,8,7,2,3,22,4]%%%}+%%%{1649267441664,[3,8,7,1,2,24,5]%%%}+%%%{-4398046511104,[3,8,7,0,1,26,6]%%%}+%%%{-17985175552,[3,8,6,5,8,16,0]%%%}+%%%{161866579968,[3,8,6,4,7,18,1]%%%}+%%%{1586990415872,[3,8,6,3,6,20,2]%%%}+%%%{-1795296329728,[3,8,6,2,5,22,3]%%%}+%%%{-4123168604160,[3,8,6,1,4,24,4]%%%}+%%%{3848290697216,[3,8,6,0,3,26,5]%%%}+%%%{12213813248,[3,8,5,4,9,18,0]%%%}+%%%{-171798691840,[3,8,5,3,8,20,1]%%%}+%%%{-212600881152,[3,8,5,2,7,22,2]%%%}+%%%{1477468749824,[3,8,5,1,6,24,3]%%%}+%%%{-1099511627776,[3,8,5,0,5,26,4]%%%}+%%%{-3221225472,[3,8,4,3,10,20,0]%%%}+%%%{57982058496,[3,8,4,2,9,22,1]%%%}+%%%{-154618822656,[3,8,4,1,8,24,2]%%%}+%%%{103079215104,[3,8,4,0,7,26,3]%%%}+%%%{1048576,[3,6,10,4,2,4,0]%%%}+%%%{8388608,[3,6,10,3,1,6,1]%%%}+%%%{16777216,[3,6,10,2,0,8,2]%%%}+%%%{-5242880,[3,6,9,3,3,6,0]%%%}+%%%{-29360128,[3,6,9,2,2,8,1]%%%}+%%%{-33554432,[3,6,9,1,1,10,2]%%%}+%%%{9699328,[3,6,8,2,4,8,0]%%%}+%%%{33554432,[3,6,8,1,3,10,1]%%%}+%%%{16777216,[3,6,8,0,2,12,2]%%%}+%%%{-7864320,[3,6,7,1,5,10,0]%%%}+%%%{-12582912,[3,6,7,0,4,12,1]%%%}+%%%{2359296,[3,6,6,0,6,12,0]%%%}+%%%{536870912,[2,7,10,6,2,8,1]%%%}+%%%{6710886400,[2,7,10,5,1,10,2]%%%}+%%%{18253611008,[2,7,10,4,0,12,3]%%%}+%%%{-134217728,[2,7,9,6,4,8,0]%%%}+%%%{-5502926848,[2,7,9,5,3,10,1]%%%}+%%%{-36909875200,[2,7,9,4,2,12,2]%%%}+%%%{-42949672960,[2,7,9,3,1,14,3]%%%}+%%%{42949672960,[2,7,9,2,0,16,4]%%%}+%%%{956301312,[2,7,8,5,5,10,0]%%%}+%%%{18656264192,[2,7,8,4,4,12,1]%%%}+%%%{64961380352,[2,7,8,3,3,14,2]%%%}+%%%{-8589934592,[2,7,8,2,2,16,3]%%%}+%%%{-85899345920,[2,7,8,1,1,18,4]%%%}+%%%{-2642411520,[2,7,7,4,6,12,0]%%%}+%%%{-27783069696,[2,7,7,3,5,14,1]%%%}+%%%{-33957085184,[2,7,7,2,4,16,2]%%%}+%%%{73014444032,[2,7,7,1,3,18,3]%%%}+%%%{42949672960,[2,7,7,0,2,20,4]%%%}+%%%{3556769792,[2,7,6,3,7,14,0]%%%}+%%%{17716740096,[2,7,6,2,6,16,1]%%%}+%%%{-12884901888,[2,7,6,1,5,18,2]%%%}+%%%{-39728447488,[2,7,6,0,4,20,3]%%%}+%%%{-2340421632,[2,7,5,2,8,16,0]%%%}+%%%{-2415919104,[2,7,5,1,7,18,1]%%%}+%%%{12079595520,[2,7,5,0,6,20,2]%%%}+%%%{603979776,[2,7,4,1,9,18,0]%%%}+%%%{-1207959552,[2,7,4,0,8,20,1]%%%}+%%%{2147483648,[1,8,10,9,3,10,1]%%%}+%%%{38654705664,[1,8,10,8,2,12,2]%%%}+%%%{51539607552,[1,8,10,7,1,14,3]%%%}+%%%{-274877906944,[1,8,10,6,0,16,4]%%%}+%%%{-536870912,[1,8,9,9,5,10,0]%%%}+%%%{-26843545600,[1,8,9,8,4,12,1]%%%}+%%%{-188978561024,[1,8,9,7,3,14,2]%%%}+%%%{146028888064,[1,8,9,6,2,16,3]%%%}+%%%{962072674304,[1,8,9,5,1,18,4]%%%}+%%%{-549755813888,[1,8,9,4,0,20,5]%%%}+%%%{4294967296,[1,8,8,8,6,12,0]%%%}+%%%{95026151424,[1,8,8,7,5,14,1]%%%}+%%%{239444426752,[1,8,8,6,4,16,2]%%%}+%%%{-858993459200,[1,8,8,5,3,18,3]%%%}+%%%{-618475290624,[1,8,8,4,2,20,4]%%%}+%%%{1099511627776,[1,8,8,3,1,22,5]%%%}+%%%{-12750684160,[1,8,7,7,7,14,0]%%%}+%%%{-136633647104,[1,8,7,6,6,16,1]%%%}+%%%{62277025792,[1,8,7,5,5,18,2]%%%}+%%%{936302870528,[1,8,7,4,4,20,3]%%%}+%%%{-549755813888,[1,8,7,3,3,22,4]%%%}+%%%{-549755813888,[1,8,7,2,2,24,5]%%%}+%%%{17985175552,[1,8,6,6,8,16,0]%%%}+%%%{71940702208,[1,8,6,5,7,18,1]%%%}+%%%{-267361714176,[1,8,6,4,6,20,2]%%%}+%%%{-137438953472,[1,8,6,3,5,22,3]%%%}+%%%{481036337152,[1,8,6,2,4,24,4]%%%}+%%%{-12213813248,[1,8,5,5,9,18,0]%%%}+%%%{7247757312,[1,8,5,4,8,20,1]%%%}+%%%{103079215104,[1,8,5,3,7,22,2]%%%}+%%%{-137438953472,[1,8,5,2,6,24,3]%%%}+%%%{3221225472,[1,8,4,4,10,20,0]%%%}+%%%{-12884901888,[1,8,4,3,9,22,1]%%%}+%%%{12884901888,[1,8,4,2,8,24,2]%%%}+%%%{-1048576,[1,6,10,5,2,4,0]%%%}+%%%{-8388608,[1,6,10,4,1,6,1]%%%}+%%%{-16777216,[1,6,10,3,0,8,2]%%%}+%%%{8388608,[1,6,9,4,3,6,0]%%%}+%%%{62914560,[1,6,9,3,2,8,1]%%%}+%%%{150994944,[1,6,9,2,1,10,2]%%%}+%%%{134217728,[1,6,9,1,0,12,3]%%%}+%%%{-26476544,[1,6,8,3,4,8,0]%%%}+%%%{-163577856,[1,6,8,2,3,10,1]%%%}+%%%{-301989888,[1,6,8,1,2,12,2]%%%}+%%%{-134217728,[1,6,8,0,1,14,3]%%%}+%%%{41156608,[1,6,7,2,5,10,0]%%%}+%%%{178257920,[1,6,7,1,4,12,1]%%%}+%%%{167772160,[1,6,7,0,3,14,2]%%%}+%%%{-31457280,[1,6,6,1,6,12,0]%%%}+%%%{-69206016,[1,6,6,0,5,14,1]%%%}+%%%{9437184,[1,6,5,0,7,14,0]%%%}+%%%{-402653184,[0,7,10,7,2,8,1]%%%}+%%%{-5637144576,[0,7,10,6,1,10,2]%%%}+%%%{-16106127360,[0,7,10,5,0,12,3]%%%}+%%%{100663296,[0,7,9,7,4,8,0]%%%}+%%%{4160749568,[0,7,9,6,3,10,1]%%%}+%%%{30198988800,[0,7,9,5,2,12,2]%%%}+%%%{28991029248,[0,7,9,4,1,14,3]%%%}+%%%{-68719476736,[0,7,9,3,0,16,4]%%%}+%%%{-687865856,[0,7,8,6,5,10,0]%%%}+%%%{-13925089280,[0,7,8,5,4,12,1]%%%}+%%%{-48184164352,[0,7,8,4,3,14,2]%%%}+%%%{49392123904,[0,7,8,3,2,16,3]%%%}+%%%{120259084288,[0,7,8,2,1,18,4]%%%}+%%%{-68719476736,[0,7,8,1,0,20,5]%%%}+%%%{1845493760,[0,7,7,5,6,12,0]%%%}+%%%{19964887040,[0,7,7,4,5,14,1]%%%}+%%%{11542724608,[0,7,7,3,4,16,2]%%%}+%%%{-113816633344,[0,7,7,2,3,18,3]%%%}+%%%{8589934592,[0,7,7,1,2,20,4]%%%}+%%%{68719476736,[0,7,7,0,1,22,5]%%%}+%%%{-2432696320,[0,7,6,4,7,14,0]%%%}+%%%{-11207180288,[0,7,6,3,6,16,1]%%%}+%%%{28185722880,[0,7,6,2,5,18,2]%%%}+%%%{34359738368,[0,7,6,1,4,20,3]%%%}+%%%{-60129542144,[0,7,6,0,3,22,4]%%%}+%%%{1577058304,[0,7,5,3,8,16,0]%%%}+%%%{-201326592,[0,7,5,2,7,18,1]%%%}+%%%{-14495514624,[0,7,5,1,6,20,2]%%%}+%%%{17179869184,[0,7,5,0,5,22,3]%%%}+%%%{-402653184,[0,7,4,2,9,18,0]%%%}+%%%{1610612736,[0,7,4,1,8,20,1]%%%}+%%%{-1610612736,[0,7,4,0,7,22,2]%%%} / %%%{-1024,[0,3,4,2,1,2,0]%%%}+%%%{-4096,[0,3,4,1,0,4,1]%%%}+%%%{2560,[0,3,3,1,2,4,0]%%%}+%%%{4096,[0,3,3,0,1,6,1]%%%}+%%%{-1536,[0,3,2,0,3,6,0]%%%} Error: Bad Argument Value","F(-2)",0
390,-1,0,0,0.000000," ","integrate(1/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
391,-1,0,0,0.000000," ","integrate(1/x^2/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
392,-1,0,0,0.000000," ","integrate(1/x^4/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
393,-1,0,0,0.000000," ","integrate(1/x^6/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
394,1,75,0,2.254341," ","integrate(x^6/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","-\frac{c^{2} d^{2} x}{{\left(c^{3} d^{2} e - b c^{2} d e^{2} + a c^{2} e^{3}\right)} \sqrt{x^{2} e + d}} - \frac{e^{\left(-\frac{3}{2}\right)} \log\left({\left(x e^{\frac{1}{2}} - \sqrt{x^{2} e + d}\right)}^{2}\right)}{2 \, c}"," ",0,"-c^2*d^2*x/((c^3*d^2*e - b*c^2*d*e^2 + a*c^2*e^3)*sqrt(x^2*e + d)) - 1/2*e^(-3/2)*log((x*e^(1/2) - sqrt(x^2*e + d))^2)/c","A",0
395,-2,0,0,0.000000," ","integrate(x^4/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,c]=[44,93,-37]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,c]=[-72,-7,6]Evaluation time: 0.6Unable to divide, perhaps due to rounding error%%%{-2147483648,[3,8,10,8,3,10,1]%%%}+%%%{-12884901888,[3,8,10,7,2,12,2]%%%}+%%%{463856467968,[3,8,10,6,1,14,3]%%%}+%%%{1924145348608,[3,8,10,5,0,16,4]%%%}+%%%{536870912,[3,8,9,8,5,10,0]%%%}+%%%{20401094656,[3,8,9,7,4,12,1]%%%}+%%%{-150323855360,[3,8,9,6,3,14,2]%%%}+%%%{-3135326126080,[3,8,9,5,2,16,3]%%%}+%%%{-4672924418048,[3,8,9,4,1,18,4]%%%}+%%%{6047313952768,[3,8,9,3,0,20,5]%%%}+%%%{-4294967296,[3,8,8,7,6,12,0]%%%}+%%%{-42412802048,[3,8,8,6,5,14,1]%%%}+%%%{1046898278400,[3,8,8,5,4,16,2]%%%}+%%%{6210522710016,[3,8,8,4,3,18,3]%%%}+%%%{-1786706395136,[3,8,8,3,2,20,4]%%%}+%%%{-11544872091648,[3,8,8,2,1,22,5]%%%}+%%%{4398046511104,[3,8,8,1,0,24,6]%%%}+%%%{12750684160,[3,8,7,6,7,14,0]%%%}+%%%{-23890755584,[3,8,7,5,6,16,1]%%%}+%%%{-2103460233216,[3,8,7,4,5,18,2]%%%}+%%%{-3324304687104,[3,8,7,3,4,20,3]%%%}+%%%{9758165696512,[3,8,7,2,3,22,4]%%%}+%%%{1649267441664,[3,8,7,1,2,24,5]%%%}+%%%{-4398046511104,[3,8,7,0,1,26,6]%%%}+%%%{-17985175552,[3,8,6,5,8,16,0]%%%}+%%%{161866579968,[3,8,6,4,7,18,1]%%%}+%%%{1586990415872,[3,8,6,3,6,20,2]%%%}+%%%{-1795296329728,[3,8,6,2,5,22,3]%%%}+%%%{-4123168604160,[3,8,6,1,4,24,4]%%%}+%%%{3848290697216,[3,8,6,0,3,26,5]%%%}+%%%{12213813248,[3,8,5,4,9,18,0]%%%}+%%%{-171798691840,[3,8,5,3,8,20,1]%%%}+%%%{-212600881152,[3,8,5,2,7,22,2]%%%}+%%%{1477468749824,[3,8,5,1,6,24,3]%%%}+%%%{-1099511627776,[3,8,5,0,5,26,4]%%%}+%%%{-3221225472,[3,8,4,3,10,20,0]%%%}+%%%{57982058496,[3,8,4,2,9,22,1]%%%}+%%%{-154618822656,[3,8,4,1,8,24,2]%%%}+%%%{103079215104,[3,8,4,0,7,26,3]%%%}+%%%{1048576,[3,6,10,4,2,4,0]%%%}+%%%{8388608,[3,6,10,3,1,6,1]%%%}+%%%{16777216,[3,6,10,2,0,8,2]%%%}+%%%{-5242880,[3,6,9,3,3,6,0]%%%}+%%%{-29360128,[3,6,9,2,2,8,1]%%%}+%%%{-33554432,[3,6,9,1,1,10,2]%%%}+%%%{9699328,[3,6,8,2,4,8,0]%%%}+%%%{33554432,[3,6,8,1,3,10,1]%%%}+%%%{16777216,[3,6,8,0,2,12,2]%%%}+%%%{-7864320,[3,6,7,1,5,10,0]%%%}+%%%{-12582912,[3,6,7,0,4,12,1]%%%}+%%%{2359296,[3,6,6,0,6,12,0]%%%}+%%%{-536870912,[2,7,10,6,2,8,1]%%%}+%%%{18446744062703697920,[2,7,10,5,1,10,2]%%%}+%%%{-18253611008,[2,7,10,4,0,12,3]%%%}+%%%{134217728,[2,7,9,6,4,8,0]%%%}+%%%{5502926848,[2,7,9,5,3,10,1]%%%}+%%%{36909875200,[2,7,9,4,2,12,2]%%%}+%%%{42949672960,[2,7,9,3,1,14,3]%%%}+%%%{-42949672960,[2,7,9,2,0,16,4]%%%}+%%%{-956301312,[2,7,8,5,5,10,0]%%%}+%%%{-18656264192,[2,7,8,4,4,12,1]%%%}+%%%{-64961380352,[2,7,8,3,3,14,2]%%%}+%%%{8589934592,[2,7,8,2,2,16,3]%%%}+%%%{85899345920,[2,7,8,1,1,18,4]%%%}+%%%{2642411520,[2,7,7,4,6,12,0]%%%}+%%%{27783069696,[2,7,7,3,5,14,1]%%%}+%%%{33957085184,[2,7,7,2,4,16,2]%%%}+%%%{-73014444032,[2,7,7,1,3,18,3]%%%}+%%%{-42949672960,[2,7,7,0,2,20,4]%%%}+%%%{-3556769792,[2,7,6,3,7,14,0]%%%}+%%%{-17716740096,[2,7,6,2,6,16,1]%%%}+%%%{12884901888,[2,7,6,1,5,18,2]%%%}+%%%{39728447488,[2,7,6,0,4,20,3]%%%}+%%%{2340421632,[2,7,5,2,8,16,0]%%%}+%%%{2415919104,[2,7,5,1,7,18,1]%%%}+%%%{-12079595520,[2,7,5,0,6,20,2]%%%}+%%%{-603979776,[2,7,4,1,9,18,0]%%%}+%%%{1207959552,[2,7,4,0,8,20,1]%%%}+%%%{2147483648,[1,8,10,9,3,10,1]%%%}+%%%{38654705664,[1,8,10,8,2,12,2]%%%}+%%%{51539607552,[1,8,10,7,1,14,3]%%%}+%%%{-274877906944,[1,8,10,6,0,16,4]%%%}+%%%{-536870912,[1,8,9,9,5,10,0]%%%}+%%%{-26843545600,[1,8,9,8,4,12,1]%%%}+%%%{-188978561024,[1,8,9,7,3,14,2]%%%}+%%%{146028888064,[1,8,9,6,2,16,3]%%%}+%%%{962072674304,[1,8,9,5,1,18,4]%%%}+%%%{-549755813888,[1,8,9,4,0,20,5]%%%}+%%%{4294967296,[1,8,8,8,6,12,0]%%%}+%%%{95026151424,[1,8,8,7,5,14,1]%%%}+%%%{239444426752,[1,8,8,6,4,16,2]%%%}+%%%{-858993459200,[1,8,8,5,3,18,3]%%%}+%%%{-618475290624,[1,8,8,4,2,20,4]%%%}+%%%{1099511627776,[1,8,8,3,1,22,5]%%%}+%%%{-12750684160,[1,8,7,7,7,14,0]%%%}+%%%{-136633647104,[1,8,7,6,6,16,1]%%%}+%%%{62277025792,[1,8,7,5,5,18,2]%%%}+%%%{936302870528,[1,8,7,4,4,20,3]%%%}+%%%{-549755813888,[1,8,7,3,3,22,4]%%%}+%%%{-549755813888,[1,8,7,2,2,24,5]%%%}+%%%{17985175552,[1,8,6,6,8,16,0]%%%}+%%%{71940702208,[1,8,6,5,7,18,1]%%%}+%%%{-267361714176,[1,8,6,4,6,20,2]%%%}+%%%{-137438953472,[1,8,6,3,5,22,3]%%%}+%%%{481036337152,[1,8,6,2,4,24,4]%%%}+%%%{-12213813248,[1,8,5,5,9,18,0]%%%}+%%%{7247757312,[1,8,5,4,8,20,1]%%%}+%%%{103079215104,[1,8,5,3,7,22,2]%%%}+%%%{-137438953472,[1,8,5,2,6,24,3]%%%}+%%%{3221225472,[1,8,4,4,10,20,0]%%%}+%%%{-12884901888,[1,8,4,3,9,22,1]%%%}+%%%{12884901888,[1,8,4,2,8,24,2]%%%}+%%%{-1048576,[1,6,10,5,2,4,0]%%%}+%%%{-8388608,[1,6,10,4,1,6,1]%%%}+%%%{-16777216,[1,6,10,3,0,8,2]%%%}+%%%{8388608,[1,6,9,4,3,6,0]%%%}+%%%{62914560,[1,6,9,3,2,8,1]%%%}+%%%{150994944,[1,6,9,2,1,10,2]%%%}+%%%{134217728,[1,6,9,1,0,12,3]%%%}+%%%{-26476544,[1,6,8,3,4,8,0]%%%}+%%%{-163577856,[1,6,8,2,3,10,1]%%%}+%%%{-301989888,[1,6,8,1,2,12,2]%%%}+%%%{-134217728,[1,6,8,0,1,14,3]%%%}+%%%{41156608,[1,6,7,2,5,10,0]%%%}+%%%{178257920,[1,6,7,1,4,12,1]%%%}+%%%{167772160,[1,6,7,0,3,14,2]%%%}+%%%{-31457280,[1,6,6,1,6,12,0]%%%}+%%%{-69206016,[1,6,6,0,5,14,1]%%%}+%%%{9437184,[1,6,5,0,7,14,0]%%%}+%%%{402653184,[0,7,10,7,2,8,1]%%%}+%%%{5637144576,[0,7,10,6,1,10,2]%%%}+%%%{16106127360,[0,7,10,5,0,12,3]%%%}+%%%{-100663296,[0,7,9,7,4,8,0]%%%}+%%%{-4160749568,[0,7,9,6,3,10,1]%%%}+%%%{-30198988800,[0,7,9,5,2,12,2]%%%}+%%%{-28991029248,[0,7,9,4,1,14,3]%%%}+%%%{68719476736,[0,7,9,3,0,16,4]%%%}+%%%{687865856,[0,7,8,6,5,10,0]%%%}+%%%{13925089280,[0,7,8,5,4,12,1]%%%}+%%%{48184164352,[0,7,8,4,3,14,2]%%%}+%%%{-49392123904,[0,7,8,3,2,16,3]%%%}+%%%{-120259084288,[0,7,8,2,1,18,4]%%%}+%%%{68719476736,[0,7,8,1,0,20,5]%%%}+%%%{-1845493760,[0,7,7,5,6,12,0]%%%}+%%%{-19964887040,[0,7,7,4,5,14,1]%%%}+%%%{-11542724608,[0,7,7,3,4,16,2]%%%}+%%%{113816633344,[0,7,7,2,3,18,3]%%%}+%%%{-8589934592,[0,7,7,1,2,20,4]%%%}+%%%{-68719476736,[0,7,7,0,1,22,5]%%%}+%%%{2432696320,[0,7,6,4,7,14,0]%%%}+%%%{11207180288,[0,7,6,3,6,16,1]%%%}+%%%{-28185722880,[0,7,6,2,5,18,2]%%%}+%%%{-34359738368,[0,7,6,1,4,20,3]%%%}+%%%{60129542144,[0,7,6,0,3,22,4]%%%}+%%%{-1577058304,[0,7,5,3,8,16,0]%%%}+%%%{201326592,[0,7,5,2,7,18,1]%%%}+%%%{14495514624,[0,7,5,1,6,20,2]%%%}+%%%{-17179869184,[0,7,5,0,5,22,3]%%%}+%%%{402653184,[0,7,4,2,9,18,0]%%%}+%%%{-1610612736,[0,7,4,1,8,20,1]%%%}+%%%{1610612736,[0,7,4,0,7,22,2]%%%} / %%%{1024,[0,3,4,2,1,2,0]%%%}+%%%{4096,[0,3,4,1,0,4,1]%%%}+%%%{-2560,[0,3,3,1,2,4,0]%%%}+%%%{-4096,[0,3,3,0,1,6,1]%%%}+%%%{1536,[0,3,2,0,3,6,0]%%%} Error: Bad Argument Value","F(-2)",0
396,-2,0,0,0.000000," ","integrate(x^2/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,c]=[44,93,-37]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,c]=[-72,-7,6]Evaluation time: 0.57Unable to divide, perhaps due to rounding error%%%{-2147483648,[3,8,10,8,3,10,1]%%%}+%%%{-12884901888,[3,8,10,7,2,12,2]%%%}+%%%{463856467968,[3,8,10,6,1,14,3]%%%}+%%%{1924145348608,[3,8,10,5,0,16,4]%%%}+%%%{536870912,[3,8,9,8,5,10,0]%%%}+%%%{20401094656,[3,8,9,7,4,12,1]%%%}+%%%{-150323855360,[3,8,9,6,3,14,2]%%%}+%%%{-3135326126080,[3,8,9,5,2,16,3]%%%}+%%%{-4672924418048,[3,8,9,4,1,18,4]%%%}+%%%{6047313952768,[3,8,9,3,0,20,5]%%%}+%%%{-4294967296,[3,8,8,7,6,12,0]%%%}+%%%{-42412802048,[3,8,8,6,5,14,1]%%%}+%%%{1046898278400,[3,8,8,5,4,16,2]%%%}+%%%{6210522710016,[3,8,8,4,3,18,3]%%%}+%%%{-1786706395136,[3,8,8,3,2,20,4]%%%}+%%%{-11544872091648,[3,8,8,2,1,22,5]%%%}+%%%{4398046511104,[3,8,8,1,0,24,6]%%%}+%%%{12750684160,[3,8,7,6,7,14,0]%%%}+%%%{-23890755584,[3,8,7,5,6,16,1]%%%}+%%%{-2103460233216,[3,8,7,4,5,18,2]%%%}+%%%{-3324304687104,[3,8,7,3,4,20,3]%%%}+%%%{9758165696512,[3,8,7,2,3,22,4]%%%}+%%%{1649267441664,[3,8,7,1,2,24,5]%%%}+%%%{-4398046511104,[3,8,7,0,1,26,6]%%%}+%%%{-17985175552,[3,8,6,5,8,16,0]%%%}+%%%{161866579968,[3,8,6,4,7,18,1]%%%}+%%%{1586990415872,[3,8,6,3,6,20,2]%%%}+%%%{-1795296329728,[3,8,6,2,5,22,3]%%%}+%%%{-4123168604160,[3,8,6,1,4,24,4]%%%}+%%%{3848290697216,[3,8,6,0,3,26,5]%%%}+%%%{12213813248,[3,8,5,4,9,18,0]%%%}+%%%{-171798691840,[3,8,5,3,8,20,1]%%%}+%%%{-212600881152,[3,8,5,2,7,22,2]%%%}+%%%{1477468749824,[3,8,5,1,6,24,3]%%%}+%%%{-1099511627776,[3,8,5,0,5,26,4]%%%}+%%%{-3221225472,[3,8,4,3,10,20,0]%%%}+%%%{57982058496,[3,8,4,2,9,22,1]%%%}+%%%{-154618822656,[3,8,4,1,8,24,2]%%%}+%%%{103079215104,[3,8,4,0,7,26,3]%%%}+%%%{1048576,[3,6,10,4,2,4,0]%%%}+%%%{8388608,[3,6,10,3,1,6,1]%%%}+%%%{16777216,[3,6,10,2,0,8,2]%%%}+%%%{-5242880,[3,6,9,3,3,6,0]%%%}+%%%{-29360128,[3,6,9,2,2,8,1]%%%}+%%%{-33554432,[3,6,9,1,1,10,2]%%%}+%%%{9699328,[3,6,8,2,4,8,0]%%%}+%%%{33554432,[3,6,8,1,3,10,1]%%%}+%%%{16777216,[3,6,8,0,2,12,2]%%%}+%%%{-7864320,[3,6,7,1,5,10,0]%%%}+%%%{-12582912,[3,6,7,0,4,12,1]%%%}+%%%{2359296,[3,6,6,0,6,12,0]%%%}+%%%{-536870912,[2,7,10,6,2,8,1]%%%}+%%%{18446744062703697920,[2,7,10,5,1,10,2]%%%}+%%%{-18253611008,[2,7,10,4,0,12,3]%%%}+%%%{134217728,[2,7,9,6,4,8,0]%%%}+%%%{5502926848,[2,7,9,5,3,10,1]%%%}+%%%{36909875200,[2,7,9,4,2,12,2]%%%}+%%%{42949672960,[2,7,9,3,1,14,3]%%%}+%%%{-42949672960,[2,7,9,2,0,16,4]%%%}+%%%{-956301312,[2,7,8,5,5,10,0]%%%}+%%%{-18656264192,[2,7,8,4,4,12,1]%%%}+%%%{-64961380352,[2,7,8,3,3,14,2]%%%}+%%%{8589934592,[2,7,8,2,2,16,3]%%%}+%%%{85899345920,[2,7,8,1,1,18,4]%%%}+%%%{2642411520,[2,7,7,4,6,12,0]%%%}+%%%{27783069696,[2,7,7,3,5,14,1]%%%}+%%%{33957085184,[2,7,7,2,4,16,2]%%%}+%%%{-73014444032,[2,7,7,1,3,18,3]%%%}+%%%{-42949672960,[2,7,7,0,2,20,4]%%%}+%%%{-3556769792,[2,7,6,3,7,14,0]%%%}+%%%{-17716740096,[2,7,6,2,6,16,1]%%%}+%%%{12884901888,[2,7,6,1,5,18,2]%%%}+%%%{39728447488,[2,7,6,0,4,20,3]%%%}+%%%{2340421632,[2,7,5,2,8,16,0]%%%}+%%%{2415919104,[2,7,5,1,7,18,1]%%%}+%%%{-12079595520,[2,7,5,0,6,20,2]%%%}+%%%{-603979776,[2,7,4,1,9,18,0]%%%}+%%%{1207959552,[2,7,4,0,8,20,1]%%%}+%%%{2147483648,[1,8,10,9,3,10,1]%%%}+%%%{38654705664,[1,8,10,8,2,12,2]%%%}+%%%{51539607552,[1,8,10,7,1,14,3]%%%}+%%%{-274877906944,[1,8,10,6,0,16,4]%%%}+%%%{-536870912,[1,8,9,9,5,10,0]%%%}+%%%{-26843545600,[1,8,9,8,4,12,1]%%%}+%%%{-188978561024,[1,8,9,7,3,14,2]%%%}+%%%{146028888064,[1,8,9,6,2,16,3]%%%}+%%%{962072674304,[1,8,9,5,1,18,4]%%%}+%%%{-549755813888,[1,8,9,4,0,20,5]%%%}+%%%{4294967296,[1,8,8,8,6,12,0]%%%}+%%%{95026151424,[1,8,8,7,5,14,1]%%%}+%%%{239444426752,[1,8,8,6,4,16,2]%%%}+%%%{-858993459200,[1,8,8,5,3,18,3]%%%}+%%%{-618475290624,[1,8,8,4,2,20,4]%%%}+%%%{1099511627776,[1,8,8,3,1,22,5]%%%}+%%%{-12750684160,[1,8,7,7,7,14,0]%%%}+%%%{-136633647104,[1,8,7,6,6,16,1]%%%}+%%%{62277025792,[1,8,7,5,5,18,2]%%%}+%%%{936302870528,[1,8,7,4,4,20,3]%%%}+%%%{-549755813888,[1,8,7,3,3,22,4]%%%}+%%%{-549755813888,[1,8,7,2,2,24,5]%%%}+%%%{17985175552,[1,8,6,6,8,16,0]%%%}+%%%{71940702208,[1,8,6,5,7,18,1]%%%}+%%%{-267361714176,[1,8,6,4,6,20,2]%%%}+%%%{-137438953472,[1,8,6,3,5,22,3]%%%}+%%%{481036337152,[1,8,6,2,4,24,4]%%%}+%%%{-12213813248,[1,8,5,5,9,18,0]%%%}+%%%{7247757312,[1,8,5,4,8,20,1]%%%}+%%%{103079215104,[1,8,5,3,7,22,2]%%%}+%%%{-137438953472,[1,8,5,2,6,24,3]%%%}+%%%{3221225472,[1,8,4,4,10,20,0]%%%}+%%%{-12884901888,[1,8,4,3,9,22,1]%%%}+%%%{12884901888,[1,8,4,2,8,24,2]%%%}+%%%{-1048576,[1,6,10,5,2,4,0]%%%}+%%%{-8388608,[1,6,10,4,1,6,1]%%%}+%%%{-16777216,[1,6,10,3,0,8,2]%%%}+%%%{8388608,[1,6,9,4,3,6,0]%%%}+%%%{62914560,[1,6,9,3,2,8,1]%%%}+%%%{150994944,[1,6,9,2,1,10,2]%%%}+%%%{134217728,[1,6,9,1,0,12,3]%%%}+%%%{-26476544,[1,6,8,3,4,8,0]%%%}+%%%{-163577856,[1,6,8,2,3,10,1]%%%}+%%%{-301989888,[1,6,8,1,2,12,2]%%%}+%%%{-134217728,[1,6,8,0,1,14,3]%%%}+%%%{41156608,[1,6,7,2,5,10,0]%%%}+%%%{178257920,[1,6,7,1,4,12,1]%%%}+%%%{167772160,[1,6,7,0,3,14,2]%%%}+%%%{-31457280,[1,6,6,1,6,12,0]%%%}+%%%{-69206016,[1,6,6,0,5,14,1]%%%}+%%%{9437184,[1,6,5,0,7,14,0]%%%}+%%%{402653184,[0,7,10,7,2,8,1]%%%}+%%%{5637144576,[0,7,10,6,1,10,2]%%%}+%%%{16106127360,[0,7,10,5,0,12,3]%%%}+%%%{-100663296,[0,7,9,7,4,8,0]%%%}+%%%{-4160749568,[0,7,9,6,3,10,1]%%%}+%%%{-30198988800,[0,7,9,5,2,12,2]%%%}+%%%{-28991029248,[0,7,9,4,1,14,3]%%%}+%%%{68719476736,[0,7,9,3,0,16,4]%%%}+%%%{687865856,[0,7,8,6,5,10,0]%%%}+%%%{13925089280,[0,7,8,5,4,12,1]%%%}+%%%{48184164352,[0,7,8,4,3,14,2]%%%}+%%%{-49392123904,[0,7,8,3,2,16,3]%%%}+%%%{-120259084288,[0,7,8,2,1,18,4]%%%}+%%%{68719476736,[0,7,8,1,0,20,5]%%%}+%%%{-1845493760,[0,7,7,5,6,12,0]%%%}+%%%{-19964887040,[0,7,7,4,5,14,1]%%%}+%%%{-11542724608,[0,7,7,3,4,16,2]%%%}+%%%{113816633344,[0,7,7,2,3,18,3]%%%}+%%%{-8589934592,[0,7,7,1,2,20,4]%%%}+%%%{-68719476736,[0,7,7,0,1,22,5]%%%}+%%%{2432696320,[0,7,6,4,7,14,0]%%%}+%%%{11207180288,[0,7,6,3,6,16,1]%%%}+%%%{-28185722880,[0,7,6,2,5,18,2]%%%}+%%%{-34359738368,[0,7,6,1,4,20,3]%%%}+%%%{60129542144,[0,7,6,0,3,22,4]%%%}+%%%{-1577058304,[0,7,5,3,8,16,0]%%%}+%%%{201326592,[0,7,5,2,7,18,1]%%%}+%%%{14495514624,[0,7,5,1,6,20,2]%%%}+%%%{-17179869184,[0,7,5,0,5,22,3]%%%}+%%%{402653184,[0,7,4,2,9,18,0]%%%}+%%%{-1610612736,[0,7,4,1,8,20,1]%%%}+%%%{1610612736,[0,7,4,0,7,22,2]%%%} / %%%{1024,[0,3,4,2,1,2,0]%%%}+%%%{4096,[0,3,4,1,0,4,1]%%%}+%%%{-2560,[0,3,3,1,2,4,0]%%%}+%%%{-4096,[0,3,3,0,1,6,1]%%%}+%%%{1536,[0,3,2,0,3,6,0]%%%} Error: Bad Argument Value","F(-2)",0
397,-2,0,0,0.000000," ","integrate(1/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,c]=[44,93,-37]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,c]=[-72,-7,6]Evaluation time: 0.58Unable to divide, perhaps due to rounding error%%%{-2147483648,[3,8,10,8,3,10,1]%%%}+%%%{-12884901888,[3,8,10,7,2,12,2]%%%}+%%%{463856467968,[3,8,10,6,1,14,3]%%%}+%%%{1924145348608,[3,8,10,5,0,16,4]%%%}+%%%{536870912,[3,8,9,8,5,10,0]%%%}+%%%{20401094656,[3,8,9,7,4,12,1]%%%}+%%%{-150323855360,[3,8,9,6,3,14,2]%%%}+%%%{-3135326126080,[3,8,9,5,2,16,3]%%%}+%%%{-4672924418048,[3,8,9,4,1,18,4]%%%}+%%%{6047313952768,[3,8,9,3,0,20,5]%%%}+%%%{-4294967296,[3,8,8,7,6,12,0]%%%}+%%%{-42412802048,[3,8,8,6,5,14,1]%%%}+%%%{1046898278400,[3,8,8,5,4,16,2]%%%}+%%%{6210522710016,[3,8,8,4,3,18,3]%%%}+%%%{-1786706395136,[3,8,8,3,2,20,4]%%%}+%%%{-11544872091648,[3,8,8,2,1,22,5]%%%}+%%%{4398046511104,[3,8,8,1,0,24,6]%%%}+%%%{12750684160,[3,8,7,6,7,14,0]%%%}+%%%{-23890755584,[3,8,7,5,6,16,1]%%%}+%%%{-2103460233216,[3,8,7,4,5,18,2]%%%}+%%%{-3324304687104,[3,8,7,3,4,20,3]%%%}+%%%{9758165696512,[3,8,7,2,3,22,4]%%%}+%%%{1649267441664,[3,8,7,1,2,24,5]%%%}+%%%{-4398046511104,[3,8,7,0,1,26,6]%%%}+%%%{-17985175552,[3,8,6,5,8,16,0]%%%}+%%%{161866579968,[3,8,6,4,7,18,1]%%%}+%%%{1586990415872,[3,8,6,3,6,20,2]%%%}+%%%{-1795296329728,[3,8,6,2,5,22,3]%%%}+%%%{-4123168604160,[3,8,6,1,4,24,4]%%%}+%%%{3848290697216,[3,8,6,0,3,26,5]%%%}+%%%{12213813248,[3,8,5,4,9,18,0]%%%}+%%%{-171798691840,[3,8,5,3,8,20,1]%%%}+%%%{-212600881152,[3,8,5,2,7,22,2]%%%}+%%%{1477468749824,[3,8,5,1,6,24,3]%%%}+%%%{-1099511627776,[3,8,5,0,5,26,4]%%%}+%%%{-3221225472,[3,8,4,3,10,20,0]%%%}+%%%{57982058496,[3,8,4,2,9,22,1]%%%}+%%%{-154618822656,[3,8,4,1,8,24,2]%%%}+%%%{103079215104,[3,8,4,0,7,26,3]%%%}+%%%{1048576,[3,6,10,4,2,4,0]%%%}+%%%{8388608,[3,6,10,3,1,6,1]%%%}+%%%{16777216,[3,6,10,2,0,8,2]%%%}+%%%{-5242880,[3,6,9,3,3,6,0]%%%}+%%%{-29360128,[3,6,9,2,2,8,1]%%%}+%%%{-33554432,[3,6,9,1,1,10,2]%%%}+%%%{9699328,[3,6,8,2,4,8,0]%%%}+%%%{33554432,[3,6,8,1,3,10,1]%%%}+%%%{16777216,[3,6,8,0,2,12,2]%%%}+%%%{-7864320,[3,6,7,1,5,10,0]%%%}+%%%{-12582912,[3,6,7,0,4,12,1]%%%}+%%%{2359296,[3,6,6,0,6,12,0]%%%}+%%%{-536870912,[2,7,10,6,2,8,1]%%%}+%%%{18446744062703697920,[2,7,10,5,1,10,2]%%%}+%%%{-18253611008,[2,7,10,4,0,12,3]%%%}+%%%{134217728,[2,7,9,6,4,8,0]%%%}+%%%{5502926848,[2,7,9,5,3,10,1]%%%}+%%%{36909875200,[2,7,9,4,2,12,2]%%%}+%%%{42949672960,[2,7,9,3,1,14,3]%%%}+%%%{-42949672960,[2,7,9,2,0,16,4]%%%}+%%%{-956301312,[2,7,8,5,5,10,0]%%%}+%%%{-18656264192,[2,7,8,4,4,12,1]%%%}+%%%{-64961380352,[2,7,8,3,3,14,2]%%%}+%%%{8589934592,[2,7,8,2,2,16,3]%%%}+%%%{85899345920,[2,7,8,1,1,18,4]%%%}+%%%{2642411520,[2,7,7,4,6,12,0]%%%}+%%%{27783069696,[2,7,7,3,5,14,1]%%%}+%%%{33957085184,[2,7,7,2,4,16,2]%%%}+%%%{-73014444032,[2,7,7,1,3,18,3]%%%}+%%%{-42949672960,[2,7,7,0,2,20,4]%%%}+%%%{-3556769792,[2,7,6,3,7,14,0]%%%}+%%%{-17716740096,[2,7,6,2,6,16,1]%%%}+%%%{12884901888,[2,7,6,1,5,18,2]%%%}+%%%{39728447488,[2,7,6,0,4,20,3]%%%}+%%%{2340421632,[2,7,5,2,8,16,0]%%%}+%%%{2415919104,[2,7,5,1,7,18,1]%%%}+%%%{-12079595520,[2,7,5,0,6,20,2]%%%}+%%%{-603979776,[2,7,4,1,9,18,0]%%%}+%%%{1207959552,[2,7,4,0,8,20,1]%%%}+%%%{2147483648,[1,8,10,9,3,10,1]%%%}+%%%{38654705664,[1,8,10,8,2,12,2]%%%}+%%%{51539607552,[1,8,10,7,1,14,3]%%%}+%%%{-274877906944,[1,8,10,6,0,16,4]%%%}+%%%{-536870912,[1,8,9,9,5,10,0]%%%}+%%%{-26843545600,[1,8,9,8,4,12,1]%%%}+%%%{-188978561024,[1,8,9,7,3,14,2]%%%}+%%%{146028888064,[1,8,9,6,2,16,3]%%%}+%%%{962072674304,[1,8,9,5,1,18,4]%%%}+%%%{-549755813888,[1,8,9,4,0,20,5]%%%}+%%%{4294967296,[1,8,8,8,6,12,0]%%%}+%%%{95026151424,[1,8,8,7,5,14,1]%%%}+%%%{239444426752,[1,8,8,6,4,16,2]%%%}+%%%{-858993459200,[1,8,8,5,3,18,3]%%%}+%%%{-618475290624,[1,8,8,4,2,20,4]%%%}+%%%{1099511627776,[1,8,8,3,1,22,5]%%%}+%%%{-12750684160,[1,8,7,7,7,14,0]%%%}+%%%{-136633647104,[1,8,7,6,6,16,1]%%%}+%%%{62277025792,[1,8,7,5,5,18,2]%%%}+%%%{936302870528,[1,8,7,4,4,20,3]%%%}+%%%{-549755813888,[1,8,7,3,3,22,4]%%%}+%%%{-549755813888,[1,8,7,2,2,24,5]%%%}+%%%{17985175552,[1,8,6,6,8,16,0]%%%}+%%%{71940702208,[1,8,6,5,7,18,1]%%%}+%%%{-267361714176,[1,8,6,4,6,20,2]%%%}+%%%{-137438953472,[1,8,6,3,5,22,3]%%%}+%%%{481036337152,[1,8,6,2,4,24,4]%%%}+%%%{-12213813248,[1,8,5,5,9,18,0]%%%}+%%%{7247757312,[1,8,5,4,8,20,1]%%%}+%%%{103079215104,[1,8,5,3,7,22,2]%%%}+%%%{-137438953472,[1,8,5,2,6,24,3]%%%}+%%%{3221225472,[1,8,4,4,10,20,0]%%%}+%%%{-12884901888,[1,8,4,3,9,22,1]%%%}+%%%{12884901888,[1,8,4,2,8,24,2]%%%}+%%%{-1048576,[1,6,10,5,2,4,0]%%%}+%%%{-8388608,[1,6,10,4,1,6,1]%%%}+%%%{-16777216,[1,6,10,3,0,8,2]%%%}+%%%{8388608,[1,6,9,4,3,6,0]%%%}+%%%{62914560,[1,6,9,3,2,8,1]%%%}+%%%{150994944,[1,6,9,2,1,10,2]%%%}+%%%{134217728,[1,6,9,1,0,12,3]%%%}+%%%{-26476544,[1,6,8,3,4,8,0]%%%}+%%%{-163577856,[1,6,8,2,3,10,1]%%%}+%%%{-301989888,[1,6,8,1,2,12,2]%%%}+%%%{-134217728,[1,6,8,0,1,14,3]%%%}+%%%{41156608,[1,6,7,2,5,10,0]%%%}+%%%{178257920,[1,6,7,1,4,12,1]%%%}+%%%{167772160,[1,6,7,0,3,14,2]%%%}+%%%{-31457280,[1,6,6,1,6,12,0]%%%}+%%%{-69206016,[1,6,6,0,5,14,1]%%%}+%%%{9437184,[1,6,5,0,7,14,0]%%%}+%%%{402653184,[0,7,10,7,2,8,1]%%%}+%%%{5637144576,[0,7,10,6,1,10,2]%%%}+%%%{16106127360,[0,7,10,5,0,12,3]%%%}+%%%{-100663296,[0,7,9,7,4,8,0]%%%}+%%%{-4160749568,[0,7,9,6,3,10,1]%%%}+%%%{-30198988800,[0,7,9,5,2,12,2]%%%}+%%%{-28991029248,[0,7,9,4,1,14,3]%%%}+%%%{68719476736,[0,7,9,3,0,16,4]%%%}+%%%{687865856,[0,7,8,6,5,10,0]%%%}+%%%{13925089280,[0,7,8,5,4,12,1]%%%}+%%%{48184164352,[0,7,8,4,3,14,2]%%%}+%%%{-49392123904,[0,7,8,3,2,16,3]%%%}+%%%{-120259084288,[0,7,8,2,1,18,4]%%%}+%%%{68719476736,[0,7,8,1,0,20,5]%%%}+%%%{-1845493760,[0,7,7,5,6,12,0]%%%}+%%%{-19964887040,[0,7,7,4,5,14,1]%%%}+%%%{-11542724608,[0,7,7,3,4,16,2]%%%}+%%%{113816633344,[0,7,7,2,3,18,3]%%%}+%%%{-8589934592,[0,7,7,1,2,20,4]%%%}+%%%{-68719476736,[0,7,7,0,1,22,5]%%%}+%%%{2432696320,[0,7,6,4,7,14,0]%%%}+%%%{11207180288,[0,7,6,3,6,16,1]%%%}+%%%{-28185722880,[0,7,6,2,5,18,2]%%%}+%%%{-34359738368,[0,7,6,1,4,20,3]%%%}+%%%{60129542144,[0,7,6,0,3,22,4]%%%}+%%%{-1577058304,[0,7,5,3,8,16,0]%%%}+%%%{201326592,[0,7,5,2,7,18,1]%%%}+%%%{14495514624,[0,7,5,1,6,20,2]%%%}+%%%{-17179869184,[0,7,5,0,5,22,3]%%%}+%%%{402653184,[0,7,4,2,9,18,0]%%%}+%%%{-1610612736,[0,7,4,1,8,20,1]%%%}+%%%{1610612736,[0,7,4,0,7,22,2]%%%} / %%%{1024,[0,3,4,2,1,2,0]%%%}+%%%{4096,[0,3,4,1,0,4,1]%%%}+%%%{-2560,[0,3,3,1,2,4,0]%%%}+%%%{-4096,[0,3,3,0,1,6,1]%%%}+%%%{1536,[0,3,2,0,3,6,0]%%%} Error: Bad Argument Value","F(-2)",0
398,-1,0,0,0.000000," ","integrate(1/x^2/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
399,-1,0,0,0.000000," ","integrate(1/x^4/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
400,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)^q/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{q} \left(f x\right)^{m}}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate((e*x^2 + d)^q*(f*x)^m/(c*x^4 + b*x^2 + a), x)","F",0
401,0,0,0,0.000000," ","integrate(x^7*(e*x^2+d)^q/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{q} x^{7}}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate((e*x^2 + d)^q*x^7/(c*x^4 + b*x^2 + a), x)","F",0
402,0,0,0,0.000000," ","integrate(x^5*(e*x^2+d)^q/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{q} x^{5}}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate((e*x^2 + d)^q*x^5/(c*x^4 + b*x^2 + a), x)","F",0
403,0,0,0,0.000000," ","integrate(x^3*(e*x^2+d)^q/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{q} x^{3}}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate((e*x^2 + d)^q*x^3/(c*x^4 + b*x^2 + a), x)","F",0
404,0,0,0,0.000000," ","integrate(x*(e*x^2+d)^q/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{q} x}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate((e*x^2 + d)^q*x/(c*x^4 + b*x^2 + a), x)","F",0
405,0,0,0,0.000000," ","integrate((e*x^2+d)^q/x/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{q}}{{\left(c x^{4} + b x^{2} + a\right)} x}\,{d x}"," ",0,"integrate((e*x^2 + d)^q/((c*x^4 + b*x^2 + a)*x), x)","F",0
406,0,0,0,0.000000," ","integrate((e*x^2+d)^q/x^3/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{q}}{{\left(c x^{4} + b x^{2} + a\right)} x^{3}}\,{d x}"," ",0,"integrate((e*x^2 + d)^q/((c*x^4 + b*x^2 + a)*x^3), x)","F",0
407,0,0,0,0.000000," ","integrate(x^6*(e*x^2+d)^q/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{q} x^{6}}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate((e*x^2 + d)^q*x^6/(c*x^4 + b*x^2 + a), x)","F",0
408,0,0,0,0.000000," ","integrate(x^4*(e*x^2+d)^q/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{q} x^{4}}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate((e*x^2 + d)^q*x^4/(c*x^4 + b*x^2 + a), x)","F",0
409,0,0,0,0.000000," ","integrate(x^2*(e*x^2+d)^q/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{q} x^{2}}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate((e*x^2 + d)^q*x^2/(c*x^4 + b*x^2 + a), x)","F",0
410,0,0,0,0.000000," ","integrate((e*x^2+d)^q/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{q}}{c x^{4} + b x^{2} + a}\,{d x}"," ",0,"integrate((e*x^2 + d)^q/(c*x^4 + b*x^2 + a), x)","F",0
411,0,0,0,0.000000," ","integrate((e*x^2+d)^q/x^2/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{q}}{{\left(c x^{4} + b x^{2} + a\right)} x^{2}}\,{d x}"," ",0,"integrate((e*x^2 + d)^q/((c*x^4 + b*x^2 + a)*x^2), x)","F",0
412,0,0,0,0.000000," ","integrate((e*x^2+d)^q/x^4/(c*x^4+b*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{q}}{{\left(c x^{4} + b x^{2} + a\right)} x^{4}}\,{d x}"," ",0,"integrate((e*x^2 + d)^q/((c*x^4 + b*x^2 + a)*x^4), x)","F",0
413,1,42,0,0.222135," ","integrate((1+1/c^2/x^2)^(1/2)/(-c^4*x^4+1)^(1/2),x, algorithm=""giac"")","-\frac{{\left(\log\left(\sqrt{-c^{2} x^{2} + 1} + 1\right) - \log\left(-\sqrt{-c^{2} x^{2} + 1} + 1\right)\right)} {\left| c \right|}}{2 \, c^{2}}"," ",0,"-1/2*(log(sqrt(-c^2*x^2 + 1) + 1) - log(-sqrt(-c^2*x^2 + 1) + 1))*abs(c)/c^2","A",0
