1,1,125,0,0.553860," ","integrate(x^3*(e*x^2+d)*(c*x^4+a)^5,x, algorithm=""fricas"")","\frac{1}{26} x^{26} e c^{5} + \frac{1}{24} x^{24} d c^{5} + \frac{5}{22} x^{22} e c^{4} a + \frac{1}{4} x^{20} d c^{4} a + \frac{5}{9} x^{18} e c^{3} a^{2} + \frac{5}{8} x^{16} d c^{3} a^{2} + \frac{5}{7} x^{14} e c^{2} a^{3} + \frac{5}{6} x^{12} d c^{2} a^{3} + \frac{1}{2} x^{10} e c a^{4} + \frac{5}{8} x^{8} d c a^{4} + \frac{1}{6} x^{6} e a^{5} + \frac{1}{4} x^{4} d a^{5}"," ",0,"1/26*x^26*e*c^5 + 1/24*x^24*d*c^5 + 5/22*x^22*e*c^4*a + 1/4*x^20*d*c^4*a + 5/9*x^18*e*c^3*a^2 + 5/8*x^16*d*c^3*a^2 + 5/7*x^14*e*c^2*a^3 + 5/6*x^12*d*c^2*a^3 + 1/2*x^10*e*c*a^4 + 5/8*x^8*d*c*a^4 + 1/6*x^6*e*a^5 + 1/4*x^4*d*a^5","A",0
2,1,125,0,0.571483," ","integrate(x^2*(e*x^2+d)*(c*x^4+a)^5,x, algorithm=""fricas"")","\frac{1}{25} x^{25} e c^{5} + \frac{1}{23} x^{23} d c^{5} + \frac{5}{21} x^{21} e c^{4} a + \frac{5}{19} x^{19} d c^{4} a + \frac{10}{17} x^{17} e c^{3} a^{2} + \frac{2}{3} x^{15} d c^{3} a^{2} + \frac{10}{13} x^{13} e c^{2} a^{3} + \frac{10}{11} x^{11} d c^{2} a^{3} + \frac{5}{9} x^{9} e c a^{4} + \frac{5}{7} x^{7} d c a^{4} + \frac{1}{5} x^{5} e a^{5} + \frac{1}{3} x^{3} d a^{5}"," ",0,"1/25*x^25*e*c^5 + 1/23*x^23*d*c^5 + 5/21*x^21*e*c^4*a + 5/19*x^19*d*c^4*a + 10/17*x^17*e*c^3*a^2 + 2/3*x^15*d*c^3*a^2 + 10/13*x^13*e*c^2*a^3 + 10/11*x^11*d*c^2*a^3 + 5/9*x^9*e*c*a^4 + 5/7*x^7*d*c*a^4 + 1/5*x^5*e*a^5 + 1/3*x^3*d*a^5","A",0
3,1,124,0,0.790227," ","integrate(x*(e*x^2+d)*(c*x^4+a)^5,x, algorithm=""fricas"")","\frac{1}{24} x^{24} e c^{5} + \frac{1}{22} x^{22} d c^{5} + \frac{1}{4} x^{20} e c^{4} a + \frac{5}{18} x^{18} d c^{4} a + \frac{5}{8} x^{16} e c^{3} a^{2} + \frac{5}{7} x^{14} d c^{3} a^{2} + \frac{5}{6} x^{12} e c^{2} a^{3} + x^{10} d c^{2} a^{3} + \frac{5}{8} x^{8} e c a^{4} + \frac{5}{6} x^{6} d c a^{4} + \frac{1}{4} x^{4} e a^{5} + \frac{1}{2} x^{2} d a^{5}"," ",0,"1/24*x^24*e*c^5 + 1/22*x^22*d*c^5 + 1/4*x^20*e*c^4*a + 5/18*x^18*d*c^4*a + 5/8*x^16*e*c^3*a^2 + 5/7*x^14*d*c^3*a^2 + 5/6*x^12*e*c^2*a^3 + x^10*d*c^2*a^3 + 5/8*x^8*e*c*a^4 + 5/6*x^6*d*c*a^4 + 1/4*x^4*e*a^5 + 1/2*x^2*d*a^5","A",0
4,1,121,0,0.566597," ","integrate((e*x^2+d)*(c*x^4+a)^5,x, algorithm=""fricas"")","\frac{1}{23} x^{23} e c^{5} + \frac{1}{21} x^{21} d c^{5} + \frac{5}{19} x^{19} e c^{4} a + \frac{5}{17} x^{17} d c^{4} a + \frac{2}{3} x^{15} e c^{3} a^{2} + \frac{10}{13} x^{13} d c^{3} a^{2} + \frac{10}{11} x^{11} e c^{2} a^{3} + \frac{10}{9} x^{9} d c^{2} a^{3} + \frac{5}{7} x^{7} e c a^{4} + x^{5} d c a^{4} + \frac{1}{3} x^{3} e a^{5} + x d a^{5}"," ",0,"1/23*x^23*e*c^5 + 1/21*x^21*d*c^5 + 5/19*x^19*e*c^4*a + 5/17*x^17*d*c^4*a + 2/3*x^15*e*c^3*a^2 + 10/13*x^13*d*c^3*a^2 + 10/11*x^11*e*c^2*a^3 + 10/9*x^9*d*c^2*a^3 + 5/7*x^7*e*c*a^4 + x^5*d*c*a^4 + 1/3*x^3*e*a^5 + x*d*a^5","A",0
5,1,122,0,0.503829," ","integrate((e*x^2+d)*(c*x^4+a)^5/x,x, algorithm=""fricas"")","\frac{1}{22} \, c^{5} e x^{22} + \frac{1}{20} \, c^{5} d x^{20} + \frac{5}{18} \, a c^{4} e x^{18} + \frac{5}{16} \, a c^{4} d x^{16} + \frac{5}{7} \, a^{2} c^{3} e x^{14} + \frac{5}{6} \, a^{2} c^{3} d x^{12} + a^{3} c^{2} e x^{10} + \frac{5}{4} \, a^{3} c^{2} d x^{8} + \frac{5}{6} \, a^{4} c e x^{6} + \frac{5}{4} \, a^{4} c d x^{4} + \frac{1}{2} \, a^{5} e x^{2} + a^{5} d \log\left(x\right)"," ",0,"1/22*c^5*e*x^22 + 1/20*c^5*d*x^20 + 5/18*a*c^4*e*x^18 + 5/16*a*c^4*d*x^16 + 5/7*a^2*c^3*e*x^14 + 5/6*a^2*c^3*d*x^12 + a^3*c^2*e*x^10 + 5/4*a^3*c^2*d*x^8 + 5/6*a^4*c*e*x^6 + 5/4*a^4*c*d*x^4 + 1/2*a^5*e*x^2 + a^5*d*log(x)","A",0
6,1,127,0,0.527250," ","integrate((e*x^2+d)*(c*x^4+a)^5/x^2,x, algorithm=""fricas"")","\frac{138567 \, c^{5} e x^{22} + 153153 \, c^{5} d x^{20} + 855855 \, a c^{4} e x^{18} + 969969 \, a c^{4} d x^{16} + 2238390 \, a^{2} c^{3} e x^{14} + 2645370 \, a^{2} c^{3} d x^{12} + 3233230 \, a^{3} c^{2} e x^{10} + 4157010 \, a^{3} c^{2} d x^{8} + 2909907 \, a^{4} c e x^{6} + 4849845 \, a^{4} c d x^{4} + 2909907 \, a^{5} e x^{2} - 2909907 \, a^{5} d}{2909907 \, x}"," ",0,"1/2909907*(138567*c^5*e*x^22 + 153153*c^5*d*x^20 + 855855*a*c^4*e*x^18 + 969969*a*c^4*d*x^16 + 2238390*a^2*c^3*e*x^14 + 2645370*a^2*c^3*d*x^12 + 3233230*a^3*c^2*e*x^10 + 4157010*a^3*c^2*d*x^8 + 2909907*a^4*c*e*x^6 + 4849845*a^4*c*d*x^4 + 2909907*a^5*e*x^2 - 2909907*a^5*d)/x","A",0
7,1,129,0,0.646109," ","integrate((e*x^2+d)*(c*x^4+a)^5/x^3,x, algorithm=""fricas"")","\frac{252 \, c^{5} e x^{22} + 280 \, c^{5} d x^{20} + 1575 \, a c^{4} e x^{18} + 1800 \, a c^{4} d x^{16} + 4200 \, a^{2} c^{3} e x^{14} + 5040 \, a^{2} c^{3} d x^{12} + 6300 \, a^{3} c^{2} e x^{10} + 8400 \, a^{3} c^{2} d x^{8} + 6300 \, a^{4} c e x^{6} + 12600 \, a^{4} c d x^{4} + 5040 \, a^{5} e x^{2} \log\left(x\right) - 2520 \, a^{5} d}{5040 \, x^{2}}"," ",0,"1/5040*(252*c^5*e*x^22 + 280*c^5*d*x^20 + 1575*a*c^4*e*x^18 + 1800*a*c^4*d*x^16 + 4200*a^2*c^3*e*x^14 + 5040*a^2*c^3*d*x^12 + 6300*a^3*c^2*e*x^10 + 8400*a^3*c^2*d*x^8 + 6300*a^4*c*e*x^6 + 12600*a^4*c*d*x^4 + 5040*a^5*e*x^2*log(x) - 2520*a^5*d)/x^2","A",0
8,1,48,0,0.611452," ","integrate(x^5*(3*x^2+2)*(x^4+5)^(1/2),x, algorithm=""fricas"")","\frac{1}{40} \, {\left(12 \, x^{8} + 10 \, x^{6} + 20 \, x^{4} + 25 \, x^{2} - 200\right)} \sqrt{x^{4} + 5} + \frac{25}{8} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/40*(12*x^8 + 10*x^6 + 20*x^4 + 25*x^2 - 200)*sqrt(x^4 + 5) + 25/8*log(-x^2 + sqrt(x^4 + 5))","A",0
9,1,43,0,0.745558," ","integrate(x^3*(3*x^2+2)*(x^4+5)^(1/2),x, algorithm=""fricas"")","\frac{1}{48} \, {\left(18 \, x^{6} + 16 \, x^{4} + 45 \, x^{2} + 80\right)} \sqrt{x^{4} + 5} + \frac{75}{16} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/48*(18*x^6 + 16*x^4 + 45*x^2 + 80)*sqrt(x^4 + 5) + 75/16*log(-x^2 + sqrt(x^4 + 5))","A",0
10,1,34,0,0.638886," ","integrate(x*(3*x^2+2)*(x^4+5)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(x^{4} + x^{2} + 5\right)} \sqrt{x^{4} + 5} - \frac{5}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/2*(x^4 + x^2 + 5)*sqrt(x^4 + 5) - 5/2*log(-x^2 + sqrt(x^4 + 5))","A",0
11,1,56,0,0.629887," ","integrate((3*x^2+2)*(x^4+5)^(1/2)/x,x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{x^{4} + 5} {\left(3 \, x^{2} + 4\right)} + \sqrt{5} \log\left(-\frac{\sqrt{5} - \sqrt{x^{4} + 5}}{x^{2}}\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(-(sqrt(5) - sqrt(x^4 + 5))/x^2) - 15/4*log(-x^2 + sqrt(x^4 + 5))","A",0
12,1,72,0,0.664922," ","integrate((3*x^2+2)*(x^4+5)^(1/2)/x^3,x, algorithm=""fricas"")","\frac{3 \, \sqrt{5} x^{2} \log\left(-\frac{\sqrt{5} - \sqrt{x^{4} + 5}}{x^{2}}\right) - 2 \, x^{2} \log\left(-x^{2} + \sqrt{x^{4} + 5}\right) - 2 \, x^{2} + \sqrt{x^{4} + 5} {\left(3 \, x^{2} - 2\right)}}{2 \, x^{2}}"," ",0,"1/2*(3*sqrt(5)*x^2*log(-(sqrt(5) - sqrt(x^4 + 5))/x^2) - 2*x^2*log(-x^2 + sqrt(x^4 + 5)) - 2*x^2 + sqrt(x^4 + 5)*(3*x^2 - 2))/x^2","A",0
13,1,72,0,0.613886," ","integrate((3*x^2+2)*(x^4+5)^(1/2)/x^5,x, algorithm=""fricas"")","\frac{\sqrt{5} x^{4} \log\left(-\frac{\sqrt{5} - \sqrt{x^{4} + 5}}{x^{2}}\right) - 15 \, x^{4} \log\left(-x^{2} + \sqrt{x^{4} + 5}\right) - 15 \, x^{4} - 5 \, \sqrt{x^{4} + 5} {\left(3 \, x^{2} + 1\right)}}{10 \, x^{4}}"," ",0,"1/10*(sqrt(5)*x^4*log(-(sqrt(5) - sqrt(x^4 + 5))/x^2) - 15*x^4*log(-x^2 + sqrt(x^4 + 5)) - 15*x^4 - 5*sqrt(x^4 + 5)*(3*x^2 + 1))/x^4","A",0
14,1,59,0,0.728024," ","integrate((3*x^2+2)*(x^4+5)^(1/2)/x^7,x, algorithm=""fricas"")","\frac{9 \, \sqrt{5} x^{6} \log\left(-\frac{\sqrt{5} - \sqrt{x^{4} + 5}}{x^{2}}\right) - 4 \, x^{6} - {\left(4 \, x^{4} + 45 \, x^{2} + 20\right)} \sqrt{x^{4} + 5}}{60 \, x^{6}}"," ",0,"1/60*(9*sqrt(5)*x^6*log(-(sqrt(5) - sqrt(x^4 + 5))/x^2) - 4*x^6 - (4*x^4 + 45*x^2 + 20)*sqrt(x^4 + 5))/x^6","A",0
15,0,0,0,0.800890," ","integrate(x^4*(3*x^2+2)*(x^4+5)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(3 \, x^{6} + 2 \, x^{4}\right)} \sqrt{x^{4} + 5}, x\right)"," ",0,"integral((3*x^6 + 2*x^4)*sqrt(x^4 + 5), x)","F",0
16,0,0,0,0.689549," ","integrate(x^2*(3*x^2+2)*(x^4+5)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(3 \, x^{4} + 2 \, x^{2}\right)} \sqrt{x^{4} + 5}, x\right)"," ",0,"integral((3*x^4 + 2*x^2)*sqrt(x^4 + 5), x)","F",0
17,0,0,0,0.649154," ","integrate((3*x^2+2)*(x^4+5)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{x^{4} + 5} {\left(3 \, x^{2} + 2\right)}, x\right)"," ",0,"integral(sqrt(x^4 + 5)*(3*x^2 + 2), x)","F",0
18,0,0,0,0.656118," ","integrate((3*x^2+2)*(x^4+5)^(1/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 5} {\left(3 \, x^{2} + 2\right)}}{x^{2}}, x\right)"," ",0,"integral(sqrt(x^4 + 5)*(3*x^2 + 2)/x^2, x)","F",0
19,0,0,0,0.767596," ","integrate((3*x^2+2)*(x^4+5)^(1/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 5} {\left(3 \, x^{2} + 2\right)}}{x^{4}}, x\right)"," ",0,"integral(sqrt(x^4 + 5)*(3*x^2 + 2)/x^4, x)","F",0
20,1,58,0,0.630505," ","integrate(x^5*(3*x^2+2)*(x^4+5)^(3/2),x, algorithm=""fricas"")","\frac{1}{336} \, {\left(72 \, x^{12} + 56 \, x^{10} + 576 \, x^{8} + 490 \, x^{6} + 360 \, x^{4} + 525 \, x^{2} - 3600\right)} \sqrt{x^{4} + 5} + \frac{125}{16} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/336*(72*x^12 + 56*x^10 + 576*x^8 + 490*x^6 + 360*x^4 + 525*x^2 - 3600)*sqrt(x^4 + 5) + 125/16*log(-x^2 + sqrt(x^4 + 5))","A",0
21,1,53,0,0.648020," ","integrate(x^3*(3*x^2+2)*(x^4+5)^(3/2),x, algorithm=""fricas"")","\frac{1}{160} \, {\left(40 \, x^{10} + 32 \, x^{8} + 350 \, x^{6} + 320 \, x^{4} + 375 \, x^{2} + 800\right)} \sqrt{x^{4} + 5} + \frac{375}{32} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/160*(40*x^10 + 32*x^8 + 350*x^6 + 320*x^4 + 375*x^2 + 800)*sqrt(x^4 + 5) + 375/32*log(-x^2 + sqrt(x^4 + 5))","A",0
22,1,48,0,0.823910," ","integrate(x*(3*x^2+2)*(x^4+5)^(3/2),x, algorithm=""fricas"")","\frac{1}{40} \, {\left(12 \, x^{8} + 10 \, x^{6} + 120 \, x^{4} + 125 \, x^{2} + 300\right)} \sqrt{x^{4} + 5} - \frac{75}{8} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/40*(12*x^8 + 10*x^6 + 120*x^4 + 125*x^2 + 300)*sqrt(x^4 + 5) - 75/8*log(-x^2 + sqrt(x^4 + 5))","A",0
23,1,67,0,0.537004," ","integrate((3*x^2+2)*(x^4+5)^(3/2)/x,x, algorithm=""fricas"")","\frac{1}{48} \, {\left(18 \, x^{6} + 16 \, x^{4} + 225 \, x^{2} + 320\right)} \sqrt{x^{4} + 5} + 5 \, \sqrt{5} \log\left(-\frac{\sqrt{5} - \sqrt{x^{4} + 5}}{x^{2}}\right) - \frac{225}{16} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/48*(18*x^6 + 16*x^4 + 225*x^2 + 320)*sqrt(x^4 + 5) + 5*sqrt(5)*log(-(sqrt(5) - sqrt(x^4 + 5))/x^2) - 225/16*log(-x^2 + sqrt(x^4 + 5))","A",0
24,1,78,0,0.604362," ","integrate((3*x^2+2)*(x^4+5)^(3/2)/x^3,x, algorithm=""fricas"")","\frac{15 \, \sqrt{5} x^{2} \log\left(-\frac{\sqrt{5} - \sqrt{x^{4} + 5}}{x^{2}}\right) - 15 \, x^{2} \log\left(-x^{2} + \sqrt{x^{4} + 5}\right) - 10 \, x^{2} + {\left(x^{6} + x^{4} + 20 \, x^{2} - 10\right)} \sqrt{x^{4} + 5}}{2 \, x^{2}}"," ",0,"1/2*(15*sqrt(5)*x^2*log(-(sqrt(5) - sqrt(x^4 + 5))/x^2) - 15*x^2*log(-x^2 + sqrt(x^4 + 5)) - 10*x^2 + (x^6 + x^4 + 20*x^2 - 10)*sqrt(x^4 + 5))/x^2","A",0
25,1,82,0,0.585998," ","integrate((3*x^2+2)*(x^4+5)^(3/2)/x^5,x, algorithm=""fricas"")","\frac{6 \, \sqrt{5} x^{4} \log\left(-\frac{\sqrt{5} - \sqrt{x^{4} + 5}}{x^{2}}\right) - 45 \, x^{4} \log\left(-x^{2} + \sqrt{x^{4} + 5}\right) - 30 \, x^{4} + {\left(3 \, x^{6} + 4 \, x^{4} - 30 \, x^{2} - 10\right)} \sqrt{x^{4} + 5}}{4 \, x^{4}}"," ",0,"1/4*(6*sqrt(5)*x^4*log(-(sqrt(5) - sqrt(x^4 + 5))/x^2) - 45*x^4*log(-x^2 + sqrt(x^4 + 5)) - 30*x^4 + (3*x^6 + 4*x^4 - 30*x^2 - 10)*sqrt(x^4 + 5))/x^4","A",0
26,1,82,0,0.485551," ","integrate((3*x^2+2)*(x^4+5)^(3/2)/x^7,x, algorithm=""fricas"")","\frac{27 \, \sqrt{5} x^{6} \log\left(-\frac{\sqrt{5} - \sqrt{x^{4} + 5}}{x^{2}}\right) - 12 \, x^{6} \log\left(-x^{2} + \sqrt{x^{4} + 5}\right) - 16 \, x^{6} + {\left(18 \, x^{6} - 16 \, x^{4} - 45 \, x^{2} - 20\right)} \sqrt{x^{4} + 5}}{12 \, x^{6}}"," ",0,"1/12*(27*sqrt(5)*x^6*log(-(sqrt(5) - sqrt(x^4 + 5))/x^2) - 12*x^6*log(-x^2 + sqrt(x^4 + 5)) - 16*x^6 + (18*x^6 - 16*x^4 - 45*x^2 - 20)*sqrt(x^4 + 5))/x^6","A",0
27,0,0,0,0.711610," ","integrate(x^4*(3*x^2+2)*(x^4+5)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(3 \, x^{10} + 2 \, x^{8} + 15 \, x^{6} + 10 \, x^{4}\right)} \sqrt{x^{4} + 5}, x\right)"," ",0,"integral((3*x^10 + 2*x^8 + 15*x^6 + 10*x^4)*sqrt(x^4 + 5), x)","F",0
28,0,0,0,0.692838," ","integrate(x^2*(3*x^2+2)*(x^4+5)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(3 \, x^{8} + 2 \, x^{6} + 15 \, x^{4} + 10 \, x^{2}\right)} \sqrt{x^{4} + 5}, x\right)"," ",0,"integral((3*x^8 + 2*x^6 + 15*x^4 + 10*x^2)*sqrt(x^4 + 5), x)","F",0
29,0,0,0,0.670281," ","integrate((3*x^2+2)*(x^4+5)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(3 \, x^{6} + 2 \, x^{4} + 15 \, x^{2} + 10\right)} \sqrt{x^{4} + 5}, x\right)"," ",0,"integral((3*x^6 + 2*x^4 + 15*x^2 + 10)*sqrt(x^4 + 5), x)","F",0
30,0,0,0,0.807102," ","integrate((3*x^2+2)*(x^4+5)^(3/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x^{6} + 2 \, x^{4} + 15 \, x^{2} + 10\right)} \sqrt{x^{4} + 5}}{x^{2}}, x\right)"," ",0,"integral((3*x^6 + 2*x^4 + 15*x^2 + 10)*sqrt(x^4 + 5)/x^2, x)","F",0
31,0,0,0,0.761256," ","integrate((3*x^2+2)*(x^4+5)^(3/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x^{6} + 2 \, x^{4} + 15 \, x^{2} + 10\right)} \sqrt{x^{4} + 5}}{x^{4}}, x\right)"," ",0,"integral((3*x^6 + 2*x^4 + 15*x^2 + 10)*sqrt(x^4 + 5)/x^4, x)","F",0
32,1,43,0,0.548317," ","integrate(x^7*(3*x^2+2)/(x^4+5)^(1/2),x, algorithm=""fricas"")","\frac{1}{48} \, {\left(18 \, x^{6} + 16 \, x^{4} - 135 \, x^{2} - 160\right)} \sqrt{x^{4} + 5} - \frac{225}{16} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/48*(18*x^6 + 16*x^4 - 135*x^2 - 160)*sqrt(x^4 + 5) - 225/16*log(-x^2 + sqrt(x^4 + 5))","A",0
33,1,34,0,0.741983," ","integrate(x^5*(3*x^2+2)/(x^4+5)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(x^{4} + x^{2} - 10\right)} \sqrt{x^{4} + 5} + \frac{5}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/2*(x^4 + x^2 - 10)*sqrt(x^4 + 5) + 5/2*log(-x^2 + sqrt(x^4 + 5))","A",0
34,1,33,0,0.616023," ","integrate(x^3*(3*x^2+2)/(x^4+5)^(1/2),x, algorithm=""fricas"")","\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
35,1,26,0,0.546759," ","integrate(x*(3*x^2+2)/(x^4+5)^(1/2),x, algorithm=""fricas"")","\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
36,1,41,0,0.540067," ","integrate((3*x^2+2)/x/(x^4+5)^(1/2),x, algorithm=""fricas"")","\frac{1}{5} \, \sqrt{5} \log\left(-\frac{\sqrt{5} - \sqrt{x^{4} + 5}}{x^{2}}\right) - \frac{3}{2} \, \log\left(-x^{2} + \sqrt{x^{4} + 5}\right)"," ",0,"1/5*sqrt(5)*log(-(sqrt(5) - sqrt(x^4 + 5))/x^2) - 3/2*log(-x^2 + sqrt(x^4 + 5))","A",0
37,1,47,0,0.612101," ","integrate((3*x^2+2)/x^3/(x^4+5)^(1/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{5} x^{2} \log\left(-\frac{\sqrt{5} - \sqrt{x^{4} + 5}}{x^{2}}\right) - 2 \, x^{2} - 2 \, \sqrt{x^{4} + 5}}{10 \, x^{2}}"," ",0,"1/10*(3*sqrt(5)*x^2*log(-(sqrt(5) - sqrt(x^4 + 5))/x^2) - 2*x^2 - 2*sqrt(x^4 + 5))/x^2","A",0
38,1,50,0,0.724088," ","integrate((3*x^2+2)/x^5/(x^4+5)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{5} x^{4} \log\left(\frac{\sqrt{5} + \sqrt{x^{4} + 5}}{x^{2}}\right) - 15 \, x^{4} - 5 \, \sqrt{x^{4} + 5} {\left(3 \, x^{2} + 1\right)}}{50 \, x^{4}}"," ",0,"1/50*(sqrt(5)*x^4*log((sqrt(5) + sqrt(x^4 + 5))/x^2) - 15*x^4 - 5*sqrt(x^4 + 5)*(3*x^2 + 1))/x^4","A",0
39,0,0,0,0.741363," ","integrate(x^4*(3*x^2+2)/(x^4+5)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{3 \, x^{6} + 2 \, x^{4}}{\sqrt{x^{4} + 5}}, x\right)"," ",0,"integral((3*x^6 + 2*x^4)/sqrt(x^4 + 5), x)","F",0
40,0,0,0,0.604022," ","integrate(x^2*(3*x^2+2)/(x^4+5)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{3 \, x^{4} + 2 \, x^{2}}{\sqrt{x^{4} + 5}}, x\right)"," ",0,"integral((3*x^4 + 2*x^2)/sqrt(x^4 + 5), x)","F",0
41,0,0,0,0.666235," ","integrate((3*x^2+2)/(x^4+5)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{3 \, x^{2} + 2}{\sqrt{x^{4} + 5}}, x\right)"," ",0,"integral((3*x^2 + 2)/sqrt(x^4 + 5), x)","F",0
42,0,0,0,0.569357," ","integrate((3*x^2+2)/x^2/(x^4+5)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 5} {\left(3 \, x^{2} + 2\right)}}{x^{6} + 5 \, x^{2}}, x\right)"," ",0,"integral(sqrt(x^4 + 5)*(3*x^2 + 2)/(x^6 + 5*x^2), x)","F",0
43,0,0,0,0.590933," ","integrate((3*x^2+2)/x^4/(x^4+5)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 5} {\left(3 \, x^{2} + 2\right)}}{x^{8} + 5 \, x^{4}}, x\right)"," ",0,"integral(sqrt(x^4 + 5)*(3*x^2 + 2)/(x^8 + 5*x^4), x)","F",0
44,1,62,0,0.872705," ","integrate(x^7*(3*x^2+2)/(x^4+5)^(3/2),x, algorithm=""fricas"")","\frac{30 \, x^{4} + 45 \, {\left(x^{4} + 5\right)} \log\left(-x^{2} + \sqrt{x^{4} + 5}\right) + {\left(3 \, x^{6} + 4 \, x^{4} + 45 \, x^{2} + 40\right)} \sqrt{x^{4} + 5} + 150}{4 \, {\left(x^{4} + 5\right)}}"," ",0,"1/4*(30*x^4 + 45*(x^4 + 5)*log(-x^2 + sqrt(x^4 + 5)) + (3*x^6 + 4*x^4 + 45*x^2 + 40)*sqrt(x^4 + 5) + 150)/(x^4 + 5)","A",0
45,1,58,0,0.749629," ","integrate(x^5*(3*x^2+2)/(x^4+5)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, x^{4} + 2 \, {\left(x^{4} + 5\right)} \log\left(-x^{2} + \sqrt{x^{4} + 5}\right) - {\left(3 \, x^{4} - 2 \, x^{2} + 30\right)} \sqrt{x^{4} + 5} + 10}{2 \, {\left(x^{4} + 5\right)}}"," ",0,"-1/2*(2*x^4 + 2*(x^4 + 5)*log(-x^2 + sqrt(x^4 + 5)) - (3*x^4 - 2*x^2 + 30)*sqrt(x^4 + 5) + 10)/(x^4 + 5)","A",0
46,1,52,0,0.697233," ","integrate(x^3*(3*x^2+2)/(x^4+5)^(3/2),x, algorithm=""fricas"")","-\frac{3 \, x^{4} + 3 \, {\left(x^{4} + 5\right)} \log\left(-x^{2} + \sqrt{x^{4} + 5}\right) + \sqrt{x^{4} + 5} {\left(3 \, x^{2} + 2\right)} + 15}{2 \, {\left(x^{4} + 5\right)}}"," ",0,"-1/2*(3*x^4 + 3*(x^4 + 5)*log(-x^2 + sqrt(x^4 + 5)) + sqrt(x^4 + 5)*(3*x^2 + 2) + 15)/(x^4 + 5)","A",0
47,1,31,0,0.536476," ","integrate(x*(3*x^2+2)/(x^4+5)^(3/2),x, algorithm=""fricas"")","\frac{2 \, x^{4} + \sqrt{x^{4} + 5} {\left(2 \, x^{2} - 15\right)} + 10}{10 \, {\left(x^{4} + 5\right)}}"," ",0,"1/10*(2*x^4 + sqrt(x^4 + 5)*(2*x^2 - 15) + 10)/(x^4 + 5)","A",0
48,1,61,0,0.539892," ","integrate((3*x^2+2)/x/(x^4+5)^(3/2),x, algorithm=""fricas"")","\frac{15 \, x^{4} + 2 \, \sqrt{5} {\left(x^{4} + 5\right)} \log\left(-\frac{\sqrt{5} - \sqrt{x^{4} + 5}}{x^{2}}\right) + 5 \, \sqrt{x^{4} + 5} {\left(3 \, x^{2} + 2\right)} + 75}{50 \, {\left(x^{4} + 5\right)}}"," ",0,"1/50*(15*x^4 + 2*sqrt(5)*(x^4 + 5)*log(-(sqrt(5) - sqrt(x^4 + 5))/x^2) + 5*sqrt(x^4 + 5)*(3*x^2 + 2) + 75)/(x^4 + 5)","A",0
49,1,77,0,0.629341," ","integrate((3*x^2+2)/x^3/(x^4+5)^(3/2),x, algorithm=""fricas"")","-\frac{4 \, x^{6} - 3 \, \sqrt{5} {\left(x^{6} + 5 \, x^{2}\right)} \log\left(-\frac{\sqrt{5} - \sqrt{x^{4} + 5}}{x^{2}}\right) + 20 \, x^{2} + {\left(4 \, x^{4} - 15 \, x^{2} + 10\right)} \sqrt{x^{4} + 5}}{50 \, {\left(x^{6} + 5 \, x^{2}\right)}}"," ",0,"-1/50*(4*x^6 - 3*sqrt(5)*(x^6 + 5*x^2)*log(-(sqrt(5) - sqrt(x^4 + 5))/x^2) + 20*x^2 + (4*x^4 - 15*x^2 + 10)*sqrt(x^4 + 5))/(x^6 + 5*x^2)","A",0
50,0,0,0,0.572620," ","integrate(x^4*(3*x^2+2)/(x^4+5)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x^{6} + 2 \, x^{4}\right)} \sqrt{x^{4} + 5}}{x^{8} + 10 \, x^{4} + 25}, x\right)"," ",0,"integral((3*x^6 + 2*x^4)*sqrt(x^4 + 5)/(x^8 + 10*x^4 + 25), x)","F",0
51,0,0,0,0.740691," ","integrate(x^2*(3*x^2+2)/(x^4+5)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x^{4} + 2 \, x^{2}\right)} \sqrt{x^{4} + 5}}{x^{8} + 10 \, x^{4} + 25}, x\right)"," ",0,"integral((3*x^4 + 2*x^2)*sqrt(x^4 + 5)/(x^8 + 10*x^4 + 25), x)","F",0
52,0,0,0,0.521614," ","integrate((3*x^2+2)/(x^4+5)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 5} {\left(3 \, x^{2} + 2\right)}}{x^{8} + 10 \, x^{4} + 25}, x\right)"," ",0,"integral(sqrt(x^4 + 5)*(3*x^2 + 2)/(x^8 + 10*x^4 + 25), x)","F",0
53,0,0,0,0.736769," ","integrate((3*x^2+2)/x^2/(x^4+5)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 5} {\left(3 \, x^{2} + 2\right)}}{x^{10} + 10 \, x^{6} + 25 \, x^{2}}, x\right)"," ",0,"integral(sqrt(x^4 + 5)*(3*x^2 + 2)/(x^10 + 10*x^6 + 25*x^2), x)","F",0
54,0,0,0,0.872560," ","integrate((3*x^2+2)/x^4/(x^4+5)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 5} {\left(3 \, x^{2} + 2\right)}}{x^{12} + 10 \, x^{8} + 25 \, x^{4}}, x\right)"," ",0,"integral(sqrt(x^4 + 5)*(3*x^2 + 2)/(x^12 + 10*x^8 + 25*x^4), x)","F",0
55,1,1571,0,0.819232," ","integrate((f*x)^m*(e*x^2+d)*(x^4+2*x^2+1)^5,x, algorithm=""fricas"")","\frac{{\left({\left(e m^{11} + 121 \, e m^{10} + 6435 \, e m^{9} + 197835 \, e m^{8} + 3889578 \, e m^{7} + 51069018 \, e m^{6} + 453714470 \, e m^{5} + 2702025590 \, e m^{4} + 10431670821 \, e m^{3} + 24372200061 \, e m^{2} + 29985521895 \, e m + 13749310575 \, e\right)} x^{23} + {\left({\left(d + 10 \, e\right)} m^{11} + 123 \, {\left(d + 10 \, e\right)} m^{10} + 6635 \, {\left(d + 10 \, e\right)} m^{9} + 206505 \, {\left(d + 10 \, e\right)} m^{8} + 4103178 \, {\left(d + 10 \, e\right)} m^{7} + 54362574 \, {\left(d + 10 \, e\right)} m^{6} + 486687830 \, {\left(d + 10 \, e\right)} m^{5} + 2917013970 \, {\left(d + 10 \, e\right)} m^{4} + 11320966021 \, {\left(d + 10 \, e\right)} m^{3} + 26560342503 \, {\left(d + 10 \, e\right)} m^{2} + 32778930735 \, {\left(d + 10 \, e\right)} m + 15058768725 \, d + 150587687250 \, e\right)} x^{21} + 5 \, {\left({\left(2 \, d + 9 \, e\right)} m^{11} + 125 \, {\left(2 \, d + 9 \, e\right)} m^{10} + 6843 \, {\left(2 \, d + 9 \, e\right)} m^{9} + 215823 \, {\left(2 \, d + 9 \, e\right)} m^{8} + 4339146 \, {\left(2 \, d + 9 \, e\right)} m^{7} + 58085538 \, {\left(2 \, d + 9 \, e\right)} m^{6} + 524676662 \, {\left(2 \, d + 9 \, e\right)} m^{5} + 3168601822 \, {\left(2 \, d + 9 \, e\right)} m^{4} + 12374824773 \, {\left(2 \, d + 9 \, e\right)} m^{3} + 29178958257 \, {\left(2 \, d + 9 \, e\right)} m^{2} + 36145916415 \, {\left(2 \, d + 9 \, e\right)} m + 33287804550 \, d + 149795120475 \, e\right)} x^{19} + 15 \, {\left({\left(3 \, d + 8 \, e\right)} m^{11} + 127 \, {\left(3 \, d + 8 \, e\right)} m^{10} + 7059 \, {\left(3 \, d + 8 \, e\right)} m^{9} + 225837 \, {\left(3 \, d + 8 \, e\right)} m^{8} + 4600554 \, {\left(3 \, d + 8 \, e\right)} m^{7} + 62319894 \, {\left(3 \, d + 8 \, e\right)} m^{6} + 568863686 \, {\left(3 \, d + 8 \, e\right)} m^{5} + 3466775738 \, {\left(3 \, d + 8 \, e\right)} m^{4} + 13643071845 \, {\left(3 \, d + 8 \, e\right)} m^{3} + 32368407579 \, {\left(3 \, d + 8 \, e\right)} m^{2} + 40283194455 \, {\left(3 \, d + 8 \, e\right)} m + 55806025275 \, d + 148816067400 \, e\right)} x^{17} + 30 \, {\left({\left(4 \, d + 7 \, e\right)} m^{11} + 129 \, {\left(4 \, d + 7 \, e\right)} m^{10} + 7283 \, {\left(4 \, d + 7 \, e\right)} m^{9} + 236595 \, {\left(4 \, d + 7 \, e\right)} m^{8} + 4890858 \, {\left(4 \, d + 7 \, e\right)} m^{7} + 67166442 \, {\left(4 \, d + 7 \, e\right)} m^{6} + 620805254 \, {\left(4 \, d + 7 \, e\right)} m^{5} + 3825379590 \, {\left(4 \, d + 7 \, e\right)} m^{4} + 15197565541 \, {\left(4 \, d + 7 \, e\right)} m^{3} + 36337145829 \, {\left(4 \, d + 7 \, e\right)} m^{2} + 45488935863 \, {\left(4 \, d + 7 \, e\right)} m + 84329104860 \, d + 147575933505 \, e\right)} x^{15} + 42 \, {\left({\left(5 \, d + 6 \, e\right)} m^{11} + 131 \, {\left(5 \, d + 6 \, e\right)} m^{10} + 7515 \, {\left(5 \, d + 6 \, e\right)} m^{9} + 248145 \, {\left(5 \, d + 6 \, e\right)} m^{8} + 5213898 \, {\left(5 \, d + 6 \, e\right)} m^{7} + 72748638 \, {\left(5 \, d + 6 \, e\right)} m^{6} + 682569590 \, {\left(5 \, d + 6 \, e\right)} m^{5} + 4264053730 \, {\left(5 \, d + 6 \, e\right)} m^{4} + 17145560901 \, {\left(5 \, d + 6 \, e\right)} m^{3} + 41408337231 \, {\left(5 \, d + 6 \, e\right)} m^{2} + 52237739295 \, {\left(5 \, d + 6 \, e\right)} m + 121628516625 \, d + 145954219950 \, e\right)} x^{13} + 42 \, {\left({\left(6 \, d + 5 \, e\right)} m^{11} + 133 \, {\left(6 \, d + 5 \, e\right)} m^{10} + 7755 \, {\left(6 \, d + 5 \, e\right)} m^{9} + 260535 \, {\left(6 \, d + 5 \, e\right)} m^{8} + 5573898 \, {\left(6 \, d + 5 \, e\right)} m^{7} + 79216434 \, {\left(6 \, d + 5 \, e\right)} m^{6} + 756921110 \, {\left(6 \, d + 5 \, e\right)} m^{5} + 4811326190 \, {\left(6 \, d + 5 \, e\right)} m^{4} + 19653671301 \, {\left(6 \, d + 5 \, e\right)} m^{3} + 48110244633 \, {\left(6 \, d + 5 \, e\right)} m^{2} + 61333432335 \, {\left(6 \, d + 5 \, e\right)} m + 172491350850 \, d + 143742792375 \, e\right)} x^{11} + 30 \, {\left({\left(7 \, d + 4 \, e\right)} m^{11} + 135 \, {\left(7 \, d + 4 \, e\right)} m^{10} + 8003 \, {\left(7 \, d + 4 \, e\right)} m^{9} + 273813 \, {\left(7 \, d + 4 \, e\right)} m^{8} + 5975466 \, {\left(7 \, d + 4 \, e\right)} m^{7} + 86750118 \, {\left(7 \, d + 4 \, e\right)} m^{6} + 847550822 \, {\left(7 \, d + 4 \, e\right)} m^{5} + 5509501002 \, {\left(7 \, d + 4 \, e\right)} m^{4} + 22992750373 \, {\left(7 \, d + 4 \, e\right)} m^{3} + 57365875587 \, {\left(7 \, d + 4 \, e\right)} m^{2} + 74253243015 \, {\left(7 \, d + 4 \, e\right)} m + 245959889175 \, d + 140548508100 \, e\right)} x^{9} + 15 \, {\left({\left(8 \, d + 3 \, e\right)} m^{11} + 137 \, {\left(8 \, d + 3 \, e\right)} m^{10} + 8259 \, {\left(8 \, d + 3 \, e\right)} m^{9} + 288027 \, {\left(8 \, d + 3 \, e\right)} m^{8} + 6423594 \, {\left(8 \, d + 3 \, e\right)} m^{7} + 95564154 \, {\left(8 \, d + 3 \, e\right)} m^{6} + 959352806 \, {\left(8 \, d + 3 \, e\right)} m^{5} + 6421988758 \, {\left(8 \, d + 3 \, e\right)} m^{4} + 27624338085 \, {\left(8 \, d + 3 \, e\right)} m^{3} + 70930262349 \, {\left(8 \, d + 3 \, e\right)} m^{2} + 94034286855 \, {\left(8 \, d + 3 \, e\right)} m + 361410449400 \, d + 135528918525 \, e\right)} x^{7} + 5 \, {\left({\left(9 \, d + 2 \, e\right)} m^{11} + 139 \, {\left(9 \, d + 2 \, e\right)} m^{10} + 8523 \, {\left(9 \, d + 2 \, e\right)} m^{9} + 303225 \, {\left(9 \, d + 2 \, e\right)} m^{8} + 6923658 \, {\left(9 \, d + 2 \, e\right)} m^{7} + 105911022 \, {\left(9 \, d + 2 \, e\right)} m^{6} + 1098746774 \, {\left(9 \, d + 2 \, e\right)} m^{5} + 7643724530 \, {\left(9 \, d + 2 \, e\right)} m^{4} + 34359636741 \, {\left(9 \, d + 2 \, e\right)} m^{3} + 92502445239 \, {\left(9 \, d + 2 \, e\right)} m^{2} + 128033897103 \, {\left(9 \, d + 2 \, e\right)} m + 569221457805 \, d + 126493657290 \, e\right)} x^{5} + {\left({\left(10 \, d + e\right)} m^{11} + 141 \, {\left(10 \, d + e\right)} m^{10} + 8795 \, {\left(10 \, d + e\right)} m^{9} + 319455 \, {\left(10 \, d + e\right)} m^{8} + 7481418 \, {\left(10 \, d + e\right)} m^{7} + 118085058 \, {\left(10 \, d + e\right)} m^{6} + 1274046710 \, {\left(10 \, d + e\right)} m^{5} + 9315318270 \, {\left(10 \, d + e\right)} m^{4} + 44632304581 \, {\left(10 \, d + e\right)} m^{3} + 130403715201 \, {\left(10 \, d + e\right)} m^{2} + 199334977695 \, {\left(10 \, d + e\right)} m + 1054113810750 \, d + 105411381075 \, e\right)} x^{3} + {\left(d m^{11} + 143 \, d m^{10} + 9075 \, d m^{9} + 336765 \, d m^{8} + 8103018 \, d m^{7} + 132426294 \, d m^{6} + 1495875590 \, d m^{5} + 11641582810 \, d m^{4} + 60936676581 \, d m^{3} + 203363952363 \, d m^{2} + 387182170935 \, d m + 316234143225 \, d\right)} x\right)} \left(f x\right)^{m}}{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,"((e*m^11 + 121*e*m^10 + 6435*e*m^9 + 197835*e*m^8 + 3889578*e*m^7 + 51069018*e*m^6 + 453714470*e*m^5 + 2702025590*e*m^4 + 10431670821*e*m^3 + 24372200061*e*m^2 + 29985521895*e*m + 13749310575*e)*x^23 + ((d + 10*e)*m^11 + 123*(d + 10*e)*m^10 + 6635*(d + 10*e)*m^9 + 206505*(d + 10*e)*m^8 + 4103178*(d + 10*e)*m^7 + 54362574*(d + 10*e)*m^6 + 486687830*(d + 10*e)*m^5 + 2917013970*(d + 10*e)*m^4 + 11320966021*(d + 10*e)*m^3 + 26560342503*(d + 10*e)*m^2 + 32778930735*(d + 10*e)*m + 15058768725*d + 150587687250*e)*x^21 + 5*((2*d + 9*e)*m^11 + 125*(2*d + 9*e)*m^10 + 6843*(2*d + 9*e)*m^9 + 215823*(2*d + 9*e)*m^8 + 4339146*(2*d + 9*e)*m^7 + 58085538*(2*d + 9*e)*m^6 + 524676662*(2*d + 9*e)*m^5 + 3168601822*(2*d + 9*e)*m^4 + 12374824773*(2*d + 9*e)*m^3 + 29178958257*(2*d + 9*e)*m^2 + 36145916415*(2*d + 9*e)*m + 33287804550*d + 149795120475*e)*x^19 + 15*((3*d + 8*e)*m^11 + 127*(3*d + 8*e)*m^10 + 7059*(3*d + 8*e)*m^9 + 225837*(3*d + 8*e)*m^8 + 4600554*(3*d + 8*e)*m^7 + 62319894*(3*d + 8*e)*m^6 + 568863686*(3*d + 8*e)*m^5 + 3466775738*(3*d + 8*e)*m^4 + 13643071845*(3*d + 8*e)*m^3 + 32368407579*(3*d + 8*e)*m^2 + 40283194455*(3*d + 8*e)*m + 55806025275*d + 148816067400*e)*x^17 + 30*((4*d + 7*e)*m^11 + 129*(4*d + 7*e)*m^10 + 7283*(4*d + 7*e)*m^9 + 236595*(4*d + 7*e)*m^8 + 4890858*(4*d + 7*e)*m^7 + 67166442*(4*d + 7*e)*m^6 + 620805254*(4*d + 7*e)*m^5 + 3825379590*(4*d + 7*e)*m^4 + 15197565541*(4*d + 7*e)*m^3 + 36337145829*(4*d + 7*e)*m^2 + 45488935863*(4*d + 7*e)*m + 84329104860*d + 147575933505*e)*x^15 + 42*((5*d + 6*e)*m^11 + 131*(5*d + 6*e)*m^10 + 7515*(5*d + 6*e)*m^9 + 248145*(5*d + 6*e)*m^8 + 5213898*(5*d + 6*e)*m^7 + 72748638*(5*d + 6*e)*m^6 + 682569590*(5*d + 6*e)*m^5 + 4264053730*(5*d + 6*e)*m^4 + 17145560901*(5*d + 6*e)*m^3 + 41408337231*(5*d + 6*e)*m^2 + 52237739295*(5*d + 6*e)*m + 121628516625*d + 145954219950*e)*x^13 + 42*((6*d + 5*e)*m^11 + 133*(6*d + 5*e)*m^10 + 7755*(6*d + 5*e)*m^9 + 260535*(6*d + 5*e)*m^8 + 5573898*(6*d + 5*e)*m^7 + 79216434*(6*d + 5*e)*m^6 + 756921110*(6*d + 5*e)*m^5 + 4811326190*(6*d + 5*e)*m^4 + 19653671301*(6*d + 5*e)*m^3 + 48110244633*(6*d + 5*e)*m^2 + 61333432335*(6*d + 5*e)*m + 172491350850*d + 143742792375*e)*x^11 + 30*((7*d + 4*e)*m^11 + 135*(7*d + 4*e)*m^10 + 8003*(7*d + 4*e)*m^9 + 273813*(7*d + 4*e)*m^8 + 5975466*(7*d + 4*e)*m^7 + 86750118*(7*d + 4*e)*m^6 + 847550822*(7*d + 4*e)*m^5 + 5509501002*(7*d + 4*e)*m^4 + 22992750373*(7*d + 4*e)*m^3 + 57365875587*(7*d + 4*e)*m^2 + 74253243015*(7*d + 4*e)*m + 245959889175*d + 140548508100*e)*x^9 + 15*((8*d + 3*e)*m^11 + 137*(8*d + 3*e)*m^10 + 8259*(8*d + 3*e)*m^9 + 288027*(8*d + 3*e)*m^8 + 6423594*(8*d + 3*e)*m^7 + 95564154*(8*d + 3*e)*m^6 + 959352806*(8*d + 3*e)*m^5 + 6421988758*(8*d + 3*e)*m^4 + 27624338085*(8*d + 3*e)*m^3 + 70930262349*(8*d + 3*e)*m^2 + 94034286855*(8*d + 3*e)*m + 361410449400*d + 135528918525*e)*x^7 + 5*((9*d + 2*e)*m^11 + 139*(9*d + 2*e)*m^10 + 8523*(9*d + 2*e)*m^9 + 303225*(9*d + 2*e)*m^8 + 6923658*(9*d + 2*e)*m^7 + 105911022*(9*d + 2*e)*m^6 + 1098746774*(9*d + 2*e)*m^5 + 7643724530*(9*d + 2*e)*m^4 + 34359636741*(9*d + 2*e)*m^3 + 92502445239*(9*d + 2*e)*m^2 + 128033897103*(9*d + 2*e)*m + 569221457805*d + 126493657290*e)*x^5 + ((10*d + e)*m^11 + 141*(10*d + e)*m^10 + 8795*(10*d + e)*m^9 + 319455*(10*d + e)*m^8 + 7481418*(10*d + e)*m^7 + 118085058*(10*d + e)*m^6 + 1274046710*(10*d + e)*m^5 + 9315318270*(10*d + e)*m^4 + 44632304581*(10*d + e)*m^3 + 130403715201*(10*d + e)*m^2 + 199334977695*(10*d + e)*m + 1054113810750*d + 105411381075*e)*x^3 + (d*m^11 + 143*d*m^10 + 9075*d*m^9 + 336765*d*m^8 + 8103018*d*m^7 + 132426294*d*m^6 + 1495875590*d*m^5 + 11641582810*d*m^4 + 60936676581*d*m^3 + 203363952363*d*m^2 + 387182170935*d*m + 316234143225*d)*x)*(f*x)^m/(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
56,1,132,0,0.505658," ","integrate(x^5*(e*x^2+d)*(x^4+2*x^2+1)^5,x, algorithm=""fricas"")","\frac{1}{28} x^{28} e + \frac{5}{13} x^{26} e + \frac{1}{26} x^{26} d + \frac{15}{8} x^{24} e + \frac{5}{12} x^{24} d + \frac{60}{11} x^{22} e + \frac{45}{22} x^{22} d + \frac{21}{2} x^{20} e + 6 x^{20} d + 14 x^{18} e + \frac{35}{3} x^{18} d + \frac{105}{8} x^{16} e + \frac{63}{4} x^{16} d + \frac{60}{7} x^{14} e + 15 x^{14} d + \frac{15}{4} x^{12} e + 10 x^{12} d + x^{10} e + \frac{9}{2} x^{10} d + \frac{1}{8} x^{8} e + \frac{5}{4} x^{8} d + \frac{1}{6} x^{6} d"," ",0,"1/28*x^28*e + 5/13*x^26*e + 1/26*x^26*d + 15/8*x^24*e + 5/12*x^24*d + 60/11*x^22*e + 45/22*x^22*d + 21/2*x^20*e + 6*x^20*d + 14*x^18*e + 35/3*x^18*d + 105/8*x^16*e + 63/4*x^16*d + 60/7*x^14*e + 15*x^14*d + 15/4*x^12*e + 10*x^12*d + x^10*e + 9/2*x^10*d + 1/8*x^8*e + 5/4*x^8*d + 1/6*x^6*d","B",0
57,1,133,0,0.865179," ","integrate(x^4*(e*x^2+d)*(x^4+2*x^2+1)^5,x, algorithm=""fricas"")","\frac{1}{27} x^{27} e + \frac{2}{5} x^{25} e + \frac{1}{25} x^{25} d + \frac{45}{23} x^{23} e + \frac{10}{23} x^{23} d + \frac{40}{7} x^{21} e + \frac{15}{7} x^{21} d + \frac{210}{19} x^{19} e + \frac{120}{19} x^{19} d + \frac{252}{17} x^{17} e + \frac{210}{17} x^{17} d + 14 x^{15} e + \frac{84}{5} x^{15} d + \frac{120}{13} x^{13} e + \frac{210}{13} x^{13} d + \frac{45}{11} x^{11} e + \frac{120}{11} x^{11} d + \frac{10}{9} x^{9} e + 5 x^{9} d + \frac{1}{7} x^{7} e + \frac{10}{7} x^{7} d + \frac{1}{5} x^{5} d"," ",0,"1/27*x^27*e + 2/5*x^25*e + 1/25*x^25*d + 45/23*x^23*e + 10/23*x^23*d + 40/7*x^21*e + 15/7*x^21*d + 210/19*x^19*e + 120/19*x^19*d + 252/17*x^17*e + 210/17*x^17*d + 14*x^15*e + 84/5*x^15*d + 120/13*x^13*e + 210/13*x^13*d + 45/11*x^11*e + 120/11*x^11*d + 10/9*x^9*e + 5*x^9*d + 1/7*x^7*e + 10/7*x^7*d + 1/5*x^5*d","A",0
58,1,133,0,0.482168," ","integrate(x^3*(e*x^2+d)*(x^4+2*x^2+1)^5,x, algorithm=""fricas"")","\frac{1}{26} x^{26} e + \frac{5}{12} x^{24} e + \frac{1}{24} x^{24} d + \frac{45}{22} x^{22} e + \frac{5}{11} x^{22} d + 6 x^{20} e + \frac{9}{4} x^{20} d + \frac{35}{3} x^{18} e + \frac{20}{3} x^{18} d + \frac{63}{4} x^{16} e + \frac{105}{8} x^{16} d + 15 x^{14} e + 18 x^{14} d + 10 x^{12} e + \frac{35}{2} x^{12} d + \frac{9}{2} x^{10} e + 12 x^{10} d + \frac{5}{4} x^{8} e + \frac{45}{8} x^{8} d + \frac{1}{6} x^{6} e + \frac{5}{3} x^{6} d + \frac{1}{4} x^{4} d"," ",0,"1/26*x^26*e + 5/12*x^24*e + 1/24*x^24*d + 45/22*x^22*e + 5/11*x^22*d + 6*x^20*e + 9/4*x^20*d + 35/3*x^18*e + 20/3*x^18*d + 63/4*x^16*e + 105/8*x^16*d + 15*x^14*e + 18*x^14*d + 10*x^12*e + 35/2*x^12*d + 9/2*x^10*e + 12*x^10*d + 5/4*x^8*e + 45/8*x^8*d + 1/6*x^6*e + 5/3*x^6*d + 1/4*x^4*d","B",0
59,1,133,0,0.812565," ","integrate(x^2*(e*x^2+d)*(x^4+2*x^2+1)^5,x, algorithm=""fricas"")","\frac{1}{25} x^{25} e + \frac{10}{23} x^{23} e + \frac{1}{23} x^{23} d + \frac{15}{7} x^{21} e + \frac{10}{21} x^{21} d + \frac{120}{19} x^{19} e + \frac{45}{19} x^{19} d + \frac{210}{17} x^{17} e + \frac{120}{17} x^{17} d + \frac{84}{5} x^{15} e + 14 x^{15} d + \frac{210}{13} x^{13} e + \frac{252}{13} x^{13} d + \frac{120}{11} x^{11} e + \frac{210}{11} x^{11} d + 5 x^{9} e + \frac{40}{3} x^{9} d + \frac{10}{7} x^{7} e + \frac{45}{7} x^{7} d + \frac{1}{5} x^{5} e + 2 x^{5} d + \frac{1}{3} x^{3} d"," ",0,"1/25*x^25*e + 10/23*x^23*e + 1/23*x^23*d + 15/7*x^21*e + 10/21*x^21*d + 120/19*x^19*e + 45/19*x^19*d + 210/17*x^17*e + 120/17*x^17*d + 84/5*x^15*e + 14*x^15*d + 210/13*x^13*e + 252/13*x^13*d + 120/11*x^11*e + 210/11*x^11*d + 5*x^9*e + 40/3*x^9*d + 10/7*x^7*e + 45/7*x^7*d + 1/5*x^5*e + 2*x^5*d + 1/3*x^3*d","A",0
60,1,133,0,0.836111," ","integrate(x*(e*x^2+d)*(x^4+2*x^2+1)^5,x, algorithm=""fricas"")","\frac{1}{24} x^{24} e + \frac{5}{11} x^{22} e + \frac{1}{22} x^{22} d + \frac{9}{4} x^{20} e + \frac{1}{2} x^{20} d + \frac{20}{3} x^{18} e + \frac{5}{2} x^{18} d + \frac{105}{8} x^{16} e + \frac{15}{2} x^{16} d + 18 x^{14} e + 15 x^{14} d + \frac{35}{2} x^{12} e + 21 x^{12} d + 12 x^{10} e + 21 x^{10} d + \frac{45}{8} x^{8} e + 15 x^{8} d + \frac{5}{3} x^{6} e + \frac{15}{2} x^{6} d + \frac{1}{4} x^{4} e + \frac{5}{2} x^{4} d + \frac{1}{2} x^{2} d"," ",0,"1/24*x^24*e + 5/11*x^22*e + 1/22*x^22*d + 9/4*x^20*e + 1/2*x^20*d + 20/3*x^18*e + 5/2*x^18*d + 105/8*x^16*e + 15/2*x^16*d + 18*x^14*e + 15*x^14*d + 35/2*x^12*e + 21*x^12*d + 12*x^10*e + 21*x^10*d + 45/8*x^8*e + 15*x^8*d + 5/3*x^6*e + 15/2*x^6*d + 1/4*x^4*e + 5/2*x^4*d + 1/2*x^2*d","B",0
61,1,130,0,0.564331," ","integrate((e*x^2+d)*(x^4+2*x^2+1)^5,x, algorithm=""fricas"")","\frac{1}{23} x^{23} e + \frac{10}{21} x^{21} e + \frac{1}{21} x^{21} d + \frac{45}{19} x^{19} e + \frac{10}{19} x^{19} d + \frac{120}{17} x^{17} e + \frac{45}{17} x^{17} d + 14 x^{15} e + 8 x^{15} d + \frac{252}{13} x^{13} e + \frac{210}{13} x^{13} d + \frac{210}{11} x^{11} e + \frac{252}{11} x^{11} d + \frac{40}{3} x^{9} e + \frac{70}{3} x^{9} d + \frac{45}{7} x^{7} e + \frac{120}{7} x^{7} d + 2 x^{5} e + 9 x^{5} d + \frac{1}{3} x^{3} e + \frac{10}{3} x^{3} d + x d"," ",0,"1/23*x^23*e + 10/21*x^21*e + 1/21*x^21*d + 45/19*x^19*e + 10/19*x^19*d + 120/17*x^17*e + 45/17*x^17*d + 14*x^15*e + 8*x^15*d + 252/13*x^13*e + 210/13*x^13*d + 210/11*x^11*e + 252/11*x^11*d + 40/3*x^9*e + 70/3*x^9*d + 45/7*x^7*e + 120/7*x^7*d + 2*x^5*e + 9*x^5*d + 1/3*x^3*e + 10/3*x^3*d + x*d","A",0
62,1,127,0,0.758147," ","integrate((e*x^2+d)*(x^4+2*x^2+1)^5/x,x, algorithm=""fricas"")","\frac{1}{22} \, e x^{22} + \frac{1}{20} \, {\left(d + 10 \, e\right)} x^{20} + \frac{5}{18} \, {\left(2 \, d + 9 \, e\right)} x^{18} + \frac{15}{16} \, {\left(3 \, d + 8 \, e\right)} x^{16} + \frac{15}{7} \, {\left(4 \, d + 7 \, e\right)} x^{14} + \frac{7}{2} \, {\left(5 \, d + 6 \, e\right)} x^{12} + \frac{21}{5} \, {\left(6 \, d + 5 \, e\right)} x^{10} + \frac{15}{4} \, {\left(7 \, d + 4 \, e\right)} x^{8} + \frac{5}{2} \, {\left(8 \, d + 3 \, e\right)} x^{6} + \frac{5}{4} \, {\left(9 \, d + 2 \, e\right)} x^{4} + \frac{1}{2} \, {\left(10 \, d + e\right)} x^{2} + d \log\left(x\right)"," ",0,"1/22*e*x^22 + 1/20*(d + 10*e)*x^20 + 5/18*(2*d + 9*e)*x^18 + 15/16*(3*d + 8*e)*x^16 + 15/7*(4*d + 7*e)*x^14 + 7/2*(5*d + 6*e)*x^12 + 21/5*(6*d + 5*e)*x^10 + 15/4*(7*d + 4*e)*x^8 + 5/2*(8*d + 3*e)*x^6 + 5/4*(9*d + 2*e)*x^4 + 1/2*(10*d + e)*x^2 + d*log(x)","A",0
63,1,131,0,0.880405," ","integrate((e*x^2+d)*(x^4+2*x^2+1)^5/x^2,x, algorithm=""fricas"")","\frac{46189 \, e x^{22} + 51051 \, {\left(d + 10 \, e\right)} x^{20} + 285285 \, {\left(2 \, d + 9 \, e\right)} x^{18} + 969969 \, {\left(3 \, d + 8 \, e\right)} x^{16} + 2238390 \, {\left(4 \, d + 7 \, e\right)} x^{14} + 3703518 \, {\left(5 \, d + 6 \, e\right)} x^{12} + 4526522 \, {\left(6 \, d + 5 \, e\right)} x^{10} + 4157010 \, {\left(7 \, d + 4 \, e\right)} x^{8} + 2909907 \, {\left(8 \, d + 3 \, e\right)} x^{6} + 1616615 \, {\left(9 \, d + 2 \, e\right)} x^{4} + 969969 \, {\left(10 \, d + e\right)} x^{2} - 969969 \, d}{969969 \, x}"," ",0,"1/969969*(46189*e*x^22 + 51051*(d + 10*e)*x^20 + 285285*(2*d + 9*e)*x^18 + 969969*(3*d + 8*e)*x^16 + 2238390*(4*d + 7*e)*x^14 + 3703518*(5*d + 6*e)*x^12 + 4526522*(6*d + 5*e)*x^10 + 4157010*(7*d + 4*e)*x^8 + 2909907*(8*d + 3*e)*x^6 + 1616615*(9*d + 2*e)*x^4 + 969969*(10*d + e)*x^2 - 969969*d)/x","A",0
64,1,133,0,0.783689," ","integrate((e*x^2+d)*(x^4+2*x^2+1)^5/x^3,x, algorithm=""fricas"")","\frac{252 \, e x^{22} + 280 \, {\left(d + 10 \, e\right)} x^{20} + 1575 \, {\left(2 \, d + 9 \, e\right)} x^{18} + 5400 \, {\left(3 \, d + 8 \, e\right)} x^{16} + 12600 \, {\left(4 \, d + 7 \, e\right)} x^{14} + 21168 \, {\left(5 \, d + 6 \, e\right)} x^{12} + 26460 \, {\left(6 \, d + 5 \, e\right)} x^{10} + 25200 \, {\left(7 \, d + 4 \, e\right)} x^{8} + 18900 \, {\left(8 \, d + 3 \, e\right)} x^{6} + 12600 \, {\left(9 \, d + 2 \, e\right)} x^{4} + 5040 \, {\left(10 \, d + e\right)} x^{2} \log\left(x\right) - 2520 \, d}{5040 \, x^{2}}"," ",0,"1/5040*(252*e*x^22 + 280*(d + 10*e)*x^20 + 1575*(2*d + 9*e)*x^18 + 5400*(3*d + 8*e)*x^16 + 12600*(4*d + 7*e)*x^14 + 21168*(5*d + 6*e)*x^12 + 26460*(6*d + 5*e)*x^10 + 25200*(7*d + 4*e)*x^8 + 18900*(8*d + 3*e)*x^6 + 12600*(9*d + 2*e)*x^4 + 5040*(10*d + e)*x^2*log(x) - 2520*d)/x^2","A",0
65,1,759,0,0.819300," ","integrate((f*x)^m*(x^2+1)*(x^4+2*x^2+1)^5,x, algorithm=""fricas"")","\frac{{\left({\left(m^{11} + 121 \, m^{10} + 6435 \, m^{9} + 197835 \, m^{8} + 3889578 \, m^{7} + 51069018 \, m^{6} + 453714470 \, m^{5} + 2702025590 \, m^{4} + 10431670821 \, m^{3} + 24372200061 \, m^{2} + 29985521895 \, m + 13749310575\right)} x^{23} + 11 \, {\left(m^{11} + 123 \, m^{10} + 6635 \, m^{9} + 206505 \, m^{8} + 4103178 \, m^{7} + 54362574 \, m^{6} + 486687830 \, m^{5} + 2917013970 \, m^{4} + 11320966021 \, m^{3} + 26560342503 \, m^{2} + 32778930735 \, m + 15058768725\right)} x^{21} + 55 \, {\left(m^{11} + 125 \, m^{10} + 6843 \, m^{9} + 215823 \, m^{8} + 4339146 \, m^{7} + 58085538 \, m^{6} + 524676662 \, m^{5} + 3168601822 \, m^{4} + 12374824773 \, m^{3} + 29178958257 \, m^{2} + 36145916415 \, m + 16643902275\right)} x^{19} + 165 \, {\left(m^{11} + 127 \, m^{10} + 7059 \, m^{9} + 225837 \, m^{8} + 4600554 \, m^{7} + 62319894 \, m^{6} + 568863686 \, m^{5} + 3466775738 \, m^{4} + 13643071845 \, m^{3} + 32368407579 \, m^{2} + 40283194455 \, m + 18602008425\right)} x^{17} + 330 \, {\left(m^{11} + 129 \, m^{10} + 7283 \, m^{9} + 236595 \, m^{8} + 4890858 \, m^{7} + 67166442 \, m^{6} + 620805254 \, m^{5} + 3825379590 \, m^{4} + 15197565541 \, m^{3} + 36337145829 \, m^{2} + 45488935863 \, m + 21082276215\right)} x^{15} + 462 \, {\left(m^{11} + 131 \, m^{10} + 7515 \, m^{9} + 248145 \, m^{8} + 5213898 \, m^{7} + 72748638 \, m^{6} + 682569590 \, m^{5} + 4264053730 \, m^{4} + 17145560901 \, m^{3} + 41408337231 \, m^{2} + 52237739295 \, m + 24325703325\right)} x^{13} + 462 \, {\left(m^{11} + 133 \, m^{10} + 7755 \, m^{9} + 260535 \, m^{8} + 5573898 \, m^{7} + 79216434 \, m^{6} + 756921110 \, m^{5} + 4811326190 \, m^{4} + 19653671301 \, m^{3} + 48110244633 \, m^{2} + 61333432335 \, m + 28748558475\right)} x^{11} + 330 \, {\left(m^{11} + 135 \, m^{10} + 8003 \, m^{9} + 273813 \, m^{8} + 5975466 \, m^{7} + 86750118 \, m^{6} + 847550822 \, m^{5} + 5509501002 \, m^{4} + 22992750373 \, m^{3} + 57365875587 \, m^{2} + 74253243015 \, m + 35137127025\right)} x^{9} + 165 \, {\left(m^{11} + 137 \, m^{10} + 8259 \, m^{9} + 288027 \, m^{8} + 6423594 \, m^{7} + 95564154 \, m^{6} + 959352806 \, m^{5} + 6421988758 \, m^{4} + 27624338085 \, m^{3} + 70930262349 \, m^{2} + 94034286855 \, m + 45176306175\right)} x^{7} + 55 \, {\left(m^{11} + 139 \, m^{10} + 8523 \, m^{9} + 303225 \, m^{8} + 6923658 \, m^{7} + 105911022 \, m^{6} + 1098746774 \, m^{5} + 7643724530 \, m^{4} + 34359636741 \, m^{3} + 92502445239 \, m^{2} + 128033897103 \, m + 63246828645\right)} x^{5} + 11 \, {\left(m^{11} + 141 \, m^{10} + 8795 \, m^{9} + 319455 \, m^{8} + 7481418 \, m^{7} + 118085058 \, m^{6} + 1274046710 \, m^{5} + 9315318270 \, m^{4} + 44632304581 \, m^{3} + 130403715201 \, m^{2} + 199334977695 \, m + 105411381075\right)} x^{3} + {\left(m^{11} + 143 \, m^{10} + 9075 \, m^{9} + 336765 \, m^{8} + 8103018 \, m^{7} + 132426294 \, m^{6} + 1495875590 \, m^{5} + 11641582810 \, m^{4} + 60936676581 \, m^{3} + 203363952363 \, m^{2} + 387182170935 \, m + 316234143225\right)} x\right)} \left(f x\right)^{m}}{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,"((m^11 + 121*m^10 + 6435*m^9 + 197835*m^8 + 3889578*m^7 + 51069018*m^6 + 453714470*m^5 + 2702025590*m^4 + 10431670821*m^3 + 24372200061*m^2 + 29985521895*m + 13749310575)*x^23 + 11*(m^11 + 123*m^10 + 6635*m^9 + 206505*m^8 + 4103178*m^7 + 54362574*m^6 + 486687830*m^5 + 2917013970*m^4 + 11320966021*m^3 + 26560342503*m^2 + 32778930735*m + 15058768725)*x^21 + 55*(m^11 + 125*m^10 + 6843*m^9 + 215823*m^8 + 4339146*m^7 + 58085538*m^6 + 524676662*m^5 + 3168601822*m^4 + 12374824773*m^3 + 29178958257*m^2 + 36145916415*m + 16643902275)*x^19 + 165*(m^11 + 127*m^10 + 7059*m^9 + 225837*m^8 + 4600554*m^7 + 62319894*m^6 + 568863686*m^5 + 3466775738*m^4 + 13643071845*m^3 + 32368407579*m^2 + 40283194455*m + 18602008425)*x^17 + 330*(m^11 + 129*m^10 + 7283*m^9 + 236595*m^8 + 4890858*m^7 + 67166442*m^6 + 620805254*m^5 + 3825379590*m^4 + 15197565541*m^3 + 36337145829*m^2 + 45488935863*m + 21082276215)*x^15 + 462*(m^11 + 131*m^10 + 7515*m^9 + 248145*m^8 + 5213898*m^7 + 72748638*m^6 + 682569590*m^5 + 4264053730*m^4 + 17145560901*m^3 + 41408337231*m^2 + 52237739295*m + 24325703325)*x^13 + 462*(m^11 + 133*m^10 + 7755*m^9 + 260535*m^8 + 5573898*m^7 + 79216434*m^6 + 756921110*m^5 + 4811326190*m^4 + 19653671301*m^3 + 48110244633*m^2 + 61333432335*m + 28748558475)*x^11 + 330*(m^11 + 135*m^10 + 8003*m^9 + 273813*m^8 + 5975466*m^7 + 86750118*m^6 + 847550822*m^5 + 5509501002*m^4 + 22992750373*m^3 + 57365875587*m^2 + 74253243015*m + 35137127025)*x^9 + 165*(m^11 + 137*m^10 + 8259*m^9 + 288027*m^8 + 6423594*m^7 + 95564154*m^6 + 959352806*m^5 + 6421988758*m^4 + 27624338085*m^3 + 70930262349*m^2 + 94034286855*m + 45176306175)*x^7 + 55*(m^11 + 139*m^10 + 8523*m^9 + 303225*m^8 + 6923658*m^7 + 105911022*m^6 + 1098746774*m^5 + 7643724530*m^4 + 34359636741*m^3 + 92502445239*m^2 + 128033897103*m + 63246828645)*x^5 + 11*(m^11 + 141*m^10 + 8795*m^9 + 319455*m^8 + 7481418*m^7 + 118085058*m^6 + 1274046710*m^5 + 9315318270*m^4 + 44632304581*m^3 + 130403715201*m^2 + 199334977695*m + 105411381075)*x^3 + (m^11 + 143*m^10 + 9075*m^9 + 336765*m^8 + 8103018*m^7 + 132426294*m^6 + 1495875590*m^5 + 11641582810*m^4 + 60936676581*m^3 + 203363952363*m^2 + 387182170935*m + 316234143225)*x)*(f*x)^m/(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
66,1,61,0,0.560341," ","integrate(x^5*(x^2+1)*(x^4+2*x^2+1)^5,x, algorithm=""fricas"")","\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
67,1,61,0,0.764835," ","integrate(x^4*(x^2+1)*(x^4+2*x^2+1)^5,x, algorithm=""fricas"")","\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
68,1,61,0,0.859069," ","integrate(x^3*(x^2+1)*(x^4+2*x^2+1)^5,x, algorithm=""fricas"")","\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
69,1,61,0,0.566009," ","integrate(x^2*(x^2+1)*(x^4+2*x^2+1)^5,x, algorithm=""fricas"")","\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
70,1,61,0,0.512146," ","integrate(x*(x^2+1)*(x^4+2*x^2+1)^5,x, algorithm=""fricas"")","\frac{1}{24} x^{24} + \frac{1}{2} x^{22} + \frac{11}{4} x^{20} + \frac{55}{6} x^{18} + \frac{165}{8} x^{16} + 33 x^{14} + \frac{77}{2} x^{12} + 33 x^{10} + \frac{165}{8} x^{8} + \frac{55}{6} x^{6} + \frac{11}{4} x^{4} + \frac{1}{2} x^{2}"," ",0,"1/24*x^24 + 1/2*x^22 + 11/4*x^20 + 55/6*x^18 + 165/8*x^16 + 33*x^14 + 77/2*x^12 + 33*x^10 + 165/8*x^8 + 55/6*x^6 + 11/4*x^4 + 1/2*x^2","B",0
71,1,57,0,1.103494," ","integrate((x^2+1)*(x^4+2*x^2+1)^5,x, algorithm=""fricas"")","\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
72,1,58,0,0.846221," ","integrate((x^2+1)*(x^4+2*x^2+1)^5/x,x, algorithm=""fricas"")","\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} + \log\left(x\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 + log(x)","A",0
73,1,62,0,0.786282," ","integrate((x^2+1)*(x^4+2*x^2+1)^5/x^2,x, algorithm=""fricas"")","\frac{4199 \, x^{22} + 51051 \, x^{20} + 285285 \, x^{18} + 969969 \, x^{16} + 2238390 \, x^{14} + 3703518 \, x^{12} + 4526522 \, x^{10} + 4157010 \, x^{8} + 2909907 \, x^{6} + 1616615 \, x^{4} + 969969 \, x^{2} - 88179}{88179 \, x}"," ",0,"1/88179*(4199*x^22 + 51051*x^20 + 285285*x^18 + 969969*x^16 + 2238390*x^14 + 3703518*x^12 + 4526522*x^10 + 4157010*x^8 + 2909907*x^6 + 1616615*x^4 + 969969*x^2 - 88179)/x","A",0
74,1,64,0,0.503745," ","integrate((x^2+1)*(x^4+2*x^2+1)^5/x^3,x, algorithm=""fricas"")","\frac{252 \, x^{22} + 3080 \, x^{20} + 17325 \, x^{18} + 59400 \, x^{16} + 138600 \, x^{14} + 232848 \, x^{12} + 291060 \, x^{10} + 277200 \, x^{8} + 207900 \, x^{6} + 138600 \, x^{4} + 55440 \, x^{2} \log\left(x\right) - 2520}{5040 \, x^{2}}"," ",0,"1/5040*(252*x^22 + 3080*x^20 + 17325*x^18 + 59400*x^16 + 138600*x^14 + 232848*x^12 + 291060*x^10 + 277200*x^8 + 207900*x^6 + 138600*x^4 + 55440*x^2*log(x) - 2520)/x^2","A",0
75,1,129,0,0.770039," ","integrate(x^2*(e*x^2+d)/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, b e x^{3} - 3 \, {\left(b d - a e\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 6 \, {\left(b d - a e\right)} x}{6 \, b^{2}}, \frac{b e x^{3} - 3 \, {\left(b d - a e\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 3 \, {\left(b d - a e\right)} x}{3 \, b^{2}}\right]"," ",0,"[1/6*(2*b*e*x^3 - 3*(b*d - a*e)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 6*(b*d - a*e)*x)/b^2, 1/3*(b*e*x^3 - 3*(b*d - a*e)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 3*(b*d - a*e)*x)/b^2]","A",0
76,1,29,0,0.833599," ","integrate(x*(e*x^2+d)/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{b e x^{2} + {\left(b d - a e\right)} \log\left(b x^{2} + a\right)}{2 \, b^{2}}"," ",0,"1/2*(b*e*x^2 + (b*d - a*e)*log(b*x^2 + a))/b^2","A",0
77,1,98,0,0.593283," ","integrate((e*x^2+d)/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a b e x + \sqrt{-a b} {\left(b d - a e\right)} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{2 \, a b^{2}}, \frac{a b e x + \sqrt{a b} {\left(b d - a e\right)} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{a b^{2}}\right]"," ",0,"[1/2*(2*a*b*e*x + sqrt(-a*b)*(b*d - a*e)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a*b^2), (a*b*e*x + sqrt(a*b)*(b*d - a*e)*arctan(sqrt(a*b)*x/a))/(a*b^2)]","A",0
78,1,33,0,0.779748," ","integrate((e*x^2+d)/x/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, b d \log\left(x\right) - {\left(b d - a e\right)} \log\left(b x^{2} + a\right)}{2 \, a b}"," ",0,"1/2*(2*b*d*log(x) - (b*d - a*e)*log(b*x^2 + a))/(a*b)","A",0
79,1,105,0,0.702473," ","integrate((e*x^2+d)/x^2/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a b} {\left(b d - a e\right)} x \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 2 \, a b d}{2 \, a^{2} b x}, -\frac{\sqrt{a b} {\left(b d - a e\right)} x \arctan\left(\frac{\sqrt{a b} x}{a}\right) + a b d}{a^{2} b x}\right]"," ",0,"[1/2*(sqrt(-a*b)*(b*d - a*e)*x*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 2*a*b*d)/(a^2*b*x), -(sqrt(a*b)*(b*d - a*e)*x*arctan(sqrt(a*b)*x/a) + a*b*d)/(a^2*b*x)]","A",0
80,1,48,0,0.711752," ","integrate((e*x^2+d)/x^3/((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(b d - a e\right)} x^{2} \log\left(b x^{2} + a\right) - 2 \, {\left(b d - a e\right)} x^{2} \log\left(x\right) - a d}{2 \, a^{2} x^{2}}"," ",0,"1/2*((b*d - a*e)*x^2*log(b*x^2 + a) - 2*(b*d - a*e)*x^2*log(x) - a*d)/(a^2*x^2)","A",0
81,1,300,0,0.934127," ","integrate(x^2*(e*x^2+d)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a b^{3} d - 5 \, a^{2} b^{2} e\right)} x^{3} - {\left({\left(b^{3} d + 3 \, a b^{2} e\right)} x^{4} + a^{2} b d + 3 \, a^{3} e + 2 \, {\left(a b^{2} d + 3 \, a^{2} b e\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 2 \, {\left(a^{2} b^{2} d + 3 \, a^{3} b e\right)} x}{16 \, {\left(a^{2} b^{5} x^{4} + 2 \, a^{3} b^{4} x^{2} + a^{4} b^{3}\right)}}, \frac{{\left(a b^{3} d - 5 \, a^{2} b^{2} e\right)} x^{3} + {\left({\left(b^{3} d + 3 \, a b^{2} e\right)} x^{4} + a^{2} b d + 3 \, a^{3} e + 2 \, {\left(a b^{2} d + 3 \, a^{2} b e\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - {\left(a^{2} b^{2} d + 3 \, a^{3} b e\right)} x}{8 \, {\left(a^{2} b^{5} x^{4} + 2 \, a^{3} b^{4} x^{2} + a^{4} b^{3}\right)}}\right]"," ",0,"[1/16*(2*(a*b^3*d - 5*a^2*b^2*e)*x^3 - ((b^3*d + 3*a*b^2*e)*x^4 + a^2*b*d + 3*a^3*e + 2*(a*b^2*d + 3*a^2*b*e)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 2*(a^2*b^2*d + 3*a^3*b*e)*x)/(a^2*b^5*x^4 + 2*a^3*b^4*x^2 + a^4*b^3), 1/8*((a*b^3*d - 5*a^2*b^2*e)*x^3 + ((b^3*d + 3*a*b^2*e)*x^4 + a^2*b*d + 3*a^3*e + 2*(a*b^2*d + 3*a^2*b*e)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) - (a^2*b^2*d + 3*a^3*b*e)*x)/(a^2*b^5*x^4 + 2*a^3*b^4*x^2 + a^4*b^3)]","A",0
82,1,42,0,0.846926," ","integrate(x*(e*x^2+d)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, b e x^{2} + b d + a e}{4 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{2} + a^{2} b^{2}\right)}}"," ",0,"-1/4*(2*b*e*x^2 + b*d + a*e)/(b^4*x^4 + 2*a*b^3*x^2 + a^2*b^2)","A",0
83,1,301,0,0.782337," ","integrate((e*x^2+d)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(3 \, a b^{3} d + a^{2} b^{2} e\right)} x^{3} - {\left({\left(3 \, b^{3} d + a b^{2} e\right)} x^{4} + 3 \, a^{2} b d + a^{3} e + 2 \, {\left(3 \, a b^{2} d + a^{2} b e\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, {\left(5 \, a^{2} b^{2} d - a^{3} b e\right)} x}{16 \, {\left(a^{3} b^{4} x^{4} + 2 \, a^{4} b^{3} x^{2} + a^{5} b^{2}\right)}}, \frac{{\left(3 \, a b^{3} d + a^{2} b^{2} e\right)} x^{3} + {\left({\left(3 \, b^{3} d + a b^{2} e\right)} x^{4} + 3 \, a^{2} b d + a^{3} e + 2 \, {\left(3 \, a b^{2} d + a^{2} b e\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(5 \, a^{2} b^{2} d - a^{3} b e\right)} x}{8 \, {\left(a^{3} b^{4} x^{4} + 2 \, a^{4} b^{3} x^{2} + a^{5} b^{2}\right)}}\right]"," ",0,"[1/16*(2*(3*a*b^3*d + a^2*b^2*e)*x^3 - ((3*b^3*d + a*b^2*e)*x^4 + 3*a^2*b*d + a^3*e + 2*(3*a*b^2*d + a^2*b*e)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*(5*a^2*b^2*d - a^3*b*e)*x)/(a^3*b^4*x^4 + 2*a^4*b^3*x^2 + a^5*b^2), 1/8*((3*a*b^3*d + a^2*b^2*e)*x^3 + ((3*b^3*d + a*b^2*e)*x^4 + 3*a^2*b*d + a^3*e + 2*(3*a*b^2*d + a^2*b*e)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (5*a^2*b^2*d - a^3*b*e)*x)/(a^3*b^4*x^4 + 2*a^4*b^3*x^2 + a^5*b^2)]","A",0
84,1,119,0,0.645494," ","integrate((e*x^2+d)/x/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, a b^{2} d x^{2} + 3 \, a^{2} b d - a^{3} e - 2 \, {\left(b^{3} d x^{4} + 2 \, a b^{2} d x^{2} + a^{2} b d\right)} \log\left(b x^{2} + a\right) + 4 \, {\left(b^{3} d x^{4} + 2 \, a b^{2} d x^{2} + a^{2} b d\right)} \log\left(x\right)}{4 \, {\left(a^{3} b^{3} x^{4} + 2 \, a^{4} b^{2} x^{2} + a^{5} b\right)}}"," ",0,"1/4*(2*a*b^2*d*x^2 + 3*a^2*b*d - a^3*e - 2*(b^3*d*x^4 + 2*a*b^2*d*x^2 + a^2*b*d)*log(b*x^2 + a) + 4*(b^3*d*x^4 + 2*a*b^2*d*x^2 + a^2*b*d)*log(x))/(a^3*b^3*x^4 + 2*a^4*b^2*x^2 + a^5*b)","A",0
85,1,334,0,0.964132," ","integrate((e*x^2+d)/x^2/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{16 \, a^{3} b d + 6 \, {\left(5 \, a b^{3} d - a^{2} b^{2} e\right)} x^{4} + 10 \, {\left(5 \, a^{2} b^{2} d - a^{3} b e\right)} x^{2} - 3 \, {\left({\left(5 \, b^{3} d - a b^{2} e\right)} x^{5} + 2 \, {\left(5 \, a b^{2} d - a^{2} b e\right)} x^{3} + {\left(5 \, a^{2} b d - a^{3} e\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{16 \, {\left(a^{4} b^{3} x^{5} + 2 \, a^{5} b^{2} x^{3} + a^{6} b x\right)}}, -\frac{8 \, a^{3} b d + 3 \, {\left(5 \, a b^{3} d - a^{2} b^{2} e\right)} x^{4} + 5 \, {\left(5 \, a^{2} b^{2} d - a^{3} b e\right)} x^{2} + 3 \, {\left({\left(5 \, b^{3} d - a b^{2} e\right)} x^{5} + 2 \, {\left(5 \, a b^{2} d - a^{2} b e\right)} x^{3} + {\left(5 \, a^{2} b d - a^{3} e\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{8 \, {\left(a^{4} b^{3} x^{5} + 2 \, a^{5} b^{2} x^{3} + a^{6} b x\right)}}\right]"," ",0,"[-1/16*(16*a^3*b*d + 6*(5*a*b^3*d - a^2*b^2*e)*x^4 + 10*(5*a^2*b^2*d - a^3*b*e)*x^2 - 3*((5*b^3*d - a*b^2*e)*x^5 + 2*(5*a*b^2*d - a^2*b*e)*x^3 + (5*a^2*b*d - a^3*e)*x)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^4*b^3*x^5 + 2*a^5*b^2*x^3 + a^6*b*x), -1/8*(8*a^3*b*d + 3*(5*a*b^3*d - a^2*b^2*e)*x^4 + 5*(5*a^2*b^2*d - a^3*b*e)*x^2 + 3*((5*b^3*d - a*b^2*e)*x^5 + 2*(5*a*b^2*d - a^2*b*e)*x^3 + (5*a^2*b*d - a^3*e)*x)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^4*b^3*x^5 + 2*a^5*b^2*x^3 + a^6*b*x)]","A",0
86,1,205,0,0.666491," ","integrate((e*x^2+d)/x^3/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","-\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} - 2 \, {\left({\left(3 \, b^{3} d - a b^{2} e\right)} x^{6} + 2 \, {\left(3 \, a b^{2} d - a^{2} b e\right)} x^{4} + {\left(3 \, a^{2} b d - a^{3} e\right)} x^{2}\right)} \log\left(b x^{2} + a\right) + 4 \, {\left({\left(3 \, b^{3} d - a b^{2} e\right)} x^{6} + 2 \, {\left(3 \, a b^{2} d - a^{2} b e\right)} x^{4} + {\left(3 \, a^{2} b d - a^{3} e\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left(a^{4} b^{2} x^{6} + 2 \, a^{5} b x^{4} + a^{6} x^{2}\right)}}"," ",0,"-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 - 2*((3*b^3*d - a*b^2*e)*x^6 + 2*(3*a*b^2*d - a^2*b*e)*x^4 + (3*a^2*b*d - a^3*e)*x^2)*log(b*x^2 + a) + 4*((3*b^3*d - a*b^2*e)*x^6 + 2*(3*a*b^2*d - a^2*b*e)*x^4 + (3*a^2*b*d - a^3*e)*x^2)*log(x))/(a^4*b^2*x^6 + 2*a^5*b*x^4 + a^6*x^2)","A",0
87,1,853,0,0.858592," ","integrate((f*x)^m*(e*x^2+d)*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left({\left(b^{5} e m^{6} + 36 \, b^{5} e m^{5} + 505 \, b^{5} e m^{4} + 3480 \, b^{5} e m^{3} + 12139 \, b^{5} e m^{2} + 19524 \, b^{5} e m + 10395 \, b^{5} e\right)} x^{13} + {\left({\left(b^{5} d + 5 \, a b^{4} e\right)} m^{6} + 12285 \, b^{5} d + 61425 \, a b^{4} e + 38 \, {\left(b^{5} d + 5 \, a b^{4} e\right)} m^{5} + 555 \, {\left(b^{5} d + 5 \, a b^{4} e\right)} m^{4} + 3940 \, {\left(b^{5} d + 5 \, a b^{4} e\right)} m^{3} + 14039 \, {\left(b^{5} d + 5 \, a b^{4} e\right)} m^{2} + 22902 \, {\left(b^{5} d + 5 \, a b^{4} e\right)} m\right)} x^{11} + 5 \, {\left({\left(a b^{4} d + 2 \, a^{2} b^{3} e\right)} m^{6} + 15015 \, a b^{4} d + 30030 \, a^{2} b^{3} e + 40 \, {\left(a b^{4} d + 2 \, a^{2} b^{3} e\right)} m^{5} + 613 \, {\left(a b^{4} d + 2 \, a^{2} b^{3} e\right)} m^{4} + 4528 \, {\left(a b^{4} d + 2 \, a^{2} b^{3} e\right)} m^{3} + 16627 \, {\left(a b^{4} d + 2 \, a^{2} b^{3} e\right)} m^{2} + 27688 \, {\left(a b^{4} d + 2 \, a^{2} b^{3} e\right)} m\right)} x^{9} + 10 \, {\left({\left(a^{2} b^{3} d + a^{3} b^{2} e\right)} m^{6} + 19305 \, a^{2} b^{3} d + 19305 \, a^{3} b^{2} e + 42 \, {\left(a^{2} b^{3} d + a^{3} b^{2} e\right)} m^{5} + 679 \, {\left(a^{2} b^{3} d + a^{3} b^{2} e\right)} m^{4} + 5292 \, {\left(a^{2} b^{3} d + a^{3} b^{2} e\right)} m^{3} + 20335 \, {\left(a^{2} b^{3} d + a^{3} b^{2} e\right)} m^{2} + 34986 \, {\left(a^{2} b^{3} d + a^{3} b^{2} e\right)} m\right)} x^{7} + 5 \, {\left({\left(2 \, a^{3} b^{2} d + a^{4} b e\right)} m^{6} + 54054 \, a^{3} b^{2} d + 27027 \, a^{4} b e + 44 \, {\left(2 \, a^{3} b^{2} d + a^{4} b e\right)} m^{5} + 753 \, {\left(2 \, a^{3} b^{2} d + a^{4} b e\right)} m^{4} + 6280 \, {\left(2 \, a^{3} b^{2} d + a^{4} b e\right)} m^{3} + 25979 \, {\left(2 \, a^{3} b^{2} d + a^{4} b e\right)} m^{2} + 47436 \, {\left(2 \, a^{3} b^{2} d + a^{4} b e\right)} m\right)} x^{5} + {\left({\left(5 \, a^{4} b d + a^{5} e\right)} m^{6} + 225225 \, a^{4} b d + 45045 \, a^{5} e + 46 \, {\left(5 \, a^{4} b d + a^{5} e\right)} m^{5} + 835 \, {\left(5 \, a^{4} b d + a^{5} e\right)} m^{4} + 7540 \, {\left(5 \, a^{4} b d + a^{5} e\right)} m^{3} + 34759 \, {\left(5 \, a^{4} b d + a^{5} e\right)} m^{2} + 73054 \, {\left(5 \, a^{4} b d + a^{5} e\right)} m\right)} x^{3} + {\left(a^{5} d m^{6} + 48 \, a^{5} d m^{5} + 925 \, a^{5} d m^{4} + 9120 \, a^{5} d m^{3} + 48259 \, a^{5} d m^{2} + 129072 \, a^{5} d m + 135135 \, a^{5} d\right)} x\right)} \left(f x\right)^{m}}{m^{7} + 49 \, m^{6} + 973 \, m^{5} + 10045 \, m^{4} + 57379 \, m^{3} + 177331 \, m^{2} + 264207 \, m + 135135}"," ",0,"((b^5*e*m^6 + 36*b^5*e*m^5 + 505*b^5*e*m^4 + 3480*b^5*e*m^3 + 12139*b^5*e*m^2 + 19524*b^5*e*m + 10395*b^5*e)*x^13 + ((b^5*d + 5*a*b^4*e)*m^6 + 12285*b^5*d + 61425*a*b^4*e + 38*(b^5*d + 5*a*b^4*e)*m^5 + 555*(b^5*d + 5*a*b^4*e)*m^4 + 3940*(b^5*d + 5*a*b^4*e)*m^3 + 14039*(b^5*d + 5*a*b^4*e)*m^2 + 22902*(b^5*d + 5*a*b^4*e)*m)*x^11 + 5*((a*b^4*d + 2*a^2*b^3*e)*m^6 + 15015*a*b^4*d + 30030*a^2*b^3*e + 40*(a*b^4*d + 2*a^2*b^3*e)*m^5 + 613*(a*b^4*d + 2*a^2*b^3*e)*m^4 + 4528*(a*b^4*d + 2*a^2*b^3*e)*m^3 + 16627*(a*b^4*d + 2*a^2*b^3*e)*m^2 + 27688*(a*b^4*d + 2*a^2*b^3*e)*m)*x^9 + 10*((a^2*b^3*d + a^3*b^2*e)*m^6 + 19305*a^2*b^3*d + 19305*a^3*b^2*e + 42*(a^2*b^3*d + a^3*b^2*e)*m^5 + 679*(a^2*b^3*d + a^3*b^2*e)*m^4 + 5292*(a^2*b^3*d + a^3*b^2*e)*m^3 + 20335*(a^2*b^3*d + a^3*b^2*e)*m^2 + 34986*(a^2*b^3*d + a^3*b^2*e)*m)*x^7 + 5*((2*a^3*b^2*d + a^4*b*e)*m^6 + 54054*a^3*b^2*d + 27027*a^4*b*e + 44*(2*a^3*b^2*d + a^4*b*e)*m^5 + 753*(2*a^3*b^2*d + a^4*b*e)*m^4 + 6280*(2*a^3*b^2*d + a^4*b*e)*m^3 + 25979*(2*a^3*b^2*d + a^4*b*e)*m^2 + 47436*(2*a^3*b^2*d + a^4*b*e)*m)*x^5 + ((5*a^4*b*d + a^5*e)*m^6 + 225225*a^4*b*d + 45045*a^5*e + 46*(5*a^4*b*d + a^5*e)*m^5 + 835*(5*a^4*b*d + a^5*e)*m^4 + 7540*(5*a^4*b*d + a^5*e)*m^3 + 34759*(5*a^4*b*d + a^5*e)*m^2 + 73054*(5*a^4*b*d + a^5*e)*m)*x^3 + (a^5*d*m^6 + 48*a^5*d*m^5 + 925*a^5*d*m^4 + 9120*a^5*d*m^3 + 48259*a^5*d*m^2 + 129072*a^5*d*m + 135135*a^5*d)*x)*(f*x)^m/(m^7 + 49*m^6 + 973*m^5 + 10045*m^4 + 57379*m^3 + 177331*m^2 + 264207*m + 135135)","B",0
88,1,381,0,0.692712," ","integrate((f*x)^m*(e*x^2+d)*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(b^{3} e m^{4} + 16 \, b^{3} e m^{3} + 86 \, b^{3} e m^{2} + 176 \, b^{3} e m + 105 \, b^{3} e\right)} x^{9} + {\left({\left(b^{3} d + 3 \, a b^{2} e\right)} m^{4} + 135 \, b^{3} d + 405 \, a b^{2} e + 18 \, {\left(b^{3} d + 3 \, a b^{2} e\right)} m^{3} + 104 \, {\left(b^{3} d + 3 \, a b^{2} e\right)} m^{2} + 222 \, {\left(b^{3} d + 3 \, a b^{2} e\right)} m\right)} x^{7} + 3 \, {\left({\left(a b^{2} d + a^{2} b e\right)} m^{4} + 189 \, a b^{2} d + 189 \, a^{2} b e + 20 \, {\left(a b^{2} d + a^{2} b e\right)} m^{3} + 130 \, {\left(a b^{2} d + a^{2} b e\right)} m^{2} + 300 \, {\left(a b^{2} d + a^{2} b e\right)} m\right)} x^{5} + {\left({\left(3 \, a^{2} b d + a^{3} e\right)} m^{4} + 945 \, a^{2} b d + 315 \, a^{3} e + 22 \, {\left(3 \, a^{2} b d + a^{3} e\right)} m^{3} + 164 \, {\left(3 \, a^{2} b d + a^{3} e\right)} m^{2} + 458 \, {\left(3 \, a^{2} b d + a^{3} e\right)} m\right)} x^{3} + {\left(a^{3} d m^{4} + 24 \, a^{3} d m^{3} + 206 \, a^{3} d m^{2} + 744 \, a^{3} d m + 945 \, a^{3} d\right)} x\right)} \left(f x\right)^{m}}{m^{5} + 25 \, m^{4} + 230 \, m^{3} + 950 \, m^{2} + 1689 \, m + 945}"," ",0,"((b^3*e*m^4 + 16*b^3*e*m^3 + 86*b^3*e*m^2 + 176*b^3*e*m + 105*b^3*e)*x^9 + ((b^3*d + 3*a*b^2*e)*m^4 + 135*b^3*d + 405*a*b^2*e + 18*(b^3*d + 3*a*b^2*e)*m^3 + 104*(b^3*d + 3*a*b^2*e)*m^2 + 222*(b^3*d + 3*a*b^2*e)*m)*x^7 + 3*((a*b^2*d + a^2*b*e)*m^4 + 189*a*b^2*d + 189*a^2*b*e + 20*(a*b^2*d + a^2*b*e)*m^3 + 130*(a*b^2*d + a^2*b*e)*m^2 + 300*(a*b^2*d + a^2*b*e)*m)*x^5 + ((3*a^2*b*d + a^3*e)*m^4 + 945*a^2*b*d + 315*a^3*e + 22*(3*a^2*b*d + a^3*e)*m^3 + 164*(3*a^2*b*d + a^3*e)*m^2 + 458*(3*a^2*b*d + a^3*e)*m)*x^3 + (a^3*d*m^4 + 24*a^3*d*m^3 + 206*a^3*d*m^2 + 744*a^3*d*m + 945*a^3*d)*x)*(f*x)^m/(m^5 + 25*m^4 + 230*m^3 + 950*m^2 + 1689*m + 945)","A",0
89,1,94,0,0.726198," ","integrate((f*x)^m*(e*x^2+d)*(b^2*x^4+2*a*b*x^2+a^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left({\left(b e m^{2} + 4 \, b e m + 3 \, b e\right)} x^{5} + {\left({\left(b d + a e\right)} m^{2} + 5 \, b d + 5 \, a e + 6 \, {\left(b d + a e\right)} m\right)} x^{3} + {\left(a d m^{2} + 8 \, a d m + 15 \, a d\right)} x\right)} \left(f x\right)^{m}}{m^{3} + 9 \, m^{2} + 23 \, m + 15}"," ",0,"((b*e*m^2 + 4*b*e*m + 3*b*e)*x^5 + ((b*d + a*e)*m^2 + 5*b*d + 5*a*e + 6*(b*d + a*e)*m)*x^3 + (a*d*m^2 + 8*a*d*m + 15*a*d)*x)*(f*x)^m/(m^3 + 9*m^2 + 23*m + 15)","A",0
90,0,0,0,0.833249," ","integrate((f*x)^m*(e*x^2+d)/(b^2*x^4+2*a*b*x^2+a^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{2} + d\right)} \left(f x\right)^{m}}{\sqrt{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}}, x\right)"," ",0,"integral((e*x^2 + d)*(f*x)^m/sqrt(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
91,0,0,0,0.922694," ","integrate((f*x)^m*(e*x^2+d)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}} {\left(e x^{2} + d\right)} \left(f x\right)^{m}}{b^{4} x^{8} + 4 \, a b^{3} x^{6} + 6 \, a^{2} b^{2} x^{4} + 4 \, a^{3} b x^{2} + a^{4}}, x\right)"," ",0,"integral(sqrt(b^2*x^4 + 2*a*b*x^2 + a^2)*(e*x^2 + d)*(f*x)^m/(b^4*x^8 + 4*a*b^3*x^6 + 6*a^2*b^2*x^4 + 4*a^3*b*x^2 + a^4), x)","F",0
92,1,47,0,0.709228," ","integrate(x*(b*x^2+a)*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""fricas"")","\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{4 \, {\left(b p + b\right)}}"," ",0,"1/4*(b^2*x^4 + 2*a*b*x^2 + a^2)*(b^2*x^4 + 2*a*b*x^2 + a^2)^p/(b*p + b)","A",0
93,1,92,0,0.663877," ","integrate(x^3*(b*x^2+a)*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(b^{3} p + b^{3}\right)} x^{6} + 2 \, a^{2} b p x^{2} + {\left(4 \, a b^{2} p + 3 \, a b^{2}\right)} x^{4} - a^{3}\right)} {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{4 \, {\left(2 \, b^{2} p^{2} + 5 \, b^{2} p + 3 \, b^{2}\right)}}"," ",0,"1/4*(2*(b^3*p + b^3)*x^6 + 2*a^2*b*p*x^2 + (4*a*b^2*p + 3*a*b^2)*x^4 - a^3)*(b^2*x^4 + 2*a*b*x^2 + a^2)^p/(2*b^2*p^2 + 5*b^2*p + 3*b^2)","A",0
94,1,140,0,0.774393," ","integrate(x^5*(b*x^2+a)*(b^2*x^4+2*a*b*x^2+a^2)^p,x, algorithm=""fricas"")","\frac{{\left({\left(2 \, b^{4} p^{2} + 5 \, b^{4} p + 3 \, b^{4}\right)} x^{8} - 2 \, a^{3} b p x^{2} + 4 \, {\left(a b^{3} p^{2} + 2 \, a b^{3} p + a b^{3}\right)} x^{6} + {\left(2 \, a^{2} b^{2} p^{2} + a^{2} b^{2} p\right)} x^{4} + a^{4}\right)} {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)}^{p}}{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^4*p^2 + 5*b^4*p + 3*b^4)*x^8 - 2*a^3*b*p*x^2 + 4*(a*b^3*p^2 + 2*a*b^3*p + a*b^3)*x^6 + (2*a^2*b^2*p^2 + a^2*b^2*p)*x^4 + a^4)*(b^2*x^4 + 2*a*b*x^2 + a^2)^p/(2*b^3*p^3 + 9*b^3*p^2 + 13*b^3*p + 6*b^3)","A",0
95,1,193,0,0.714285," ","integrate(x^3*(B*x^2+A)*(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{18} x^{18} c^{3} B + \frac{3}{16} x^{16} c^{2} b B + \frac{1}{16} x^{16} c^{3} A + \frac{3}{14} x^{14} c b^{2} B + \frac{3}{14} x^{14} c^{2} a B + \frac{3}{14} x^{14} c^{2} b A + \frac{1}{12} x^{12} b^{3} B + \frac{1}{2} x^{12} c b a B + \frac{1}{4} x^{12} c b^{2} A + \frac{1}{4} x^{12} c^{2} a A + \frac{3}{10} x^{10} b^{2} a B + \frac{3}{10} x^{10} c a^{2} B + \frac{1}{10} x^{10} b^{3} A + \frac{3}{5} x^{10} c b a A + \frac{3}{8} x^{8} b a^{2} B + \frac{3}{8} x^{8} b^{2} a A + \frac{3}{8} x^{8} c a^{2} A + \frac{1}{6} x^{6} a^{3} B + \frac{1}{2} x^{6} b a^{2} A + \frac{1}{4} x^{4} a^{3} A"," ",0,"1/18*x^18*c^3*B + 3/16*x^16*c^2*b*B + 1/16*x^16*c^3*A + 3/14*x^14*c*b^2*B + 3/14*x^14*c^2*a*B + 3/14*x^14*c^2*b*A + 1/12*x^12*b^3*B + 1/2*x^12*c*b*a*B + 1/4*x^12*c*b^2*A + 1/4*x^12*c^2*a*A + 3/10*x^10*b^2*a*B + 3/10*x^10*c*a^2*B + 1/10*x^10*b^3*A + 3/5*x^10*c*b*a*A + 3/8*x^8*b*a^2*B + 3/8*x^8*b^2*a*A + 3/8*x^8*c*a^2*A + 1/6*x^6*a^3*B + 1/2*x^6*b*a^2*A + 1/4*x^4*a^3*A","A",0
96,1,193,0,0.614853," ","integrate(x^2*(B*x^2+A)*(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{17} x^{17} c^{3} B + \frac{1}{5} x^{15} c^{2} b B + \frac{1}{15} x^{15} c^{3} A + \frac{3}{13} x^{13} c b^{2} B + \frac{3}{13} x^{13} c^{2} a B + \frac{3}{13} x^{13} c^{2} b A + \frac{1}{11} x^{11} b^{3} B + \frac{6}{11} x^{11} c b a B + \frac{3}{11} x^{11} c b^{2} A + \frac{3}{11} x^{11} c^{2} a A + \frac{1}{3} x^{9} b^{2} a B + \frac{1}{3} x^{9} c a^{2} B + \frac{1}{9} x^{9} b^{3} A + \frac{2}{3} x^{9} c b a A + \frac{3}{7} x^{7} b a^{2} B + \frac{3}{7} x^{7} b^{2} a A + \frac{3}{7} x^{7} c a^{2} A + \frac{1}{5} x^{5} a^{3} B + \frac{3}{5} x^{5} b a^{2} A + \frac{1}{3} x^{3} a^{3} A"," ",0,"1/17*x^17*c^3*B + 1/5*x^15*c^2*b*B + 1/15*x^15*c^3*A + 3/13*x^13*c*b^2*B + 3/13*x^13*c^2*a*B + 3/13*x^13*c^2*b*A + 1/11*x^11*b^3*B + 6/11*x^11*c*b*a*B + 3/11*x^11*c*b^2*A + 3/11*x^11*c^2*a*A + 1/3*x^9*b^2*a*B + 1/3*x^9*c*a^2*B + 1/9*x^9*b^3*A + 2/3*x^9*c*b*a*A + 3/7*x^7*b*a^2*B + 3/7*x^7*b^2*a*A + 3/7*x^7*c*a^2*A + 1/5*x^5*a^3*B + 3/5*x^5*b*a^2*A + 1/3*x^3*a^3*A","A",0
97,1,193,0,0.596404," ","integrate(x*(B*x^2+A)*(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{16} x^{16} c^{3} B + \frac{3}{14} x^{14} c^{2} b B + \frac{1}{14} x^{14} c^{3} A + \frac{1}{4} x^{12} c b^{2} B + \frac{1}{4} x^{12} c^{2} a B + \frac{1}{4} x^{12} c^{2} b A + \frac{1}{10} x^{10} b^{3} B + \frac{3}{5} x^{10} c b a B + \frac{3}{10} x^{10} c b^{2} A + \frac{3}{10} x^{10} c^{2} a A + \frac{3}{8} x^{8} b^{2} a B + \frac{3}{8} x^{8} c a^{2} B + \frac{1}{8} x^{8} b^{3} A + \frac{3}{4} x^{8} c b a A + \frac{1}{2} x^{6} b a^{2} B + \frac{1}{2} x^{6} b^{2} a A + \frac{1}{2} x^{6} c a^{2} A + \frac{1}{4} x^{4} a^{3} B + \frac{3}{4} x^{4} b a^{2} A + \frac{1}{2} x^{2} a^{3} A"," ",0,"1/16*x^16*c^3*B + 3/14*x^14*c^2*b*B + 1/14*x^14*c^3*A + 1/4*x^12*c*b^2*B + 1/4*x^12*c^2*a*B + 1/4*x^12*c^2*b*A + 1/10*x^10*b^3*B + 3/5*x^10*c*b*a*B + 3/10*x^10*c*b^2*A + 3/10*x^10*c^2*a*A + 3/8*x^8*b^2*a*B + 3/8*x^8*c*a^2*B + 1/8*x^8*b^3*A + 3/4*x^8*c*b*a*A + 1/2*x^6*b*a^2*B + 1/2*x^6*b^2*a*A + 1/2*x^6*c*a^2*A + 1/4*x^4*a^3*B + 3/4*x^4*b*a^2*A + 1/2*x^2*a^3*A","A",0
98,1,189,0,0.764227," ","integrate((B*x^2+A)*(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{15} x^{15} c^{3} B + \frac{3}{13} x^{13} c^{2} b B + \frac{1}{13} x^{13} c^{3} A + \frac{3}{11} x^{11} c b^{2} B + \frac{3}{11} x^{11} c^{2} a B + \frac{3}{11} x^{11} c^{2} b A + \frac{1}{9} x^{9} b^{3} B + \frac{2}{3} x^{9} c b a B + \frac{1}{3} x^{9} c b^{2} A + \frac{1}{3} x^{9} c^{2} a A + \frac{3}{7} x^{7} b^{2} a B + \frac{3}{7} x^{7} c a^{2} B + \frac{1}{7} x^{7} b^{3} A + \frac{6}{7} x^{7} c b a A + \frac{3}{5} x^{5} b a^{2} B + \frac{3}{5} x^{5} b^{2} a A + \frac{3}{5} x^{5} c a^{2} A + \frac{1}{3} x^{3} a^{3} B + x^{3} b a^{2} A + x a^{3} A"," ",0,"1/15*x^15*c^3*B + 3/13*x^13*c^2*b*B + 1/13*x^13*c^3*A + 3/11*x^11*c*b^2*B + 3/11*x^11*c^2*a*B + 3/11*x^11*c^2*b*A + 1/9*x^9*b^3*B + 2/3*x^9*c*b*a*B + 1/3*x^9*c*b^2*A + 1/3*x^9*c^2*a*A + 3/7*x^7*b^2*a*B + 3/7*x^7*c*a^2*B + 1/7*x^7*b^3*A + 6/7*x^7*c*b*a*A + 3/5*x^5*b*a^2*B + 3/5*x^5*b^2*a*A + 3/5*x^5*c*a^2*A + 1/3*x^3*a^3*B + x^3*b*a^2*A + x*a^3*A","A",0
99,1,164,0,0.817621," ","integrate((B*x^2+A)*(c*x^4+b*x^2+a)^3/x,x, algorithm=""fricas"")","\frac{1}{14} \, B c^{3} x^{14} + \frac{1}{12} \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{12} + \frac{3}{10} \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{10} + \frac{1}{8} \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{8} + \frac{1}{6} \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{6} + \frac{3}{4} \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{4} + A a^{3} \log\left(x\right) + \frac{1}{2} \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{2}"," ",0,"1/14*B*c^3*x^14 + 1/12*(3*B*b*c^2 + A*c^3)*x^12 + 3/10*(B*b^2*c + (B*a + A*b)*c^2)*x^10 + 1/8*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^8 + 1/6*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^6 + 3/4*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^4 + A*a^3*log(x) + 1/2*(B*a^3 + 3*A*a^2*b)*x^2","A",0
100,1,168,0,0.955302," ","integrate((B*x^2+A)*(c*x^4+b*x^2+a)^3/x^2,x, algorithm=""fricas"")","\frac{1155 \, B c^{3} x^{14} + 1365 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{12} + 5005 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{10} + 2145 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{8} + 3003 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{6} + 15015 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{4} - 15015 \, A a^{3} + 15015 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{2}}{15015 \, x}"," ",0,"1/15015*(1155*B*c^3*x^14 + 1365*(3*B*b*c^2 + A*c^3)*x^12 + 5005*(B*b^2*c + (B*a + A*b)*c^2)*x^10 + 2145*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^8 + 3003*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^6 + 15015*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^4 - 15015*A*a^3 + 15015*(B*a^3 + 3*A*a^2*b)*x^2)/x","A",0
101,1,170,0,0.841774," ","integrate((B*x^2+A)*(c*x^4+b*x^2+a)^3/x^3,x, algorithm=""fricas"")","\frac{10 \, B c^{3} x^{14} + 12 \, {\left(3 \, B b c^{2} + A c^{3}\right)} x^{12} + 45 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} x^{10} + 20 \, {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{8} + 30 \, {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} x^{6} + 180 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} x^{4} - 60 \, A a^{3} + 120 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{2} \log\left(x\right)}{120 \, x^{2}}"," ",0,"1/120*(10*B*c^3*x^14 + 12*(3*B*b*c^2 + A*c^3)*x^12 + 45*(B*b^2*c + (B*a + A*b)*c^2)*x^10 + 20*(B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*x^8 + 30*(3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*x^6 + 180*(B*a^2*b + A*a*b^2 + A*a^2*c)*x^4 - 60*A*a^3 + 120*(B*a^3 + 3*A*a^2*b)*x^2*log(x))/x^2","A",0
102,1,421,0,1.585567," ","integrate(x^5*(B*x^2+A)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\left[\frac{{\left(B b^{2} c^{2} - 4 \, B a c^{3}\right)} x^{4} - 2 \, {\left(B b^{3} c + 4 \, A a c^{3} - {\left(4 \, B a b + A b^{2}\right)} c^{2}\right)} x^{2} + {\left(B b^{3} + 2 \, A a c^{2} - {\left(3 \, B a b + A b^{2}\right)} c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) + {\left(B b^{4} + 4 \, {\left(B a^{2} + A a b\right)} c^{2} - {\left(5 \, B a b^{2} + A b^{3}\right)} c\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}, \frac{{\left(B b^{2} c^{2} - 4 \, B a c^{3}\right)} x^{4} - 2 \, {\left(B b^{3} c + 4 \, A a c^{3} - {\left(4 \, B a b + A b^{2}\right)} c^{2}\right)} x^{2} + 2 \, {\left(B b^{3} + 2 \, A a c^{2} - {\left(3 \, B a b + A b^{2}\right)} c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) + {\left(B b^{4} + 4 \, {\left(B a^{2} + A a b\right)} c^{2} - {\left(5 \, B a b^{2} + A b^{3}\right)} c\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}\right]"," ",0,"[1/4*((B*b^2*c^2 - 4*B*a*c^3)*x^4 - 2*(B*b^3*c + 4*A*a*c^3 - (4*B*a*b + A*b^2)*c^2)*x^2 + (B*b^3 + 2*A*a*c^2 - (3*B*a*b + A*b^2)*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) + (B*b^4 + 4*(B*a^2 + A*a*b)*c^2 - (5*B*a*b^2 + A*b^3)*c)*log(c*x^4 + b*x^2 + a))/(b^2*c^3 - 4*a*c^4), 1/4*((B*b^2*c^2 - 4*B*a*c^3)*x^4 - 2*(B*b^3*c + 4*A*a*c^3 - (4*B*a*b + A*b^2)*c^2)*x^2 + 2*(B*b^3 + 2*A*a*c^2 - (3*B*a*b + A*b^2)*c)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) + (B*b^4 + 4*(B*a^2 + A*a*b)*c^2 - (5*B*a*b^2 + A*b^3)*c)*log(c*x^4 + b*x^2 + a))/(b^2*c^3 - 4*a*c^4)]","A",0
103,1,312,0,0.772233," ","integrate(x^3*(B*x^2+A)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(B b^{2} c - 4 \, B a c^{2}\right)} x^{2} - {\left(B b^{2} - {\left(2 \, B a + A b\right)} c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) - {\left(B b^{3} + 4 \, A a c^{2} - {\left(4 \, B a b + A b^{2}\right)} c\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}, \frac{2 \, {\left(B b^{2} c - 4 \, B a c^{2}\right)} x^{2} - 2 \, {\left(B b^{2} - {\left(2 \, B a + A b\right)} c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left(B b^{3} + 4 \, A a c^{2} - {\left(4 \, B a b + A b^{2}\right)} c\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}\right]"," ",0,"[1/4*(2*(B*b^2*c - 4*B*a*c^2)*x^2 - (B*b^2 - (2*B*a + A*b)*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) - (B*b^3 + 4*A*a*c^2 - (4*B*a*b + A*b^2)*c)*log(c*x^4 + b*x^2 + a))/(b^2*c^2 - 4*a*c^3), 1/4*(2*(B*b^2*c - 4*B*a*c^2)*x^2 - 2*(B*b^2 - (2*B*a + A*b)*c)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - (B*b^3 + 4*A*a*c^2 - (4*B*a*b + A*b^2)*c)*log(c*x^4 + b*x^2 + a))/(b^2*c^2 - 4*a*c^3)]","A",0
104,1,219,0,0.827387," ","integrate(x*(B*x^2+A)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{{\left(B b - 2 \, A c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c - {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) - {\left(B b^{2} - 4 \, B a c\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}, \frac{2 \, {\left(B b - 2 \, A c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) + {\left(B b^{2} - 4 \, B a c\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\right]"," ",0,"[-1/4*((B*b - 2*A*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c - (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) - (B*b^2 - 4*B*a*c)*log(c*x^4 + b*x^2 + a))/(b^2*c - 4*a*c^2), 1/4*(2*(B*b - 2*A*c)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) + (B*b^2 - 4*B*a*c)*log(c*x^4 + b*x^2 + a))/(b^2*c - 4*a*c^2)]","A",0
105,1,249,0,1.144876," ","integrate((B*x^2+A)/x/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, B a - A b\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) + {\left(A b^{2} - 4 \, A a c\right)} \log\left(c x^{4} + b x^{2} + a\right) - 4 \, {\left(A b^{2} - 4 \, A a c\right)} \log\left(x\right)}{4 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}, -\frac{2 \, {\left(2 \, B a - A b\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) + {\left(A b^{2} - 4 \, A a c\right)} \log\left(c x^{4} + b x^{2} + a\right) - 4 \, {\left(A b^{2} - 4 \, A a c\right)} \log\left(x\right)}{4 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}\right]"," ",0,"[-1/4*((2*B*a - A*b)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) + (A*b^2 - 4*A*a*c)*log(c*x^4 + b*x^2 + a) - 4*(A*b^2 - 4*A*a*c)*log(x))/(a*b^2 - 4*a^2*c), -1/4*(2*(2*B*a - A*b)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) + (A*b^2 - 4*A*a*c)*log(c*x^4 + b*x^2 + a) - 4*(A*b^2 - 4*A*a*c)*log(x))/(a*b^2 - 4*a^2*c)]","A",0
106,1,385,0,1.075275," ","integrate((B*x^2+A)/x^3/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\left[\frac{{\left(B a b - A b^{2} + 2 \, A a c\right)} \sqrt{b^{2} - 4 \, a c} x^{2} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) - 2 \, A a b^{2} + 8 \, A a^{2} c - {\left(B a b^{2} - A b^{3} - 4 \, {\left(B a^{2} - A a b\right)} c\right)} x^{2} \log\left(c x^{4} + b x^{2} + a\right) + 4 \, {\left(B a b^{2} - A b^{3} - 4 \, {\left(B a^{2} - A a b\right)} c\right)} x^{2} \log\left(x\right)}{4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x^{2}}, \frac{2 \, {\left(B a b - A b^{2} + 2 \, A a c\right)} \sqrt{-b^{2} + 4 \, a c} x^{2} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - 2 \, A a b^{2} + 8 \, A a^{2} c - {\left(B a b^{2} - A b^{3} - 4 \, {\left(B a^{2} - A a b\right)} c\right)} x^{2} \log\left(c x^{4} + b x^{2} + a\right) + 4 \, {\left(B a b^{2} - A b^{3} - 4 \, {\left(B a^{2} - A a b\right)} c\right)} x^{2} \log\left(x\right)}{4 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x^{2}}\right]"," ",0,"[1/4*((B*a*b - A*b^2 + 2*A*a*c)*sqrt(b^2 - 4*a*c)*x^2*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) - 2*A*a*b^2 + 8*A*a^2*c - (B*a*b^2 - A*b^3 - 4*(B*a^2 - A*a*b)*c)*x^2*log(c*x^4 + b*x^2 + a) + 4*(B*a*b^2 - A*b^3 - 4*(B*a^2 - A*a*b)*c)*x^2*log(x))/((a^2*b^2 - 4*a^3*c)*x^2), 1/4*(2*(B*a*b - A*b^2 + 2*A*a*c)*sqrt(-b^2 + 4*a*c)*x^2*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - 2*A*a*b^2 + 8*A*a^2*c - (B*a*b^2 - A*b^3 - 4*(B*a^2 - A*a*b)*c)*x^2*log(c*x^4 + b*x^2 + a) + 4*(B*a*b^2 - A*b^3 - 4*(B*a^2 - A*a*b)*c)*x^2*log(x))/((a^2*b^2 - 4*a^3*c)*x^2)]","A",0
107,1,5140,0,3.519054," ","integrate(x^4*(B*x^2+A)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{2 \, B c x^{3} + 3 \, \sqrt{\frac{1}{2}} c^{2} \sqrt{-\frac{B^{2} b^{5} - {\left(4 \, A B a^{2} + 3 \, A^{2} a b\right)} c^{3} + {\left(5 \, B^{2} a^{2} b + 8 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a b^{3} + 2 \, A B b^{4}\right)} c + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(-2 \, {\left(B^{4} a^{2} b^{4} - A B^{3} a b^{5} - A^{4} a^{2} c^{4} + {\left(5 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{3} + {\left(B^{4} a^{4} + 3 \, A B^{3} a^{3} b - 6 \, A^{2} B^{2} a^{2} b^{2} - 3 \, A^{3} B a b^{3}\right)} c^{2} - {\left(3 \, B^{4} a^{3} b^{2} - A B^{3} a^{2} b^{3} - 3 \, A^{2} B^{2} a b^{4}\right)} c\right)} x + \sqrt{\frac{1}{2}} {\left(B^{3} b^{7} - 4 \, A^{3} a^{2} c^{5} + {\left(4 \, A B^{2} a^{3} + 20 \, A^{2} B a^{2} b + 5 \, A^{3} a b^{2}\right)} c^{4} - {\left(4 \, B^{3} a^{3} b + 29 \, A B^{2} a^{2} b^{2} + 17 \, A^{2} B a b^{3} + A^{3} b^{4}\right)} c^{3} + {\left(13 \, B^{3} a^{2} b^{3} + 19 \, A B^{2} a b^{4} + 3 \, A^{2} B b^{5}\right)} c^{2} - {\left(7 \, B^{3} a b^{5} + 3 \, A B^{2} b^{6}\right)} c - {\left(B b^{4} c^{5} + 4 \, {\left(2 \, B a^{2} + A a b\right)} c^{7} - {\left(6 \, B a b^{2} + A b^{3}\right)} c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{-\frac{B^{2} b^{5} - {\left(4 \, A B a^{2} + 3 \, A^{2} a b\right)} c^{3} + {\left(5 \, B^{2} a^{2} b + 8 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a b^{3} + 2 \, A B b^{4}\right)} c + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}}\right) - 3 \, \sqrt{\frac{1}{2}} c^{2} \sqrt{-\frac{B^{2} b^{5} - {\left(4 \, A B a^{2} + 3 \, A^{2} a b\right)} c^{3} + {\left(5 \, B^{2} a^{2} b + 8 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a b^{3} + 2 \, A B b^{4}\right)} c + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(-2 \, {\left(B^{4} a^{2} b^{4} - A B^{3} a b^{5} - A^{4} a^{2} c^{4} + {\left(5 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{3} + {\left(B^{4} a^{4} + 3 \, A B^{3} a^{3} b - 6 \, A^{2} B^{2} a^{2} b^{2} - 3 \, A^{3} B a b^{3}\right)} c^{2} - {\left(3 \, B^{4} a^{3} b^{2} - A B^{3} a^{2} b^{3} - 3 \, A^{2} B^{2} a b^{4}\right)} c\right)} x - \sqrt{\frac{1}{2}} {\left(B^{3} b^{7} - 4 \, A^{3} a^{2} c^{5} + {\left(4 \, A B^{2} a^{3} + 20 \, A^{2} B a^{2} b + 5 \, A^{3} a b^{2}\right)} c^{4} - {\left(4 \, B^{3} a^{3} b + 29 \, A B^{2} a^{2} b^{2} + 17 \, A^{2} B a b^{3} + A^{3} b^{4}\right)} c^{3} + {\left(13 \, B^{3} a^{2} b^{3} + 19 \, A B^{2} a b^{4} + 3 \, A^{2} B b^{5}\right)} c^{2} - {\left(7 \, B^{3} a b^{5} + 3 \, A B^{2} b^{6}\right)} c - {\left(B b^{4} c^{5} + 4 \, {\left(2 \, B a^{2} + A a b\right)} c^{7} - {\left(6 \, B a b^{2} + A b^{3}\right)} c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{-\frac{B^{2} b^{5} - {\left(4 \, A B a^{2} + 3 \, A^{2} a b\right)} c^{3} + {\left(5 \, B^{2} a^{2} b + 8 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a b^{3} + 2 \, A B b^{4}\right)} c + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}}\right) + 3 \, \sqrt{\frac{1}{2}} c^{2} \sqrt{-\frac{B^{2} b^{5} - {\left(4 \, A B a^{2} + 3 \, A^{2} a b\right)} c^{3} + {\left(5 \, B^{2} a^{2} b + 8 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a b^{3} + 2 \, A B b^{4}\right)} c - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(-2 \, {\left(B^{4} a^{2} b^{4} - A B^{3} a b^{5} - A^{4} a^{2} c^{4} + {\left(5 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{3} + {\left(B^{4} a^{4} + 3 \, A B^{3} a^{3} b - 6 \, A^{2} B^{2} a^{2} b^{2} - 3 \, A^{3} B a b^{3}\right)} c^{2} - {\left(3 \, B^{4} a^{3} b^{2} - A B^{3} a^{2} b^{3} - 3 \, A^{2} B^{2} a b^{4}\right)} c\right)} x + \sqrt{\frac{1}{2}} {\left(B^{3} b^{7} - 4 \, A^{3} a^{2} c^{5} + {\left(4 \, A B^{2} a^{3} + 20 \, A^{2} B a^{2} b + 5 \, A^{3} a b^{2}\right)} c^{4} - {\left(4 \, B^{3} a^{3} b + 29 \, A B^{2} a^{2} b^{2} + 17 \, A^{2} B a b^{3} + A^{3} b^{4}\right)} c^{3} + {\left(13 \, B^{3} a^{2} b^{3} + 19 \, A B^{2} a b^{4} + 3 \, A^{2} B b^{5}\right)} c^{2} - {\left(7 \, B^{3} a b^{5} + 3 \, A B^{2} b^{6}\right)} c + {\left(B b^{4} c^{5} + 4 \, {\left(2 \, B a^{2} + A a b\right)} c^{7} - {\left(6 \, B a b^{2} + A b^{3}\right)} c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{-\frac{B^{2} b^{5} - {\left(4 \, A B a^{2} + 3 \, A^{2} a b\right)} c^{3} + {\left(5 \, B^{2} a^{2} b + 8 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a b^{3} + 2 \, A B b^{4}\right)} c - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}}\right) - 3 \, \sqrt{\frac{1}{2}} c^{2} \sqrt{-\frac{B^{2} b^{5} - {\left(4 \, A B a^{2} + 3 \, A^{2} a b\right)} c^{3} + {\left(5 \, B^{2} a^{2} b + 8 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a b^{3} + 2 \, A B b^{4}\right)} c - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(-2 \, {\left(B^{4} a^{2} b^{4} - A B^{3} a b^{5} - A^{4} a^{2} c^{4} + {\left(5 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{3} + {\left(B^{4} a^{4} + 3 \, A B^{3} a^{3} b - 6 \, A^{2} B^{2} a^{2} b^{2} - 3 \, A^{3} B a b^{3}\right)} c^{2} - {\left(3 \, B^{4} a^{3} b^{2} - A B^{3} a^{2} b^{3} - 3 \, A^{2} B^{2} a b^{4}\right)} c\right)} x - \sqrt{\frac{1}{2}} {\left(B^{3} b^{7} - 4 \, A^{3} a^{2} c^{5} + {\left(4 \, A B^{2} a^{3} + 20 \, A^{2} B a^{2} b + 5 \, A^{3} a b^{2}\right)} c^{4} - {\left(4 \, B^{3} a^{3} b + 29 \, A B^{2} a^{2} b^{2} + 17 \, A^{2} B a b^{3} + A^{3} b^{4}\right)} c^{3} + {\left(13 \, B^{3} a^{2} b^{3} + 19 \, A B^{2} a b^{4} + 3 \, A^{2} B b^{5}\right)} c^{2} - {\left(7 \, B^{3} a b^{5} + 3 \, A B^{2} b^{6}\right)} c + {\left(B b^{4} c^{5} + 4 \, {\left(2 \, B a^{2} + A a b\right)} c^{7} - {\left(6 \, B a b^{2} + A b^{3}\right)} c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{-\frac{B^{2} b^{5} - {\left(4 \, A B a^{2} + 3 \, A^{2} a b\right)} c^{3} + {\left(5 \, B^{2} a^{2} b + 8 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(5 \, B^{2} a b^{3} + 2 \, A B b^{4}\right)} c - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{B^{4} b^{8} + A^{4} a^{2} c^{6} - 2 \, {\left(A^{2} B^{2} a^{3} + 4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(B^{4} a^{4} + 8 \, A B^{3} a^{3} b + 24 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 2 \, {\left(3 \, B^{4} a^{3} b^{2} + 14 \, A B^{3} a^{2} b^{3} + 12 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + {\left(11 \, B^{4} a^{2} b^{4} + 20 \, A B^{3} a b^{5} + 6 \, A^{2} B^{2} b^{6}\right)} c^{2} - 2 \, {\left(3 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}}\right) - 6 \, {\left(B b - A c\right)} x}{6 \, c^{2}}"," ",0,"1/6*(2*B*c*x^3 + 3*sqrt(1/2)*c^2*sqrt(-(B^2*b^5 - (4*A*B*a^2 + 3*A^2*a*b)*c^3 + (5*B^2*a^2*b + 8*A*B*a*b^2 + A^2*b^3)*c^2 - (5*B^2*a*b^3 + 2*A*B*b^4)*c + (b^2*c^5 - 4*a*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(-2*(B^4*a^2*b^4 - A*B^3*a*b^5 - A^4*a^2*c^4 + (5*A^3*B*a^2*b + A^4*a*b^2)*c^3 + (B^4*a^4 + 3*A*B^3*a^3*b - 6*A^2*B^2*a^2*b^2 - 3*A^3*B*a*b^3)*c^2 - (3*B^4*a^3*b^2 - A*B^3*a^2*b^3 - 3*A^2*B^2*a*b^4)*c)*x + sqrt(1/2)*(B^3*b^7 - 4*A^3*a^2*c^5 + (4*A*B^2*a^3 + 20*A^2*B*a^2*b + 5*A^3*a*b^2)*c^4 - (4*B^3*a^3*b + 29*A*B^2*a^2*b^2 + 17*A^2*B*a*b^3 + A^3*b^4)*c^3 + (13*B^3*a^2*b^3 + 19*A*B^2*a*b^4 + 3*A^2*B*b^5)*c^2 - (7*B^3*a*b^5 + 3*A*B^2*b^6)*c - (B*b^4*c^5 + 4*(2*B*a^2 + A*a*b)*c^7 - (6*B*a*b^2 + A*b^3)*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))*sqrt(-(B^2*b^5 - (4*A*B*a^2 + 3*A^2*a*b)*c^3 + (5*B^2*a^2*b + 8*A*B*a*b^2 + A^2*b^3)*c^2 - (5*B^2*a*b^3 + 2*A*B*b^4)*c + (b^2*c^5 - 4*a*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))) - 3*sqrt(1/2)*c^2*sqrt(-(B^2*b^5 - (4*A*B*a^2 + 3*A^2*a*b)*c^3 + (5*B^2*a^2*b + 8*A*B*a*b^2 + A^2*b^3)*c^2 - (5*B^2*a*b^3 + 2*A*B*b^4)*c + (b^2*c^5 - 4*a*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(-2*(B^4*a^2*b^4 - A*B^3*a*b^5 - A^4*a^2*c^4 + (5*A^3*B*a^2*b + A^4*a*b^2)*c^3 + (B^4*a^4 + 3*A*B^3*a^3*b - 6*A^2*B^2*a^2*b^2 - 3*A^3*B*a*b^3)*c^2 - (3*B^4*a^3*b^2 - A*B^3*a^2*b^3 - 3*A^2*B^2*a*b^4)*c)*x - sqrt(1/2)*(B^3*b^7 - 4*A^3*a^2*c^5 + (4*A*B^2*a^3 + 20*A^2*B*a^2*b + 5*A^3*a*b^2)*c^4 - (4*B^3*a^3*b + 29*A*B^2*a^2*b^2 + 17*A^2*B*a*b^3 + A^3*b^4)*c^3 + (13*B^3*a^2*b^3 + 19*A*B^2*a*b^4 + 3*A^2*B*b^5)*c^2 - (7*B^3*a*b^5 + 3*A*B^2*b^6)*c - (B*b^4*c^5 + 4*(2*B*a^2 + A*a*b)*c^7 - (6*B*a*b^2 + A*b^3)*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))*sqrt(-(B^2*b^5 - (4*A*B*a^2 + 3*A^2*a*b)*c^3 + (5*B^2*a^2*b + 8*A*B*a*b^2 + A^2*b^3)*c^2 - (5*B^2*a*b^3 + 2*A*B*b^4)*c + (b^2*c^5 - 4*a*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))) + 3*sqrt(1/2)*c^2*sqrt(-(B^2*b^5 - (4*A*B*a^2 + 3*A^2*a*b)*c^3 + (5*B^2*a^2*b + 8*A*B*a*b^2 + A^2*b^3)*c^2 - (5*B^2*a*b^3 + 2*A*B*b^4)*c - (b^2*c^5 - 4*a*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(-2*(B^4*a^2*b^4 - A*B^3*a*b^5 - A^4*a^2*c^4 + (5*A^3*B*a^2*b + A^4*a*b^2)*c^3 + (B^4*a^4 + 3*A*B^3*a^3*b - 6*A^2*B^2*a^2*b^2 - 3*A^3*B*a*b^3)*c^2 - (3*B^4*a^3*b^2 - A*B^3*a^2*b^3 - 3*A^2*B^2*a*b^4)*c)*x + sqrt(1/2)*(B^3*b^7 - 4*A^3*a^2*c^5 + (4*A*B^2*a^3 + 20*A^2*B*a^2*b + 5*A^3*a*b^2)*c^4 - (4*B^3*a^3*b + 29*A*B^2*a^2*b^2 + 17*A^2*B*a*b^3 + A^3*b^4)*c^3 + (13*B^3*a^2*b^3 + 19*A*B^2*a*b^4 + 3*A^2*B*b^5)*c^2 - (7*B^3*a*b^5 + 3*A*B^2*b^6)*c + (B*b^4*c^5 + 4*(2*B*a^2 + A*a*b)*c^7 - (6*B*a*b^2 + A*b^3)*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))*sqrt(-(B^2*b^5 - (4*A*B*a^2 + 3*A^2*a*b)*c^3 + (5*B^2*a^2*b + 8*A*B*a*b^2 + A^2*b^3)*c^2 - (5*B^2*a*b^3 + 2*A*B*b^4)*c - (b^2*c^5 - 4*a*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))) - 3*sqrt(1/2)*c^2*sqrt(-(B^2*b^5 - (4*A*B*a^2 + 3*A^2*a*b)*c^3 + (5*B^2*a^2*b + 8*A*B*a*b^2 + A^2*b^3)*c^2 - (5*B^2*a*b^3 + 2*A*B*b^4)*c - (b^2*c^5 - 4*a*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(-2*(B^4*a^2*b^4 - A*B^3*a*b^5 - A^4*a^2*c^4 + (5*A^3*B*a^2*b + A^4*a*b^2)*c^3 + (B^4*a^4 + 3*A*B^3*a^3*b - 6*A^2*B^2*a^2*b^2 - 3*A^3*B*a*b^3)*c^2 - (3*B^4*a^3*b^2 - A*B^3*a^2*b^3 - 3*A^2*B^2*a*b^4)*c)*x - sqrt(1/2)*(B^3*b^7 - 4*A^3*a^2*c^5 + (4*A*B^2*a^3 + 20*A^2*B*a^2*b + 5*A^3*a*b^2)*c^4 - (4*B^3*a^3*b + 29*A*B^2*a^2*b^2 + 17*A^2*B*a*b^3 + A^3*b^4)*c^3 + (13*B^3*a^2*b^3 + 19*A*B^2*a*b^4 + 3*A^2*B*b^5)*c^2 - (7*B^3*a*b^5 + 3*A*B^2*b^6)*c + (B*b^4*c^5 + 4*(2*B*a^2 + A*a*b)*c^7 - (6*B*a*b^2 + A*b^3)*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))*sqrt(-(B^2*b^5 - (4*A*B*a^2 + 3*A^2*a*b)*c^3 + (5*B^2*a^2*b + 8*A*B*a*b^2 + A^2*b^3)*c^2 - (5*B^2*a*b^3 + 2*A*B*b^4)*c - (b^2*c^5 - 4*a*c^6)*sqrt((B^4*b^8 + A^4*a^2*c^6 - 2*(A^2*B^2*a^3 + 4*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (B^4*a^4 + 8*A*B^3*a^3*b + 24*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)*c^4 - 2*(3*B^4*a^3*b^2 + 14*A*B^3*a^2*b^3 + 12*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + (11*B^4*a^2*b^4 + 20*A*B^3*a*b^5 + 6*A^2*B^2*b^6)*c^2 - 2*(3*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))) - 6*(B*b - A*c)*x)/c^2","B",0
108,1,2632,0,1.296249," ","integrate(x^2*(B*x^2+A)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} c \sqrt{-\frac{B^{2} b^{3} + {\left(4 \, A B a + A^{2} b\right)} c^{2} - {\left(3 \, B^{2} a b + 2 \, A B b^{2}\right)} c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(2 \, {\left(B^{4} a b^{2} - A B^{3} b^{3} - 3 \, A^{3} B b c^{2} + A^{4} c^{3} - {\left(B^{4} a^{2} + A B^{3} a b - 3 \, A^{2} B^{2} b^{2}\right)} c\right)} x + \sqrt{\frac{1}{2}} {\left(B^{3} b^{4} - 4 \, A^{2} B a c^{3} + {\left(4 \, B^{3} a^{2} + 8 \, A B^{2} a b + A^{2} B b^{2}\right)} c^{2} - {\left(5 \, B^{3} a b^{2} + 2 \, A B^{2} b^{3}\right)} c - {\left(B b^{3} c^{3} + 8 \, A a c^{5} - 2 \, {\left(2 \, B a b + A b^{2}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{B^{2} b^{3} + {\left(4 \, A B a + A^{2} b\right)} c^{2} - {\left(3 \, B^{2} a b + 2 \, A B b^{2}\right)} c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}}\right) - \sqrt{\frac{1}{2}} c \sqrt{-\frac{B^{2} b^{3} + {\left(4 \, A B a + A^{2} b\right)} c^{2} - {\left(3 \, B^{2} a b + 2 \, A B b^{2}\right)} c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(2 \, {\left(B^{4} a b^{2} - A B^{3} b^{3} - 3 \, A^{3} B b c^{2} + A^{4} c^{3} - {\left(B^{4} a^{2} + A B^{3} a b - 3 \, A^{2} B^{2} b^{2}\right)} c\right)} x - \sqrt{\frac{1}{2}} {\left(B^{3} b^{4} - 4 \, A^{2} B a c^{3} + {\left(4 \, B^{3} a^{2} + 8 \, A B^{2} a b + A^{2} B b^{2}\right)} c^{2} - {\left(5 \, B^{3} a b^{2} + 2 \, A B^{2} b^{3}\right)} c - {\left(B b^{3} c^{3} + 8 \, A a c^{5} - 2 \, {\left(2 \, B a b + A b^{2}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{B^{2} b^{3} + {\left(4 \, A B a + A^{2} b\right)} c^{2} - {\left(3 \, B^{2} a b + 2 \, A B b^{2}\right)} c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}}\right) + \sqrt{\frac{1}{2}} c \sqrt{-\frac{B^{2} b^{3} + {\left(4 \, A B a + A^{2} b\right)} c^{2} - {\left(3 \, B^{2} a b + 2 \, A B b^{2}\right)} c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(2 \, {\left(B^{4} a b^{2} - A B^{3} b^{3} - 3 \, A^{3} B b c^{2} + A^{4} c^{3} - {\left(B^{4} a^{2} + A B^{3} a b - 3 \, A^{2} B^{2} b^{2}\right)} c\right)} x + \sqrt{\frac{1}{2}} {\left(B^{3} b^{4} - 4 \, A^{2} B a c^{3} + {\left(4 \, B^{3} a^{2} + 8 \, A B^{2} a b + A^{2} B b^{2}\right)} c^{2} - {\left(5 \, B^{3} a b^{2} + 2 \, A B^{2} b^{3}\right)} c + {\left(B b^{3} c^{3} + 8 \, A a c^{5} - 2 \, {\left(2 \, B a b + A b^{2}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{B^{2} b^{3} + {\left(4 \, A B a + A^{2} b\right)} c^{2} - {\left(3 \, B^{2} a b + 2 \, A B b^{2}\right)} c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}}\right) - \sqrt{\frac{1}{2}} c \sqrt{-\frac{B^{2} b^{3} + {\left(4 \, A B a + A^{2} b\right)} c^{2} - {\left(3 \, B^{2} a b + 2 \, A B b^{2}\right)} c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(2 \, {\left(B^{4} a b^{2} - A B^{3} b^{3} - 3 \, A^{3} B b c^{2} + A^{4} c^{3} - {\left(B^{4} a^{2} + A B^{3} a b - 3 \, A^{2} B^{2} b^{2}\right)} c\right)} x - \sqrt{\frac{1}{2}} {\left(B^{3} b^{4} - 4 \, A^{2} B a c^{3} + {\left(4 \, B^{3} a^{2} + 8 \, A B^{2} a b + A^{2} B b^{2}\right)} c^{2} - {\left(5 \, B^{3} a b^{2} + 2 \, A B^{2} b^{3}\right)} c + {\left(B b^{3} c^{3} + 8 \, A a c^{5} - 2 \, {\left(2 \, B a b + A b^{2}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{B^{2} b^{3} + {\left(4 \, A B a + A^{2} b\right)} c^{2} - {\left(3 \, B^{2} a b + 2 \, A B b^{2}\right)} c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a + 2 \, A^{3} B b\right)} c^{3} + {\left(B^{4} a^{2} + 4 \, A B^{3} a b + 6 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(B^{4} a b^{2} + 2 \, A B^{3} b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}}\right) + 2 \, B x}{2 \, c}"," ",0,"1/2*(sqrt(1/2)*c*sqrt(-(B^2*b^3 + (4*A*B*a + A^2*b)*c^2 - (3*B^2*a*b + 2*A*B*b^2)*c + (b^2*c^3 - 4*a*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(2*(B^4*a*b^2 - A*B^3*b^3 - 3*A^3*B*b*c^2 + A^4*c^3 - (B^4*a^2 + A*B^3*a*b - 3*A^2*B^2*b^2)*c)*x + sqrt(1/2)*(B^3*b^4 - 4*A^2*B*a*c^3 + (4*B^3*a^2 + 8*A*B^2*a*b + A^2*B*b^2)*c^2 - (5*B^3*a*b^2 + 2*A*B^2*b^3)*c - (B*b^3*c^3 + 8*A*a*c^5 - 2*(2*B*a*b + A*b^2)*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(B^2*b^3 + (4*A*B*a + A^2*b)*c^2 - (3*B^2*a*b + 2*A*B*b^2)*c + (b^2*c^3 - 4*a*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))) - sqrt(1/2)*c*sqrt(-(B^2*b^3 + (4*A*B*a + A^2*b)*c^2 - (3*B^2*a*b + 2*A*B*b^2)*c + (b^2*c^3 - 4*a*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(2*(B^4*a*b^2 - A*B^3*b^3 - 3*A^3*B*b*c^2 + A^4*c^3 - (B^4*a^2 + A*B^3*a*b - 3*A^2*B^2*b^2)*c)*x - sqrt(1/2)*(B^3*b^4 - 4*A^2*B*a*c^3 + (4*B^3*a^2 + 8*A*B^2*a*b + A^2*B*b^2)*c^2 - (5*B^3*a*b^2 + 2*A*B^2*b^3)*c - (B*b^3*c^3 + 8*A*a*c^5 - 2*(2*B*a*b + A*b^2)*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(B^2*b^3 + (4*A*B*a + A^2*b)*c^2 - (3*B^2*a*b + 2*A*B*b^2)*c + (b^2*c^3 - 4*a*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))) + sqrt(1/2)*c*sqrt(-(B^2*b^3 + (4*A*B*a + A^2*b)*c^2 - (3*B^2*a*b + 2*A*B*b^2)*c - (b^2*c^3 - 4*a*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(2*(B^4*a*b^2 - A*B^3*b^3 - 3*A^3*B*b*c^2 + A^4*c^3 - (B^4*a^2 + A*B^3*a*b - 3*A^2*B^2*b^2)*c)*x + sqrt(1/2)*(B^3*b^4 - 4*A^2*B*a*c^3 + (4*B^3*a^2 + 8*A*B^2*a*b + A^2*B*b^2)*c^2 - (5*B^3*a*b^2 + 2*A*B^2*b^3)*c + (B*b^3*c^3 + 8*A*a*c^5 - 2*(2*B*a*b + A*b^2)*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(B^2*b^3 + (4*A*B*a + A^2*b)*c^2 - (3*B^2*a*b + 2*A*B*b^2)*c - (b^2*c^3 - 4*a*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))) - sqrt(1/2)*c*sqrt(-(B^2*b^3 + (4*A*B*a + A^2*b)*c^2 - (3*B^2*a*b + 2*A*B*b^2)*c - (b^2*c^3 - 4*a*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(2*(B^4*a*b^2 - A*B^3*b^3 - 3*A^3*B*b*c^2 + A^4*c^3 - (B^4*a^2 + A*B^3*a*b - 3*A^2*B^2*b^2)*c)*x - sqrt(1/2)*(B^3*b^4 - 4*A^2*B*a*c^3 + (4*B^3*a^2 + 8*A*B^2*a*b + A^2*B*b^2)*c^2 - (5*B^3*a*b^2 + 2*A*B^2*b^3)*c + (B*b^3*c^3 + 8*A*a*c^5 - 2*(2*B*a*b + A*b^2)*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(B^2*b^3 + (4*A*B*a + A^2*b)*c^2 - (3*B^2*a*b + 2*A*B*b^2)*c - (b^2*c^3 - 4*a*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(A^2*B^2*a + 2*A^3*B*b)*c^3 + (B^4*a^2 + 4*A*B^3*a*b + 6*A^2*B^2*b^2)*c^2 - 2*(B^4*a*b^2 + 2*A*B^3*b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))) + 2*B*x)/c","B",0
109,1,1569,0,1.327100," ","integrate((B*x^2+A)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{B^{2} a b - {\left(4 \, A B a - A^{2} b\right)} c + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}} \log\left(-2 \, {\left(B^{4} a^{2} - A B^{3} a b + A^{3} B b c - A^{4} c^{2}\right)} x + \sqrt{\frac{1}{2}} {\left(A B^{2} a b^{2} + 4 \, A^{3} a c^{2} - {\left(4 \, A B^{2} a^{2} + A^{3} b^{2}\right)} c + {\left(4 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{2} - {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}\right)} \sqrt{-\frac{B^{2} a b - {\left(4 \, A B a - A^{2} b\right)} c + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}}\right) - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{B^{2} a b - {\left(4 \, A B a - A^{2} b\right)} c + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}} \log\left(-2 \, {\left(B^{4} a^{2} - A B^{3} a b + A^{3} B b c - A^{4} c^{2}\right)} x - \sqrt{\frac{1}{2}} {\left(A B^{2} a b^{2} + 4 \, A^{3} a c^{2} - {\left(4 \, A B^{2} a^{2} + A^{3} b^{2}\right)} c + {\left(4 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{2} - {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}\right)} \sqrt{-\frac{B^{2} a b - {\left(4 \, A B a - A^{2} b\right)} c + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}}\right) + \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{B^{2} a b - {\left(4 \, A B a - A^{2} b\right)} c - {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}} \log\left(-2 \, {\left(B^{4} a^{2} - A B^{3} a b + A^{3} B b c - A^{4} c^{2}\right)} x + \sqrt{\frac{1}{2}} {\left(A B^{2} a b^{2} + 4 \, A^{3} a c^{2} - {\left(4 \, A B^{2} a^{2} + A^{3} b^{2}\right)} c - {\left(4 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{2} - {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}\right)} \sqrt{-\frac{B^{2} a b - {\left(4 \, A B a - A^{2} b\right)} c - {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}}\right) - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{B^{2} a b - {\left(4 \, A B a - A^{2} b\right)} c - {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}} \log\left(-2 \, {\left(B^{4} a^{2} - A B^{3} a b + A^{3} B b c - A^{4} c^{2}\right)} x - \sqrt{\frac{1}{2}} {\left(A B^{2} a b^{2} + 4 \, A^{3} a c^{2} - {\left(4 \, A B^{2} a^{2} + A^{3} b^{2}\right)} c - {\left(4 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{2} - {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}\right)} \sqrt{-\frac{B^{2} a b - {\left(4 \, A B a - A^{2} b\right)} c - {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}}\right)"," ",0,"1/2*sqrt(1/2)*sqrt(-(B^2*a*b - (4*A*B*a - A^2*b)*c + (a*b^2*c - 4*a^2*c^2)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))*log(-2*(B^4*a^2 - A*B^3*a*b + A^3*B*b*c - A^4*c^2)*x + sqrt(1/2)*(A*B^2*a*b^2 + 4*A^3*a*c^2 - (4*A*B^2*a^2 + A^3*b^2)*c + (4*(2*B*a^3 - A*a^2*b)*c^2 - (2*B*a^2*b^2 - A*a*b^3)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))*sqrt(-(B^2*a*b - (4*A*B*a - A^2*b)*c + (a*b^2*c - 4*a^2*c^2)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))) - 1/2*sqrt(1/2)*sqrt(-(B^2*a*b - (4*A*B*a - A^2*b)*c + (a*b^2*c - 4*a^2*c^2)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))*log(-2*(B^4*a^2 - A*B^3*a*b + A^3*B*b*c - A^4*c^2)*x - sqrt(1/2)*(A*B^2*a*b^2 + 4*A^3*a*c^2 - (4*A*B^2*a^2 + A^3*b^2)*c + (4*(2*B*a^3 - A*a^2*b)*c^2 - (2*B*a^2*b^2 - A*a*b^3)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))*sqrt(-(B^2*a*b - (4*A*B*a - A^2*b)*c + (a*b^2*c - 4*a^2*c^2)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))) + 1/2*sqrt(1/2)*sqrt(-(B^2*a*b - (4*A*B*a - A^2*b)*c - (a*b^2*c - 4*a^2*c^2)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))*log(-2*(B^4*a^2 - A*B^3*a*b + A^3*B*b*c - A^4*c^2)*x + sqrt(1/2)*(A*B^2*a*b^2 + 4*A^3*a*c^2 - (4*A*B^2*a^2 + A^3*b^2)*c - (4*(2*B*a^3 - A*a^2*b)*c^2 - (2*B*a^2*b^2 - A*a*b^3)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))*sqrt(-(B^2*a*b - (4*A*B*a - A^2*b)*c - (a*b^2*c - 4*a^2*c^2)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))) - 1/2*sqrt(1/2)*sqrt(-(B^2*a*b - (4*A*B*a - A^2*b)*c - (a*b^2*c - 4*a^2*c^2)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))*log(-2*(B^4*a^2 - A*B^3*a*b + A^3*B*b*c - A^4*c^2)*x - sqrt(1/2)*(A*B^2*a*b^2 + 4*A^3*a*c^2 - (4*A*B^2*a^2 + A^3*b^2)*c - (4*(2*B*a^3 - A*a^2*b)*c^2 - (2*B*a^2*b^2 - A*a*b^3)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))*sqrt(-(B^2*a*b - (4*A*B*a - A^2*b)*c - (a*b^2*c - 4*a^2*c^2)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2)))","B",0
110,1,2914,0,1.474563," ","integrate((B*x^2+A)/x^2/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} a x \sqrt{-\frac{B^{2} a^{2} b - 2 \, A B a b^{2} + A^{2} b^{3} + {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(2 \, {\left(A^{4} a c^{3} + {\left(A^{3} B a b - A^{4} b^{2}\right)} c^{2} - {\left(B^{4} a^{3} - 3 \, A B^{3} a^{2} b + 3 \, A^{2} B^{2} a b^{2} - A^{3} B b^{3}\right)} c\right)} x + \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{2} - 3 \, A B^{2} a^{2} b^{3} + 3 \, A^{2} B a b^{4} - A^{3} b^{5} + 4 \, {\left(A^{2} B a^{3} - A^{3} a^{2} b\right)} c^{2} - {\left(4 \, B^{3} a^{4} - 12 \, A B^{2} a^{3} b + 13 \, A^{2} B a^{2} b^{2} - 5 \, A^{3} a b^{3}\right)} c - {\left(B a^{4} b^{3} - A a^{3} b^{4} - 8 \, A a^{5} c^{2} - 2 \, {\left(2 \, B a^{5} b - 3 \, A a^{4} b^{2}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b - 2 \, A B a b^{2} + A^{2} b^{3} + {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}\right) - \sqrt{\frac{1}{2}} a x \sqrt{-\frac{B^{2} a^{2} b - 2 \, A B a b^{2} + A^{2} b^{3} + {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(2 \, {\left(A^{4} a c^{3} + {\left(A^{3} B a b - A^{4} b^{2}\right)} c^{2} - {\left(B^{4} a^{3} - 3 \, A B^{3} a^{2} b + 3 \, A^{2} B^{2} a b^{2} - A^{3} B b^{3}\right)} c\right)} x - \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{2} - 3 \, A B^{2} a^{2} b^{3} + 3 \, A^{2} B a b^{4} - A^{3} b^{5} + 4 \, {\left(A^{2} B a^{3} - A^{3} a^{2} b\right)} c^{2} - {\left(4 \, B^{3} a^{4} - 12 \, A B^{2} a^{3} b + 13 \, A^{2} B a^{2} b^{2} - 5 \, A^{3} a b^{3}\right)} c - {\left(B a^{4} b^{3} - A a^{3} b^{4} - 8 \, A a^{5} c^{2} - 2 \, {\left(2 \, B a^{5} b - 3 \, A a^{4} b^{2}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b - 2 \, A B a b^{2} + A^{2} b^{3} + {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}\right) + \sqrt{\frac{1}{2}} a x \sqrt{-\frac{B^{2} a^{2} b - 2 \, A B a b^{2} + A^{2} b^{3} + {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(2 \, {\left(A^{4} a c^{3} + {\left(A^{3} B a b - A^{4} b^{2}\right)} c^{2} - {\left(B^{4} a^{3} - 3 \, A B^{3} a^{2} b + 3 \, A^{2} B^{2} a b^{2} - A^{3} B b^{3}\right)} c\right)} x + \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{2} - 3 \, A B^{2} a^{2} b^{3} + 3 \, A^{2} B a b^{4} - A^{3} b^{5} + 4 \, {\left(A^{2} B a^{3} - A^{3} a^{2} b\right)} c^{2} - {\left(4 \, B^{3} a^{4} - 12 \, A B^{2} a^{3} b + 13 \, A^{2} B a^{2} b^{2} - 5 \, A^{3} a b^{3}\right)} c + {\left(B a^{4} b^{3} - A a^{3} b^{4} - 8 \, A a^{5} c^{2} - 2 \, {\left(2 \, B a^{5} b - 3 \, A a^{4} b^{2}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b - 2 \, A B a b^{2} + A^{2} b^{3} + {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}\right) - \sqrt{\frac{1}{2}} a x \sqrt{-\frac{B^{2} a^{2} b - 2 \, A B a b^{2} + A^{2} b^{3} + {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(2 \, {\left(A^{4} a c^{3} + {\left(A^{3} B a b - A^{4} b^{2}\right)} c^{2} - {\left(B^{4} a^{3} - 3 \, A B^{3} a^{2} b + 3 \, A^{2} B^{2} a b^{2} - A^{3} B b^{3}\right)} c\right)} x - \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{2} - 3 \, A B^{2} a^{2} b^{3} + 3 \, A^{2} B a b^{4} - A^{3} b^{5} + 4 \, {\left(A^{2} B a^{3} - A^{3} a^{2} b\right)} c^{2} - {\left(4 \, B^{3} a^{4} - 12 \, A B^{2} a^{3} b + 13 \, A^{2} B a^{2} b^{2} - 5 \, A^{3} a b^{3}\right)} c + {\left(B a^{4} b^{3} - A a^{3} b^{4} - 8 \, A a^{5} c^{2} - 2 \, {\left(2 \, B a^{5} b - 3 \, A a^{4} b^{2}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b - 2 \, A B a b^{2} + A^{2} b^{3} + {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4} + A^{4} a^{2} c^{2} - 2 \, {\left(A^{2} B^{2} a^{3} - 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}\right) - 2 \, A}{2 \, a x}"," ",0,"1/2*(sqrt(1/2)*a*x*sqrt(-(B^2*a^2*b - 2*A*B*a*b^2 + A^2*b^3 + (4*A*B*a^2 - 3*A^2*a*b)*c + (a^3*b^2 - 4*a^4*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log(2*(A^4*a*c^3 + (A^3*B*a*b - A^4*b^2)*c^2 - (B^4*a^3 - 3*A*B^3*a^2*b + 3*A^2*B^2*a*b^2 - A^3*B*b^3)*c)*x + sqrt(1/2)*(B^3*a^3*b^2 - 3*A*B^2*a^2*b^3 + 3*A^2*B*a*b^4 - A^3*b^5 + 4*(A^2*B*a^3 - A^3*a^2*b)*c^2 - (4*B^3*a^4 - 12*A*B^2*a^3*b + 13*A^2*B*a^2*b^2 - 5*A^3*a*b^3)*c - (B*a^4*b^3 - A*a^3*b^4 - 8*A*a^5*c^2 - 2*(2*B*a^5*b - 3*A*a^4*b^2)*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(B^2*a^2*b - 2*A*B*a*b^2 + A^2*b^3 + (4*A*B*a^2 - 3*A^2*a*b)*c + (a^3*b^2 - 4*a^4*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))) - sqrt(1/2)*a*x*sqrt(-(B^2*a^2*b - 2*A*B*a*b^2 + A^2*b^3 + (4*A*B*a^2 - 3*A^2*a*b)*c + (a^3*b^2 - 4*a^4*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log(2*(A^4*a*c^3 + (A^3*B*a*b - A^4*b^2)*c^2 - (B^4*a^3 - 3*A*B^3*a^2*b + 3*A^2*B^2*a*b^2 - A^3*B*b^3)*c)*x - sqrt(1/2)*(B^3*a^3*b^2 - 3*A*B^2*a^2*b^3 + 3*A^2*B*a*b^4 - A^3*b^5 + 4*(A^2*B*a^3 - A^3*a^2*b)*c^2 - (4*B^3*a^4 - 12*A*B^2*a^3*b + 13*A^2*B*a^2*b^2 - 5*A^3*a*b^3)*c - (B*a^4*b^3 - A*a^3*b^4 - 8*A*a^5*c^2 - 2*(2*B*a^5*b - 3*A*a^4*b^2)*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(B^2*a^2*b - 2*A*B*a*b^2 + A^2*b^3 + (4*A*B*a^2 - 3*A^2*a*b)*c + (a^3*b^2 - 4*a^4*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))) + sqrt(1/2)*a*x*sqrt(-(B^2*a^2*b - 2*A*B*a*b^2 + A^2*b^3 + (4*A*B*a^2 - 3*A^2*a*b)*c - (a^3*b^2 - 4*a^4*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log(2*(A^4*a*c^3 + (A^3*B*a*b - A^4*b^2)*c^2 - (B^4*a^3 - 3*A*B^3*a^2*b + 3*A^2*B^2*a*b^2 - A^3*B*b^3)*c)*x + sqrt(1/2)*(B^3*a^3*b^2 - 3*A*B^2*a^2*b^3 + 3*A^2*B*a*b^4 - A^3*b^5 + 4*(A^2*B*a^3 - A^3*a^2*b)*c^2 - (4*B^3*a^4 - 12*A*B^2*a^3*b + 13*A^2*B*a^2*b^2 - 5*A^3*a*b^3)*c + (B*a^4*b^3 - A*a^3*b^4 - 8*A*a^5*c^2 - 2*(2*B*a^5*b - 3*A*a^4*b^2)*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(B^2*a^2*b - 2*A*B*a*b^2 + A^2*b^3 + (4*A*B*a^2 - 3*A^2*a*b)*c - (a^3*b^2 - 4*a^4*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))) - sqrt(1/2)*a*x*sqrt(-(B^2*a^2*b - 2*A*B*a*b^2 + A^2*b^3 + (4*A*B*a^2 - 3*A^2*a*b)*c - (a^3*b^2 - 4*a^4*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log(2*(A^4*a*c^3 + (A^3*B*a*b - A^4*b^2)*c^2 - (B^4*a^3 - 3*A*B^3*a^2*b + 3*A^2*B^2*a*b^2 - A^3*B*b^3)*c)*x - sqrt(1/2)*(B^3*a^3*b^2 - 3*A*B^2*a^2*b^3 + 3*A^2*B*a*b^4 - A^3*b^5 + 4*(A^2*B*a^3 - A^3*a^2*b)*c^2 - (4*B^3*a^4 - 12*A*B^2*a^3*b + 13*A^2*B*a^2*b^2 - 5*A^3*a*b^3)*c + (B*a^4*b^3 - A*a^3*b^4 - 8*A*a^5*c^2 - 2*(2*B*a^5*b - 3*A*a^4*b^2)*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(B^2*a^2*b - 2*A*B*a*b^2 + A^2*b^3 + (4*A*B*a^2 - 3*A^2*a*b)*c - (a^3*b^2 - 4*a^4*c)*sqrt((B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4 + A^4*a^2*c^2 - 2*(A^2*B^2*a^3 - 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))) - 2*A)/(a*x)","B",0
111,1,5442,0,3.554040," ","integrate((B*x^2+A)/x^4/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{1}{2}} a^{2} x^{3} \sqrt{-\frac{B^{2} a^{2} b^{3} - 2 \, A B a b^{4} + A^{2} b^{5} - {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} - {\left(3 \, B^{2} a^{3} b - 8 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} \log\left(2 \, {\left(A^{4} a^{2} c^{5} + 3 \, {\left(A^{3} B a^{2} b - A^{4} a b^{2}\right)} c^{4} - {\left(B^{4} a^{4} - 5 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - A^{3} B a b^{3} - A^{4} b^{4}\right)} c^{3} + {\left(B^{4} a^{3} b^{2} - 3 \, A B^{3} a^{2} b^{3} + 3 \, A^{2} B^{2} a b^{4} - A^{3} B b^{5}\right)} c^{2}\right)} x + \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{5} - 3 \, A B^{2} a^{2} b^{6} + 3 \, A^{2} B a b^{7} - A^{3} b^{8} - 4 \, A^{3} a^{4} c^{4} + {\left(4 \, A B^{2} a^{5} - 20 \, A^{2} B a^{4} b + 17 \, A^{3} a^{3} b^{2}\right)} c^{3} + {\left(4 \, B^{3} a^{5} b - 25 \, A B^{2} a^{4} b^{2} + 41 \, A^{2} B a^{3} b^{3} - 20 \, A^{3} a^{2} b^{4}\right)} c^{2} - {\left(5 \, B^{3} a^{4} b^{3} - 18 \, A B^{2} a^{3} b^{4} + 21 \, A^{2} B a^{2} b^{5} - 8 \, A^{3} a b^{6}\right)} c - {\left(B a^{6} b^{4} - A a^{5} b^{5} + 4 \, {\left(2 \, B a^{8} - 3 \, A a^{7} b\right)} c^{2} - {\left(6 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} - 2 \, A B a b^{4} + A^{2} b^{5} - {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} - {\left(3 \, B^{2} a^{3} b - 8 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} x^{3} \sqrt{-\frac{B^{2} a^{2} b^{3} - 2 \, A B a b^{4} + A^{2} b^{5} - {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} - {\left(3 \, B^{2} a^{3} b - 8 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} \log\left(2 \, {\left(A^{4} a^{2} c^{5} + 3 \, {\left(A^{3} B a^{2} b - A^{4} a b^{2}\right)} c^{4} - {\left(B^{4} a^{4} - 5 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - A^{3} B a b^{3} - A^{4} b^{4}\right)} c^{3} + {\left(B^{4} a^{3} b^{2} - 3 \, A B^{3} a^{2} b^{3} + 3 \, A^{2} B^{2} a b^{4} - A^{3} B b^{5}\right)} c^{2}\right)} x - \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{5} - 3 \, A B^{2} a^{2} b^{6} + 3 \, A^{2} B a b^{7} - A^{3} b^{8} - 4 \, A^{3} a^{4} c^{4} + {\left(4 \, A B^{2} a^{5} - 20 \, A^{2} B a^{4} b + 17 \, A^{3} a^{3} b^{2}\right)} c^{3} + {\left(4 \, B^{3} a^{5} b - 25 \, A B^{2} a^{4} b^{2} + 41 \, A^{2} B a^{3} b^{3} - 20 \, A^{3} a^{2} b^{4}\right)} c^{2} - {\left(5 \, B^{3} a^{4} b^{3} - 18 \, A B^{2} a^{3} b^{4} + 21 \, A^{2} B a^{2} b^{5} - 8 \, A^{3} a b^{6}\right)} c - {\left(B a^{6} b^{4} - A a^{5} b^{5} + 4 \, {\left(2 \, B a^{8} - 3 \, A a^{7} b\right)} c^{2} - {\left(6 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} - 2 \, A B a b^{4} + A^{2} b^{5} - {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} - {\left(3 \, B^{2} a^{3} b - 8 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}}\right) + 3 \, \sqrt{\frac{1}{2}} a^{2} x^{3} \sqrt{-\frac{B^{2} a^{2} b^{3} - 2 \, A B a b^{4} + A^{2} b^{5} - {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} - {\left(3 \, B^{2} a^{3} b - 8 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} \log\left(2 \, {\left(A^{4} a^{2} c^{5} + 3 \, {\left(A^{3} B a^{2} b - A^{4} a b^{2}\right)} c^{4} - {\left(B^{4} a^{4} - 5 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - A^{3} B a b^{3} - A^{4} b^{4}\right)} c^{3} + {\left(B^{4} a^{3} b^{2} - 3 \, A B^{3} a^{2} b^{3} + 3 \, A^{2} B^{2} a b^{4} - A^{3} B b^{5}\right)} c^{2}\right)} x + \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{5} - 3 \, A B^{2} a^{2} b^{6} + 3 \, A^{2} B a b^{7} - A^{3} b^{8} - 4 \, A^{3} a^{4} c^{4} + {\left(4 \, A B^{2} a^{5} - 20 \, A^{2} B a^{4} b + 17 \, A^{3} a^{3} b^{2}\right)} c^{3} + {\left(4 \, B^{3} a^{5} b - 25 \, A B^{2} a^{4} b^{2} + 41 \, A^{2} B a^{3} b^{3} - 20 \, A^{3} a^{2} b^{4}\right)} c^{2} - {\left(5 \, B^{3} a^{4} b^{3} - 18 \, A B^{2} a^{3} b^{4} + 21 \, A^{2} B a^{2} b^{5} - 8 \, A^{3} a b^{6}\right)} c + {\left(B a^{6} b^{4} - A a^{5} b^{5} + 4 \, {\left(2 \, B a^{8} - 3 \, A a^{7} b\right)} c^{2} - {\left(6 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} - 2 \, A B a b^{4} + A^{2} b^{5} - {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} - {\left(3 \, B^{2} a^{3} b - 8 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} x^{3} \sqrt{-\frac{B^{2} a^{2} b^{3} - 2 \, A B a b^{4} + A^{2} b^{5} - {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} - {\left(3 \, B^{2} a^{3} b - 8 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} \log\left(2 \, {\left(A^{4} a^{2} c^{5} + 3 \, {\left(A^{3} B a^{2} b - A^{4} a b^{2}\right)} c^{4} - {\left(B^{4} a^{4} - 5 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - A^{3} B a b^{3} - A^{4} b^{4}\right)} c^{3} + {\left(B^{4} a^{3} b^{2} - 3 \, A B^{3} a^{2} b^{3} + 3 \, A^{2} B^{2} a b^{4} - A^{3} B b^{5}\right)} c^{2}\right)} x - \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{5} - 3 \, A B^{2} a^{2} b^{6} + 3 \, A^{2} B a b^{7} - A^{3} b^{8} - 4 \, A^{3} a^{4} c^{4} + {\left(4 \, A B^{2} a^{5} - 20 \, A^{2} B a^{4} b + 17 \, A^{3} a^{3} b^{2}\right)} c^{3} + {\left(4 \, B^{3} a^{5} b - 25 \, A B^{2} a^{4} b^{2} + 41 \, A^{2} B a^{3} b^{3} - 20 \, A^{3} a^{2} b^{4}\right)} c^{2} - {\left(5 \, B^{3} a^{4} b^{3} - 18 \, A B^{2} a^{3} b^{4} + 21 \, A^{2} B a^{2} b^{5} - 8 \, A^{3} a b^{6}\right)} c + {\left(B a^{6} b^{4} - A a^{5} b^{5} + 4 \, {\left(2 \, B a^{8} - 3 \, A a^{7} b\right)} c^{2} - {\left(6 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} - 2 \, A B a b^{4} + A^{2} b^{5} - {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} - {\left(3 \, B^{2} a^{3} b - 8 \, A B a^{2} b^{2} + 5 \, A^{2} a b^{3}\right)} c - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 4 \, A B^{3} a^{3} b^{5} + 6 \, A^{2} B^{2} a^{2} b^{6} - 4 \, A^{3} B a b^{7} + A^{4} b^{8} + A^{4} a^{4} c^{4} - 2 \, {\left(A^{2} B^{2} a^{5} - 4 \, A^{3} B a^{4} b + 3 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(B^{4} a^{6} - 8 \, A B^{3} a^{5} b + 24 \, A^{2} B^{2} a^{4} b^{2} - 28 \, A^{3} B a^{3} b^{3} + 11 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(B^{4} a^{5} b^{2} - 6 \, A B^{3} a^{4} b^{3} + 12 \, A^{2} B^{2} a^{3} b^{4} - 10 \, A^{3} B a^{2} b^{5} + 3 \, A^{4} a b^{6}\right)} c}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}}\right) - 6 \, {\left(B a - A b\right)} x^{2} - 2 \, A a}{6 \, a^{2} x^{3}}"," ",0,"1/6*(3*sqrt(1/2)*a^2*x^3*sqrt(-(B^2*a^2*b^3 - 2*A*B*a*b^4 + A^2*b^5 - (4*A*B*a^3 - 5*A^2*a^2*b)*c^2 - (3*B^2*a^3*b - 8*A*B*a^2*b^2 + 5*A^2*a*b^3)*c + (a^5*b^2 - 4*a^6*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))*log(2*(A^4*a^2*c^5 + 3*(A^3*B*a^2*b - A^4*a*b^2)*c^4 - (B^4*a^4 - 5*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - A^3*B*a*b^3 - A^4*b^4)*c^3 + (B^4*a^3*b^2 - 3*A*B^3*a^2*b^3 + 3*A^2*B^2*a*b^4 - A^3*B*b^5)*c^2)*x + sqrt(1/2)*(B^3*a^3*b^5 - 3*A*B^2*a^2*b^6 + 3*A^2*B*a*b^7 - A^3*b^8 - 4*A^3*a^4*c^4 + (4*A*B^2*a^5 - 20*A^2*B*a^4*b + 17*A^3*a^3*b^2)*c^3 + (4*B^3*a^5*b - 25*A*B^2*a^4*b^2 + 41*A^2*B*a^3*b^3 - 20*A^3*a^2*b^4)*c^2 - (5*B^3*a^4*b^3 - 18*A*B^2*a^3*b^4 + 21*A^2*B*a^2*b^5 - 8*A^3*a*b^6)*c - (B*a^6*b^4 - A*a^5*b^5 + 4*(2*B*a^8 - 3*A*a^7*b)*c^2 - (6*B*a^7*b^2 - 7*A*a^6*b^3)*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))*sqrt(-(B^2*a^2*b^3 - 2*A*B*a*b^4 + A^2*b^5 - (4*A*B*a^3 - 5*A^2*a^2*b)*c^2 - (3*B^2*a^3*b - 8*A*B*a^2*b^2 + 5*A^2*a*b^3)*c + (a^5*b^2 - 4*a^6*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))) - 3*sqrt(1/2)*a^2*x^3*sqrt(-(B^2*a^2*b^3 - 2*A*B*a*b^4 + A^2*b^5 - (4*A*B*a^3 - 5*A^2*a^2*b)*c^2 - (3*B^2*a^3*b - 8*A*B*a^2*b^2 + 5*A^2*a*b^3)*c + (a^5*b^2 - 4*a^6*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))*log(2*(A^4*a^2*c^5 + 3*(A^3*B*a^2*b - A^4*a*b^2)*c^4 - (B^4*a^4 - 5*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - A^3*B*a*b^3 - A^4*b^4)*c^3 + (B^4*a^3*b^2 - 3*A*B^3*a^2*b^3 + 3*A^2*B^2*a*b^4 - A^3*B*b^5)*c^2)*x - sqrt(1/2)*(B^3*a^3*b^5 - 3*A*B^2*a^2*b^6 + 3*A^2*B*a*b^7 - A^3*b^8 - 4*A^3*a^4*c^4 + (4*A*B^2*a^5 - 20*A^2*B*a^4*b + 17*A^3*a^3*b^2)*c^3 + (4*B^3*a^5*b - 25*A*B^2*a^4*b^2 + 41*A^2*B*a^3*b^3 - 20*A^3*a^2*b^4)*c^2 - (5*B^3*a^4*b^3 - 18*A*B^2*a^3*b^4 + 21*A^2*B*a^2*b^5 - 8*A^3*a*b^6)*c - (B*a^6*b^4 - A*a^5*b^5 + 4*(2*B*a^8 - 3*A*a^7*b)*c^2 - (6*B*a^7*b^2 - 7*A*a^6*b^3)*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))*sqrt(-(B^2*a^2*b^3 - 2*A*B*a*b^4 + A^2*b^5 - (4*A*B*a^3 - 5*A^2*a^2*b)*c^2 - (3*B^2*a^3*b - 8*A*B*a^2*b^2 + 5*A^2*a*b^3)*c + (a^5*b^2 - 4*a^6*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))) + 3*sqrt(1/2)*a^2*x^3*sqrt(-(B^2*a^2*b^3 - 2*A*B*a*b^4 + A^2*b^5 - (4*A*B*a^3 - 5*A^2*a^2*b)*c^2 - (3*B^2*a^3*b - 8*A*B*a^2*b^2 + 5*A^2*a*b^3)*c - (a^5*b^2 - 4*a^6*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))*log(2*(A^4*a^2*c^5 + 3*(A^3*B*a^2*b - A^4*a*b^2)*c^4 - (B^4*a^4 - 5*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - A^3*B*a*b^3 - A^4*b^4)*c^3 + (B^4*a^3*b^2 - 3*A*B^3*a^2*b^3 + 3*A^2*B^2*a*b^4 - A^3*B*b^5)*c^2)*x + sqrt(1/2)*(B^3*a^3*b^5 - 3*A*B^2*a^2*b^6 + 3*A^2*B*a*b^7 - A^3*b^8 - 4*A^3*a^4*c^4 + (4*A*B^2*a^5 - 20*A^2*B*a^4*b + 17*A^3*a^3*b^2)*c^3 + (4*B^3*a^5*b - 25*A*B^2*a^4*b^2 + 41*A^2*B*a^3*b^3 - 20*A^3*a^2*b^4)*c^2 - (5*B^3*a^4*b^3 - 18*A*B^2*a^3*b^4 + 21*A^2*B*a^2*b^5 - 8*A^3*a*b^6)*c + (B*a^6*b^4 - A*a^5*b^5 + 4*(2*B*a^8 - 3*A*a^7*b)*c^2 - (6*B*a^7*b^2 - 7*A*a^6*b^3)*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))*sqrt(-(B^2*a^2*b^3 - 2*A*B*a*b^4 + A^2*b^5 - (4*A*B*a^3 - 5*A^2*a^2*b)*c^2 - (3*B^2*a^3*b - 8*A*B*a^2*b^2 + 5*A^2*a*b^3)*c - (a^5*b^2 - 4*a^6*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))) - 3*sqrt(1/2)*a^2*x^3*sqrt(-(B^2*a^2*b^3 - 2*A*B*a*b^4 + A^2*b^5 - (4*A*B*a^3 - 5*A^2*a^2*b)*c^2 - (3*B^2*a^3*b - 8*A*B*a^2*b^2 + 5*A^2*a*b^3)*c - (a^5*b^2 - 4*a^6*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))*log(2*(A^4*a^2*c^5 + 3*(A^3*B*a^2*b - A^4*a*b^2)*c^4 - (B^4*a^4 - 5*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - A^3*B*a*b^3 - A^4*b^4)*c^3 + (B^4*a^3*b^2 - 3*A*B^3*a^2*b^3 + 3*A^2*B^2*a*b^4 - A^3*B*b^5)*c^2)*x - sqrt(1/2)*(B^3*a^3*b^5 - 3*A*B^2*a^2*b^6 + 3*A^2*B*a*b^7 - A^3*b^8 - 4*A^3*a^4*c^4 + (4*A*B^2*a^5 - 20*A^2*B*a^4*b + 17*A^3*a^3*b^2)*c^3 + (4*B^3*a^5*b - 25*A*B^2*a^4*b^2 + 41*A^2*B*a^3*b^3 - 20*A^3*a^2*b^4)*c^2 - (5*B^3*a^4*b^3 - 18*A*B^2*a^3*b^4 + 21*A^2*B*a^2*b^5 - 8*A^3*a*b^6)*c + (B*a^6*b^4 - A*a^5*b^5 + 4*(2*B*a^8 - 3*A*a^7*b)*c^2 - (6*B*a^7*b^2 - 7*A*a^6*b^3)*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))*sqrt(-(B^2*a^2*b^3 - 2*A*B*a*b^4 + A^2*b^5 - (4*A*B*a^3 - 5*A^2*a^2*b)*c^2 - (3*B^2*a^3*b - 8*A*B*a^2*b^2 + 5*A^2*a*b^3)*c - (a^5*b^2 - 4*a^6*c)*sqrt((B^4*a^4*b^4 - 4*A*B^3*a^3*b^5 + 6*A^2*B^2*a^2*b^6 - 4*A^3*B*a*b^7 + A^4*b^8 + A^4*a^4*c^4 - 2*(A^2*B^2*a^5 - 4*A^3*B*a^4*b + 3*A^4*a^3*b^2)*c^3 + (B^4*a^6 - 8*A*B^3*a^5*b + 24*A^2*B^2*a^4*b^2 - 28*A^3*B*a^3*b^3 + 11*A^4*a^2*b^4)*c^2 - 2*(B^4*a^5*b^2 - 6*A*B^3*a^4*b^3 + 12*A^2*B^2*a^3*b^4 - 10*A^3*B*a^2*b^5 + 3*A^4*a*b^6)*c)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))) - 6*(B*a - A*b)*x^2 - 2*A*a)/(a^2*x^3)","B",0
112,1,1323,0,0.778827," ","integrate(x^7*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, B a b^{5} - 16 \, A a^{3} c^{3} - 2 \, {\left(B b^{4} c^{2} - 8 \, B a b^{2} c^{3} + 16 \, B a^{2} c^{4}\right)} x^{6} - 2 \, {\left(B b^{5} c - 8 \, B a b^{3} c^{2} + 16 \, B a^{2} b c^{3}\right)} x^{4} + 12 \, {\left(2 \, B a^{3} b + A a^{2} b^{2}\right)} c^{2} + 2 \, {\left(B b^{6} - 12 \, {\left(2 \, B a^{3} + A a^{2} b\right)} c^{3} + {\left(26 \, B a^{2} b^{2} + 7 \, A a b^{3}\right)} c^{2} - {\left(9 \, B a b^{4} + A b^{5}\right)} c\right)} x^{2} + {\left(2 \, B a b^{4} + {\left(2 \, B b^{4} c + 6 \, {\left(2 \, B a^{2} + A a b\right)} c^{3} - {\left(12 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} x^{4} + 6 \, {\left(2 \, B a^{3} + A a^{2} b\right)} c^{2} + {\left(2 \, B b^{5} + 6 \, {\left(2 \, B a^{2} b + A a b^{2}\right)} c^{2} - {\left(12 \, B a b^{3} + A b^{4}\right)} c\right)} x^{2} - {\left(12 \, B a^{2} b^{2} + A a b^{3}\right)} c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) - 2 \, {\left(7 \, B a^{2} b^{3} + A a b^{4}\right)} c + {\left(2 \, B a b^{5} - 16 \, A a^{3} c^{3} + {\left(2 \, B b^{5} c - 16 \, A a^{2} c^{4} + 8 \, {\left(4 \, B a^{2} b + A a b^{2}\right)} c^{3} - {\left(16 \, B a b^{3} + A b^{4}\right)} c^{2}\right)} x^{4} + 8 \, {\left(4 \, B a^{3} b + A a^{2} b^{2}\right)} c^{2} + {\left(2 \, B b^{6} - 16 \, A a^{2} b c^{3} + 8 \, {\left(4 \, B a^{2} b^{2} + A a b^{3}\right)} c^{2} - {\left(16 \, B a b^{4} + A b^{5}\right)} c\right)} x^{2} - {\left(16 \, B a^{2} b^{3} + A a b^{4}\right)} c\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{4} + {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{2}\right)}}, -\frac{2 \, B a b^{5} - 16 \, A a^{3} c^{3} - 2 \, {\left(B b^{4} c^{2} - 8 \, B a b^{2} c^{3} + 16 \, B a^{2} c^{4}\right)} x^{6} - 2 \, {\left(B b^{5} c - 8 \, B a b^{3} c^{2} + 16 \, B a^{2} b c^{3}\right)} x^{4} + 12 \, {\left(2 \, B a^{3} b + A a^{2} b^{2}\right)} c^{2} + 2 \, {\left(B b^{6} - 12 \, {\left(2 \, B a^{3} + A a^{2} b\right)} c^{3} + {\left(26 \, B a^{2} b^{2} + 7 \, A a b^{3}\right)} c^{2} - {\left(9 \, B a b^{4} + A b^{5}\right)} c\right)} x^{2} + 2 \, {\left(2 \, B a b^{4} + {\left(2 \, B b^{4} c + 6 \, {\left(2 \, B a^{2} + A a b\right)} c^{3} - {\left(12 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} x^{4} + 6 \, {\left(2 \, B a^{3} + A a^{2} b\right)} c^{2} + {\left(2 \, B b^{5} + 6 \, {\left(2 \, B a^{2} b + A a b^{2}\right)} c^{2} - {\left(12 \, B a b^{3} + A b^{4}\right)} c\right)} x^{2} - {\left(12 \, B a^{2} b^{2} + A a b^{3}\right)} c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - 2 \, {\left(7 \, B a^{2} b^{3} + A a b^{4}\right)} c + {\left(2 \, B a b^{5} - 16 \, A a^{3} c^{3} + {\left(2 \, B b^{5} c - 16 \, A a^{2} c^{4} + 8 \, {\left(4 \, B a^{2} b + A a b^{2}\right)} c^{3} - {\left(16 \, B a b^{3} + A b^{4}\right)} c^{2}\right)} x^{4} + 8 \, {\left(4 \, B a^{3} b + A a^{2} b^{2}\right)} c^{2} + {\left(2 \, B b^{6} - 16 \, A a^{2} b c^{3} + 8 \, {\left(4 \, B a^{2} b^{2} + A a b^{3}\right)} c^{2} - {\left(16 \, B a b^{4} + A b^{5}\right)} c\right)} x^{2} - {\left(16 \, B a^{2} b^{3} + A a b^{4}\right)} c\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{4} + {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(2*B*a*b^5 - 16*A*a^3*c^3 - 2*(B*b^4*c^2 - 8*B*a*b^2*c^3 + 16*B*a^2*c^4)*x^6 - 2*(B*b^5*c - 8*B*a*b^3*c^2 + 16*B*a^2*b*c^3)*x^4 + 12*(2*B*a^3*b + A*a^2*b^2)*c^2 + 2*(B*b^6 - 12*(2*B*a^3 + A*a^2*b)*c^3 + (26*B*a^2*b^2 + 7*A*a*b^3)*c^2 - (9*B*a*b^4 + A*b^5)*c)*x^2 + (2*B*a*b^4 + (2*B*b^4*c + 6*(2*B*a^2 + A*a*b)*c^3 - (12*B*a*b^2 + A*b^3)*c^2)*x^4 + 6*(2*B*a^3 + A*a^2*b)*c^2 + (2*B*b^5 + 6*(2*B*a^2*b + A*a*b^2)*c^2 - (12*B*a*b^3 + A*b^4)*c)*x^2 - (12*B*a^2*b^2 + A*a*b^3)*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) - 2*(7*B*a^2*b^3 + A*a*b^4)*c + (2*B*a*b^5 - 16*A*a^3*c^3 + (2*B*b^5*c - 16*A*a^2*c^4 + 8*(4*B*a^2*b + A*a*b^2)*c^3 - (16*B*a*b^3 + A*b^4)*c^2)*x^4 + 8*(4*B*a^3*b + A*a^2*b^2)*c^2 + (2*B*b^6 - 16*A*a^2*b*c^3 + 8*(4*B*a^2*b^2 + A*a*b^3)*c^2 - (16*B*a*b^4 + A*b^5)*c)*x^2 - (16*B*a^2*b^3 + A*a*b^4)*c)*log(c*x^4 + b*x^2 + a))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^4 + (b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^2), -1/4*(2*B*a*b^5 - 16*A*a^3*c^3 - 2*(B*b^4*c^2 - 8*B*a*b^2*c^3 + 16*B*a^2*c^4)*x^6 - 2*(B*b^5*c - 8*B*a*b^3*c^2 + 16*B*a^2*b*c^3)*x^4 + 12*(2*B*a^3*b + A*a^2*b^2)*c^2 + 2*(B*b^6 - 12*(2*B*a^3 + A*a^2*b)*c^3 + (26*B*a^2*b^2 + 7*A*a*b^3)*c^2 - (9*B*a*b^4 + A*b^5)*c)*x^2 + 2*(2*B*a*b^4 + (2*B*b^4*c + 6*(2*B*a^2 + A*a*b)*c^3 - (12*B*a*b^2 + A*b^3)*c^2)*x^4 + 6*(2*B*a^3 + A*a^2*b)*c^2 + (2*B*b^5 + 6*(2*B*a^2*b + A*a*b^2)*c^2 - (12*B*a*b^3 + A*b^4)*c)*x^2 - (12*B*a^2*b^2 + A*a*b^3)*c)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - 2*(7*B*a^2*b^3 + A*a*b^4)*c + (2*B*a*b^5 - 16*A*a^3*c^3 + (2*B*b^5*c - 16*A*a^2*c^4 + 8*(4*B*a^2*b + A*a*b^2)*c^3 - (16*B*a*b^3 + A*b^4)*c^2)*x^4 + 8*(4*B*a^3*b + A*a^2*b^2)*c^2 + (2*B*b^6 - 16*A*a^2*b*c^3 + 8*(4*B*a^2*b^2 + A*a*b^3)*c^2 - (16*B*a*b^4 + A*b^5)*c)*x^2 - (16*B*a^2*b^3 + A*a*b^4)*c)*log(c*x^4 + b*x^2 + a))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^4 + (b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^2)]","B",0
113,1,849,0,1.007662," ","integrate(x^5*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, B a b^{4} + 8 \, {\left(2 \, B a^{3} + A a^{2} b\right)} c^{2} + 2 \, {\left(B b^{5} - 8 \, A a^{2} c^{3} + 6 \, {\left(2 \, B a^{2} b + A a b^{2}\right)} c^{2} - {\left(7 \, B a b^{3} + A b^{4}\right)} c\right)} x^{2} - {\left(B a b^{3} - 6 \, B a^{2} b c + 4 \, A a^{2} c^{2} + {\left(B b^{3} c - 6 \, B a b c^{2} + 4 \, A a c^{3}\right)} x^{4} + {\left(B b^{4} - 6 \, B a b^{2} c + 4 \, A a b c^{2}\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c - {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) - 2 \, {\left(6 \, B a^{2} b^{2} + A a b^{3}\right)} c + {\left(B a b^{4} - 8 \, B a^{2} b^{2} c + 16 \, B a^{3} c^{2} + {\left(B b^{4} c - 8 \, B a b^{2} c^{2} + 16 \, B a^{2} c^{3}\right)} x^{4} + {\left(B b^{5} - 8 \, B a b^{3} c + 16 \, B a^{2} b c^{2}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{4} + {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{2}\right)}}, \frac{2 \, B a b^{4} + 8 \, {\left(2 \, B a^{3} + A a^{2} b\right)} c^{2} + 2 \, {\left(B b^{5} - 8 \, A a^{2} c^{3} + 6 \, {\left(2 \, B a^{2} b + A a b^{2}\right)} c^{2} - {\left(7 \, B a b^{3} + A b^{4}\right)} c\right)} x^{2} + 2 \, {\left(B a b^{3} - 6 \, B a^{2} b c + 4 \, A a^{2} c^{2} + {\left(B b^{3} c - 6 \, B a b c^{2} + 4 \, A a c^{3}\right)} x^{4} + {\left(B b^{4} - 6 \, B a b^{2} c + 4 \, A a b c^{2}\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - 2 \, {\left(6 \, B a^{2} b^{2} + A a b^{3}\right)} c + {\left(B a b^{4} - 8 \, B a^{2} b^{2} c + 16 \, B a^{3} c^{2} + {\left(B b^{4} c - 8 \, B a b^{2} c^{2} + 16 \, B a^{2} c^{3}\right)} x^{4} + {\left(B b^{5} - 8 \, B a b^{3} c + 16 \, B a^{2} b c^{2}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{4} + {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(2*B*a*b^4 + 8*(2*B*a^3 + A*a^2*b)*c^2 + 2*(B*b^5 - 8*A*a^2*c^3 + 6*(2*B*a^2*b + A*a*b^2)*c^2 - (7*B*a*b^3 + A*b^4)*c)*x^2 - (B*a*b^3 - 6*B*a^2*b*c + 4*A*a^2*c^2 + (B*b^3*c - 6*B*a*b*c^2 + 4*A*a*c^3)*x^4 + (B*b^4 - 6*B*a*b^2*c + 4*A*a*b*c^2)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c - (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) - 2*(6*B*a^2*b^2 + A*a*b^3)*c + (B*a*b^4 - 8*B*a^2*b^2*c + 16*B*a^3*c^2 + (B*b^4*c - 8*B*a*b^2*c^2 + 16*B*a^2*c^3)*x^4 + (B*b^5 - 8*B*a*b^3*c + 16*B*a^2*b*c^2)*x^2)*log(c*x^4 + b*x^2 + a))/(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)*x^4 + (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^2), 1/4*(2*B*a*b^4 + 8*(2*B*a^3 + A*a^2*b)*c^2 + 2*(B*b^5 - 8*A*a^2*c^3 + 6*(2*B*a^2*b + A*a*b^2)*c^2 - (7*B*a*b^3 + A*b^4)*c)*x^2 + 2*(B*a*b^3 - 6*B*a^2*b*c + 4*A*a^2*c^2 + (B*b^3*c - 6*B*a*b*c^2 + 4*A*a*c^3)*x^4 + (B*b^4 - 6*B*a*b^2*c + 4*A*a*b*c^2)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - 2*(6*B*a^2*b^2 + A*a*b^3)*c + (B*a*b^4 - 8*B*a^2*b^2*c + 16*B*a^3*c^2 + (B*b^4*c - 8*B*a*b^2*c^2 + 16*B*a^2*c^3)*x^4 + (B*b^5 - 8*B*a*b^3*c + 16*B*a^2*b*c^2)*x^2)*log(c*x^4 + b*x^2 + a))/(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)*x^4 + (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^2)]","B",0
114,1,538,0,0.799935," ","integrate(x^3*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{B a b^{3} + 8 \, A a^{2} c^{2} + {\left(B b^{4} + 4 \, {\left(2 \, B a^{2} + A a b\right)} c^{2} - {\left(6 \, B a b^{2} + A b^{3}\right)} c\right)} x^{2} - {\left({\left(2 \, B a - A b\right)} c^{2} x^{4} + {\left(2 \, B a b - A b^{2}\right)} c x^{2} + {\left(2 \, B a^{2} - A a b\right)} c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) - 2 \, {\left(2 \, B a^{2} b + A a b^{2}\right)} c}{2 \, {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{2}\right)}}, -\frac{B a b^{3} + 8 \, A a^{2} c^{2} + {\left(B b^{4} + 4 \, {\left(2 \, B a^{2} + A a b\right)} c^{2} - {\left(6 \, B a b^{2} + A b^{3}\right)} c\right)} x^{2} - 2 \, {\left({\left(2 \, B a - A b\right)} c^{2} x^{4} + {\left(2 \, B a b - A b^{2}\right)} c x^{2} + {\left(2 \, B a^{2} - A a b\right)} c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - 2 \, {\left(2 \, B a^{2} b + A a b^{2}\right)} c}{2 \, {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/2*(B*a*b^3 + 8*A*a^2*c^2 + (B*b^4 + 4*(2*B*a^2 + A*a*b)*c^2 - (6*B*a*b^2 + A*b^3)*c)*x^2 - ((2*B*a - A*b)*c^2*x^4 + (2*B*a*b - A*b^2)*c*x^2 + (2*B*a^2 - A*a*b)*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) - 2*(2*B*a^2*b + A*a*b^2)*c)/(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)*x^4 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^2), -1/2*(B*a*b^3 + 8*A*a^2*c^2 + (B*b^4 + 4*(2*B*a^2 + A*a*b)*c^2 - (6*B*a*b^2 + A*b^3)*c)*x^2 - 2*((2*B*a - A*b)*c^2*x^4 + (2*B*a*b - A*b^2)*c*x^2 + (2*B*a^2 - A*a*b)*c)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - 2*(2*B*a^2*b + A*a*b^2)*c)/(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)*x^4 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^2)]","B",0
115,1,474,0,0.691321," ","integrate(x*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, B a b^{2} - A b^{3} + {\left(B b^{3} + 8 \, A a c^{2} - 2 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{2} + {\left({\left(B b c - 2 \, A c^{2}\right)} x^{4} + B a b - 2 \, A a c + {\left(B b^{2} - 2 \, A b c\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c - {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) - 4 \, {\left(2 \, B a^{2} - A a b\right)} c}{2 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{2}\right)}}, \frac{2 \, B a b^{2} - A b^{3} + {\left(B b^{3} + 8 \, A a c^{2} - 2 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} x^{2} - 2 \, {\left({\left(B b c - 2 \, A c^{2}\right)} x^{4} + B a b - 2 \, A a c + {\left(B b^{2} - 2 \, A b c\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - 4 \, {\left(2 \, B a^{2} - A a b\right)} c}{2 \, {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/2*(2*B*a*b^2 - A*b^3 + (B*b^3 + 8*A*a*c^2 - 2*(2*B*a*b + A*b^2)*c)*x^2 + ((B*b*c - 2*A*c^2)*x^4 + B*a*b - 2*A*a*c + (B*b^2 - 2*A*b*c)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c - (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) - 4*(2*B*a^2 - A*a*b)*c)/(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)*x^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x^2), 1/2*(2*B*a*b^2 - A*b^3 + (B*b^3 + 8*A*a*c^2 - 2*(2*B*a*b + A*b^2)*c)*x^2 - 2*((B*b*c - 2*A*c^2)*x^4 + B*a*b - 2*A*a*c + (B*b^2 - 2*A*b*c)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - 4*(2*B*a^2 - A*a*b)*c)/(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)*x^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x^2)]","B",0
116,1,1014,0,1.817011," ","integrate((B*x^2+A)/x/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, B a^{2} b^{3} - 2 \, A a b^{4} - 16 \, A a^{3} c^{2} - 2 \, {\left(4 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{2} - {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} x^{2} - {\left(A a b^{3} + {\left(A b^{3} c + 2 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c^{2}\right)} x^{4} + {\left(A b^{4} + 2 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c\right)} x^{2} + 2 \, {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) - 4 \, {\left(2 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c + {\left(A a b^{4} - 8 \, A a^{2} b^{2} c + 16 \, A a^{3} c^{2} + {\left(A b^{4} c - 8 \, A a b^{2} c^{2} + 16 \, A a^{2} c^{3}\right)} x^{4} + {\left(A b^{5} - 8 \, A a b^{3} c + 16 \, A a^{2} b c^{2}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right) - 4 \, {\left(A a b^{4} - 8 \, A a^{2} b^{2} c + 16 \, A a^{3} c^{2} + {\left(A b^{4} c - 8 \, A a b^{2} c^{2} + 16 \, A a^{2} c^{3}\right)} x^{4} + {\left(A b^{5} - 8 \, A a b^{3} c + 16 \, A a^{2} b c^{2}\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} x^{4} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2}\right)}}, -\frac{2 \, B a^{2} b^{3} - 2 \, A a b^{4} - 16 \, A a^{3} c^{2} - 2 \, {\left(4 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{2} - {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} x^{2} - 2 \, {\left(A a b^{3} + {\left(A b^{3} c + 2 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c^{2}\right)} x^{4} + {\left(A b^{4} + 2 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c\right)} x^{2} + 2 \, {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - 4 \, {\left(2 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} c + {\left(A a b^{4} - 8 \, A a^{2} b^{2} c + 16 \, A a^{3} c^{2} + {\left(A b^{4} c - 8 \, A a b^{2} c^{2} + 16 \, A a^{2} c^{3}\right)} x^{4} + {\left(A b^{5} - 8 \, A a b^{3} c + 16 \, A a^{2} b c^{2}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right) - 4 \, {\left(A a b^{4} - 8 \, A a^{2} b^{2} c + 16 \, A a^{3} c^{2} + {\left(A b^{4} c - 8 \, A a b^{2} c^{2} + 16 \, A a^{2} c^{3}\right)} x^{4} + {\left(A b^{5} - 8 \, A a b^{3} c + 16 \, A a^{2} b c^{2}\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} x^{4} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(2*B*a^2*b^3 - 2*A*a*b^4 - 16*A*a^3*c^2 - 2*(4*(2*B*a^3 - A*a^2*b)*c^2 - (2*B*a^2*b^2 - A*a*b^3)*c)*x^2 - (A*a*b^3 + (A*b^3*c + 2*(2*B*a^2 - 3*A*a*b)*c^2)*x^4 + (A*b^4 + 2*(2*B*a^2*b - 3*A*a*b^2)*c)*x^2 + 2*(2*B*a^3 - 3*A*a^2*b)*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) - 4*(2*B*a^3*b - 3*A*a^2*b^2)*c + (A*a*b^4 - 8*A*a^2*b^2*c + 16*A*a^3*c^2 + (A*b^4*c - 8*A*a*b^2*c^2 + 16*A*a^2*c^3)*x^4 + (A*b^5 - 8*A*a*b^3*c + 16*A*a^2*b*c^2)*x^2)*log(c*x^4 + b*x^2 + a) - 4*(A*a*b^4 - 8*A*a^2*b^2*c + 16*A*a^3*c^2 + (A*b^4*c - 8*A*a*b^2*c^2 + 16*A*a^2*c^3)*x^4 + (A*b^5 - 8*A*a*b^3*c + 16*A*a^2*b*c^2)*x^2)*log(x))/(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)*x^4 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2), -1/4*(2*B*a^2*b^3 - 2*A*a*b^4 - 16*A*a^3*c^2 - 2*(4*(2*B*a^3 - A*a^2*b)*c^2 - (2*B*a^2*b^2 - A*a*b^3)*c)*x^2 - 2*(A*a*b^3 + (A*b^3*c + 2*(2*B*a^2 - 3*A*a*b)*c^2)*x^4 + (A*b^4 + 2*(2*B*a^2*b - 3*A*a*b^2)*c)*x^2 + 2*(2*B*a^3 - 3*A*a^2*b)*c)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - 4*(2*B*a^3*b - 3*A*a^2*b^2)*c + (A*a*b^4 - 8*A*a^2*b^2*c + 16*A*a^3*c^2 + (A*b^4*c - 8*A*a*b^2*c^2 + 16*A*a^2*c^3)*x^4 + (A*b^5 - 8*A*a*b^3*c + 16*A*a^2*b*c^2)*x^2)*log(c*x^4 + b*x^2 + a) - 4*(A*a*b^4 - 8*A*a^2*b^2*c + 16*A*a^3*c^2 + (A*b^4*c - 8*A*a*b^2*c^2 + 16*A*a^2*c^3)*x^4 + (A*b^5 - 8*A*a*b^3*c + 16*A*a^2*b*c^2)*x^2)*log(x))/(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)*x^4 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2)]","B",0
117,1,1635,0,3.863326," ","integrate((B*x^2+A)/x^3/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, A a^{2} b^{4} - 16 \, A a^{3} b^{2} c + 32 \, A a^{4} c^{2} + 2 \, {\left(24 \, A a^{3} c^{3} + 2 \, {\left(2 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} c^{2} - {\left(B a^{2} b^{3} - 2 \, A a b^{4}\right)} c\right)} x^{4} - 2 \, {\left(B a^{2} b^{4} - 2 \, A a b^{5} + 4 \, {\left(2 \, B a^{4} - 7 \, A a^{3} b\right)} c^{2} - 3 \, {\left(2 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} c\right)} x^{2} + {\left({\left(12 \, A a^{2} c^{3} + 6 \, {\left(B a^{2} b - 2 \, A a b^{2}\right)} c^{2} - {\left(B a b^{3} - 2 \, A b^{4}\right)} c\right)} x^{6} - {\left(B a b^{4} - 2 \, A b^{5} - 12 \, A a^{2} b c^{2} - 6 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} c\right)} x^{4} - {\left(B a^{2} b^{3} - 2 \, A a b^{4} - 12 \, A a^{3} c^{2} - 6 \, {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} c\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) + {\left({\left(16 \, {\left(B a^{3} - 2 \, A a^{2} b\right)} c^{3} - 8 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} c^{2} + {\left(B a b^{4} - 2 \, A b^{5}\right)} c\right)} x^{6} + {\left(B a b^{5} - 2 \, A b^{6} + 16 \, {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} c^{2} - 8 \, {\left(B a^{2} b^{3} - 2 \, A a b^{4}\right)} c\right)} x^{4} + {\left(B a^{2} b^{4} - 2 \, A a b^{5} + 16 \, {\left(B a^{4} - 2 \, A a^{3} b\right)} c^{2} - 8 \, {\left(B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} c\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right) - 4 \, {\left({\left(16 \, {\left(B a^{3} - 2 \, A a^{2} b\right)} c^{3} - 8 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} c^{2} + {\left(B a b^{4} - 2 \, A b^{5}\right)} c\right)} x^{6} + {\left(B a b^{5} - 2 \, A b^{6} + 16 \, {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} c^{2} - 8 \, {\left(B a^{2} b^{3} - 2 \, A a b^{4}\right)} c\right)} x^{4} + {\left(B a^{2} b^{4} - 2 \, A a b^{5} + 16 \, {\left(B a^{4} - 2 \, A a^{3} b\right)} c^{2} - 8 \, {\left(B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} c\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left({\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} x^{6} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{4} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} x^{2}\right)}}, -\frac{2 \, A a^{2} b^{4} - 16 \, A a^{3} b^{2} c + 32 \, A a^{4} c^{2} + 2 \, {\left(24 \, A a^{3} c^{3} + 2 \, {\left(2 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} c^{2} - {\left(B a^{2} b^{3} - 2 \, A a b^{4}\right)} c\right)} x^{4} - 2 \, {\left(B a^{2} b^{4} - 2 \, A a b^{5} + 4 \, {\left(2 \, B a^{4} - 7 \, A a^{3} b\right)} c^{2} - 3 \, {\left(2 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} c\right)} x^{2} + 2 \, {\left({\left(12 \, A a^{2} c^{3} + 6 \, {\left(B a^{2} b - 2 \, A a b^{2}\right)} c^{2} - {\left(B a b^{3} - 2 \, A b^{4}\right)} c\right)} x^{6} - {\left(B a b^{4} - 2 \, A b^{5} - 12 \, A a^{2} b c^{2} - 6 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} c\right)} x^{4} - {\left(B a^{2} b^{3} - 2 \, A a b^{4} - 12 \, A a^{3} c^{2} - 6 \, {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} c\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) + {\left({\left(16 \, {\left(B a^{3} - 2 \, A a^{2} b\right)} c^{3} - 8 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} c^{2} + {\left(B a b^{4} - 2 \, A b^{5}\right)} c\right)} x^{6} + {\left(B a b^{5} - 2 \, A b^{6} + 16 \, {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} c^{2} - 8 \, {\left(B a^{2} b^{3} - 2 \, A a b^{4}\right)} c\right)} x^{4} + {\left(B a^{2} b^{4} - 2 \, A a b^{5} + 16 \, {\left(B a^{4} - 2 \, A a^{3} b\right)} c^{2} - 8 \, {\left(B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} c\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right) - 4 \, {\left({\left(16 \, {\left(B a^{3} - 2 \, A a^{2} b\right)} c^{3} - 8 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} c^{2} + {\left(B a b^{4} - 2 \, A b^{5}\right)} c\right)} x^{6} + {\left(B a b^{5} - 2 \, A b^{6} + 16 \, {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} c^{2} - 8 \, {\left(B a^{2} b^{3} - 2 \, A a b^{4}\right)} c\right)} x^{4} + {\left(B a^{2} b^{4} - 2 \, A a b^{5} + 16 \, {\left(B a^{4} - 2 \, A a^{3} b\right)} c^{2} - 8 \, {\left(B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} c\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left({\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} x^{6} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{4} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(2*A*a^2*b^4 - 16*A*a^3*b^2*c + 32*A*a^4*c^2 + 2*(24*A*a^3*c^3 + 2*(2*B*a^3*b - 7*A*a^2*b^2)*c^2 - (B*a^2*b^3 - 2*A*a*b^4)*c)*x^4 - 2*(B*a^2*b^4 - 2*A*a*b^5 + 4*(2*B*a^4 - 7*A*a^3*b)*c^2 - 3*(2*B*a^3*b^2 - 5*A*a^2*b^3)*c)*x^2 + ((12*A*a^2*c^3 + 6*(B*a^2*b - 2*A*a*b^2)*c^2 - (B*a*b^3 - 2*A*b^4)*c)*x^6 - (B*a*b^4 - 2*A*b^5 - 12*A*a^2*b*c^2 - 6*(B*a^2*b^2 - 2*A*a*b^3)*c)*x^4 - (B*a^2*b^3 - 2*A*a*b^4 - 12*A*a^3*c^2 - 6*(B*a^3*b - 2*A*a^2*b^2)*c)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) + ((16*(B*a^3 - 2*A*a^2*b)*c^3 - 8*(B*a^2*b^2 - 2*A*a*b^3)*c^2 + (B*a*b^4 - 2*A*b^5)*c)*x^6 + (B*a*b^5 - 2*A*b^6 + 16*(B*a^3*b - 2*A*a^2*b^2)*c^2 - 8*(B*a^2*b^3 - 2*A*a*b^4)*c)*x^4 + (B*a^2*b^4 - 2*A*a*b^5 + 16*(B*a^4 - 2*A*a^3*b)*c^2 - 8*(B*a^3*b^2 - 2*A*a^2*b^3)*c)*x^2)*log(c*x^4 + b*x^2 + a) - 4*((16*(B*a^3 - 2*A*a^2*b)*c^3 - 8*(B*a^2*b^2 - 2*A*a*b^3)*c^2 + (B*a*b^4 - 2*A*b^5)*c)*x^6 + (B*a*b^5 - 2*A*b^6 + 16*(B*a^3*b - 2*A*a^2*b^2)*c^2 - 8*(B*a^2*b^3 - 2*A*a*b^4)*c)*x^4 + (B*a^2*b^4 - 2*A*a*b^5 + 16*(B*a^4 - 2*A*a^3*b)*c^2 - 8*(B*a^3*b^2 - 2*A*a^2*b^3)*c)*x^2)*log(x))/((a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*x^6 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^4 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*x^2), -1/4*(2*A*a^2*b^4 - 16*A*a^3*b^2*c + 32*A*a^4*c^2 + 2*(24*A*a^3*c^3 + 2*(2*B*a^3*b - 7*A*a^2*b^2)*c^2 - (B*a^2*b^3 - 2*A*a*b^4)*c)*x^4 - 2*(B*a^2*b^4 - 2*A*a*b^5 + 4*(2*B*a^4 - 7*A*a^3*b)*c^2 - 3*(2*B*a^3*b^2 - 5*A*a^2*b^3)*c)*x^2 + 2*((12*A*a^2*c^3 + 6*(B*a^2*b - 2*A*a*b^2)*c^2 - (B*a*b^3 - 2*A*b^4)*c)*x^6 - (B*a*b^4 - 2*A*b^5 - 12*A*a^2*b*c^2 - 6*(B*a^2*b^2 - 2*A*a*b^3)*c)*x^4 - (B*a^2*b^3 - 2*A*a*b^4 - 12*A*a^3*c^2 - 6*(B*a^3*b - 2*A*a^2*b^2)*c)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) + ((16*(B*a^3 - 2*A*a^2*b)*c^3 - 8*(B*a^2*b^2 - 2*A*a*b^3)*c^2 + (B*a*b^4 - 2*A*b^5)*c)*x^6 + (B*a*b^5 - 2*A*b^6 + 16*(B*a^3*b - 2*A*a^2*b^2)*c^2 - 8*(B*a^2*b^3 - 2*A*a*b^4)*c)*x^4 + (B*a^2*b^4 - 2*A*a*b^5 + 16*(B*a^4 - 2*A*a^3*b)*c^2 - 8*(B*a^3*b^2 - 2*A*a^2*b^3)*c)*x^2)*log(c*x^4 + b*x^2 + a) - 4*((16*(B*a^3 - 2*A*a^2*b)*c^3 - 8*(B*a^2*b^2 - 2*A*a*b^3)*c^2 + (B*a*b^4 - 2*A*b^5)*c)*x^6 + (B*a*b^5 - 2*A*b^6 + 16*(B*a^3*b - 2*A*a^2*b^2)*c^2 - 8*(B*a^2*b^3 - 2*A*a*b^4)*c)*x^4 + (B*a^2*b^4 - 2*A*a*b^5 + 16*(B*a^4 - 2*A*a^3*b)*c^2 - 8*(B*a^3*b^2 - 2*A*a^2*b^3)*c)*x^2)*log(x))/((a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*x^6 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^4 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*x^2)]","B",0
118,1,7252,0,8.558034," ","integrate(x^6*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(B b^{2} c - 4 \, B a c^{2}\right)} x^{5} + 2 \, {\left(3 \, B b^{3} + 2 \, A a c^{2} - {\left(11 \, B a b + A b^{2}\right)} c\right)} x^{3} - \sqrt{\frac{1}{2}} {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{4} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2}\right)} \sqrt{-\frac{9 \, B^{2} b^{7} + 60 \, {\left(4 \, A B a^{3} + A^{2} a^{2} b\right)} c^{4} - 15 \, {\left(28 \, B^{2} a^{3} b + 20 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{3} + {\left(385 \, B^{2} a^{2} b^{3} + 80 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - 3 \, {\left(35 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} \log\left({\left(189 \, B^{4} a^{2} b^{6} - 135 \, A B^{3} a b^{7} + 324 \, A^{4} a^{3} c^{5} - 81 \, {\left(28 \, A^{3} B a^{3} b + A^{4} a^{2} b^{2}\right)} c^{4} - {\left(2500 \, B^{4} a^{5} + 2500 \, A B^{3} a^{4} b - 5016 \, A^{2} B^{2} a^{3} b^{2} - 647 \, A^{3} B a^{2} b^{3} - 5 \, A^{4} a b^{4}\right)} c^{3} + 9 \, {\left(625 \, B^{4} a^{4} b^{2} - 303 \, A B^{3} a^{3} b^{3} - 186 \, A^{2} B^{2} a^{2} b^{4} - 5 \, A^{3} B a b^{5}\right)} c^{2} - 27 \, {\left(73 \, B^{4} a^{3} b^{4} - 49 \, A B^{3} a^{2} b^{5} - 5 \, A^{2} B^{2} a b^{6}\right)} c\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} b^{10} + 144 \, {\left(10 \, A^{2} B a^{4} + A^{3} a^{3} b\right)} c^{6} - 8 \, {\left(500 \, B^{3} a^{5} + 930 \, A B^{2} a^{4} b + 252 \, A^{2} B a^{3} b^{2} + 11 \, A^{3} a^{2} b^{3}\right)} c^{5} + {\left(11360 \, B^{3} a^{4} b^{2} + 7608 \, A B^{2} a^{3} b^{3} + 882 \, A^{2} B a^{2} b^{4} + 17 \, A^{3} a b^{5}\right)} c^{4} - {\left(8818 \, B^{3} a^{3} b^{4} + 2841 \, A B^{2} a^{2} b^{5} + 153 \, A^{2} B a b^{6} + A^{3} b^{7}\right)} c^{3} + 9 \, {\left(329 \, B^{3} a^{2} b^{6} + 51 \, A B^{2} a b^{7} + A^{2} B b^{8}\right)} c^{2} - 27 \, {\left(17 \, B^{3} a b^{8} + A B^{2} b^{9}\right)} c - {\left(3 \, B b^{9} c^{5} - 768 \, A a^{4} c^{10} + 128 \, {\left(8 \, B a^{4} b + 5 \, A a^{3} b^{2}\right)} c^{9} - 192 \, {\left(5 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} c^{8} + 24 \, {\left(14 \, B a^{2} b^{5} + A a b^{6}\right)} c^{7} - {\left(52 \, B a b^{7} + A b^{8}\right)} c^{6}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{-\frac{9 \, B^{2} b^{7} + 60 \, {\left(4 \, A B a^{3} + A^{2} a^{2} b\right)} c^{4} - 15 \, {\left(28 \, B^{2} a^{3} b + 20 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{3} + {\left(385 \, B^{2} a^{2} b^{3} + 80 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - 3 \, {\left(35 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}}\right) + \sqrt{\frac{1}{2}} {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{4} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2}\right)} \sqrt{-\frac{9 \, B^{2} b^{7} + 60 \, {\left(4 \, A B a^{3} + A^{2} a^{2} b\right)} c^{4} - 15 \, {\left(28 \, B^{2} a^{3} b + 20 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{3} + {\left(385 \, B^{2} a^{2} b^{3} + 80 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - 3 \, {\left(35 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} \log\left({\left(189 \, B^{4} a^{2} b^{6} - 135 \, A B^{3} a b^{7} + 324 \, A^{4} a^{3} c^{5} - 81 \, {\left(28 \, A^{3} B a^{3} b + A^{4} a^{2} b^{2}\right)} c^{4} - {\left(2500 \, B^{4} a^{5} + 2500 \, A B^{3} a^{4} b - 5016 \, A^{2} B^{2} a^{3} b^{2} - 647 \, A^{3} B a^{2} b^{3} - 5 \, A^{4} a b^{4}\right)} c^{3} + 9 \, {\left(625 \, B^{4} a^{4} b^{2} - 303 \, A B^{3} a^{3} b^{3} - 186 \, A^{2} B^{2} a^{2} b^{4} - 5 \, A^{3} B a b^{5}\right)} c^{2} - 27 \, {\left(73 \, B^{4} a^{3} b^{4} - 49 \, A B^{3} a^{2} b^{5} - 5 \, A^{2} B^{2} a b^{6}\right)} c\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} b^{10} + 144 \, {\left(10 \, A^{2} B a^{4} + A^{3} a^{3} b\right)} c^{6} - 8 \, {\left(500 \, B^{3} a^{5} + 930 \, A B^{2} a^{4} b + 252 \, A^{2} B a^{3} b^{2} + 11 \, A^{3} a^{2} b^{3}\right)} c^{5} + {\left(11360 \, B^{3} a^{4} b^{2} + 7608 \, A B^{2} a^{3} b^{3} + 882 \, A^{2} B a^{2} b^{4} + 17 \, A^{3} a b^{5}\right)} c^{4} - {\left(8818 \, B^{3} a^{3} b^{4} + 2841 \, A B^{2} a^{2} b^{5} + 153 \, A^{2} B a b^{6} + A^{3} b^{7}\right)} c^{3} + 9 \, {\left(329 \, B^{3} a^{2} b^{6} + 51 \, A B^{2} a b^{7} + A^{2} B b^{8}\right)} c^{2} - 27 \, {\left(17 \, B^{3} a b^{8} + A B^{2} b^{9}\right)} c - {\left(3 \, B b^{9} c^{5} - 768 \, A a^{4} c^{10} + 128 \, {\left(8 \, B a^{4} b + 5 \, A a^{3} b^{2}\right)} c^{9} - 192 \, {\left(5 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} c^{8} + 24 \, {\left(14 \, B a^{2} b^{5} + A a b^{6}\right)} c^{7} - {\left(52 \, B a b^{7} + A b^{8}\right)} c^{6}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{-\frac{9 \, B^{2} b^{7} + 60 \, {\left(4 \, A B a^{3} + A^{2} a^{2} b\right)} c^{4} - 15 \, {\left(28 \, B^{2} a^{3} b + 20 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{3} + {\left(385 \, B^{2} a^{2} b^{3} + 80 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - 3 \, {\left(35 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}}\right) - \sqrt{\frac{1}{2}} {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{4} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2}\right)} \sqrt{-\frac{9 \, B^{2} b^{7} + 60 \, {\left(4 \, A B a^{3} + A^{2} a^{2} b\right)} c^{4} - 15 \, {\left(28 \, B^{2} a^{3} b + 20 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{3} + {\left(385 \, B^{2} a^{2} b^{3} + 80 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - 3 \, {\left(35 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c - {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} \log\left({\left(189 \, B^{4} a^{2} b^{6} - 135 \, A B^{3} a b^{7} + 324 \, A^{4} a^{3} c^{5} - 81 \, {\left(28 \, A^{3} B a^{3} b + A^{4} a^{2} b^{2}\right)} c^{4} - {\left(2500 \, B^{4} a^{5} + 2500 \, A B^{3} a^{4} b - 5016 \, A^{2} B^{2} a^{3} b^{2} - 647 \, A^{3} B a^{2} b^{3} - 5 \, A^{4} a b^{4}\right)} c^{3} + 9 \, {\left(625 \, B^{4} a^{4} b^{2} - 303 \, A B^{3} a^{3} b^{3} - 186 \, A^{2} B^{2} a^{2} b^{4} - 5 \, A^{3} B a b^{5}\right)} c^{2} - 27 \, {\left(73 \, B^{4} a^{3} b^{4} - 49 \, A B^{3} a^{2} b^{5} - 5 \, A^{2} B^{2} a b^{6}\right)} c\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} b^{10} + 144 \, {\left(10 \, A^{2} B a^{4} + A^{3} a^{3} b\right)} c^{6} - 8 \, {\left(500 \, B^{3} a^{5} + 930 \, A B^{2} a^{4} b + 252 \, A^{2} B a^{3} b^{2} + 11 \, A^{3} a^{2} b^{3}\right)} c^{5} + {\left(11360 \, B^{3} a^{4} b^{2} + 7608 \, A B^{2} a^{3} b^{3} + 882 \, A^{2} B a^{2} b^{4} + 17 \, A^{3} a b^{5}\right)} c^{4} - {\left(8818 \, B^{3} a^{3} b^{4} + 2841 \, A B^{2} a^{2} b^{5} + 153 \, A^{2} B a b^{6} + A^{3} b^{7}\right)} c^{3} + 9 \, {\left(329 \, B^{3} a^{2} b^{6} + 51 \, A B^{2} a b^{7} + A^{2} B b^{8}\right)} c^{2} - 27 \, {\left(17 \, B^{3} a b^{8} + A B^{2} b^{9}\right)} c + {\left(3 \, B b^{9} c^{5} - 768 \, A a^{4} c^{10} + 128 \, {\left(8 \, B a^{4} b + 5 \, A a^{3} b^{2}\right)} c^{9} - 192 \, {\left(5 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} c^{8} + 24 \, {\left(14 \, B a^{2} b^{5} + A a b^{6}\right)} c^{7} - {\left(52 \, B a b^{7} + A b^{8}\right)} c^{6}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{-\frac{9 \, B^{2} b^{7} + 60 \, {\left(4 \, A B a^{3} + A^{2} a^{2} b\right)} c^{4} - 15 \, {\left(28 \, B^{2} a^{3} b + 20 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{3} + {\left(385 \, B^{2} a^{2} b^{3} + 80 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - 3 \, {\left(35 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c - {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}}\right) + \sqrt{\frac{1}{2}} {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{4} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2}\right)} \sqrt{-\frac{9 \, B^{2} b^{7} + 60 \, {\left(4 \, A B a^{3} + A^{2} a^{2} b\right)} c^{4} - 15 \, {\left(28 \, B^{2} a^{3} b + 20 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{3} + {\left(385 \, B^{2} a^{2} b^{3} + 80 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - 3 \, {\left(35 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c - {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} \log\left({\left(189 \, B^{4} a^{2} b^{6} - 135 \, A B^{3} a b^{7} + 324 \, A^{4} a^{3} c^{5} - 81 \, {\left(28 \, A^{3} B a^{3} b + A^{4} a^{2} b^{2}\right)} c^{4} - {\left(2500 \, B^{4} a^{5} + 2500 \, A B^{3} a^{4} b - 5016 \, A^{2} B^{2} a^{3} b^{2} - 647 \, A^{3} B a^{2} b^{3} - 5 \, A^{4} a b^{4}\right)} c^{3} + 9 \, {\left(625 \, B^{4} a^{4} b^{2} - 303 \, A B^{3} a^{3} b^{3} - 186 \, A^{2} B^{2} a^{2} b^{4} - 5 \, A^{3} B a b^{5}\right)} c^{2} - 27 \, {\left(73 \, B^{4} a^{3} b^{4} - 49 \, A B^{3} a^{2} b^{5} - 5 \, A^{2} B^{2} a b^{6}\right)} c\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} b^{10} + 144 \, {\left(10 \, A^{2} B a^{4} + A^{3} a^{3} b\right)} c^{6} - 8 \, {\left(500 \, B^{3} a^{5} + 930 \, A B^{2} a^{4} b + 252 \, A^{2} B a^{3} b^{2} + 11 \, A^{3} a^{2} b^{3}\right)} c^{5} + {\left(11360 \, B^{3} a^{4} b^{2} + 7608 \, A B^{2} a^{3} b^{3} + 882 \, A^{2} B a^{2} b^{4} + 17 \, A^{3} a b^{5}\right)} c^{4} - {\left(8818 \, B^{3} a^{3} b^{4} + 2841 \, A B^{2} a^{2} b^{5} + 153 \, A^{2} B a b^{6} + A^{3} b^{7}\right)} c^{3} + 9 \, {\left(329 \, B^{3} a^{2} b^{6} + 51 \, A B^{2} a b^{7} + A^{2} B b^{8}\right)} c^{2} - 27 \, {\left(17 \, B^{3} a b^{8} + A B^{2} b^{9}\right)} c + {\left(3 \, B b^{9} c^{5} - 768 \, A a^{4} c^{10} + 128 \, {\left(8 \, B a^{4} b + 5 \, A a^{3} b^{2}\right)} c^{9} - 192 \, {\left(5 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} c^{8} + 24 \, {\left(14 \, B a^{2} b^{5} + A a b^{6}\right)} c^{7} - {\left(52 \, B a b^{7} + A b^{8}\right)} c^{6}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{-\frac{9 \, B^{2} b^{7} + 60 \, {\left(4 \, A B a^{3} + A^{2} a^{2} b\right)} c^{4} - 15 \, {\left(28 \, B^{2} a^{3} b + 20 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{3} + {\left(385 \, B^{2} a^{2} b^{3} + 80 \, A B a b^{4} + A^{2} b^{5}\right)} c^{2} - 3 \, {\left(35 \, B^{2} a b^{5} + 2 \, A B b^{6}\right)} c - {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 81 \, A^{4} a^{2} c^{6} - 18 \, {\left(25 \, A^{2} B^{2} a^{3} + 44 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{4} + 2200 \, A B^{3} a^{3} b + 2904 \, A^{2} B^{2} a^{2} b^{2} + 196 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(425 \, B^{4} a^{3} b^{2} + 798 \, A B^{3} a^{2} b^{3} + 132 \, A^{2} B^{2} a b^{4} + 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(113 \, B^{4} a^{2} b^{4} + 52 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(17 \, B^{4} a b^{6} + 2 \, A B^{3} b^{7}\right)} c}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}}\right) + 2 \, {\left(3 \, B a b^{2} - {\left(10 \, B a^{2} + A a b\right)} c\right)} x}{4 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{4} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2}\right)}}"," ",0,"1/4*(4*(B*b^2*c - 4*B*a*c^2)*x^5 + 2*(3*B*b^3 + 2*A*a*c^2 - (11*B*a*b + A*b^2)*c)*x^3 - sqrt(1/2)*(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^4 + (b^3*c^2 - 4*a*b*c^3)*x^2)*sqrt(-(9*B^2*b^7 + 60*(4*A*B*a^3 + A^2*a^2*b)*c^4 - 15*(28*B^2*a^3*b + 20*A*B*a^2*b^2 + A^2*a*b^3)*c^3 + (385*B^2*a^2*b^3 + 80*A*B*a*b^4 + A^2*b^5)*c^2 - 3*(35*B^2*a*b^5 + 2*A*B*b^6)*c + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))*log((189*B^4*a^2*b^6 - 135*A*B^3*a*b^7 + 324*A^4*a^3*c^5 - 81*(28*A^3*B*a^3*b + A^4*a^2*b^2)*c^4 - (2500*B^4*a^5 + 2500*A*B^3*a^4*b - 5016*A^2*B^2*a^3*b^2 - 647*A^3*B*a^2*b^3 - 5*A^4*a*b^4)*c^3 + 9*(625*B^4*a^4*b^2 - 303*A*B^3*a^3*b^3 - 186*A^2*B^2*a^2*b^4 - 5*A^3*B*a*b^5)*c^2 - 27*(73*B^4*a^3*b^4 - 49*A*B^3*a^2*b^5 - 5*A^2*B^2*a*b^6)*c)*x + 1/2*sqrt(1/2)*(27*B^3*b^10 + 144*(10*A^2*B*a^4 + A^3*a^3*b)*c^6 - 8*(500*B^3*a^5 + 930*A*B^2*a^4*b + 252*A^2*B*a^3*b^2 + 11*A^3*a^2*b^3)*c^5 + (11360*B^3*a^4*b^2 + 7608*A*B^2*a^3*b^3 + 882*A^2*B*a^2*b^4 + 17*A^3*a*b^5)*c^4 - (8818*B^3*a^3*b^4 + 2841*A*B^2*a^2*b^5 + 153*A^2*B*a*b^6 + A^3*b^7)*c^3 + 9*(329*B^3*a^2*b^6 + 51*A*B^2*a*b^7 + A^2*B*b^8)*c^2 - 27*(17*B^3*a*b^8 + A*B^2*b^9)*c - (3*B*b^9*c^5 - 768*A*a^4*c^10 + 128*(8*B*a^4*b + 5*A*a^3*b^2)*c^9 - 192*(5*B*a^3*b^3 + A*a^2*b^4)*c^8 + 24*(14*B*a^2*b^5 + A*a*b^6)*c^7 - (52*B*a*b^7 + A*b^8)*c^6)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(-(9*B^2*b^7 + 60*(4*A*B*a^3 + A^2*a^2*b)*c^4 - 15*(28*B^2*a^3*b + 20*A*B*a^2*b^2 + A^2*a*b^3)*c^3 + (385*B^2*a^2*b^3 + 80*A*B*a*b^4 + A^2*b^5)*c^2 - 3*(35*B^2*a*b^5 + 2*A*B*b^6)*c + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))) + sqrt(1/2)*(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^4 + (b^3*c^2 - 4*a*b*c^3)*x^2)*sqrt(-(9*B^2*b^7 + 60*(4*A*B*a^3 + A^2*a^2*b)*c^4 - 15*(28*B^2*a^3*b + 20*A*B*a^2*b^2 + A^2*a*b^3)*c^3 + (385*B^2*a^2*b^3 + 80*A*B*a*b^4 + A^2*b^5)*c^2 - 3*(35*B^2*a*b^5 + 2*A*B*b^6)*c + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))*log((189*B^4*a^2*b^6 - 135*A*B^3*a*b^7 + 324*A^4*a^3*c^5 - 81*(28*A^3*B*a^3*b + A^4*a^2*b^2)*c^4 - (2500*B^4*a^5 + 2500*A*B^3*a^4*b - 5016*A^2*B^2*a^3*b^2 - 647*A^3*B*a^2*b^3 - 5*A^4*a*b^4)*c^3 + 9*(625*B^4*a^4*b^2 - 303*A*B^3*a^3*b^3 - 186*A^2*B^2*a^2*b^4 - 5*A^3*B*a*b^5)*c^2 - 27*(73*B^4*a^3*b^4 - 49*A*B^3*a^2*b^5 - 5*A^2*B^2*a*b^6)*c)*x - 1/2*sqrt(1/2)*(27*B^3*b^10 + 144*(10*A^2*B*a^4 + A^3*a^3*b)*c^6 - 8*(500*B^3*a^5 + 930*A*B^2*a^4*b + 252*A^2*B*a^3*b^2 + 11*A^3*a^2*b^3)*c^5 + (11360*B^3*a^4*b^2 + 7608*A*B^2*a^3*b^3 + 882*A^2*B*a^2*b^4 + 17*A^3*a*b^5)*c^4 - (8818*B^3*a^3*b^4 + 2841*A*B^2*a^2*b^5 + 153*A^2*B*a*b^6 + A^3*b^7)*c^3 + 9*(329*B^3*a^2*b^6 + 51*A*B^2*a*b^7 + A^2*B*b^8)*c^2 - 27*(17*B^3*a*b^8 + A*B^2*b^9)*c - (3*B*b^9*c^5 - 768*A*a^4*c^10 + 128*(8*B*a^4*b + 5*A*a^3*b^2)*c^9 - 192*(5*B*a^3*b^3 + A*a^2*b^4)*c^8 + 24*(14*B*a^2*b^5 + A*a*b^6)*c^7 - (52*B*a*b^7 + A*b^8)*c^6)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(-(9*B^2*b^7 + 60*(4*A*B*a^3 + A^2*a^2*b)*c^4 - 15*(28*B^2*a^3*b + 20*A*B*a^2*b^2 + A^2*a*b^3)*c^3 + (385*B^2*a^2*b^3 + 80*A*B*a*b^4 + A^2*b^5)*c^2 - 3*(35*B^2*a*b^5 + 2*A*B*b^6)*c + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))) - sqrt(1/2)*(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^4 + (b^3*c^2 - 4*a*b*c^3)*x^2)*sqrt(-(9*B^2*b^7 + 60*(4*A*B*a^3 + A^2*a^2*b)*c^4 - 15*(28*B^2*a^3*b + 20*A*B*a^2*b^2 + A^2*a*b^3)*c^3 + (385*B^2*a^2*b^3 + 80*A*B*a*b^4 + A^2*b^5)*c^2 - 3*(35*B^2*a*b^5 + 2*A*B*b^6)*c - (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))*log((189*B^4*a^2*b^6 - 135*A*B^3*a*b^7 + 324*A^4*a^3*c^5 - 81*(28*A^3*B*a^3*b + A^4*a^2*b^2)*c^4 - (2500*B^4*a^5 + 2500*A*B^3*a^4*b - 5016*A^2*B^2*a^3*b^2 - 647*A^3*B*a^2*b^3 - 5*A^4*a*b^4)*c^3 + 9*(625*B^4*a^4*b^2 - 303*A*B^3*a^3*b^3 - 186*A^2*B^2*a^2*b^4 - 5*A^3*B*a*b^5)*c^2 - 27*(73*B^4*a^3*b^4 - 49*A*B^3*a^2*b^5 - 5*A^2*B^2*a*b^6)*c)*x + 1/2*sqrt(1/2)*(27*B^3*b^10 + 144*(10*A^2*B*a^4 + A^3*a^3*b)*c^6 - 8*(500*B^3*a^5 + 930*A*B^2*a^4*b + 252*A^2*B*a^3*b^2 + 11*A^3*a^2*b^3)*c^5 + (11360*B^3*a^4*b^2 + 7608*A*B^2*a^3*b^3 + 882*A^2*B*a^2*b^4 + 17*A^3*a*b^5)*c^4 - (8818*B^3*a^3*b^4 + 2841*A*B^2*a^2*b^5 + 153*A^2*B*a*b^6 + A^3*b^7)*c^3 + 9*(329*B^3*a^2*b^6 + 51*A*B^2*a*b^7 + A^2*B*b^8)*c^2 - 27*(17*B^3*a*b^8 + A*B^2*b^9)*c + (3*B*b^9*c^5 - 768*A*a^4*c^10 + 128*(8*B*a^4*b + 5*A*a^3*b^2)*c^9 - 192*(5*B*a^3*b^3 + A*a^2*b^4)*c^8 + 24*(14*B*a^2*b^5 + A*a*b^6)*c^7 - (52*B*a*b^7 + A*b^8)*c^6)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(-(9*B^2*b^7 + 60*(4*A*B*a^3 + A^2*a^2*b)*c^4 - 15*(28*B^2*a^3*b + 20*A*B*a^2*b^2 + A^2*a*b^3)*c^3 + (385*B^2*a^2*b^3 + 80*A*B*a*b^4 + A^2*b^5)*c^2 - 3*(35*B^2*a*b^5 + 2*A*B*b^6)*c - (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))) + sqrt(1/2)*(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^4 + (b^3*c^2 - 4*a*b*c^3)*x^2)*sqrt(-(9*B^2*b^7 + 60*(4*A*B*a^3 + A^2*a^2*b)*c^4 - 15*(28*B^2*a^3*b + 20*A*B*a^2*b^2 + A^2*a*b^3)*c^3 + (385*B^2*a^2*b^3 + 80*A*B*a*b^4 + A^2*b^5)*c^2 - 3*(35*B^2*a*b^5 + 2*A*B*b^6)*c - (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))*log((189*B^4*a^2*b^6 - 135*A*B^3*a*b^7 + 324*A^4*a^3*c^5 - 81*(28*A^3*B*a^3*b + A^4*a^2*b^2)*c^4 - (2500*B^4*a^5 + 2500*A*B^3*a^4*b - 5016*A^2*B^2*a^3*b^2 - 647*A^3*B*a^2*b^3 - 5*A^4*a*b^4)*c^3 + 9*(625*B^4*a^4*b^2 - 303*A*B^3*a^3*b^3 - 186*A^2*B^2*a^2*b^4 - 5*A^3*B*a*b^5)*c^2 - 27*(73*B^4*a^3*b^4 - 49*A*B^3*a^2*b^5 - 5*A^2*B^2*a*b^6)*c)*x - 1/2*sqrt(1/2)*(27*B^3*b^10 + 144*(10*A^2*B*a^4 + A^3*a^3*b)*c^6 - 8*(500*B^3*a^5 + 930*A*B^2*a^4*b + 252*A^2*B*a^3*b^2 + 11*A^3*a^2*b^3)*c^5 + (11360*B^3*a^4*b^2 + 7608*A*B^2*a^3*b^3 + 882*A^2*B*a^2*b^4 + 17*A^3*a*b^5)*c^4 - (8818*B^3*a^3*b^4 + 2841*A*B^2*a^2*b^5 + 153*A^2*B*a*b^6 + A^3*b^7)*c^3 + 9*(329*B^3*a^2*b^6 + 51*A*B^2*a*b^7 + A^2*B*b^8)*c^2 - 27*(17*B^3*a*b^8 + A*B^2*b^9)*c + (3*B*b^9*c^5 - 768*A*a^4*c^10 + 128*(8*B*a^4*b + 5*A*a^3*b^2)*c^9 - 192*(5*B*a^3*b^3 + A*a^2*b^4)*c^8 + 24*(14*B*a^2*b^5 + A*a*b^6)*c^7 - (52*B*a*b^7 + A*b^8)*c^6)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(-(9*B^2*b^7 + 60*(4*A*B*a^3 + A^2*a^2*b)*c^4 - 15*(28*B^2*a^3*b + 20*A*B*a^2*b^2 + A^2*a*b^3)*c^3 + (385*B^2*a^2*b^3 + 80*A*B*a*b^4 + A^2*b^5)*c^2 - 3*(35*B^2*a*b^5 + 2*A*B*b^6)*c - (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((81*B^4*b^8 + 81*A^4*a^2*c^6 - 18*(25*A^2*B^2*a^3 + 44*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (625*B^4*a^4 + 2200*A*B^3*a^3*b + 2904*A^2*B^2*a^2*b^2 + 196*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(425*B^4*a^3*b^2 + 798*A*B^3*a^2*b^3 + 132*A^2*B^2*a*b^4 + 2*A^3*B*b^5)*c^3 + 27*(113*B^4*a^2*b^4 + 52*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(17*B^4*a*b^6 + 2*A*B^3*b^7)*c)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))) + 2*(3*B*a*b^2 - (10*B*a^2 + A*a*b)*c)*x)/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^4 + (b^3*c^2 - 4*a*b*c^3)*x^2)","B",0
119,1,4658,0,2.816597," ","integrate(x^4*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(B b^{2} - {\left(2 \, B a + A b\right)} c\right)} x^{3} + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{B^{2} b^{5} - 12 \, {\left(4 \, A B a^{2} - A^{2} a b\right)} c^{3} + {\left(60 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(15 \, B^{2} a b^{3} - 2 \, A B b^{4}\right)} c + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} \log\left(-{\left(5 \, B^{4} a b^{4} - 3 \, A B^{3} b^{5} - 4 \, A^{4} a c^{4} + {\left(20 \, A^{3} B a b - 3 \, A^{4} b^{2}\right)} c^{3} + 3 \, {\left(108 \, B^{4} a^{3} - 108 \, A B^{3} a^{2} b + 28 \, A^{2} B^{2} a b^{2} - 3 \, A^{3} B b^{3}\right)} c^{2} - {\left(81 \, B^{4} a^{2} b^{2} - 65 \, A B^{3} a b^{3} + 9 \, A^{2} B^{2} b^{4}\right)} c\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} b^{7} - 17 \, B^{3} a b^{5} c - 32 \, A^{3} a^{2} c^{5} + 16 \, {\left(18 \, A B^{2} a^{3} - 3 \, A^{2} B a^{2} b + A^{3} a b^{2}\right)} c^{4} - 2 \, {\left(72 \, B^{3} a^{3} b + 72 \, A B^{2} a^{2} b^{2} - 12 \, A^{2} B a b^{3} + A^{3} b^{4}\right)} c^{3} + {\left(88 \, B^{3} a^{2} b^{3} + 18 \, A B^{2} a b^{4} - 3 \, A^{2} B b^{5}\right)} c^{2} - {\left(B b^{8} c^{3} + 256 \, {\left(3 \, B a^{4} - A a^{3} b\right)} c^{7} - 64 \, {\left(10 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c^{6} + 48 \, {\left(4 \, B a^{2} b^{4} - A a b^{5}\right)} c^{5} - 4 \, {\left(6 \, B a b^{6} - A b^{7}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{-\frac{B^{2} b^{5} - 12 \, {\left(4 \, A B a^{2} - A^{2} a b\right)} c^{3} + {\left(60 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(15 \, B^{2} a b^{3} - 2 \, A B b^{4}\right)} c + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{B^{2} b^{5} - 12 \, {\left(4 \, A B a^{2} - A^{2} a b\right)} c^{3} + {\left(60 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(15 \, B^{2} a b^{3} - 2 \, A B b^{4}\right)} c + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} \log\left(-{\left(5 \, B^{4} a b^{4} - 3 \, A B^{3} b^{5} - 4 \, A^{4} a c^{4} + {\left(20 \, A^{3} B a b - 3 \, A^{4} b^{2}\right)} c^{3} + 3 \, {\left(108 \, B^{4} a^{3} - 108 \, A B^{3} a^{2} b + 28 \, A^{2} B^{2} a b^{2} - 3 \, A^{3} B b^{3}\right)} c^{2} - {\left(81 \, B^{4} a^{2} b^{2} - 65 \, A B^{3} a b^{3} + 9 \, A^{2} B^{2} b^{4}\right)} c\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} b^{7} - 17 \, B^{3} a b^{5} c - 32 \, A^{3} a^{2} c^{5} + 16 \, {\left(18 \, A B^{2} a^{3} - 3 \, A^{2} B a^{2} b + A^{3} a b^{2}\right)} c^{4} - 2 \, {\left(72 \, B^{3} a^{3} b + 72 \, A B^{2} a^{2} b^{2} - 12 \, A^{2} B a b^{3} + A^{3} b^{4}\right)} c^{3} + {\left(88 \, B^{3} a^{2} b^{3} + 18 \, A B^{2} a b^{4} - 3 \, A^{2} B b^{5}\right)} c^{2} - {\left(B b^{8} c^{3} + 256 \, {\left(3 \, B a^{4} - A a^{3} b\right)} c^{7} - 64 \, {\left(10 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c^{6} + 48 \, {\left(4 \, B a^{2} b^{4} - A a b^{5}\right)} c^{5} - 4 \, {\left(6 \, B a b^{6} - A b^{7}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{-\frac{B^{2} b^{5} - 12 \, {\left(4 \, A B a^{2} - A^{2} a b\right)} c^{3} + {\left(60 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(15 \, B^{2} a b^{3} - 2 \, A B b^{4}\right)} c + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{B^{2} b^{5} - 12 \, {\left(4 \, A B a^{2} - A^{2} a b\right)} c^{3} + {\left(60 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(15 \, B^{2} a b^{3} - 2 \, A B b^{4}\right)} c - {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} \log\left(-{\left(5 \, B^{4} a b^{4} - 3 \, A B^{3} b^{5} - 4 \, A^{4} a c^{4} + {\left(20 \, A^{3} B a b - 3 \, A^{4} b^{2}\right)} c^{3} + 3 \, {\left(108 \, B^{4} a^{3} - 108 \, A B^{3} a^{2} b + 28 \, A^{2} B^{2} a b^{2} - 3 \, A^{3} B b^{3}\right)} c^{2} - {\left(81 \, B^{4} a^{2} b^{2} - 65 \, A B^{3} a b^{3} + 9 \, A^{2} B^{2} b^{4}\right)} c\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} b^{7} - 17 \, B^{3} a b^{5} c - 32 \, A^{3} a^{2} c^{5} + 16 \, {\left(18 \, A B^{2} a^{3} - 3 \, A^{2} B a^{2} b + A^{3} a b^{2}\right)} c^{4} - 2 \, {\left(72 \, B^{3} a^{3} b + 72 \, A B^{2} a^{2} b^{2} - 12 \, A^{2} B a b^{3} + A^{3} b^{4}\right)} c^{3} + {\left(88 \, B^{3} a^{2} b^{3} + 18 \, A B^{2} a b^{4} - 3 \, A^{2} B b^{5}\right)} c^{2} + {\left(B b^{8} c^{3} + 256 \, {\left(3 \, B a^{4} - A a^{3} b\right)} c^{7} - 64 \, {\left(10 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c^{6} + 48 \, {\left(4 \, B a^{2} b^{4} - A a b^{5}\right)} c^{5} - 4 \, {\left(6 \, B a b^{6} - A b^{7}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{-\frac{B^{2} b^{5} - 12 \, {\left(4 \, A B a^{2} - A^{2} a b\right)} c^{3} + {\left(60 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(15 \, B^{2} a b^{3} - 2 \, A B b^{4}\right)} c - {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{B^{2} b^{5} - 12 \, {\left(4 \, A B a^{2} - A^{2} a b\right)} c^{3} + {\left(60 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(15 \, B^{2} a b^{3} - 2 \, A B b^{4}\right)} c - {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} \log\left(-{\left(5 \, B^{4} a b^{4} - 3 \, A B^{3} b^{5} - 4 \, A^{4} a c^{4} + {\left(20 \, A^{3} B a b - 3 \, A^{4} b^{2}\right)} c^{3} + 3 \, {\left(108 \, B^{4} a^{3} - 108 \, A B^{3} a^{2} b + 28 \, A^{2} B^{2} a b^{2} - 3 \, A^{3} B b^{3}\right)} c^{2} - {\left(81 \, B^{4} a^{2} b^{2} - 65 \, A B^{3} a b^{3} + 9 \, A^{2} B^{2} b^{4}\right)} c\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} b^{7} - 17 \, B^{3} a b^{5} c - 32 \, A^{3} a^{2} c^{5} + 16 \, {\left(18 \, A B^{2} a^{3} - 3 \, A^{2} B a^{2} b + A^{3} a b^{2}\right)} c^{4} - 2 \, {\left(72 \, B^{3} a^{3} b + 72 \, A B^{2} a^{2} b^{2} - 12 \, A^{2} B a b^{3} + A^{3} b^{4}\right)} c^{3} + {\left(88 \, B^{3} a^{2} b^{3} + 18 \, A B^{2} a b^{4} - 3 \, A^{2} B b^{5}\right)} c^{2} + {\left(B b^{8} c^{3} + 256 \, {\left(3 \, B a^{4} - A a^{3} b\right)} c^{7} - 64 \, {\left(10 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c^{6} + 48 \, {\left(4 \, B a^{2} b^{4} - A a b^{5}\right)} c^{5} - 4 \, {\left(6 \, B a b^{6} - A b^{7}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{-\frac{B^{2} b^{5} - 12 \, {\left(4 \, A B a^{2} - A^{2} a b\right)} c^{3} + {\left(60 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c^{2} - {\left(15 \, B^{2} a b^{3} - 2 \, A B b^{4}\right)} c - {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{\frac{B^{4} b^{4} + A^{4} c^{4} - 2 \, {\left(9 \, A^{2} B^{2} a - 2 \, A^{3} B b\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{2} - 12 \, A B^{3} a b + 2 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a b^{2} - 2 \, A B^{3} b^{3}\right)} c}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}}\right) + 2 \, {\left(B a b - 2 \, A a c\right)} x}{4 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2}\right)}}"," ",0,"-1/4*(2*(B*b^2 - (2*B*a + A*b)*c)*x^3 + sqrt(1/2)*((b^2*c^2 - 4*a*c^3)*x^4 + a*b^2*c - 4*a^2*c^2 + (b^3*c - 4*a*b*c^2)*x^2)*sqrt(-(B^2*b^5 - 12*(4*A*B*a^2 - A^2*a*b)*c^3 + (60*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c^2 - (15*B^2*a*b^3 - 2*A*B*b^4)*c + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*log(-(5*B^4*a*b^4 - 3*A*B^3*b^5 - 4*A^4*a*c^4 + (20*A^3*B*a*b - 3*A^4*b^2)*c^3 + 3*(108*B^4*a^3 - 108*A*B^3*a^2*b + 28*A^2*B^2*a*b^2 - 3*A^3*B*b^3)*c^2 - (81*B^4*a^2*b^2 - 65*A*B^3*a*b^3 + 9*A^2*B^2*b^4)*c)*x + 1/2*sqrt(1/2)*(B^3*b^7 - 17*B^3*a*b^5*c - 32*A^3*a^2*c^5 + 16*(18*A*B^2*a^3 - 3*A^2*B*a^2*b + A^3*a*b^2)*c^4 - 2*(72*B^3*a^3*b + 72*A*B^2*a^2*b^2 - 12*A^2*B*a*b^3 + A^3*b^4)*c^3 + (88*B^3*a^2*b^3 + 18*A*B^2*a*b^4 - 3*A^2*B*b^5)*c^2 - (B*b^8*c^3 + 256*(3*B*a^4 - A*a^3*b)*c^7 - 64*(10*B*a^3*b^2 - 3*A*a^2*b^3)*c^6 + 48*(4*B*a^2*b^4 - A*a*b^5)*c^5 - 4*(6*B*a*b^6 - A*b^7)*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt(-(B^2*b^5 - 12*(4*A*B*a^2 - A^2*a*b)*c^3 + (60*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c^2 - (15*B^2*a*b^3 - 2*A*B*b^4)*c + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))) - sqrt(1/2)*((b^2*c^2 - 4*a*c^3)*x^4 + a*b^2*c - 4*a^2*c^2 + (b^3*c - 4*a*b*c^2)*x^2)*sqrt(-(B^2*b^5 - 12*(4*A*B*a^2 - A^2*a*b)*c^3 + (60*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c^2 - (15*B^2*a*b^3 - 2*A*B*b^4)*c + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*log(-(5*B^4*a*b^4 - 3*A*B^3*b^5 - 4*A^4*a*c^4 + (20*A^3*B*a*b - 3*A^4*b^2)*c^3 + 3*(108*B^4*a^3 - 108*A*B^3*a^2*b + 28*A^2*B^2*a*b^2 - 3*A^3*B*b^3)*c^2 - (81*B^4*a^2*b^2 - 65*A*B^3*a*b^3 + 9*A^2*B^2*b^4)*c)*x - 1/2*sqrt(1/2)*(B^3*b^7 - 17*B^3*a*b^5*c - 32*A^3*a^2*c^5 + 16*(18*A*B^2*a^3 - 3*A^2*B*a^2*b + A^3*a*b^2)*c^4 - 2*(72*B^3*a^3*b + 72*A*B^2*a^2*b^2 - 12*A^2*B*a*b^3 + A^3*b^4)*c^3 + (88*B^3*a^2*b^3 + 18*A*B^2*a*b^4 - 3*A^2*B*b^5)*c^2 - (B*b^8*c^3 + 256*(3*B*a^4 - A*a^3*b)*c^7 - 64*(10*B*a^3*b^2 - 3*A*a^2*b^3)*c^6 + 48*(4*B*a^2*b^4 - A*a*b^5)*c^5 - 4*(6*B*a*b^6 - A*b^7)*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt(-(B^2*b^5 - 12*(4*A*B*a^2 - A^2*a*b)*c^3 + (60*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c^2 - (15*B^2*a*b^3 - 2*A*B*b^4)*c + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))) + sqrt(1/2)*((b^2*c^2 - 4*a*c^3)*x^4 + a*b^2*c - 4*a^2*c^2 + (b^3*c - 4*a*b*c^2)*x^2)*sqrt(-(B^2*b^5 - 12*(4*A*B*a^2 - A^2*a*b)*c^3 + (60*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c^2 - (15*B^2*a*b^3 - 2*A*B*b^4)*c - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*log(-(5*B^4*a*b^4 - 3*A*B^3*b^5 - 4*A^4*a*c^4 + (20*A^3*B*a*b - 3*A^4*b^2)*c^3 + 3*(108*B^4*a^3 - 108*A*B^3*a^2*b + 28*A^2*B^2*a*b^2 - 3*A^3*B*b^3)*c^2 - (81*B^4*a^2*b^2 - 65*A*B^3*a*b^3 + 9*A^2*B^2*b^4)*c)*x + 1/2*sqrt(1/2)*(B^3*b^7 - 17*B^3*a*b^5*c - 32*A^3*a^2*c^5 + 16*(18*A*B^2*a^3 - 3*A^2*B*a^2*b + A^3*a*b^2)*c^4 - 2*(72*B^3*a^3*b + 72*A*B^2*a^2*b^2 - 12*A^2*B*a*b^3 + A^3*b^4)*c^3 + (88*B^3*a^2*b^3 + 18*A*B^2*a*b^4 - 3*A^2*B*b^5)*c^2 + (B*b^8*c^3 + 256*(3*B*a^4 - A*a^3*b)*c^7 - 64*(10*B*a^3*b^2 - 3*A*a^2*b^3)*c^6 + 48*(4*B*a^2*b^4 - A*a*b^5)*c^5 - 4*(6*B*a*b^6 - A*b^7)*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt(-(B^2*b^5 - 12*(4*A*B*a^2 - A^2*a*b)*c^3 + (60*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c^2 - (15*B^2*a*b^3 - 2*A*B*b^4)*c - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))) - sqrt(1/2)*((b^2*c^2 - 4*a*c^3)*x^4 + a*b^2*c - 4*a^2*c^2 + (b^3*c - 4*a*b*c^2)*x^2)*sqrt(-(B^2*b^5 - 12*(4*A*B*a^2 - A^2*a*b)*c^3 + (60*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c^2 - (15*B^2*a*b^3 - 2*A*B*b^4)*c - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*log(-(5*B^4*a*b^4 - 3*A*B^3*b^5 - 4*A^4*a*c^4 + (20*A^3*B*a*b - 3*A^4*b^2)*c^3 + 3*(108*B^4*a^3 - 108*A*B^3*a^2*b + 28*A^2*B^2*a*b^2 - 3*A^3*B*b^3)*c^2 - (81*B^4*a^2*b^2 - 65*A*B^3*a*b^3 + 9*A^2*B^2*b^4)*c)*x - 1/2*sqrt(1/2)*(B^3*b^7 - 17*B^3*a*b^5*c - 32*A^3*a^2*c^5 + 16*(18*A*B^2*a^3 - 3*A^2*B*a^2*b + A^3*a*b^2)*c^4 - 2*(72*B^3*a^3*b + 72*A*B^2*a^2*b^2 - 12*A^2*B*a*b^3 + A^3*b^4)*c^3 + (88*B^3*a^2*b^3 + 18*A*B^2*a*b^4 - 3*A^2*B*b^5)*c^2 + (B*b^8*c^3 + 256*(3*B*a^4 - A*a^3*b)*c^7 - 64*(10*B*a^3*b^2 - 3*A*a^2*b^3)*c^6 + 48*(4*B*a^2*b^4 - A*a*b^5)*c^5 - 4*(6*B*a*b^6 - A*b^7)*c^4)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt(-(B^2*b^5 - 12*(4*A*B*a^2 - A^2*a*b)*c^3 + (60*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c^2 - (15*B^2*a*b^3 - 2*A*B*b^4)*c - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((B^4*b^4 + A^4*c^4 - 2*(9*A^2*B^2*a - 2*A^3*B*b)*c^3 + 3*(27*B^4*a^2 - 12*A*B^3*a*b + 2*A^2*B^2*b^2)*c^2 - 2*(9*B^4*a*b^2 - 2*A*B^3*b^3)*c)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))) + 2*(B*a*b - 2*A*a*c)*x)/((b^2*c^2 - 4*a*c^3)*x^4 + a*b^2*c - 4*a^2*c^2 + (b^3*c - 4*a*b*c^2)*x^2)","B",0
120,1,3467,0,1.915606," ","integrate(x^2*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(B b - 2 \, A c\right)} x^{3} - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)} \sqrt{-\frac{B^{2} a b^{3} - 4 \, {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c^{2} + {\left(12 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c + {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}}{a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}}} \log\left(-{\left(3 \, B^{4} a^{2} b^{2} - A B^{3} a b^{3} - 4 \, A^{4} a c^{3} + 3 \, {\left(4 \, A^{3} B a b - A^{4} b^{2}\right)} c^{2} + {\left(4 \, B^{4} a^{3} - 12 \, A B^{3} a^{2} b + A^{3} B b^{3}\right)} c\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(2 \, B^{3} a^{2} b^{4} - A B^{2} a b^{5} - 16 \, {\left(2 \, A^{2} B a^{3} - A^{3} a^{2} b\right)} c^{3} + 8 \, {\left(4 \, B^{3} a^{4} - 2 \, A B^{2} a^{3} b + 2 \, A^{2} B a^{2} b^{2} - A^{3} a b^{3}\right)} c^{2} - {\left(16 \, B^{3} a^{3} b^{2} - 8 \, A B^{2} a^{2} b^{3} + 2 \, A^{2} B a b^{4} - A^{3} b^{5}\right)} c + {\left(192 \, B a^{4} b^{3} c^{3} + 256 \, A a^{5} c^{5} - 128 \, {\left(2 \, B a^{5} b + A a^{4} b^{2}\right)} c^{4} - 8 \, {\left(6 \, B a^{3} b^{5} - A a^{2} b^{6}\right)} c^{2} + {\left(4 \, B a^{2} b^{7} - A a b^{8}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}\right)} \sqrt{-\frac{B^{2} a b^{3} - 4 \, {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c^{2} + {\left(12 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c + {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}}{a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)} \sqrt{-\frac{B^{2} a b^{3} - 4 \, {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c^{2} + {\left(12 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c + {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}}{a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}}} \log\left(-{\left(3 \, B^{4} a^{2} b^{2} - A B^{3} a b^{3} - 4 \, A^{4} a c^{3} + 3 \, {\left(4 \, A^{3} B a b - A^{4} b^{2}\right)} c^{2} + {\left(4 \, B^{4} a^{3} - 12 \, A B^{3} a^{2} b + A^{3} B b^{3}\right)} c\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(2 \, B^{3} a^{2} b^{4} - A B^{2} a b^{5} - 16 \, {\left(2 \, A^{2} B a^{3} - A^{3} a^{2} b\right)} c^{3} + 8 \, {\left(4 \, B^{3} a^{4} - 2 \, A B^{2} a^{3} b + 2 \, A^{2} B a^{2} b^{2} - A^{3} a b^{3}\right)} c^{2} - {\left(16 \, B^{3} a^{3} b^{2} - 8 \, A B^{2} a^{2} b^{3} + 2 \, A^{2} B a b^{4} - A^{3} b^{5}\right)} c + {\left(192 \, B a^{4} b^{3} c^{3} + 256 \, A a^{5} c^{5} - 128 \, {\left(2 \, B a^{5} b + A a^{4} b^{2}\right)} c^{4} - 8 \, {\left(6 \, B a^{3} b^{5} - A a^{2} b^{6}\right)} c^{2} + {\left(4 \, B a^{2} b^{7} - A a b^{8}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}\right)} \sqrt{-\frac{B^{2} a b^{3} - 4 \, {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c^{2} + {\left(12 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c + {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}}{a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)} \sqrt{-\frac{B^{2} a b^{3} - 4 \, {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c^{2} + {\left(12 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c - {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}}{a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}}} \log\left(-{\left(3 \, B^{4} a^{2} b^{2} - A B^{3} a b^{3} - 4 \, A^{4} a c^{3} + 3 \, {\left(4 \, A^{3} B a b - A^{4} b^{2}\right)} c^{2} + {\left(4 \, B^{4} a^{3} - 12 \, A B^{3} a^{2} b + A^{3} B b^{3}\right)} c\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(2 \, B^{3} a^{2} b^{4} - A B^{2} a b^{5} - 16 \, {\left(2 \, A^{2} B a^{3} - A^{3} a^{2} b\right)} c^{3} + 8 \, {\left(4 \, B^{3} a^{4} - 2 \, A B^{2} a^{3} b + 2 \, A^{2} B a^{2} b^{2} - A^{3} a b^{3}\right)} c^{2} - {\left(16 \, B^{3} a^{3} b^{2} - 8 \, A B^{2} a^{2} b^{3} + 2 \, A^{2} B a b^{4} - A^{3} b^{5}\right)} c - {\left(192 \, B a^{4} b^{3} c^{3} + 256 \, A a^{5} c^{5} - 128 \, {\left(2 \, B a^{5} b + A a^{4} b^{2}\right)} c^{4} - 8 \, {\left(6 \, B a^{3} b^{5} - A a^{2} b^{6}\right)} c^{2} + {\left(4 \, B a^{2} b^{7} - A a b^{8}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}\right)} \sqrt{-\frac{B^{2} a b^{3} - 4 \, {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c^{2} + {\left(12 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c - {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}}{a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)} \sqrt{-\frac{B^{2} a b^{3} - 4 \, {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c^{2} + {\left(12 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c - {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}}{a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}}} \log\left(-{\left(3 \, B^{4} a^{2} b^{2} - A B^{3} a b^{3} - 4 \, A^{4} a c^{3} + 3 \, {\left(4 \, A^{3} B a b - A^{4} b^{2}\right)} c^{2} + {\left(4 \, B^{4} a^{3} - 12 \, A B^{3} a^{2} b + A^{3} B b^{3}\right)} c\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(2 \, B^{3} a^{2} b^{4} - A B^{2} a b^{5} - 16 \, {\left(2 \, A^{2} B a^{3} - A^{3} a^{2} b\right)} c^{3} + 8 \, {\left(4 \, B^{3} a^{4} - 2 \, A B^{2} a^{3} b + 2 \, A^{2} B a^{2} b^{2} - A^{3} a b^{3}\right)} c^{2} - {\left(16 \, B^{3} a^{3} b^{2} - 8 \, A B^{2} a^{2} b^{3} + 2 \, A^{2} B a b^{4} - A^{3} b^{5}\right)} c - {\left(192 \, B a^{4} b^{3} c^{3} + 256 \, A a^{5} c^{5} - 128 \, {\left(2 \, B a^{5} b + A a^{4} b^{2}\right)} c^{4} - 8 \, {\left(6 \, B a^{3} b^{5} - A a^{2} b^{6}\right)} c^{2} + {\left(4 \, B a^{2} b^{7} - A a b^{8}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}\right)} \sqrt{-\frac{B^{2} a b^{3} - 4 \, {\left(4 \, A B a^{2} - 3 \, A^{2} a b\right)} c^{2} + {\left(12 \, B^{2} a^{2} b - 12 \, A B a b^{2} + A^{2} b^{3}\right)} c - {\left(a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}}}}{a b^{6} c - 12 \, a^{2} b^{4} c^{2} + 48 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}}}\right) + 2 \, {\left(2 \, B a - A b\right)} x}{4 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} x^{2}\right)}}"," ",0,"1/4*(2*(B*b - 2*A*c)*x^3 - sqrt(1/2)*((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2)*sqrt(-(B^2*a*b^3 - 4*(4*A*B*a^2 - 3*A^2*a*b)*c^2 + (12*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c + (a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))/(a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4))*log(-(3*B^4*a^2*b^2 - A*B^3*a*b^3 - 4*A^4*a*c^3 + 3*(4*A^3*B*a*b - A^4*b^2)*c^2 + (4*B^4*a^3 - 12*A*B^3*a^2*b + A^3*B*b^3)*c)*x + 1/2*sqrt(1/2)*(2*B^3*a^2*b^4 - A*B^2*a*b^5 - 16*(2*A^2*B*a^3 - A^3*a^2*b)*c^3 + 8*(4*B^3*a^4 - 2*A*B^2*a^3*b + 2*A^2*B*a^2*b^2 - A^3*a*b^3)*c^2 - (16*B^3*a^3*b^2 - 8*A*B^2*a^2*b^3 + 2*A^2*B*a*b^4 - A^3*b^5)*c + (192*B*a^4*b^3*c^3 + 256*A*a^5*c^5 - 128*(2*B*a^5*b + A*a^4*b^2)*c^4 - 8*(6*B*a^3*b^5 - A*a^2*b^6)*c^2 + (4*B*a^2*b^7 - A*a*b^8)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))*sqrt(-(B^2*a*b^3 - 4*(4*A*B*a^2 - 3*A^2*a*b)*c^2 + (12*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c + (a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))/(a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4))) + sqrt(1/2)*((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2)*sqrt(-(B^2*a*b^3 - 4*(4*A*B*a^2 - 3*A^2*a*b)*c^2 + (12*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c + (a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))/(a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4))*log(-(3*B^4*a^2*b^2 - A*B^3*a*b^3 - 4*A^4*a*c^3 + 3*(4*A^3*B*a*b - A^4*b^2)*c^2 + (4*B^4*a^3 - 12*A*B^3*a^2*b + A^3*B*b^3)*c)*x - 1/2*sqrt(1/2)*(2*B^3*a^2*b^4 - A*B^2*a*b^5 - 16*(2*A^2*B*a^3 - A^3*a^2*b)*c^3 + 8*(4*B^3*a^4 - 2*A*B^2*a^3*b + 2*A^2*B*a^2*b^2 - A^3*a*b^3)*c^2 - (16*B^3*a^3*b^2 - 8*A*B^2*a^2*b^3 + 2*A^2*B*a*b^4 - A^3*b^5)*c + (192*B*a^4*b^3*c^3 + 256*A*a^5*c^5 - 128*(2*B*a^5*b + A*a^4*b^2)*c^4 - 8*(6*B*a^3*b^5 - A*a^2*b^6)*c^2 + (4*B*a^2*b^7 - A*a*b^8)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))*sqrt(-(B^2*a*b^3 - 4*(4*A*B*a^2 - 3*A^2*a*b)*c^2 + (12*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c + (a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))/(a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4))) - sqrt(1/2)*((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2)*sqrt(-(B^2*a*b^3 - 4*(4*A*B*a^2 - 3*A^2*a*b)*c^2 + (12*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c - (a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))/(a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4))*log(-(3*B^4*a^2*b^2 - A*B^3*a*b^3 - 4*A^4*a*c^3 + 3*(4*A^3*B*a*b - A^4*b^2)*c^2 + (4*B^4*a^3 - 12*A*B^3*a^2*b + A^3*B*b^3)*c)*x + 1/2*sqrt(1/2)*(2*B^3*a^2*b^4 - A*B^2*a*b^5 - 16*(2*A^2*B*a^3 - A^3*a^2*b)*c^3 + 8*(4*B^3*a^4 - 2*A*B^2*a^3*b + 2*A^2*B*a^2*b^2 - A^3*a*b^3)*c^2 - (16*B^3*a^3*b^2 - 8*A*B^2*a^2*b^3 + 2*A^2*B*a*b^4 - A^3*b^5)*c - (192*B*a^4*b^3*c^3 + 256*A*a^5*c^5 - 128*(2*B*a^5*b + A*a^4*b^2)*c^4 - 8*(6*B*a^3*b^5 - A*a^2*b^6)*c^2 + (4*B*a^2*b^7 - A*a*b^8)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))*sqrt(-(B^2*a*b^3 - 4*(4*A*B*a^2 - 3*A^2*a*b)*c^2 + (12*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c - (a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))/(a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4))) + sqrt(1/2)*((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2)*sqrt(-(B^2*a*b^3 - 4*(4*A*B*a^2 - 3*A^2*a*b)*c^2 + (12*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c - (a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))/(a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4))*log(-(3*B^4*a^2*b^2 - A*B^3*a*b^3 - 4*A^4*a*c^3 + 3*(4*A^3*B*a*b - A^4*b^2)*c^2 + (4*B^4*a^3 - 12*A*B^3*a^2*b + A^3*B*b^3)*c)*x - 1/2*sqrt(1/2)*(2*B^3*a^2*b^4 - A*B^2*a*b^5 - 16*(2*A^2*B*a^3 - A^3*a^2*b)*c^3 + 8*(4*B^3*a^4 - 2*A*B^2*a^3*b + 2*A^2*B*a^2*b^2 - A^3*a*b^3)*c^2 - (16*B^3*a^3*b^2 - 8*A*B^2*a^2*b^3 + 2*A^2*B*a*b^4 - A^3*b^5)*c - (192*B*a^4*b^3*c^3 + 256*A*a^5*c^5 - 128*(2*B*a^5*b + A*a^4*b^2)*c^4 - 8*(6*B*a^3*b^5 - A*a^2*b^6)*c^2 + (4*B*a^2*b^7 - A*a*b^8)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))*sqrt(-(B^2*a*b^3 - 4*(4*A*B*a^2 - 3*A^2*a*b)*c^2 + (12*B^2*a^2*b - 12*A*B*a*b^2 + A^2*b^3)*c - (a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)))/(a*b^6*c - 12*a^2*b^4*c^2 + 48*a^3*b^2*c^3 - 64*a^4*c^4))) + 2*(2*B*a - A*b)*x)/((b^2*c - 4*a*c^2)*x^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*x^2)","B",0
121,1,4885,0,3.720617," ","integrate((B*x^2+A)/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, B a - A b\right)} c x^{3} - \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} + 2 \, A B a b^{4} + A^{2} b^{5} - 12 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} + 3 \, {\left(4 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} - 5 \, A^{2} a b^{3}\right)} c + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} \log\left({\left(324 \, A^{4} a^{2} c^{4} - 81 \, {\left(4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{3} - {\left(4 \, B^{4} a^{4} - 20 \, A B^{3} a^{3} b - 84 \, A^{2} B^{2} a^{2} b^{2} - 65 \, A^{3} B a b^{3} - 5 \, A^{4} b^{4}\right)} c^{2} - 3 \, {\left(B^{4} a^{3} b^{2} + 3 \, A B^{3} a^{2} b^{3} + 3 \, A^{2} B^{2} a b^{4} + A^{3} B b^{5}\right)} c\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{5} + 3 \, A B^{2} a^{2} b^{6} + 3 \, A^{2} B a b^{7} + A^{3} b^{8} + 864 \, A^{3} a^{4} c^{4} - 48 \, {\left(2 \, A B^{2} a^{5} + 7 \, A^{2} B a^{4} b + 14 \, A^{3} a^{3} b^{2}\right)} c^{3} + 2 \, {\left(8 \, B^{3} a^{5} b + 48 \, A B^{2} a^{4} b^{2} + 108 \, A^{2} B a^{3} b^{3} + 95 \, A^{3} a^{2} b^{4}\right)} c^{2} - {\left(8 \, B^{3} a^{4} b^{3} + 30 \, A B^{2} a^{3} b^{4} + 45 \, A^{2} B a^{2} b^{5} + 23 \, A^{3} a b^{6}\right)} c - {\left(B a^{4} b^{8} + A a^{3} b^{9} + 144 \, A a^{5} b^{5} c^{2} - 256 \, {\left(B a^{8} - 2 \, A a^{7} b\right)} c^{4} + 64 \, {\left(2 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c^{3} - 4 \, {\left(2 \, B a^{5} b^{6} + 5 \, A a^{4} b^{7}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} + 2 \, A B a b^{4} + A^{2} b^{5} - 12 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} + 3 \, {\left(4 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} - 5 \, A^{2} a b^{3}\right)} c + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} + 2 \, A B a b^{4} + A^{2} b^{5} - 12 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} + 3 \, {\left(4 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} - 5 \, A^{2} a b^{3}\right)} c + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} \log\left({\left(324 \, A^{4} a^{2} c^{4} - 81 \, {\left(4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{3} - {\left(4 \, B^{4} a^{4} - 20 \, A B^{3} a^{3} b - 84 \, A^{2} B^{2} a^{2} b^{2} - 65 \, A^{3} B a b^{3} - 5 \, A^{4} b^{4}\right)} c^{2} - 3 \, {\left(B^{4} a^{3} b^{2} + 3 \, A B^{3} a^{2} b^{3} + 3 \, A^{2} B^{2} a b^{4} + A^{3} B b^{5}\right)} c\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{5} + 3 \, A B^{2} a^{2} b^{6} + 3 \, A^{2} B a b^{7} + A^{3} b^{8} + 864 \, A^{3} a^{4} c^{4} - 48 \, {\left(2 \, A B^{2} a^{5} + 7 \, A^{2} B a^{4} b + 14 \, A^{3} a^{3} b^{2}\right)} c^{3} + 2 \, {\left(8 \, B^{3} a^{5} b + 48 \, A B^{2} a^{4} b^{2} + 108 \, A^{2} B a^{3} b^{3} + 95 \, A^{3} a^{2} b^{4}\right)} c^{2} - {\left(8 \, B^{3} a^{4} b^{3} + 30 \, A B^{2} a^{3} b^{4} + 45 \, A^{2} B a^{2} b^{5} + 23 \, A^{3} a b^{6}\right)} c - {\left(B a^{4} b^{8} + A a^{3} b^{9} + 144 \, A a^{5} b^{5} c^{2} - 256 \, {\left(B a^{8} - 2 \, A a^{7} b\right)} c^{4} + 64 \, {\left(2 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c^{3} - 4 \, {\left(2 \, B a^{5} b^{6} + 5 \, A a^{4} b^{7}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} + 2 \, A B a b^{4} + A^{2} b^{5} - 12 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} + 3 \, {\left(4 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} - 5 \, A^{2} a b^{3}\right)} c + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} + 2 \, A B a b^{4} + A^{2} b^{5} - 12 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} + 3 \, {\left(4 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} - 5 \, A^{2} a b^{3}\right)} c - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} \log\left({\left(324 \, A^{4} a^{2} c^{4} - 81 \, {\left(4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{3} - {\left(4 \, B^{4} a^{4} - 20 \, A B^{3} a^{3} b - 84 \, A^{2} B^{2} a^{2} b^{2} - 65 \, A^{3} B a b^{3} - 5 \, A^{4} b^{4}\right)} c^{2} - 3 \, {\left(B^{4} a^{3} b^{2} + 3 \, A B^{3} a^{2} b^{3} + 3 \, A^{2} B^{2} a b^{4} + A^{3} B b^{5}\right)} c\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{5} + 3 \, A B^{2} a^{2} b^{6} + 3 \, A^{2} B a b^{7} + A^{3} b^{8} + 864 \, A^{3} a^{4} c^{4} - 48 \, {\left(2 \, A B^{2} a^{5} + 7 \, A^{2} B a^{4} b + 14 \, A^{3} a^{3} b^{2}\right)} c^{3} + 2 \, {\left(8 \, B^{3} a^{5} b + 48 \, A B^{2} a^{4} b^{2} + 108 \, A^{2} B a^{3} b^{3} + 95 \, A^{3} a^{2} b^{4}\right)} c^{2} - {\left(8 \, B^{3} a^{4} b^{3} + 30 \, A B^{2} a^{3} b^{4} + 45 \, A^{2} B a^{2} b^{5} + 23 \, A^{3} a b^{6}\right)} c + {\left(B a^{4} b^{8} + A a^{3} b^{9} + 144 \, A a^{5} b^{5} c^{2} - 256 \, {\left(B a^{8} - 2 \, A a^{7} b\right)} c^{4} + 64 \, {\left(2 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c^{3} - 4 \, {\left(2 \, B a^{5} b^{6} + 5 \, A a^{4} b^{7}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} + 2 \, A B a b^{4} + A^{2} b^{5} - 12 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} + 3 \, {\left(4 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} - 5 \, A^{2} a b^{3}\right)} c - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} + 2 \, A B a b^{4} + A^{2} b^{5} - 12 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} + 3 \, {\left(4 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} - 5 \, A^{2} a b^{3}\right)} c - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} \log\left({\left(324 \, A^{4} a^{2} c^{4} - 81 \, {\left(4 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{3} - {\left(4 \, B^{4} a^{4} - 20 \, A B^{3} a^{3} b - 84 \, A^{2} B^{2} a^{2} b^{2} - 65 \, A^{3} B a b^{3} - 5 \, A^{4} b^{4}\right)} c^{2} - 3 \, {\left(B^{4} a^{3} b^{2} + 3 \, A B^{3} a^{2} b^{3} + 3 \, A^{2} B^{2} a b^{4} + A^{3} B b^{5}\right)} c\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{5} + 3 \, A B^{2} a^{2} b^{6} + 3 \, A^{2} B a b^{7} + A^{3} b^{8} + 864 \, A^{3} a^{4} c^{4} - 48 \, {\left(2 \, A B^{2} a^{5} + 7 \, A^{2} B a^{4} b + 14 \, A^{3} a^{3} b^{2}\right)} c^{3} + 2 \, {\left(8 \, B^{3} a^{5} b + 48 \, A B^{2} a^{4} b^{2} + 108 \, A^{2} B a^{3} b^{3} + 95 \, A^{3} a^{2} b^{4}\right)} c^{2} - {\left(8 \, B^{3} a^{4} b^{3} + 30 \, A B^{2} a^{3} b^{4} + 45 \, A^{2} B a^{2} b^{5} + 23 \, A^{3} a b^{6}\right)} c + {\left(B a^{4} b^{8} + A a^{3} b^{9} + 144 \, A a^{5} b^{5} c^{2} - 256 \, {\left(B a^{8} - 2 \, A a^{7} b\right)} c^{4} + 64 \, {\left(2 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c^{3} - 4 \, {\left(2 \, B a^{5} b^{6} + 5 \, A a^{4} b^{7}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{3} + 2 \, A B a b^{4} + A^{2} b^{5} - 12 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{2} + 3 \, {\left(4 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} - 5 \, A^{2} a b^{3}\right)} c - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} + 4 \, A^{3} B a b^{3} + A^{4} b^{4} + 81 \, A^{4} a^{2} c^{2} - 18 \, {\left(A^{2} B^{2} a^{3} + 2 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}}\right) + 2 \, {\left(B a b - A b^{2} + 2 \, A a c\right)} x}{4 \, {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)}}"," ",0,"-1/4*(2*(2*B*a - A*b)*c*x^3 - sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-(B^2*a^2*b^3 + 2*A*B*a*b^4 + A^2*b^5 - 12*(4*A*B*a^3 - 5*A^2*a^2*b)*c^2 + 3*(4*B^2*a^3*b - 4*A*B*a^2*b^2 - 5*A^2*a*b^3)*c + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))*log((324*A^4*a^2*c^4 - 81*(4*A^3*B*a^2*b + A^4*a*b^2)*c^3 - (4*B^4*a^4 - 20*A*B^3*a^3*b - 84*A^2*B^2*a^2*b^2 - 65*A^3*B*a*b^3 - 5*A^4*b^4)*c^2 - 3*(B^4*a^3*b^2 + 3*A*B^3*a^2*b^3 + 3*A^2*B^2*a*b^4 + A^3*B*b^5)*c)*x + 1/2*sqrt(1/2)*(B^3*a^3*b^5 + 3*A*B^2*a^2*b^6 + 3*A^2*B*a*b^7 + A^3*b^8 + 864*A^3*a^4*c^4 - 48*(2*A*B^2*a^5 + 7*A^2*B*a^4*b + 14*A^3*a^3*b^2)*c^3 + 2*(8*B^3*a^5*b + 48*A*B^2*a^4*b^2 + 108*A^2*B*a^3*b^3 + 95*A^3*a^2*b^4)*c^2 - (8*B^3*a^4*b^3 + 30*A*B^2*a^3*b^4 + 45*A^2*B*a^2*b^5 + 23*A^3*a*b^6)*c - (B*a^4*b^8 + A*a^3*b^9 + 144*A*a^5*b^5*c^2 - 256*(B*a^8 - 2*A*a^7*b)*c^4 + 64*(2*B*a^7*b^2 - 7*A*a^6*b^3)*c^3 - 4*(2*B*a^5*b^6 + 5*A*a^4*b^7)*c)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-(B^2*a^2*b^3 + 2*A*B*a*b^4 + A^2*b^5 - 12*(4*A*B*a^3 - 5*A^2*a^2*b)*c^2 + 3*(4*B^2*a^3*b - 4*A*B*a^2*b^2 - 5*A^2*a*b^3)*c + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))) + sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-(B^2*a^2*b^3 + 2*A*B*a*b^4 + A^2*b^5 - 12*(4*A*B*a^3 - 5*A^2*a^2*b)*c^2 + 3*(4*B^2*a^3*b - 4*A*B*a^2*b^2 - 5*A^2*a*b^3)*c + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))*log((324*A^4*a^2*c^4 - 81*(4*A^3*B*a^2*b + A^4*a*b^2)*c^3 - (4*B^4*a^4 - 20*A*B^3*a^3*b - 84*A^2*B^2*a^2*b^2 - 65*A^3*B*a*b^3 - 5*A^4*b^4)*c^2 - 3*(B^4*a^3*b^2 + 3*A*B^3*a^2*b^3 + 3*A^2*B^2*a*b^4 + A^3*B*b^5)*c)*x - 1/2*sqrt(1/2)*(B^3*a^3*b^5 + 3*A*B^2*a^2*b^6 + 3*A^2*B*a*b^7 + A^3*b^8 + 864*A^3*a^4*c^4 - 48*(2*A*B^2*a^5 + 7*A^2*B*a^4*b + 14*A^3*a^3*b^2)*c^3 + 2*(8*B^3*a^5*b + 48*A*B^2*a^4*b^2 + 108*A^2*B*a^3*b^3 + 95*A^3*a^2*b^4)*c^2 - (8*B^3*a^4*b^3 + 30*A*B^2*a^3*b^4 + 45*A^2*B*a^2*b^5 + 23*A^3*a*b^6)*c - (B*a^4*b^8 + A*a^3*b^9 + 144*A*a^5*b^5*c^2 - 256*(B*a^8 - 2*A*a^7*b)*c^4 + 64*(2*B*a^7*b^2 - 7*A*a^6*b^3)*c^3 - 4*(2*B*a^5*b^6 + 5*A*a^4*b^7)*c)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-(B^2*a^2*b^3 + 2*A*B*a*b^4 + A^2*b^5 - 12*(4*A*B*a^3 - 5*A^2*a^2*b)*c^2 + 3*(4*B^2*a^3*b - 4*A*B*a^2*b^2 - 5*A^2*a*b^3)*c + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))) - sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-(B^2*a^2*b^3 + 2*A*B*a*b^4 + A^2*b^5 - 12*(4*A*B*a^3 - 5*A^2*a^2*b)*c^2 + 3*(4*B^2*a^3*b - 4*A*B*a^2*b^2 - 5*A^2*a*b^3)*c - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))*log((324*A^4*a^2*c^4 - 81*(4*A^3*B*a^2*b + A^4*a*b^2)*c^3 - (4*B^4*a^4 - 20*A*B^3*a^3*b - 84*A^2*B^2*a^2*b^2 - 65*A^3*B*a*b^3 - 5*A^4*b^4)*c^2 - 3*(B^4*a^3*b^2 + 3*A*B^3*a^2*b^3 + 3*A^2*B^2*a*b^4 + A^3*B*b^5)*c)*x + 1/2*sqrt(1/2)*(B^3*a^3*b^5 + 3*A*B^2*a^2*b^6 + 3*A^2*B*a*b^7 + A^3*b^8 + 864*A^3*a^4*c^4 - 48*(2*A*B^2*a^5 + 7*A^2*B*a^4*b + 14*A^3*a^3*b^2)*c^3 + 2*(8*B^3*a^5*b + 48*A*B^2*a^4*b^2 + 108*A^2*B*a^3*b^3 + 95*A^3*a^2*b^4)*c^2 - (8*B^3*a^4*b^3 + 30*A*B^2*a^3*b^4 + 45*A^2*B*a^2*b^5 + 23*A^3*a*b^6)*c + (B*a^4*b^8 + A*a^3*b^9 + 144*A*a^5*b^5*c^2 - 256*(B*a^8 - 2*A*a^7*b)*c^4 + 64*(2*B*a^7*b^2 - 7*A*a^6*b^3)*c^3 - 4*(2*B*a^5*b^6 + 5*A*a^4*b^7)*c)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-(B^2*a^2*b^3 + 2*A*B*a*b^4 + A^2*b^5 - 12*(4*A*B*a^3 - 5*A^2*a^2*b)*c^2 + 3*(4*B^2*a^3*b - 4*A*B*a^2*b^2 - 5*A^2*a*b^3)*c - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))) + sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-(B^2*a^2*b^3 + 2*A*B*a*b^4 + A^2*b^5 - 12*(4*A*B*a^3 - 5*A^2*a^2*b)*c^2 + 3*(4*B^2*a^3*b - 4*A*B*a^2*b^2 - 5*A^2*a*b^3)*c - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))*log((324*A^4*a^2*c^4 - 81*(4*A^3*B*a^2*b + A^4*a*b^2)*c^3 - (4*B^4*a^4 - 20*A*B^3*a^3*b - 84*A^2*B^2*a^2*b^2 - 65*A^3*B*a*b^3 - 5*A^4*b^4)*c^2 - 3*(B^4*a^3*b^2 + 3*A*B^3*a^2*b^3 + 3*A^2*B^2*a*b^4 + A^3*B*b^5)*c)*x - 1/2*sqrt(1/2)*(B^3*a^3*b^5 + 3*A*B^2*a^2*b^6 + 3*A^2*B*a*b^7 + A^3*b^8 + 864*A^3*a^4*c^4 - 48*(2*A*B^2*a^5 + 7*A^2*B*a^4*b + 14*A^3*a^3*b^2)*c^3 + 2*(8*B^3*a^5*b + 48*A*B^2*a^4*b^2 + 108*A^2*B*a^3*b^3 + 95*A^3*a^2*b^4)*c^2 - (8*B^3*a^4*b^3 + 30*A*B^2*a^3*b^4 + 45*A^2*B*a^2*b^5 + 23*A^3*a*b^6)*c + (B*a^4*b^8 + A*a^3*b^9 + 144*A*a^5*b^5*c^2 - 256*(B*a^8 - 2*A*a^7*b)*c^4 + 64*(2*B*a^7*b^2 - 7*A*a^6*b^3)*c^3 - 4*(2*B*a^5*b^6 + 5*A*a^4*b^7)*c)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-(B^2*a^2*b^3 + 2*A*B*a*b^4 + A^2*b^5 - 12*(4*A*B*a^3 - 5*A^2*a^2*b)*c^2 + 3*(4*B^2*a^3*b - 4*A*B*a^2*b^2 - 5*A^2*a*b^3)*c - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((B^4*a^4 + 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 + 4*A^3*B*a*b^3 + A^4*b^4 + 81*A^4*a^2*c^2 - 18*(A^2*B^2*a^3 + 2*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))) + 2*(B*a*b - A*b^2 + 2*A*a*c)*x)/((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)","B",0
122,1,7583,0,9.541087," ","integrate((B*x^2+A)/x^2/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(10 \, A a c^{2} + {\left(B a b - 3 \, A b^{2}\right)} c\right)} x^{4} - 4 \, A a b^{2} + 16 \, A a^{2} c + 2 \, {\left(B a b^{2} - 3 \, A b^{3} - {\left(2 \, B a^{2} - 11 \, A a b\right)} c\right)} x^{2} - \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)} \sqrt{-\frac{B^{2} a^{2} b^{5} - 6 \, A B a b^{6} + 9 \, A^{2} b^{7} + 60 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 5 \, {\left(12 \, B^{2} a^{4} b - 60 \, A B a^{3} b^{2} + 77 \, A^{2} a^{2} b^{3}\right)} c^{2} - 5 \, {\left(3 \, B^{2} a^{3} b^{3} - 16 \, A B a^{2} b^{4} + 21 \, A^{2} a b^{5}\right)} c + {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}} \log\left({\left(2500 \, A^{4} a^{3} c^{6} + 625 \, {\left(4 \, A^{3} B a^{3} b - 9 \, A^{4} a^{2} b^{2}\right)} c^{5} - 3 \, {\left(108 \, B^{4} a^{5} - 756 \, A B^{3} a^{4} b + 1672 \, A^{2} B^{2} a^{3} b^{2} - 909 \, A^{3} B a^{2} b^{3} - 657 \, A^{4} a b^{4}\right)} c^{4} + {\left(81 \, B^{4} a^{4} b^{2} - 647 \, A B^{3} a^{3} b^{3} + 1674 \, A^{2} B^{2} a^{2} b^{4} - 1323 \, A^{3} B a b^{5} - 189 \, A^{4} b^{6}\right)} c^{3} - 5 \, {\left(B^{4} a^{3} b^{4} - 9 \, A B^{3} a^{2} b^{5} + 27 \, A^{2} B^{2} a b^{6} - 27 \, A^{3} B b^{7}\right)} c^{2}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{8} - 9 \, A B^{2} a^{2} b^{9} + 27 \, A^{2} B a b^{10} - 27 \, A^{3} b^{11} - 400 \, {\left(6 \, A^{2} B a^{6} - 13 \, A^{3} a^{5} b\right)} c^{5} + 8 \, {\left(108 \, B^{3} a^{7} - 762 \, A B^{2} a^{6} b + 1956 \, A^{2} B a^{5} b^{2} - 1801 \, A^{3} a^{4} b^{3}\right)} c^{4} - {\left(672 \, B^{3} a^{6} b^{2} - 4968 \, A B^{2} a^{5} b^{3} + 12414 \, A^{2} B a^{4} b^{4} - 10549 \, A^{3} a^{3} b^{5}\right)} c^{3} + 5 \, {\left(38 \, B^{3} a^{5} b^{4} - 297 \, A B^{2} a^{4} b^{5} + 771 \, A^{2} B a^{3} b^{6} - 666 \, A^{3} a^{2} b^{7}\right)} c^{2} - {\left(23 \, B^{3} a^{4} b^{6} - 192 \, A B^{2} a^{3} b^{7} + 531 \, A^{2} B a^{2} b^{8} - 486 \, A^{3} a b^{9}\right)} c - {\left(B a^{6} b^{9} - 3 \, A a^{5} b^{10} + 1280 \, A a^{10} c^{5} + 128 \, {\left(4 \, B a^{10} b - 17 \, A a^{9} b^{2}\right)} c^{4} - 448 \, {\left(B a^{9} b^{3} - 3 \, A a^{8} b^{4}\right)} c^{3} + 8 \, {\left(18 \, B a^{8} b^{5} - 49 \, A a^{7} b^{6}\right)} c^{2} - 5 \, {\left(4 \, B a^{7} b^{7} - 11 \, A a^{6} b^{8}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{5} - 6 \, A B a b^{6} + 9 \, A^{2} b^{7} + 60 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 5 \, {\left(12 \, B^{2} a^{4} b - 60 \, A B a^{3} b^{2} + 77 \, A^{2} a^{2} b^{3}\right)} c^{2} - 5 \, {\left(3 \, B^{2} a^{3} b^{3} - 16 \, A B a^{2} b^{4} + 21 \, A^{2} a b^{5}\right)} c + {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)} \sqrt{-\frac{B^{2} a^{2} b^{5} - 6 \, A B a b^{6} + 9 \, A^{2} b^{7} + 60 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 5 \, {\left(12 \, B^{2} a^{4} b - 60 \, A B a^{3} b^{2} + 77 \, A^{2} a^{2} b^{3}\right)} c^{2} - 5 \, {\left(3 \, B^{2} a^{3} b^{3} - 16 \, A B a^{2} b^{4} + 21 \, A^{2} a b^{5}\right)} c + {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}} \log\left({\left(2500 \, A^{4} a^{3} c^{6} + 625 \, {\left(4 \, A^{3} B a^{3} b - 9 \, A^{4} a^{2} b^{2}\right)} c^{5} - 3 \, {\left(108 \, B^{4} a^{5} - 756 \, A B^{3} a^{4} b + 1672 \, A^{2} B^{2} a^{3} b^{2} - 909 \, A^{3} B a^{2} b^{3} - 657 \, A^{4} a b^{4}\right)} c^{4} + {\left(81 \, B^{4} a^{4} b^{2} - 647 \, A B^{3} a^{3} b^{3} + 1674 \, A^{2} B^{2} a^{2} b^{4} - 1323 \, A^{3} B a b^{5} - 189 \, A^{4} b^{6}\right)} c^{3} - 5 \, {\left(B^{4} a^{3} b^{4} - 9 \, A B^{3} a^{2} b^{5} + 27 \, A^{2} B^{2} a b^{6} - 27 \, A^{3} B b^{7}\right)} c^{2}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{8} - 9 \, A B^{2} a^{2} b^{9} + 27 \, A^{2} B a b^{10} - 27 \, A^{3} b^{11} - 400 \, {\left(6 \, A^{2} B a^{6} - 13 \, A^{3} a^{5} b\right)} c^{5} + 8 \, {\left(108 \, B^{3} a^{7} - 762 \, A B^{2} a^{6} b + 1956 \, A^{2} B a^{5} b^{2} - 1801 \, A^{3} a^{4} b^{3}\right)} c^{4} - {\left(672 \, B^{3} a^{6} b^{2} - 4968 \, A B^{2} a^{5} b^{3} + 12414 \, A^{2} B a^{4} b^{4} - 10549 \, A^{3} a^{3} b^{5}\right)} c^{3} + 5 \, {\left(38 \, B^{3} a^{5} b^{4} - 297 \, A B^{2} a^{4} b^{5} + 771 \, A^{2} B a^{3} b^{6} - 666 \, A^{3} a^{2} b^{7}\right)} c^{2} - {\left(23 \, B^{3} a^{4} b^{6} - 192 \, A B^{2} a^{3} b^{7} + 531 \, A^{2} B a^{2} b^{8} - 486 \, A^{3} a b^{9}\right)} c - {\left(B a^{6} b^{9} - 3 \, A a^{5} b^{10} + 1280 \, A a^{10} c^{5} + 128 \, {\left(4 \, B a^{10} b - 17 \, A a^{9} b^{2}\right)} c^{4} - 448 \, {\left(B a^{9} b^{3} - 3 \, A a^{8} b^{4}\right)} c^{3} + 8 \, {\left(18 \, B a^{8} b^{5} - 49 \, A a^{7} b^{6}\right)} c^{2} - 5 \, {\left(4 \, B a^{7} b^{7} - 11 \, A a^{6} b^{8}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{5} - 6 \, A B a b^{6} + 9 \, A^{2} b^{7} + 60 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 5 \, {\left(12 \, B^{2} a^{4} b - 60 \, A B a^{3} b^{2} + 77 \, A^{2} a^{2} b^{3}\right)} c^{2} - 5 \, {\left(3 \, B^{2} a^{3} b^{3} - 16 \, A B a^{2} b^{4} + 21 \, A^{2} a b^{5}\right)} c + {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)} \sqrt{-\frac{B^{2} a^{2} b^{5} - 6 \, A B a b^{6} + 9 \, A^{2} b^{7} + 60 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 5 \, {\left(12 \, B^{2} a^{4} b - 60 \, A B a^{3} b^{2} + 77 \, A^{2} a^{2} b^{3}\right)} c^{2} - 5 \, {\left(3 \, B^{2} a^{3} b^{3} - 16 \, A B a^{2} b^{4} + 21 \, A^{2} a b^{5}\right)} c - {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}} \log\left({\left(2500 \, A^{4} a^{3} c^{6} + 625 \, {\left(4 \, A^{3} B a^{3} b - 9 \, A^{4} a^{2} b^{2}\right)} c^{5} - 3 \, {\left(108 \, B^{4} a^{5} - 756 \, A B^{3} a^{4} b + 1672 \, A^{2} B^{2} a^{3} b^{2} - 909 \, A^{3} B a^{2} b^{3} - 657 \, A^{4} a b^{4}\right)} c^{4} + {\left(81 \, B^{4} a^{4} b^{2} - 647 \, A B^{3} a^{3} b^{3} + 1674 \, A^{2} B^{2} a^{2} b^{4} - 1323 \, A^{3} B a b^{5} - 189 \, A^{4} b^{6}\right)} c^{3} - 5 \, {\left(B^{4} a^{3} b^{4} - 9 \, A B^{3} a^{2} b^{5} + 27 \, A^{2} B^{2} a b^{6} - 27 \, A^{3} B b^{7}\right)} c^{2}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{8} - 9 \, A B^{2} a^{2} b^{9} + 27 \, A^{2} B a b^{10} - 27 \, A^{3} b^{11} - 400 \, {\left(6 \, A^{2} B a^{6} - 13 \, A^{3} a^{5} b\right)} c^{5} + 8 \, {\left(108 \, B^{3} a^{7} - 762 \, A B^{2} a^{6} b + 1956 \, A^{2} B a^{5} b^{2} - 1801 \, A^{3} a^{4} b^{3}\right)} c^{4} - {\left(672 \, B^{3} a^{6} b^{2} - 4968 \, A B^{2} a^{5} b^{3} + 12414 \, A^{2} B a^{4} b^{4} - 10549 \, A^{3} a^{3} b^{5}\right)} c^{3} + 5 \, {\left(38 \, B^{3} a^{5} b^{4} - 297 \, A B^{2} a^{4} b^{5} + 771 \, A^{2} B a^{3} b^{6} - 666 \, A^{3} a^{2} b^{7}\right)} c^{2} - {\left(23 \, B^{3} a^{4} b^{6} - 192 \, A B^{2} a^{3} b^{7} + 531 \, A^{2} B a^{2} b^{8} - 486 \, A^{3} a b^{9}\right)} c + {\left(B a^{6} b^{9} - 3 \, A a^{5} b^{10} + 1280 \, A a^{10} c^{5} + 128 \, {\left(4 \, B a^{10} b - 17 \, A a^{9} b^{2}\right)} c^{4} - 448 \, {\left(B a^{9} b^{3} - 3 \, A a^{8} b^{4}\right)} c^{3} + 8 \, {\left(18 \, B a^{8} b^{5} - 49 \, A a^{7} b^{6}\right)} c^{2} - 5 \, {\left(4 \, B a^{7} b^{7} - 11 \, A a^{6} b^{8}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{5} - 6 \, A B a b^{6} + 9 \, A^{2} b^{7} + 60 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 5 \, {\left(12 \, B^{2} a^{4} b - 60 \, A B a^{3} b^{2} + 77 \, A^{2} a^{2} b^{3}\right)} c^{2} - 5 \, {\left(3 \, B^{2} a^{3} b^{3} - 16 \, A B a^{2} b^{4} + 21 \, A^{2} a b^{5}\right)} c - {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)} \sqrt{-\frac{B^{2} a^{2} b^{5} - 6 \, A B a b^{6} + 9 \, A^{2} b^{7} + 60 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 5 \, {\left(12 \, B^{2} a^{4} b - 60 \, A B a^{3} b^{2} + 77 \, A^{2} a^{2} b^{3}\right)} c^{2} - 5 \, {\left(3 \, B^{2} a^{3} b^{3} - 16 \, A B a^{2} b^{4} + 21 \, A^{2} a b^{5}\right)} c - {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}} \log\left({\left(2500 \, A^{4} a^{3} c^{6} + 625 \, {\left(4 \, A^{3} B a^{3} b - 9 \, A^{4} a^{2} b^{2}\right)} c^{5} - 3 \, {\left(108 \, B^{4} a^{5} - 756 \, A B^{3} a^{4} b + 1672 \, A^{2} B^{2} a^{3} b^{2} - 909 \, A^{3} B a^{2} b^{3} - 657 \, A^{4} a b^{4}\right)} c^{4} + {\left(81 \, B^{4} a^{4} b^{2} - 647 \, A B^{3} a^{3} b^{3} + 1674 \, A^{2} B^{2} a^{2} b^{4} - 1323 \, A^{3} B a b^{5} - 189 \, A^{4} b^{6}\right)} c^{3} - 5 \, {\left(B^{4} a^{3} b^{4} - 9 \, A B^{3} a^{2} b^{5} + 27 \, A^{2} B^{2} a b^{6} - 27 \, A^{3} B b^{7}\right)} c^{2}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{8} - 9 \, A B^{2} a^{2} b^{9} + 27 \, A^{2} B a b^{10} - 27 \, A^{3} b^{11} - 400 \, {\left(6 \, A^{2} B a^{6} - 13 \, A^{3} a^{5} b\right)} c^{5} + 8 \, {\left(108 \, B^{3} a^{7} - 762 \, A B^{2} a^{6} b + 1956 \, A^{2} B a^{5} b^{2} - 1801 \, A^{3} a^{4} b^{3}\right)} c^{4} - {\left(672 \, B^{3} a^{6} b^{2} - 4968 \, A B^{2} a^{5} b^{3} + 12414 \, A^{2} B a^{4} b^{4} - 10549 \, A^{3} a^{3} b^{5}\right)} c^{3} + 5 \, {\left(38 \, B^{3} a^{5} b^{4} - 297 \, A B^{2} a^{4} b^{5} + 771 \, A^{2} B a^{3} b^{6} - 666 \, A^{3} a^{2} b^{7}\right)} c^{2} - {\left(23 \, B^{3} a^{4} b^{6} - 192 \, A B^{2} a^{3} b^{7} + 531 \, A^{2} B a^{2} b^{8} - 486 \, A^{3} a b^{9}\right)} c + {\left(B a^{6} b^{9} - 3 \, A a^{5} b^{10} + 1280 \, A a^{10} c^{5} + 128 \, {\left(4 \, B a^{10} b - 17 \, A a^{9} b^{2}\right)} c^{4} - 448 \, {\left(B a^{9} b^{3} - 3 \, A a^{8} b^{4}\right)} c^{3} + 8 \, {\left(18 \, B a^{8} b^{5} - 49 \, A a^{7} b^{6}\right)} c^{2} - 5 \, {\left(4 \, B a^{7} b^{7} - 11 \, A a^{6} b^{8}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{5} - 6 \, A B a b^{6} + 9 \, A^{2} b^{7} + 60 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 5 \, {\left(12 \, B^{2} a^{4} b - 60 \, A B a^{3} b^{2} + 77 \, A^{2} a^{2} b^{3}\right)} c^{2} - 5 \, {\left(3 \, B^{2} a^{3} b^{3} - 16 \, A B a^{2} b^{4} + 21 \, A^{2} a b^{5}\right)} c - {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} - 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} - 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 625 \, A^{4} a^{4} c^{4} - 50 \, {\left(9 \, A^{2} B^{2} a^{5} - 44 \, A^{3} B a^{4} b + 51 \, A^{4} a^{3} b^{2}\right)} c^{3} + 3 \, {\left(27 \, B^{4} a^{6} - 264 \, A B^{3} a^{5} b + 968 \, A^{2} B^{2} a^{4} b^{2} - 1596 \, A^{3} B a^{3} b^{3} + 1017 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(9 \, B^{4} a^{5} b^{2} - 98 \, A B^{3} a^{4} b^{3} + 396 \, A^{2} B^{2} a^{3} b^{4} - 702 \, A^{3} B a^{2} b^{5} + 459 \, A^{4} a b^{6}\right)} c}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}}{a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}}}\right)}{4 \, {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x\right)}}"," ",0,"1/4*(2*(10*A*a*c^2 + (B*a*b - 3*A*b^2)*c)*x^4 - 4*A*a*b^2 + 16*A*a^2*c + 2*(B*a*b^2 - 3*A*b^3 - (2*B*a^2 - 11*A*a*b)*c)*x^2 - sqrt(1/2)*((a^2*b^2*c - 4*a^3*c^2)*x^5 + (a^2*b^3 - 4*a^3*b*c)*x^3 + (a^3*b^2 - 4*a^4*c)*x)*sqrt(-(B^2*a^2*b^5 - 6*A*B*a*b^6 + 9*A^2*b^7 + 60*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 5*(12*B^2*a^4*b - 60*A*B*a^3*b^2 + 77*A^2*a^2*b^3)*c^2 - 5*(3*B^2*a^3*b^3 - 16*A*B*a^2*b^4 + 21*A^2*a*b^5)*c + (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3))*log((2500*A^4*a^3*c^6 + 625*(4*A^3*B*a^3*b - 9*A^4*a^2*b^2)*c^5 - 3*(108*B^4*a^5 - 756*A*B^3*a^4*b + 1672*A^2*B^2*a^3*b^2 - 909*A^3*B*a^2*b^3 - 657*A^4*a*b^4)*c^4 + (81*B^4*a^4*b^2 - 647*A*B^3*a^3*b^3 + 1674*A^2*B^2*a^2*b^4 - 1323*A^3*B*a*b^5 - 189*A^4*b^6)*c^3 - 5*(B^4*a^3*b^4 - 9*A*B^3*a^2*b^5 + 27*A^2*B^2*a*b^6 - 27*A^3*B*b^7)*c^2)*x + 1/2*sqrt(1/2)*(B^3*a^3*b^8 - 9*A*B^2*a^2*b^9 + 27*A^2*B*a*b^10 - 27*A^3*b^11 - 400*(6*A^2*B*a^6 - 13*A^3*a^5*b)*c^5 + 8*(108*B^3*a^7 - 762*A*B^2*a^6*b + 1956*A^2*B*a^5*b^2 - 1801*A^3*a^4*b^3)*c^4 - (672*B^3*a^6*b^2 - 4968*A*B^2*a^5*b^3 + 12414*A^2*B*a^4*b^4 - 10549*A^3*a^3*b^5)*c^3 + 5*(38*B^3*a^5*b^4 - 297*A*B^2*a^4*b^5 + 771*A^2*B*a^3*b^6 - 666*A^3*a^2*b^7)*c^2 - (23*B^3*a^4*b^6 - 192*A*B^2*a^3*b^7 + 531*A^2*B*a^2*b^8 - 486*A^3*a*b^9)*c - (B*a^6*b^9 - 3*A*a^5*b^10 + 1280*A*a^10*c^5 + 128*(4*B*a^10*b - 17*A*a^9*b^2)*c^4 - 448*(B*a^9*b^3 - 3*A*a^8*b^4)*c^3 + 8*(18*B*a^8*b^5 - 49*A*a^7*b^6)*c^2 - 5*(4*B*a^7*b^7 - 11*A*a^6*b^8)*c)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(-(B^2*a^2*b^5 - 6*A*B*a*b^6 + 9*A^2*b^7 + 60*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 5*(12*B^2*a^4*b - 60*A*B*a^3*b^2 + 77*A^2*a^2*b^3)*c^2 - 5*(3*B^2*a^3*b^3 - 16*A*B*a^2*b^4 + 21*A^2*a*b^5)*c + (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3))) + sqrt(1/2)*((a^2*b^2*c - 4*a^3*c^2)*x^5 + (a^2*b^3 - 4*a^3*b*c)*x^3 + (a^3*b^2 - 4*a^4*c)*x)*sqrt(-(B^2*a^2*b^5 - 6*A*B*a*b^6 + 9*A^2*b^7 + 60*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 5*(12*B^2*a^4*b - 60*A*B*a^3*b^2 + 77*A^2*a^2*b^3)*c^2 - 5*(3*B^2*a^3*b^3 - 16*A*B*a^2*b^4 + 21*A^2*a*b^5)*c + (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3))*log((2500*A^4*a^3*c^6 + 625*(4*A^3*B*a^3*b - 9*A^4*a^2*b^2)*c^5 - 3*(108*B^4*a^5 - 756*A*B^3*a^4*b + 1672*A^2*B^2*a^3*b^2 - 909*A^3*B*a^2*b^3 - 657*A^4*a*b^4)*c^4 + (81*B^4*a^4*b^2 - 647*A*B^3*a^3*b^3 + 1674*A^2*B^2*a^2*b^4 - 1323*A^3*B*a*b^5 - 189*A^4*b^6)*c^3 - 5*(B^4*a^3*b^4 - 9*A*B^3*a^2*b^5 + 27*A^2*B^2*a*b^6 - 27*A^3*B*b^7)*c^2)*x - 1/2*sqrt(1/2)*(B^3*a^3*b^8 - 9*A*B^2*a^2*b^9 + 27*A^2*B*a*b^10 - 27*A^3*b^11 - 400*(6*A^2*B*a^6 - 13*A^3*a^5*b)*c^5 + 8*(108*B^3*a^7 - 762*A*B^2*a^6*b + 1956*A^2*B*a^5*b^2 - 1801*A^3*a^4*b^3)*c^4 - (672*B^3*a^6*b^2 - 4968*A*B^2*a^5*b^3 + 12414*A^2*B*a^4*b^4 - 10549*A^3*a^3*b^5)*c^3 + 5*(38*B^3*a^5*b^4 - 297*A*B^2*a^4*b^5 + 771*A^2*B*a^3*b^6 - 666*A^3*a^2*b^7)*c^2 - (23*B^3*a^4*b^6 - 192*A*B^2*a^3*b^7 + 531*A^2*B*a^2*b^8 - 486*A^3*a*b^9)*c - (B*a^6*b^9 - 3*A*a^5*b^10 + 1280*A*a^10*c^5 + 128*(4*B*a^10*b - 17*A*a^9*b^2)*c^4 - 448*(B*a^9*b^3 - 3*A*a^8*b^4)*c^3 + 8*(18*B*a^8*b^5 - 49*A*a^7*b^6)*c^2 - 5*(4*B*a^7*b^7 - 11*A*a^6*b^8)*c)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(-(B^2*a^2*b^5 - 6*A*B*a*b^6 + 9*A^2*b^7 + 60*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 5*(12*B^2*a^4*b - 60*A*B*a^3*b^2 + 77*A^2*a^2*b^3)*c^2 - 5*(3*B^2*a^3*b^3 - 16*A*B*a^2*b^4 + 21*A^2*a*b^5)*c + (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3))) - sqrt(1/2)*((a^2*b^2*c - 4*a^3*c^2)*x^5 + (a^2*b^3 - 4*a^3*b*c)*x^3 + (a^3*b^2 - 4*a^4*c)*x)*sqrt(-(B^2*a^2*b^5 - 6*A*B*a*b^6 + 9*A^2*b^7 + 60*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 5*(12*B^2*a^4*b - 60*A*B*a^3*b^2 + 77*A^2*a^2*b^3)*c^2 - 5*(3*B^2*a^3*b^3 - 16*A*B*a^2*b^4 + 21*A^2*a*b^5)*c - (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3))*log((2500*A^4*a^3*c^6 + 625*(4*A^3*B*a^3*b - 9*A^4*a^2*b^2)*c^5 - 3*(108*B^4*a^5 - 756*A*B^3*a^4*b + 1672*A^2*B^2*a^3*b^2 - 909*A^3*B*a^2*b^3 - 657*A^4*a*b^4)*c^4 + (81*B^4*a^4*b^2 - 647*A*B^3*a^3*b^3 + 1674*A^2*B^2*a^2*b^4 - 1323*A^3*B*a*b^5 - 189*A^4*b^6)*c^3 - 5*(B^4*a^3*b^4 - 9*A*B^3*a^2*b^5 + 27*A^2*B^2*a*b^6 - 27*A^3*B*b^7)*c^2)*x + 1/2*sqrt(1/2)*(B^3*a^3*b^8 - 9*A*B^2*a^2*b^9 + 27*A^2*B*a*b^10 - 27*A^3*b^11 - 400*(6*A^2*B*a^6 - 13*A^3*a^5*b)*c^5 + 8*(108*B^3*a^7 - 762*A*B^2*a^6*b + 1956*A^2*B*a^5*b^2 - 1801*A^3*a^4*b^3)*c^4 - (672*B^3*a^6*b^2 - 4968*A*B^2*a^5*b^3 + 12414*A^2*B*a^4*b^4 - 10549*A^3*a^3*b^5)*c^3 + 5*(38*B^3*a^5*b^4 - 297*A*B^2*a^4*b^5 + 771*A^2*B*a^3*b^6 - 666*A^3*a^2*b^7)*c^2 - (23*B^3*a^4*b^6 - 192*A*B^2*a^3*b^7 + 531*A^2*B*a^2*b^8 - 486*A^3*a*b^9)*c + (B*a^6*b^9 - 3*A*a^5*b^10 + 1280*A*a^10*c^5 + 128*(4*B*a^10*b - 17*A*a^9*b^2)*c^4 - 448*(B*a^9*b^3 - 3*A*a^8*b^4)*c^3 + 8*(18*B*a^8*b^5 - 49*A*a^7*b^6)*c^2 - 5*(4*B*a^7*b^7 - 11*A*a^6*b^8)*c)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(-(B^2*a^2*b^5 - 6*A*B*a*b^6 + 9*A^2*b^7 + 60*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 5*(12*B^2*a^4*b - 60*A*B*a^3*b^2 + 77*A^2*a^2*b^3)*c^2 - 5*(3*B^2*a^3*b^3 - 16*A*B*a^2*b^4 + 21*A^2*a*b^5)*c - (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3))) + sqrt(1/2)*((a^2*b^2*c - 4*a^3*c^2)*x^5 + (a^2*b^3 - 4*a^3*b*c)*x^3 + (a^3*b^2 - 4*a^4*c)*x)*sqrt(-(B^2*a^2*b^5 - 6*A*B*a*b^6 + 9*A^2*b^7 + 60*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 5*(12*B^2*a^4*b - 60*A*B*a^3*b^2 + 77*A^2*a^2*b^3)*c^2 - 5*(3*B^2*a^3*b^3 - 16*A*B*a^2*b^4 + 21*A^2*a*b^5)*c - (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3))*log((2500*A^4*a^3*c^6 + 625*(4*A^3*B*a^3*b - 9*A^4*a^2*b^2)*c^5 - 3*(108*B^4*a^5 - 756*A*B^3*a^4*b + 1672*A^2*B^2*a^3*b^2 - 909*A^3*B*a^2*b^3 - 657*A^4*a*b^4)*c^4 + (81*B^4*a^4*b^2 - 647*A*B^3*a^3*b^3 + 1674*A^2*B^2*a^2*b^4 - 1323*A^3*B*a*b^5 - 189*A^4*b^6)*c^3 - 5*(B^4*a^3*b^4 - 9*A*B^3*a^2*b^5 + 27*A^2*B^2*a*b^6 - 27*A^3*B*b^7)*c^2)*x - 1/2*sqrt(1/2)*(B^3*a^3*b^8 - 9*A*B^2*a^2*b^9 + 27*A^2*B*a*b^10 - 27*A^3*b^11 - 400*(6*A^2*B*a^6 - 13*A^3*a^5*b)*c^5 + 8*(108*B^3*a^7 - 762*A*B^2*a^6*b + 1956*A^2*B*a^5*b^2 - 1801*A^3*a^4*b^3)*c^4 - (672*B^3*a^6*b^2 - 4968*A*B^2*a^5*b^3 + 12414*A^2*B*a^4*b^4 - 10549*A^3*a^3*b^5)*c^3 + 5*(38*B^3*a^5*b^4 - 297*A*B^2*a^4*b^5 + 771*A^2*B*a^3*b^6 - 666*A^3*a^2*b^7)*c^2 - (23*B^3*a^4*b^6 - 192*A*B^2*a^3*b^7 + 531*A^2*B*a^2*b^8 - 486*A^3*a*b^9)*c + (B*a^6*b^9 - 3*A*a^5*b^10 + 1280*A*a^10*c^5 + 128*(4*B*a^10*b - 17*A*a^9*b^2)*c^4 - 448*(B*a^9*b^3 - 3*A*a^8*b^4)*c^3 + 8*(18*B*a^8*b^5 - 49*A*a^7*b^6)*c^2 - 5*(4*B*a^7*b^7 - 11*A*a^6*b^8)*c)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(-(B^2*a^2*b^5 - 6*A*B*a*b^6 + 9*A^2*b^7 + 60*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 5*(12*B^2*a^4*b - 60*A*B*a^3*b^2 + 77*A^2*a^2*b^3)*c^2 - 5*(3*B^2*a^3*b^3 - 16*A*B*a^2*b^4 + 21*A^2*a*b^5)*c - (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt((B^4*a^4*b^4 - 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 - 108*A^3*B*a*b^7 + 81*A^4*b^8 + 625*A^4*a^4*c^4 - 50*(9*A^2*B^2*a^5 - 44*A^3*B*a^4*b + 51*A^4*a^3*b^2)*c^3 + 3*(27*B^4*a^6 - 264*A*B^3*a^5*b + 968*A^2*B^2*a^4*b^2 - 1596*A^3*B*a^3*b^3 + 1017*A^4*a^2*b^4)*c^2 - 2*(9*B^4*a^5*b^2 - 98*A*B^3*a^4*b^3 + 396*A^2*B^2*a^3*b^4 - 702*A^3*B*a^2*b^5 + 459*A^4*a*b^6)*c)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3))))/((a^2*b^2*c - 4*a^3*c^2)*x^5 + (a^2*b^3 - 4*a^3*b*c)*x^3 + (a^3*b^2 - 4*a^4*c)*x)","B",0
123,1,10190,0,22.199691," ","integrate((B*x^2+A)/x^4/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\frac{6 \, {\left({\left(10 \, B a^{2} - 19 \, A a b\right)} c^{2} - {\left(3 \, B a b^{2} - 5 \, A b^{3}\right)} c\right)} x^{6} - 4 \, A a^{2} b^{2} + 16 \, A a^{3} c - 2 \, {\left(9 \, B a b^{3} - 15 \, A b^{4} - 14 \, A a^{2} c^{2} - {\left(33 \, B a^{2} b - 62 \, A a b^{2}\right)} c\right)} x^{4} - 4 \, {\left(3 \, B a^{2} b^{2} - 5 \, A a b^{3} - 4 \, {\left(3 \, B a^{3} - 5 \, A a^{2} b\right)} c\right)} x^{2} - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{7} - 30 \, A B a b^{8} + 25 \, A^{2} b^{9} - 140 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - 105 \, {\left(4 \, B^{2} a^{5} b - 20 \, A B a^{4} b^{2} + 23 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(55 \, B^{2} a^{4} b^{3} - 210 \, A B a^{3} b^{4} + 198 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(15 \, B^{2} a^{3} b^{5} - 52 \, A B a^{2} b^{6} + 45 \, A^{2} a b^{7}\right)} c + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} \log\left({\left(9604 \, A^{4} a^{4} c^{8} + 7203 \, {\left(4 \, A^{3} B a^{4} b - 7 \, A^{4} a^{3} b^{2}\right)} c^{7} - {\left(2500 \, B^{4} a^{6} - 22500 \, A B^{3} a^{5} b + 43524 \, A^{2} B^{2} a^{4} b^{2} + 4343 \, A^{3} B a^{3} b^{3} - 43410 \, A^{4} a^{2} b^{4}\right)} c^{6} + {\left(5625 \, B^{4} a^{5} b^{2} - 31137 \, A B^{3} a^{4} b^{3} + 52821 \, A^{2} B^{2} a^{3} b^{4} - 20190 \, A^{3} B a^{2} b^{5} - 12325 \, A^{4} a b^{6}\right)} c^{5} - 3 \, {\left(657 \, B^{4} a^{4} b^{4} - 3351 \, A B^{3} a^{3} b^{5} + 5560 \, A^{2} B^{2} a^{2} b^{6} - 2775 \, A^{3} B a b^{7} - 375 \, A^{4} b^{8}\right)} c^{4} + 7 \, {\left(27 \, B^{4} a^{3} b^{6} - 135 \, A B^{3} a^{2} b^{7} + 225 \, A^{2} B^{2} a b^{8} - 125 \, A^{3} B b^{9}\right)} c^{3}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} a^{3} b^{11} - 135 \, A B^{2} a^{2} b^{12} + 225 \, A^{2} B a b^{13} - 125 \, A^{3} b^{14} + 10976 \, A^{3} a^{7} c^{7} - 112 \, {\left(50 \, A B^{2} a^{8} - 463 \, A^{2} B a^{7} b + 709 \, A^{3} a^{6} b^{2}\right)} c^{6} - 2 \, {\left(2600 \, B^{3} a^{8} b - 31256 \, A B^{2} a^{7} b^{2} + 96044 \, A^{2} B a^{6} b^{3} - 86495 \, A^{3} a^{5} b^{4}\right)} c^{5} + {\left(14408 \, B^{3} a^{7} b^{3} - 101006 \, A B^{2} a^{6} b^{4} + 224705 \, A^{2} B a^{5} b^{5} - 160932 \, A^{3} a^{4} b^{6}\right)} c^{4} - 7 \, {\left(1507 \, B^{3} a^{6} b^{5} - 8820 \, A B^{2} a^{5} b^{6} + 16991 \, A^{2} B a^{4} b^{7} - 10797 \, A^{3} a^{3} b^{8}\right)} c^{3} + {\left(3330 \, B^{3} a^{5} b^{7} - 17889 \, A B^{2} a^{4} b^{8} + 31929 \, A^{2} B a^{3} b^{9} - 18940 \, A^{3} a^{2} b^{10}\right)} c^{2} - {\left(486 \, B^{3} a^{4} b^{9} - 2493 \, A B^{2} a^{3} b^{10} + 4260 \, A^{2} B a^{2} b^{11} - 2425 \, A^{3} a b^{12}\right)} c - {\left(3 \, B a^{8} b^{10} - 5 \, A a^{7} b^{11} - 256 \, {\left(5 \, B a^{13} - 13 \, A a^{12} b\right)} c^{5} + 64 \, {\left(34 \, B a^{12} b^{2} - 73 \, A a^{11} b^{3}\right)} c^{4} - 112 \, {\left(12 \, B a^{11} b^{4} - 23 \, A a^{10} b^{5}\right)} c^{3} + 28 \, {\left(14 \, B a^{10} b^{6} - 25 \, A a^{9} b^{7}\right)} c^{2} - {\left(55 \, B a^{9} b^{8} - 94 \, A a^{8} b^{9}\right)} c\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{7} - 30 \, A B a b^{8} + 25 \, A^{2} b^{9} - 140 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - 105 \, {\left(4 \, B^{2} a^{5} b - 20 \, A B a^{4} b^{2} + 23 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(55 \, B^{2} a^{4} b^{3} - 210 \, A B a^{3} b^{4} + 198 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(15 \, B^{2} a^{3} b^{5} - 52 \, A B a^{2} b^{6} + 45 \, A^{2} a b^{7}\right)} c + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{7} - 30 \, A B a b^{8} + 25 \, A^{2} b^{9} - 140 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - 105 \, {\left(4 \, B^{2} a^{5} b - 20 \, A B a^{4} b^{2} + 23 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(55 \, B^{2} a^{4} b^{3} - 210 \, A B a^{3} b^{4} + 198 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(15 \, B^{2} a^{3} b^{5} - 52 \, A B a^{2} b^{6} + 45 \, A^{2} a b^{7}\right)} c + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} \log\left({\left(9604 \, A^{4} a^{4} c^{8} + 7203 \, {\left(4 \, A^{3} B a^{4} b - 7 \, A^{4} a^{3} b^{2}\right)} c^{7} - {\left(2500 \, B^{4} a^{6} - 22500 \, A B^{3} a^{5} b + 43524 \, A^{2} B^{2} a^{4} b^{2} + 4343 \, A^{3} B a^{3} b^{3} - 43410 \, A^{4} a^{2} b^{4}\right)} c^{6} + {\left(5625 \, B^{4} a^{5} b^{2} - 31137 \, A B^{3} a^{4} b^{3} + 52821 \, A^{2} B^{2} a^{3} b^{4} - 20190 \, A^{3} B a^{2} b^{5} - 12325 \, A^{4} a b^{6}\right)} c^{5} - 3 \, {\left(657 \, B^{4} a^{4} b^{4} - 3351 \, A B^{3} a^{3} b^{5} + 5560 \, A^{2} B^{2} a^{2} b^{6} - 2775 \, A^{3} B a b^{7} - 375 \, A^{4} b^{8}\right)} c^{4} + 7 \, {\left(27 \, B^{4} a^{3} b^{6} - 135 \, A B^{3} a^{2} b^{7} + 225 \, A^{2} B^{2} a b^{8} - 125 \, A^{3} B b^{9}\right)} c^{3}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} a^{3} b^{11} - 135 \, A B^{2} a^{2} b^{12} + 225 \, A^{2} B a b^{13} - 125 \, A^{3} b^{14} + 10976 \, A^{3} a^{7} c^{7} - 112 \, {\left(50 \, A B^{2} a^{8} - 463 \, A^{2} B a^{7} b + 709 \, A^{3} a^{6} b^{2}\right)} c^{6} - 2 \, {\left(2600 \, B^{3} a^{8} b - 31256 \, A B^{2} a^{7} b^{2} + 96044 \, A^{2} B a^{6} b^{3} - 86495 \, A^{3} a^{5} b^{4}\right)} c^{5} + {\left(14408 \, B^{3} a^{7} b^{3} - 101006 \, A B^{2} a^{6} b^{4} + 224705 \, A^{2} B a^{5} b^{5} - 160932 \, A^{3} a^{4} b^{6}\right)} c^{4} - 7 \, {\left(1507 \, B^{3} a^{6} b^{5} - 8820 \, A B^{2} a^{5} b^{6} + 16991 \, A^{2} B a^{4} b^{7} - 10797 \, A^{3} a^{3} b^{8}\right)} c^{3} + {\left(3330 \, B^{3} a^{5} b^{7} - 17889 \, A B^{2} a^{4} b^{8} + 31929 \, A^{2} B a^{3} b^{9} - 18940 \, A^{3} a^{2} b^{10}\right)} c^{2} - {\left(486 \, B^{3} a^{4} b^{9} - 2493 \, A B^{2} a^{3} b^{10} + 4260 \, A^{2} B a^{2} b^{11} - 2425 \, A^{3} a b^{12}\right)} c - {\left(3 \, B a^{8} b^{10} - 5 \, A a^{7} b^{11} - 256 \, {\left(5 \, B a^{13} - 13 \, A a^{12} b\right)} c^{5} + 64 \, {\left(34 \, B a^{12} b^{2} - 73 \, A a^{11} b^{3}\right)} c^{4} - 112 \, {\left(12 \, B a^{11} b^{4} - 23 \, A a^{10} b^{5}\right)} c^{3} + 28 \, {\left(14 \, B a^{10} b^{6} - 25 \, A a^{9} b^{7}\right)} c^{2} - {\left(55 \, B a^{9} b^{8} - 94 \, A a^{8} b^{9}\right)} c\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{7} - 30 \, A B a b^{8} + 25 \, A^{2} b^{9} - 140 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - 105 \, {\left(4 \, B^{2} a^{5} b - 20 \, A B a^{4} b^{2} + 23 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(55 \, B^{2} a^{4} b^{3} - 210 \, A B a^{3} b^{4} + 198 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(15 \, B^{2} a^{3} b^{5} - 52 \, A B a^{2} b^{6} + 45 \, A^{2} a b^{7}\right)} c + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{7} - 30 \, A B a b^{8} + 25 \, A^{2} b^{9} - 140 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - 105 \, {\left(4 \, B^{2} a^{5} b - 20 \, A B a^{4} b^{2} + 23 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(55 \, B^{2} a^{4} b^{3} - 210 \, A B a^{3} b^{4} + 198 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(15 \, B^{2} a^{3} b^{5} - 52 \, A B a^{2} b^{6} + 45 \, A^{2} a b^{7}\right)} c - {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} \log\left({\left(9604 \, A^{4} a^{4} c^{8} + 7203 \, {\left(4 \, A^{3} B a^{4} b - 7 \, A^{4} a^{3} b^{2}\right)} c^{7} - {\left(2500 \, B^{4} a^{6} - 22500 \, A B^{3} a^{5} b + 43524 \, A^{2} B^{2} a^{4} b^{2} + 4343 \, A^{3} B a^{3} b^{3} - 43410 \, A^{4} a^{2} b^{4}\right)} c^{6} + {\left(5625 \, B^{4} a^{5} b^{2} - 31137 \, A B^{3} a^{4} b^{3} + 52821 \, A^{2} B^{2} a^{3} b^{4} - 20190 \, A^{3} B a^{2} b^{5} - 12325 \, A^{4} a b^{6}\right)} c^{5} - 3 \, {\left(657 \, B^{4} a^{4} b^{4} - 3351 \, A B^{3} a^{3} b^{5} + 5560 \, A^{2} B^{2} a^{2} b^{6} - 2775 \, A^{3} B a b^{7} - 375 \, A^{4} b^{8}\right)} c^{4} + 7 \, {\left(27 \, B^{4} a^{3} b^{6} - 135 \, A B^{3} a^{2} b^{7} + 225 \, A^{2} B^{2} a b^{8} - 125 \, A^{3} B b^{9}\right)} c^{3}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} a^{3} b^{11} - 135 \, A B^{2} a^{2} b^{12} + 225 \, A^{2} B a b^{13} - 125 \, A^{3} b^{14} + 10976 \, A^{3} a^{7} c^{7} - 112 \, {\left(50 \, A B^{2} a^{8} - 463 \, A^{2} B a^{7} b + 709 \, A^{3} a^{6} b^{2}\right)} c^{6} - 2 \, {\left(2600 \, B^{3} a^{8} b - 31256 \, A B^{2} a^{7} b^{2} + 96044 \, A^{2} B a^{6} b^{3} - 86495 \, A^{3} a^{5} b^{4}\right)} c^{5} + {\left(14408 \, B^{3} a^{7} b^{3} - 101006 \, A B^{2} a^{6} b^{4} + 224705 \, A^{2} B a^{5} b^{5} - 160932 \, A^{3} a^{4} b^{6}\right)} c^{4} - 7 \, {\left(1507 \, B^{3} a^{6} b^{5} - 8820 \, A B^{2} a^{5} b^{6} + 16991 \, A^{2} B a^{4} b^{7} - 10797 \, A^{3} a^{3} b^{8}\right)} c^{3} + {\left(3330 \, B^{3} a^{5} b^{7} - 17889 \, A B^{2} a^{4} b^{8} + 31929 \, A^{2} B a^{3} b^{9} - 18940 \, A^{3} a^{2} b^{10}\right)} c^{2} - {\left(486 \, B^{3} a^{4} b^{9} - 2493 \, A B^{2} a^{3} b^{10} + 4260 \, A^{2} B a^{2} b^{11} - 2425 \, A^{3} a b^{12}\right)} c + {\left(3 \, B a^{8} b^{10} - 5 \, A a^{7} b^{11} - 256 \, {\left(5 \, B a^{13} - 13 \, A a^{12} b\right)} c^{5} + 64 \, {\left(34 \, B a^{12} b^{2} - 73 \, A a^{11} b^{3}\right)} c^{4} - 112 \, {\left(12 \, B a^{11} b^{4} - 23 \, A a^{10} b^{5}\right)} c^{3} + 28 \, {\left(14 \, B a^{10} b^{6} - 25 \, A a^{9} b^{7}\right)} c^{2} - {\left(55 \, B a^{9} b^{8} - 94 \, A a^{8} b^{9}\right)} c\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{7} - 30 \, A B a b^{8} + 25 \, A^{2} b^{9} - 140 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - 105 \, {\left(4 \, B^{2} a^{5} b - 20 \, A B a^{4} b^{2} + 23 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(55 \, B^{2} a^{4} b^{3} - 210 \, A B a^{3} b^{4} + 198 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(15 \, B^{2} a^{3} b^{5} - 52 \, A B a^{2} b^{6} + 45 \, A^{2} a b^{7}\right)} c - {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{7} - 30 \, A B a b^{8} + 25 \, A^{2} b^{9} - 140 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - 105 \, {\left(4 \, B^{2} a^{5} b - 20 \, A B a^{4} b^{2} + 23 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(55 \, B^{2} a^{4} b^{3} - 210 \, A B a^{3} b^{4} + 198 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(15 \, B^{2} a^{3} b^{5} - 52 \, A B a^{2} b^{6} + 45 \, A^{2} a b^{7}\right)} c - {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} \log\left({\left(9604 \, A^{4} a^{4} c^{8} + 7203 \, {\left(4 \, A^{3} B a^{4} b - 7 \, A^{4} a^{3} b^{2}\right)} c^{7} - {\left(2500 \, B^{4} a^{6} - 22500 \, A B^{3} a^{5} b + 43524 \, A^{2} B^{2} a^{4} b^{2} + 4343 \, A^{3} B a^{3} b^{3} - 43410 \, A^{4} a^{2} b^{4}\right)} c^{6} + {\left(5625 \, B^{4} a^{5} b^{2} - 31137 \, A B^{3} a^{4} b^{3} + 52821 \, A^{2} B^{2} a^{3} b^{4} - 20190 \, A^{3} B a^{2} b^{5} - 12325 \, A^{4} a b^{6}\right)} c^{5} - 3 \, {\left(657 \, B^{4} a^{4} b^{4} - 3351 \, A B^{3} a^{3} b^{5} + 5560 \, A^{2} B^{2} a^{2} b^{6} - 2775 \, A^{3} B a b^{7} - 375 \, A^{4} b^{8}\right)} c^{4} + 7 \, {\left(27 \, B^{4} a^{3} b^{6} - 135 \, A B^{3} a^{2} b^{7} + 225 \, A^{2} B^{2} a b^{8} - 125 \, A^{3} B b^{9}\right)} c^{3}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} a^{3} b^{11} - 135 \, A B^{2} a^{2} b^{12} + 225 \, A^{2} B a b^{13} - 125 \, A^{3} b^{14} + 10976 \, A^{3} a^{7} c^{7} - 112 \, {\left(50 \, A B^{2} a^{8} - 463 \, A^{2} B a^{7} b + 709 \, A^{3} a^{6} b^{2}\right)} c^{6} - 2 \, {\left(2600 \, B^{3} a^{8} b - 31256 \, A B^{2} a^{7} b^{2} + 96044 \, A^{2} B a^{6} b^{3} - 86495 \, A^{3} a^{5} b^{4}\right)} c^{5} + {\left(14408 \, B^{3} a^{7} b^{3} - 101006 \, A B^{2} a^{6} b^{4} + 224705 \, A^{2} B a^{5} b^{5} - 160932 \, A^{3} a^{4} b^{6}\right)} c^{4} - 7 \, {\left(1507 \, B^{3} a^{6} b^{5} - 8820 \, A B^{2} a^{5} b^{6} + 16991 \, A^{2} B a^{4} b^{7} - 10797 \, A^{3} a^{3} b^{8}\right)} c^{3} + {\left(3330 \, B^{3} a^{5} b^{7} - 17889 \, A B^{2} a^{4} b^{8} + 31929 \, A^{2} B a^{3} b^{9} - 18940 \, A^{3} a^{2} b^{10}\right)} c^{2} - {\left(486 \, B^{3} a^{4} b^{9} - 2493 \, A B^{2} a^{3} b^{10} + 4260 \, A^{2} B a^{2} b^{11} - 2425 \, A^{3} a b^{12}\right)} c + {\left(3 \, B a^{8} b^{10} - 5 \, A a^{7} b^{11} - 256 \, {\left(5 \, B a^{13} - 13 \, A a^{12} b\right)} c^{5} + 64 \, {\left(34 \, B a^{12} b^{2} - 73 \, A a^{11} b^{3}\right)} c^{4} - 112 \, {\left(12 \, B a^{11} b^{4} - 23 \, A a^{10} b^{5}\right)} c^{3} + 28 \, {\left(14 \, B a^{10} b^{6} - 25 \, A a^{9} b^{7}\right)} c^{2} - {\left(55 \, B a^{9} b^{8} - 94 \, A a^{8} b^{9}\right)} c\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{7} - 30 \, A B a b^{8} + 25 \, A^{2} b^{9} - 140 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} - 105 \, {\left(4 \, B^{2} a^{5} b - 20 \, A B a^{4} b^{2} + 23 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(55 \, B^{2} a^{4} b^{3} - 210 \, A B a^{3} b^{4} + 198 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(15 \, B^{2} a^{3} b^{5} - 52 \, A B a^{2} b^{6} + 45 \, A^{2} a b^{7}\right)} c - {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{81 \, B^{4} a^{4} b^{8} - 540 \, A B^{3} a^{3} b^{9} + 1350 \, A^{2} B^{2} a^{2} b^{10} - 1500 \, A^{3} B a b^{11} + 625 \, A^{4} b^{12} + 2401 \, A^{4} a^{6} c^{6} - 98 \, {\left(25 \, A^{2} B^{2} a^{7} - 186 \, A^{3} B a^{6} b + 246 \, A^{4} a^{5} b^{2}\right)} c^{5} + {\left(625 \, B^{4} a^{8} - 9300 \, A B^{3} a^{7} b + 51894 \, A^{2} B^{2} a^{6} b^{2} - 109544 \, A^{3} B a^{5} b^{3} + 76686 \, A^{4} a^{4} b^{4}\right)} c^{4} - 2 \, {\left(1275 \, B^{4} a^{7} b^{2} - 14086 \, A B^{3} a^{6} b^{3} + 51336 \, A^{2} B^{2} a^{5} b^{4} - 77424 \, A^{3} B a^{4} b^{5} + 41815 \, A^{4} a^{3} b^{6}\right)} c^{3} + 3 \, {\left(1017 \, B^{4} a^{6} b^{4} - 7872 \, A B^{3} a^{5} b^{5} + 22508 \, A^{2} B^{2} a^{4} b^{6} - 28260 \, A^{3} B a^{3} b^{7} + 13175 \, A^{4} a^{2} b^{8}\right)} c^{2} - 2 \, {\left(459 \, B^{4} a^{5} b^{6} - 3186 \, A B^{3} a^{4} b^{7} + 8280 \, A^{2} B^{2} a^{3} b^{8} - 9550 \, A^{3} B a^{2} b^{9} + 4125 \, A^{4} a b^{10}\right)} c}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}}\right)}{12 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}\right)}}"," ",0,"1/12*(6*((10*B*a^2 - 19*A*a*b)*c^2 - (3*B*a*b^2 - 5*A*b^3)*c)*x^6 - 4*A*a^2*b^2 + 16*A*a^3*c - 2*(9*B*a*b^3 - 15*A*b^4 - 14*A*a^2*c^2 - (33*B*a^2*b - 62*A*a*b^2)*c)*x^4 - 4*(3*B*a^2*b^2 - 5*A*a*b^3 - 4*(3*B*a^3 - 5*A*a^2*b)*c)*x^2 - 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*x^7 + (a^3*b^3 - 4*a^4*b*c)*x^5 + (a^4*b^2 - 4*a^5*c)*x^3)*sqrt(-(9*B^2*a^2*b^7 - 30*A*B*a*b^8 + 25*A^2*b^9 - 140*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - 105*(4*B^2*a^5*b - 20*A*B*a^4*b^2 + 23*A^2*a^3*b^3)*c^3 + 7*(55*B^2*a^4*b^3 - 210*A*B*a^3*b^4 + 198*A^2*a^2*b^5)*c^2 - 7*(15*B^2*a^3*b^5 - 52*A*B*a^2*b^6 + 45*A^2*a*b^7)*c + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))*log((9604*A^4*a^4*c^8 + 7203*(4*A^3*B*a^4*b - 7*A^4*a^3*b^2)*c^7 - (2500*B^4*a^6 - 22500*A*B^3*a^5*b + 43524*A^2*B^2*a^4*b^2 + 4343*A^3*B*a^3*b^3 - 43410*A^4*a^2*b^4)*c^6 + (5625*B^4*a^5*b^2 - 31137*A*B^3*a^4*b^3 + 52821*A^2*B^2*a^3*b^4 - 20190*A^3*B*a^2*b^5 - 12325*A^4*a*b^6)*c^5 - 3*(657*B^4*a^4*b^4 - 3351*A*B^3*a^3*b^5 + 5560*A^2*B^2*a^2*b^6 - 2775*A^3*B*a*b^7 - 375*A^4*b^8)*c^4 + 7*(27*B^4*a^3*b^6 - 135*A*B^3*a^2*b^7 + 225*A^2*B^2*a*b^8 - 125*A^3*B*b^9)*c^3)*x + 1/2*sqrt(1/2)*(27*B^3*a^3*b^11 - 135*A*B^2*a^2*b^12 + 225*A^2*B*a*b^13 - 125*A^3*b^14 + 10976*A^3*a^7*c^7 - 112*(50*A*B^2*a^8 - 463*A^2*B*a^7*b + 709*A^3*a^6*b^2)*c^6 - 2*(2600*B^3*a^8*b - 31256*A*B^2*a^7*b^2 + 96044*A^2*B*a^6*b^3 - 86495*A^3*a^5*b^4)*c^5 + (14408*B^3*a^7*b^3 - 101006*A*B^2*a^6*b^4 + 224705*A^2*B*a^5*b^5 - 160932*A^3*a^4*b^6)*c^4 - 7*(1507*B^3*a^6*b^5 - 8820*A*B^2*a^5*b^6 + 16991*A^2*B*a^4*b^7 - 10797*A^3*a^3*b^8)*c^3 + (3330*B^3*a^5*b^7 - 17889*A*B^2*a^4*b^8 + 31929*A^2*B*a^3*b^9 - 18940*A^3*a^2*b^10)*c^2 - (486*B^3*a^4*b^9 - 2493*A*B^2*a^3*b^10 + 4260*A^2*B*a^2*b^11 - 2425*A^3*a*b^12)*c - (3*B*a^8*b^10 - 5*A*a^7*b^11 - 256*(5*B*a^13 - 13*A*a^12*b)*c^5 + 64*(34*B*a^12*b^2 - 73*A*a^11*b^3)*c^4 - 112*(12*B*a^11*b^4 - 23*A*a^10*b^5)*c^3 + 28*(14*B*a^10*b^6 - 25*A*a^9*b^7)*c^2 - (55*B*a^9*b^8 - 94*A*a^8*b^9)*c)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(-(9*B^2*a^2*b^7 - 30*A*B*a*b^8 + 25*A^2*b^9 - 140*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - 105*(4*B^2*a^5*b - 20*A*B*a^4*b^2 + 23*A^2*a^3*b^3)*c^3 + 7*(55*B^2*a^4*b^3 - 210*A*B*a^3*b^4 + 198*A^2*a^2*b^5)*c^2 - 7*(15*B^2*a^3*b^5 - 52*A*B*a^2*b^6 + 45*A^2*a*b^7)*c + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))) + 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*x^7 + (a^3*b^3 - 4*a^4*b*c)*x^5 + (a^4*b^2 - 4*a^5*c)*x^3)*sqrt(-(9*B^2*a^2*b^7 - 30*A*B*a*b^8 + 25*A^2*b^9 - 140*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - 105*(4*B^2*a^5*b - 20*A*B*a^4*b^2 + 23*A^2*a^3*b^3)*c^3 + 7*(55*B^2*a^4*b^3 - 210*A*B*a^3*b^4 + 198*A^2*a^2*b^5)*c^2 - 7*(15*B^2*a^3*b^5 - 52*A*B*a^2*b^6 + 45*A^2*a*b^7)*c + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))*log((9604*A^4*a^4*c^8 + 7203*(4*A^3*B*a^4*b - 7*A^4*a^3*b^2)*c^7 - (2500*B^4*a^6 - 22500*A*B^3*a^5*b + 43524*A^2*B^2*a^4*b^2 + 4343*A^3*B*a^3*b^3 - 43410*A^4*a^2*b^4)*c^6 + (5625*B^4*a^5*b^2 - 31137*A*B^3*a^4*b^3 + 52821*A^2*B^2*a^3*b^4 - 20190*A^3*B*a^2*b^5 - 12325*A^4*a*b^6)*c^5 - 3*(657*B^4*a^4*b^4 - 3351*A*B^3*a^3*b^5 + 5560*A^2*B^2*a^2*b^6 - 2775*A^3*B*a*b^7 - 375*A^4*b^8)*c^4 + 7*(27*B^4*a^3*b^6 - 135*A*B^3*a^2*b^7 + 225*A^2*B^2*a*b^8 - 125*A^3*B*b^9)*c^3)*x - 1/2*sqrt(1/2)*(27*B^3*a^3*b^11 - 135*A*B^2*a^2*b^12 + 225*A^2*B*a*b^13 - 125*A^3*b^14 + 10976*A^3*a^7*c^7 - 112*(50*A*B^2*a^8 - 463*A^2*B*a^7*b + 709*A^3*a^6*b^2)*c^6 - 2*(2600*B^3*a^8*b - 31256*A*B^2*a^7*b^2 + 96044*A^2*B*a^6*b^3 - 86495*A^3*a^5*b^4)*c^5 + (14408*B^3*a^7*b^3 - 101006*A*B^2*a^6*b^4 + 224705*A^2*B*a^5*b^5 - 160932*A^3*a^4*b^6)*c^4 - 7*(1507*B^3*a^6*b^5 - 8820*A*B^2*a^5*b^6 + 16991*A^2*B*a^4*b^7 - 10797*A^3*a^3*b^8)*c^3 + (3330*B^3*a^5*b^7 - 17889*A*B^2*a^4*b^8 + 31929*A^2*B*a^3*b^9 - 18940*A^3*a^2*b^10)*c^2 - (486*B^3*a^4*b^9 - 2493*A*B^2*a^3*b^10 + 4260*A^2*B*a^2*b^11 - 2425*A^3*a*b^12)*c - (3*B*a^8*b^10 - 5*A*a^7*b^11 - 256*(5*B*a^13 - 13*A*a^12*b)*c^5 + 64*(34*B*a^12*b^2 - 73*A*a^11*b^3)*c^4 - 112*(12*B*a^11*b^4 - 23*A*a^10*b^5)*c^3 + 28*(14*B*a^10*b^6 - 25*A*a^9*b^7)*c^2 - (55*B*a^9*b^8 - 94*A*a^8*b^9)*c)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(-(9*B^2*a^2*b^7 - 30*A*B*a*b^8 + 25*A^2*b^9 - 140*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - 105*(4*B^2*a^5*b - 20*A*B*a^4*b^2 + 23*A^2*a^3*b^3)*c^3 + 7*(55*B^2*a^4*b^3 - 210*A*B*a^3*b^4 + 198*A^2*a^2*b^5)*c^2 - 7*(15*B^2*a^3*b^5 - 52*A*B*a^2*b^6 + 45*A^2*a*b^7)*c + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))) - 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*x^7 + (a^3*b^3 - 4*a^4*b*c)*x^5 + (a^4*b^2 - 4*a^5*c)*x^3)*sqrt(-(9*B^2*a^2*b^7 - 30*A*B*a*b^8 + 25*A^2*b^9 - 140*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - 105*(4*B^2*a^5*b - 20*A*B*a^4*b^2 + 23*A^2*a^3*b^3)*c^3 + 7*(55*B^2*a^4*b^3 - 210*A*B*a^3*b^4 + 198*A^2*a^2*b^5)*c^2 - 7*(15*B^2*a^3*b^5 - 52*A*B*a^2*b^6 + 45*A^2*a*b^7)*c - (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))*log((9604*A^4*a^4*c^8 + 7203*(4*A^3*B*a^4*b - 7*A^4*a^3*b^2)*c^7 - (2500*B^4*a^6 - 22500*A*B^3*a^5*b + 43524*A^2*B^2*a^4*b^2 + 4343*A^3*B*a^3*b^3 - 43410*A^4*a^2*b^4)*c^6 + (5625*B^4*a^5*b^2 - 31137*A*B^3*a^4*b^3 + 52821*A^2*B^2*a^3*b^4 - 20190*A^3*B*a^2*b^5 - 12325*A^4*a*b^6)*c^5 - 3*(657*B^4*a^4*b^4 - 3351*A*B^3*a^3*b^5 + 5560*A^2*B^2*a^2*b^6 - 2775*A^3*B*a*b^7 - 375*A^4*b^8)*c^4 + 7*(27*B^4*a^3*b^6 - 135*A*B^3*a^2*b^7 + 225*A^2*B^2*a*b^8 - 125*A^3*B*b^9)*c^3)*x + 1/2*sqrt(1/2)*(27*B^3*a^3*b^11 - 135*A*B^2*a^2*b^12 + 225*A^2*B*a*b^13 - 125*A^3*b^14 + 10976*A^3*a^7*c^7 - 112*(50*A*B^2*a^8 - 463*A^2*B*a^7*b + 709*A^3*a^6*b^2)*c^6 - 2*(2600*B^3*a^8*b - 31256*A*B^2*a^7*b^2 + 96044*A^2*B*a^6*b^3 - 86495*A^3*a^5*b^4)*c^5 + (14408*B^3*a^7*b^3 - 101006*A*B^2*a^6*b^4 + 224705*A^2*B*a^5*b^5 - 160932*A^3*a^4*b^6)*c^4 - 7*(1507*B^3*a^6*b^5 - 8820*A*B^2*a^5*b^6 + 16991*A^2*B*a^4*b^7 - 10797*A^3*a^3*b^8)*c^3 + (3330*B^3*a^5*b^7 - 17889*A*B^2*a^4*b^8 + 31929*A^2*B*a^3*b^9 - 18940*A^3*a^2*b^10)*c^2 - (486*B^3*a^4*b^9 - 2493*A*B^2*a^3*b^10 + 4260*A^2*B*a^2*b^11 - 2425*A^3*a*b^12)*c + (3*B*a^8*b^10 - 5*A*a^7*b^11 - 256*(5*B*a^13 - 13*A*a^12*b)*c^5 + 64*(34*B*a^12*b^2 - 73*A*a^11*b^3)*c^4 - 112*(12*B*a^11*b^4 - 23*A*a^10*b^5)*c^3 + 28*(14*B*a^10*b^6 - 25*A*a^9*b^7)*c^2 - (55*B*a^9*b^8 - 94*A*a^8*b^9)*c)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(-(9*B^2*a^2*b^7 - 30*A*B*a*b^8 + 25*A^2*b^9 - 140*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - 105*(4*B^2*a^5*b - 20*A*B*a^4*b^2 + 23*A^2*a^3*b^3)*c^3 + 7*(55*B^2*a^4*b^3 - 210*A*B*a^3*b^4 + 198*A^2*a^2*b^5)*c^2 - 7*(15*B^2*a^3*b^5 - 52*A*B*a^2*b^6 + 45*A^2*a*b^7)*c - (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))) + 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*x^7 + (a^3*b^3 - 4*a^4*b*c)*x^5 + (a^4*b^2 - 4*a^5*c)*x^3)*sqrt(-(9*B^2*a^2*b^7 - 30*A*B*a*b^8 + 25*A^2*b^9 - 140*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - 105*(4*B^2*a^5*b - 20*A*B*a^4*b^2 + 23*A^2*a^3*b^3)*c^3 + 7*(55*B^2*a^4*b^3 - 210*A*B*a^3*b^4 + 198*A^2*a^2*b^5)*c^2 - 7*(15*B^2*a^3*b^5 - 52*A*B*a^2*b^6 + 45*A^2*a*b^7)*c - (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))*log((9604*A^4*a^4*c^8 + 7203*(4*A^3*B*a^4*b - 7*A^4*a^3*b^2)*c^7 - (2500*B^4*a^6 - 22500*A*B^3*a^5*b + 43524*A^2*B^2*a^4*b^2 + 4343*A^3*B*a^3*b^3 - 43410*A^4*a^2*b^4)*c^6 + (5625*B^4*a^5*b^2 - 31137*A*B^3*a^4*b^3 + 52821*A^2*B^2*a^3*b^4 - 20190*A^3*B*a^2*b^5 - 12325*A^4*a*b^6)*c^5 - 3*(657*B^4*a^4*b^4 - 3351*A*B^3*a^3*b^5 + 5560*A^2*B^2*a^2*b^6 - 2775*A^3*B*a*b^7 - 375*A^4*b^8)*c^4 + 7*(27*B^4*a^3*b^6 - 135*A*B^3*a^2*b^7 + 225*A^2*B^2*a*b^8 - 125*A^3*B*b^9)*c^3)*x - 1/2*sqrt(1/2)*(27*B^3*a^3*b^11 - 135*A*B^2*a^2*b^12 + 225*A^2*B*a*b^13 - 125*A^3*b^14 + 10976*A^3*a^7*c^7 - 112*(50*A*B^2*a^8 - 463*A^2*B*a^7*b + 709*A^3*a^6*b^2)*c^6 - 2*(2600*B^3*a^8*b - 31256*A*B^2*a^7*b^2 + 96044*A^2*B*a^6*b^3 - 86495*A^3*a^5*b^4)*c^5 + (14408*B^3*a^7*b^3 - 101006*A*B^2*a^6*b^4 + 224705*A^2*B*a^5*b^5 - 160932*A^3*a^4*b^6)*c^4 - 7*(1507*B^3*a^6*b^5 - 8820*A*B^2*a^5*b^6 + 16991*A^2*B*a^4*b^7 - 10797*A^3*a^3*b^8)*c^3 + (3330*B^3*a^5*b^7 - 17889*A*B^2*a^4*b^8 + 31929*A^2*B*a^3*b^9 - 18940*A^3*a^2*b^10)*c^2 - (486*B^3*a^4*b^9 - 2493*A*B^2*a^3*b^10 + 4260*A^2*B*a^2*b^11 - 2425*A^3*a*b^12)*c + (3*B*a^8*b^10 - 5*A*a^7*b^11 - 256*(5*B*a^13 - 13*A*a^12*b)*c^5 + 64*(34*B*a^12*b^2 - 73*A*a^11*b^3)*c^4 - 112*(12*B*a^11*b^4 - 23*A*a^10*b^5)*c^3 + 28*(14*B*a^10*b^6 - 25*A*a^9*b^7)*c^2 - (55*B*a^9*b^8 - 94*A*a^8*b^9)*c)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(-(9*B^2*a^2*b^7 - 30*A*B*a*b^8 + 25*A^2*b^9 - 140*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 - 105*(4*B^2*a^5*b - 20*A*B*a^4*b^2 + 23*A^2*a^3*b^3)*c^3 + 7*(55*B^2*a^4*b^3 - 210*A*B*a^3*b^4 + 198*A^2*a^2*b^5)*c^2 - 7*(15*B^2*a^3*b^5 - 52*A*B*a^2*b^6 + 45*A^2*a*b^7)*c - (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((81*B^4*a^4*b^8 - 540*A*B^3*a^3*b^9 + 1350*A^2*B^2*a^2*b^10 - 1500*A^3*B*a*b^11 + 625*A^4*b^12 + 2401*A^4*a^6*c^6 - 98*(25*A^2*B^2*a^7 - 186*A^3*B*a^6*b + 246*A^4*a^5*b^2)*c^5 + (625*B^4*a^8 - 9300*A*B^3*a^7*b + 51894*A^2*B^2*a^6*b^2 - 109544*A^3*B*a^5*b^3 + 76686*A^4*a^4*b^4)*c^4 - 2*(1275*B^4*a^7*b^2 - 14086*A*B^3*a^6*b^3 + 51336*A^2*B^2*a^5*b^4 - 77424*A^3*B*a^4*b^5 + 41815*A^4*a^3*b^6)*c^3 + 3*(1017*B^4*a^6*b^4 - 7872*A*B^3*a^5*b^5 + 22508*A^2*B^2*a^4*b^6 - 28260*A^3*B*a^3*b^7 + 13175*A^4*a^2*b^8)*c^2 - 2*(459*B^4*a^5*b^6 - 3186*A*B^3*a^4*b^7 + 8280*A^2*B^2*a^3*b^8 - 9550*A^3*B*a^2*b^9 + 4125*A^4*a*b^10)*c)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))))/((a^3*b^2*c - 4*a^4*c^2)*x^7 + (a^3*b^3 - 4*a^4*b*c)*x^5 + (a^4*b^2 - 4*a^5*c)*x^3)","B",0
124,1,3196,0,1.407644," ","integrate(x^11*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(B b^{6} c^{3} - 12 \, B a b^{4} c^{4} + 48 \, B a^{2} b^{2} c^{5} - 64 \, B a^{3} c^{6}\right)} x^{10} - 5 \, B a^{2} b^{7} - 96 \, A a^{5} c^{4} + 4 \, {\left(B b^{7} c^{2} - 12 \, B a b^{5} c^{3} + 48 \, B a^{2} b^{3} c^{4} - 64 \, B a^{3} b c^{5}\right)} x^{8} - 2 \, {\left(2 \, B b^{8} c + 100 \, {\left(2 \, B a^{4} + A a^{3} b\right)} c^{5} - {\left(254 \, B a^{3} b^{2} + 85 \, A a^{2} b^{3}\right)} c^{4} + {\left(123 \, B a^{2} b^{4} + 23 \, A a b^{5}\right)} c^{3} - 2 \, {\left(13 \, B a b^{6} + A b^{7}\right)} c^{2}\right)} x^{6} - {\left(5 \, B b^{9} + 128 \, A a^{4} c^{5} + 4 \, {\left(22 \, B a^{4} b + 3 \, A a^{3} b^{2}\right)} c^{4} - {\left(314 \, B a^{3} b^{3} + 87 \, A a^{2} b^{4}\right)} c^{3} + {\left(225 \, B a^{2} b^{5} + 31 \, A a b^{6}\right)} c^{2} - {\left(58 \, B a b^{7} + 3 \, A b^{8}\right)} c\right)} x^{4} + 4 \, {\left(58 \, B a^{5} b + 27 \, A a^{4} b^{2}\right)} c^{3} - {\left(202 \, B a^{4} b^{3} + 33 \, A a^{3} b^{4}\right)} c^{2} - 2 \, {\left(5 \, B a b^{8} + 4 \, {\left(30 \, B a^{5} + 31 \, A a^{4} b\right)} c^{4} - {\left(346 \, B a^{4} b^{2} + 119 \, A a^{3} b^{3}\right)} c^{3} + {\left(235 \, B a^{3} b^{4} + 34 \, A a^{2} b^{5}\right)} c^{2} - {\left(59 \, B a^{2} b^{6} + 3 \, A a b^{7}\right)} c\right)} x^{2} - {\left(3 \, B a^{2} b^{6} + {\left(3 \, B b^{6} c^{2} - 30 \, {\left(2 \, B a^{3} + A a^{2} b\right)} c^{5} + 10 \, {\left(9 \, B a^{2} b^{2} + A a b^{3}\right)} c^{4} - {\left(30 \, B a b^{4} + A b^{5}\right)} c^{3}\right)} x^{8} + 2 \, {\left(3 \, B b^{7} c - 30 \, {\left(2 \, B a^{3} b + A a^{2} b^{2}\right)} c^{4} + 10 \, {\left(9 \, B a^{2} b^{3} + A a b^{4}\right)} c^{3} - {\left(30 \, B a b^{5} + A b^{6}\right)} c^{2}\right)} x^{6} + {\left(3 \, B b^{8} - 60 \, {\left(2 \, B a^{4} + A a^{3} b\right)} c^{4} + 10 \, {\left(12 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} c^{3} + 2 \, {\left(15 \, B a^{2} b^{4} + 4 \, A a b^{5}\right)} c^{2} - {\left(24 \, B a b^{6} + A b^{7}\right)} c\right)} x^{4} - 30 \, {\left(2 \, B a^{5} + A a^{4} b\right)} c^{3} + 10 \, {\left(9 \, B a^{4} b^{2} + A a^{3} b^{3}\right)} c^{2} + 2 \, {\left(3 \, B a b^{7} - 30 \, {\left(2 \, B a^{4} b + A a^{3} b^{2}\right)} c^{3} + 10 \, {\left(9 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} c^{2} - {\left(30 \, B a^{2} b^{5} + A a b^{6}\right)} c\right)} x^{2} - {\left(30 \, B a^{3} b^{4} + A a^{2} b^{5}\right)} c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) + {\left(56 \, B a^{3} b^{5} + 3 \, A a^{2} b^{6}\right)} c - {\left(3 \, B a^{2} b^{7} + 64 \, A a^{5} c^{4} + {\left(3 \, B b^{7} c^{2} + 64 \, A a^{3} c^{6} - 48 \, {\left(4 \, B a^{3} b + A a^{2} b^{2}\right)} c^{5} + 12 \, {\left(12 \, B a^{2} b^{3} + A a b^{4}\right)} c^{4} - {\left(36 \, B a b^{5} + A b^{6}\right)} c^{3}\right)} x^{8} + 2 \, {\left(3 \, B b^{8} c + 64 \, A a^{3} b c^{5} - 48 \, {\left(4 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} c^{4} + 12 \, {\left(12 \, B a^{2} b^{4} + A a b^{5}\right)} c^{3} - {\left(36 \, B a b^{6} + A b^{7}\right)} c^{2}\right)} x^{6} + {\left(3 \, B b^{9} + 128 \, A a^{4} c^{5} - 32 \, {\left(12 \, B a^{4} b + A a^{3} b^{2}\right)} c^{4} + 24 \, {\left(4 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} c^{3} + 2 \, {\left(36 \, B a^{2} b^{5} + 5 \, A a b^{6}\right)} c^{2} - {\left(30 \, B a b^{7} + A b^{8}\right)} c\right)} x^{4} - 48 \, {\left(4 \, B a^{5} b + A a^{4} b^{2}\right)} c^{3} + 12 \, {\left(12 \, B a^{4} b^{3} + A a^{3} b^{4}\right)} c^{2} + 2 \, {\left(3 \, B a b^{8} + 64 \, A a^{4} b c^{4} - 48 \, {\left(4 \, B a^{4} b^{2} + A a^{3} b^{3}\right)} c^{3} + 12 \, {\left(12 \, B a^{3} b^{4} + A a^{2} b^{5}\right)} c^{2} - {\left(36 \, B a^{2} b^{6} + A a b^{7}\right)} c\right)} x^{2} - {\left(36 \, B a^{3} b^{5} + A a^{2} b^{6}\right)} c\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7} + {\left(b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}\right)} x^{8} + 2 \, {\left(b^{7} c^{5} - 12 \, a b^{5} c^{6} + 48 \, a^{2} b^{3} c^{7} - 64 \, a^{3} b c^{8}\right)} x^{6} + {\left(b^{8} c^{4} - 10 \, a b^{6} c^{5} + 24 \, a^{2} b^{4} c^{6} + 32 \, a^{3} b^{2} c^{7} - 128 \, a^{4} c^{8}\right)} x^{4} + 2 \, {\left(a b^{7} c^{4} - 12 \, a^{2} b^{5} c^{5} + 48 \, a^{3} b^{3} c^{6} - 64 \, a^{4} b c^{7}\right)} x^{2}\right)}}, \frac{2 \, {\left(B b^{6} c^{3} - 12 \, B a b^{4} c^{4} + 48 \, B a^{2} b^{2} c^{5} - 64 \, B a^{3} c^{6}\right)} x^{10} - 5 \, B a^{2} b^{7} - 96 \, A a^{5} c^{4} + 4 \, {\left(B b^{7} c^{2} - 12 \, B a b^{5} c^{3} + 48 \, B a^{2} b^{3} c^{4} - 64 \, B a^{3} b c^{5}\right)} x^{8} - 2 \, {\left(2 \, B b^{8} c + 100 \, {\left(2 \, B a^{4} + A a^{3} b\right)} c^{5} - {\left(254 \, B a^{3} b^{2} + 85 \, A a^{2} b^{3}\right)} c^{4} + {\left(123 \, B a^{2} b^{4} + 23 \, A a b^{5}\right)} c^{3} - 2 \, {\left(13 \, B a b^{6} + A b^{7}\right)} c^{2}\right)} x^{6} - {\left(5 \, B b^{9} + 128 \, A a^{4} c^{5} + 4 \, {\left(22 \, B a^{4} b + 3 \, A a^{3} b^{2}\right)} c^{4} - {\left(314 \, B a^{3} b^{3} + 87 \, A a^{2} b^{4}\right)} c^{3} + {\left(225 \, B a^{2} b^{5} + 31 \, A a b^{6}\right)} c^{2} - {\left(58 \, B a b^{7} + 3 \, A b^{8}\right)} c\right)} x^{4} + 4 \, {\left(58 \, B a^{5} b + 27 \, A a^{4} b^{2}\right)} c^{3} - {\left(202 \, B a^{4} b^{3} + 33 \, A a^{3} b^{4}\right)} c^{2} - 2 \, {\left(5 \, B a b^{8} + 4 \, {\left(30 \, B a^{5} + 31 \, A a^{4} b\right)} c^{4} - {\left(346 \, B a^{4} b^{2} + 119 \, A a^{3} b^{3}\right)} c^{3} + {\left(235 \, B a^{3} b^{4} + 34 \, A a^{2} b^{5}\right)} c^{2} - {\left(59 \, B a^{2} b^{6} + 3 \, A a b^{7}\right)} c\right)} x^{2} - 2 \, {\left(3 \, B a^{2} b^{6} + {\left(3 \, B b^{6} c^{2} - 30 \, {\left(2 \, B a^{3} + A a^{2} b\right)} c^{5} + 10 \, {\left(9 \, B a^{2} b^{2} + A a b^{3}\right)} c^{4} - {\left(30 \, B a b^{4} + A b^{5}\right)} c^{3}\right)} x^{8} + 2 \, {\left(3 \, B b^{7} c - 30 \, {\left(2 \, B a^{3} b + A a^{2} b^{2}\right)} c^{4} + 10 \, {\left(9 \, B a^{2} b^{3} + A a b^{4}\right)} c^{3} - {\left(30 \, B a b^{5} + A b^{6}\right)} c^{2}\right)} x^{6} + {\left(3 \, B b^{8} - 60 \, {\left(2 \, B a^{4} + A a^{3} b\right)} c^{4} + 10 \, {\left(12 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} c^{3} + 2 \, {\left(15 \, B a^{2} b^{4} + 4 \, A a b^{5}\right)} c^{2} - {\left(24 \, B a b^{6} + A b^{7}\right)} c\right)} x^{4} - 30 \, {\left(2 \, B a^{5} + A a^{4} b\right)} c^{3} + 10 \, {\left(9 \, B a^{4} b^{2} + A a^{3} b^{3}\right)} c^{2} + 2 \, {\left(3 \, B a b^{7} - 30 \, {\left(2 \, B a^{4} b + A a^{3} b^{2}\right)} c^{3} + 10 \, {\left(9 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} c^{2} - {\left(30 \, B a^{2} b^{5} + A a b^{6}\right)} c\right)} x^{2} - {\left(30 \, B a^{3} b^{4} + A a^{2} b^{5}\right)} c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) + {\left(56 \, B a^{3} b^{5} + 3 \, A a^{2} b^{6}\right)} c - {\left(3 \, B a^{2} b^{7} + 64 \, A a^{5} c^{4} + {\left(3 \, B b^{7} c^{2} + 64 \, A a^{3} c^{6} - 48 \, {\left(4 \, B a^{3} b + A a^{2} b^{2}\right)} c^{5} + 12 \, {\left(12 \, B a^{2} b^{3} + A a b^{4}\right)} c^{4} - {\left(36 \, B a b^{5} + A b^{6}\right)} c^{3}\right)} x^{8} + 2 \, {\left(3 \, B b^{8} c + 64 \, A a^{3} b c^{5} - 48 \, {\left(4 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} c^{4} + 12 \, {\left(12 \, B a^{2} b^{4} + A a b^{5}\right)} c^{3} - {\left(36 \, B a b^{6} + A b^{7}\right)} c^{2}\right)} x^{6} + {\left(3 \, B b^{9} + 128 \, A a^{4} c^{5} - 32 \, {\left(12 \, B a^{4} b + A a^{3} b^{2}\right)} c^{4} + 24 \, {\left(4 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} c^{3} + 2 \, {\left(36 \, B a^{2} b^{5} + 5 \, A a b^{6}\right)} c^{2} - {\left(30 \, B a b^{7} + A b^{8}\right)} c\right)} x^{4} - 48 \, {\left(4 \, B a^{5} b + A a^{4} b^{2}\right)} c^{3} + 12 \, {\left(12 \, B a^{4} b^{3} + A a^{3} b^{4}\right)} c^{2} + 2 \, {\left(3 \, B a b^{8} + 64 \, A a^{4} b c^{4} - 48 \, {\left(4 \, B a^{4} b^{2} + A a^{3} b^{3}\right)} c^{3} + 12 \, {\left(12 \, B a^{3} b^{4} + A a^{2} b^{5}\right)} c^{2} - {\left(36 \, B a^{2} b^{6} + A a b^{7}\right)} c\right)} x^{2} - {\left(36 \, B a^{3} b^{5} + A a^{2} b^{6}\right)} c\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7} + {\left(b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}\right)} x^{8} + 2 \, {\left(b^{7} c^{5} - 12 \, a b^{5} c^{6} + 48 \, a^{2} b^{3} c^{7} - 64 \, a^{3} b c^{8}\right)} x^{6} + {\left(b^{8} c^{4} - 10 \, a b^{6} c^{5} + 24 \, a^{2} b^{4} c^{6} + 32 \, a^{3} b^{2} c^{7} - 128 \, a^{4} c^{8}\right)} x^{4} + 2 \, {\left(a b^{7} c^{4} - 12 \, a^{2} b^{5} c^{5} + 48 \, a^{3} b^{3} c^{6} - 64 \, a^{4} b c^{7}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(2*(B*b^6*c^3 - 12*B*a*b^4*c^4 + 48*B*a^2*b^2*c^5 - 64*B*a^3*c^6)*x^10 - 5*B*a^2*b^7 - 96*A*a^5*c^4 + 4*(B*b^7*c^2 - 12*B*a*b^5*c^3 + 48*B*a^2*b^3*c^4 - 64*B*a^3*b*c^5)*x^8 - 2*(2*B*b^8*c + 100*(2*B*a^4 + A*a^3*b)*c^5 - (254*B*a^3*b^2 + 85*A*a^2*b^3)*c^4 + (123*B*a^2*b^4 + 23*A*a*b^5)*c^3 - 2*(13*B*a*b^6 + A*b^7)*c^2)*x^6 - (5*B*b^9 + 128*A*a^4*c^5 + 4*(22*B*a^4*b + 3*A*a^3*b^2)*c^4 - (314*B*a^3*b^3 + 87*A*a^2*b^4)*c^3 + (225*B*a^2*b^5 + 31*A*a*b^6)*c^2 - (58*B*a*b^7 + 3*A*b^8)*c)*x^4 + 4*(58*B*a^5*b + 27*A*a^4*b^2)*c^3 - (202*B*a^4*b^3 + 33*A*a^3*b^4)*c^2 - 2*(5*B*a*b^8 + 4*(30*B*a^5 + 31*A*a^4*b)*c^4 - (346*B*a^4*b^2 + 119*A*a^3*b^3)*c^3 + (235*B*a^3*b^4 + 34*A*a^2*b^5)*c^2 - (59*B*a^2*b^6 + 3*A*a*b^7)*c)*x^2 - (3*B*a^2*b^6 + (3*B*b^6*c^2 - 30*(2*B*a^3 + A*a^2*b)*c^5 + 10*(9*B*a^2*b^2 + A*a*b^3)*c^4 - (30*B*a*b^4 + A*b^5)*c^3)*x^8 + 2*(3*B*b^7*c - 30*(2*B*a^3*b + A*a^2*b^2)*c^4 + 10*(9*B*a^2*b^3 + A*a*b^4)*c^3 - (30*B*a*b^5 + A*b^6)*c^2)*x^6 + (3*B*b^8 - 60*(2*B*a^4 + A*a^3*b)*c^4 + 10*(12*B*a^3*b^2 - A*a^2*b^3)*c^3 + 2*(15*B*a^2*b^4 + 4*A*a*b^5)*c^2 - (24*B*a*b^6 + A*b^7)*c)*x^4 - 30*(2*B*a^5 + A*a^4*b)*c^3 + 10*(9*B*a^4*b^2 + A*a^3*b^3)*c^2 + 2*(3*B*a*b^7 - 30*(2*B*a^4*b + A*a^3*b^2)*c^3 + 10*(9*B*a^3*b^3 + A*a^2*b^4)*c^2 - (30*B*a^2*b^5 + A*a*b^6)*c)*x^2 - (30*B*a^3*b^4 + A*a^2*b^5)*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) + (56*B*a^3*b^5 + 3*A*a^2*b^6)*c - (3*B*a^2*b^7 + 64*A*a^5*c^4 + (3*B*b^7*c^2 + 64*A*a^3*c^6 - 48*(4*B*a^3*b + A*a^2*b^2)*c^5 + 12*(12*B*a^2*b^3 + A*a*b^4)*c^4 - (36*B*a*b^5 + A*b^6)*c^3)*x^8 + 2*(3*B*b^8*c + 64*A*a^3*b*c^5 - 48*(4*B*a^3*b^2 + A*a^2*b^3)*c^4 + 12*(12*B*a^2*b^4 + A*a*b^5)*c^3 - (36*B*a*b^6 + A*b^7)*c^2)*x^6 + (3*B*b^9 + 128*A*a^4*c^5 - 32*(12*B*a^4*b + A*a^3*b^2)*c^4 + 24*(4*B*a^3*b^3 - A*a^2*b^4)*c^3 + 2*(36*B*a^2*b^5 + 5*A*a*b^6)*c^2 - (30*B*a*b^7 + A*b^8)*c)*x^4 - 48*(4*B*a^5*b + A*a^4*b^2)*c^3 + 12*(12*B*a^4*b^3 + A*a^3*b^4)*c^2 + 2*(3*B*a*b^8 + 64*A*a^4*b*c^4 - 48*(4*B*a^4*b^2 + A*a^3*b^3)*c^3 + 12*(12*B*a^3*b^4 + A*a^2*b^5)*c^2 - (36*B*a^2*b^6 + A*a*b^7)*c)*x^2 - (36*B*a^3*b^5 + A*a^2*b^6)*c)*log(c*x^4 + b*x^2 + a))/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7 + (b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)*x^8 + 2*(b^7*c^5 - 12*a*b^5*c^6 + 48*a^2*b^3*c^7 - 64*a^3*b*c^8)*x^6 + (b^8*c^4 - 10*a*b^6*c^5 + 24*a^2*b^4*c^6 + 32*a^3*b^2*c^7 - 128*a^4*c^8)*x^4 + 2*(a*b^7*c^4 - 12*a^2*b^5*c^5 + 48*a^3*b^3*c^6 - 64*a^4*b*c^7)*x^2), 1/4*(2*(B*b^6*c^3 - 12*B*a*b^4*c^4 + 48*B*a^2*b^2*c^5 - 64*B*a^3*c^6)*x^10 - 5*B*a^2*b^7 - 96*A*a^5*c^4 + 4*(B*b^7*c^2 - 12*B*a*b^5*c^3 + 48*B*a^2*b^3*c^4 - 64*B*a^3*b*c^5)*x^8 - 2*(2*B*b^8*c + 100*(2*B*a^4 + A*a^3*b)*c^5 - (254*B*a^3*b^2 + 85*A*a^2*b^3)*c^4 + (123*B*a^2*b^4 + 23*A*a*b^5)*c^3 - 2*(13*B*a*b^6 + A*b^7)*c^2)*x^6 - (5*B*b^9 + 128*A*a^4*c^5 + 4*(22*B*a^4*b + 3*A*a^3*b^2)*c^4 - (314*B*a^3*b^3 + 87*A*a^2*b^4)*c^3 + (225*B*a^2*b^5 + 31*A*a*b^6)*c^2 - (58*B*a*b^7 + 3*A*b^8)*c)*x^4 + 4*(58*B*a^5*b + 27*A*a^4*b^2)*c^3 - (202*B*a^4*b^3 + 33*A*a^3*b^4)*c^2 - 2*(5*B*a*b^8 + 4*(30*B*a^5 + 31*A*a^4*b)*c^4 - (346*B*a^4*b^2 + 119*A*a^3*b^3)*c^3 + (235*B*a^3*b^4 + 34*A*a^2*b^5)*c^2 - (59*B*a^2*b^6 + 3*A*a*b^7)*c)*x^2 - 2*(3*B*a^2*b^6 + (3*B*b^6*c^2 - 30*(2*B*a^3 + A*a^2*b)*c^5 + 10*(9*B*a^2*b^2 + A*a*b^3)*c^4 - (30*B*a*b^4 + A*b^5)*c^3)*x^8 + 2*(3*B*b^7*c - 30*(2*B*a^3*b + A*a^2*b^2)*c^4 + 10*(9*B*a^2*b^3 + A*a*b^4)*c^3 - (30*B*a*b^5 + A*b^6)*c^2)*x^6 + (3*B*b^8 - 60*(2*B*a^4 + A*a^3*b)*c^4 + 10*(12*B*a^3*b^2 - A*a^2*b^3)*c^3 + 2*(15*B*a^2*b^4 + 4*A*a*b^5)*c^2 - (24*B*a*b^6 + A*b^7)*c)*x^4 - 30*(2*B*a^5 + A*a^4*b)*c^3 + 10*(9*B*a^4*b^2 + A*a^3*b^3)*c^2 + 2*(3*B*a*b^7 - 30*(2*B*a^4*b + A*a^3*b^2)*c^3 + 10*(9*B*a^3*b^3 + A*a^2*b^4)*c^2 - (30*B*a^2*b^5 + A*a*b^6)*c)*x^2 - (30*B*a^3*b^4 + A*a^2*b^5)*c)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) + (56*B*a^3*b^5 + 3*A*a^2*b^6)*c - (3*B*a^2*b^7 + 64*A*a^5*c^4 + (3*B*b^7*c^2 + 64*A*a^3*c^6 - 48*(4*B*a^3*b + A*a^2*b^2)*c^5 + 12*(12*B*a^2*b^3 + A*a*b^4)*c^4 - (36*B*a*b^5 + A*b^6)*c^3)*x^8 + 2*(3*B*b^8*c + 64*A*a^3*b*c^5 - 48*(4*B*a^3*b^2 + A*a^2*b^3)*c^4 + 12*(12*B*a^2*b^4 + A*a*b^5)*c^3 - (36*B*a*b^6 + A*b^7)*c^2)*x^6 + (3*B*b^9 + 128*A*a^4*c^5 - 32*(12*B*a^4*b + A*a^3*b^2)*c^4 + 24*(4*B*a^3*b^3 - A*a^2*b^4)*c^3 + 2*(36*B*a^2*b^5 + 5*A*a*b^6)*c^2 - (30*B*a*b^7 + A*b^8)*c)*x^4 - 48*(4*B*a^5*b + A*a^4*b^2)*c^3 + 12*(12*B*a^4*b^3 + A*a^3*b^4)*c^2 + 2*(3*B*a*b^8 + 64*A*a^4*b*c^4 - 48*(4*B*a^4*b^2 + A*a^3*b^3)*c^3 + 12*(12*B*a^3*b^4 + A*a^2*b^5)*c^2 - (36*B*a^2*b^6 + A*a*b^7)*c)*x^2 - (36*B*a^3*b^5 + A*a^2*b^6)*c)*log(c*x^4 + b*x^2 + a))/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7 + (b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)*x^8 + 2*(b^7*c^5 - 12*a*b^5*c^6 + 48*a^2*b^3*c^7 - 64*a^3*b*c^8)*x^6 + (b^8*c^4 - 10*a*b^6*c^5 + 24*a^2*b^4*c^6 + 32*a^3*b^2*c^7 - 128*a^4*c^8)*x^4 + 2*(a*b^7*c^4 - 12*a^2*b^5*c^5 + 48*a^3*b^3*c^6 - 64*a^4*b*c^7)*x^2)]","B",0
125,1,2167,0,1.162679," ","integrate(x^9*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{3 \, B a^{2} b^{6} + 2 \, {\left(2 \, B b^{7} c + 40 \, A a^{3} c^{5} - 2 \, {\left(50 \, B a^{3} b + 21 \, A a^{2} b^{2}\right)} c^{4} + {\left(85 \, B a^{2} b^{3} + 12 \, A a b^{4}\right)} c^{3} - {\left(23 \, B a b^{5} + A b^{6}\right)} c^{2}\right)} x^{6} + {\left(3 \, B b^{8} - 8 \, {\left(16 \, B a^{4} + A a^{3} b\right)} c^{4} - 6 \, {\left(2 \, B a^{3} b^{2} + 5 \, A a^{2} b^{3}\right)} c^{3} + 3 \, {\left(29 \, B a^{2} b^{4} + 4 \, A a b^{5}\right)} c^{2} - {\left(31 \, B a b^{6} + A b^{7}\right)} c\right)} x^{4} - 8 \, {\left(12 \, B a^{5} + 5 \, A a^{4} b\right)} c^{3} + 2 \, {\left(54 \, B a^{4} b^{2} + 7 \, A a^{3} b^{3}\right)} c^{2} + 2 \, {\left(3 \, B a b^{7} + 24 \, A a^{4} c^{4} - 2 \, {\left(62 \, B a^{4} b + 23 \, A a^{3} b^{2}\right)} c^{3} + 7 \, {\left(17 \, B a^{3} b^{3} + 2 \, A a^{2} b^{4}\right)} c^{2} - {\left(34 \, B a^{2} b^{5} + A a b^{6}\right)} c\right)} x^{2} - {\left({\left(B b^{5} c^{2} - 10 \, B a b^{3} c^{3} + 30 \, B a^{2} b c^{4} - 12 \, A a^{2} c^{5}\right)} x^{8} + B a^{2} b^{5} - 10 \, B a^{3} b^{3} c + 30 \, B a^{4} b c^{2} - 12 \, A a^{4} c^{3} + 2 \, {\left(B b^{6} c - 10 \, B a b^{4} c^{2} + 30 \, B a^{2} b^{2} c^{3} - 12 \, A a^{2} b c^{4}\right)} x^{6} + {\left(B b^{7} - 8 \, B a b^{5} c + 10 \, B a^{2} b^{3} c^{2} - 24 \, A a^{3} c^{4} + 12 \, {\left(5 \, B a^{3} b - A a^{2} b^{2}\right)} c^{3}\right)} x^{4} + 2 \, {\left(B a b^{6} - 10 \, B a^{2} b^{4} c + 30 \, B a^{3} b^{2} c^{2} - 12 \, A a^{3} b c^{3}\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c - {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) - {\left(33 \, B a^{3} b^{4} + A a^{2} b^{5}\right)} c + {\left(B a^{2} b^{6} - 12 \, B a^{3} b^{4} c + 48 \, B a^{4} b^{2} c^{2} - 64 \, B a^{5} c^{3} + {\left(B b^{6} c^{2} - 12 \, B a b^{4} c^{3} + 48 \, B a^{2} b^{2} c^{4} - 64 \, B a^{3} c^{5}\right)} x^{8} + 2 \, {\left(B b^{7} c - 12 \, B a b^{5} c^{2} + 48 \, B a^{2} b^{3} c^{3} - 64 \, B a^{3} b c^{4}\right)} x^{6} + {\left(B b^{8} - 10 \, B a b^{6} c + 24 \, B a^{2} b^{4} c^{2} + 32 \, B a^{3} b^{2} c^{3} - 128 \, B a^{4} c^{4}\right)} x^{4} + 2 \, {\left(B a b^{7} - 12 \, B a^{2} b^{5} c + 48 \, B a^{3} b^{3} c^{2} - 64 \, B a^{4} b c^{3}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(a^{2} b^{6} c^{3} - 12 \, a^{3} b^{4} c^{4} + 48 \, a^{4} b^{2} c^{5} - 64 \, a^{5} c^{6} + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} x^{8} + 2 \, {\left(b^{7} c^{4} - 12 \, a b^{5} c^{5} + 48 \, a^{2} b^{3} c^{6} - 64 \, a^{3} b c^{7}\right)} x^{6} + {\left(b^{8} c^{3} - 10 \, a b^{6} c^{4} + 24 \, a^{2} b^{4} c^{5} + 32 \, a^{3} b^{2} c^{6} - 128 \, a^{4} c^{7}\right)} x^{4} + 2 \, {\left(a b^{7} c^{3} - 12 \, a^{2} b^{5} c^{4} + 48 \, a^{3} b^{3} c^{5} - 64 \, a^{4} b c^{6}\right)} x^{2}\right)}}, \frac{3 \, B a^{2} b^{6} + 2 \, {\left(2 \, B b^{7} c + 40 \, A a^{3} c^{5} - 2 \, {\left(50 \, B a^{3} b + 21 \, A a^{2} b^{2}\right)} c^{4} + {\left(85 \, B a^{2} b^{3} + 12 \, A a b^{4}\right)} c^{3} - {\left(23 \, B a b^{5} + A b^{6}\right)} c^{2}\right)} x^{6} + {\left(3 \, B b^{8} - 8 \, {\left(16 \, B a^{4} + A a^{3} b\right)} c^{4} - 6 \, {\left(2 \, B a^{3} b^{2} + 5 \, A a^{2} b^{3}\right)} c^{3} + 3 \, {\left(29 \, B a^{2} b^{4} + 4 \, A a b^{5}\right)} c^{2} - {\left(31 \, B a b^{6} + A b^{7}\right)} c\right)} x^{4} - 8 \, {\left(12 \, B a^{5} + 5 \, A a^{4} b\right)} c^{3} + 2 \, {\left(54 \, B a^{4} b^{2} + 7 \, A a^{3} b^{3}\right)} c^{2} + 2 \, {\left(3 \, B a b^{7} + 24 \, A a^{4} c^{4} - 2 \, {\left(62 \, B a^{4} b + 23 \, A a^{3} b^{2}\right)} c^{3} + 7 \, {\left(17 \, B a^{3} b^{3} + 2 \, A a^{2} b^{4}\right)} c^{2} - {\left(34 \, B a^{2} b^{5} + A a b^{6}\right)} c\right)} x^{2} + 2 \, {\left({\left(B b^{5} c^{2} - 10 \, B a b^{3} c^{3} + 30 \, B a^{2} b c^{4} - 12 \, A a^{2} c^{5}\right)} x^{8} + B a^{2} b^{5} - 10 \, B a^{3} b^{3} c + 30 \, B a^{4} b c^{2} - 12 \, A a^{4} c^{3} + 2 \, {\left(B b^{6} c - 10 \, B a b^{4} c^{2} + 30 \, B a^{2} b^{2} c^{3} - 12 \, A a^{2} b c^{4}\right)} x^{6} + {\left(B b^{7} - 8 \, B a b^{5} c + 10 \, B a^{2} b^{3} c^{2} - 24 \, A a^{3} c^{4} + 12 \, {\left(5 \, B a^{3} b - A a^{2} b^{2}\right)} c^{3}\right)} x^{4} + 2 \, {\left(B a b^{6} - 10 \, B a^{2} b^{4} c + 30 \, B a^{3} b^{2} c^{2} - 12 \, A a^{3} b c^{3}\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left(33 \, B a^{3} b^{4} + A a^{2} b^{5}\right)} c + {\left(B a^{2} b^{6} - 12 \, B a^{3} b^{4} c + 48 \, B a^{4} b^{2} c^{2} - 64 \, B a^{5} c^{3} + {\left(B b^{6} c^{2} - 12 \, B a b^{4} c^{3} + 48 \, B a^{2} b^{2} c^{4} - 64 \, B a^{3} c^{5}\right)} x^{8} + 2 \, {\left(B b^{7} c - 12 \, B a b^{5} c^{2} + 48 \, B a^{2} b^{3} c^{3} - 64 \, B a^{3} b c^{4}\right)} x^{6} + {\left(B b^{8} - 10 \, B a b^{6} c + 24 \, B a^{2} b^{4} c^{2} + 32 \, B a^{3} b^{2} c^{3} - 128 \, B a^{4} c^{4}\right)} x^{4} + 2 \, {\left(B a b^{7} - 12 \, B a^{2} b^{5} c + 48 \, B a^{3} b^{3} c^{2} - 64 \, B a^{4} b c^{3}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left(a^{2} b^{6} c^{3} - 12 \, a^{3} b^{4} c^{4} + 48 \, a^{4} b^{2} c^{5} - 64 \, a^{5} c^{6} + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} x^{8} + 2 \, {\left(b^{7} c^{4} - 12 \, a b^{5} c^{5} + 48 \, a^{2} b^{3} c^{6} - 64 \, a^{3} b c^{7}\right)} x^{6} + {\left(b^{8} c^{3} - 10 \, a b^{6} c^{4} + 24 \, a^{2} b^{4} c^{5} + 32 \, a^{3} b^{2} c^{6} - 128 \, a^{4} c^{7}\right)} x^{4} + 2 \, {\left(a b^{7} c^{3} - 12 \, a^{2} b^{5} c^{4} + 48 \, a^{3} b^{3} c^{5} - 64 \, a^{4} b c^{6}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(3*B*a^2*b^6 + 2*(2*B*b^7*c + 40*A*a^3*c^5 - 2*(50*B*a^3*b + 21*A*a^2*b^2)*c^4 + (85*B*a^2*b^3 + 12*A*a*b^4)*c^3 - (23*B*a*b^5 + A*b^6)*c^2)*x^6 + (3*B*b^8 - 8*(16*B*a^4 + A*a^3*b)*c^4 - 6*(2*B*a^3*b^2 + 5*A*a^2*b^3)*c^3 + 3*(29*B*a^2*b^4 + 4*A*a*b^5)*c^2 - (31*B*a*b^6 + A*b^7)*c)*x^4 - 8*(12*B*a^5 + 5*A*a^4*b)*c^3 + 2*(54*B*a^4*b^2 + 7*A*a^3*b^3)*c^2 + 2*(3*B*a*b^7 + 24*A*a^4*c^4 - 2*(62*B*a^4*b + 23*A*a^3*b^2)*c^3 + 7*(17*B*a^3*b^3 + 2*A*a^2*b^4)*c^2 - (34*B*a^2*b^5 + A*a*b^6)*c)*x^2 - ((B*b^5*c^2 - 10*B*a*b^3*c^3 + 30*B*a^2*b*c^4 - 12*A*a^2*c^5)*x^8 + B*a^2*b^5 - 10*B*a^3*b^3*c + 30*B*a^4*b*c^2 - 12*A*a^4*c^3 + 2*(B*b^6*c - 10*B*a*b^4*c^2 + 30*B*a^2*b^2*c^3 - 12*A*a^2*b*c^4)*x^6 + (B*b^7 - 8*B*a*b^5*c + 10*B*a^2*b^3*c^2 - 24*A*a^3*c^4 + 12*(5*B*a^3*b - A*a^2*b^2)*c^3)*x^4 + 2*(B*a*b^6 - 10*B*a^2*b^4*c + 30*B*a^3*b^2*c^2 - 12*A*a^3*b*c^3)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c - (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) - (33*B*a^3*b^4 + A*a^2*b^5)*c + (B*a^2*b^6 - 12*B*a^3*b^4*c + 48*B*a^4*b^2*c^2 - 64*B*a^5*c^3 + (B*b^6*c^2 - 12*B*a*b^4*c^3 + 48*B*a^2*b^2*c^4 - 64*B*a^3*c^5)*x^8 + 2*(B*b^7*c - 12*B*a*b^5*c^2 + 48*B*a^2*b^3*c^3 - 64*B*a^3*b*c^4)*x^6 + (B*b^8 - 10*B*a*b^6*c + 24*B*a^2*b^4*c^2 + 32*B*a^3*b^2*c^3 - 128*B*a^4*c^4)*x^4 + 2*(B*a*b^7 - 12*B*a^2*b^5*c + 48*B*a^3*b^3*c^2 - 64*B*a^4*b*c^3)*x^2)*log(c*x^4 + b*x^2 + a))/(a^2*b^6*c^3 - 12*a^3*b^4*c^4 + 48*a^4*b^2*c^5 - 64*a^5*c^6 + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*x^8 + 2*(b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*x^6 + (b^8*c^3 - 10*a*b^6*c^4 + 24*a^2*b^4*c^5 + 32*a^3*b^2*c^6 - 128*a^4*c^7)*x^4 + 2*(a*b^7*c^3 - 12*a^2*b^5*c^4 + 48*a^3*b^3*c^5 - 64*a^4*b*c^6)*x^2), 1/4*(3*B*a^2*b^6 + 2*(2*B*b^7*c + 40*A*a^3*c^5 - 2*(50*B*a^3*b + 21*A*a^2*b^2)*c^4 + (85*B*a^2*b^3 + 12*A*a*b^4)*c^3 - (23*B*a*b^5 + A*b^6)*c^2)*x^6 + (3*B*b^8 - 8*(16*B*a^4 + A*a^3*b)*c^4 - 6*(2*B*a^3*b^2 + 5*A*a^2*b^3)*c^3 + 3*(29*B*a^2*b^4 + 4*A*a*b^5)*c^2 - (31*B*a*b^6 + A*b^7)*c)*x^4 - 8*(12*B*a^5 + 5*A*a^4*b)*c^3 + 2*(54*B*a^4*b^2 + 7*A*a^3*b^3)*c^2 + 2*(3*B*a*b^7 + 24*A*a^4*c^4 - 2*(62*B*a^4*b + 23*A*a^3*b^2)*c^3 + 7*(17*B*a^3*b^3 + 2*A*a^2*b^4)*c^2 - (34*B*a^2*b^5 + A*a*b^6)*c)*x^2 + 2*((B*b^5*c^2 - 10*B*a*b^3*c^3 + 30*B*a^2*b*c^4 - 12*A*a^2*c^5)*x^8 + B*a^2*b^5 - 10*B*a^3*b^3*c + 30*B*a^4*b*c^2 - 12*A*a^4*c^3 + 2*(B*b^6*c - 10*B*a*b^4*c^2 + 30*B*a^2*b^2*c^3 - 12*A*a^2*b*c^4)*x^6 + (B*b^7 - 8*B*a*b^5*c + 10*B*a^2*b^3*c^2 - 24*A*a^3*c^4 + 12*(5*B*a^3*b - A*a^2*b^2)*c^3)*x^4 + 2*(B*a*b^6 - 10*B*a^2*b^4*c + 30*B*a^3*b^2*c^2 - 12*A*a^3*b*c^3)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - (33*B*a^3*b^4 + A*a^2*b^5)*c + (B*a^2*b^6 - 12*B*a^3*b^4*c + 48*B*a^4*b^2*c^2 - 64*B*a^5*c^3 + (B*b^6*c^2 - 12*B*a*b^4*c^3 + 48*B*a^2*b^2*c^4 - 64*B*a^3*c^5)*x^8 + 2*(B*b^7*c - 12*B*a*b^5*c^2 + 48*B*a^2*b^3*c^3 - 64*B*a^3*b*c^4)*x^6 + (B*b^8 - 10*B*a*b^6*c + 24*B*a^2*b^4*c^2 + 32*B*a^3*b^2*c^3 - 128*B*a^4*c^4)*x^4 + 2*(B*a*b^7 - 12*B*a^2*b^5*c + 48*B*a^3*b^3*c^2 - 64*B*a^4*b*c^3)*x^2)*log(c*x^4 + b*x^2 + a))/(a^2*b^6*c^3 - 12*a^3*b^4*c^4 + 48*a^4*b^2*c^5 - 64*a^5*c^6 + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*x^8 + 2*(b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*x^6 + (b^8*c^3 - 10*a*b^6*c^4 + 24*a^2*b^4*c^5 + 32*a^3*b^2*c^6 - 128*a^4*c^7)*x^4 + 2*(a*b^7*c^3 - 12*a^2*b^5*c^4 + 48*a^3*b^3*c^5 - 64*a^4*b*c^6)*x^2)]","B",0
126,1,1378,0,0.947808," ","integrate(x^7*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{B a^{2} b^{5} - 32 \, A a^{4} c^{3} + 2 \, {\left(B b^{6} c - 12 \, B a b^{4} c^{2} - 4 \, {\left(10 \, B a^{3} + 3 \, A a^{2} b\right)} c^{4} + 3 \, {\left(14 \, B a^{2} b^{2} + A a b^{3}\right)} c^{3}\right)} x^{6} + {\left(B b^{7} - 64 \, A a^{3} c^{4} + 4 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} c^{3} + 3 \, {\left(10 \, B a^{2} b^{3} - A a b^{4}\right)} c^{2} - {\left(12 \, B a b^{5} - A b^{6}\right)} c\right)} x^{4} + 4 \, {\left(10 \, B a^{4} b + A a^{3} b^{2}\right)} c^{2} + 2 \, {\left(B a b^{6} - 4 \, {\left(6 \, B a^{4} + 5 \, A a^{3} b\right)} c^{3} + {\left(46 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} c^{2} - {\left(14 \, B a^{2} b^{4} - A a b^{5}\right)} c\right)} x^{2} + 6 \, {\left({\left(2 \, B a^{2} - A a b\right)} c^{4} x^{8} + 2 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} c^{3} x^{6} + 2 \, {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} c^{2} x^{2} + {\left(2 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{3} + {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c^{2}\right)} x^{4} + {\left(2 \, B a^{4} - A a^{3} b\right)} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) - {\left(14 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} c}{4 \, {\left(a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5} + {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} x^{8} + 2 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} x^{6} + {\left(b^{8} c^{2} - 10 \, a b^{6} c^{3} + 24 \, a^{2} b^{4} c^{4} + 32 \, a^{3} b^{2} c^{5} - 128 \, a^{4} c^{6}\right)} x^{4} + 2 \, {\left(a b^{7} c^{2} - 12 \, a^{2} b^{5} c^{3} + 48 \, a^{3} b^{3} c^{4} - 64 \, a^{4} b c^{5}\right)} x^{2}\right)}}, -\frac{B a^{2} b^{5} - 32 \, A a^{4} c^{3} + 2 \, {\left(B b^{6} c - 12 \, B a b^{4} c^{2} - 4 \, {\left(10 \, B a^{3} + 3 \, A a^{2} b\right)} c^{4} + 3 \, {\left(14 \, B a^{2} b^{2} + A a b^{3}\right)} c^{3}\right)} x^{6} + {\left(B b^{7} - 64 \, A a^{3} c^{4} + 4 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} c^{3} + 3 \, {\left(10 \, B a^{2} b^{3} - A a b^{4}\right)} c^{2} - {\left(12 \, B a b^{5} - A b^{6}\right)} c\right)} x^{4} + 4 \, {\left(10 \, B a^{4} b + A a^{3} b^{2}\right)} c^{2} + 2 \, {\left(B a b^{6} - 4 \, {\left(6 \, B a^{4} + 5 \, A a^{3} b\right)} c^{3} + {\left(46 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} c^{2} - {\left(14 \, B a^{2} b^{4} - A a b^{5}\right)} c\right)} x^{2} + 12 \, {\left({\left(2 \, B a^{2} - A a b\right)} c^{4} x^{8} + 2 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} c^{3} x^{6} + 2 \, {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} c^{2} x^{2} + {\left(2 \, {\left(2 \, B a^{3} - A a^{2} b\right)} c^{3} + {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} c^{2}\right)} x^{4} + {\left(2 \, B a^{4} - A a^{3} b\right)} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left(14 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} c}{4 \, {\left(a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5} + {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} x^{8} + 2 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} x^{6} + {\left(b^{8} c^{2} - 10 \, a b^{6} c^{3} + 24 \, a^{2} b^{4} c^{4} + 32 \, a^{3} b^{2} c^{5} - 128 \, a^{4} c^{6}\right)} x^{4} + 2 \, {\left(a b^{7} c^{2} - 12 \, a^{2} b^{5} c^{3} + 48 \, a^{3} b^{3} c^{4} - 64 \, a^{4} b c^{5}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(B*a^2*b^5 - 32*A*a^4*c^3 + 2*(B*b^6*c - 12*B*a*b^4*c^2 - 4*(10*B*a^3 + 3*A*a^2*b)*c^4 + 3*(14*B*a^2*b^2 + A*a*b^3)*c^3)*x^6 + (B*b^7 - 64*A*a^3*c^4 + 4*(2*B*a^3*b + 3*A*a^2*b^2)*c^3 + 3*(10*B*a^2*b^3 - A*a*b^4)*c^2 - (12*B*a*b^5 - A*b^6)*c)*x^4 + 4*(10*B*a^4*b + A*a^3*b^2)*c^2 + 2*(B*a*b^6 - 4*(6*B*a^4 + 5*A*a^3*b)*c^3 + (46*B*a^3*b^2 + A*a^2*b^3)*c^2 - (14*B*a^2*b^4 - A*a*b^5)*c)*x^2 + 6*((2*B*a^2 - A*a*b)*c^4*x^8 + 2*(2*B*a^2*b - A*a*b^2)*c^3*x^6 + 2*(2*B*a^3*b - A*a^2*b^2)*c^2*x^2 + (2*(2*B*a^3 - A*a^2*b)*c^3 + (2*B*a^2*b^2 - A*a*b^3)*c^2)*x^4 + (2*B*a^4 - A*a^3*b)*c^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) - (14*B*a^3*b^3 - A*a^2*b^4)*c)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5 + (b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*x^8 + 2*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*x^6 + (b^8*c^2 - 10*a*b^6*c^3 + 24*a^2*b^4*c^4 + 32*a^3*b^2*c^5 - 128*a^4*c^6)*x^4 + 2*(a*b^7*c^2 - 12*a^2*b^5*c^3 + 48*a^3*b^3*c^4 - 64*a^4*b*c^5)*x^2), -1/4*(B*a^2*b^5 - 32*A*a^4*c^3 + 2*(B*b^6*c - 12*B*a*b^4*c^2 - 4*(10*B*a^3 + 3*A*a^2*b)*c^4 + 3*(14*B*a^2*b^2 + A*a*b^3)*c^3)*x^6 + (B*b^7 - 64*A*a^3*c^4 + 4*(2*B*a^3*b + 3*A*a^2*b^2)*c^3 + 3*(10*B*a^2*b^3 - A*a*b^4)*c^2 - (12*B*a*b^5 - A*b^6)*c)*x^4 + 4*(10*B*a^4*b + A*a^3*b^2)*c^2 + 2*(B*a*b^6 - 4*(6*B*a^4 + 5*A*a^3*b)*c^3 + (46*B*a^3*b^2 + A*a^2*b^3)*c^2 - (14*B*a^2*b^4 - A*a*b^5)*c)*x^2 + 12*((2*B*a^2 - A*a*b)*c^4*x^8 + 2*(2*B*a^2*b - A*a*b^2)*c^3*x^6 + 2*(2*B*a^3*b - A*a^2*b^2)*c^2*x^2 + (2*(2*B*a^3 - A*a^2*b)*c^3 + (2*B*a^2*b^2 - A*a*b^3)*c^2)*x^4 + (2*B*a^4 - A*a^3*b)*c^2)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - (14*B*a^3*b^3 - A*a^2*b^4)*c)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5 + (b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*x^8 + 2*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*x^6 + (b^8*c^2 - 10*a*b^6*c^3 + 24*a^2*b^4*c^4 + 32*a^3*b^2*c^5 - 128*a^4*c^6)*x^4 + 2*(a*b^7*c^2 - 12*a^2*b^5*c^3 + 48*a^3*b^3*c^4 - 64*a^4*b*c^5)*x^2)]","B",0
127,1,1369,0,0.953101," ","integrate(x^5*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{B a^{2} b^{4} + 2 \, {\left(8 \, A a^{2} c^{4} - 2 \, {\left(6 \, B a^{2} b - A a b^{2}\right)} c^{3} + {\left(3 \, B a b^{3} - A b^{4}\right)} c^{2}\right)} x^{6} + {\left(B b^{6} - 8 \, {\left(8 \, B a^{3} - 3 \, A a^{2} b\right)} c^{3} + 6 \, {\left(2 \, B a^{2} b^{2} + A a b^{3}\right)} c^{2} - 3 \, {\left(B a b^{4} + A b^{5}\right)} c\right)} x^{4} - 8 \, {\left(4 \, B a^{4} - 3 \, A a^{3} b\right)} c^{2} + 2 \, {\left(B a b^{5} - 8 \, A a^{3} c^{3} - 2 \, {\left(10 \, B a^{3} b - 11 \, A a^{2} b^{2}\right)} c^{2} + {\left(B a^{2} b^{3} - 5 \, A a b^{4}\right)} c\right)} x^{2} - 2 \, {\left({\left(2 \, A a c^{4} - {\left(3 \, B a b - A b^{2}\right)} c^{3}\right)} x^{8} + 2 \, {\left(2 \, A a b c^{3} - {\left(3 \, B a b^{2} - A b^{3}\right)} c^{2}\right)} x^{6} + 2 \, A a^{3} c^{2} + {\left(4 \, A a^{2} c^{3} - 2 \, {\left(3 \, B a^{2} b - 2 \, A a b^{2}\right)} c^{2} - {\left(3 \, B a b^{3} - A b^{4}\right)} c\right)} x^{4} + 2 \, {\left(2 \, A a^{2} b c^{2} - {\left(3 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} x^{2} - {\left(3 \, B a^{3} b - A a^{2} b^{2}\right)} c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c - {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) + 2 \, {\left(2 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c}{4 \, {\left(a^{2} b^{6} c - 12 \, a^{3} b^{4} c^{2} + 48 \, a^{4} b^{2} c^{3} - 64 \, a^{5} c^{4} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} x^{8} + 2 \, {\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} x^{6} + {\left(b^{8} c - 10 \, a b^{6} c^{2} + 24 \, a^{2} b^{4} c^{3} + 32 \, a^{3} b^{2} c^{4} - 128 \, a^{4} c^{5}\right)} x^{4} + 2 \, {\left(a b^{7} c - 12 \, a^{2} b^{5} c^{2} + 48 \, a^{3} b^{3} c^{3} - 64 \, a^{4} b c^{4}\right)} x^{2}\right)}}, -\frac{B a^{2} b^{4} + 2 \, {\left(8 \, A a^{2} c^{4} - 2 \, {\left(6 \, B a^{2} b - A a b^{2}\right)} c^{3} + {\left(3 \, B a b^{3} - A b^{4}\right)} c^{2}\right)} x^{6} + {\left(B b^{6} - 8 \, {\left(8 \, B a^{3} - 3 \, A a^{2} b\right)} c^{3} + 6 \, {\left(2 \, B a^{2} b^{2} + A a b^{3}\right)} c^{2} - 3 \, {\left(B a b^{4} + A b^{5}\right)} c\right)} x^{4} - 8 \, {\left(4 \, B a^{4} - 3 \, A a^{3} b\right)} c^{2} + 2 \, {\left(B a b^{5} - 8 \, A a^{3} c^{3} - 2 \, {\left(10 \, B a^{3} b - 11 \, A a^{2} b^{2}\right)} c^{2} + {\left(B a^{2} b^{3} - 5 \, A a b^{4}\right)} c\right)} x^{2} + 4 \, {\left({\left(2 \, A a c^{4} - {\left(3 \, B a b - A b^{2}\right)} c^{3}\right)} x^{8} + 2 \, {\left(2 \, A a b c^{3} - {\left(3 \, B a b^{2} - A b^{3}\right)} c^{2}\right)} x^{6} + 2 \, A a^{3} c^{2} + {\left(4 \, A a^{2} c^{3} - 2 \, {\left(3 \, B a^{2} b - 2 \, A a b^{2}\right)} c^{2} - {\left(3 \, B a b^{3} - A b^{4}\right)} c\right)} x^{4} + 2 \, {\left(2 \, A a^{2} b c^{2} - {\left(3 \, B a^{2} b^{2} - A a b^{3}\right)} c\right)} x^{2} - {\left(3 \, B a^{3} b - A a^{2} b^{2}\right)} c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(2 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c}{4 \, {\left(a^{2} b^{6} c - 12 \, a^{3} b^{4} c^{2} + 48 \, a^{4} b^{2} c^{3} - 64 \, a^{5} c^{4} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} x^{8} + 2 \, {\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} x^{6} + {\left(b^{8} c - 10 \, a b^{6} c^{2} + 24 \, a^{2} b^{4} c^{3} + 32 \, a^{3} b^{2} c^{4} - 128 \, a^{4} c^{5}\right)} x^{4} + 2 \, {\left(a b^{7} c - 12 \, a^{2} b^{5} c^{2} + 48 \, a^{3} b^{3} c^{3} - 64 \, a^{4} b c^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(B*a^2*b^4 + 2*(8*A*a^2*c^4 - 2*(6*B*a^2*b - A*a*b^2)*c^3 + (3*B*a*b^3 - A*b^4)*c^2)*x^6 + (B*b^6 - 8*(8*B*a^3 - 3*A*a^2*b)*c^3 + 6*(2*B*a^2*b^2 + A*a*b^3)*c^2 - 3*(B*a*b^4 + A*b^5)*c)*x^4 - 8*(4*B*a^4 - 3*A*a^3*b)*c^2 + 2*(B*a*b^5 - 8*A*a^3*c^3 - 2*(10*B*a^3*b - 11*A*a^2*b^2)*c^2 + (B*a^2*b^3 - 5*A*a*b^4)*c)*x^2 - 2*((2*A*a*c^4 - (3*B*a*b - A*b^2)*c^3)*x^8 + 2*(2*A*a*b*c^3 - (3*B*a*b^2 - A*b^3)*c^2)*x^6 + 2*A*a^3*c^2 + (4*A*a^2*c^3 - 2*(3*B*a^2*b - 2*A*a*b^2)*c^2 - (3*B*a*b^3 - A*b^4)*c)*x^4 + 2*(2*A*a^2*b*c^2 - (3*B*a^2*b^2 - A*a*b^3)*c)*x^2 - (3*B*a^3*b - A*a^2*b^2)*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c - (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) + 2*(2*B*a^3*b^2 - 3*A*a^2*b^3)*c)/(a^2*b^6*c - 12*a^3*b^4*c^2 + 48*a^4*b^2*c^3 - 64*a^5*c^4 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*x^8 + 2*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^6 + (b^8*c - 10*a*b^6*c^2 + 24*a^2*b^4*c^3 + 32*a^3*b^2*c^4 - 128*a^4*c^5)*x^4 + 2*(a*b^7*c - 12*a^2*b^5*c^2 + 48*a^3*b^3*c^3 - 64*a^4*b*c^4)*x^2), -1/4*(B*a^2*b^4 + 2*(8*A*a^2*c^4 - 2*(6*B*a^2*b - A*a*b^2)*c^3 + (3*B*a*b^3 - A*b^4)*c^2)*x^6 + (B*b^6 - 8*(8*B*a^3 - 3*A*a^2*b)*c^3 + 6*(2*B*a^2*b^2 + A*a*b^3)*c^2 - 3*(B*a*b^4 + A*b^5)*c)*x^4 - 8*(4*B*a^4 - 3*A*a^3*b)*c^2 + 2*(B*a*b^5 - 8*A*a^3*c^3 - 2*(10*B*a^3*b - 11*A*a^2*b^2)*c^2 + (B*a^2*b^3 - 5*A*a*b^4)*c)*x^2 + 4*((2*A*a*c^4 - (3*B*a*b - A*b^2)*c^3)*x^8 + 2*(2*A*a*b*c^3 - (3*B*a*b^2 - A*b^3)*c^2)*x^6 + 2*A*a^3*c^2 + (4*A*a^2*c^3 - 2*(3*B*a^2*b - 2*A*a*b^2)*c^2 - (3*B*a*b^3 - A*b^4)*c)*x^4 + 2*(2*A*a^2*b*c^2 - (3*B*a^2*b^2 - A*a*b^3)*c)*x^2 - (3*B*a^3*b - A*a^2*b^2)*c)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) + 2*(2*B*a^3*b^2 - 3*A*a^2*b^3)*c)/(a^2*b^6*c - 12*a^3*b^4*c^2 + 48*a^4*b^2*c^3 - 64*a^5*c^4 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*x^8 + 2*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^6 + (b^8*c - 10*a*b^6*c^2 + 24*a^2*b^4*c^3 + 32*a^3*b^2*c^4 - 128*a^4*c^5)*x^4 + 2*(a*b^7*c - 12*a^2*b^5*c^2 + 48*a^3*b^3*c^3 - 64*a^4*b*c^4)*x^2)]","B",0
128,1,1226,0,0.928375," ","integrate(x^3*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(B b^{4} c - 4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c^{3} - {\left(2 \, B a b^{2} + 3 \, A b^{3}\right)} c^{2}\right)} x^{6} + 6 \, B a^{2} b^{3} - A a b^{4} + 32 \, A a^{3} c^{2} + 3 \, {\left(B b^{5} - 4 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c^{2} - {\left(2 \, B a b^{3} + 3 \, A b^{4}\right)} c\right)} x^{4} + 2 \, {\left(5 \, B a b^{4} - A b^{5} + 4 \, {\left(2 \, B a^{3} + 5 \, A a^{2} b\right)} c^{2} - {\left(22 \, B a^{2} b^{2} + A a b^{3}\right)} c\right)} x^{2} - 2 \, {\left({\left(B b^{2} c^{2} + {\left(2 \, B a - 3 \, A b\right)} c^{3}\right)} x^{8} + 2 \, {\left(B b^{3} c + {\left(2 \, B a b - 3 \, A b^{2}\right)} c^{2}\right)} x^{6} + B a^{2} b^{2} + {\left(B b^{4} + 2 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c^{2} + {\left(4 \, B a b^{2} - 3 \, A b^{3}\right)} c\right)} x^{4} + 2 \, {\left(B a b^{3} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c\right)} x^{2} + {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) - 4 \, {\left(6 \, B a^{3} b + A a^{2} b^{2}\right)} c}{4 \, {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{8} + a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} x^{6} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x^{2}\right)}}, \frac{2 \, {\left(B b^{4} c - 4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c^{3} - {\left(2 \, B a b^{2} + 3 \, A b^{3}\right)} c^{2}\right)} x^{6} + 6 \, B a^{2} b^{3} - A a b^{4} + 32 \, A a^{3} c^{2} + 3 \, {\left(B b^{5} - 4 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c^{2} - {\left(2 \, B a b^{3} + 3 \, A b^{4}\right)} c\right)} x^{4} + 2 \, {\left(5 \, B a b^{4} - A b^{5} + 4 \, {\left(2 \, B a^{3} + 5 \, A a^{2} b\right)} c^{2} - {\left(22 \, B a^{2} b^{2} + A a b^{3}\right)} c\right)} x^{2} - 4 \, {\left({\left(B b^{2} c^{2} + {\left(2 \, B a - 3 \, A b\right)} c^{3}\right)} x^{8} + 2 \, {\left(B b^{3} c + {\left(2 \, B a b - 3 \, A b^{2}\right)} c^{2}\right)} x^{6} + B a^{2} b^{2} + {\left(B b^{4} + 2 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c^{2} + {\left(4 \, B a b^{2} - 3 \, A b^{3}\right)} c\right)} x^{4} + 2 \, {\left(B a b^{3} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} c\right)} x^{2} + {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - 4 \, {\left(6 \, B a^{3} b + A a^{2} b^{2}\right)} c}{4 \, {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{8} + a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} x^{6} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(2*(B*b^4*c - 4*(2*B*a^2 - 3*A*a*b)*c^3 - (2*B*a*b^2 + 3*A*b^3)*c^2)*x^6 + 6*B*a^2*b^3 - A*a*b^4 + 32*A*a^3*c^2 + 3*(B*b^5 - 4*(2*B*a^2*b - 3*A*a*b^2)*c^2 - (2*B*a*b^3 + 3*A*b^4)*c)*x^4 + 2*(5*B*a*b^4 - A*b^5 + 4*(2*B*a^3 + 5*A*a^2*b)*c^2 - (22*B*a^2*b^2 + A*a*b^3)*c)*x^2 - 2*((B*b^2*c^2 + (2*B*a - 3*A*b)*c^3)*x^8 + 2*(B*b^3*c + (2*B*a*b - 3*A*b^2)*c^2)*x^6 + B*a^2*b^2 + (B*b^4 + 2*(2*B*a^2 - 3*A*a*b)*c^2 + (4*B*a*b^2 - 3*A*b^3)*c)*x^4 + 2*(B*a*b^3 + (2*B*a^2*b - 3*A*a*b^2)*c)*x^2 + (2*B*a^3 - 3*A*a^2*b)*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) - 4*(6*B*a^3*b + A*a^2*b^2)*c)/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^8 + a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^6 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x^2), 1/4*(2*(B*b^4*c - 4*(2*B*a^2 - 3*A*a*b)*c^3 - (2*B*a*b^2 + 3*A*b^3)*c^2)*x^6 + 6*B*a^2*b^3 - A*a*b^4 + 32*A*a^3*c^2 + 3*(B*b^5 - 4*(2*B*a^2*b - 3*A*a*b^2)*c^2 - (2*B*a*b^3 + 3*A*b^4)*c)*x^4 + 2*(5*B*a*b^4 - A*b^5 + 4*(2*B*a^3 + 5*A*a^2*b)*c^2 - (22*B*a^2*b^2 + A*a*b^3)*c)*x^2 - 4*((B*b^2*c^2 + (2*B*a - 3*A*b)*c^3)*x^8 + 2*(B*b^3*c + (2*B*a*b - 3*A*b^2)*c^2)*x^6 + B*a^2*b^2 + (B*b^4 + 2*(2*B*a^2 - 3*A*a*b)*c^2 + (4*B*a*b^2 - 3*A*b^3)*c)*x^4 + 2*(B*a*b^3 + (2*B*a^2*b - 3*A*a*b^2)*c)*x^2 + (2*B*a^3 - 3*A*a^2*b)*c)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - 4*(6*B*a^3*b + A*a^2*b^2)*c)/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^8 + a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^6 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x^2)]","B",0
129,1,1109,0,0.687665," ","integrate(x*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(B b^{3} c^{2} + 8 \, A a c^{4} - 2 \, {\left(2 \, B a b + A b^{2}\right)} c^{3}\right)} x^{6} + B a b^{4} + A b^{5} + 9 \, {\left(B b^{4} c + 8 \, A a b c^{3} - 2 \, {\left(2 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} x^{4} - 8 \, {\left(4 \, B a^{3} - 5 \, A a^{2} b\right)} c^{2} + 2 \, {\left(B b^{5} + 40 \, A a^{2} c^{3} - 2 \, {\left(10 \, B a^{2} b + A a b^{2}\right)} c^{2} + {\left(B a b^{3} - 2 \, A b^{4}\right)} c\right)} x^{2} + 6 \, {\left({\left(B b c^{3} - 2 \, A c^{4}\right)} x^{8} + 2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} x^{6} + B a^{2} b c - 2 \, A a^{2} c^{2} + {\left(B b^{3} c - 4 \, A a c^{3} + 2 \, {\left(B a b - A b^{2}\right)} c^{2}\right)} x^{4} + 2 \, {\left(B a b^{2} c - 2 \, A a b c^{2}\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c - {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) + 2 \, {\left(2 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} c}{4 \, {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{8} + a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} x^{6} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x^{2}\right)}}, -\frac{6 \, {\left(B b^{3} c^{2} + 8 \, A a c^{4} - 2 \, {\left(2 \, B a b + A b^{2}\right)} c^{3}\right)} x^{6} + B a b^{4} + A b^{5} + 9 \, {\left(B b^{4} c + 8 \, A a b c^{3} - 2 \, {\left(2 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} x^{4} - 8 \, {\left(4 \, B a^{3} - 5 \, A a^{2} b\right)} c^{2} + 2 \, {\left(B b^{5} + 40 \, A a^{2} c^{3} - 2 \, {\left(10 \, B a^{2} b + A a b^{2}\right)} c^{2} + {\left(B a b^{3} - 2 \, A b^{4}\right)} c\right)} x^{2} - 12 \, {\left({\left(B b c^{3} - 2 \, A c^{4}\right)} x^{8} + 2 \, {\left(B b^{2} c^{2} - 2 \, A b c^{3}\right)} x^{6} + B a^{2} b c - 2 \, A a^{2} c^{2} + {\left(B b^{3} c - 4 \, A a c^{3} + 2 \, {\left(B a b - A b^{2}\right)} c^{2}\right)} x^{4} + 2 \, {\left(B a b^{2} c - 2 \, A a b c^{2}\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(2 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} c}{4 \, {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{8} + a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} x^{6} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{4} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(6*(B*b^3*c^2 + 8*A*a*c^4 - 2*(2*B*a*b + A*b^2)*c^3)*x^6 + B*a*b^4 + A*b^5 + 9*(B*b^4*c + 8*A*a*b*c^3 - 2*(2*B*a*b^2 + A*b^3)*c^2)*x^4 - 8*(4*B*a^3 - 5*A*a^2*b)*c^2 + 2*(B*b^5 + 40*A*a^2*c^3 - 2*(10*B*a^2*b + A*a*b^2)*c^2 + (B*a*b^3 - 2*A*b^4)*c)*x^2 + 6*((B*b*c^3 - 2*A*c^4)*x^8 + 2*(B*b^2*c^2 - 2*A*b*c^3)*x^6 + B*a^2*b*c - 2*A*a^2*c^2 + (B*b^3*c - 4*A*a*c^3 + 2*(B*a*b - A*b^2)*c^2)*x^4 + 2*(B*a*b^2*c - 2*A*a*b*c^2)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c - (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) + 2*(2*B*a^2*b^2 - 7*A*a*b^3)*c)/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^8 + a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^6 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x^2), -1/4*(6*(B*b^3*c^2 + 8*A*a*c^4 - 2*(2*B*a*b + A*b^2)*c^3)*x^6 + B*a*b^4 + A*b^5 + 9*(B*b^4*c + 8*A*a*b*c^3 - 2*(2*B*a*b^2 + A*b^3)*c^2)*x^4 - 8*(4*B*a^3 - 5*A*a^2*b)*c^2 + 2*(B*b^5 + 40*A*a^2*c^3 - 2*(10*B*a^2*b + A*a*b^2)*c^2 + (B*a*b^3 - 2*A*b^4)*c)*x^2 - 12*((B*b*c^3 - 2*A*c^4)*x^8 + 2*(B*b^2*c^2 - 2*A*b*c^3)*x^6 + B*a^2*b*c - 2*A*a^2*c^2 + (B*b^3*c - 4*A*a*c^3 + 2*(B*a*b - A*b^2)*c^2)*x^4 + 2*(B*a*b^2*c - 2*A*a*b*c^2)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) + 2*(2*B*a^2*b^2 - 7*A*a*b^3)*c)/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^8 + a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^6 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x^2)]","B",0
130,1,2494,0,7.447554," ","integrate((B*x^2+A)/x/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{B a^{3} b^{5} - 3 \, A a^{2} b^{6} + 96 \, A a^{5} c^{3} - 2 \, {\left(A a b^{5} c^{2} - 4 \, {\left(6 \, B a^{4} - 7 \, A a^{3} b\right)} c^{4} + {\left(6 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} c^{3}\right)} x^{6} - {\left(4 \, A a b^{6} c - 64 \, A a^{4} c^{4} - 12 \, {\left(6 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} c^{3} + 9 \, {\left(2 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} c^{2}\right)} x^{4} + 4 \, {\left(10 \, B a^{5} b - 27 \, A a^{4} b^{2}\right)} c^{2} - 2 \, {\left(A a b^{7} - 4 \, {\left(10 \, B a^{5} - A a^{4} b\right)} c^{3} + {\left(2 \, B a^{4} b^{2} + 23 \, A a^{3} b^{3}\right)} c^{2} + 2 \, {\left(B a^{3} b^{4} - 5 \, A a^{2} b^{5}\right)} c\right)} x^{2} - {\left({\left(A b^{5} c^{2} - 10 \, A a b^{3} c^{3} - 6 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c^{4}\right)} x^{8} + A a^{2} b^{5} - 10 \, A a^{3} b^{3} c + 2 \, {\left(A b^{6} c - 10 \, A a b^{4} c^{2} - 6 \, {\left(2 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} c^{3}\right)} x^{6} + {\left(A b^{7} - 8 \, A a b^{5} c - 12 \, {\left(2 \, B a^{4} - 5 \, A a^{3} b\right)} c^{3} - 2 \, {\left(6 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} c^{2}\right)} x^{4} - 6 \, {\left(2 \, B a^{5} - 5 \, A a^{4} b\right)} c^{2} + 2 \, {\left(A a b^{6} - 10 \, A a^{2} b^{4} c - 6 \, {\left(2 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} c^{2}\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) - {\left(14 \, B a^{4} b^{3} - 33 \, A a^{3} b^{4}\right)} c + {\left(A a^{2} b^{6} - 12 \, A a^{3} b^{4} c + 48 \, A a^{4} b^{2} c^{2} - 64 \, A a^{5} c^{3} + {\left(A b^{6} c^{2} - 12 \, A a b^{4} c^{3} + 48 \, A a^{2} b^{2} c^{4} - 64 \, A a^{3} c^{5}\right)} x^{8} + 2 \, {\left(A b^{7} c - 12 \, A a b^{5} c^{2} + 48 \, A a^{2} b^{3} c^{3} - 64 \, A a^{3} b c^{4}\right)} x^{6} + {\left(A b^{8} - 10 \, A a b^{6} c + 24 \, A a^{2} b^{4} c^{2} + 32 \, A a^{3} b^{2} c^{3} - 128 \, A a^{4} c^{4}\right)} x^{4} + 2 \, {\left(A a b^{7} - 12 \, A a^{2} b^{5} c + 48 \, A a^{3} b^{3} c^{2} - 64 \, A a^{4} b c^{3}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right) - 4 \, {\left(A a^{2} b^{6} - 12 \, A a^{3} b^{4} c + 48 \, A a^{4} b^{2} c^{2} - 64 \, A a^{5} c^{3} + {\left(A b^{6} c^{2} - 12 \, A a b^{4} c^{3} + 48 \, A a^{2} b^{2} c^{4} - 64 \, A a^{3} c^{5}\right)} x^{8} + 2 \, {\left(A b^{7} c - 12 \, A a b^{5} c^{2} + 48 \, A a^{2} b^{3} c^{3} - 64 \, A a^{3} b c^{4}\right)} x^{6} + {\left(A b^{8} - 10 \, A a b^{6} c + 24 \, A a^{2} b^{4} c^{2} + 32 \, A a^{3} b^{2} c^{3} - 128 \, A a^{4} c^{4}\right)} x^{4} + 2 \, {\left(A a b^{7} - 12 \, A a^{2} b^{5} c + 48 \, A a^{3} b^{3} c^{2} - 64 \, A a^{4} b c^{3}\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3} + {\left(a^{3} b^{6} c^{2} - 12 \, a^{4} b^{4} c^{3} + 48 \, a^{5} b^{2} c^{4} - 64 \, a^{6} c^{5}\right)} x^{8} + 2 \, {\left(a^{3} b^{7} c - 12 \, a^{4} b^{5} c^{2} + 48 \, a^{5} b^{3} c^{3} - 64 \, a^{6} b c^{4}\right)} x^{6} + {\left(a^{3} b^{8} - 10 \, a^{4} b^{6} c + 24 \, a^{5} b^{4} c^{2} + 32 \, a^{6} b^{2} c^{3} - 128 \, a^{7} c^{4}\right)} x^{4} + 2 \, {\left(a^{4} b^{7} - 12 \, a^{5} b^{5} c + 48 \, a^{6} b^{3} c^{2} - 64 \, a^{7} b c^{3}\right)} x^{2}\right)}}, -\frac{B a^{3} b^{5} - 3 \, A a^{2} b^{6} + 96 \, A a^{5} c^{3} - 2 \, {\left(A a b^{5} c^{2} - 4 \, {\left(6 \, B a^{4} - 7 \, A a^{3} b\right)} c^{4} + {\left(6 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} c^{3}\right)} x^{6} - {\left(4 \, A a b^{6} c - 64 \, A a^{4} c^{4} - 12 \, {\left(6 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} c^{3} + 9 \, {\left(2 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} c^{2}\right)} x^{4} + 4 \, {\left(10 \, B a^{5} b - 27 \, A a^{4} b^{2}\right)} c^{2} - 2 \, {\left(A a b^{7} - 4 \, {\left(10 \, B a^{5} - A a^{4} b\right)} c^{3} + {\left(2 \, B a^{4} b^{2} + 23 \, A a^{3} b^{3}\right)} c^{2} + 2 \, {\left(B a^{3} b^{4} - 5 \, A a^{2} b^{5}\right)} c\right)} x^{2} - 2 \, {\left({\left(A b^{5} c^{2} - 10 \, A a b^{3} c^{3} - 6 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} c^{4}\right)} x^{8} + A a^{2} b^{5} - 10 \, A a^{3} b^{3} c + 2 \, {\left(A b^{6} c - 10 \, A a b^{4} c^{2} - 6 \, {\left(2 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} c^{3}\right)} x^{6} + {\left(A b^{7} - 8 \, A a b^{5} c - 12 \, {\left(2 \, B a^{4} - 5 \, A a^{3} b\right)} c^{3} - 2 \, {\left(6 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} c^{2}\right)} x^{4} - 6 \, {\left(2 \, B a^{5} - 5 \, A a^{4} b\right)} c^{2} + 2 \, {\left(A a b^{6} - 10 \, A a^{2} b^{4} c - 6 \, {\left(2 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} c^{2}\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left(14 \, B a^{4} b^{3} - 33 \, A a^{3} b^{4}\right)} c + {\left(A a^{2} b^{6} - 12 \, A a^{3} b^{4} c + 48 \, A a^{4} b^{2} c^{2} - 64 \, A a^{5} c^{3} + {\left(A b^{6} c^{2} - 12 \, A a b^{4} c^{3} + 48 \, A a^{2} b^{2} c^{4} - 64 \, A a^{3} c^{5}\right)} x^{8} + 2 \, {\left(A b^{7} c - 12 \, A a b^{5} c^{2} + 48 \, A a^{2} b^{3} c^{3} - 64 \, A a^{3} b c^{4}\right)} x^{6} + {\left(A b^{8} - 10 \, A a b^{6} c + 24 \, A a^{2} b^{4} c^{2} + 32 \, A a^{3} b^{2} c^{3} - 128 \, A a^{4} c^{4}\right)} x^{4} + 2 \, {\left(A a b^{7} - 12 \, A a^{2} b^{5} c + 48 \, A a^{3} b^{3} c^{2} - 64 \, A a^{4} b c^{3}\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right) - 4 \, {\left(A a^{2} b^{6} - 12 \, A a^{3} b^{4} c + 48 \, A a^{4} b^{2} c^{2} - 64 \, A a^{5} c^{3} + {\left(A b^{6} c^{2} - 12 \, A a b^{4} c^{3} + 48 \, A a^{2} b^{2} c^{4} - 64 \, A a^{3} c^{5}\right)} x^{8} + 2 \, {\left(A b^{7} c - 12 \, A a b^{5} c^{2} + 48 \, A a^{2} b^{3} c^{3} - 64 \, A a^{3} b c^{4}\right)} x^{6} + {\left(A b^{8} - 10 \, A a b^{6} c + 24 \, A a^{2} b^{4} c^{2} + 32 \, A a^{3} b^{2} c^{3} - 128 \, A a^{4} c^{4}\right)} x^{4} + 2 \, {\left(A a b^{7} - 12 \, A a^{2} b^{5} c + 48 \, A a^{3} b^{3} c^{2} - 64 \, A a^{4} b c^{3}\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3} + {\left(a^{3} b^{6} c^{2} - 12 \, a^{4} b^{4} c^{3} + 48 \, a^{5} b^{2} c^{4} - 64 \, a^{6} c^{5}\right)} x^{8} + 2 \, {\left(a^{3} b^{7} c - 12 \, a^{4} b^{5} c^{2} + 48 \, a^{5} b^{3} c^{3} - 64 \, a^{6} b c^{4}\right)} x^{6} + {\left(a^{3} b^{8} - 10 \, a^{4} b^{6} c + 24 \, a^{5} b^{4} c^{2} + 32 \, a^{6} b^{2} c^{3} - 128 \, a^{7} c^{4}\right)} x^{4} + 2 \, {\left(a^{4} b^{7} - 12 \, a^{5} b^{5} c + 48 \, a^{6} b^{3} c^{2} - 64 \, a^{7} b c^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(B*a^3*b^5 - 3*A*a^2*b^6 + 96*A*a^5*c^3 - 2*(A*a*b^5*c^2 - 4*(6*B*a^4 - 7*A*a^3*b)*c^4 + (6*B*a^3*b^2 - 11*A*a^2*b^3)*c^3)*x^6 - (4*A*a*b^6*c - 64*A*a^4*c^4 - 12*(6*B*a^4*b - 11*A*a^3*b^2)*c^3 + 9*(2*B*a^3*b^3 - 5*A*a^2*b^4)*c^2)*x^4 + 4*(10*B*a^5*b - 27*A*a^4*b^2)*c^2 - 2*(A*a*b^7 - 4*(10*B*a^5 - A*a^4*b)*c^3 + (2*B*a^4*b^2 + 23*A*a^3*b^3)*c^2 + 2*(B*a^3*b^4 - 5*A*a^2*b^5)*c)*x^2 - ((A*b^5*c^2 - 10*A*a*b^3*c^3 - 6*(2*B*a^3 - 5*A*a^2*b)*c^4)*x^8 + A*a^2*b^5 - 10*A*a^3*b^3*c + 2*(A*b^6*c - 10*A*a*b^4*c^2 - 6*(2*B*a^3*b - 5*A*a^2*b^2)*c^3)*x^6 + (A*b^7 - 8*A*a*b^5*c - 12*(2*B*a^4 - 5*A*a^3*b)*c^3 - 2*(6*B*a^3*b^2 - 5*A*a^2*b^3)*c^2)*x^4 - 6*(2*B*a^5 - 5*A*a^4*b)*c^2 + 2*(A*a*b^6 - 10*A*a^2*b^4*c - 6*(2*B*a^4*b - 5*A*a^3*b^2)*c^2)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) - (14*B*a^4*b^3 - 33*A*a^3*b^4)*c + (A*a^2*b^6 - 12*A*a^3*b^4*c + 48*A*a^4*b^2*c^2 - 64*A*a^5*c^3 + (A*b^6*c^2 - 12*A*a*b^4*c^3 + 48*A*a^2*b^2*c^4 - 64*A*a^3*c^5)*x^8 + 2*(A*b^7*c - 12*A*a*b^5*c^2 + 48*A*a^2*b^3*c^3 - 64*A*a^3*b*c^4)*x^6 + (A*b^8 - 10*A*a*b^6*c + 24*A*a^2*b^4*c^2 + 32*A*a^3*b^2*c^3 - 128*A*a^4*c^4)*x^4 + 2*(A*a*b^7 - 12*A*a^2*b^5*c + 48*A*a^3*b^3*c^2 - 64*A*a^4*b*c^3)*x^2)*log(c*x^4 + b*x^2 + a) - 4*(A*a^2*b^6 - 12*A*a^3*b^4*c + 48*A*a^4*b^2*c^2 - 64*A*a^5*c^3 + (A*b^6*c^2 - 12*A*a*b^4*c^3 + 48*A*a^2*b^2*c^4 - 64*A*a^3*c^5)*x^8 + 2*(A*b^7*c - 12*A*a*b^5*c^2 + 48*A*a^2*b^3*c^3 - 64*A*a^3*b*c^4)*x^6 + (A*b^8 - 10*A*a*b^6*c + 24*A*a^2*b^4*c^2 + 32*A*a^3*b^2*c^3 - 128*A*a^4*c^4)*x^4 + 2*(A*a*b^7 - 12*A*a^2*b^5*c + 48*A*a^3*b^3*c^2 - 64*A*a^4*b*c^3)*x^2)*log(x))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3 + (a^3*b^6*c^2 - 12*a^4*b^4*c^3 + 48*a^5*b^2*c^4 - 64*a^6*c^5)*x^8 + 2*(a^3*b^7*c - 12*a^4*b^5*c^2 + 48*a^5*b^3*c^3 - 64*a^6*b*c^4)*x^6 + (a^3*b^8 - 10*a^4*b^6*c + 24*a^5*b^4*c^2 + 32*a^6*b^2*c^3 - 128*a^7*c^4)*x^4 + 2*(a^4*b^7 - 12*a^5*b^5*c + 48*a^6*b^3*c^2 - 64*a^7*b*c^3)*x^2), -1/4*(B*a^3*b^5 - 3*A*a^2*b^6 + 96*A*a^5*c^3 - 2*(A*a*b^5*c^2 - 4*(6*B*a^4 - 7*A*a^3*b)*c^4 + (6*B*a^3*b^2 - 11*A*a^2*b^3)*c^3)*x^6 - (4*A*a*b^6*c - 64*A*a^4*c^4 - 12*(6*B*a^4*b - 11*A*a^3*b^2)*c^3 + 9*(2*B*a^3*b^3 - 5*A*a^2*b^4)*c^2)*x^4 + 4*(10*B*a^5*b - 27*A*a^4*b^2)*c^2 - 2*(A*a*b^7 - 4*(10*B*a^5 - A*a^4*b)*c^3 + (2*B*a^4*b^2 + 23*A*a^3*b^3)*c^2 + 2*(B*a^3*b^4 - 5*A*a^2*b^5)*c)*x^2 - 2*((A*b^5*c^2 - 10*A*a*b^3*c^3 - 6*(2*B*a^3 - 5*A*a^2*b)*c^4)*x^8 + A*a^2*b^5 - 10*A*a^3*b^3*c + 2*(A*b^6*c - 10*A*a*b^4*c^2 - 6*(2*B*a^3*b - 5*A*a^2*b^2)*c^3)*x^6 + (A*b^7 - 8*A*a*b^5*c - 12*(2*B*a^4 - 5*A*a^3*b)*c^3 - 2*(6*B*a^3*b^2 - 5*A*a^2*b^3)*c^2)*x^4 - 6*(2*B*a^5 - 5*A*a^4*b)*c^2 + 2*(A*a*b^6 - 10*A*a^2*b^4*c - 6*(2*B*a^4*b - 5*A*a^3*b^2)*c^2)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - (14*B*a^4*b^3 - 33*A*a^3*b^4)*c + (A*a^2*b^6 - 12*A*a^3*b^4*c + 48*A*a^4*b^2*c^2 - 64*A*a^5*c^3 + (A*b^6*c^2 - 12*A*a*b^4*c^3 + 48*A*a^2*b^2*c^4 - 64*A*a^3*c^5)*x^8 + 2*(A*b^7*c - 12*A*a*b^5*c^2 + 48*A*a^2*b^3*c^3 - 64*A*a^3*b*c^4)*x^6 + (A*b^8 - 10*A*a*b^6*c + 24*A*a^2*b^4*c^2 + 32*A*a^3*b^2*c^3 - 128*A*a^4*c^4)*x^4 + 2*(A*a*b^7 - 12*A*a^2*b^5*c + 48*A*a^3*b^3*c^2 - 64*A*a^4*b*c^3)*x^2)*log(c*x^4 + b*x^2 + a) - 4*(A*a^2*b^6 - 12*A*a^3*b^4*c + 48*A*a^4*b^2*c^2 - 64*A*a^5*c^3 + (A*b^6*c^2 - 12*A*a*b^4*c^3 + 48*A*a^2*b^2*c^4 - 64*A*a^3*c^5)*x^8 + 2*(A*b^7*c - 12*A*a*b^5*c^2 + 48*A*a^2*b^3*c^3 - 64*A*a^3*b*c^4)*x^6 + (A*b^8 - 10*A*a*b^6*c + 24*A*a^2*b^4*c^2 + 32*A*a^3*b^2*c^3 - 128*A*a^4*c^4)*x^4 + 2*(A*a*b^7 - 12*A*a^2*b^5*c + 48*A*a^3*b^3*c^2 - 64*A*a^4*b*c^3)*x^2)*log(x))/(a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3 + (a^3*b^6*c^2 - 12*a^4*b^4*c^3 + 48*a^5*b^2*c^4 - 64*a^6*c^5)*x^8 + 2*(a^3*b^7*c - 12*a^4*b^5*c^2 + 48*a^5*b^3*c^3 - 64*a^6*b*c^4)*x^6 + (a^3*b^8 - 10*a^4*b^6*c + 24*a^5*b^4*c^2 + 32*a^6*b^2*c^3 - 128*a^7*c^4)*x^4 + 2*(a^4*b^7 - 12*a^5*b^5*c + 48*a^6*b^3*c^2 - 64*a^7*b*c^3)*x^2)]","B",0
131,1,3956,0,14.441127," ","integrate((B*x^2+A)/x^3/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{2 \, A a^{3} b^{6} - 24 \, A a^{4} b^{4} c + 96 \, A a^{5} b^{2} c^{2} - 128 \, A a^{6} c^{3} - 2 \, {\left(120 \, A a^{4} c^{5} + 2 \, {\left(14 \, B a^{4} b - 57 \, A a^{3} b^{2}\right)} c^{4} - 11 \, {\left(B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} c^{3} + {\left(B a^{2} b^{5} - 3 \, A a b^{6}\right)} c^{2}\right)} x^{8} + {\left(8 \, {\left(8 \, B a^{5} - 69 \, A a^{4} b\right)} c^{4} - 6 \, {\left(22 \, B a^{4} b^{2} - 81 \, A a^{3} b^{3}\right)} c^{3} + 45 \, {\left(B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} c^{2} - 4 \, {\left(B a^{2} b^{6} - 3 \, A a b^{7}\right)} c\right)} x^{6} - 2 \, {\left(B a^{2} b^{7} - 3 \, A a b^{8} + 200 \, A a^{5} c^{4} + 2 \, {\left(2 \, B a^{5} b - 11 \, A a^{4} b^{2}\right)} c^{3} + {\left(23 \, B a^{4} b^{3} - 79 \, A a^{3} b^{4}\right)} c^{2} - 10 \, {\left(B a^{3} b^{5} - 3 \, A a^{2} b^{6}\right)} c\right)} x^{4} - {\left(3 \, B a^{3} b^{6} - 9 \, A a^{2} b^{7} - 8 \, {\left(12 \, B a^{6} - 61 \, A a^{5} b\right)} c^{3} + 2 \, {\left(54 \, B a^{5} b^{2} - 197 \, A a^{4} b^{3}\right)} c^{2} - {\left(33 \, B a^{4} b^{4} - 104 \, A a^{3} b^{5}\right)} c\right)} x^{2} - {\left({\left(60 \, A a^{3} c^{5} + 30 \, {\left(B a^{3} b - 3 \, A a^{2} b^{2}\right)} c^{4} - 10 \, {\left(B a^{2} b^{3} - 3 \, A a b^{4}\right)} c^{3} + {\left(B a b^{5} - 3 \, A b^{6}\right)} c^{2}\right)} x^{10} + 2 \, {\left(60 \, A a^{3} b c^{4} + 30 \, {\left(B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c^{3} - 10 \, {\left(B a^{2} b^{4} - 3 \, A a b^{5}\right)} c^{2} + {\left(B a b^{6} - 3 \, A b^{7}\right)} c\right)} x^{8} + {\left(B a b^{7} - 3 \, A b^{8} + 120 \, A a^{4} c^{4} + 60 \, {\left(B a^{4} b - 2 \, A a^{3} b^{2}\right)} c^{3} + 10 \, {\left(B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} c^{2} - 8 \, {\left(B a^{2} b^{5} - 3 \, A a b^{6}\right)} c\right)} x^{6} + 2 \, {\left(B a^{2} b^{6} - 3 \, A a b^{7} + 60 \, A a^{4} b c^{3} + 30 \, {\left(B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} c^{2} - 10 \, {\left(B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} c\right)} x^{4} + {\left(B a^{3} b^{5} - 3 \, A a^{2} b^{6} + 60 \, A a^{5} c^{3} + 30 \, {\left(B a^{5} b - 3 \, A a^{4} b^{2}\right)} c^{2} - 10 \, {\left(B a^{4} b^{3} - 3 \, A a^{3} b^{4}\right)} c\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) - {\left({\left(64 \, {\left(B a^{4} - 3 \, A a^{3} b\right)} c^{5} - 48 \, {\left(B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c^{4} + 12 \, {\left(B a^{2} b^{4} - 3 \, A a b^{5}\right)} c^{3} - {\left(B a b^{6} - 3 \, A b^{7}\right)} c^{2}\right)} x^{10} + 2 \, {\left(64 \, {\left(B a^{4} b - 3 \, A a^{3} b^{2}\right)} c^{4} - 48 \, {\left(B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} c^{3} + 12 \, {\left(B a^{2} b^{5} - 3 \, A a b^{6}\right)} c^{2} - {\left(B a b^{7} - 3 \, A b^{8}\right)} c\right)} x^{8} - {\left(B a b^{8} - 3 \, A b^{9} - 128 \, {\left(B a^{5} - 3 \, A a^{4} b\right)} c^{4} + 32 \, {\left(B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} c^{3} + 24 \, {\left(B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} c^{2} - 10 \, {\left(B a^{2} b^{6} - 3 \, A a b^{7}\right)} c\right)} x^{6} - 2 \, {\left(B a^{2} b^{7} - 3 \, A a b^{8} - 64 \, {\left(B a^{5} b - 3 \, A a^{4} b^{2}\right)} c^{3} + 48 \, {\left(B a^{4} b^{3} - 3 \, A a^{3} b^{4}\right)} c^{2} - 12 \, {\left(B a^{3} b^{5} - 3 \, A a^{2} b^{6}\right)} c\right)} x^{4} - {\left(B a^{3} b^{6} - 3 \, A a^{2} b^{7} - 64 \, {\left(B a^{6} - 3 \, A a^{5} b\right)} c^{3} + 48 \, {\left(B a^{5} b^{2} - 3 \, A a^{4} b^{3}\right)} c^{2} - 12 \, {\left(B a^{4} b^{4} - 3 \, A a^{3} b^{5}\right)} c\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right) + 4 \, {\left({\left(64 \, {\left(B a^{4} - 3 \, A a^{3} b\right)} c^{5} - 48 \, {\left(B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c^{4} + 12 \, {\left(B a^{2} b^{4} - 3 \, A a b^{5}\right)} c^{3} - {\left(B a b^{6} - 3 \, A b^{7}\right)} c^{2}\right)} x^{10} + 2 \, {\left(64 \, {\left(B a^{4} b - 3 \, A a^{3} b^{2}\right)} c^{4} - 48 \, {\left(B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} c^{3} + 12 \, {\left(B a^{2} b^{5} - 3 \, A a b^{6}\right)} c^{2} - {\left(B a b^{7} - 3 \, A b^{8}\right)} c\right)} x^{8} - {\left(B a b^{8} - 3 \, A b^{9} - 128 \, {\left(B a^{5} - 3 \, A a^{4} b\right)} c^{4} + 32 \, {\left(B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} c^{3} + 24 \, {\left(B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} c^{2} - 10 \, {\left(B a^{2} b^{6} - 3 \, A a b^{7}\right)} c\right)} x^{6} - 2 \, {\left(B a^{2} b^{7} - 3 \, A a b^{8} - 64 \, {\left(B a^{5} b - 3 \, A a^{4} b^{2}\right)} c^{3} + 48 \, {\left(B a^{4} b^{3} - 3 \, A a^{3} b^{4}\right)} c^{2} - 12 \, {\left(B a^{3} b^{5} - 3 \, A a^{2} b^{6}\right)} c\right)} x^{4} - {\left(B a^{3} b^{6} - 3 \, A a^{2} b^{7} - 64 \, {\left(B a^{6} - 3 \, A a^{5} b\right)} c^{3} + 48 \, {\left(B a^{5} b^{2} - 3 \, A a^{4} b^{3}\right)} c^{2} - 12 \, {\left(B a^{4} b^{4} - 3 \, A a^{3} b^{5}\right)} c\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left({\left(a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}\right)} x^{10} + 2 \, {\left(a^{4} b^{7} c - 12 \, a^{5} b^{5} c^{2} + 48 \, a^{6} b^{3} c^{3} - 64 \, a^{7} b c^{4}\right)} x^{8} + {\left(a^{4} b^{8} - 10 \, a^{5} b^{6} c + 24 \, a^{6} b^{4} c^{2} + 32 \, a^{7} b^{2} c^{3} - 128 \, a^{8} c^{4}\right)} x^{6} + 2 \, {\left(a^{5} b^{7} - 12 \, a^{6} b^{5} c + 48 \, a^{7} b^{3} c^{2} - 64 \, a^{8} b c^{3}\right)} x^{4} + {\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} x^{2}\right)}}, -\frac{2 \, A a^{3} b^{6} - 24 \, A a^{4} b^{4} c + 96 \, A a^{5} b^{2} c^{2} - 128 \, A a^{6} c^{3} - 2 \, {\left(120 \, A a^{4} c^{5} + 2 \, {\left(14 \, B a^{4} b - 57 \, A a^{3} b^{2}\right)} c^{4} - 11 \, {\left(B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} c^{3} + {\left(B a^{2} b^{5} - 3 \, A a b^{6}\right)} c^{2}\right)} x^{8} + {\left(8 \, {\left(8 \, B a^{5} - 69 \, A a^{4} b\right)} c^{4} - 6 \, {\left(22 \, B a^{4} b^{2} - 81 \, A a^{3} b^{3}\right)} c^{3} + 45 \, {\left(B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} c^{2} - 4 \, {\left(B a^{2} b^{6} - 3 \, A a b^{7}\right)} c\right)} x^{6} - 2 \, {\left(B a^{2} b^{7} - 3 \, A a b^{8} + 200 \, A a^{5} c^{4} + 2 \, {\left(2 \, B a^{5} b - 11 \, A a^{4} b^{2}\right)} c^{3} + {\left(23 \, B a^{4} b^{3} - 79 \, A a^{3} b^{4}\right)} c^{2} - 10 \, {\left(B a^{3} b^{5} - 3 \, A a^{2} b^{6}\right)} c\right)} x^{4} - {\left(3 \, B a^{3} b^{6} - 9 \, A a^{2} b^{7} - 8 \, {\left(12 \, B a^{6} - 61 \, A a^{5} b\right)} c^{3} + 2 \, {\left(54 \, B a^{5} b^{2} - 197 \, A a^{4} b^{3}\right)} c^{2} - {\left(33 \, B a^{4} b^{4} - 104 \, A a^{3} b^{5}\right)} c\right)} x^{2} - 2 \, {\left({\left(60 \, A a^{3} c^{5} + 30 \, {\left(B a^{3} b - 3 \, A a^{2} b^{2}\right)} c^{4} - 10 \, {\left(B a^{2} b^{3} - 3 \, A a b^{4}\right)} c^{3} + {\left(B a b^{5} - 3 \, A b^{6}\right)} c^{2}\right)} x^{10} + 2 \, {\left(60 \, A a^{3} b c^{4} + 30 \, {\left(B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c^{3} - 10 \, {\left(B a^{2} b^{4} - 3 \, A a b^{5}\right)} c^{2} + {\left(B a b^{6} - 3 \, A b^{7}\right)} c\right)} x^{8} + {\left(B a b^{7} - 3 \, A b^{8} + 120 \, A a^{4} c^{4} + 60 \, {\left(B a^{4} b - 2 \, A a^{3} b^{2}\right)} c^{3} + 10 \, {\left(B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} c^{2} - 8 \, {\left(B a^{2} b^{5} - 3 \, A a b^{6}\right)} c\right)} x^{6} + 2 \, {\left(B a^{2} b^{6} - 3 \, A a b^{7} + 60 \, A a^{4} b c^{3} + 30 \, {\left(B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} c^{2} - 10 \, {\left(B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} c\right)} x^{4} + {\left(B a^{3} b^{5} - 3 \, A a^{2} b^{6} + 60 \, A a^{5} c^{3} + 30 \, {\left(B a^{5} b - 3 \, A a^{4} b^{2}\right)} c^{2} - 10 \, {\left(B a^{4} b^{3} - 3 \, A a^{3} b^{4}\right)} c\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left({\left(64 \, {\left(B a^{4} - 3 \, A a^{3} b\right)} c^{5} - 48 \, {\left(B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c^{4} + 12 \, {\left(B a^{2} b^{4} - 3 \, A a b^{5}\right)} c^{3} - {\left(B a b^{6} - 3 \, A b^{7}\right)} c^{2}\right)} x^{10} + 2 \, {\left(64 \, {\left(B a^{4} b - 3 \, A a^{3} b^{2}\right)} c^{4} - 48 \, {\left(B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} c^{3} + 12 \, {\left(B a^{2} b^{5} - 3 \, A a b^{6}\right)} c^{2} - {\left(B a b^{7} - 3 \, A b^{8}\right)} c\right)} x^{8} - {\left(B a b^{8} - 3 \, A b^{9} - 128 \, {\left(B a^{5} - 3 \, A a^{4} b\right)} c^{4} + 32 \, {\left(B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} c^{3} + 24 \, {\left(B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} c^{2} - 10 \, {\left(B a^{2} b^{6} - 3 \, A a b^{7}\right)} c\right)} x^{6} - 2 \, {\left(B a^{2} b^{7} - 3 \, A a b^{8} - 64 \, {\left(B a^{5} b - 3 \, A a^{4} b^{2}\right)} c^{3} + 48 \, {\left(B a^{4} b^{3} - 3 \, A a^{3} b^{4}\right)} c^{2} - 12 \, {\left(B a^{3} b^{5} - 3 \, A a^{2} b^{6}\right)} c\right)} x^{4} - {\left(B a^{3} b^{6} - 3 \, A a^{2} b^{7} - 64 \, {\left(B a^{6} - 3 \, A a^{5} b\right)} c^{3} + 48 \, {\left(B a^{5} b^{2} - 3 \, A a^{4} b^{3}\right)} c^{2} - 12 \, {\left(B a^{4} b^{4} - 3 \, A a^{3} b^{5}\right)} c\right)} x^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right) + 4 \, {\left({\left(64 \, {\left(B a^{4} - 3 \, A a^{3} b\right)} c^{5} - 48 \, {\left(B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} c^{4} + 12 \, {\left(B a^{2} b^{4} - 3 \, A a b^{5}\right)} c^{3} - {\left(B a b^{6} - 3 \, A b^{7}\right)} c^{2}\right)} x^{10} + 2 \, {\left(64 \, {\left(B a^{4} b - 3 \, A a^{3} b^{2}\right)} c^{4} - 48 \, {\left(B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} c^{3} + 12 \, {\left(B a^{2} b^{5} - 3 \, A a b^{6}\right)} c^{2} - {\left(B a b^{7} - 3 \, A b^{8}\right)} c\right)} x^{8} - {\left(B a b^{8} - 3 \, A b^{9} - 128 \, {\left(B a^{5} - 3 \, A a^{4} b\right)} c^{4} + 32 \, {\left(B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} c^{3} + 24 \, {\left(B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} c^{2} - 10 \, {\left(B a^{2} b^{6} - 3 \, A a b^{7}\right)} c\right)} x^{6} - 2 \, {\left(B a^{2} b^{7} - 3 \, A a b^{8} - 64 \, {\left(B a^{5} b - 3 \, A a^{4} b^{2}\right)} c^{3} + 48 \, {\left(B a^{4} b^{3} - 3 \, A a^{3} b^{4}\right)} c^{2} - 12 \, {\left(B a^{3} b^{5} - 3 \, A a^{2} b^{6}\right)} c\right)} x^{4} - {\left(B a^{3} b^{6} - 3 \, A a^{2} b^{7} - 64 \, {\left(B a^{6} - 3 \, A a^{5} b\right)} c^{3} + 48 \, {\left(B a^{5} b^{2} - 3 \, A a^{4} b^{3}\right)} c^{2} - 12 \, {\left(B a^{4} b^{4} - 3 \, A a^{3} b^{5}\right)} c\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left({\left(a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}\right)} x^{10} + 2 \, {\left(a^{4} b^{7} c - 12 \, a^{5} b^{5} c^{2} + 48 \, a^{6} b^{3} c^{3} - 64 \, a^{7} b c^{4}\right)} x^{8} + {\left(a^{4} b^{8} - 10 \, a^{5} b^{6} c + 24 \, a^{6} b^{4} c^{2} + 32 \, a^{7} b^{2} c^{3} - 128 \, a^{8} c^{4}\right)} x^{6} + 2 \, {\left(a^{5} b^{7} - 12 \, a^{6} b^{5} c + 48 \, a^{7} b^{3} c^{2} - 64 \, a^{8} b c^{3}\right)} x^{4} + {\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(2*A*a^3*b^6 - 24*A*a^4*b^4*c + 96*A*a^5*b^2*c^2 - 128*A*a^6*c^3 - 2*(120*A*a^4*c^5 + 2*(14*B*a^4*b - 57*A*a^3*b^2)*c^4 - 11*(B*a^3*b^3 - 3*A*a^2*b^4)*c^3 + (B*a^2*b^5 - 3*A*a*b^6)*c^2)*x^8 + (8*(8*B*a^5 - 69*A*a^4*b)*c^4 - 6*(22*B*a^4*b^2 - 81*A*a^3*b^3)*c^3 + 45*(B*a^3*b^4 - 3*A*a^2*b^5)*c^2 - 4*(B*a^2*b^6 - 3*A*a*b^7)*c)*x^6 - 2*(B*a^2*b^7 - 3*A*a*b^8 + 200*A*a^5*c^4 + 2*(2*B*a^5*b - 11*A*a^4*b^2)*c^3 + (23*B*a^4*b^3 - 79*A*a^3*b^4)*c^2 - 10*(B*a^3*b^5 - 3*A*a^2*b^6)*c)*x^4 - (3*B*a^3*b^6 - 9*A*a^2*b^7 - 8*(12*B*a^6 - 61*A*a^5*b)*c^3 + 2*(54*B*a^5*b^2 - 197*A*a^4*b^3)*c^2 - (33*B*a^4*b^4 - 104*A*a^3*b^5)*c)*x^2 - ((60*A*a^3*c^5 + 30*(B*a^3*b - 3*A*a^2*b^2)*c^4 - 10*(B*a^2*b^3 - 3*A*a*b^4)*c^3 + (B*a*b^5 - 3*A*b^6)*c^2)*x^10 + 2*(60*A*a^3*b*c^4 + 30*(B*a^3*b^2 - 3*A*a^2*b^3)*c^3 - 10*(B*a^2*b^4 - 3*A*a*b^5)*c^2 + (B*a*b^6 - 3*A*b^7)*c)*x^8 + (B*a*b^7 - 3*A*b^8 + 120*A*a^4*c^4 + 60*(B*a^4*b - 2*A*a^3*b^2)*c^3 + 10*(B*a^3*b^3 - 3*A*a^2*b^4)*c^2 - 8*(B*a^2*b^5 - 3*A*a*b^6)*c)*x^6 + 2*(B*a^2*b^6 - 3*A*a*b^7 + 60*A*a^4*b*c^3 + 30*(B*a^4*b^2 - 3*A*a^3*b^3)*c^2 - 10*(B*a^3*b^4 - 3*A*a^2*b^5)*c)*x^4 + (B*a^3*b^5 - 3*A*a^2*b^6 + 60*A*a^5*c^3 + 30*(B*a^5*b - 3*A*a^4*b^2)*c^2 - 10*(B*a^4*b^3 - 3*A*a^3*b^4)*c)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) - ((64*(B*a^4 - 3*A*a^3*b)*c^5 - 48*(B*a^3*b^2 - 3*A*a^2*b^3)*c^4 + 12*(B*a^2*b^4 - 3*A*a*b^5)*c^3 - (B*a*b^6 - 3*A*b^7)*c^2)*x^10 + 2*(64*(B*a^4*b - 3*A*a^3*b^2)*c^4 - 48*(B*a^3*b^3 - 3*A*a^2*b^4)*c^3 + 12*(B*a^2*b^5 - 3*A*a*b^6)*c^2 - (B*a*b^7 - 3*A*b^8)*c)*x^8 - (B*a*b^8 - 3*A*b^9 - 128*(B*a^5 - 3*A*a^4*b)*c^4 + 32*(B*a^4*b^2 - 3*A*a^3*b^3)*c^3 + 24*(B*a^3*b^4 - 3*A*a^2*b^5)*c^2 - 10*(B*a^2*b^6 - 3*A*a*b^7)*c)*x^6 - 2*(B*a^2*b^7 - 3*A*a*b^8 - 64*(B*a^5*b - 3*A*a^4*b^2)*c^3 + 48*(B*a^4*b^3 - 3*A*a^3*b^4)*c^2 - 12*(B*a^3*b^5 - 3*A*a^2*b^6)*c)*x^4 - (B*a^3*b^6 - 3*A*a^2*b^7 - 64*(B*a^6 - 3*A*a^5*b)*c^3 + 48*(B*a^5*b^2 - 3*A*a^4*b^3)*c^2 - 12*(B*a^4*b^4 - 3*A*a^3*b^5)*c)*x^2)*log(c*x^4 + b*x^2 + a) + 4*((64*(B*a^4 - 3*A*a^3*b)*c^5 - 48*(B*a^3*b^2 - 3*A*a^2*b^3)*c^4 + 12*(B*a^2*b^4 - 3*A*a*b^5)*c^3 - (B*a*b^6 - 3*A*b^7)*c^2)*x^10 + 2*(64*(B*a^4*b - 3*A*a^3*b^2)*c^4 - 48*(B*a^3*b^3 - 3*A*a^2*b^4)*c^3 + 12*(B*a^2*b^5 - 3*A*a*b^6)*c^2 - (B*a*b^7 - 3*A*b^8)*c)*x^8 - (B*a*b^8 - 3*A*b^9 - 128*(B*a^5 - 3*A*a^4*b)*c^4 + 32*(B*a^4*b^2 - 3*A*a^3*b^3)*c^3 + 24*(B*a^3*b^4 - 3*A*a^2*b^5)*c^2 - 10*(B*a^2*b^6 - 3*A*a*b^7)*c)*x^6 - 2*(B*a^2*b^7 - 3*A*a*b^8 - 64*(B*a^5*b - 3*A*a^4*b^2)*c^3 + 48*(B*a^4*b^3 - 3*A*a^3*b^4)*c^2 - 12*(B*a^3*b^5 - 3*A*a^2*b^6)*c)*x^4 - (B*a^3*b^6 - 3*A*a^2*b^7 - 64*(B*a^6 - 3*A*a^5*b)*c^3 + 48*(B*a^5*b^2 - 3*A*a^4*b^3)*c^2 - 12*(B*a^4*b^4 - 3*A*a^3*b^5)*c)*x^2)*log(x))/((a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)*x^10 + 2*(a^4*b^7*c - 12*a^5*b^5*c^2 + 48*a^6*b^3*c^3 - 64*a^7*b*c^4)*x^8 + (a^4*b^8 - 10*a^5*b^6*c + 24*a^6*b^4*c^2 + 32*a^7*b^2*c^3 - 128*a^8*c^4)*x^6 + 2*(a^5*b^7 - 12*a^6*b^5*c + 48*a^7*b^3*c^2 - 64*a^8*b*c^3)*x^4 + (a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*x^2), -1/4*(2*A*a^3*b^6 - 24*A*a^4*b^4*c + 96*A*a^5*b^2*c^2 - 128*A*a^6*c^3 - 2*(120*A*a^4*c^5 + 2*(14*B*a^4*b - 57*A*a^3*b^2)*c^4 - 11*(B*a^3*b^3 - 3*A*a^2*b^4)*c^3 + (B*a^2*b^5 - 3*A*a*b^6)*c^2)*x^8 + (8*(8*B*a^5 - 69*A*a^4*b)*c^4 - 6*(22*B*a^4*b^2 - 81*A*a^3*b^3)*c^3 + 45*(B*a^3*b^4 - 3*A*a^2*b^5)*c^2 - 4*(B*a^2*b^6 - 3*A*a*b^7)*c)*x^6 - 2*(B*a^2*b^7 - 3*A*a*b^8 + 200*A*a^5*c^4 + 2*(2*B*a^5*b - 11*A*a^4*b^2)*c^3 + (23*B*a^4*b^3 - 79*A*a^3*b^4)*c^2 - 10*(B*a^3*b^5 - 3*A*a^2*b^6)*c)*x^4 - (3*B*a^3*b^6 - 9*A*a^2*b^7 - 8*(12*B*a^6 - 61*A*a^5*b)*c^3 + 2*(54*B*a^5*b^2 - 197*A*a^4*b^3)*c^2 - (33*B*a^4*b^4 - 104*A*a^3*b^5)*c)*x^2 - 2*((60*A*a^3*c^5 + 30*(B*a^3*b - 3*A*a^2*b^2)*c^4 - 10*(B*a^2*b^3 - 3*A*a*b^4)*c^3 + (B*a*b^5 - 3*A*b^6)*c^2)*x^10 + 2*(60*A*a^3*b*c^4 + 30*(B*a^3*b^2 - 3*A*a^2*b^3)*c^3 - 10*(B*a^2*b^4 - 3*A*a*b^5)*c^2 + (B*a*b^6 - 3*A*b^7)*c)*x^8 + (B*a*b^7 - 3*A*b^8 + 120*A*a^4*c^4 + 60*(B*a^4*b - 2*A*a^3*b^2)*c^3 + 10*(B*a^3*b^3 - 3*A*a^2*b^4)*c^2 - 8*(B*a^2*b^5 - 3*A*a*b^6)*c)*x^6 + 2*(B*a^2*b^6 - 3*A*a*b^7 + 60*A*a^4*b*c^3 + 30*(B*a^4*b^2 - 3*A*a^3*b^3)*c^2 - 10*(B*a^3*b^4 - 3*A*a^2*b^5)*c)*x^4 + (B*a^3*b^5 - 3*A*a^2*b^6 + 60*A*a^5*c^3 + 30*(B*a^5*b - 3*A*a^4*b^2)*c^2 - 10*(B*a^4*b^3 - 3*A*a^3*b^4)*c)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - ((64*(B*a^4 - 3*A*a^3*b)*c^5 - 48*(B*a^3*b^2 - 3*A*a^2*b^3)*c^4 + 12*(B*a^2*b^4 - 3*A*a*b^5)*c^3 - (B*a*b^6 - 3*A*b^7)*c^2)*x^10 + 2*(64*(B*a^4*b - 3*A*a^3*b^2)*c^4 - 48*(B*a^3*b^3 - 3*A*a^2*b^4)*c^3 + 12*(B*a^2*b^5 - 3*A*a*b^6)*c^2 - (B*a*b^7 - 3*A*b^8)*c)*x^8 - (B*a*b^8 - 3*A*b^9 - 128*(B*a^5 - 3*A*a^4*b)*c^4 + 32*(B*a^4*b^2 - 3*A*a^3*b^3)*c^3 + 24*(B*a^3*b^4 - 3*A*a^2*b^5)*c^2 - 10*(B*a^2*b^6 - 3*A*a*b^7)*c)*x^6 - 2*(B*a^2*b^7 - 3*A*a*b^8 - 64*(B*a^5*b - 3*A*a^4*b^2)*c^3 + 48*(B*a^4*b^3 - 3*A*a^3*b^4)*c^2 - 12*(B*a^3*b^5 - 3*A*a^2*b^6)*c)*x^4 - (B*a^3*b^6 - 3*A*a^2*b^7 - 64*(B*a^6 - 3*A*a^5*b)*c^3 + 48*(B*a^5*b^2 - 3*A*a^4*b^3)*c^2 - 12*(B*a^4*b^4 - 3*A*a^3*b^5)*c)*x^2)*log(c*x^4 + b*x^2 + a) + 4*((64*(B*a^4 - 3*A*a^3*b)*c^5 - 48*(B*a^3*b^2 - 3*A*a^2*b^3)*c^4 + 12*(B*a^2*b^4 - 3*A*a*b^5)*c^3 - (B*a*b^6 - 3*A*b^7)*c^2)*x^10 + 2*(64*(B*a^4*b - 3*A*a^3*b^2)*c^4 - 48*(B*a^3*b^3 - 3*A*a^2*b^4)*c^3 + 12*(B*a^2*b^5 - 3*A*a*b^6)*c^2 - (B*a*b^7 - 3*A*b^8)*c)*x^8 - (B*a*b^8 - 3*A*b^9 - 128*(B*a^5 - 3*A*a^4*b)*c^4 + 32*(B*a^4*b^2 - 3*A*a^3*b^3)*c^3 + 24*(B*a^3*b^4 - 3*A*a^2*b^5)*c^2 - 10*(B*a^2*b^6 - 3*A*a*b^7)*c)*x^6 - 2*(B*a^2*b^7 - 3*A*a*b^8 - 64*(B*a^5*b - 3*A*a^4*b^2)*c^3 + 48*(B*a^4*b^3 - 3*A*a^3*b^4)*c^2 - 12*(B*a^3*b^5 - 3*A*a^2*b^6)*c)*x^4 - (B*a^3*b^6 - 3*A*a^2*b^7 - 64*(B*a^6 - 3*A*a^5*b)*c^3 + 48*(B*a^5*b^2 - 3*A*a^4*b^3)*c^2 - 12*(B*a^4*b^4 - 3*A*a^3*b^5)*c)*x^2)*log(x))/((a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)*x^10 + 2*(a^4*b^7*c - 12*a^5*b^5*c^2 + 48*a^6*b^3*c^3 - 64*a^7*b*c^4)*x^8 + (a^4*b^8 - 10*a^5*b^6*c + 24*a^6*b^4*c^2 + 32*a^7*b^2*c^3 - 128*a^8*c^4)*x^6 + 2*(a^5*b^7 - 12*a^6*b^5*c + 48*a^7*b^3*c^2 - 64*a^8*b*c^3)*x^4 + (a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*x^2)]","B",0
132,1,9636,0,20.776646," ","integrate(x^8*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, B b^{4} c + 4 \, {\left(11 \, B a^{2} + 4 \, A a b\right)} c^{3} - {\left(37 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} x^{7} + 2 \, {\left(3 \, B b^{5} + 36 \, A a^{2} c^{3} - {\left(4 \, B a^{2} b - 5 \, A a b^{2}\right)} c^{2} - {\left(20 \, B a b^{3} - A b^{4}\right)} c\right)} x^{5} + 2 \, {\left(6 \, B a b^{4} + 28 \, {\left(B a^{3} + A a^{2} b\right)} c^{2} - {\left(49 \, B a^{2} b^{2} - 2 \, A a b^{3}\right)} c\right)} x^{3} - \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{8} + a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{6} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x^{2}\right)} \sqrt{-\frac{9 \, B^{2} b^{9} - 1680 \, {\left(4 \, A B a^{4} - A^{2} a^{3} b\right)} c^{5} + 280 \, {\left(54 \, B^{2} a^{4} b - 12 \, A B a^{3} b^{2} + A^{2} a^{2} b^{3}\right)} c^{4} - 35 \, {\left(216 \, B^{2} a^{3} b^{3} - 36 \, A B a^{2} b^{4} + A^{2} a b^{5}\right)} c^{3} + {\left(1701 \, B^{2} a^{2} b^{5} - 168 \, A B a b^{6} + A^{2} b^{7}\right)} c^{2} - 3 \, {\left(63 \, B^{2} a b^{7} - 2 \, A B b^{8}\right)} c + {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} \log\left(-{\left(1701 \, B^{4} a^{2} b^{8} - 945 \, A B^{3} a b^{9} - 10000 \, A^{4} a^{4} c^{6} + 15000 \, {\left(6 \, A^{3} B a^{4} b - A^{4} a^{3} b^{2}\right)} c^{5} + 3 \, {\left(1037232 \, B^{4} a^{6} - 1037232 \, A B^{3} a^{5} b + 287712 \, A^{2} B^{2} a^{4} b^{2} - 32952 \, A^{3} B a^{3} b^{3} + 497 \, A^{4} a^{2} b^{4}\right)} c^{4} - {\left(1555848 \, B^{4} a^{5} b^{2} - 1298376 \, A B^{3} a^{4} b^{3} + 238464 \, A^{2} B^{2} a^{3} b^{4} - 11277 \, A^{3} B a^{2} b^{5} + 35 \, A^{4} a b^{6}\right)} c^{3} + 9 \, {\left(37701 \, B^{4} a^{4} b^{4} - 26973 \, A B^{3} a^{3} b^{5} + 3066 \, A^{2} B^{2} a^{2} b^{6} - 35 \, A^{3} B a b^{7}\right)} c^{2} - 27 \, {\left(1341 \, B^{4} a^{3} b^{6} - 819 \, A B^{3} a^{2} b^{7} + 35 \, A^{2} B^{2} a b^{8}\right)} c\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} b^{13} + 32000 \, A^{3} a^{5} c^{8} - 640 \, {\left(882 \, A B^{2} a^{6} - 156 \, A^{2} B a^{5} b + 37 \, A^{3} a^{4} b^{2}\right)} c^{7} + 64 \, {\left(10584 \, B^{3} a^{6} b + 5562 \, A B^{2} a^{5} b^{2} - 1083 \, A^{2} B a^{4} b^{3} + 89 \, A^{3} a^{3} b^{4}\right)} c^{6} - 8 \, {\left(93096 \, B^{3} a^{5} b^{3} + 3816 \, A B^{2} a^{4} b^{4} - 1746 \, A^{2} B a^{3} b^{5} + 49 \, A^{3} a^{2} b^{6}\right)} c^{5} + {\left(337392 \, B^{3} a^{4} b^{5} - 24120 \, A B^{2} a^{3} b^{6} - 84 \, A^{2} B a^{2} b^{7} - 17 \, A^{3} a b^{8}\right)} c^{4} - {\left(81324 \, B^{3} a^{3} b^{7} - 6993 \, A B^{2} a^{2} b^{8} + 195 \, A^{2} B a b^{9} - A^{3} b^{10}\right)} c^{3} + 9 \, {\left(1239 \, B^{3} a^{2} b^{9} - 79 \, A B^{2} a b^{10} + A^{2} B b^{11}\right)} c^{2} - 27 \, {\left(31 \, B^{3} a b^{11} - A B^{2} b^{12}\right)} c - {\left(3 \, B b^{14} c^{5} - 4096 \, {\left(42 \, B a^{7} - 13 \, A a^{6} b\right)} c^{12} + 6144 \, {\left(40 \, B a^{6} b^{2} - 11 \, A a^{5} b^{3}\right)} c^{11} - 768 \, {\left(194 \, B a^{5} b^{4} - 45 \, A a^{4} b^{5}\right)} c^{10} + 1280 \, {\left(39 \, B a^{4} b^{6} - 7 \, A a^{3} b^{7}\right)} c^{9} - 240 \, {\left(42 \, B a^{3} b^{8} - 5 \, A a^{2} b^{9}\right)} c^{8} + 24 \, {\left(52 \, B a^{2} b^{10} - 3 \, A a b^{11}\right)} c^{7} - {\left(90 \, B a b^{12} - A b^{13}\right)} c^{6}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}\right)} \sqrt{-\frac{9 \, B^{2} b^{9} - 1680 \, {\left(4 \, A B a^{4} - A^{2} a^{3} b\right)} c^{5} + 280 \, {\left(54 \, B^{2} a^{4} b - 12 \, A B a^{3} b^{2} + A^{2} a^{2} b^{3}\right)} c^{4} - 35 \, {\left(216 \, B^{2} a^{3} b^{3} - 36 \, A B a^{2} b^{4} + A^{2} a b^{5}\right)} c^{3} + {\left(1701 \, B^{2} a^{2} b^{5} - 168 \, A B a b^{6} + A^{2} b^{7}\right)} c^{2} - 3 \, {\left(63 \, B^{2} a b^{7} - 2 \, A B b^{8}\right)} c + {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{8} + a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{6} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x^{2}\right)} \sqrt{-\frac{9 \, B^{2} b^{9} - 1680 \, {\left(4 \, A B a^{4} - A^{2} a^{3} b\right)} c^{5} + 280 \, {\left(54 \, B^{2} a^{4} b - 12 \, A B a^{3} b^{2} + A^{2} a^{2} b^{3}\right)} c^{4} - 35 \, {\left(216 \, B^{2} a^{3} b^{3} - 36 \, A B a^{2} b^{4} + A^{2} a b^{5}\right)} c^{3} + {\left(1701 \, B^{2} a^{2} b^{5} - 168 \, A B a b^{6} + A^{2} b^{7}\right)} c^{2} - 3 \, {\left(63 \, B^{2} a b^{7} - 2 \, A B b^{8}\right)} c + {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} \log\left(-{\left(1701 \, B^{4} a^{2} b^{8} - 945 \, A B^{3} a b^{9} - 10000 \, A^{4} a^{4} c^{6} + 15000 \, {\left(6 \, A^{3} B a^{4} b - A^{4} a^{3} b^{2}\right)} c^{5} + 3 \, {\left(1037232 \, B^{4} a^{6} - 1037232 \, A B^{3} a^{5} b + 287712 \, A^{2} B^{2} a^{4} b^{2} - 32952 \, A^{3} B a^{3} b^{3} + 497 \, A^{4} a^{2} b^{4}\right)} c^{4} - {\left(1555848 \, B^{4} a^{5} b^{2} - 1298376 \, A B^{3} a^{4} b^{3} + 238464 \, A^{2} B^{2} a^{3} b^{4} - 11277 \, A^{3} B a^{2} b^{5} + 35 \, A^{4} a b^{6}\right)} c^{3} + 9 \, {\left(37701 \, B^{4} a^{4} b^{4} - 26973 \, A B^{3} a^{3} b^{5} + 3066 \, A^{2} B^{2} a^{2} b^{6} - 35 \, A^{3} B a b^{7}\right)} c^{2} - 27 \, {\left(1341 \, B^{4} a^{3} b^{6} - 819 \, A B^{3} a^{2} b^{7} + 35 \, A^{2} B^{2} a b^{8}\right)} c\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} b^{13} + 32000 \, A^{3} a^{5} c^{8} - 640 \, {\left(882 \, A B^{2} a^{6} - 156 \, A^{2} B a^{5} b + 37 \, A^{3} a^{4} b^{2}\right)} c^{7} + 64 \, {\left(10584 \, B^{3} a^{6} b + 5562 \, A B^{2} a^{5} b^{2} - 1083 \, A^{2} B a^{4} b^{3} + 89 \, A^{3} a^{3} b^{4}\right)} c^{6} - 8 \, {\left(93096 \, B^{3} a^{5} b^{3} + 3816 \, A B^{2} a^{4} b^{4} - 1746 \, A^{2} B a^{3} b^{5} + 49 \, A^{3} a^{2} b^{6}\right)} c^{5} + {\left(337392 \, B^{3} a^{4} b^{5} - 24120 \, A B^{2} a^{3} b^{6} - 84 \, A^{2} B a^{2} b^{7} - 17 \, A^{3} a b^{8}\right)} c^{4} - {\left(81324 \, B^{3} a^{3} b^{7} - 6993 \, A B^{2} a^{2} b^{8} + 195 \, A^{2} B a b^{9} - A^{3} b^{10}\right)} c^{3} + 9 \, {\left(1239 \, B^{3} a^{2} b^{9} - 79 \, A B^{2} a b^{10} + A^{2} B b^{11}\right)} c^{2} - 27 \, {\left(31 \, B^{3} a b^{11} - A B^{2} b^{12}\right)} c - {\left(3 \, B b^{14} c^{5} - 4096 \, {\left(42 \, B a^{7} - 13 \, A a^{6} b\right)} c^{12} + 6144 \, {\left(40 \, B a^{6} b^{2} - 11 \, A a^{5} b^{3}\right)} c^{11} - 768 \, {\left(194 \, B a^{5} b^{4} - 45 \, A a^{4} b^{5}\right)} c^{10} + 1280 \, {\left(39 \, B a^{4} b^{6} - 7 \, A a^{3} b^{7}\right)} c^{9} - 240 \, {\left(42 \, B a^{3} b^{8} - 5 \, A a^{2} b^{9}\right)} c^{8} + 24 \, {\left(52 \, B a^{2} b^{10} - 3 \, A a b^{11}\right)} c^{7} - {\left(90 \, B a b^{12} - A b^{13}\right)} c^{6}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}\right)} \sqrt{-\frac{9 \, B^{2} b^{9} - 1680 \, {\left(4 \, A B a^{4} - A^{2} a^{3} b\right)} c^{5} + 280 \, {\left(54 \, B^{2} a^{4} b - 12 \, A B a^{3} b^{2} + A^{2} a^{2} b^{3}\right)} c^{4} - 35 \, {\left(216 \, B^{2} a^{3} b^{3} - 36 \, A B a^{2} b^{4} + A^{2} a b^{5}\right)} c^{3} + {\left(1701 \, B^{2} a^{2} b^{5} - 168 \, A B a b^{6} + A^{2} b^{7}\right)} c^{2} - 3 \, {\left(63 \, B^{2} a b^{7} - 2 \, A B b^{8}\right)} c + {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{8} + a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{6} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x^{2}\right)} \sqrt{-\frac{9 \, B^{2} b^{9} - 1680 \, {\left(4 \, A B a^{4} - A^{2} a^{3} b\right)} c^{5} + 280 \, {\left(54 \, B^{2} a^{4} b - 12 \, A B a^{3} b^{2} + A^{2} a^{2} b^{3}\right)} c^{4} - 35 \, {\left(216 \, B^{2} a^{3} b^{3} - 36 \, A B a^{2} b^{4} + A^{2} a b^{5}\right)} c^{3} + {\left(1701 \, B^{2} a^{2} b^{5} - 168 \, A B a b^{6} + A^{2} b^{7}\right)} c^{2} - 3 \, {\left(63 \, B^{2} a b^{7} - 2 \, A B b^{8}\right)} c - {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} \log\left(-{\left(1701 \, B^{4} a^{2} b^{8} - 945 \, A B^{3} a b^{9} - 10000 \, A^{4} a^{4} c^{6} + 15000 \, {\left(6 \, A^{3} B a^{4} b - A^{4} a^{3} b^{2}\right)} c^{5} + 3 \, {\left(1037232 \, B^{4} a^{6} - 1037232 \, A B^{3} a^{5} b + 287712 \, A^{2} B^{2} a^{4} b^{2} - 32952 \, A^{3} B a^{3} b^{3} + 497 \, A^{4} a^{2} b^{4}\right)} c^{4} - {\left(1555848 \, B^{4} a^{5} b^{2} - 1298376 \, A B^{3} a^{4} b^{3} + 238464 \, A^{2} B^{2} a^{3} b^{4} - 11277 \, A^{3} B a^{2} b^{5} + 35 \, A^{4} a b^{6}\right)} c^{3} + 9 \, {\left(37701 \, B^{4} a^{4} b^{4} - 26973 \, A B^{3} a^{3} b^{5} + 3066 \, A^{2} B^{2} a^{2} b^{6} - 35 \, A^{3} B a b^{7}\right)} c^{2} - 27 \, {\left(1341 \, B^{4} a^{3} b^{6} - 819 \, A B^{3} a^{2} b^{7} + 35 \, A^{2} B^{2} a b^{8}\right)} c\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} b^{13} + 32000 \, A^{3} a^{5} c^{8} - 640 \, {\left(882 \, A B^{2} a^{6} - 156 \, A^{2} B a^{5} b + 37 \, A^{3} a^{4} b^{2}\right)} c^{7} + 64 \, {\left(10584 \, B^{3} a^{6} b + 5562 \, A B^{2} a^{5} b^{2} - 1083 \, A^{2} B a^{4} b^{3} + 89 \, A^{3} a^{3} b^{4}\right)} c^{6} - 8 \, {\left(93096 \, B^{3} a^{5} b^{3} + 3816 \, A B^{2} a^{4} b^{4} - 1746 \, A^{2} B a^{3} b^{5} + 49 \, A^{3} a^{2} b^{6}\right)} c^{5} + {\left(337392 \, B^{3} a^{4} b^{5} - 24120 \, A B^{2} a^{3} b^{6} - 84 \, A^{2} B a^{2} b^{7} - 17 \, A^{3} a b^{8}\right)} c^{4} - {\left(81324 \, B^{3} a^{3} b^{7} - 6993 \, A B^{2} a^{2} b^{8} + 195 \, A^{2} B a b^{9} - A^{3} b^{10}\right)} c^{3} + 9 \, {\left(1239 \, B^{3} a^{2} b^{9} - 79 \, A B^{2} a b^{10} + A^{2} B b^{11}\right)} c^{2} - 27 \, {\left(31 \, B^{3} a b^{11} - A B^{2} b^{12}\right)} c + {\left(3 \, B b^{14} c^{5} - 4096 \, {\left(42 \, B a^{7} - 13 \, A a^{6} b\right)} c^{12} + 6144 \, {\left(40 \, B a^{6} b^{2} - 11 \, A a^{5} b^{3}\right)} c^{11} - 768 \, {\left(194 \, B a^{5} b^{4} - 45 \, A a^{4} b^{5}\right)} c^{10} + 1280 \, {\left(39 \, B a^{4} b^{6} - 7 \, A a^{3} b^{7}\right)} c^{9} - 240 \, {\left(42 \, B a^{3} b^{8} - 5 \, A a^{2} b^{9}\right)} c^{8} + 24 \, {\left(52 \, B a^{2} b^{10} - 3 \, A a b^{11}\right)} c^{7} - {\left(90 \, B a b^{12} - A b^{13}\right)} c^{6}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}\right)} \sqrt{-\frac{9 \, B^{2} b^{9} - 1680 \, {\left(4 \, A B a^{4} - A^{2} a^{3} b\right)} c^{5} + 280 \, {\left(54 \, B^{2} a^{4} b - 12 \, A B a^{3} b^{2} + A^{2} a^{2} b^{3}\right)} c^{4} - 35 \, {\left(216 \, B^{2} a^{3} b^{3} - 36 \, A B a^{2} b^{4} + A^{2} a b^{5}\right)} c^{3} + {\left(1701 \, B^{2} a^{2} b^{5} - 168 \, A B a b^{6} + A^{2} b^{7}\right)} c^{2} - 3 \, {\left(63 \, B^{2} a b^{7} - 2 \, A B b^{8}\right)} c - {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{8} + a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{6} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x^{2}\right)} \sqrt{-\frac{9 \, B^{2} b^{9} - 1680 \, {\left(4 \, A B a^{4} - A^{2} a^{3} b\right)} c^{5} + 280 \, {\left(54 \, B^{2} a^{4} b - 12 \, A B a^{3} b^{2} + A^{2} a^{2} b^{3}\right)} c^{4} - 35 \, {\left(216 \, B^{2} a^{3} b^{3} - 36 \, A B a^{2} b^{4} + A^{2} a b^{5}\right)} c^{3} + {\left(1701 \, B^{2} a^{2} b^{5} - 168 \, A B a b^{6} + A^{2} b^{7}\right)} c^{2} - 3 \, {\left(63 \, B^{2} a b^{7} - 2 \, A B b^{8}\right)} c - {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} \log\left(-{\left(1701 \, B^{4} a^{2} b^{8} - 945 \, A B^{3} a b^{9} - 10000 \, A^{4} a^{4} c^{6} + 15000 \, {\left(6 \, A^{3} B a^{4} b - A^{4} a^{3} b^{2}\right)} c^{5} + 3 \, {\left(1037232 \, B^{4} a^{6} - 1037232 \, A B^{3} a^{5} b + 287712 \, A^{2} B^{2} a^{4} b^{2} - 32952 \, A^{3} B a^{3} b^{3} + 497 \, A^{4} a^{2} b^{4}\right)} c^{4} - {\left(1555848 \, B^{4} a^{5} b^{2} - 1298376 \, A B^{3} a^{4} b^{3} + 238464 \, A^{2} B^{2} a^{3} b^{4} - 11277 \, A^{3} B a^{2} b^{5} + 35 \, A^{4} a b^{6}\right)} c^{3} + 9 \, {\left(37701 \, B^{4} a^{4} b^{4} - 26973 \, A B^{3} a^{3} b^{5} + 3066 \, A^{2} B^{2} a^{2} b^{6} - 35 \, A^{3} B a b^{7}\right)} c^{2} - 27 \, {\left(1341 \, B^{4} a^{3} b^{6} - 819 \, A B^{3} a^{2} b^{7} + 35 \, A^{2} B^{2} a b^{8}\right)} c\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} b^{13} + 32000 \, A^{3} a^{5} c^{8} - 640 \, {\left(882 \, A B^{2} a^{6} - 156 \, A^{2} B a^{5} b + 37 \, A^{3} a^{4} b^{2}\right)} c^{7} + 64 \, {\left(10584 \, B^{3} a^{6} b + 5562 \, A B^{2} a^{5} b^{2} - 1083 \, A^{2} B a^{4} b^{3} + 89 \, A^{3} a^{3} b^{4}\right)} c^{6} - 8 \, {\left(93096 \, B^{3} a^{5} b^{3} + 3816 \, A B^{2} a^{4} b^{4} - 1746 \, A^{2} B a^{3} b^{5} + 49 \, A^{3} a^{2} b^{6}\right)} c^{5} + {\left(337392 \, B^{3} a^{4} b^{5} - 24120 \, A B^{2} a^{3} b^{6} - 84 \, A^{2} B a^{2} b^{7} - 17 \, A^{3} a b^{8}\right)} c^{4} - {\left(81324 \, B^{3} a^{3} b^{7} - 6993 \, A B^{2} a^{2} b^{8} + 195 \, A^{2} B a b^{9} - A^{3} b^{10}\right)} c^{3} + 9 \, {\left(1239 \, B^{3} a^{2} b^{9} - 79 \, A B^{2} a b^{10} + A^{2} B b^{11}\right)} c^{2} - 27 \, {\left(31 \, B^{3} a b^{11} - A B^{2} b^{12}\right)} c + {\left(3 \, B b^{14} c^{5} - 4096 \, {\left(42 \, B a^{7} - 13 \, A a^{6} b\right)} c^{12} + 6144 \, {\left(40 \, B a^{6} b^{2} - 11 \, A a^{5} b^{3}\right)} c^{11} - 768 \, {\left(194 \, B a^{5} b^{4} - 45 \, A a^{4} b^{5}\right)} c^{10} + 1280 \, {\left(39 \, B a^{4} b^{6} - 7 \, A a^{3} b^{7}\right)} c^{9} - 240 \, {\left(42 \, B a^{3} b^{8} - 5 \, A a^{2} b^{9}\right)} c^{8} + 24 \, {\left(52 \, B a^{2} b^{10} - 3 \, A a b^{11}\right)} c^{7} - {\left(90 \, B a b^{12} - A b^{13}\right)} c^{6}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}\right)} \sqrt{-\frac{9 \, B^{2} b^{9} - 1680 \, {\left(4 \, A B a^{4} - A^{2} a^{3} b\right)} c^{5} + 280 \, {\left(54 \, B^{2} a^{4} b - 12 \, A B a^{3} b^{2} + A^{2} a^{2} b^{3}\right)} c^{4} - 35 \, {\left(216 \, B^{2} a^{3} b^{3} - 36 \, A B a^{2} b^{4} + A^{2} a b^{5}\right)} c^{3} + {\left(1701 \, B^{2} a^{2} b^{5} - 168 \, A B a b^{6} + A^{2} b^{7}\right)} c^{2} - 3 \, {\left(63 \, B^{2} a b^{7} - 2 \, A B b^{8}\right)} c - {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{81 \, B^{4} b^{8} + 625 \, A^{4} a^{2} c^{6} - 50 \, {\left(441 \, A^{2} B^{2} a^{3} - 108 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c^{5} + {\left(194481 \, B^{4} a^{4} - 95256 \, A B^{3} a^{3} b + 17496 \, A^{2} B^{2} a^{2} b^{2} - 516 \, A^{3} B a b^{3} + A^{4} b^{4}\right)} c^{4} - 6 \, {\left(14553 \, B^{4} a^{3} b^{2} - 4446 \, A B^{3} a^{2} b^{3} + 324 \, A^{2} B^{2} a b^{4} - 2 \, A^{3} B b^{5}\right)} c^{3} + 27 \, {\left(657 \, B^{4} a^{2} b^{4} - 116 \, A B^{3} a b^{5} + 2 \, A^{2} B^{2} b^{6}\right)} c^{2} - 54 \, {\left(33 \, B^{4} a b^{6} - 2 \, A B^{3} b^{7}\right)} c}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}}\right) + 2 \, {\left(3 \, B a^{2} b^{3} + 20 \, A a^{3} c^{2} - {\left(24 \, B a^{3} b - A a^{2} b^{2}\right)} c\right)} x}{16 \, {\left({\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{8} + a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{6} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x^{2}\right)}}"," ",0,"-1/16*(2*(5*B*b^4*c + 4*(11*B*a^2 + 4*A*a*b)*c^3 - (37*B*a*b^2 + A*b^3)*c^2)*x^7 + 2*(3*B*b^5 + 36*A*a^2*c^3 - (4*B*a^2*b - 5*A*a*b^2)*c^2 - (20*B*a*b^3 - A*b^4)*c)*x^5 + 2*(6*B*a*b^4 + 28*(B*a^3 + A*a^2*b)*c^2 - (49*B*a^2*b^2 - 2*A*a*b^3)*c)*x^3 - sqrt(1/2)*((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^8 + a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^6 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^4 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x^2)*sqrt(-(9*B^2*b^9 - 1680*(4*A*B*a^4 - A^2*a^3*b)*c^5 + 280*(54*B^2*a^4*b - 12*A*B*a^3*b^2 + A^2*a^2*b^3)*c^4 - 35*(216*B^2*a^3*b^3 - 36*A*B*a^2*b^4 + A^2*a*b^5)*c^3 + (1701*B^2*a^2*b^5 - 168*A*B*a*b^6 + A^2*b^7)*c^2 - 3*(63*B^2*a*b^7 - 2*A*B*b^8)*c + (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))*log(-(1701*B^4*a^2*b^8 - 945*A*B^3*a*b^9 - 10000*A^4*a^4*c^6 + 15000*(6*A^3*B*a^4*b - A^4*a^3*b^2)*c^5 + 3*(1037232*B^4*a^6 - 1037232*A*B^3*a^5*b + 287712*A^2*B^2*a^4*b^2 - 32952*A^3*B*a^3*b^3 + 497*A^4*a^2*b^4)*c^4 - (1555848*B^4*a^5*b^2 - 1298376*A*B^3*a^4*b^3 + 238464*A^2*B^2*a^3*b^4 - 11277*A^3*B*a^2*b^5 + 35*A^4*a*b^6)*c^3 + 9*(37701*B^4*a^4*b^4 - 26973*A*B^3*a^3*b^5 + 3066*A^2*B^2*a^2*b^6 - 35*A^3*B*a*b^7)*c^2 - 27*(1341*B^4*a^3*b^6 - 819*A*B^3*a^2*b^7 + 35*A^2*B^2*a*b^8)*c)*x + 1/2*sqrt(1/2)*(27*B^3*b^13 + 32000*A^3*a^5*c^8 - 640*(882*A*B^2*a^6 - 156*A^2*B*a^5*b + 37*A^3*a^4*b^2)*c^7 + 64*(10584*B^3*a^6*b + 5562*A*B^2*a^5*b^2 - 1083*A^2*B*a^4*b^3 + 89*A^3*a^3*b^4)*c^6 - 8*(93096*B^3*a^5*b^3 + 3816*A*B^2*a^4*b^4 - 1746*A^2*B*a^3*b^5 + 49*A^3*a^2*b^6)*c^5 + (337392*B^3*a^4*b^5 - 24120*A*B^2*a^3*b^6 - 84*A^2*B*a^2*b^7 - 17*A^3*a*b^8)*c^4 - (81324*B^3*a^3*b^7 - 6993*A*B^2*a^2*b^8 + 195*A^2*B*a*b^9 - A^3*b^10)*c^3 + 9*(1239*B^3*a^2*b^9 - 79*A*B^2*a*b^10 + A^2*B*b^11)*c^2 - 27*(31*B^3*a*b^11 - A*B^2*b^12)*c - (3*B*b^14*c^5 - 4096*(42*B*a^7 - 13*A*a^6*b)*c^12 + 6144*(40*B*a^6*b^2 - 11*A*a^5*b^3)*c^11 - 768*(194*B*a^5*b^4 - 45*A*a^4*b^5)*c^10 + 1280*(39*B*a^4*b^6 - 7*A*a^3*b^7)*c^9 - 240*(42*B*a^3*b^8 - 5*A*a^2*b^9)*c^8 + 24*(52*B*a^2*b^10 - 3*A*a*b^11)*c^7 - (90*B*a*b^12 - A*b^13)*c^6)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))*sqrt(-(9*B^2*b^9 - 1680*(4*A*B*a^4 - A^2*a^3*b)*c^5 + 280*(54*B^2*a^4*b - 12*A*B*a^3*b^2 + A^2*a^2*b^3)*c^4 - 35*(216*B^2*a^3*b^3 - 36*A*B*a^2*b^4 + A^2*a*b^5)*c^3 + (1701*B^2*a^2*b^5 - 168*A*B*a*b^6 + A^2*b^7)*c^2 - 3*(63*B^2*a*b^7 - 2*A*B*b^8)*c + (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))) + sqrt(1/2)*((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^8 + a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^6 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^4 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x^2)*sqrt(-(9*B^2*b^9 - 1680*(4*A*B*a^4 - A^2*a^3*b)*c^5 + 280*(54*B^2*a^4*b - 12*A*B*a^3*b^2 + A^2*a^2*b^3)*c^4 - 35*(216*B^2*a^3*b^3 - 36*A*B*a^2*b^4 + A^2*a*b^5)*c^3 + (1701*B^2*a^2*b^5 - 168*A*B*a*b^6 + A^2*b^7)*c^2 - 3*(63*B^2*a*b^7 - 2*A*B*b^8)*c + (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))*log(-(1701*B^4*a^2*b^8 - 945*A*B^3*a*b^9 - 10000*A^4*a^4*c^6 + 15000*(6*A^3*B*a^4*b - A^4*a^3*b^2)*c^5 + 3*(1037232*B^4*a^6 - 1037232*A*B^3*a^5*b + 287712*A^2*B^2*a^4*b^2 - 32952*A^3*B*a^3*b^3 + 497*A^4*a^2*b^4)*c^4 - (1555848*B^4*a^5*b^2 - 1298376*A*B^3*a^4*b^3 + 238464*A^2*B^2*a^3*b^4 - 11277*A^3*B*a^2*b^5 + 35*A^4*a*b^6)*c^3 + 9*(37701*B^4*a^4*b^4 - 26973*A*B^3*a^3*b^5 + 3066*A^2*B^2*a^2*b^6 - 35*A^3*B*a*b^7)*c^2 - 27*(1341*B^4*a^3*b^6 - 819*A*B^3*a^2*b^7 + 35*A^2*B^2*a*b^8)*c)*x - 1/2*sqrt(1/2)*(27*B^3*b^13 + 32000*A^3*a^5*c^8 - 640*(882*A*B^2*a^6 - 156*A^2*B*a^5*b + 37*A^3*a^4*b^2)*c^7 + 64*(10584*B^3*a^6*b + 5562*A*B^2*a^5*b^2 - 1083*A^2*B*a^4*b^3 + 89*A^3*a^3*b^4)*c^6 - 8*(93096*B^3*a^5*b^3 + 3816*A*B^2*a^4*b^4 - 1746*A^2*B*a^3*b^5 + 49*A^3*a^2*b^6)*c^5 + (337392*B^3*a^4*b^5 - 24120*A*B^2*a^3*b^6 - 84*A^2*B*a^2*b^7 - 17*A^3*a*b^8)*c^4 - (81324*B^3*a^3*b^7 - 6993*A*B^2*a^2*b^8 + 195*A^2*B*a*b^9 - A^3*b^10)*c^3 + 9*(1239*B^3*a^2*b^9 - 79*A*B^2*a*b^10 + A^2*B*b^11)*c^2 - 27*(31*B^3*a*b^11 - A*B^2*b^12)*c - (3*B*b^14*c^5 - 4096*(42*B*a^7 - 13*A*a^6*b)*c^12 + 6144*(40*B*a^6*b^2 - 11*A*a^5*b^3)*c^11 - 768*(194*B*a^5*b^4 - 45*A*a^4*b^5)*c^10 + 1280*(39*B*a^4*b^6 - 7*A*a^3*b^7)*c^9 - 240*(42*B*a^3*b^8 - 5*A*a^2*b^9)*c^8 + 24*(52*B*a^2*b^10 - 3*A*a*b^11)*c^7 - (90*B*a*b^12 - A*b^13)*c^6)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))*sqrt(-(9*B^2*b^9 - 1680*(4*A*B*a^4 - A^2*a^3*b)*c^5 + 280*(54*B^2*a^4*b - 12*A*B*a^3*b^2 + A^2*a^2*b^3)*c^4 - 35*(216*B^2*a^3*b^3 - 36*A*B*a^2*b^4 + A^2*a*b^5)*c^3 + (1701*B^2*a^2*b^5 - 168*A*B*a*b^6 + A^2*b^7)*c^2 - 3*(63*B^2*a*b^7 - 2*A*B*b^8)*c + (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))) - sqrt(1/2)*((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^8 + a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^6 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^4 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x^2)*sqrt(-(9*B^2*b^9 - 1680*(4*A*B*a^4 - A^2*a^3*b)*c^5 + 280*(54*B^2*a^4*b - 12*A*B*a^3*b^2 + A^2*a^2*b^3)*c^4 - 35*(216*B^2*a^3*b^3 - 36*A*B*a^2*b^4 + A^2*a*b^5)*c^3 + (1701*B^2*a^2*b^5 - 168*A*B*a*b^6 + A^2*b^7)*c^2 - 3*(63*B^2*a*b^7 - 2*A*B*b^8)*c - (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))*log(-(1701*B^4*a^2*b^8 - 945*A*B^3*a*b^9 - 10000*A^4*a^4*c^6 + 15000*(6*A^3*B*a^4*b - A^4*a^3*b^2)*c^5 + 3*(1037232*B^4*a^6 - 1037232*A*B^3*a^5*b + 287712*A^2*B^2*a^4*b^2 - 32952*A^3*B*a^3*b^3 + 497*A^4*a^2*b^4)*c^4 - (1555848*B^4*a^5*b^2 - 1298376*A*B^3*a^4*b^3 + 238464*A^2*B^2*a^3*b^4 - 11277*A^3*B*a^2*b^5 + 35*A^4*a*b^6)*c^3 + 9*(37701*B^4*a^4*b^4 - 26973*A*B^3*a^3*b^5 + 3066*A^2*B^2*a^2*b^6 - 35*A^3*B*a*b^7)*c^2 - 27*(1341*B^4*a^3*b^6 - 819*A*B^3*a^2*b^7 + 35*A^2*B^2*a*b^8)*c)*x + 1/2*sqrt(1/2)*(27*B^3*b^13 + 32000*A^3*a^5*c^8 - 640*(882*A*B^2*a^6 - 156*A^2*B*a^5*b + 37*A^3*a^4*b^2)*c^7 + 64*(10584*B^3*a^6*b + 5562*A*B^2*a^5*b^2 - 1083*A^2*B*a^4*b^3 + 89*A^3*a^3*b^4)*c^6 - 8*(93096*B^3*a^5*b^3 + 3816*A*B^2*a^4*b^4 - 1746*A^2*B*a^3*b^5 + 49*A^3*a^2*b^6)*c^5 + (337392*B^3*a^4*b^5 - 24120*A*B^2*a^3*b^6 - 84*A^2*B*a^2*b^7 - 17*A^3*a*b^8)*c^4 - (81324*B^3*a^3*b^7 - 6993*A*B^2*a^2*b^8 + 195*A^2*B*a*b^9 - A^3*b^10)*c^3 + 9*(1239*B^3*a^2*b^9 - 79*A*B^2*a*b^10 + A^2*B*b^11)*c^2 - 27*(31*B^3*a*b^11 - A*B^2*b^12)*c + (3*B*b^14*c^5 - 4096*(42*B*a^7 - 13*A*a^6*b)*c^12 + 6144*(40*B*a^6*b^2 - 11*A*a^5*b^3)*c^11 - 768*(194*B*a^5*b^4 - 45*A*a^4*b^5)*c^10 + 1280*(39*B*a^4*b^6 - 7*A*a^3*b^7)*c^9 - 240*(42*B*a^3*b^8 - 5*A*a^2*b^9)*c^8 + 24*(52*B*a^2*b^10 - 3*A*a*b^11)*c^7 - (90*B*a*b^12 - A*b^13)*c^6)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))*sqrt(-(9*B^2*b^9 - 1680*(4*A*B*a^4 - A^2*a^3*b)*c^5 + 280*(54*B^2*a^4*b - 12*A*B*a^3*b^2 + A^2*a^2*b^3)*c^4 - 35*(216*B^2*a^3*b^3 - 36*A*B*a^2*b^4 + A^2*a*b^5)*c^3 + (1701*B^2*a^2*b^5 - 168*A*B*a*b^6 + A^2*b^7)*c^2 - 3*(63*B^2*a*b^7 - 2*A*B*b^8)*c - (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))) + sqrt(1/2)*((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^8 + a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^6 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^4 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x^2)*sqrt(-(9*B^2*b^9 - 1680*(4*A*B*a^4 - A^2*a^3*b)*c^5 + 280*(54*B^2*a^4*b - 12*A*B*a^3*b^2 + A^2*a^2*b^3)*c^4 - 35*(216*B^2*a^3*b^3 - 36*A*B*a^2*b^4 + A^2*a*b^5)*c^3 + (1701*B^2*a^2*b^5 - 168*A*B*a*b^6 + A^2*b^7)*c^2 - 3*(63*B^2*a*b^7 - 2*A*B*b^8)*c - (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))*log(-(1701*B^4*a^2*b^8 - 945*A*B^3*a*b^9 - 10000*A^4*a^4*c^6 + 15000*(6*A^3*B*a^4*b - A^4*a^3*b^2)*c^5 + 3*(1037232*B^4*a^6 - 1037232*A*B^3*a^5*b + 287712*A^2*B^2*a^4*b^2 - 32952*A^3*B*a^3*b^3 + 497*A^4*a^2*b^4)*c^4 - (1555848*B^4*a^5*b^2 - 1298376*A*B^3*a^4*b^3 + 238464*A^2*B^2*a^3*b^4 - 11277*A^3*B*a^2*b^5 + 35*A^4*a*b^6)*c^3 + 9*(37701*B^4*a^4*b^4 - 26973*A*B^3*a^3*b^5 + 3066*A^2*B^2*a^2*b^6 - 35*A^3*B*a*b^7)*c^2 - 27*(1341*B^4*a^3*b^6 - 819*A*B^3*a^2*b^7 + 35*A^2*B^2*a*b^8)*c)*x - 1/2*sqrt(1/2)*(27*B^3*b^13 + 32000*A^3*a^5*c^8 - 640*(882*A*B^2*a^6 - 156*A^2*B*a^5*b + 37*A^3*a^4*b^2)*c^7 + 64*(10584*B^3*a^6*b + 5562*A*B^2*a^5*b^2 - 1083*A^2*B*a^4*b^3 + 89*A^3*a^3*b^4)*c^6 - 8*(93096*B^3*a^5*b^3 + 3816*A*B^2*a^4*b^4 - 1746*A^2*B*a^3*b^5 + 49*A^3*a^2*b^6)*c^5 + (337392*B^3*a^4*b^5 - 24120*A*B^2*a^3*b^6 - 84*A^2*B*a^2*b^7 - 17*A^3*a*b^8)*c^4 - (81324*B^3*a^3*b^7 - 6993*A*B^2*a^2*b^8 + 195*A^2*B*a*b^9 - A^3*b^10)*c^3 + 9*(1239*B^3*a^2*b^9 - 79*A*B^2*a*b^10 + A^2*B*b^11)*c^2 - 27*(31*B^3*a*b^11 - A*B^2*b^12)*c + (3*B*b^14*c^5 - 4096*(42*B*a^7 - 13*A*a^6*b)*c^12 + 6144*(40*B*a^6*b^2 - 11*A*a^5*b^3)*c^11 - 768*(194*B*a^5*b^4 - 45*A*a^4*b^5)*c^10 + 1280*(39*B*a^4*b^6 - 7*A*a^3*b^7)*c^9 - 240*(42*B*a^3*b^8 - 5*A*a^2*b^9)*c^8 + 24*(52*B*a^2*b^10 - 3*A*a*b^11)*c^7 - (90*B*a*b^12 - A*b^13)*c^6)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))*sqrt(-(9*B^2*b^9 - 1680*(4*A*B*a^4 - A^2*a^3*b)*c^5 + 280*(54*B^2*a^4*b - 12*A*B*a^3*b^2 + A^2*a^2*b^3)*c^4 - 35*(216*B^2*a^3*b^3 - 36*A*B*a^2*b^4 + A^2*a*b^5)*c^3 + (1701*B^2*a^2*b^5 - 168*A*B*a*b^6 + A^2*b^7)*c^2 - 3*(63*B^2*a*b^7 - 2*A*B*b^8)*c - (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((81*B^4*b^8 + 625*A^4*a^2*c^6 - 50*(441*A^2*B^2*a^3 - 108*A^3*B*a^2*b + A^4*a*b^2)*c^5 + (194481*B^4*a^4 - 95256*A*B^3*a^3*b + 17496*A^2*B^2*a^2*b^2 - 516*A^3*B*a*b^3 + A^4*b^4)*c^4 - 6*(14553*B^4*a^3*b^2 - 4446*A*B^3*a^2*b^3 + 324*A^2*B^2*a*b^4 - 2*A^3*B*b^5)*c^3 + 27*(657*B^4*a^2*b^4 - 116*A*B^3*a*b^5 + 2*A^2*B^2*b^6)*c^2 - 54*(33*B^4*a*b^6 - 2*A*B^3*b^7)*c)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))) + 2*(3*B*a^2*b^3 + 20*A*a^3*c^2 - (24*B*a^3*b - A*a^2*b^2)*c)*x)/((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^8 + a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^6 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^4 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x^2)","B",0
133,1,7060,0,6.935072," ","integrate(x^6*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(B b^{3} c + 12 \, A a c^{3} - {\left(16 \, B a b - 3 \, A b^{2}\right)} c^{2}\right)} x^{7} - 2 \, {\left(B b^{4} + 4 \, {\left(9 \, B a^{2} - 4 \, A a b\right)} c^{2} + 5 \, {\left(B a b^{2} - A b^{3}\right)} c\right)} x^{5} - 2 \, {\left(2 \, B a b^{3} + 4 \, A a^{2} c^{2} + {\left(28 \, B a^{2} b - 19 \, A a b^{2}\right)} c\right)} x^{3} - \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{8} + a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{6} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{4} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{2}\right)} \sqrt{-\frac{B^{2} b^{7} - 240 \, {\left(4 \, A B a^{3} - 3 \, A^{2} a^{2} b\right)} c^{4} + 120 \, {\left(14 \, B^{2} a^{3} b - 16 \, A B a^{2} b^{2} + 3 \, A^{2} a b^{3}\right)} c^{3} + {\left(280 \, B^{2} a^{2} b^{3} - 60 \, A B a b^{4} + 9 \, A^{2} b^{5}\right)} c^{2} - {\left(35 \, B^{2} a b^{5} - 6 \, A B b^{6}\right)} c + {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} \log\left(-{\left(35 \, B^{4} a b^{6} - 15 \, A B^{3} b^{7} - 1296 \, A^{4} a^{2} c^{5} + 648 \, {\left(14 \, A^{3} B a^{2} b - 5 \, A^{4} a b^{2}\right)} c^{4} + {\left(10000 \, B^{4} a^{4} - 30000 \, A B^{3} a^{3} b + 9936 \, A^{2} B^{2} a^{2} b^{2} + 1080 \, A^{3} B a b^{3} - 405 \, A^{4} b^{4}\right)} c^{3} + 3 \, {\left(5000 \, B^{4} a^{3} b^{2} - 3864 \, A B^{3} a^{2} b^{3} + 1080 \, A^{2} B^{2} a b^{4} - 135 \, A^{3} B b^{5}\right)} c^{2} - 3 \, {\left(497 \, B^{4} a^{2} b^{4} - 315 \, A B^{3} a b^{5} + 45 \, A^{2} B^{2} b^{6}\right)} c\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} b^{10} - 2304 \, {\left(5 \, A^{2} B a^{4} - 3 \, A^{3} a^{3} b\right)} c^{6} + 64 \, {\left(500 \, B^{3} a^{5} - 420 \, A B^{2} a^{4} b + 198 \, A^{2} B a^{3} b^{2} - 81 \, A^{3} a^{2} b^{3}\right)} c^{5} - 16 \, {\left(1480 \, B^{3} a^{4} b^{2} - 1284 \, A B^{2} a^{3} b^{3} + 324 \, A^{2} B a^{2} b^{4} - 81 \, A^{3} a b^{5}\right)} c^{4} + 4 \, {\left(1424 \, B^{3} a^{3} b^{4} - 1332 \, A B^{2} a^{2} b^{5} + 234 \, A^{2} B a b^{6} - 27 \, A^{3} b^{7}\right)} c^{3} - {\left(392 \, B^{3} a^{2} b^{6} - 492 \, A B^{2} a b^{7} + 63 \, A^{2} B b^{8}\right)} c^{2} - {\left(17 \, B^{3} a b^{8} + 6 \, A B^{2} b^{9}\right)} c - {\left(B b^{13} c^{3} - 24576 \, A a^{6} c^{10} + 4096 \, {\left(13 \, B a^{6} b + 3 \, A a^{5} b^{2}\right)} c^{9} - 1536 \, {\left(44 \, B a^{5} b^{3} - 5 \, A a^{4} b^{4}\right)} c^{8} + 3840 \, {\left(9 \, B a^{4} b^{5} - 2 \, A a^{3} b^{6}\right)} c^{7} - 160 \, {\left(56 \, B a^{3} b^{7} - 15 \, A a^{2} b^{8}\right)} c^{6} + 48 \, {\left(25 \, B a^{2} b^{9} - 7 \, A a b^{10}\right)} c^{5} - 18 \, {\left(4 \, B a b^{11} - A b^{12}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}\right)} \sqrt{-\frac{B^{2} b^{7} - 240 \, {\left(4 \, A B a^{3} - 3 \, A^{2} a^{2} b\right)} c^{4} + 120 \, {\left(14 \, B^{2} a^{3} b - 16 \, A B a^{2} b^{2} + 3 \, A^{2} a b^{3}\right)} c^{3} + {\left(280 \, B^{2} a^{2} b^{3} - 60 \, A B a b^{4} + 9 \, A^{2} b^{5}\right)} c^{2} - {\left(35 \, B^{2} a b^{5} - 6 \, A B b^{6}\right)} c + {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{8} + a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{6} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{4} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{2}\right)} \sqrt{-\frac{B^{2} b^{7} - 240 \, {\left(4 \, A B a^{3} - 3 \, A^{2} a^{2} b\right)} c^{4} + 120 \, {\left(14 \, B^{2} a^{3} b - 16 \, A B a^{2} b^{2} + 3 \, A^{2} a b^{3}\right)} c^{3} + {\left(280 \, B^{2} a^{2} b^{3} - 60 \, A B a b^{4} + 9 \, A^{2} b^{5}\right)} c^{2} - {\left(35 \, B^{2} a b^{5} - 6 \, A B b^{6}\right)} c + {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} \log\left(-{\left(35 \, B^{4} a b^{6} - 15 \, A B^{3} b^{7} - 1296 \, A^{4} a^{2} c^{5} + 648 \, {\left(14 \, A^{3} B a^{2} b - 5 \, A^{4} a b^{2}\right)} c^{4} + {\left(10000 \, B^{4} a^{4} - 30000 \, A B^{3} a^{3} b + 9936 \, A^{2} B^{2} a^{2} b^{2} + 1080 \, A^{3} B a b^{3} - 405 \, A^{4} b^{4}\right)} c^{3} + 3 \, {\left(5000 \, B^{4} a^{3} b^{2} - 3864 \, A B^{3} a^{2} b^{3} + 1080 \, A^{2} B^{2} a b^{4} - 135 \, A^{3} B b^{5}\right)} c^{2} - 3 \, {\left(497 \, B^{4} a^{2} b^{4} - 315 \, A B^{3} a b^{5} + 45 \, A^{2} B^{2} b^{6}\right)} c\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} b^{10} - 2304 \, {\left(5 \, A^{2} B a^{4} - 3 \, A^{3} a^{3} b\right)} c^{6} + 64 \, {\left(500 \, B^{3} a^{5} - 420 \, A B^{2} a^{4} b + 198 \, A^{2} B a^{3} b^{2} - 81 \, A^{3} a^{2} b^{3}\right)} c^{5} - 16 \, {\left(1480 \, B^{3} a^{4} b^{2} - 1284 \, A B^{2} a^{3} b^{3} + 324 \, A^{2} B a^{2} b^{4} - 81 \, A^{3} a b^{5}\right)} c^{4} + 4 \, {\left(1424 \, B^{3} a^{3} b^{4} - 1332 \, A B^{2} a^{2} b^{5} + 234 \, A^{2} B a b^{6} - 27 \, A^{3} b^{7}\right)} c^{3} - {\left(392 \, B^{3} a^{2} b^{6} - 492 \, A B^{2} a b^{7} + 63 \, A^{2} B b^{8}\right)} c^{2} - {\left(17 \, B^{3} a b^{8} + 6 \, A B^{2} b^{9}\right)} c - {\left(B b^{13} c^{3} - 24576 \, A a^{6} c^{10} + 4096 \, {\left(13 \, B a^{6} b + 3 \, A a^{5} b^{2}\right)} c^{9} - 1536 \, {\left(44 \, B a^{5} b^{3} - 5 \, A a^{4} b^{4}\right)} c^{8} + 3840 \, {\left(9 \, B a^{4} b^{5} - 2 \, A a^{3} b^{6}\right)} c^{7} - 160 \, {\left(56 \, B a^{3} b^{7} - 15 \, A a^{2} b^{8}\right)} c^{6} + 48 \, {\left(25 \, B a^{2} b^{9} - 7 \, A a b^{10}\right)} c^{5} - 18 \, {\left(4 \, B a b^{11} - A b^{12}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}\right)} \sqrt{-\frac{B^{2} b^{7} - 240 \, {\left(4 \, A B a^{3} - 3 \, A^{2} a^{2} b\right)} c^{4} + 120 \, {\left(14 \, B^{2} a^{3} b - 16 \, A B a^{2} b^{2} + 3 \, A^{2} a b^{3}\right)} c^{3} + {\left(280 \, B^{2} a^{2} b^{3} - 60 \, A B a b^{4} + 9 \, A^{2} b^{5}\right)} c^{2} - {\left(35 \, B^{2} a b^{5} - 6 \, A B b^{6}\right)} c + {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{8} + a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{6} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{4} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{2}\right)} \sqrt{-\frac{B^{2} b^{7} - 240 \, {\left(4 \, A B a^{3} - 3 \, A^{2} a^{2} b\right)} c^{4} + 120 \, {\left(14 \, B^{2} a^{3} b - 16 \, A B a^{2} b^{2} + 3 \, A^{2} a b^{3}\right)} c^{3} + {\left(280 \, B^{2} a^{2} b^{3} - 60 \, A B a b^{4} + 9 \, A^{2} b^{5}\right)} c^{2} - {\left(35 \, B^{2} a b^{5} - 6 \, A B b^{6}\right)} c - {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} \log\left(-{\left(35 \, B^{4} a b^{6} - 15 \, A B^{3} b^{7} - 1296 \, A^{4} a^{2} c^{5} + 648 \, {\left(14 \, A^{3} B a^{2} b - 5 \, A^{4} a b^{2}\right)} c^{4} + {\left(10000 \, B^{4} a^{4} - 30000 \, A B^{3} a^{3} b + 9936 \, A^{2} B^{2} a^{2} b^{2} + 1080 \, A^{3} B a b^{3} - 405 \, A^{4} b^{4}\right)} c^{3} + 3 \, {\left(5000 \, B^{4} a^{3} b^{2} - 3864 \, A B^{3} a^{2} b^{3} + 1080 \, A^{2} B^{2} a b^{4} - 135 \, A^{3} B b^{5}\right)} c^{2} - 3 \, {\left(497 \, B^{4} a^{2} b^{4} - 315 \, A B^{3} a b^{5} + 45 \, A^{2} B^{2} b^{6}\right)} c\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} b^{10} - 2304 \, {\left(5 \, A^{2} B a^{4} - 3 \, A^{3} a^{3} b\right)} c^{6} + 64 \, {\left(500 \, B^{3} a^{5} - 420 \, A B^{2} a^{4} b + 198 \, A^{2} B a^{3} b^{2} - 81 \, A^{3} a^{2} b^{3}\right)} c^{5} - 16 \, {\left(1480 \, B^{3} a^{4} b^{2} - 1284 \, A B^{2} a^{3} b^{3} + 324 \, A^{2} B a^{2} b^{4} - 81 \, A^{3} a b^{5}\right)} c^{4} + 4 \, {\left(1424 \, B^{3} a^{3} b^{4} - 1332 \, A B^{2} a^{2} b^{5} + 234 \, A^{2} B a b^{6} - 27 \, A^{3} b^{7}\right)} c^{3} - {\left(392 \, B^{3} a^{2} b^{6} - 492 \, A B^{2} a b^{7} + 63 \, A^{2} B b^{8}\right)} c^{2} - {\left(17 \, B^{3} a b^{8} + 6 \, A B^{2} b^{9}\right)} c + {\left(B b^{13} c^{3} - 24576 \, A a^{6} c^{10} + 4096 \, {\left(13 \, B a^{6} b + 3 \, A a^{5} b^{2}\right)} c^{9} - 1536 \, {\left(44 \, B a^{5} b^{3} - 5 \, A a^{4} b^{4}\right)} c^{8} + 3840 \, {\left(9 \, B a^{4} b^{5} - 2 \, A a^{3} b^{6}\right)} c^{7} - 160 \, {\left(56 \, B a^{3} b^{7} - 15 \, A a^{2} b^{8}\right)} c^{6} + 48 \, {\left(25 \, B a^{2} b^{9} - 7 \, A a b^{10}\right)} c^{5} - 18 \, {\left(4 \, B a b^{11} - A b^{12}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}\right)} \sqrt{-\frac{B^{2} b^{7} - 240 \, {\left(4 \, A B a^{3} - 3 \, A^{2} a^{2} b\right)} c^{4} + 120 \, {\left(14 \, B^{2} a^{3} b - 16 \, A B a^{2} b^{2} + 3 \, A^{2} a b^{3}\right)} c^{3} + {\left(280 \, B^{2} a^{2} b^{3} - 60 \, A B a b^{4} + 9 \, A^{2} b^{5}\right)} c^{2} - {\left(35 \, B^{2} a b^{5} - 6 \, A B b^{6}\right)} c - {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{8} + a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{6} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{4} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{2}\right)} \sqrt{-\frac{B^{2} b^{7} - 240 \, {\left(4 \, A B a^{3} - 3 \, A^{2} a^{2} b\right)} c^{4} + 120 \, {\left(14 \, B^{2} a^{3} b - 16 \, A B a^{2} b^{2} + 3 \, A^{2} a b^{3}\right)} c^{3} + {\left(280 \, B^{2} a^{2} b^{3} - 60 \, A B a b^{4} + 9 \, A^{2} b^{5}\right)} c^{2} - {\left(35 \, B^{2} a b^{5} - 6 \, A B b^{6}\right)} c - {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} \log\left(-{\left(35 \, B^{4} a b^{6} - 15 \, A B^{3} b^{7} - 1296 \, A^{4} a^{2} c^{5} + 648 \, {\left(14 \, A^{3} B a^{2} b - 5 \, A^{4} a b^{2}\right)} c^{4} + {\left(10000 \, B^{4} a^{4} - 30000 \, A B^{3} a^{3} b + 9936 \, A^{2} B^{2} a^{2} b^{2} + 1080 \, A^{3} B a b^{3} - 405 \, A^{4} b^{4}\right)} c^{3} + 3 \, {\left(5000 \, B^{4} a^{3} b^{2} - 3864 \, A B^{3} a^{2} b^{3} + 1080 \, A^{2} B^{2} a b^{4} - 135 \, A^{3} B b^{5}\right)} c^{2} - 3 \, {\left(497 \, B^{4} a^{2} b^{4} - 315 \, A B^{3} a b^{5} + 45 \, A^{2} B^{2} b^{6}\right)} c\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} b^{10} - 2304 \, {\left(5 \, A^{2} B a^{4} - 3 \, A^{3} a^{3} b\right)} c^{6} + 64 \, {\left(500 \, B^{3} a^{5} - 420 \, A B^{2} a^{4} b + 198 \, A^{2} B a^{3} b^{2} - 81 \, A^{3} a^{2} b^{3}\right)} c^{5} - 16 \, {\left(1480 \, B^{3} a^{4} b^{2} - 1284 \, A B^{2} a^{3} b^{3} + 324 \, A^{2} B a^{2} b^{4} - 81 \, A^{3} a b^{5}\right)} c^{4} + 4 \, {\left(1424 \, B^{3} a^{3} b^{4} - 1332 \, A B^{2} a^{2} b^{5} + 234 \, A^{2} B a b^{6} - 27 \, A^{3} b^{7}\right)} c^{3} - {\left(392 \, B^{3} a^{2} b^{6} - 492 \, A B^{2} a b^{7} + 63 \, A^{2} B b^{8}\right)} c^{2} - {\left(17 \, B^{3} a b^{8} + 6 \, A B^{2} b^{9}\right)} c + {\left(B b^{13} c^{3} - 24576 \, A a^{6} c^{10} + 4096 \, {\left(13 \, B a^{6} b + 3 \, A a^{5} b^{2}\right)} c^{9} - 1536 \, {\left(44 \, B a^{5} b^{3} - 5 \, A a^{4} b^{4}\right)} c^{8} + 3840 \, {\left(9 \, B a^{4} b^{5} - 2 \, A a^{3} b^{6}\right)} c^{7} - 160 \, {\left(56 \, B a^{3} b^{7} - 15 \, A a^{2} b^{8}\right)} c^{6} + 48 \, {\left(25 \, B a^{2} b^{9} - 7 \, A a b^{10}\right)} c^{5} - 18 \, {\left(4 \, B a b^{11} - A b^{12}\right)} c^{4}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}\right)} \sqrt{-\frac{B^{2} b^{7} - 240 \, {\left(4 \, A B a^{3} - 3 \, A^{2} a^{2} b\right)} c^{4} + 120 \, {\left(14 \, B^{2} a^{3} b - 16 \, A B a^{2} b^{2} + 3 \, A^{2} a b^{3}\right)} c^{3} + {\left(280 \, B^{2} a^{2} b^{3} - 60 \, A B a b^{4} + 9 \, A^{2} b^{5}\right)} c^{2} - {\left(35 \, B^{2} a b^{5} - 6 \, A B b^{6}\right)} c - {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{B^{4} b^{4} + 81 \, A^{4} c^{4} - 18 \, {\left(25 \, A^{2} B^{2} a - 6 \, A^{3} B b\right)} c^{3} + {\left(625 \, B^{4} a^{2} - 300 \, A B^{3} a b + 54 \, A^{2} B^{2} b^{2}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a b^{2} - 6 \, A B^{3} b^{3}\right)} c}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}}\right) - 2 \, {\left(B a^{2} b^{2} + 4 \, {\left(5 \, B a^{3} - 3 \, A a^{2} b\right)} c\right)} x}{16 \, {\left({\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{8} + a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{6} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{4} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{2}\right)}}"," ",0,"1/16*(2*(B*b^3*c + 12*A*a*c^3 - (16*B*a*b - 3*A*b^2)*c^2)*x^7 - 2*(B*b^4 + 4*(9*B*a^2 - 4*A*a*b)*c^2 + 5*(B*a*b^2 - A*b^3)*c)*x^5 - 2*(2*B*a*b^3 + 4*A*a^2*c^2 + (28*B*a^2*b - 19*A*a*b^2)*c)*x^3 - sqrt(1/2)*((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^8 + a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^6 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^4 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^2)*sqrt(-(B^2*b^7 - 240*(4*A*B*a^3 - 3*A^2*a^2*b)*c^4 + 120*(14*B^2*a^3*b - 16*A*B*a^2*b^2 + 3*A^2*a*b^3)*c^3 + (280*B^2*a^2*b^3 - 60*A*B*a*b^4 + 9*A^2*b^5)*c^2 - (35*B^2*a*b^5 - 6*A*B*b^6)*c + (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))*log(-(35*B^4*a*b^6 - 15*A*B^3*b^7 - 1296*A^4*a^2*c^5 + 648*(14*A^3*B*a^2*b - 5*A^4*a*b^2)*c^4 + (10000*B^4*a^4 - 30000*A*B^3*a^3*b + 9936*A^2*B^2*a^2*b^2 + 1080*A^3*B*a*b^3 - 405*A^4*b^4)*c^3 + 3*(5000*B^4*a^3*b^2 - 3864*A*B^3*a^2*b^3 + 1080*A^2*B^2*a*b^4 - 135*A^3*B*b^5)*c^2 - 3*(497*B^4*a^2*b^4 - 315*A*B^3*a*b^5 + 45*A^2*B^2*b^6)*c)*x + 1/2*sqrt(1/2)*(B^3*b^10 - 2304*(5*A^2*B*a^4 - 3*A^3*a^3*b)*c^6 + 64*(500*B^3*a^5 - 420*A*B^2*a^4*b + 198*A^2*B*a^3*b^2 - 81*A^3*a^2*b^3)*c^5 - 16*(1480*B^3*a^4*b^2 - 1284*A*B^2*a^3*b^3 + 324*A^2*B*a^2*b^4 - 81*A^3*a*b^5)*c^4 + 4*(1424*B^3*a^3*b^4 - 1332*A*B^2*a^2*b^5 + 234*A^2*B*a*b^6 - 27*A^3*b^7)*c^3 - (392*B^3*a^2*b^6 - 492*A*B^2*a*b^7 + 63*A^2*B*b^8)*c^2 - (17*B^3*a*b^8 + 6*A*B^2*b^9)*c - (B*b^13*c^3 - 24576*A*a^6*c^10 + 4096*(13*B*a^6*b + 3*A*a^5*b^2)*c^9 - 1536*(44*B*a^5*b^3 - 5*A*a^4*b^4)*c^8 + 3840*(9*B*a^4*b^5 - 2*A*a^3*b^6)*c^7 - 160*(56*B*a^3*b^7 - 15*A*a^2*b^8)*c^6 + 48*(25*B*a^2*b^9 - 7*A*a*b^10)*c^5 - 18*(4*B*a*b^11 - A*b^12)*c^4)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))*sqrt(-(B^2*b^7 - 240*(4*A*B*a^3 - 3*A^2*a^2*b)*c^4 + 120*(14*B^2*a^3*b - 16*A*B*a^2*b^2 + 3*A^2*a*b^3)*c^3 + (280*B^2*a^2*b^3 - 60*A*B*a*b^4 + 9*A^2*b^5)*c^2 - (35*B^2*a*b^5 - 6*A*B*b^6)*c + (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))) + sqrt(1/2)*((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^8 + a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^6 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^4 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^2)*sqrt(-(B^2*b^7 - 240*(4*A*B*a^3 - 3*A^2*a^2*b)*c^4 + 120*(14*B^2*a^3*b - 16*A*B*a^2*b^2 + 3*A^2*a*b^3)*c^3 + (280*B^2*a^2*b^3 - 60*A*B*a*b^4 + 9*A^2*b^5)*c^2 - (35*B^2*a*b^5 - 6*A*B*b^6)*c + (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))*log(-(35*B^4*a*b^6 - 15*A*B^3*b^7 - 1296*A^4*a^2*c^5 + 648*(14*A^3*B*a^2*b - 5*A^4*a*b^2)*c^4 + (10000*B^4*a^4 - 30000*A*B^3*a^3*b + 9936*A^2*B^2*a^2*b^2 + 1080*A^3*B*a*b^3 - 405*A^4*b^4)*c^3 + 3*(5000*B^4*a^3*b^2 - 3864*A*B^3*a^2*b^3 + 1080*A^2*B^2*a*b^4 - 135*A^3*B*b^5)*c^2 - 3*(497*B^4*a^2*b^4 - 315*A*B^3*a*b^5 + 45*A^2*B^2*b^6)*c)*x - 1/2*sqrt(1/2)*(B^3*b^10 - 2304*(5*A^2*B*a^4 - 3*A^3*a^3*b)*c^6 + 64*(500*B^3*a^5 - 420*A*B^2*a^4*b + 198*A^2*B*a^3*b^2 - 81*A^3*a^2*b^3)*c^5 - 16*(1480*B^3*a^4*b^2 - 1284*A*B^2*a^3*b^3 + 324*A^2*B*a^2*b^4 - 81*A^3*a*b^5)*c^4 + 4*(1424*B^3*a^3*b^4 - 1332*A*B^2*a^2*b^5 + 234*A^2*B*a*b^6 - 27*A^3*b^7)*c^3 - (392*B^3*a^2*b^6 - 492*A*B^2*a*b^7 + 63*A^2*B*b^8)*c^2 - (17*B^3*a*b^8 + 6*A*B^2*b^9)*c - (B*b^13*c^3 - 24576*A*a^6*c^10 + 4096*(13*B*a^6*b + 3*A*a^5*b^2)*c^9 - 1536*(44*B*a^5*b^3 - 5*A*a^4*b^4)*c^8 + 3840*(9*B*a^4*b^5 - 2*A*a^3*b^6)*c^7 - 160*(56*B*a^3*b^7 - 15*A*a^2*b^8)*c^6 + 48*(25*B*a^2*b^9 - 7*A*a*b^10)*c^5 - 18*(4*B*a*b^11 - A*b^12)*c^4)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))*sqrt(-(B^2*b^7 - 240*(4*A*B*a^3 - 3*A^2*a^2*b)*c^4 + 120*(14*B^2*a^3*b - 16*A*B*a^2*b^2 + 3*A^2*a*b^3)*c^3 + (280*B^2*a^2*b^3 - 60*A*B*a*b^4 + 9*A^2*b^5)*c^2 - (35*B^2*a*b^5 - 6*A*B*b^6)*c + (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))) - sqrt(1/2)*((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^8 + a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^6 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^4 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^2)*sqrt(-(B^2*b^7 - 240*(4*A*B*a^3 - 3*A^2*a^2*b)*c^4 + 120*(14*B^2*a^3*b - 16*A*B*a^2*b^2 + 3*A^2*a*b^3)*c^3 + (280*B^2*a^2*b^3 - 60*A*B*a*b^4 + 9*A^2*b^5)*c^2 - (35*B^2*a*b^5 - 6*A*B*b^6)*c - (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))*log(-(35*B^4*a*b^6 - 15*A*B^3*b^7 - 1296*A^4*a^2*c^5 + 648*(14*A^3*B*a^2*b - 5*A^4*a*b^2)*c^4 + (10000*B^4*a^4 - 30000*A*B^3*a^3*b + 9936*A^2*B^2*a^2*b^2 + 1080*A^3*B*a*b^3 - 405*A^4*b^4)*c^3 + 3*(5000*B^4*a^3*b^2 - 3864*A*B^3*a^2*b^3 + 1080*A^2*B^2*a*b^4 - 135*A^3*B*b^5)*c^2 - 3*(497*B^4*a^2*b^4 - 315*A*B^3*a*b^5 + 45*A^2*B^2*b^6)*c)*x + 1/2*sqrt(1/2)*(B^3*b^10 - 2304*(5*A^2*B*a^4 - 3*A^3*a^3*b)*c^6 + 64*(500*B^3*a^5 - 420*A*B^2*a^4*b + 198*A^2*B*a^3*b^2 - 81*A^3*a^2*b^3)*c^5 - 16*(1480*B^3*a^4*b^2 - 1284*A*B^2*a^3*b^3 + 324*A^2*B*a^2*b^4 - 81*A^3*a*b^5)*c^4 + 4*(1424*B^3*a^3*b^4 - 1332*A*B^2*a^2*b^5 + 234*A^2*B*a*b^6 - 27*A^3*b^7)*c^3 - (392*B^3*a^2*b^6 - 492*A*B^2*a*b^7 + 63*A^2*B*b^8)*c^2 - (17*B^3*a*b^8 + 6*A*B^2*b^9)*c + (B*b^13*c^3 - 24576*A*a^6*c^10 + 4096*(13*B*a^6*b + 3*A*a^5*b^2)*c^9 - 1536*(44*B*a^5*b^3 - 5*A*a^4*b^4)*c^8 + 3840*(9*B*a^4*b^5 - 2*A*a^3*b^6)*c^7 - 160*(56*B*a^3*b^7 - 15*A*a^2*b^8)*c^6 + 48*(25*B*a^2*b^9 - 7*A*a*b^10)*c^5 - 18*(4*B*a*b^11 - A*b^12)*c^4)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))*sqrt(-(B^2*b^7 - 240*(4*A*B*a^3 - 3*A^2*a^2*b)*c^4 + 120*(14*B^2*a^3*b - 16*A*B*a^2*b^2 + 3*A^2*a*b^3)*c^3 + (280*B^2*a^2*b^3 - 60*A*B*a*b^4 + 9*A^2*b^5)*c^2 - (35*B^2*a*b^5 - 6*A*B*b^6)*c - (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))) + sqrt(1/2)*((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^8 + a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^6 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^4 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^2)*sqrt(-(B^2*b^7 - 240*(4*A*B*a^3 - 3*A^2*a^2*b)*c^4 + 120*(14*B^2*a^3*b - 16*A*B*a^2*b^2 + 3*A^2*a*b^3)*c^3 + (280*B^2*a^2*b^3 - 60*A*B*a*b^4 + 9*A^2*b^5)*c^2 - (35*B^2*a*b^5 - 6*A*B*b^6)*c - (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))*log(-(35*B^4*a*b^6 - 15*A*B^3*b^7 - 1296*A^4*a^2*c^5 + 648*(14*A^3*B*a^2*b - 5*A^4*a*b^2)*c^4 + (10000*B^4*a^4 - 30000*A*B^3*a^3*b + 9936*A^2*B^2*a^2*b^2 + 1080*A^3*B*a*b^3 - 405*A^4*b^4)*c^3 + 3*(5000*B^4*a^3*b^2 - 3864*A*B^3*a^2*b^3 + 1080*A^2*B^2*a*b^4 - 135*A^3*B*b^5)*c^2 - 3*(497*B^4*a^2*b^4 - 315*A*B^3*a*b^5 + 45*A^2*B^2*b^6)*c)*x - 1/2*sqrt(1/2)*(B^3*b^10 - 2304*(5*A^2*B*a^4 - 3*A^3*a^3*b)*c^6 + 64*(500*B^3*a^5 - 420*A*B^2*a^4*b + 198*A^2*B*a^3*b^2 - 81*A^3*a^2*b^3)*c^5 - 16*(1480*B^3*a^4*b^2 - 1284*A*B^2*a^3*b^3 + 324*A^2*B*a^2*b^4 - 81*A^3*a*b^5)*c^4 + 4*(1424*B^3*a^3*b^4 - 1332*A*B^2*a^2*b^5 + 234*A^2*B*a*b^6 - 27*A^3*b^7)*c^3 - (392*B^3*a^2*b^6 - 492*A*B^2*a*b^7 + 63*A^2*B*b^8)*c^2 - (17*B^3*a*b^8 + 6*A*B^2*b^9)*c + (B*b^13*c^3 - 24576*A*a^6*c^10 + 4096*(13*B*a^6*b + 3*A*a^5*b^2)*c^9 - 1536*(44*B*a^5*b^3 - 5*A*a^4*b^4)*c^8 + 3840*(9*B*a^4*b^5 - 2*A*a^3*b^6)*c^7 - 160*(56*B*a^3*b^7 - 15*A*a^2*b^8)*c^6 + 48*(25*B*a^2*b^9 - 7*A*a*b^10)*c^5 - 18*(4*B*a*b^11 - A*b^12)*c^4)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))*sqrt(-(B^2*b^7 - 240*(4*A*B*a^3 - 3*A^2*a^2*b)*c^4 + 120*(14*B^2*a^3*b - 16*A*B*a^2*b^2 + 3*A^2*a*b^3)*c^3 + (280*B^2*a^2*b^3 - 60*A*B*a*b^4 + 9*A^2*b^5)*c^2 - (35*B^2*a*b^5 - 6*A*B*b^6)*c - (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((B^4*b^4 + 81*A^4*c^4 - 18*(25*A^2*B^2*a - 6*A^3*B*b)*c^3 + (625*B^4*a^2 - 300*A*B^3*a*b + 54*A^2*B^2*b^2)*c^2 - 2*(25*B^4*a*b^2 - 6*A*B^3*b^3)*c)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))) - 2*(B*a^2*b^2 + 4*(5*B*a^3 - 3*A*a^2*b)*c)*x)/((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^8 + a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^6 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^4 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^2)","B",0
134,1,5650,0,5.874226," ","integrate(x^4*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\frac{6 \, {\left(B b^{2} c + 4 \, {\left(B a - A b\right)} c^{2}\right)} x^{7} + 2 \, {\left(5 \, B b^{3} + 4 \, A a c^{2} + {\left(16 \, B a b - 19 \, A b^{2}\right)} c\right)} x^{5} + 2 \, {\left(19 \, B a b^{2} - 5 \, A b^{3} - 4 \, {\left(B a^{2} + 4 \, A a b\right)} c\right)} x^{3} - 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{B^{2} a b^{5} - 16 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{3} + 40 \, {\left(2 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{2} + {\left(40 \, B^{2} a^{2} b^{3} - 20 \, A B a b^{4} + A^{2} b^{5}\right)} c + {\left(a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}}{a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}}} \log\left(-27 \, {\left(5 \, B^{4} a^{2} b^{4} - A B^{3} a b^{5} - 16 \, A^{4} a^{2} c^{4} + 40 \, {\left(2 \, A^{3} B a^{2} b - A^{4} a b^{2}\right)} c^{3} + {\left(16 \, B^{4} a^{4} - 80 \, A B^{3} a^{3} b + 40 \, A^{3} B a b^{3} - 5 \, A^{4} b^{4}\right)} c^{2} + {\left(40 \, B^{4} a^{3} b^{2} - 40 \, A B^{3} a^{2} b^{3} + A^{3} B b^{5}\right)} c\right)} x + \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(4 \, B^{3} a^{2} b^{7} - A B^{2} a b^{8} - 256 \, A^{3} a^{4} c^{5} + 128 \, {\left(2 \, A B^{2} a^{5} + 2 \, A^{2} B a^{4} b + A^{3} a^{3} b^{2}\right)} c^{4} - 64 \, {\left(4 \, B^{3} a^{5} b + 2 \, A B^{2} a^{4} b^{2} + 3 \, A^{2} B a^{3} b^{3}\right)} c^{3} + 8 \, {\left(24 \, B^{3} a^{4} b^{3} + 6 \, A^{2} B a^{2} b^{5} - A^{3} a b^{6}\right)} c^{2} - {\left(48 \, B^{3} a^{3} b^{5} - 8 \, A B^{2} a^{2} b^{6} + 4 \, A^{2} B a b^{7} - A^{3} b^{8}\right)} c - {\left(4096 \, {\left(2 \, B a^{8} - 3 \, A a^{7} b\right)} c^{7} - 2048 \, {\left(2 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c^{6} - 1280 \, {\left(2 \, B a^{6} b^{4} + 5 \, A a^{5} b^{5}\right)} c^{5} + 1280 \, {\left(2 \, B a^{5} b^{6} + A a^{4} b^{7}\right)} c^{4} - 80 \, {\left(10 \, B a^{4} b^{8} + A a^{3} b^{9}\right)} c^{3} + 8 \, {\left(14 \, B a^{3} b^{10} - A a^{2} b^{11}\right)} c^{2} - {\left(6 \, B a^{2} b^{12} - A a b^{13}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}\right)} \sqrt{-\frac{B^{2} a b^{5} - 16 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{3} + 40 \, {\left(2 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{2} + {\left(40 \, B^{2} a^{2} b^{3} - 20 \, A B a b^{4} + A^{2} b^{5}\right)} c + {\left(a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}}{a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{B^{2} a b^{5} - 16 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{3} + 40 \, {\left(2 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{2} + {\left(40 \, B^{2} a^{2} b^{3} - 20 \, A B a b^{4} + A^{2} b^{5}\right)} c + {\left(a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}}{a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}}} \log\left(-27 \, {\left(5 \, B^{4} a^{2} b^{4} - A B^{3} a b^{5} - 16 \, A^{4} a^{2} c^{4} + 40 \, {\left(2 \, A^{3} B a^{2} b - A^{4} a b^{2}\right)} c^{3} + {\left(16 \, B^{4} a^{4} - 80 \, A B^{3} a^{3} b + 40 \, A^{3} B a b^{3} - 5 \, A^{4} b^{4}\right)} c^{2} + {\left(40 \, B^{4} a^{3} b^{2} - 40 \, A B^{3} a^{2} b^{3} + A^{3} B b^{5}\right)} c\right)} x - \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(4 \, B^{3} a^{2} b^{7} - A B^{2} a b^{8} - 256 \, A^{3} a^{4} c^{5} + 128 \, {\left(2 \, A B^{2} a^{5} + 2 \, A^{2} B a^{4} b + A^{3} a^{3} b^{2}\right)} c^{4} - 64 \, {\left(4 \, B^{3} a^{5} b + 2 \, A B^{2} a^{4} b^{2} + 3 \, A^{2} B a^{3} b^{3}\right)} c^{3} + 8 \, {\left(24 \, B^{3} a^{4} b^{3} + 6 \, A^{2} B a^{2} b^{5} - A^{3} a b^{6}\right)} c^{2} - {\left(48 \, B^{3} a^{3} b^{5} - 8 \, A B^{2} a^{2} b^{6} + 4 \, A^{2} B a b^{7} - A^{3} b^{8}\right)} c - {\left(4096 \, {\left(2 \, B a^{8} - 3 \, A a^{7} b\right)} c^{7} - 2048 \, {\left(2 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c^{6} - 1280 \, {\left(2 \, B a^{6} b^{4} + 5 \, A a^{5} b^{5}\right)} c^{5} + 1280 \, {\left(2 \, B a^{5} b^{6} + A a^{4} b^{7}\right)} c^{4} - 80 \, {\left(10 \, B a^{4} b^{8} + A a^{3} b^{9}\right)} c^{3} + 8 \, {\left(14 \, B a^{3} b^{10} - A a^{2} b^{11}\right)} c^{2} - {\left(6 \, B a^{2} b^{12} - A a b^{13}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}\right)} \sqrt{-\frac{B^{2} a b^{5} - 16 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{3} + 40 \, {\left(2 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{2} + {\left(40 \, B^{2} a^{2} b^{3} - 20 \, A B a b^{4} + A^{2} b^{5}\right)} c + {\left(a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}}{a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{B^{2} a b^{5} - 16 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{3} + 40 \, {\left(2 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{2} + {\left(40 \, B^{2} a^{2} b^{3} - 20 \, A B a b^{4} + A^{2} b^{5}\right)} c - {\left(a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}}{a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}}} \log\left(-27 \, {\left(5 \, B^{4} a^{2} b^{4} - A B^{3} a b^{5} - 16 \, A^{4} a^{2} c^{4} + 40 \, {\left(2 \, A^{3} B a^{2} b - A^{4} a b^{2}\right)} c^{3} + {\left(16 \, B^{4} a^{4} - 80 \, A B^{3} a^{3} b + 40 \, A^{3} B a b^{3} - 5 \, A^{4} b^{4}\right)} c^{2} + {\left(40 \, B^{4} a^{3} b^{2} - 40 \, A B^{3} a^{2} b^{3} + A^{3} B b^{5}\right)} c\right)} x + \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(4 \, B^{3} a^{2} b^{7} - A B^{2} a b^{8} - 256 \, A^{3} a^{4} c^{5} + 128 \, {\left(2 \, A B^{2} a^{5} + 2 \, A^{2} B a^{4} b + A^{3} a^{3} b^{2}\right)} c^{4} - 64 \, {\left(4 \, B^{3} a^{5} b + 2 \, A B^{2} a^{4} b^{2} + 3 \, A^{2} B a^{3} b^{3}\right)} c^{3} + 8 \, {\left(24 \, B^{3} a^{4} b^{3} + 6 \, A^{2} B a^{2} b^{5} - A^{3} a b^{6}\right)} c^{2} - {\left(48 \, B^{3} a^{3} b^{5} - 8 \, A B^{2} a^{2} b^{6} + 4 \, A^{2} B a b^{7} - A^{3} b^{8}\right)} c + {\left(4096 \, {\left(2 \, B a^{8} - 3 \, A a^{7} b\right)} c^{7} - 2048 \, {\left(2 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c^{6} - 1280 \, {\left(2 \, B a^{6} b^{4} + 5 \, A a^{5} b^{5}\right)} c^{5} + 1280 \, {\left(2 \, B a^{5} b^{6} + A a^{4} b^{7}\right)} c^{4} - 80 \, {\left(10 \, B a^{4} b^{8} + A a^{3} b^{9}\right)} c^{3} + 8 \, {\left(14 \, B a^{3} b^{10} - A a^{2} b^{11}\right)} c^{2} - {\left(6 \, B a^{2} b^{12} - A a b^{13}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}\right)} \sqrt{-\frac{B^{2} a b^{5} - 16 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{3} + 40 \, {\left(2 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{2} + {\left(40 \, B^{2} a^{2} b^{3} - 20 \, A B a b^{4} + A^{2} b^{5}\right)} c - {\left(a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}}{a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{B^{2} a b^{5} - 16 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{3} + 40 \, {\left(2 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{2} + {\left(40 \, B^{2} a^{2} b^{3} - 20 \, A B a b^{4} + A^{2} b^{5}\right)} c - {\left(a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}}{a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}}} \log\left(-27 \, {\left(5 \, B^{4} a^{2} b^{4} - A B^{3} a b^{5} - 16 \, A^{4} a^{2} c^{4} + 40 \, {\left(2 \, A^{3} B a^{2} b - A^{4} a b^{2}\right)} c^{3} + {\left(16 \, B^{4} a^{4} - 80 \, A B^{3} a^{3} b + 40 \, A^{3} B a b^{3} - 5 \, A^{4} b^{4}\right)} c^{2} + {\left(40 \, B^{4} a^{3} b^{2} - 40 \, A B^{3} a^{2} b^{3} + A^{3} B b^{5}\right)} c\right)} x - \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(4 \, B^{3} a^{2} b^{7} - A B^{2} a b^{8} - 256 \, A^{3} a^{4} c^{5} + 128 \, {\left(2 \, A B^{2} a^{5} + 2 \, A^{2} B a^{4} b + A^{3} a^{3} b^{2}\right)} c^{4} - 64 \, {\left(4 \, B^{3} a^{5} b + 2 \, A B^{2} a^{4} b^{2} + 3 \, A^{2} B a^{3} b^{3}\right)} c^{3} + 8 \, {\left(24 \, B^{3} a^{4} b^{3} + 6 \, A^{2} B a^{2} b^{5} - A^{3} a b^{6}\right)} c^{2} - {\left(48 \, B^{3} a^{3} b^{5} - 8 \, A B^{2} a^{2} b^{6} + 4 \, A^{2} B a b^{7} - A^{3} b^{8}\right)} c + {\left(4096 \, {\left(2 \, B a^{8} - 3 \, A a^{7} b\right)} c^{7} - 2048 \, {\left(2 \, B a^{7} b^{2} - 7 \, A a^{6} b^{3}\right)} c^{6} - 1280 \, {\left(2 \, B a^{6} b^{4} + 5 \, A a^{5} b^{5}\right)} c^{5} + 1280 \, {\left(2 \, B a^{5} b^{6} + A a^{4} b^{7}\right)} c^{4} - 80 \, {\left(10 \, B a^{4} b^{8} + A a^{3} b^{9}\right)} c^{3} + 8 \, {\left(14 \, B a^{3} b^{10} - A a^{2} b^{11}\right)} c^{2} - {\left(6 \, B a^{2} b^{12} - A a b^{13}\right)} c\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}\right)} \sqrt{-\frac{B^{2} a b^{5} - 16 \, {\left(4 \, A B a^{3} - 5 \, A^{2} a^{2} b\right)} c^{3} + 40 \, {\left(2 \, B^{2} a^{3} b - 4 \, A B a^{2} b^{2} + A^{2} a b^{3}\right)} c^{2} + {\left(40 \, B^{2} a^{2} b^{3} - 20 \, A B a b^{4} + A^{2} b^{5}\right)} c - {\left(a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}\right)} \sqrt{\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{2} b^{10} c^{2} - 20 \, a^{3} b^{8} c^{3} + 160 \, a^{4} b^{6} c^{4} - 640 \, a^{5} b^{4} c^{5} + 1280 \, a^{6} b^{2} c^{6} - 1024 \, a^{7} c^{7}}}}{a b^{10} c - 20 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} - 640 \, a^{4} b^{4} c^{4} + 1280 \, a^{5} b^{2} c^{5} - 1024 \, a^{6} c^{6}}}\right) + 6 \, {\left(4 \, B a^{2} b - A a b^{2} - 4 \, A a^{2} c\right)} x}{16 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{6} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x^{2}\right)}}"," ",0,"1/16*(6*(B*b^2*c + 4*(B*a - A*b)*c^2)*x^7 + 2*(5*B*b^3 + 4*A*a*c^2 + (16*B*a*b - 19*A*b^2)*c)*x^5 + 2*(19*B*a*b^2 - 5*A*b^3 - 4*(B*a^2 + 4*A*a*b)*c)*x^3 - 3*sqrt(1/2)*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2)*sqrt(-(B^2*a*b^5 - 16*(4*A*B*a^3 - 5*A^2*a^2*b)*c^3 + 40*(2*B^2*a^3*b - 4*A*B*a^2*b^2 + A^2*a*b^3)*c^2 + (40*B^2*a^2*b^3 - 20*A*B*a*b^4 + A^2*b^5)*c + (a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))/(a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6))*log(-27*(5*B^4*a^2*b^4 - A*B^3*a*b^5 - 16*A^4*a^2*c^4 + 40*(2*A^3*B*a^2*b - A^4*a*b^2)*c^3 + (16*B^4*a^4 - 80*A*B^3*a^3*b + 40*A^3*B*a*b^3 - 5*A^4*b^4)*c^2 + (40*B^4*a^3*b^2 - 40*A*B^3*a^2*b^3 + A^3*B*b^5)*c)*x + 27/2*sqrt(1/2)*(4*B^3*a^2*b^7 - A*B^2*a*b^8 - 256*A^3*a^4*c^5 + 128*(2*A*B^2*a^5 + 2*A^2*B*a^4*b + A^3*a^3*b^2)*c^4 - 64*(4*B^3*a^5*b + 2*A*B^2*a^4*b^2 + 3*A^2*B*a^3*b^3)*c^3 + 8*(24*B^3*a^4*b^3 + 6*A^2*B*a^2*b^5 - A^3*a*b^6)*c^2 - (48*B^3*a^3*b^5 - 8*A*B^2*a^2*b^6 + 4*A^2*B*a*b^7 - A^3*b^8)*c - (4096*(2*B*a^8 - 3*A*a^7*b)*c^7 - 2048*(2*B*a^7*b^2 - 7*A*a^6*b^3)*c^6 - 1280*(2*B*a^6*b^4 + 5*A*a^5*b^5)*c^5 + 1280*(2*B*a^5*b^6 + A*a^4*b^7)*c^4 - 80*(10*B*a^4*b^8 + A*a^3*b^9)*c^3 + 8*(14*B*a^3*b^10 - A*a^2*b^11)*c^2 - (6*B*a^2*b^12 - A*a*b^13)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))*sqrt(-(B^2*a*b^5 - 16*(4*A*B*a^3 - 5*A^2*a^2*b)*c^3 + 40*(2*B^2*a^3*b - 4*A*B*a^2*b^2 + A^2*a*b^3)*c^2 + (40*B^2*a^2*b^3 - 20*A*B*a*b^4 + A^2*b^5)*c + (a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))/(a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6))) + 3*sqrt(1/2)*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2)*sqrt(-(B^2*a*b^5 - 16*(4*A*B*a^3 - 5*A^2*a^2*b)*c^3 + 40*(2*B^2*a^3*b - 4*A*B*a^2*b^2 + A^2*a*b^3)*c^2 + (40*B^2*a^2*b^3 - 20*A*B*a*b^4 + A^2*b^5)*c + (a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))/(a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6))*log(-27*(5*B^4*a^2*b^4 - A*B^3*a*b^5 - 16*A^4*a^2*c^4 + 40*(2*A^3*B*a^2*b - A^4*a*b^2)*c^3 + (16*B^4*a^4 - 80*A*B^3*a^3*b + 40*A^3*B*a*b^3 - 5*A^4*b^4)*c^2 + (40*B^4*a^3*b^2 - 40*A*B^3*a^2*b^3 + A^3*B*b^5)*c)*x - 27/2*sqrt(1/2)*(4*B^3*a^2*b^7 - A*B^2*a*b^8 - 256*A^3*a^4*c^5 + 128*(2*A*B^2*a^5 + 2*A^2*B*a^4*b + A^3*a^3*b^2)*c^4 - 64*(4*B^3*a^5*b + 2*A*B^2*a^4*b^2 + 3*A^2*B*a^3*b^3)*c^3 + 8*(24*B^3*a^4*b^3 + 6*A^2*B*a^2*b^5 - A^3*a*b^6)*c^2 - (48*B^3*a^3*b^5 - 8*A*B^2*a^2*b^6 + 4*A^2*B*a*b^7 - A^3*b^8)*c - (4096*(2*B*a^8 - 3*A*a^7*b)*c^7 - 2048*(2*B*a^7*b^2 - 7*A*a^6*b^3)*c^6 - 1280*(2*B*a^6*b^4 + 5*A*a^5*b^5)*c^5 + 1280*(2*B*a^5*b^6 + A*a^4*b^7)*c^4 - 80*(10*B*a^4*b^8 + A*a^3*b^9)*c^3 + 8*(14*B*a^3*b^10 - A*a^2*b^11)*c^2 - (6*B*a^2*b^12 - A*a*b^13)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))*sqrt(-(B^2*a*b^5 - 16*(4*A*B*a^3 - 5*A^2*a^2*b)*c^3 + 40*(2*B^2*a^3*b - 4*A*B*a^2*b^2 + A^2*a*b^3)*c^2 + (40*B^2*a^2*b^3 - 20*A*B*a*b^4 + A^2*b^5)*c + (a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))/(a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6))) - 3*sqrt(1/2)*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2)*sqrt(-(B^2*a*b^5 - 16*(4*A*B*a^3 - 5*A^2*a^2*b)*c^3 + 40*(2*B^2*a^3*b - 4*A*B*a^2*b^2 + A^2*a*b^3)*c^2 + (40*B^2*a^2*b^3 - 20*A*B*a*b^4 + A^2*b^5)*c - (a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))/(a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6))*log(-27*(5*B^4*a^2*b^4 - A*B^3*a*b^5 - 16*A^4*a^2*c^4 + 40*(2*A^3*B*a^2*b - A^4*a*b^2)*c^3 + (16*B^4*a^4 - 80*A*B^3*a^3*b + 40*A^3*B*a*b^3 - 5*A^4*b^4)*c^2 + (40*B^4*a^3*b^2 - 40*A*B^3*a^2*b^3 + A^3*B*b^5)*c)*x + 27/2*sqrt(1/2)*(4*B^3*a^2*b^7 - A*B^2*a*b^8 - 256*A^3*a^4*c^5 + 128*(2*A*B^2*a^5 + 2*A^2*B*a^4*b + A^3*a^3*b^2)*c^4 - 64*(4*B^3*a^5*b + 2*A*B^2*a^4*b^2 + 3*A^2*B*a^3*b^3)*c^3 + 8*(24*B^3*a^4*b^3 + 6*A^2*B*a^2*b^5 - A^3*a*b^6)*c^2 - (48*B^3*a^3*b^5 - 8*A*B^2*a^2*b^6 + 4*A^2*B*a*b^7 - A^3*b^8)*c + (4096*(2*B*a^8 - 3*A*a^7*b)*c^7 - 2048*(2*B*a^7*b^2 - 7*A*a^6*b^3)*c^6 - 1280*(2*B*a^6*b^4 + 5*A*a^5*b^5)*c^5 + 1280*(2*B*a^5*b^6 + A*a^4*b^7)*c^4 - 80*(10*B*a^4*b^8 + A*a^3*b^9)*c^3 + 8*(14*B*a^3*b^10 - A*a^2*b^11)*c^2 - (6*B*a^2*b^12 - A*a*b^13)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))*sqrt(-(B^2*a*b^5 - 16*(4*A*B*a^3 - 5*A^2*a^2*b)*c^3 + 40*(2*B^2*a^3*b - 4*A*B*a^2*b^2 + A^2*a*b^3)*c^2 + (40*B^2*a^2*b^3 - 20*A*B*a*b^4 + A^2*b^5)*c - (a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))/(a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6))) + 3*sqrt(1/2)*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2)*sqrt(-(B^2*a*b^5 - 16*(4*A*B*a^3 - 5*A^2*a^2*b)*c^3 + 40*(2*B^2*a^3*b - 4*A*B*a^2*b^2 + A^2*a*b^3)*c^2 + (40*B^2*a^2*b^3 - 20*A*B*a*b^4 + A^2*b^5)*c - (a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))/(a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6))*log(-27*(5*B^4*a^2*b^4 - A*B^3*a*b^5 - 16*A^4*a^2*c^4 + 40*(2*A^3*B*a^2*b - A^4*a*b^2)*c^3 + (16*B^4*a^4 - 80*A*B^3*a^3*b + 40*A^3*B*a*b^3 - 5*A^4*b^4)*c^2 + (40*B^4*a^3*b^2 - 40*A*B^3*a^2*b^3 + A^3*B*b^5)*c)*x - 27/2*sqrt(1/2)*(4*B^3*a^2*b^7 - A*B^2*a*b^8 - 256*A^3*a^4*c^5 + 128*(2*A*B^2*a^5 + 2*A^2*B*a^4*b + A^3*a^3*b^2)*c^4 - 64*(4*B^3*a^5*b + 2*A*B^2*a^4*b^2 + 3*A^2*B*a^3*b^3)*c^3 + 8*(24*B^3*a^4*b^3 + 6*A^2*B*a^2*b^5 - A^3*a*b^6)*c^2 - (48*B^3*a^3*b^5 - 8*A*B^2*a^2*b^6 + 4*A^2*B*a*b^7 - A^3*b^8)*c + (4096*(2*B*a^8 - 3*A*a^7*b)*c^7 - 2048*(2*B*a^7*b^2 - 7*A*a^6*b^3)*c^6 - 1280*(2*B*a^6*b^4 + 5*A*a^5*b^5)*c^5 + 1280*(2*B*a^5*b^6 + A*a^4*b^7)*c^4 - 80*(10*B*a^4*b^8 + A*a^3*b^9)*c^3 + 8*(14*B*a^3*b^10 - A*a^2*b^11)*c^2 - (6*B*a^2*b^12 - A*a*b^13)*c)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))*sqrt(-(B^2*a*b^5 - 16*(4*A*B*a^3 - 5*A^2*a^2*b)*c^3 + 40*(2*B^2*a^3*b - 4*A*B*a^2*b^2 + A^2*a*b^3)*c^2 + (40*B^2*a^2*b^3 - 20*A*B*a*b^4 + A^2*b^5)*c - (a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6)*sqrt((B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^2*b^10*c^2 - 20*a^3*b^8*c^3 + 160*a^4*b^6*c^4 - 640*a^5*b^4*c^5 + 1280*a^6*b^2*c^6 - 1024*a^7*c^7)))/(a*b^10*c - 20*a^2*b^8*c^2 + 160*a^3*b^6*c^3 - 640*a^4*b^4*c^4 + 1280*a^5*b^2*c^5 - 1024*a^6*c^6))) + 6*(4*B*a^2*b - A*a*b^2 - 4*A*a^2*c)*x)/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^6 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x^2)","B",0
135,1,7270,0,9.418654," ","integrate(x^2*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(20 \, A a c^{3} - {\left(12 \, B a b - A b^{2}\right)} c^{2}\right)} x^{7} + 2 \, {\left(4 \, {\left(B a^{2} + 7 \, A a b\right)} c^{2} - {\left(19 \, B a b^{2} - 2 \, A b^{3}\right)} c\right)} x^{5} - 2 \, {\left(5 \, B a b^{3} - A b^{4} - 36 \, A a^{2} c^{2} + {\left(16 \, B a^{2} b - 5 \, A a b^{2}\right)} c\right)} x^{3} + \sqrt{\frac{1}{2}} {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} x^{8} + a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} x^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{5} + 6 \, A B a b^{6} + A^{2} b^{7} - 240 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 40 \, {\left(18 \, B^{2} a^{4} b - 48 \, A B a^{3} b^{2} + 7 \, A^{2} a^{2} b^{3}\right)} c^{2} + 5 \, {\left(72 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} - 7 \, A^{2} a b^{5}\right)} c + {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}} \log\left({\left(10000 \, A^{4} a^{3} c^{5} - 15000 \, {\left(2 \, A^{3} B a^{3} b - A^{4} a^{2} b^{2}\right)} c^{4} - 3 \, {\left(432 \, B^{4} a^{5} - 3024 \, A B^{3} a^{4} b - 3312 \, A^{2} B^{2} a^{3} b^{2} + 3864 \, A^{3} B a^{2} b^{3} + 497 \, A^{4} a b^{4}\right)} c^{3} - 5 \, {\left(648 \, B^{4} a^{4} b^{2} - 216 \, A B^{3} a^{3} b^{3} - 648 \, A^{2} B^{2} a^{2} b^{4} - 189 \, A^{3} B a b^{5} - 7 \, A^{4} b^{6}\right)} c^{2} - 15 \, {\left(27 \, B^{4} a^{3} b^{4} + 27 \, A B^{3} a^{2} b^{5} + 9 \, A^{2} B^{2} a b^{6} + A^{3} B b^{7}\right)} c\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} a^{3} b^{8} + 27 \, A B^{2} a^{2} b^{9} + 9 \, A^{2} B a b^{10} + A^{3} b^{11} + 6400 \, {\left(3 \, A^{2} B a^{6} - 4 \, A^{3} a^{5} b\right)} c^{5} - 64 \, {\left(108 \, B^{3} a^{7} - 72 \, A B^{2} a^{6} b + 66 \, A^{2} B a^{5} b^{2} - 341 \, A^{3} a^{4} b^{3}\right)} c^{4} + 16 \, {\left(216 \, B^{3} a^{6} b^{2} - 324 \, A B^{2} a^{5} b^{3} - 288 \, A^{2} B a^{4} b^{4} - 427 \, A^{3} a^{3} b^{5}\right)} c^{3} + 20 \, {\left(108 \, A B^{2} a^{4} b^{5} + 102 \, A^{2} B a^{3} b^{6} + 47 \, A^{3} a^{2} b^{7}\right)} c^{2} - {\left(216 \, B^{3} a^{4} b^{6} + 396 \, A B^{2} a^{3} b^{7} + 267 \, A^{2} B a^{2} b^{8} + 53 \, A^{3} a b^{9}\right)} c - {\left(3 \, B a^{4} b^{13} + A a^{3} b^{14} + 40960 \, A a^{10} c^{7} - 4096 \, {\left(9 \, B a^{10} b + 8 \, A a^{9} b^{2}\right)} c^{6} + 1536 \, {\left(28 \, B a^{9} b^{3} + A a^{8} b^{4}\right)} c^{5} - 6400 \, {\left(3 \, B a^{8} b^{5} - A a^{7} b^{6}\right)} c^{4} + 160 \, {\left(24 \, B a^{7} b^{7} - 17 \, A a^{6} b^{8}\right)} c^{3} - 240 \, {\left(B a^{6} b^{9} - 2 \, A a^{5} b^{10}\right)} c^{2} - 2 \, {\left(12 \, B a^{5} b^{11} + 19 \, A a^{4} b^{12}\right)} c\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{5} + 6 \, A B a b^{6} + A^{2} b^{7} - 240 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 40 \, {\left(18 \, B^{2} a^{4} b - 48 \, A B a^{3} b^{2} + 7 \, A^{2} a^{2} b^{3}\right)} c^{2} + 5 \, {\left(72 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} - 7 \, A^{2} a b^{5}\right)} c + {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} x^{8} + a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} x^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{5} + 6 \, A B a b^{6} + A^{2} b^{7} - 240 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 40 \, {\left(18 \, B^{2} a^{4} b - 48 \, A B a^{3} b^{2} + 7 \, A^{2} a^{2} b^{3}\right)} c^{2} + 5 \, {\left(72 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} - 7 \, A^{2} a b^{5}\right)} c + {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}} \log\left({\left(10000 \, A^{4} a^{3} c^{5} - 15000 \, {\left(2 \, A^{3} B a^{3} b - A^{4} a^{2} b^{2}\right)} c^{4} - 3 \, {\left(432 \, B^{4} a^{5} - 3024 \, A B^{3} a^{4} b - 3312 \, A^{2} B^{2} a^{3} b^{2} + 3864 \, A^{3} B a^{2} b^{3} + 497 \, A^{4} a b^{4}\right)} c^{3} - 5 \, {\left(648 \, B^{4} a^{4} b^{2} - 216 \, A B^{3} a^{3} b^{3} - 648 \, A^{2} B^{2} a^{2} b^{4} - 189 \, A^{3} B a b^{5} - 7 \, A^{4} b^{6}\right)} c^{2} - 15 \, {\left(27 \, B^{4} a^{3} b^{4} + 27 \, A B^{3} a^{2} b^{5} + 9 \, A^{2} B^{2} a b^{6} + A^{3} B b^{7}\right)} c\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} a^{3} b^{8} + 27 \, A B^{2} a^{2} b^{9} + 9 \, A^{2} B a b^{10} + A^{3} b^{11} + 6400 \, {\left(3 \, A^{2} B a^{6} - 4 \, A^{3} a^{5} b\right)} c^{5} - 64 \, {\left(108 \, B^{3} a^{7} - 72 \, A B^{2} a^{6} b + 66 \, A^{2} B a^{5} b^{2} - 341 \, A^{3} a^{4} b^{3}\right)} c^{4} + 16 \, {\left(216 \, B^{3} a^{6} b^{2} - 324 \, A B^{2} a^{5} b^{3} - 288 \, A^{2} B a^{4} b^{4} - 427 \, A^{3} a^{3} b^{5}\right)} c^{3} + 20 \, {\left(108 \, A B^{2} a^{4} b^{5} + 102 \, A^{2} B a^{3} b^{6} + 47 \, A^{3} a^{2} b^{7}\right)} c^{2} - {\left(216 \, B^{3} a^{4} b^{6} + 396 \, A B^{2} a^{3} b^{7} + 267 \, A^{2} B a^{2} b^{8} + 53 \, A^{3} a b^{9}\right)} c - {\left(3 \, B a^{4} b^{13} + A a^{3} b^{14} + 40960 \, A a^{10} c^{7} - 4096 \, {\left(9 \, B a^{10} b + 8 \, A a^{9} b^{2}\right)} c^{6} + 1536 \, {\left(28 \, B a^{9} b^{3} + A a^{8} b^{4}\right)} c^{5} - 6400 \, {\left(3 \, B a^{8} b^{5} - A a^{7} b^{6}\right)} c^{4} + 160 \, {\left(24 \, B a^{7} b^{7} - 17 \, A a^{6} b^{8}\right)} c^{3} - 240 \, {\left(B a^{6} b^{9} - 2 \, A a^{5} b^{10}\right)} c^{2} - 2 \, {\left(12 \, B a^{5} b^{11} + 19 \, A a^{4} b^{12}\right)} c\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{5} + 6 \, A B a b^{6} + A^{2} b^{7} - 240 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 40 \, {\left(18 \, B^{2} a^{4} b - 48 \, A B a^{3} b^{2} + 7 \, A^{2} a^{2} b^{3}\right)} c^{2} + 5 \, {\left(72 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} - 7 \, A^{2} a b^{5}\right)} c + {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} x^{8} + a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} x^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{5} + 6 \, A B a b^{6} + A^{2} b^{7} - 240 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 40 \, {\left(18 \, B^{2} a^{4} b - 48 \, A B a^{3} b^{2} + 7 \, A^{2} a^{2} b^{3}\right)} c^{2} + 5 \, {\left(72 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} - 7 \, A^{2} a b^{5}\right)} c - {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}} \log\left({\left(10000 \, A^{4} a^{3} c^{5} - 15000 \, {\left(2 \, A^{3} B a^{3} b - A^{4} a^{2} b^{2}\right)} c^{4} - 3 \, {\left(432 \, B^{4} a^{5} - 3024 \, A B^{3} a^{4} b - 3312 \, A^{2} B^{2} a^{3} b^{2} + 3864 \, A^{3} B a^{2} b^{3} + 497 \, A^{4} a b^{4}\right)} c^{3} - 5 \, {\left(648 \, B^{4} a^{4} b^{2} - 216 \, A B^{3} a^{3} b^{3} - 648 \, A^{2} B^{2} a^{2} b^{4} - 189 \, A^{3} B a b^{5} - 7 \, A^{4} b^{6}\right)} c^{2} - 15 \, {\left(27 \, B^{4} a^{3} b^{4} + 27 \, A B^{3} a^{2} b^{5} + 9 \, A^{2} B^{2} a b^{6} + A^{3} B b^{7}\right)} c\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} a^{3} b^{8} + 27 \, A B^{2} a^{2} b^{9} + 9 \, A^{2} B a b^{10} + A^{3} b^{11} + 6400 \, {\left(3 \, A^{2} B a^{6} - 4 \, A^{3} a^{5} b\right)} c^{5} - 64 \, {\left(108 \, B^{3} a^{7} - 72 \, A B^{2} a^{6} b + 66 \, A^{2} B a^{5} b^{2} - 341 \, A^{3} a^{4} b^{3}\right)} c^{4} + 16 \, {\left(216 \, B^{3} a^{6} b^{2} - 324 \, A B^{2} a^{5} b^{3} - 288 \, A^{2} B a^{4} b^{4} - 427 \, A^{3} a^{3} b^{5}\right)} c^{3} + 20 \, {\left(108 \, A B^{2} a^{4} b^{5} + 102 \, A^{2} B a^{3} b^{6} + 47 \, A^{3} a^{2} b^{7}\right)} c^{2} - {\left(216 \, B^{3} a^{4} b^{6} + 396 \, A B^{2} a^{3} b^{7} + 267 \, A^{2} B a^{2} b^{8} + 53 \, A^{3} a b^{9}\right)} c + {\left(3 \, B a^{4} b^{13} + A a^{3} b^{14} + 40960 \, A a^{10} c^{7} - 4096 \, {\left(9 \, B a^{10} b + 8 \, A a^{9} b^{2}\right)} c^{6} + 1536 \, {\left(28 \, B a^{9} b^{3} + A a^{8} b^{4}\right)} c^{5} - 6400 \, {\left(3 \, B a^{8} b^{5} - A a^{7} b^{6}\right)} c^{4} + 160 \, {\left(24 \, B a^{7} b^{7} - 17 \, A a^{6} b^{8}\right)} c^{3} - 240 \, {\left(B a^{6} b^{9} - 2 \, A a^{5} b^{10}\right)} c^{2} - 2 \, {\left(12 \, B a^{5} b^{11} + 19 \, A a^{4} b^{12}\right)} c\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{5} + 6 \, A B a b^{6} + A^{2} b^{7} - 240 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 40 \, {\left(18 \, B^{2} a^{4} b - 48 \, A B a^{3} b^{2} + 7 \, A^{2} a^{2} b^{3}\right)} c^{2} + 5 \, {\left(72 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} - 7 \, A^{2} a b^{5}\right)} c - {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} x^{8} + a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} x^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{5} + 6 \, A B a b^{6} + A^{2} b^{7} - 240 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 40 \, {\left(18 \, B^{2} a^{4} b - 48 \, A B a^{3} b^{2} + 7 \, A^{2} a^{2} b^{3}\right)} c^{2} + 5 \, {\left(72 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} - 7 \, A^{2} a b^{5}\right)} c - {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}} \log\left({\left(10000 \, A^{4} a^{3} c^{5} - 15000 \, {\left(2 \, A^{3} B a^{3} b - A^{4} a^{2} b^{2}\right)} c^{4} - 3 \, {\left(432 \, B^{4} a^{5} - 3024 \, A B^{3} a^{4} b - 3312 \, A^{2} B^{2} a^{3} b^{2} + 3864 \, A^{3} B a^{2} b^{3} + 497 \, A^{4} a b^{4}\right)} c^{3} - 5 \, {\left(648 \, B^{4} a^{4} b^{2} - 216 \, A B^{3} a^{3} b^{3} - 648 \, A^{2} B^{2} a^{2} b^{4} - 189 \, A^{3} B a b^{5} - 7 \, A^{4} b^{6}\right)} c^{2} - 15 \, {\left(27 \, B^{4} a^{3} b^{4} + 27 \, A B^{3} a^{2} b^{5} + 9 \, A^{2} B^{2} a b^{6} + A^{3} B b^{7}\right)} c\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(27 \, B^{3} a^{3} b^{8} + 27 \, A B^{2} a^{2} b^{9} + 9 \, A^{2} B a b^{10} + A^{3} b^{11} + 6400 \, {\left(3 \, A^{2} B a^{6} - 4 \, A^{3} a^{5} b\right)} c^{5} - 64 \, {\left(108 \, B^{3} a^{7} - 72 \, A B^{2} a^{6} b + 66 \, A^{2} B a^{5} b^{2} - 341 \, A^{3} a^{4} b^{3}\right)} c^{4} + 16 \, {\left(216 \, B^{3} a^{6} b^{2} - 324 \, A B^{2} a^{5} b^{3} - 288 \, A^{2} B a^{4} b^{4} - 427 \, A^{3} a^{3} b^{5}\right)} c^{3} + 20 \, {\left(108 \, A B^{2} a^{4} b^{5} + 102 \, A^{2} B a^{3} b^{6} + 47 \, A^{3} a^{2} b^{7}\right)} c^{2} - {\left(216 \, B^{3} a^{4} b^{6} + 396 \, A B^{2} a^{3} b^{7} + 267 \, A^{2} B a^{2} b^{8} + 53 \, A^{3} a b^{9}\right)} c + {\left(3 \, B a^{4} b^{13} + A a^{3} b^{14} + 40960 \, A a^{10} c^{7} - 4096 \, {\left(9 \, B a^{10} b + 8 \, A a^{9} b^{2}\right)} c^{6} + 1536 \, {\left(28 \, B a^{9} b^{3} + A a^{8} b^{4}\right)} c^{5} - 6400 \, {\left(3 \, B a^{8} b^{5} - A a^{7} b^{6}\right)} c^{4} + 160 \, {\left(24 \, B a^{7} b^{7} - 17 \, A a^{6} b^{8}\right)} c^{3} - 240 \, {\left(B a^{6} b^{9} - 2 \, A a^{5} b^{10}\right)} c^{2} - 2 \, {\left(12 \, B a^{5} b^{11} + 19 \, A a^{4} b^{12}\right)} c\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}\right)} \sqrt{-\frac{9 \, B^{2} a^{2} b^{5} + 6 \, A B a b^{6} + A^{2} b^{7} - 240 \, {\left(4 \, A B a^{4} - 7 \, A^{2} a^{3} b\right)} c^{3} + 40 \, {\left(18 \, B^{2} a^{4} b - 48 \, A B a^{3} b^{2} + 7 \, A^{2} a^{2} b^{3}\right)} c^{2} + 5 \, {\left(72 \, B^{2} a^{3} b^{3} - 12 \, A B a^{2} b^{4} - 7 \, A^{2} a b^{5}\right)} c - {\left(a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}\right)} \sqrt{\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4} + 625 \, A^{4} a^{2} c^{2} - 50 \, {\left(9 \, A^{2} B^{2} a^{3} + 6 \, A^{3} B a^{2} b + A^{4} a b^{2}\right)} c}{a^{6} b^{10} - 20 \, a^{7} b^{8} c + 160 \, a^{8} b^{6} c^{2} - 640 \, a^{9} b^{4} c^{3} + 1280 \, a^{10} b^{2} c^{4} - 1024 \, a^{11} c^{5}}}}{a^{3} b^{10} - 20 \, a^{4} b^{8} c + 160 \, a^{5} b^{6} c^{2} - 640 \, a^{6} b^{4} c^{3} + 1280 \, a^{7} b^{2} c^{4} - 1024 \, a^{8} c^{5}}}\right) - 2 \, {\left(3 \, B a^{2} b^{2} + A a b^{3} + 4 \, {\left(3 \, B a^{3} - 4 \, A a^{2} b\right)} c\right)} x}{16 \, {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} x^{8} + a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} x^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{2}\right)}}"," ",0,"1/16*(2*(20*A*a*c^3 - (12*B*a*b - A*b^2)*c^2)*x^7 + 2*(4*(B*a^2 + 7*A*a*b)*c^2 - (19*B*a*b^2 - 2*A*b^3)*c)*x^5 - 2*(5*B*a*b^3 - A*b^4 - 36*A*a^2*c^2 + (16*B*a^2*b - 5*A*a*b^2)*c)*x^3 + sqrt(1/2)*((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*x^8 + a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*x^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2)*sqrt(-(9*B^2*a^2*b^5 + 6*A*B*a*b^6 + A^2*b^7 - 240*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 40*(18*B^2*a^4*b - 48*A*B*a^3*b^2 + 7*A^2*a^2*b^3)*c^2 + 5*(72*B^2*a^3*b^3 - 12*A*B*a^2*b^4 - 7*A^2*a*b^5)*c + (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5))*log((10000*A^4*a^3*c^5 - 15000*(2*A^3*B*a^3*b - A^4*a^2*b^2)*c^4 - 3*(432*B^4*a^5 - 3024*A*B^3*a^4*b - 3312*A^2*B^2*a^3*b^2 + 3864*A^3*B*a^2*b^3 + 497*A^4*a*b^4)*c^3 - 5*(648*B^4*a^4*b^2 - 216*A*B^3*a^3*b^3 - 648*A^2*B^2*a^2*b^4 - 189*A^3*B*a*b^5 - 7*A^4*b^6)*c^2 - 15*(27*B^4*a^3*b^4 + 27*A*B^3*a^2*b^5 + 9*A^2*B^2*a*b^6 + A^3*B*b^7)*c)*x + 1/2*sqrt(1/2)*(27*B^3*a^3*b^8 + 27*A*B^2*a^2*b^9 + 9*A^2*B*a*b^10 + A^3*b^11 + 6400*(3*A^2*B*a^6 - 4*A^3*a^5*b)*c^5 - 64*(108*B^3*a^7 - 72*A*B^2*a^6*b + 66*A^2*B*a^5*b^2 - 341*A^3*a^4*b^3)*c^4 + 16*(216*B^3*a^6*b^2 - 324*A*B^2*a^5*b^3 - 288*A^2*B*a^4*b^4 - 427*A^3*a^3*b^5)*c^3 + 20*(108*A*B^2*a^4*b^5 + 102*A^2*B*a^3*b^6 + 47*A^3*a^2*b^7)*c^2 - (216*B^3*a^4*b^6 + 396*A*B^2*a^3*b^7 + 267*A^2*B*a^2*b^8 + 53*A^3*a*b^9)*c - (3*B*a^4*b^13 + A*a^3*b^14 + 40960*A*a^10*c^7 - 4096*(9*B*a^10*b + 8*A*a^9*b^2)*c^6 + 1536*(28*B*a^9*b^3 + A*a^8*b^4)*c^5 - 6400*(3*B*a^8*b^5 - A*a^7*b^6)*c^4 + 160*(24*B*a^7*b^7 - 17*A*a^6*b^8)*c^3 - 240*(B*a^6*b^9 - 2*A*a^5*b^10)*c^2 - 2*(12*B*a^5*b^11 + 19*A*a^4*b^12)*c)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))*sqrt(-(9*B^2*a^2*b^5 + 6*A*B*a*b^6 + A^2*b^7 - 240*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 40*(18*B^2*a^4*b - 48*A*B*a^3*b^2 + 7*A^2*a^2*b^3)*c^2 + 5*(72*B^2*a^3*b^3 - 12*A*B*a^2*b^4 - 7*A^2*a*b^5)*c + (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5))) - sqrt(1/2)*((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*x^8 + a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*x^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2)*sqrt(-(9*B^2*a^2*b^5 + 6*A*B*a*b^6 + A^2*b^7 - 240*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 40*(18*B^2*a^4*b - 48*A*B*a^3*b^2 + 7*A^2*a^2*b^3)*c^2 + 5*(72*B^2*a^3*b^3 - 12*A*B*a^2*b^4 - 7*A^2*a*b^5)*c + (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5))*log((10000*A^4*a^3*c^5 - 15000*(2*A^3*B*a^3*b - A^4*a^2*b^2)*c^4 - 3*(432*B^4*a^5 - 3024*A*B^3*a^4*b - 3312*A^2*B^2*a^3*b^2 + 3864*A^3*B*a^2*b^3 + 497*A^4*a*b^4)*c^3 - 5*(648*B^4*a^4*b^2 - 216*A*B^3*a^3*b^3 - 648*A^2*B^2*a^2*b^4 - 189*A^3*B*a*b^5 - 7*A^4*b^6)*c^2 - 15*(27*B^4*a^3*b^4 + 27*A*B^3*a^2*b^5 + 9*A^2*B^2*a*b^6 + A^3*B*b^7)*c)*x - 1/2*sqrt(1/2)*(27*B^3*a^3*b^8 + 27*A*B^2*a^2*b^9 + 9*A^2*B*a*b^10 + A^3*b^11 + 6400*(3*A^2*B*a^6 - 4*A^3*a^5*b)*c^5 - 64*(108*B^3*a^7 - 72*A*B^2*a^6*b + 66*A^2*B*a^5*b^2 - 341*A^3*a^4*b^3)*c^4 + 16*(216*B^3*a^6*b^2 - 324*A*B^2*a^5*b^3 - 288*A^2*B*a^4*b^4 - 427*A^3*a^3*b^5)*c^3 + 20*(108*A*B^2*a^4*b^5 + 102*A^2*B*a^3*b^6 + 47*A^3*a^2*b^7)*c^2 - (216*B^3*a^4*b^6 + 396*A*B^2*a^3*b^7 + 267*A^2*B*a^2*b^8 + 53*A^3*a*b^9)*c - (3*B*a^4*b^13 + A*a^3*b^14 + 40960*A*a^10*c^7 - 4096*(9*B*a^10*b + 8*A*a^9*b^2)*c^6 + 1536*(28*B*a^9*b^3 + A*a^8*b^4)*c^5 - 6400*(3*B*a^8*b^5 - A*a^7*b^6)*c^4 + 160*(24*B*a^7*b^7 - 17*A*a^6*b^8)*c^3 - 240*(B*a^6*b^9 - 2*A*a^5*b^10)*c^2 - 2*(12*B*a^5*b^11 + 19*A*a^4*b^12)*c)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))*sqrt(-(9*B^2*a^2*b^5 + 6*A*B*a*b^6 + A^2*b^7 - 240*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 40*(18*B^2*a^4*b - 48*A*B*a^3*b^2 + 7*A^2*a^2*b^3)*c^2 + 5*(72*B^2*a^3*b^3 - 12*A*B*a^2*b^4 - 7*A^2*a*b^5)*c + (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5))) + sqrt(1/2)*((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*x^8 + a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*x^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2)*sqrt(-(9*B^2*a^2*b^5 + 6*A*B*a*b^6 + A^2*b^7 - 240*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 40*(18*B^2*a^4*b - 48*A*B*a^3*b^2 + 7*A^2*a^2*b^3)*c^2 + 5*(72*B^2*a^3*b^3 - 12*A*B*a^2*b^4 - 7*A^2*a*b^5)*c - (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5))*log((10000*A^4*a^3*c^5 - 15000*(2*A^3*B*a^3*b - A^4*a^2*b^2)*c^4 - 3*(432*B^4*a^5 - 3024*A*B^3*a^4*b - 3312*A^2*B^2*a^3*b^2 + 3864*A^3*B*a^2*b^3 + 497*A^4*a*b^4)*c^3 - 5*(648*B^4*a^4*b^2 - 216*A*B^3*a^3*b^3 - 648*A^2*B^2*a^2*b^4 - 189*A^3*B*a*b^5 - 7*A^4*b^6)*c^2 - 15*(27*B^4*a^3*b^4 + 27*A*B^3*a^2*b^5 + 9*A^2*B^2*a*b^6 + A^3*B*b^7)*c)*x + 1/2*sqrt(1/2)*(27*B^3*a^3*b^8 + 27*A*B^2*a^2*b^9 + 9*A^2*B*a*b^10 + A^3*b^11 + 6400*(3*A^2*B*a^6 - 4*A^3*a^5*b)*c^5 - 64*(108*B^3*a^7 - 72*A*B^2*a^6*b + 66*A^2*B*a^5*b^2 - 341*A^3*a^4*b^3)*c^4 + 16*(216*B^3*a^6*b^2 - 324*A*B^2*a^5*b^3 - 288*A^2*B*a^4*b^4 - 427*A^3*a^3*b^5)*c^3 + 20*(108*A*B^2*a^4*b^5 + 102*A^2*B*a^3*b^6 + 47*A^3*a^2*b^7)*c^2 - (216*B^3*a^4*b^6 + 396*A*B^2*a^3*b^7 + 267*A^2*B*a^2*b^8 + 53*A^3*a*b^9)*c + (3*B*a^4*b^13 + A*a^3*b^14 + 40960*A*a^10*c^7 - 4096*(9*B*a^10*b + 8*A*a^9*b^2)*c^6 + 1536*(28*B*a^9*b^3 + A*a^8*b^4)*c^5 - 6400*(3*B*a^8*b^5 - A*a^7*b^6)*c^4 + 160*(24*B*a^7*b^7 - 17*A*a^6*b^8)*c^3 - 240*(B*a^6*b^9 - 2*A*a^5*b^10)*c^2 - 2*(12*B*a^5*b^11 + 19*A*a^4*b^12)*c)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))*sqrt(-(9*B^2*a^2*b^5 + 6*A*B*a*b^6 + A^2*b^7 - 240*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 40*(18*B^2*a^4*b - 48*A*B*a^3*b^2 + 7*A^2*a^2*b^3)*c^2 + 5*(72*B^2*a^3*b^3 - 12*A*B*a^2*b^4 - 7*A^2*a*b^5)*c - (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5))) - sqrt(1/2)*((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*x^8 + a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*x^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2)*sqrt(-(9*B^2*a^2*b^5 + 6*A*B*a*b^6 + A^2*b^7 - 240*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 40*(18*B^2*a^4*b - 48*A*B*a^3*b^2 + 7*A^2*a^2*b^3)*c^2 + 5*(72*B^2*a^3*b^3 - 12*A*B*a^2*b^4 - 7*A^2*a*b^5)*c - (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5))*log((10000*A^4*a^3*c^5 - 15000*(2*A^3*B*a^3*b - A^4*a^2*b^2)*c^4 - 3*(432*B^4*a^5 - 3024*A*B^3*a^4*b - 3312*A^2*B^2*a^3*b^2 + 3864*A^3*B*a^2*b^3 + 497*A^4*a*b^4)*c^3 - 5*(648*B^4*a^4*b^2 - 216*A*B^3*a^3*b^3 - 648*A^2*B^2*a^2*b^4 - 189*A^3*B*a*b^5 - 7*A^4*b^6)*c^2 - 15*(27*B^4*a^3*b^4 + 27*A*B^3*a^2*b^5 + 9*A^2*B^2*a*b^6 + A^3*B*b^7)*c)*x - 1/2*sqrt(1/2)*(27*B^3*a^3*b^8 + 27*A*B^2*a^2*b^9 + 9*A^2*B*a*b^10 + A^3*b^11 + 6400*(3*A^2*B*a^6 - 4*A^3*a^5*b)*c^5 - 64*(108*B^3*a^7 - 72*A*B^2*a^6*b + 66*A^2*B*a^5*b^2 - 341*A^3*a^4*b^3)*c^4 + 16*(216*B^3*a^6*b^2 - 324*A*B^2*a^5*b^3 - 288*A^2*B*a^4*b^4 - 427*A^3*a^3*b^5)*c^3 + 20*(108*A*B^2*a^4*b^5 + 102*A^2*B*a^3*b^6 + 47*A^3*a^2*b^7)*c^2 - (216*B^3*a^4*b^6 + 396*A*B^2*a^3*b^7 + 267*A^2*B*a^2*b^8 + 53*A^3*a*b^9)*c + (3*B*a^4*b^13 + A*a^3*b^14 + 40960*A*a^10*c^7 - 4096*(9*B*a^10*b + 8*A*a^9*b^2)*c^6 + 1536*(28*B*a^9*b^3 + A*a^8*b^4)*c^5 - 6400*(3*B*a^8*b^5 - A*a^7*b^6)*c^4 + 160*(24*B*a^7*b^7 - 17*A*a^6*b^8)*c^3 - 240*(B*a^6*b^9 - 2*A*a^5*b^10)*c^2 - 2*(12*B*a^5*b^11 + 19*A*a^4*b^12)*c)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))*sqrt(-(9*B^2*a^2*b^5 + 6*A*B*a*b^6 + A^2*b^7 - 240*(4*A*B*a^4 - 7*A^2*a^3*b)*c^3 + 40*(18*B^2*a^4*b - 48*A*B*a^3*b^2 + 7*A^2*a^2*b^3)*c^2 + 5*(72*B^2*a^3*b^3 - 12*A*B*a^2*b^4 - 7*A^2*a*b^5)*c - (a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5)*sqrt((81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4 + 625*A^4*a^2*c^2 - 50*(9*A^2*B^2*a^3 + 6*A^3*B*a^2*b + A^4*a*b^2)*c)/(a^6*b^10 - 20*a^7*b^8*c + 160*a^8*b^6*c^2 - 640*a^9*b^4*c^3 + 1280*a^10*b^2*c^4 - 1024*a^11*c^5)))/(a^3*b^10 - 20*a^4*b^8*c + 160*a^5*b^6*c^2 - 640*a^6*b^4*c^3 + 1280*a^7*b^2*c^4 - 1024*a^8*c^5))) - 2*(3*B*a^2*b^2 + A*a*b^3 + 4*(3*B*a^3 - 4*A*a^2*b)*c)*x)/((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*x^8 + a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*x^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^2)","B",0
136,1,9909,0,23.684409," ","integrate((B*x^2+A)/(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(4 \, {\left(5 \, B a^{2} - 6 \, A a b\right)} c^{3} + {\left(B a b^{2} + 3 \, A b^{3}\right)} c^{2}\right)} x^{7} + 2 \, {\left(28 \, A a^{2} c^{3} + 7 \, {\left(4 \, B a^{2} b - 7 \, A a b^{2}\right)} c^{2} + 2 \, {\left(B a b^{3} + 3 \, A b^{4}\right)} c\right)} x^{5} + 2 \, {\left(B a b^{4} + 3 \, A b^{5} + 4 \, {\left(9 \, B a^{3} - A a^{2} b\right)} c^{2} + 5 \, {\left(B a^{2} b^{2} - 4 \, A a b^{3}\right)} c\right)} x^{3} - \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{8} + a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{B^{2} a^{2} b^{7} + 6 \, A B a b^{8} + 9 \, A^{2} b^{9} - 1680 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} + 840 \, {\left(2 \, B^{2} a^{5} b - 4 \, A B a^{4} b^{2} - 9 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(40 \, B^{2} a^{4} b^{3} + 180 \, A B a^{3} b^{4} + 243 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(5 \, B^{2} a^{3} b^{5} + 24 \, A B a^{2} b^{6} + 27 \, A^{2} a b^{7}\right)} c + {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}} \log\left({\left(3111696 \, A^{4} a^{4} c^{7} - 1555848 \, {\left(2 \, A^{3} B a^{4} b + A^{4} a^{3} b^{2}\right)} c^{6} - {\left(10000 \, B^{4} a^{6} - 90000 \, A B^{3} a^{5} b - 863136 \, A^{2} B^{2} a^{4} b^{2} - 1298376 \, A^{3} B a^{3} b^{3} - 339309 \, A^{4} a^{2} b^{4}\right)} c^{5} - 3 \, {\left(5000 \, B^{4} a^{5} b^{2} + 32952 \, A B^{3} a^{4} b^{3} + 79488 \, A^{2} B^{2} a^{3} b^{4} + 80919 \, A^{3} B a^{2} b^{5} + 12069 \, A^{4} a b^{6}\right)} c^{4} + 21 \, {\left(71 \, B^{4} a^{4} b^{4} + 537 \, A B^{3} a^{3} b^{5} + 1314 \, A^{2} B^{2} a^{2} b^{6} + 1053 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8}\right)} c^{3} - 35 \, {\left(B^{4} a^{3} b^{6} + 9 \, A B^{3} a^{2} b^{7} + 27 \, A^{2} B^{2} a b^{8} + 27 \, A^{3} B b^{9}\right)} c^{2}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{11} + 9 \, A B^{2} a^{2} b^{12} + 27 \, A^{2} B a b^{13} + 27 \, A^{3} b^{14} - 2370816 \, A^{3} a^{7} c^{7} + 2688 \, {\left(50 \, A B^{2} a^{8} + 384 \, A^{2} B a^{7} b + 1143 \, A^{3} a^{6} b^{2}\right)} c^{6} - 64 \, {\left(400 \, B^{3} a^{8} b + 4062 \, A B^{2} a^{7} b^{2} + 17541 \, A^{2} B a^{6} b^{3} + 26865 \, A^{3} a^{5} b^{4}\right)} c^{5} + 8 \, {\left(2728 \, B^{3} a^{7} b^{3} + 20520 \, A B^{2} a^{6} b^{4} + 62694 \, A^{2} B a^{5} b^{5} + 67797 \, A^{3} a^{4} b^{6}\right)} c^{4} - 7 \, {\left(976 \, B^{3} a^{6} b^{5} + 6744 \, A B^{2} a^{5} b^{6} + 16884 \, A^{2} B a^{4} b^{7} + 14985 \, A^{3} a^{3} b^{8}\right)} c^{3} + {\left(940 \, B^{3} a^{5} b^{7} + 6591 \, A B^{2} a^{4} b^{8} + 15489 \, A^{2} B a^{3} b^{9} + 12528 \, A^{3} a^{2} b^{10}\right)} c^{2} - {\left(53 \, B^{3} a^{4} b^{9} + 414 \, A B^{2} a^{3} b^{10} + 1053 \, A^{2} B a^{2} b^{11} + 864 \, A^{3} a b^{12}\right)} c - {\left(B a^{6} b^{14} + 3 \, A a^{5} b^{15} + 4096 \, {\left(10 \, B a^{13} - 33 \, A a^{12} b\right)} c^{7} - 2048 \, {\left(16 \, B a^{12} b^{2} - 99 \, A a^{11} b^{3}\right)} c^{6} + 768 \, {\left(2 \, B a^{11} b^{4} - 169 \, A a^{10} b^{5}\right)} c^{5} + 1280 \, {\left(5 \, B a^{10} b^{6} + 36 \, A a^{9} b^{7}\right)} c^{4} - 80 \, {\left(34 \, B a^{9} b^{8} + 123 \, A a^{8} b^{9}\right)} c^{3} + 24 \, {\left(20 \, B a^{8} b^{10} + 53 \, A a^{7} b^{11}\right)} c^{2} - {\left(38 \, B a^{7} b^{12} + 93 \, A a^{6} b^{13}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{7} + 6 \, A B a b^{8} + 9 \, A^{2} b^{9} - 1680 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} + 840 \, {\left(2 \, B^{2} a^{5} b - 4 \, A B a^{4} b^{2} - 9 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(40 \, B^{2} a^{4} b^{3} + 180 \, A B a^{3} b^{4} + 243 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(5 \, B^{2} a^{3} b^{5} + 24 \, A B a^{2} b^{6} + 27 \, A^{2} a b^{7}\right)} c + {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{8} + a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{B^{2} a^{2} b^{7} + 6 \, A B a b^{8} + 9 \, A^{2} b^{9} - 1680 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} + 840 \, {\left(2 \, B^{2} a^{5} b - 4 \, A B a^{4} b^{2} - 9 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(40 \, B^{2} a^{4} b^{3} + 180 \, A B a^{3} b^{4} + 243 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(5 \, B^{2} a^{3} b^{5} + 24 \, A B a^{2} b^{6} + 27 \, A^{2} a b^{7}\right)} c + {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}} \log\left({\left(3111696 \, A^{4} a^{4} c^{7} - 1555848 \, {\left(2 \, A^{3} B a^{4} b + A^{4} a^{3} b^{2}\right)} c^{6} - {\left(10000 \, B^{4} a^{6} - 90000 \, A B^{3} a^{5} b - 863136 \, A^{2} B^{2} a^{4} b^{2} - 1298376 \, A^{3} B a^{3} b^{3} - 339309 \, A^{4} a^{2} b^{4}\right)} c^{5} - 3 \, {\left(5000 \, B^{4} a^{5} b^{2} + 32952 \, A B^{3} a^{4} b^{3} + 79488 \, A^{2} B^{2} a^{3} b^{4} + 80919 \, A^{3} B a^{2} b^{5} + 12069 \, A^{4} a b^{6}\right)} c^{4} + 21 \, {\left(71 \, B^{4} a^{4} b^{4} + 537 \, A B^{3} a^{3} b^{5} + 1314 \, A^{2} B^{2} a^{2} b^{6} + 1053 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8}\right)} c^{3} - 35 \, {\left(B^{4} a^{3} b^{6} + 9 \, A B^{3} a^{2} b^{7} + 27 \, A^{2} B^{2} a b^{8} + 27 \, A^{3} B b^{9}\right)} c^{2}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{11} + 9 \, A B^{2} a^{2} b^{12} + 27 \, A^{2} B a b^{13} + 27 \, A^{3} b^{14} - 2370816 \, A^{3} a^{7} c^{7} + 2688 \, {\left(50 \, A B^{2} a^{8} + 384 \, A^{2} B a^{7} b + 1143 \, A^{3} a^{6} b^{2}\right)} c^{6} - 64 \, {\left(400 \, B^{3} a^{8} b + 4062 \, A B^{2} a^{7} b^{2} + 17541 \, A^{2} B a^{6} b^{3} + 26865 \, A^{3} a^{5} b^{4}\right)} c^{5} + 8 \, {\left(2728 \, B^{3} a^{7} b^{3} + 20520 \, A B^{2} a^{6} b^{4} + 62694 \, A^{2} B a^{5} b^{5} + 67797 \, A^{3} a^{4} b^{6}\right)} c^{4} - 7 \, {\left(976 \, B^{3} a^{6} b^{5} + 6744 \, A B^{2} a^{5} b^{6} + 16884 \, A^{2} B a^{4} b^{7} + 14985 \, A^{3} a^{3} b^{8}\right)} c^{3} + {\left(940 \, B^{3} a^{5} b^{7} + 6591 \, A B^{2} a^{4} b^{8} + 15489 \, A^{2} B a^{3} b^{9} + 12528 \, A^{3} a^{2} b^{10}\right)} c^{2} - {\left(53 \, B^{3} a^{4} b^{9} + 414 \, A B^{2} a^{3} b^{10} + 1053 \, A^{2} B a^{2} b^{11} + 864 \, A^{3} a b^{12}\right)} c - {\left(B a^{6} b^{14} + 3 \, A a^{5} b^{15} + 4096 \, {\left(10 \, B a^{13} - 33 \, A a^{12} b\right)} c^{7} - 2048 \, {\left(16 \, B a^{12} b^{2} - 99 \, A a^{11} b^{3}\right)} c^{6} + 768 \, {\left(2 \, B a^{11} b^{4} - 169 \, A a^{10} b^{5}\right)} c^{5} + 1280 \, {\left(5 \, B a^{10} b^{6} + 36 \, A a^{9} b^{7}\right)} c^{4} - 80 \, {\left(34 \, B a^{9} b^{8} + 123 \, A a^{8} b^{9}\right)} c^{3} + 24 \, {\left(20 \, B a^{8} b^{10} + 53 \, A a^{7} b^{11}\right)} c^{2} - {\left(38 \, B a^{7} b^{12} + 93 \, A a^{6} b^{13}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{7} + 6 \, A B a b^{8} + 9 \, A^{2} b^{9} - 1680 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} + 840 \, {\left(2 \, B^{2} a^{5} b - 4 \, A B a^{4} b^{2} - 9 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(40 \, B^{2} a^{4} b^{3} + 180 \, A B a^{3} b^{4} + 243 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(5 \, B^{2} a^{3} b^{5} + 24 \, A B a^{2} b^{6} + 27 \, A^{2} a b^{7}\right)} c + {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{8} + a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{B^{2} a^{2} b^{7} + 6 \, A B a b^{8} + 9 \, A^{2} b^{9} - 1680 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} + 840 \, {\left(2 \, B^{2} a^{5} b - 4 \, A B a^{4} b^{2} - 9 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(40 \, B^{2} a^{4} b^{3} + 180 \, A B a^{3} b^{4} + 243 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(5 \, B^{2} a^{3} b^{5} + 24 \, A B a^{2} b^{6} + 27 \, A^{2} a b^{7}\right)} c - {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}} \log\left({\left(3111696 \, A^{4} a^{4} c^{7} - 1555848 \, {\left(2 \, A^{3} B a^{4} b + A^{4} a^{3} b^{2}\right)} c^{6} - {\left(10000 \, B^{4} a^{6} - 90000 \, A B^{3} a^{5} b - 863136 \, A^{2} B^{2} a^{4} b^{2} - 1298376 \, A^{3} B a^{3} b^{3} - 339309 \, A^{4} a^{2} b^{4}\right)} c^{5} - 3 \, {\left(5000 \, B^{4} a^{5} b^{2} + 32952 \, A B^{3} a^{4} b^{3} + 79488 \, A^{2} B^{2} a^{3} b^{4} + 80919 \, A^{3} B a^{2} b^{5} + 12069 \, A^{4} a b^{6}\right)} c^{4} + 21 \, {\left(71 \, B^{4} a^{4} b^{4} + 537 \, A B^{3} a^{3} b^{5} + 1314 \, A^{2} B^{2} a^{2} b^{6} + 1053 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8}\right)} c^{3} - 35 \, {\left(B^{4} a^{3} b^{6} + 9 \, A B^{3} a^{2} b^{7} + 27 \, A^{2} B^{2} a b^{8} + 27 \, A^{3} B b^{9}\right)} c^{2}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{11} + 9 \, A B^{2} a^{2} b^{12} + 27 \, A^{2} B a b^{13} + 27 \, A^{3} b^{14} - 2370816 \, A^{3} a^{7} c^{7} + 2688 \, {\left(50 \, A B^{2} a^{8} + 384 \, A^{2} B a^{7} b + 1143 \, A^{3} a^{6} b^{2}\right)} c^{6} - 64 \, {\left(400 \, B^{3} a^{8} b + 4062 \, A B^{2} a^{7} b^{2} + 17541 \, A^{2} B a^{6} b^{3} + 26865 \, A^{3} a^{5} b^{4}\right)} c^{5} + 8 \, {\left(2728 \, B^{3} a^{7} b^{3} + 20520 \, A B^{2} a^{6} b^{4} + 62694 \, A^{2} B a^{5} b^{5} + 67797 \, A^{3} a^{4} b^{6}\right)} c^{4} - 7 \, {\left(976 \, B^{3} a^{6} b^{5} + 6744 \, A B^{2} a^{5} b^{6} + 16884 \, A^{2} B a^{4} b^{7} + 14985 \, A^{3} a^{3} b^{8}\right)} c^{3} + {\left(940 \, B^{3} a^{5} b^{7} + 6591 \, A B^{2} a^{4} b^{8} + 15489 \, A^{2} B a^{3} b^{9} + 12528 \, A^{3} a^{2} b^{10}\right)} c^{2} - {\left(53 \, B^{3} a^{4} b^{9} + 414 \, A B^{2} a^{3} b^{10} + 1053 \, A^{2} B a^{2} b^{11} + 864 \, A^{3} a b^{12}\right)} c + {\left(B a^{6} b^{14} + 3 \, A a^{5} b^{15} + 4096 \, {\left(10 \, B a^{13} - 33 \, A a^{12} b\right)} c^{7} - 2048 \, {\left(16 \, B a^{12} b^{2} - 99 \, A a^{11} b^{3}\right)} c^{6} + 768 \, {\left(2 \, B a^{11} b^{4} - 169 \, A a^{10} b^{5}\right)} c^{5} + 1280 \, {\left(5 \, B a^{10} b^{6} + 36 \, A a^{9} b^{7}\right)} c^{4} - 80 \, {\left(34 \, B a^{9} b^{8} + 123 \, A a^{8} b^{9}\right)} c^{3} + 24 \, {\left(20 \, B a^{8} b^{10} + 53 \, A a^{7} b^{11}\right)} c^{2} - {\left(38 \, B a^{7} b^{12} + 93 \, A a^{6} b^{13}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{7} + 6 \, A B a b^{8} + 9 \, A^{2} b^{9} - 1680 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} + 840 \, {\left(2 \, B^{2} a^{5} b - 4 \, A B a^{4} b^{2} - 9 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(40 \, B^{2} a^{4} b^{3} + 180 \, A B a^{3} b^{4} + 243 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(5 \, B^{2} a^{3} b^{5} + 24 \, A B a^{2} b^{6} + 27 \, A^{2} a b^{7}\right)} c - {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{8} + a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{B^{2} a^{2} b^{7} + 6 \, A B a b^{8} + 9 \, A^{2} b^{9} - 1680 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} + 840 \, {\left(2 \, B^{2} a^{5} b - 4 \, A B a^{4} b^{2} - 9 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(40 \, B^{2} a^{4} b^{3} + 180 \, A B a^{3} b^{4} + 243 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(5 \, B^{2} a^{3} b^{5} + 24 \, A B a^{2} b^{6} + 27 \, A^{2} a b^{7}\right)} c - {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}} \log\left({\left(3111696 \, A^{4} a^{4} c^{7} - 1555848 \, {\left(2 \, A^{3} B a^{4} b + A^{4} a^{3} b^{2}\right)} c^{6} - {\left(10000 \, B^{4} a^{6} - 90000 \, A B^{3} a^{5} b - 863136 \, A^{2} B^{2} a^{4} b^{2} - 1298376 \, A^{3} B a^{3} b^{3} - 339309 \, A^{4} a^{2} b^{4}\right)} c^{5} - 3 \, {\left(5000 \, B^{4} a^{5} b^{2} + 32952 \, A B^{3} a^{4} b^{3} + 79488 \, A^{2} B^{2} a^{3} b^{4} + 80919 \, A^{3} B a^{2} b^{5} + 12069 \, A^{4} a b^{6}\right)} c^{4} + 21 \, {\left(71 \, B^{4} a^{4} b^{4} + 537 \, A B^{3} a^{3} b^{5} + 1314 \, A^{2} B^{2} a^{2} b^{6} + 1053 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8}\right)} c^{3} - 35 \, {\left(B^{4} a^{3} b^{6} + 9 \, A B^{3} a^{2} b^{7} + 27 \, A^{2} B^{2} a b^{8} + 27 \, A^{3} B b^{9}\right)} c^{2}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(B^{3} a^{3} b^{11} + 9 \, A B^{2} a^{2} b^{12} + 27 \, A^{2} B a b^{13} + 27 \, A^{3} b^{14} - 2370816 \, A^{3} a^{7} c^{7} + 2688 \, {\left(50 \, A B^{2} a^{8} + 384 \, A^{2} B a^{7} b + 1143 \, A^{3} a^{6} b^{2}\right)} c^{6} - 64 \, {\left(400 \, B^{3} a^{8} b + 4062 \, A B^{2} a^{7} b^{2} + 17541 \, A^{2} B a^{6} b^{3} + 26865 \, A^{3} a^{5} b^{4}\right)} c^{5} + 8 \, {\left(2728 \, B^{3} a^{7} b^{3} + 20520 \, A B^{2} a^{6} b^{4} + 62694 \, A^{2} B a^{5} b^{5} + 67797 \, A^{3} a^{4} b^{6}\right)} c^{4} - 7 \, {\left(976 \, B^{3} a^{6} b^{5} + 6744 \, A B^{2} a^{5} b^{6} + 16884 \, A^{2} B a^{4} b^{7} + 14985 \, A^{3} a^{3} b^{8}\right)} c^{3} + {\left(940 \, B^{3} a^{5} b^{7} + 6591 \, A B^{2} a^{4} b^{8} + 15489 \, A^{2} B a^{3} b^{9} + 12528 \, A^{3} a^{2} b^{10}\right)} c^{2} - {\left(53 \, B^{3} a^{4} b^{9} + 414 \, A B^{2} a^{3} b^{10} + 1053 \, A^{2} B a^{2} b^{11} + 864 \, A^{3} a b^{12}\right)} c + {\left(B a^{6} b^{14} + 3 \, A a^{5} b^{15} + 4096 \, {\left(10 \, B a^{13} - 33 \, A a^{12} b\right)} c^{7} - 2048 \, {\left(16 \, B a^{12} b^{2} - 99 \, A a^{11} b^{3}\right)} c^{6} + 768 \, {\left(2 \, B a^{11} b^{4} - 169 \, A a^{10} b^{5}\right)} c^{5} + 1280 \, {\left(5 \, B a^{10} b^{6} + 36 \, A a^{9} b^{7}\right)} c^{4} - 80 \, {\left(34 \, B a^{9} b^{8} + 123 \, A a^{8} b^{9}\right)} c^{3} + 24 \, {\left(20 \, B a^{8} b^{10} + 53 \, A a^{7} b^{11}\right)} c^{2} - {\left(38 \, B a^{7} b^{12} + 93 \, A a^{6} b^{13}\right)} c\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}\right)} \sqrt{-\frac{B^{2} a^{2} b^{7} + 6 \, A B a b^{8} + 9 \, A^{2} b^{9} - 1680 \, {\left(4 \, A B a^{5} - 9 \, A^{2} a^{4} b\right)} c^{4} + 840 \, {\left(2 \, B^{2} a^{5} b - 4 \, A B a^{4} b^{2} - 9 \, A^{2} a^{3} b^{3}\right)} c^{3} + 7 \, {\left(40 \, B^{2} a^{4} b^{3} + 180 \, A B a^{3} b^{4} + 243 \, A^{2} a^{2} b^{5}\right)} c^{2} - 7 \, {\left(5 \, B^{2} a^{3} b^{5} + 24 \, A B a^{2} b^{6} + 27 \, A^{2} a b^{7}\right)} c - {\left(a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}\right)} \sqrt{\frac{B^{4} a^{4} b^{4} + 12 \, A B^{3} a^{3} b^{5} + 54 \, A^{2} B^{2} a^{2} b^{6} + 108 \, A^{3} B a b^{7} + 81 \, A^{4} b^{8} + 194481 \, A^{4} a^{4} c^{4} - 882 \, {\left(25 \, A^{2} B^{2} a^{5} + 108 \, A^{3} B a^{4} b + 99 \, A^{4} a^{3} b^{2}\right)} c^{3} + {\left(625 \, B^{4} a^{6} + 5400 \, A B^{3} a^{5} b + 17496 \, A^{2} B^{2} a^{4} b^{2} + 26676 \, A^{3} B a^{3} b^{3} + 17739 \, A^{4} a^{2} b^{4}\right)} c^{2} - 2 \, {\left(25 \, B^{4} a^{5} b^{2} + 258 \, A B^{3} a^{4} b^{3} + 972 \, A^{2} B^{2} a^{3} b^{4} + 1566 \, A^{3} B a^{2} b^{5} + 891 \, A^{4} a b^{6}\right)} c}{a^{10} b^{10} - 20 \, a^{11} b^{8} c + 160 \, a^{12} b^{6} c^{2} - 640 \, a^{13} b^{4} c^{3} + 1280 \, a^{14} b^{2} c^{4} - 1024 \, a^{15} c^{5}}}}{a^{5} b^{10} - 20 \, a^{6} b^{8} c + 160 \, a^{7} b^{6} c^{2} - 640 \, a^{8} b^{4} c^{3} + 1280 \, a^{9} b^{2} c^{4} - 1024 \, a^{10} c^{5}}}\right) - 2 \, {\left(B a^{2} b^{3} - 5 \, A a b^{4} - 44 \, A a^{3} c^{2} - {\left(16 \, B a^{3} b - 37 \, A a^{2} b^{2}\right)} c\right)} x}{16 \, {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} x^{8} + a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} x^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2}\right)}}"," ",0,"1/16*(2*(4*(5*B*a^2 - 6*A*a*b)*c^3 + (B*a*b^2 + 3*A*b^3)*c^2)*x^7 + 2*(28*A*a^2*c^3 + 7*(4*B*a^2*b - 7*A*a*b^2)*c^2 + 2*(B*a*b^3 + 3*A*b^4)*c)*x^5 + 2*(B*a*b^4 + 3*A*b^5 + 4*(9*B*a^3 - A*a^2*b)*c^2 + 5*(B*a^2*b^2 - 4*A*a*b^3)*c)*x^3 - sqrt(1/2)*((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^8 + a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2)*sqrt(-(B^2*a^2*b^7 + 6*A*B*a*b^8 + 9*A^2*b^9 - 1680*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 + 840*(2*B^2*a^5*b - 4*A*B*a^4*b^2 - 9*A^2*a^3*b^3)*c^3 + 7*(40*B^2*a^4*b^3 + 180*A*B*a^3*b^4 + 243*A^2*a^2*b^5)*c^2 - 7*(5*B^2*a^3*b^5 + 24*A*B*a^2*b^6 + 27*A^2*a*b^7)*c + (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5))*log((3111696*A^4*a^4*c^7 - 1555848*(2*A^3*B*a^4*b + A^4*a^3*b^2)*c^6 - (10000*B^4*a^6 - 90000*A*B^3*a^5*b - 863136*A^2*B^2*a^4*b^2 - 1298376*A^3*B*a^3*b^3 - 339309*A^4*a^2*b^4)*c^5 - 3*(5000*B^4*a^5*b^2 + 32952*A*B^3*a^4*b^3 + 79488*A^2*B^2*a^3*b^4 + 80919*A^3*B*a^2*b^5 + 12069*A^4*a*b^6)*c^4 + 21*(71*B^4*a^4*b^4 + 537*A*B^3*a^3*b^5 + 1314*A^2*B^2*a^2*b^6 + 1053*A^3*B*a*b^7 + 81*A^4*b^8)*c^3 - 35*(B^4*a^3*b^6 + 9*A*B^3*a^2*b^7 + 27*A^2*B^2*a*b^8 + 27*A^3*B*b^9)*c^2)*x + 1/2*sqrt(1/2)*(B^3*a^3*b^11 + 9*A*B^2*a^2*b^12 + 27*A^2*B*a*b^13 + 27*A^3*b^14 - 2370816*A^3*a^7*c^7 + 2688*(50*A*B^2*a^8 + 384*A^2*B*a^7*b + 1143*A^3*a^6*b^2)*c^6 - 64*(400*B^3*a^8*b + 4062*A*B^2*a^7*b^2 + 17541*A^2*B*a^6*b^3 + 26865*A^3*a^5*b^4)*c^5 + 8*(2728*B^3*a^7*b^3 + 20520*A*B^2*a^6*b^4 + 62694*A^2*B*a^5*b^5 + 67797*A^3*a^4*b^6)*c^4 - 7*(976*B^3*a^6*b^5 + 6744*A*B^2*a^5*b^6 + 16884*A^2*B*a^4*b^7 + 14985*A^3*a^3*b^8)*c^3 + (940*B^3*a^5*b^7 + 6591*A*B^2*a^4*b^8 + 15489*A^2*B*a^3*b^9 + 12528*A^3*a^2*b^10)*c^2 - (53*B^3*a^4*b^9 + 414*A*B^2*a^3*b^10 + 1053*A^2*B*a^2*b^11 + 864*A^3*a*b^12)*c - (B*a^6*b^14 + 3*A*a^5*b^15 + 4096*(10*B*a^13 - 33*A*a^12*b)*c^7 - 2048*(16*B*a^12*b^2 - 99*A*a^11*b^3)*c^6 + 768*(2*B*a^11*b^4 - 169*A*a^10*b^5)*c^5 + 1280*(5*B*a^10*b^6 + 36*A*a^9*b^7)*c^4 - 80*(34*B*a^9*b^8 + 123*A*a^8*b^9)*c^3 + 24*(20*B*a^8*b^10 + 53*A*a^7*b^11)*c^2 - (38*B*a^7*b^12 + 93*A*a^6*b^13)*c)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))*sqrt(-(B^2*a^2*b^7 + 6*A*B*a*b^8 + 9*A^2*b^9 - 1680*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 + 840*(2*B^2*a^5*b - 4*A*B*a^4*b^2 - 9*A^2*a^3*b^3)*c^3 + 7*(40*B^2*a^4*b^3 + 180*A*B*a^3*b^4 + 243*A^2*a^2*b^5)*c^2 - 7*(5*B^2*a^3*b^5 + 24*A*B*a^2*b^6 + 27*A^2*a*b^7)*c + (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5))) + sqrt(1/2)*((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^8 + a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2)*sqrt(-(B^2*a^2*b^7 + 6*A*B*a*b^8 + 9*A^2*b^9 - 1680*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 + 840*(2*B^2*a^5*b - 4*A*B*a^4*b^2 - 9*A^2*a^3*b^3)*c^3 + 7*(40*B^2*a^4*b^3 + 180*A*B*a^3*b^4 + 243*A^2*a^2*b^5)*c^2 - 7*(5*B^2*a^3*b^5 + 24*A*B*a^2*b^6 + 27*A^2*a*b^7)*c + (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5))*log((3111696*A^4*a^4*c^7 - 1555848*(2*A^3*B*a^4*b + A^4*a^3*b^2)*c^6 - (10000*B^4*a^6 - 90000*A*B^3*a^5*b - 863136*A^2*B^2*a^4*b^2 - 1298376*A^3*B*a^3*b^3 - 339309*A^4*a^2*b^4)*c^5 - 3*(5000*B^4*a^5*b^2 + 32952*A*B^3*a^4*b^3 + 79488*A^2*B^2*a^3*b^4 + 80919*A^3*B*a^2*b^5 + 12069*A^4*a*b^6)*c^4 + 21*(71*B^4*a^4*b^4 + 537*A*B^3*a^3*b^5 + 1314*A^2*B^2*a^2*b^6 + 1053*A^3*B*a*b^7 + 81*A^4*b^8)*c^3 - 35*(B^4*a^3*b^6 + 9*A*B^3*a^2*b^7 + 27*A^2*B^2*a*b^8 + 27*A^3*B*b^9)*c^2)*x - 1/2*sqrt(1/2)*(B^3*a^3*b^11 + 9*A*B^2*a^2*b^12 + 27*A^2*B*a*b^13 + 27*A^3*b^14 - 2370816*A^3*a^7*c^7 + 2688*(50*A*B^2*a^8 + 384*A^2*B*a^7*b + 1143*A^3*a^6*b^2)*c^6 - 64*(400*B^3*a^8*b + 4062*A*B^2*a^7*b^2 + 17541*A^2*B*a^6*b^3 + 26865*A^3*a^5*b^4)*c^5 + 8*(2728*B^3*a^7*b^3 + 20520*A*B^2*a^6*b^4 + 62694*A^2*B*a^5*b^5 + 67797*A^3*a^4*b^6)*c^4 - 7*(976*B^3*a^6*b^5 + 6744*A*B^2*a^5*b^6 + 16884*A^2*B*a^4*b^7 + 14985*A^3*a^3*b^8)*c^3 + (940*B^3*a^5*b^7 + 6591*A*B^2*a^4*b^8 + 15489*A^2*B*a^3*b^9 + 12528*A^3*a^2*b^10)*c^2 - (53*B^3*a^4*b^9 + 414*A*B^2*a^3*b^10 + 1053*A^2*B*a^2*b^11 + 864*A^3*a*b^12)*c - (B*a^6*b^14 + 3*A*a^5*b^15 + 4096*(10*B*a^13 - 33*A*a^12*b)*c^7 - 2048*(16*B*a^12*b^2 - 99*A*a^11*b^3)*c^6 + 768*(2*B*a^11*b^4 - 169*A*a^10*b^5)*c^5 + 1280*(5*B*a^10*b^6 + 36*A*a^9*b^7)*c^4 - 80*(34*B*a^9*b^8 + 123*A*a^8*b^9)*c^3 + 24*(20*B*a^8*b^10 + 53*A*a^7*b^11)*c^2 - (38*B*a^7*b^12 + 93*A*a^6*b^13)*c)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))*sqrt(-(B^2*a^2*b^7 + 6*A*B*a*b^8 + 9*A^2*b^9 - 1680*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 + 840*(2*B^2*a^5*b - 4*A*B*a^4*b^2 - 9*A^2*a^3*b^3)*c^3 + 7*(40*B^2*a^4*b^3 + 180*A*B*a^3*b^4 + 243*A^2*a^2*b^5)*c^2 - 7*(5*B^2*a^3*b^5 + 24*A*B*a^2*b^6 + 27*A^2*a*b^7)*c + (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5))) - sqrt(1/2)*((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^8 + a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2)*sqrt(-(B^2*a^2*b^7 + 6*A*B*a*b^8 + 9*A^2*b^9 - 1680*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 + 840*(2*B^2*a^5*b - 4*A*B*a^4*b^2 - 9*A^2*a^3*b^3)*c^3 + 7*(40*B^2*a^4*b^3 + 180*A*B*a^3*b^4 + 243*A^2*a^2*b^5)*c^2 - 7*(5*B^2*a^3*b^5 + 24*A*B*a^2*b^6 + 27*A^2*a*b^7)*c - (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5))*log((3111696*A^4*a^4*c^7 - 1555848*(2*A^3*B*a^4*b + A^4*a^3*b^2)*c^6 - (10000*B^4*a^6 - 90000*A*B^3*a^5*b - 863136*A^2*B^2*a^4*b^2 - 1298376*A^3*B*a^3*b^3 - 339309*A^4*a^2*b^4)*c^5 - 3*(5000*B^4*a^5*b^2 + 32952*A*B^3*a^4*b^3 + 79488*A^2*B^2*a^3*b^4 + 80919*A^3*B*a^2*b^5 + 12069*A^4*a*b^6)*c^4 + 21*(71*B^4*a^4*b^4 + 537*A*B^3*a^3*b^5 + 1314*A^2*B^2*a^2*b^6 + 1053*A^3*B*a*b^7 + 81*A^4*b^8)*c^3 - 35*(B^4*a^3*b^6 + 9*A*B^3*a^2*b^7 + 27*A^2*B^2*a*b^8 + 27*A^3*B*b^9)*c^2)*x + 1/2*sqrt(1/2)*(B^3*a^3*b^11 + 9*A*B^2*a^2*b^12 + 27*A^2*B*a*b^13 + 27*A^3*b^14 - 2370816*A^3*a^7*c^7 + 2688*(50*A*B^2*a^8 + 384*A^2*B*a^7*b + 1143*A^3*a^6*b^2)*c^6 - 64*(400*B^3*a^8*b + 4062*A*B^2*a^7*b^2 + 17541*A^2*B*a^6*b^3 + 26865*A^3*a^5*b^4)*c^5 + 8*(2728*B^3*a^7*b^3 + 20520*A*B^2*a^6*b^4 + 62694*A^2*B*a^5*b^5 + 67797*A^3*a^4*b^6)*c^4 - 7*(976*B^3*a^6*b^5 + 6744*A*B^2*a^5*b^6 + 16884*A^2*B*a^4*b^7 + 14985*A^3*a^3*b^8)*c^3 + (940*B^3*a^5*b^7 + 6591*A*B^2*a^4*b^8 + 15489*A^2*B*a^3*b^9 + 12528*A^3*a^2*b^10)*c^2 - (53*B^3*a^4*b^9 + 414*A*B^2*a^3*b^10 + 1053*A^2*B*a^2*b^11 + 864*A^3*a*b^12)*c + (B*a^6*b^14 + 3*A*a^5*b^15 + 4096*(10*B*a^13 - 33*A*a^12*b)*c^7 - 2048*(16*B*a^12*b^2 - 99*A*a^11*b^3)*c^6 + 768*(2*B*a^11*b^4 - 169*A*a^10*b^5)*c^5 + 1280*(5*B*a^10*b^6 + 36*A*a^9*b^7)*c^4 - 80*(34*B*a^9*b^8 + 123*A*a^8*b^9)*c^3 + 24*(20*B*a^8*b^10 + 53*A*a^7*b^11)*c^2 - (38*B*a^7*b^12 + 93*A*a^6*b^13)*c)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))*sqrt(-(B^2*a^2*b^7 + 6*A*B*a*b^8 + 9*A^2*b^9 - 1680*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 + 840*(2*B^2*a^5*b - 4*A*B*a^4*b^2 - 9*A^2*a^3*b^3)*c^3 + 7*(40*B^2*a^4*b^3 + 180*A*B*a^3*b^4 + 243*A^2*a^2*b^5)*c^2 - 7*(5*B^2*a^3*b^5 + 24*A*B*a^2*b^6 + 27*A^2*a*b^7)*c - (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5))) + sqrt(1/2)*((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^8 + a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2)*sqrt(-(B^2*a^2*b^7 + 6*A*B*a*b^8 + 9*A^2*b^9 - 1680*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 + 840*(2*B^2*a^5*b - 4*A*B*a^4*b^2 - 9*A^2*a^3*b^3)*c^3 + 7*(40*B^2*a^4*b^3 + 180*A*B*a^3*b^4 + 243*A^2*a^2*b^5)*c^2 - 7*(5*B^2*a^3*b^5 + 24*A*B*a^2*b^6 + 27*A^2*a*b^7)*c - (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5))*log((3111696*A^4*a^4*c^7 - 1555848*(2*A^3*B*a^4*b + A^4*a^3*b^2)*c^6 - (10000*B^4*a^6 - 90000*A*B^3*a^5*b - 863136*A^2*B^2*a^4*b^2 - 1298376*A^3*B*a^3*b^3 - 339309*A^4*a^2*b^4)*c^5 - 3*(5000*B^4*a^5*b^2 + 32952*A*B^3*a^4*b^3 + 79488*A^2*B^2*a^3*b^4 + 80919*A^3*B*a^2*b^5 + 12069*A^4*a*b^6)*c^4 + 21*(71*B^4*a^4*b^4 + 537*A*B^3*a^3*b^5 + 1314*A^2*B^2*a^2*b^6 + 1053*A^3*B*a*b^7 + 81*A^4*b^8)*c^3 - 35*(B^4*a^3*b^6 + 9*A*B^3*a^2*b^7 + 27*A^2*B^2*a*b^8 + 27*A^3*B*b^9)*c^2)*x - 1/2*sqrt(1/2)*(B^3*a^3*b^11 + 9*A*B^2*a^2*b^12 + 27*A^2*B*a*b^13 + 27*A^3*b^14 - 2370816*A^3*a^7*c^7 + 2688*(50*A*B^2*a^8 + 384*A^2*B*a^7*b + 1143*A^3*a^6*b^2)*c^6 - 64*(400*B^3*a^8*b + 4062*A*B^2*a^7*b^2 + 17541*A^2*B*a^6*b^3 + 26865*A^3*a^5*b^4)*c^5 + 8*(2728*B^3*a^7*b^3 + 20520*A*B^2*a^6*b^4 + 62694*A^2*B*a^5*b^5 + 67797*A^3*a^4*b^6)*c^4 - 7*(976*B^3*a^6*b^5 + 6744*A*B^2*a^5*b^6 + 16884*A^2*B*a^4*b^7 + 14985*A^3*a^3*b^8)*c^3 + (940*B^3*a^5*b^7 + 6591*A*B^2*a^4*b^8 + 15489*A^2*B*a^3*b^9 + 12528*A^3*a^2*b^10)*c^2 - (53*B^3*a^4*b^9 + 414*A*B^2*a^3*b^10 + 1053*A^2*B*a^2*b^11 + 864*A^3*a*b^12)*c + (B*a^6*b^14 + 3*A*a^5*b^15 + 4096*(10*B*a^13 - 33*A*a^12*b)*c^7 - 2048*(16*B*a^12*b^2 - 99*A*a^11*b^3)*c^6 + 768*(2*B*a^11*b^4 - 169*A*a^10*b^5)*c^5 + 1280*(5*B*a^10*b^6 + 36*A*a^9*b^7)*c^4 - 80*(34*B*a^9*b^8 + 123*A*a^8*b^9)*c^3 + 24*(20*B*a^8*b^10 + 53*A*a^7*b^11)*c^2 - (38*B*a^7*b^12 + 93*A*a^6*b^13)*c)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))*sqrt(-(B^2*a^2*b^7 + 6*A*B*a*b^8 + 9*A^2*b^9 - 1680*(4*A*B*a^5 - 9*A^2*a^4*b)*c^4 + 840*(2*B^2*a^5*b - 4*A*B*a^4*b^2 - 9*A^2*a^3*b^3)*c^3 + 7*(40*B^2*a^4*b^3 + 180*A*B*a^3*b^4 + 243*A^2*a^2*b^5)*c^2 - 7*(5*B^2*a^3*b^5 + 24*A*B*a^2*b^6 + 27*A^2*a*b^7)*c - (a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5)*sqrt((B^4*a^4*b^4 + 12*A*B^3*a^3*b^5 + 54*A^2*B^2*a^2*b^6 + 108*A^3*B*a*b^7 + 81*A^4*b^8 + 194481*A^4*a^4*c^4 - 882*(25*A^2*B^2*a^5 + 108*A^3*B*a^4*b + 99*A^4*a^3*b^2)*c^3 + (625*B^4*a^6 + 5400*A*B^3*a^5*b + 17496*A^2*B^2*a^4*b^2 + 26676*A^3*B*a^3*b^3 + 17739*A^4*a^2*b^4)*c^2 - 2*(25*B^4*a^5*b^2 + 258*A*B^3*a^4*b^3 + 972*A^2*B^2*a^3*b^4 + 1566*A^3*B*a^2*b^5 + 891*A^4*a*b^6)*c)/(a^10*b^10 - 20*a^11*b^8*c + 160*a^12*b^6*c^2 - 640*a^13*b^4*c^3 + 1280*a^14*b^2*c^4 - 1024*a^15*c^5)))/(a^5*b^10 - 20*a^6*b^8*c + 160*a^7*b^6*c^2 - 640*a^8*b^4*c^3 + 1280*a^9*b^2*c^4 - 1024*a^10*c^5))) - 2*(B*a^2*b^3 - 5*A*a*b^4 - 44*A*a^3*c^2 - (16*B*a^3*b - 37*A*a^2*b^2)*c)*x)/((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*x^8 + a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*x^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2)","B",0
137,1,17,0,1.144024," ","integrate(x*(4*x^2-7)/(x^4-5*x^2+4),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(x^{2} - 1\right) + \frac{3}{2} \, \log\left(x^{2} - 4\right)"," ",0,"1/2*log(x^2 - 1) + 3/2*log(x^2 - 4)","A",0
138,1,17,0,0.664776," ","integrate((4*x^3-7*x)/(x^4-5*x^2+4),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(x^{2} - 1\right) + \frac{3}{2} \, \log\left(x^{2} - 4\right)"," ",0,"1/2*log(x^2 - 1) + 3/2*log(x^2 - 4)","A",0
139,1,30,0,0.943771," ","integrate(x*(x^2+2)/(x^4+x^2+1),x, algorithm=""fricas"")","\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
140,1,30,0,1.188546," ","integrate((x^3+2*x)/(x^4+x^2+1),x, algorithm=""fricas"")","\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
141,1,47,0,0.830194," ","integrate((2*x^3+11*x)/(x^4+2*x^2+3)^2,x, algorithm=""fricas"")","\frac{9 \, \sqrt{2} {\left(x^{4} + 2 \, x^{2} + 3\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x^{2} + 1\right)}\right) + 18 \, x^{2} + 10}{16 \, {\left(x^{4} + 2 \, x^{2} + 3\right)}}"," ",0,"1/16*(9*sqrt(2)*(x^4 + 2*x^2 + 3)*arctan(1/2*sqrt(2)*(x^2 + 1)) + 18*x^2 + 10)/(x^4 + 2*x^2 + 3)","A",0
142,1,61,0,1.361099," ","integrate(x^5*(3*x^2+2)*(x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{3840} \, {\left(1152 \, x^{8} + 1680 \, x^{6} - 2248 \, x^{4} + 12250 \, x^{2} - 78387\right)} \sqrt{x^{4} + 5 \, x^{2} + 3} - \frac{21229}{512} \, \log\left(-2 \, x^{2} + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} - 5\right)"," ",0,"1/3840*(1152*x^8 + 1680*x^6 - 2248*x^4 + 12250*x^2 - 78387)*sqrt(x^4 + 5*x^2 + 3) - 21229/512*log(-2*x^2 + 2*sqrt(x^4 + 5*x^2 + 3) - 5)","A",0
143,1,56,0,1.282516," ","integrate(x^3*(3*x^2+2)*(x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{384} \, {\left(144 \, x^{6} + 248 \, x^{4} - 374 \, x^{2} + 2469\right)} \sqrt{x^{4} + 5 \, x^{2} + 3} + \frac{3367}{256} \, \log\left(-2 \, x^{2} + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} - 5\right)"," ",0,"1/384*(144*x^6 + 248*x^4 - 374*x^2 + 2469)*sqrt(x^4 + 5*x^2 + 3) + 3367/256*log(-2*x^2 + 2*sqrt(x^4 + 5*x^2 + 3) - 5)","A",0
144,1,51,0,1.283289," ","integrate(x*(3*x^2+2)*(x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{16} \, {\left(8 \, x^{4} + 18 \, x^{2} - 31\right)} \sqrt{x^{4} + 5 \, x^{2} + 3} - \frac{143}{32} \, \log\left(-2 \, x^{2} + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} - 5\right)"," ",0,"1/16*(8*x^4 + 18*x^2 - 31)*sqrt(x^4 + 5*x^2 + 3) - 143/32*log(-2*x^2 + 2*sqrt(x^4 + 5*x^2 + 3) - 5)","A",0
145,1,95,0,1.260524," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x,x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(6 \, x^{2} + 23\right)} + \sqrt{3} \log\left(\frac{25 \, x^{2} - 2 \, \sqrt{3} {\left(5 \, x^{2} + 6\right)} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(5 \, \sqrt{3} - 6\right)} + 30}{x^{2}}\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((25*x^2 - 2*sqrt(3)*(5*x^2 + 6) - 2*sqrt(x^4 + 5*x^2 + 3)*(5*sqrt(3) - 6) + 30)/x^2) - 1/16*log(-2*x^2 + 2*sqrt(x^4 + 5*x^2 + 3) - 5)","A",0
146,1,112,0,0.711210," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^3,x, algorithm=""fricas"")","\frac{56 \, \sqrt{3} x^{2} \log\left(\frac{25 \, x^{2} - 2 \, \sqrt{3} {\left(5 \, x^{2} + 6\right)} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(5 \, \sqrt{3} - 6\right)} + 30}{x^{2}}\right) - 114 \, x^{2} \log\left(-2 \, x^{2} + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} - 5\right) + 21 \, x^{2} + 12 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(3 \, x^{2} - 2\right)}}{24 \, x^{2}}"," ",0,"1/24*(56*sqrt(3)*x^2*log((25*x^2 - 2*sqrt(3)*(5*x^2 + 6) - 2*sqrt(x^4 + 5*x^2 + 3)*(5*sqrt(3) - 6) + 30)/x^2) - 114*x^2*log(-2*x^2 + 2*sqrt(x^4 + 5*x^2 + 3) - 5) + 21*x^2 + 12*sqrt(x^4 + 5*x^2 + 3)*(3*x^2 - 2))/x^2","A",0
147,1,112,0,0.924102," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^5,x, algorithm=""fricas"")","\frac{77 \, \sqrt{3} x^{4} \log\left(\frac{25 \, x^{2} - 2 \, \sqrt{3} {\left(5 \, x^{2} + 6\right)} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(5 \, \sqrt{3} - 6\right)} + 30}{x^{2}}\right) - 108 \, x^{4} \log\left(-2 \, x^{2} + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} - 5\right) - 138 \, x^{4} - 6 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(23 \, x^{2} + 6\right)}}{72 \, x^{4}}"," ",0,"1/72*(77*sqrt(3)*x^4*log((25*x^2 - 2*sqrt(3)*(5*x^2 + 6) - 2*sqrt(x^4 + 5*x^2 + 3)*(5*sqrt(3) - 6) + 30)/x^2) - 108*x^4*log(-2*x^2 + 2*sqrt(x^4 + 5*x^2 + 3) - 5) - 138*x^4 - 6*sqrt(x^4 + 5*x^2 + 3)*(23*x^2 + 6))/x^4","A",0
148,1,90,0,0.753710," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^7,x, algorithm=""fricas"")","\frac{13 \, \sqrt{3} x^{6} \log\left(\frac{25 \, x^{2} + 2 \, \sqrt{3} {\left(5 \, x^{2} + 6\right)} + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(5 \, \sqrt{3} + 6\right)} + 30}{x^{2}}\right) - 42 \, x^{6} - 6 \, {\left(7 \, x^{4} + 16 \, x^{2} + 6\right)} \sqrt{x^{4} + 5 \, x^{2} + 3}}{108 \, x^{6}}"," ",0,"1/108*(13*sqrt(3)*x^6*log((25*x^2 + 2*sqrt(3)*(5*x^2 + 6) + 2*sqrt(x^4 + 5*x^2 + 3)*(5*sqrt(3) + 6) + 30)/x^2) - 42*x^6 - 6*(7*x^4 + 16*x^2 + 6)*sqrt(x^4 + 5*x^2 + 3))/x^6","A",0
149,1,95,0,1.217197," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^9,x, algorithm=""fricas"")","\frac{871 \, \sqrt{3} x^{8} \log\left(\frac{25 \, x^{2} - 2 \, \sqrt{3} {\left(5 \, x^{2} + 6\right)} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(5 \, \sqrt{3} - 6\right)} + 30}{x^{2}}\right) + 1482 \, x^{8} + 6 \, {\left(247 \, x^{6} - 182 \, x^{4} - 984 \, x^{2} - 432\right)} \sqrt{x^{4} + 5 \, x^{2} + 3}}{10368 \, x^{8}}"," ",0,"1/10368*(871*sqrt(3)*x^8*log((25*x^2 - 2*sqrt(3)*(5*x^2 + 6) - 2*sqrt(x^4 + 5*x^2 + 3)*(5*sqrt(3) - 6) + 30)/x^2) + 1482*x^8 + 6*(247*x^6 - 182*x^4 - 984*x^2 - 432)*sqrt(x^4 + 5*x^2 + 3))/x^8","A",0
150,1,100,0,0.931696," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^11,x, algorithm=""fricas"")","\frac{10465 \, \sqrt{3} x^{10} \log\left(\frac{25 \, x^{2} + 2 \, \sqrt{3} {\left(5 \, x^{2} + 6\right)} + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(5 \, \sqrt{3} + 6\right)} + 30}{x^{2}}\right) - 15846 \, x^{10} - 6 \, {\left(2641 \, x^{8} - 1370 \, x^{6} + 1176 \, x^{4} + 10800 \, x^{2} + 5184\right)} \sqrt{x^{4} + 5 \, x^{2} + 3}}{155520 \, x^{10}}"," ",0,"1/155520*(10465*sqrt(3)*x^10*log((25*x^2 + 2*sqrt(3)*(5*x^2 + 6) + 2*sqrt(x^4 + 5*x^2 + 3)*(5*sqrt(3) + 6) + 30)/x^2) - 15846*x^10 - 6*(2641*x^8 - 1370*x^6 + 1176*x^4 + 10800*x^2 + 5184)*sqrt(x^4 + 5*x^2 + 3))/x^10","A",0
151,0,0,0,1.223728," ","integrate(x^4*(3*x^2+2)*(x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(3 \, x^{6} + 2 \, x^{4}\right)} \sqrt{x^{4} + 5 \, x^{2} + 3}, x\right)"," ",0,"integral((3*x^6 + 2*x^4)*sqrt(x^4 + 5*x^2 + 3), x)","F",0
152,0,0,0,1.084015," ","integrate(x^2*(3*x^2+2)*(x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(3 \, x^{4} + 2 \, x^{2}\right)} \sqrt{x^{4} + 5 \, x^{2} + 3}, x\right)"," ",0,"integral((3*x^4 + 2*x^2)*sqrt(x^4 + 5*x^2 + 3), x)","F",0
153,0,0,0,0.710723," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{x^{4} + 5 \, x^{2} + 3} {\left(3 \, x^{2} + 2\right)}, x\right)"," ",0,"integral(sqrt(x^4 + 5*x^2 + 3)*(3*x^2 + 2), x)","F",0
154,0,0,0,0.956794," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 5 \, x^{2} + 3} {\left(3 \, x^{2} + 2\right)}}{x^{2}}, x\right)"," ",0,"integral(sqrt(x^4 + 5*x^2 + 3)*(3*x^2 + 2)/x^2, x)","F",0
155,0,0,0,0.904241," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 5 \, x^{2} + 3} {\left(3 \, x^{2} + 2\right)}}{x^{4}}, x\right)"," ",0,"integral(sqrt(x^4 + 5*x^2 + 3)*(3*x^2 + 2)/x^4, x)","F",0
156,1,71,0,0.995904," ","integrate(x^5*(3*x^2+2)*(x^4+5*x^2+3)^(3/2),x, algorithm=""fricas"")","\frac{1}{215040} \, {\left(46080 \, x^{12} + 323840 \, x^{10} + 482944 \, x^{8} + 154800 \, x^{6} + 283304 \, x^{4} - 1499570 \, x^{2} + 9546951\right)} \sqrt{x^{4} + 5 \, x^{2} + 3} + \frac{368927}{4096} \, \log\left(-2 \, x^{2} + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} - 5\right)"," ",0,"1/215040*(46080*x^12 + 323840*x^10 + 482944*x^8 + 154800*x^6 + 283304*x^4 - 1499570*x^2 + 9546951)*sqrt(x^4 + 5*x^2 + 3) + 368927/4096*log(-2*x^2 + 2*sqrt(x^4 + 5*x^2 + 3) - 5)","A",0
157,1,66,0,1.021816," ","integrate(x^3*(3*x^2+2)*(x^4+5*x^2+3)^(3/2),x, algorithm=""fricas"")","\frac{1}{5120} \, {\left(1280 \, x^{10} + 9344 \, x^{8} + 14960 \, x^{6} + 5064 \, x^{4} + 12390 \, x^{2} - 77229\right)} \sqrt{x^{4} + 5 \, x^{2} + 3} - \frac{62361}{2048} \, \log\left(-2 \, x^{2} + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} - 5\right)"," ",0,"1/5120*(1280*x^10 + 9344*x^8 + 14960*x^6 + 5064*x^4 + 12390*x^2 - 77229)*sqrt(x^4 + 5*x^2 + 3) - 62361/2048*log(-2*x^2 + 2*sqrt(x^4 + 5*x^2 + 3) - 5)","A",0
158,1,61,0,0.764650," ","integrate(x*(3*x^2+2)*(x^4+5*x^2+3)^(3/2),x, algorithm=""fricas"")","\frac{1}{1280} \, {\left(384 \, x^{8} + 2960 \, x^{6} + 5304 \, x^{4} + 2170 \, x^{2} + 7581\right)} \sqrt{x^{4} + 5 \, x^{2} + 3} + \frac{5577}{512} \, \log\left(-2 \, x^{2} + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} - 5\right)"," ",0,"1/1280*(384*x^8 + 2960*x^6 + 5304*x^4 + 2170*x^2 + 7581)*sqrt(x^4 + 5*x^2 + 3) + 5577/512*log(-2*x^2 + 2*sqrt(x^4 + 5*x^2 + 3) - 5)","A",0
159,1,106,0,1.232052," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x,x, algorithm=""fricas"")","\frac{1}{384} \, {\left(144 \, x^{6} + 1208 \, x^{4} + 2650 \, x^{2} + 2061\right)} \sqrt{x^{4} + 5 \, x^{2} + 3} + 3 \, \sqrt{3} \log\left(\frac{25 \, x^{2} - 2 \, \sqrt{3} {\left(5 \, x^{2} + 6\right)} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(5 \, \sqrt{3} - 6\right)} + 30}{x^{2}}\right) - \frac{2401}{256} \, \log\left(-2 \, x^{2} + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} - 5\right)"," ",0,"1/384*(144*x^6 + 1208*x^4 + 2650*x^2 + 2061)*sqrt(x^4 + 5*x^2 + 3) + 3*sqrt(3)*log((25*x^2 - 2*sqrt(3)*(5*x^2 + 6) - 2*sqrt(x^4 + 5*x^2 + 3)*(5*sqrt(3) - 6) + 30)/x^2) - 2401/256*log(-2*x^2 + 2*sqrt(x^4 + 5*x^2 + 3) - 5)","A",0
160,1,122,0,1.035229," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x^3,x, algorithm=""fricas"")","\frac{1536 \, \sqrt{3} x^{2} \log\left(\frac{25 \, x^{2} - 2 \, \sqrt{3} {\left(5 \, x^{2} + 6\right)} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(5 \, \sqrt{3} - 6\right)} + 30}{x^{2}}\right) - 2436 \, x^{2} \log\left(-2 \, x^{2} + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} - 5\right) + 1541 \, x^{2} + 8 \, {\left(8 \, x^{6} + 78 \, x^{4} + 271 \, x^{2} - 48\right)} \sqrt{x^{4} + 5 \, x^{2} + 3}}{128 \, x^{2}}"," ",0,"1/128*(1536*sqrt(3)*x^2*log((25*x^2 - 2*sqrt(3)*(5*x^2 + 6) - 2*sqrt(x^4 + 5*x^2 + 3)*(5*sqrt(3) - 6) + 30)/x^2) - 2436*x^2*log(-2*x^2 + 2*sqrt(x^4 + 5*x^2 + 3) - 5) + 1541*x^2 + 8*(8*x^6 + 78*x^4 + 271*x^2 - 48)*sqrt(x^4 + 5*x^2 + 3))/x^2","A",0
161,1,122,0,1.154723," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x^5,x, algorithm=""fricas"")","\frac{1016 \, \sqrt{3} x^{4} \log\left(\frac{25 \, x^{2} - 2 \, \sqrt{3} {\left(5 \, x^{2} + 6\right)} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(5 \, \sqrt{3} - 6\right)} + 30}{x^{2}}\right) - 1812 \, x^{4} \log\left(-2 \, x^{2} + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} - 5\right) + 67 \, x^{4} + 8 \, {\left(6 \, x^{6} + 83 \, x^{4} - 86 \, x^{2} - 12\right)} \sqrt{x^{4} + 5 \, x^{2} + 3}}{64 \, x^{4}}"," ",0,"1/64*(1016*sqrt(3)*x^4*log((25*x^2 - 2*sqrt(3)*(5*x^2 + 6) - 2*sqrt(x^4 + 5*x^2 + 3)*(5*sqrt(3) - 6) + 30)/x^2) - 1812*x^4*log(-2*x^2 + 2*sqrt(x^4 + 5*x^2 + 3) - 5) + 67*x^4 + 8*(6*x^6 + 83*x^4 - 86*x^2 - 12)*sqrt(x^4 + 5*x^2 + 3))/x^4","A",0
162,1,122,0,1.020816," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x^7,x, algorithm=""fricas"")","\frac{527 \, \sqrt{3} x^{6} \log\left(\frac{25 \, x^{2} - 2 \, \sqrt{3} {\left(5 \, x^{2} + 6\right)} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(5 \, \sqrt{3} - 6\right)} + 30}{x^{2}}\right) - 882 \, x^{6} \log\left(-2 \, x^{2} + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} - 5\right) - 711 \, x^{6} + 6 \, {\left(18 \, x^{6} - 141 \, x^{4} - 62 \, x^{2} - 12\right)} \sqrt{x^{4} + 5 \, x^{2} + 3}}{72 \, x^{6}}"," ",0,"1/72*(527*sqrt(3)*x^6*log((25*x^2 - 2*sqrt(3)*(5*x^2 + 6) - 2*sqrt(x^4 + 5*x^2 + 3)*(5*sqrt(3) - 6) + 30)/x^2) - 882*x^6*log(-2*x^2 + 2*sqrt(x^4 + 5*x^2 + 3) - 5) - 711*x^6 + 6*(18*x^6 - 141*x^4 - 62*x^2 - 12)*sqrt(x^4 + 5*x^2 + 3))/x^6","A",0
163,0,0,0,1.011470," ","integrate(x^4*(3*x^2+2)*(x^4+5*x^2+3)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(3 \, x^{10} + 17 \, x^{8} + 19 \, x^{6} + 6 \, x^{4}\right)} \sqrt{x^{4} + 5 \, x^{2} + 3}, x\right)"," ",0,"integral((3*x^10 + 17*x^8 + 19*x^6 + 6*x^4)*sqrt(x^4 + 5*x^2 + 3), x)","F",0
164,0,0,0,0.943806," ","integrate(x^2*(3*x^2+2)*(x^4+5*x^2+3)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(3 \, x^{8} + 17 \, x^{6} + 19 \, x^{4} + 6 \, x^{2}\right)} \sqrt{x^{4} + 5 \, x^{2} + 3}, x\right)"," ",0,"integral((3*x^8 + 17*x^6 + 19*x^4 + 6*x^2)*sqrt(x^4 + 5*x^2 + 3), x)","F",0
165,0,0,0,1.095648," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(3 \, x^{6} + 17 \, x^{4} + 19 \, x^{2} + 6\right)} \sqrt{x^{4} + 5 \, x^{2} + 3}, x\right)"," ",0,"integral((3*x^6 + 17*x^4 + 19*x^2 + 6)*sqrt(x^4 + 5*x^2 + 3), x)","F",0
166,0,0,0,1.245922," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x^{6} + 17 \, x^{4} + 19 \, x^{2} + 6\right)} \sqrt{x^{4} + 5 \, x^{2} + 3}}{x^{2}}, x\right)"," ",0,"integral((3*x^6 + 17*x^4 + 19*x^2 + 6)*sqrt(x^4 + 5*x^2 + 3)/x^2, x)","F",0
167,0,0,0,0.703031," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x^{6} + 17 \, x^{4} + 19 \, x^{2} + 6\right)} \sqrt{x^{4} + 5 \, x^{2} + 3}}{x^{4}}, x\right)"," ",0,"integral((3*x^6 + 17*x^4 + 19*x^2 + 6)*sqrt(x^4 + 5*x^2 + 3)/x^4, x)","F",0
168,0,0,0,1.138288," ","integrate((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x^{6} + 17 \, x^{4} + 19 \, x^{2} + 6\right)} \sqrt{x^{4} + 5 \, x^{2} + 3}}{x^{6}}, x\right)"," ",0,"integral((3*x^6 + 17*x^4 + 19*x^2 + 6)*sqrt(x^4 + 5*x^2 + 3)/x^6, x)","F",0
169,1,315,0,0.726720," ","integrate(x^5*(B*x^2+A)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, B b^{3} + 8 \, A a c^{2} - 6 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(8 \, B c^{3} x^{4} + 15 \, B b^{2} c - 2 \, {\left(8 \, B a + 9 \, A b\right)} c^{2} - 2 \, {\left(5 \, B b c^{2} - 6 \, A c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{192 \, c^{4}}, \frac{3 \, {\left(5 \, B b^{3} + 8 \, A a c^{2} - 6 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) + 2 \, {\left(8 \, B c^{3} x^{4} + 15 \, B b^{2} c - 2 \, {\left(8 \, B a + 9 \, A b\right)} c^{2} - 2 \, {\left(5 \, B b c^{2} - 6 \, A c^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{96 \, c^{4}}\right]"," ",0,"[1/192*(3*(5*B*b^3 + 8*A*a*c^2 - 6*(2*B*a*b + A*b^2)*c)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 + 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + 4*(8*B*c^3*x^4 + 15*B*b^2*c - 2*(8*B*a + 9*A*b)*c^2 - 2*(5*B*b*c^2 - 6*A*c^3)*x^2)*sqrt(c*x^4 + b*x^2 + a))/c^4, 1/96*(3*(5*B*b^3 + 8*A*a*c^2 - 6*(2*B*a*b + A*b^2)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + 2*(8*B*c^3*x^4 + 15*B*b^2*c - 2*(8*B*a + 9*A*b)*c^2 - 2*(5*B*b*c^2 - 6*A*c^3)*x^2)*sqrt(c*x^4 + b*x^2 + a))/c^4]","A",0
170,1,233,0,1.093103," ","integrate(x^3*(B*x^2+A)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, B b^{2} - 4 \, {\left(B a + A b\right)} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(2 \, B c^{2} x^{2} - 3 \, B b c + 4 \, A c^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{32 \, c^{3}}, -\frac{{\left(3 \, B b^{2} - 4 \, {\left(B a + A b\right)} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) - 2 \, {\left(2 \, B c^{2} x^{2} - 3 \, B b c + 4 \, A c^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{16 \, c^{3}}\right]"," ",0,"[-1/32*((3*B*b^2 - 4*(B*a + A*b)*c)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 + 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) - 4*(2*B*c^2*x^2 - 3*B*b*c + 4*A*c^2)*sqrt(c*x^4 + b*x^2 + a))/c^3, -1/16*((3*B*b^2 - 4*(B*a + A*b)*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) - 2*(2*B*c^2*x^2 - 3*B*b*c + 4*A*c^2)*sqrt(c*x^4 + b*x^2 + a))/c^3]","A",0
171,1,178,0,1.300035," ","integrate(x*(B*x^2+A)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{c x^{4} + b x^{2} + a} B c - {\left(B b - 2 \, A c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right)}{8 \, c^{2}}, \frac{2 \, \sqrt{c x^{4} + b x^{2} + a} B c + {\left(B b - 2 \, A c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right)}{4 \, c^{2}}\right]"," ",0,"[1/8*(4*sqrt(c*x^4 + b*x^2 + a)*B*c - (B*b - 2*A*c)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c))/c^2, 1/4*(2*sqrt(c*x^4 + b*x^2 + a)*B*c + (B*b - 2*A*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)))/c^2]","A",0
172,1,517,0,1.250026," ","integrate((B*x^2+A)/x/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{B a \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + A \sqrt{a} c \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{4} + 8 \, a b x^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{4}}\right)}{4 \, a c}, -\frac{2 \, B a \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) - A \sqrt{a} c \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{4} + 8 \, a b x^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{4}}\right)}{4 \, a c}, \frac{2 \, A \sqrt{-a} c \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{4} + a b x^{2} + a^{2}\right)}}\right) + B a \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right)}{4 \, a c}, \frac{A \sqrt{-a} c \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{4} + a b x^{2} + a^{2}\right)}}\right) - B a \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right)}{2 \, a c}\right]"," ",0,"[1/4*(B*a*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + A*sqrt(a)*c*log(-((b^2 + 4*a*c)*x^4 + 8*a*b*x^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(a) + 8*a^2)/x^4))/(a*c), -1/4*(2*B*a*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) - A*sqrt(a)*c*log(-((b^2 + 4*a*c)*x^4 + 8*a*b*x^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(a) + 8*a^2)/x^4))/(a*c), 1/4*(2*A*sqrt(-a)*c*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(-a)/(a*c*x^4 + a*b*x^2 + a^2)) + B*a*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c))/(a*c), 1/2*(A*sqrt(-a)*c*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(-a)/(a*c*x^4 + a*b*x^2 + a^2)) - B*a*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)))/(a*c)]","A",0
173,1,197,0,1.329611," ","integrate((B*x^2+A)/x^3/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, B a - A b\right)} \sqrt{a} x^{2} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{4} + 8 \, a b x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{4}}\right) + 4 \, \sqrt{c x^{4} + b x^{2} + a} A a}{8 \, a^{2} x^{2}}, \frac{{\left(2 \, B a - A b\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{4} + a b x^{2} + a^{2}\right)}}\right) - 2 \, \sqrt{c x^{4} + b x^{2} + a} A a}{4 \, a^{2} x^{2}}\right]"," ",0,"[-1/8*((2*B*a - A*b)*sqrt(a)*x^2*log(-((b^2 + 4*a*c)*x^4 + 8*a*b*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(a) + 8*a^2)/x^4) + 4*sqrt(c*x^4 + b*x^2 + a)*A*a)/(a^2*x^2), 1/4*((2*B*a - A*b)*sqrt(-a)*x^2*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(-a)/(a*c*x^4 + a*b*x^2 + a^2)) - 2*sqrt(c*x^4 + b*x^2 + a)*A*a)/(a^2*x^2)]","A",0
174,1,255,0,1.592406," ","integrate((B*x^2+A)/x^5/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(4 \, B a b - 3 \, A b^{2} + 4 \, A a c\right)} \sqrt{a} x^{4} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{4} + 8 \, a b x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{4}}\right) - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, A a^{2} + {\left(4 \, B a^{2} - 3 \, A a b\right)} x^{2}\right)}}{32 \, a^{3} x^{4}}, -\frac{{\left(4 \, B a b - 3 \, A b^{2} + 4 \, A a c\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{4} + a b x^{2} + a^{2}\right)}}\right) + 2 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, A a^{2} + {\left(4 \, B a^{2} - 3 \, A a b\right)} x^{2}\right)}}{16 \, a^{3} x^{4}}\right]"," ",0,"[1/32*((4*B*a*b - 3*A*b^2 + 4*A*a*c)*sqrt(a)*x^4*log(-((b^2 + 4*a*c)*x^4 + 8*a*b*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(a) + 8*a^2)/x^4) - 4*sqrt(c*x^4 + b*x^2 + a)*(2*A*a^2 + (4*B*a^2 - 3*A*a*b)*x^2))/(a^3*x^4), -1/16*((4*B*a*b - 3*A*b^2 + 4*A*a*c)*sqrt(-a)*x^4*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(-a)/(a*c*x^4 + a*b*x^2 + a^2)) + 2*sqrt(c*x^4 + b*x^2 + a)*(2*A*a^2 + (4*B*a^2 - 3*A*a*b)*x^2))/(a^3*x^4)]","A",0
175,1,339,0,1.883571," ","integrate((B*x^2+A)/x^7/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(6 \, B a b^{2} - 5 \, A b^{3} - 4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c\right)} \sqrt{a} x^{6} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{4} + 8 \, a b x^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{4}}\right) + 4 \, {\left({\left(18 \, B a^{2} b - 15 \, A a b^{2} + 16 \, A a^{2} c\right)} x^{4} - 8 \, A a^{3} - 2 \, {\left(6 \, B a^{3} - 5 \, A a^{2} b\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{192 \, a^{4} x^{6}}, \frac{3 \, {\left(6 \, B a b^{2} - 5 \, A b^{3} - 4 \, {\left(2 \, B a^{2} - 3 \, A a b\right)} c\right)} \sqrt{-a} x^{6} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{4} + a b x^{2} + a^{2}\right)}}\right) + 2 \, {\left({\left(18 \, B a^{2} b - 15 \, A a b^{2} + 16 \, A a^{2} c\right)} x^{4} - 8 \, A a^{3} - 2 \, {\left(6 \, B a^{3} - 5 \, A a^{2} b\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{96 \, a^{4} x^{6}}\right]"," ",0,"[1/192*(3*(6*B*a*b^2 - 5*A*b^3 - 4*(2*B*a^2 - 3*A*a*b)*c)*sqrt(a)*x^6*log(-((b^2 + 4*a*c)*x^4 + 8*a*b*x^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(a) + 8*a^2)/x^4) + 4*((18*B*a^2*b - 15*A*a*b^2 + 16*A*a^2*c)*x^4 - 8*A*a^3 - 2*(6*B*a^3 - 5*A*a^2*b)*x^2)*sqrt(c*x^4 + b*x^2 + a))/(a^4*x^6), 1/96*(3*(6*B*a*b^2 - 5*A*b^3 - 4*(2*B*a^2 - 3*A*a*b)*c)*sqrt(-a)*x^6*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(-a)/(a*c*x^4 + a*b*x^2 + a^2)) + 2*((18*B*a^2*b - 15*A*a*b^2 + 16*A*a^2*c)*x^4 - 8*A*a^3 - 2*(6*B*a^3 - 5*A*a^2*b)*x^2)*sqrt(c*x^4 + b*x^2 + a))/(a^4*x^6)]","A",0
176,0,0,0,0.767265," ","integrate(x^4*(B*x^2+A)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B x^{6} + A x^{4}}{\sqrt{c x^{4} + b x^{2} + a}}, x\right)"," ",0,"integral((B*x^6 + A*x^4)/sqrt(c*x^4 + b*x^2 + a), x)","F",0
177,0,0,0,0.921473," ","integrate(x^2*(B*x^2+A)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B x^{4} + A x^{2}}{\sqrt{c x^{4} + b x^{2} + a}}, x\right)"," ",0,"integral((B*x^4 + A*x^2)/sqrt(c*x^4 + b*x^2 + a), x)","F",0
178,0,0,0,0.979800," ","integrate((B*x^2+A)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B x^{2} + A}{\sqrt{c x^{4} + b x^{2} + a}}, x\right)"," ",0,"integral((B*x^2 + A)/sqrt(c*x^4 + b*x^2 + a), x)","F",0
179,0,0,0,0.691555," ","integrate((B*x^2+A)/x^2/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(B x^{2} + A\right)}}{c x^{6} + b x^{4} + a x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*(B*x^2 + A)/(c*x^6 + b*x^4 + a*x^2), x)","F",0
180,0,0,0,1.064516," ","integrate((B*x^2+A)/x^4/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(B x^{2} + A\right)}}{c x^{8} + b x^{6} + a x^{4}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*(B*x^2 + A)/(c*x^8 + b*x^6 + a*x^4), x)","F",0
181,1,56,0,0.620167," ","integrate(x^7*(3*x^2+2)/(x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{384} \, {\left(144 \, x^{6} - 712 \, x^{4} + 3802 \, x^{2} - 24243\right)} \sqrt{x^{4} + 5 \, x^{2} + 3} - \frac{32801}{256} \, \log\left(-2 \, x^{2} + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} - 5\right)"," ",0,"1/384*(144*x^6 - 712*x^4 + 3802*x^2 - 24243)*sqrt(x^4 + 5*x^2 + 3) - 32801/256*log(-2*x^2 + 2*sqrt(x^4 + 5*x^2 + 3) - 5)","A",0
182,1,51,0,0.967506," ","integrate(x^5*(3*x^2+2)/(x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{16} \, {\left(8 \, x^{4} - 42 \, x^{2} + 267\right)} \sqrt{x^{4} + 5 \, x^{2} + 3} + \frac{1083}{32} \, \log\left(-2 \, x^{2} + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} - 5\right)"," ",0,"1/16*(8*x^4 - 42*x^2 + 267)*sqrt(x^4 + 5*x^2 + 3) + 1083/32*log(-2*x^2 + 2*sqrt(x^4 + 5*x^2 + 3) - 5)","A",0
183,1,46,0,0.983858," ","integrate(x^3*(3*x^2+2)/(x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","\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
184,1,39,0,0.747661," ","integrate(x*(3*x^2+2)/(x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","\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
185,1,75,0,0.803624," ","integrate((3*x^2+2)/x/(x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \log\left(\frac{25 \, x^{2} - 2 \, \sqrt{3} {\left(5 \, x^{2} + 6\right)} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(5 \, \sqrt{3} - 6\right)} + 30}{x^{2}}\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((25*x^2 - 2*sqrt(3)*(5*x^2 + 6) - 2*sqrt(x^4 + 5*x^2 + 3)*(5*sqrt(3) - 6) + 30)/x^2) - 3/2*log(-2*x^2 + 2*sqrt(x^4 + 5*x^2 + 3) - 5)","A",0
186,1,78,0,0.782325," ","integrate((3*x^2+2)/x^3/(x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} x^{2} \log\left(\frac{25 \, x^{2} - 2 \, \sqrt{3} {\left(5 \, x^{2} + 6\right)} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(5 \, \sqrt{3} - 6\right)} + 30}{x^{2}}\right) - 3 \, x^{2} - 3 \, \sqrt{x^{4} + 5 \, x^{2} + 3}}{9 \, x^{2}}"," ",0,"1/9*(2*sqrt(3)*x^2*log((25*x^2 - 2*sqrt(3)*(5*x^2 + 6) - 2*sqrt(x^4 + 5*x^2 + 3)*(5*sqrt(3) - 6) + 30)/x^2) - 3*x^2 - 3*sqrt(x^4 + 5*x^2 + 3))/x^2","A",0
187,1,83,0,0.811564," ","integrate((3*x^2+2)/x^5/(x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{3} x^{4} \log\left(\frac{25 \, x^{2} + 2 \, \sqrt{3} {\left(5 \, x^{2} + 6\right)} + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(5 \, \sqrt{3} + 6\right)} + 30}{x^{2}}\right) - 2 \, x^{4} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(x^{2} + 2\right)}}{24 \, x^{4}}"," ",0,"1/24*(3*sqrt(3)*x^4*log((25*x^2 + 2*sqrt(3)*(5*x^2 + 6) + 2*sqrt(x^4 + 5*x^2 + 3)*(5*sqrt(3) + 6) + 30)/x^2) - 2*x^4 - 2*sqrt(x^4 + 5*x^2 + 3)*(x^2 + 2))/x^4","A",0
188,1,90,0,0.859600," ","integrate((3*x^2+2)/x^7/(x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","\frac{61 \, \sqrt{3} x^{6} \log\left(\frac{25 \, x^{2} - 2 \, \sqrt{3} {\left(5 \, x^{2} + 6\right)} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(5 \, \sqrt{3} - 6\right)} + 30}{x^{2}}\right) + 78 \, x^{6} + 6 \, {\left(13 \, x^{4} - 2 \, x^{2} - 12\right)} \sqrt{x^{4} + 5 \, x^{2} + 3}}{648 \, x^{6}}"," ",0,"1/648*(61*sqrt(3)*x^6*log((25*x^2 - 2*sqrt(3)*(5*x^2 + 6) - 2*sqrt(x^4 + 5*x^2 + 3)*(5*sqrt(3) - 6) + 30)/x^2) + 78*x^6 + 6*(13*x^4 - 2*x^2 - 12)*sqrt(x^4 + 5*x^2 + 3))/x^6","A",0
189,0,0,0,0.685538," ","integrate(x^4*(3*x^2+2)/(x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{3 \, x^{6} + 2 \, x^{4}}{\sqrt{x^{4} + 5 \, x^{2} + 3}}, x\right)"," ",0,"integral((3*x^6 + 2*x^4)/sqrt(x^4 + 5*x^2 + 3), x)","F",0
190,0,0,0,1.021959," ","integrate(x^2*(3*x^2+2)/(x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{3 \, x^{4} + 2 \, x^{2}}{\sqrt{x^{4} + 5 \, x^{2} + 3}}, x\right)"," ",0,"integral((3*x^4 + 2*x^2)/sqrt(x^4 + 5*x^2 + 3), x)","F",0
191,0,0,0,0.986991," ","integrate((3*x^2+2)/(x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{3 \, x^{2} + 2}{\sqrt{x^{4} + 5 \, x^{2} + 3}}, x\right)"," ",0,"integral((3*x^2 + 2)/sqrt(x^4 + 5*x^2 + 3), x)","F",0
192,0,0,0,1.107506," ","integrate((3*x^2+2)/x^2/(x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 5 \, x^{2} + 3} {\left(3 \, x^{2} + 2\right)}}{x^{6} + 5 \, x^{4} + 3 \, x^{2}}, x\right)"," ",0,"integral(sqrt(x^4 + 5*x^2 + 3)*(3*x^2 + 2)/(x^6 + 5*x^4 + 3*x^2), x)","F",0
193,0,0,0,0.978805," ","integrate((3*x^2+2)/x^4/(x^4+5*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 5 \, x^{2} + 3} {\left(3 \, x^{2} + 2\right)}}{x^{8} + 5 \, x^{6} + 3 \, x^{4}}, x\right)"," ",0,"integral(sqrt(x^4 + 5*x^2 + 3)*(3*x^2 + 2)/(x^8 + 5*x^6 + 3*x^4), x)","F",0
194,1,86,0,1.007224," ","integrate(x^5*(3*x^2+2)/(x^4+5*x^2+3)^(3/2),x, algorithm=""fricas"")","\frac{1811 \, x^{4} + 9055 \, x^{2} + 1066 \, {\left(x^{4} + 5 \, x^{2} + 3\right)} \log\left(-2 \, x^{2} + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} - 5\right) + 4 \, {\left(39 \, x^{4} + 599 \, x^{2} + 399\right)} \sqrt{x^{4} + 5 \, x^{2} + 3} + 5433}{104 \, {\left(x^{4} + 5 \, x^{2} + 3\right)}}"," ",0,"1/104*(1811*x^4 + 9055*x^2 + 1066*(x^4 + 5*x^2 + 3)*log(-2*x^2 + 2*sqrt(x^4 + 5*x^2 + 3) - 5) + 4*(39*x^4 + 599*x^2 + 399)*sqrt(x^4 + 5*x^2 + 3) + 5433)/(x^4 + 5*x^2 + 3)","A",0
195,1,81,0,0.989990," ","integrate(x^3*(3*x^2+2)/(x^4+5*x^2+3)^(3/2),x, algorithm=""fricas"")","-\frac{94 \, x^{4} + 470 \, x^{2} + 39 \, {\left(x^{4} + 5 \, x^{2} + 3\right)} \log\left(-2 \, x^{2} + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} - 5\right) + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(47 \, x^{2} + 33\right)} + 282}{26 \, {\left(x^{4} + 5 \, x^{2} + 3\right)}}"," ",0,"-1/26*(94*x^4 + 470*x^2 + 39*(x^4 + 5*x^2 + 3)*log(-2*x^2 + 2*sqrt(x^4 + 5*x^2 + 3) - 5) + 2*sqrt(x^4 + 5*x^2 + 3)*(47*x^2 + 33) + 282)/(x^4 + 5*x^2 + 3)","A",0
196,1,46,0,0.904371," ","integrate(x*(3*x^2+2)/(x^4+5*x^2+3)^(3/2),x, algorithm=""fricas"")","\frac{11 \, x^{4} + 55 \, x^{2} + \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(11 \, x^{2} + 8\right)} + 33}{13 \, {\left(x^{4} + 5 \, x^{2} + 3\right)}}"," ",0,"1/13*(11*x^4 + 55*x^2 + sqrt(x^4 + 5*x^2 + 3)*(11*x^2 + 8) + 33)/(x^4 + 5*x^2 + 3)","B",0
197,1,107,0,0.934681," ","integrate((3*x^2+2)/x/(x^4+5*x^2+3)^(3/2),x, algorithm=""fricas"")","-\frac{24 \, x^{4} - 13 \, \sqrt{3} {\left(x^{4} + 5 \, x^{2} + 3\right)} \log\left(\frac{25 \, x^{2} - 2 \, \sqrt{3} {\left(5 \, x^{2} + 6\right)} - 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(5 \, \sqrt{3} - 6\right)} + 30}{x^{2}}\right) + 120 \, x^{2} + 3 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(8 \, x^{2} + 7\right)} + 72}{117 \, {\left(x^{4} + 5 \, x^{2} + 3\right)}}"," ",0,"-1/117*(24*x^4 - 13*sqrt(3)*(x^4 + 5*x^2 + 3)*log((25*x^2 - 2*sqrt(3)*(5*x^2 + 6) - 2*sqrt(x^4 + 5*x^2 + 3)*(5*sqrt(3) - 6) + 30)/x^2) + 120*x^2 + 3*sqrt(x^4 + 5*x^2 + 3)*(8*x^2 + 7) + 72)/(x^4 + 5*x^2 + 3)","B",0
198,1,124,0,1.093860," ","integrate((3*x^2+2)/x^3/(x^4+5*x^2+3)^(3/2),x, algorithm=""fricas"")","-\frac{6 \, x^{6} + 30 \, x^{4} - 13 \, \sqrt{3} {\left(x^{6} + 5 \, x^{4} + 3 \, x^{2}\right)} \log\left(\frac{25 \, x^{2} + 2 \, \sqrt{3} {\left(5 \, x^{2} + 6\right)} + 2 \, \sqrt{x^{4} + 5 \, x^{2} + 3} {\left(5 \, \sqrt{3} + 6\right)} + 30}{x^{2}}\right) + 18 \, x^{2} + 3 \, {\left(2 \, x^{4} + 18 \, x^{2} + 13\right)} \sqrt{x^{4} + 5 \, x^{2} + 3}}{117 \, {\left(x^{6} + 5 \, x^{4} + 3 \, x^{2}\right)}}"," ",0,"-1/117*(6*x^6 + 30*x^4 - 13*sqrt(3)*(x^6 + 5*x^4 + 3*x^2)*log((25*x^2 + 2*sqrt(3)*(5*x^2 + 6) + 2*sqrt(x^4 + 5*x^2 + 3)*(5*sqrt(3) + 6) + 30)/x^2) + 18*x^2 + 3*(2*x^4 + 18*x^2 + 13)*sqrt(x^4 + 5*x^2 + 3))/(x^6 + 5*x^4 + 3*x^2)","A",0
199,0,0,0,0.966351," ","integrate(x^4*(3*x^2+2)/(x^4+5*x^2+3)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x^{6} + 2 \, x^{4}\right)} \sqrt{x^{4} + 5 \, x^{2} + 3}}{x^{8} + 10 \, x^{6} + 31 \, x^{4} + 30 \, x^{2} + 9}, x\right)"," ",0,"integral((3*x^6 + 2*x^4)*sqrt(x^4 + 5*x^2 + 3)/(x^8 + 10*x^6 + 31*x^4 + 30*x^2 + 9), x)","F",0
200,0,0,0,0.901437," ","integrate(x^2*(3*x^2+2)/(x^4+5*x^2+3)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x^{4} + 2 \, x^{2}\right)} \sqrt{x^{4} + 5 \, x^{2} + 3}}{x^{8} + 10 \, x^{6} + 31 \, x^{4} + 30 \, x^{2} + 9}, x\right)"," ",0,"integral((3*x^4 + 2*x^2)*sqrt(x^4 + 5*x^2 + 3)/(x^8 + 10*x^6 + 31*x^4 + 30*x^2 + 9), x)","F",0
201,0,0,0,0.900578," ","integrate((3*x^2+2)/(x^4+5*x^2+3)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 5 \, x^{2} + 3} {\left(3 \, x^{2} + 2\right)}}{x^{8} + 10 \, x^{6} + 31 \, x^{4} + 30 \, x^{2} + 9}, x\right)"," ",0,"integral(sqrt(x^4 + 5*x^2 + 3)*(3*x^2 + 2)/(x^8 + 10*x^6 + 31*x^4 + 30*x^2 + 9), x)","F",0
202,0,0,0,1.000536," ","integrate((3*x^2+2)/x^2/(x^4+5*x^2+3)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 5 \, x^{2} + 3} {\left(3 \, x^{2} + 2\right)}}{x^{10} + 10 \, x^{8} + 31 \, x^{6} + 30 \, x^{4} + 9 \, x^{2}}, x\right)"," ",0,"integral(sqrt(x^4 + 5*x^2 + 3)*(3*x^2 + 2)/(x^10 + 10*x^8 + 31*x^6 + 30*x^4 + 9*x^2), x)","F",0
203,0,0,0,0.861377," ","integrate((3*x^2+2)/x^4/(x^4+5*x^2+3)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 5 \, x^{2} + 3} {\left(3 \, x^{2} + 2\right)}}{x^{12} + 10 \, x^{10} + 31 \, x^{8} + 30 \, x^{6} + 9 \, x^{4}}, x\right)"," ",0,"integral(sqrt(x^4 + 5*x^2 + 3)*(3*x^2 + 2)/(x^12 + 10*x^10 + 31*x^8 + 30*x^6 + 9*x^4), x)","F",0
204,0,0,0,1.087076," ","integrate((f*x)^(3/2)*(e*x^2+d)*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(e f x^{3} + d f x\right)} \sqrt{c x^{4} + b x^{2} + a} \sqrt{f x}, x\right)"," ",0,"integral((e*f*x^3 + d*f*x)*sqrt(c*x^4 + b*x^2 + a)*sqrt(f*x), x)","F",0
205,0,0,0,0.999426," ","integrate((f*x)^(1/2)*(e*x^2+d)*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + b x^{2} + a} {\left(e x^{2} + d\right)} \sqrt{f x}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*(e*x^2 + d)*sqrt(f*x), x)","F",0
206,0,0,0,0.868076," ","integrate((e*x^2+d)*(c*x^4+b*x^2+a)^(1/2)/(f*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(e x^{2} + d\right)} \sqrt{f x}}{f x}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*(e*x^2 + d)*sqrt(f*x)/(f*x), x)","F",0
207,0,0,0,0.951905," ","integrate((e*x^2+d)*(c*x^4+b*x^2+a)^(1/2)/(f*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(e x^{2} + d\right)} \sqrt{f x}}{f^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*(e*x^2 + d)*sqrt(f*x)/(f^2*x^2), x)","F",0
208,0,0,0,0.789117," ","integrate((f*x)^(3/2)*(e*x^2+d)*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c e f x^{7} + {\left(c d + b e\right)} f x^{5} + {\left(b d + a e\right)} f x^{3} + a d f x\right)} \sqrt{c x^{4} + b x^{2} + a} \sqrt{f x}, x\right)"," ",0,"integral((c*e*f*x^7 + (c*d + b*e)*f*x^5 + (b*d + a*e)*f*x^3 + a*d*f*x)*sqrt(c*x^4 + b*x^2 + a)*sqrt(f*x), x)","F",0
209,0,0,0,1.186496," ","integrate((f*x)^(1/2)*(e*x^2+d)*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c e x^{6} + {\left(c d + b e\right)} x^{4} + {\left(b d + a e\right)} x^{2} + a d\right)} \sqrt{c x^{4} + b x^{2} + a} \sqrt{f x}, x\right)"," ",0,"integral((c*e*x^6 + (c*d + b*e)*x^4 + (b*d + a*e)*x^2 + a*d)*sqrt(c*x^4 + b*x^2 + a)*sqrt(f*x), x)","F",0
210,0,0,0,1.220978," ","integrate((e*x^2+d)*(c*x^4+b*x^2+a)^(3/2)/(f*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c e x^{6} + {\left(c d + b e\right)} x^{4} + {\left(b d + a e\right)} x^{2} + a d\right)} \sqrt{c x^{4} + b x^{2} + a} \sqrt{f x}}{f x}, x\right)"," ",0,"integral((c*e*x^6 + (c*d + b*e)*x^4 + (b*d + a*e)*x^2 + a*d)*sqrt(c*x^4 + b*x^2 + a)*sqrt(f*x)/(f*x), x)","F",0
211,0,0,0,1.317778," ","integrate((e*x^2+d)*(c*x^4+b*x^2+a)^(3/2)/(f*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c e x^{6} + {\left(c d + b e\right)} x^{4} + {\left(b d + a e\right)} x^{2} + a d\right)} \sqrt{c x^{4} + b x^{2} + a} \sqrt{f x}}{f^{2} x^{2}}, x\right)"," ",0,"integral((c*e*x^6 + (c*d + b*e)*x^4 + (b*d + a*e)*x^2 + a*d)*sqrt(c*x^4 + b*x^2 + a)*sqrt(f*x)/(f^2*x^2), x)","F",0
212,0,0,0,1.294114," ","integrate((f*x)^(3/2)*(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e f x^{3} + d f x\right)} \sqrt{f x}}{\sqrt{c x^{4} + b x^{2} + a}}, x\right)"," ",0,"integral((e*f*x^3 + d*f*x)*sqrt(f*x)/sqrt(c*x^4 + b*x^2 + a), x)","F",0
213,0,0,0,0.732895," ","integrate((f*x)^(1/2)*(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{2} + d\right)} \sqrt{f x}}{\sqrt{c x^{4} + b x^{2} + a}}, x\right)"," ",0,"integral((e*x^2 + d)*sqrt(f*x)/sqrt(c*x^4 + b*x^2 + a), x)","F",0
214,0,0,0,0.992911," ","integrate((e*x^2+d)/(f*x)^(1/2)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(e x^{2} + d\right)} \sqrt{f x}}{c f x^{5} + b f x^{3} + a f x}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*(e*x^2 + d)*sqrt(f*x)/(c*f*x^5 + b*f*x^3 + a*f*x), x)","F",0
215,0,0,0,1.114987," ","integrate((e*x^2+d)/(f*x)^(3/2)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(e x^{2} + d\right)} \sqrt{f x}}{c f^{2} x^{6} + b f^{2} x^{4} + a f^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*(e*x^2 + d)*sqrt(f*x)/(c*f^2*x^6 + b*f^2*x^4 + a*f^2*x^2), x)","F",0
216,0,0,0,1.084810," ","integrate((f*x)^(3/2)*(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e f x^{3} + d f x\right)} \sqrt{c x^{4} + b x^{2} + a} \sqrt{f x}}{c^{2} x^{8} + 2 \, b c x^{6} + {\left(b^{2} + 2 \, a c\right)} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((e*f*x^3 + d*f*x)*sqrt(c*x^4 + b*x^2 + a)*sqrt(f*x)/(c^2*x^8 + 2*b*c*x^6 + (b^2 + 2*a*c)*x^4 + 2*a*b*x^2 + a^2), x)","F",0
217,0,0,0,1.096014," ","integrate((f*x)^(1/2)*(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(e x^{2} + d\right)} \sqrt{f x}}{c^{2} x^{8} + 2 \, b c x^{6} + {\left(b^{2} + 2 \, a c\right)} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*(e*x^2 + d)*sqrt(f*x)/(c^2*x^8 + 2*b*c*x^6 + (b^2 + 2*a*c)*x^4 + 2*a*b*x^2 + a^2), x)","F",0
218,0,0,0,0.922806," ","integrate((e*x^2+d)/(f*x)^(1/2)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(e x^{2} + d\right)} \sqrt{f x}}{c^{2} f x^{9} + 2 \, b c f x^{7} + {\left(b^{2} + 2 \, a c\right)} f x^{5} + 2 \, a b f x^{3} + a^{2} f x}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*(e*x^2 + d)*sqrt(f*x)/(c^2*f*x^9 + 2*b*c*f*x^7 + (b^2 + 2*a*c)*f*x^5 + 2*a*b*f*x^3 + a^2*f*x), x)","F",0
219,0,0,0,0.728409," ","integrate((e*x^2+d)/(f*x)^(3/2)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(e x^{2} + d\right)} \sqrt{f x}}{c^{2} f^{2} x^{10} + 2 \, b c f^{2} x^{8} + {\left(b^{2} + 2 \, a c\right)} f^{2} x^{6} + 2 \, a b f^{2} x^{4} + a^{2} f^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*(e*x^2 + d)*sqrt(f*x)/(c^2*f^2*x^10 + 2*b*c*f^2*x^8 + (b^2 + 2*a*c)*f^2*x^6 + 2*a*b*f^2*x^4 + a^2*f^2*x^2), x)","F",0
220,1,1357,0,0.859857," ","integrate((f*x)^m*(e*x^2+d)*(c*x^4+b*x^2+a)^3,x, algorithm=""fricas"")","\frac{{\left({\left(c^{3} e m^{7} + 49 \, c^{3} e m^{6} + 973 \, c^{3} e m^{5} + 10045 \, c^{3} e m^{4} + 57379 \, c^{3} e m^{3} + 177331 \, c^{3} e m^{2} + 264207 \, c^{3} e m + 135135 \, c^{3} e\right)} x^{15} + {\left({\left(c^{3} d + 3 \, b c^{2} e\right)} m^{7} + 51 \, {\left(c^{3} d + 3 \, b c^{2} e\right)} m^{6} + 1045 \, {\left(c^{3} d + 3 \, b c^{2} e\right)} m^{5} + 11055 \, {\left(c^{3} d + 3 \, b c^{2} e\right)} m^{4} + 155925 \, c^{3} d + 467775 \, b c^{2} e + 64339 \, {\left(c^{3} d + 3 \, b c^{2} e\right)} m^{3} + 201609 \, {\left(c^{3} d + 3 \, b c^{2} e\right)} m^{2} + 303255 \, {\left(c^{3} d + 3 \, b c^{2} e\right)} m\right)} x^{13} + 3 \, {\left({\left(b c^{2} d + {\left(b^{2} c + a c^{2}\right)} e\right)} m^{7} + 53 \, {\left(b c^{2} d + {\left(b^{2} c + a c^{2}\right)} e\right)} m^{6} + 1125 \, {\left(b c^{2} d + {\left(b^{2} c + a c^{2}\right)} e\right)} m^{5} + 12265 \, {\left(b c^{2} d + {\left(b^{2} c + a c^{2}\right)} e\right)} m^{4} + 184275 \, b c^{2} d + 73139 \, {\left(b c^{2} d + {\left(b^{2} c + a c^{2}\right)} e\right)} m^{3} + 233487 \, {\left(b c^{2} d + {\left(b^{2} c + a c^{2}\right)} e\right)} m^{2} + 184275 \, {\left(b^{2} c + a c^{2}\right)} e + 355815 \, {\left(b c^{2} d + {\left(b^{2} c + a c^{2}\right)} e\right)} m\right)} x^{11} + {\left({\left(3 \, {\left(b^{2} c + a c^{2}\right)} d + {\left(b^{3} + 6 \, a b c\right)} e\right)} m^{7} + 55 \, {\left(3 \, {\left(b^{2} c + a c^{2}\right)} d + {\left(b^{3} + 6 \, a b c\right)} e\right)} m^{6} + 1213 \, {\left(3 \, {\left(b^{2} c + a c^{2}\right)} d + {\left(b^{3} + 6 \, a b c\right)} e\right)} m^{5} + 13723 \, {\left(3 \, {\left(b^{2} c + a c^{2}\right)} d + {\left(b^{3} + 6 \, a b c\right)} e\right)} m^{4} + 84547 \, {\left(3 \, {\left(b^{2} c + a c^{2}\right)} d + {\left(b^{3} + 6 \, a b c\right)} e\right)} m^{3} + 277093 \, {\left(3 \, {\left(b^{2} c + a c^{2}\right)} d + {\left(b^{3} + 6 \, a b c\right)} e\right)} m^{2} + 675675 \, {\left(b^{2} c + a c^{2}\right)} d + 225225 \, {\left(b^{3} + 6 \, a b c\right)} e + 430335 \, {\left(3 \, {\left(b^{2} c + a c^{2}\right)} d + {\left(b^{3} + 6 \, a b c\right)} e\right)} m\right)} x^{9} + {\left({\left({\left(b^{3} + 6 \, a b c\right)} d + 3 \, {\left(a b^{2} + a^{2} c\right)} e\right)} m^{7} + 57 \, {\left({\left(b^{3} + 6 \, a b c\right)} d + 3 \, {\left(a b^{2} + a^{2} c\right)} e\right)} m^{6} + 1309 \, {\left({\left(b^{3} + 6 \, a b c\right)} d + 3 \, {\left(a b^{2} + a^{2} c\right)} e\right)} m^{5} + 15477 \, {\left({\left(b^{3} + 6 \, a b c\right)} d + 3 \, {\left(a b^{2} + a^{2} c\right)} e\right)} m^{4} + 99715 \, {\left({\left(b^{3} + 6 \, a b c\right)} d + 3 \, {\left(a b^{2} + a^{2} c\right)} e\right)} m^{3} + 340011 \, {\left({\left(b^{3} + 6 \, a b c\right)} d + 3 \, {\left(a b^{2} + a^{2} c\right)} e\right)} m^{2} + 289575 \, {\left(b^{3} + 6 \, a b c\right)} d + 868725 \, {\left(a b^{2} + a^{2} c\right)} e + 544095 \, {\left({\left(b^{3} + 6 \, a b c\right)} d + 3 \, {\left(a b^{2} + a^{2} c\right)} e\right)} m\right)} x^{7} + 3 \, {\left({\left(a^{2} b e + {\left(a b^{2} + a^{2} c\right)} d\right)} m^{7} + 59 \, {\left(a^{2} b e + {\left(a b^{2} + a^{2} c\right)} d\right)} m^{6} + 1413 \, {\left(a^{2} b e + {\left(a b^{2} + a^{2} c\right)} d\right)} m^{5} + 17575 \, {\left(a^{2} b e + {\left(a b^{2} + a^{2} c\right)} d\right)} m^{4} + 405405 \, a^{2} b e + 120179 \, {\left(a^{2} b e + {\left(a b^{2} + a^{2} c\right)} d\right)} m^{3} + 437121 \, {\left(a^{2} b e + {\left(a b^{2} + a^{2} c\right)} d\right)} m^{2} + 405405 \, {\left(a b^{2} + a^{2} c\right)} d + 738567 \, {\left(a^{2} b e + {\left(a b^{2} + a^{2} c\right)} d\right)} m\right)} x^{5} + {\left({\left(3 \, a^{2} b d + a^{3} e\right)} m^{7} + 61 \, {\left(3 \, a^{2} b d + a^{3} e\right)} m^{6} + 1525 \, {\left(3 \, a^{2} b d + a^{3} e\right)} m^{5} + 20065 \, {\left(3 \, a^{2} b d + a^{3} e\right)} m^{4} + 2027025 \, a^{2} b d + 675675 \, a^{3} e + 147859 \, {\left(3 \, a^{2} b d + a^{3} e\right)} m^{3} + 594439 \, {\left(3 \, a^{2} b d + a^{3} e\right)} m^{2} + 1140855 \, {\left(3 \, a^{2} b d + a^{3} e\right)} m\right)} x^{3} + {\left(a^{3} d m^{7} + 63 \, a^{3} d m^{6} + 1645 \, a^{3} d m^{5} + 22995 \, a^{3} d m^{4} + 185059 \, a^{3} d m^{3} + 852957 \, a^{3} d m^{2} + 2071215 \, a^{3} d m + 2027025 \, a^{3} d\right)} x\right)} \left(f x\right)^{m}}{m^{8} + 64 \, m^{7} + 1708 \, m^{6} + 24640 \, m^{5} + 208054 \, m^{4} + 1038016 \, m^{3} + 2924172 \, m^{2} + 4098240 \, m + 2027025}"," ",0,"((c^3*e*m^7 + 49*c^3*e*m^6 + 973*c^3*e*m^5 + 10045*c^3*e*m^4 + 57379*c^3*e*m^3 + 177331*c^3*e*m^2 + 264207*c^3*e*m + 135135*c^3*e)*x^15 + ((c^3*d + 3*b*c^2*e)*m^7 + 51*(c^3*d + 3*b*c^2*e)*m^6 + 1045*(c^3*d + 3*b*c^2*e)*m^5 + 11055*(c^3*d + 3*b*c^2*e)*m^4 + 155925*c^3*d + 467775*b*c^2*e + 64339*(c^3*d + 3*b*c^2*e)*m^3 + 201609*(c^3*d + 3*b*c^2*e)*m^2 + 303255*(c^3*d + 3*b*c^2*e)*m)*x^13 + 3*((b*c^2*d + (b^2*c + a*c^2)*e)*m^7 + 53*(b*c^2*d + (b^2*c + a*c^2)*e)*m^6 + 1125*(b*c^2*d + (b^2*c + a*c^2)*e)*m^5 + 12265*(b*c^2*d + (b^2*c + a*c^2)*e)*m^4 + 184275*b*c^2*d + 73139*(b*c^2*d + (b^2*c + a*c^2)*e)*m^3 + 233487*(b*c^2*d + (b^2*c + a*c^2)*e)*m^2 + 184275*(b^2*c + a*c^2)*e + 355815*(b*c^2*d + (b^2*c + a*c^2)*e)*m)*x^11 + ((3*(b^2*c + a*c^2)*d + (b^3 + 6*a*b*c)*e)*m^7 + 55*(3*(b^2*c + a*c^2)*d + (b^3 + 6*a*b*c)*e)*m^6 + 1213*(3*(b^2*c + a*c^2)*d + (b^3 + 6*a*b*c)*e)*m^5 + 13723*(3*(b^2*c + a*c^2)*d + (b^3 + 6*a*b*c)*e)*m^4 + 84547*(3*(b^2*c + a*c^2)*d + (b^3 + 6*a*b*c)*e)*m^3 + 277093*(3*(b^2*c + a*c^2)*d + (b^3 + 6*a*b*c)*e)*m^2 + 675675*(b^2*c + a*c^2)*d + 225225*(b^3 + 6*a*b*c)*e + 430335*(3*(b^2*c + a*c^2)*d + (b^3 + 6*a*b*c)*e)*m)*x^9 + (((b^3 + 6*a*b*c)*d + 3*(a*b^2 + a^2*c)*e)*m^7 + 57*((b^3 + 6*a*b*c)*d + 3*(a*b^2 + a^2*c)*e)*m^6 + 1309*((b^3 + 6*a*b*c)*d + 3*(a*b^2 + a^2*c)*e)*m^5 + 15477*((b^3 + 6*a*b*c)*d + 3*(a*b^2 + a^2*c)*e)*m^4 + 99715*((b^3 + 6*a*b*c)*d + 3*(a*b^2 + a^2*c)*e)*m^3 + 340011*((b^3 + 6*a*b*c)*d + 3*(a*b^2 + a^2*c)*e)*m^2 + 289575*(b^3 + 6*a*b*c)*d + 868725*(a*b^2 + a^2*c)*e + 544095*((b^3 + 6*a*b*c)*d + 3*(a*b^2 + a^2*c)*e)*m)*x^7 + 3*((a^2*b*e + (a*b^2 + a^2*c)*d)*m^7 + 59*(a^2*b*e + (a*b^2 + a^2*c)*d)*m^6 + 1413*(a^2*b*e + (a*b^2 + a^2*c)*d)*m^5 + 17575*(a^2*b*e + (a*b^2 + a^2*c)*d)*m^4 + 405405*a^2*b*e + 120179*(a^2*b*e + (a*b^2 + a^2*c)*d)*m^3 + 437121*(a^2*b*e + (a*b^2 + a^2*c)*d)*m^2 + 405405*(a*b^2 + a^2*c)*d + 738567*(a^2*b*e + (a*b^2 + a^2*c)*d)*m)*x^5 + ((3*a^2*b*d + a^3*e)*m^7 + 61*(3*a^2*b*d + a^3*e)*m^6 + 1525*(3*a^2*b*d + a^3*e)*m^5 + 20065*(3*a^2*b*d + a^3*e)*m^4 + 2027025*a^2*b*d + 675675*a^3*e + 147859*(3*a^2*b*d + a^3*e)*m^3 + 594439*(3*a^2*b*d + a^3*e)*m^2 + 1140855*(3*a^2*b*d + a^3*e)*m)*x^3 + (a^3*d*m^7 + 63*a^3*d*m^6 + 1645*a^3*d*m^5 + 22995*a^3*d*m^4 + 185059*a^3*d*m^3 + 852957*a^3*d*m^2 + 2071215*a^3*d*m + 2027025*a^3*d)*x)*(f*x)^m/(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
221,1,573,0,0.704025," ","integrate((f*x)^m*(e*x^2+d)*(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\frac{{\left({\left(c^{2} e m^{5} + 25 \, c^{2} e m^{4} + 230 \, c^{2} e m^{3} + 950 \, c^{2} e m^{2} + 1689 \, c^{2} e m + 945 \, c^{2} e\right)} x^{11} + {\left({\left(c^{2} d + 2 \, b c e\right)} m^{5} + 27 \, {\left(c^{2} d + 2 \, b c e\right)} m^{4} + 262 \, {\left(c^{2} d + 2 \, b c e\right)} m^{3} + 1155 \, c^{2} d + 2310 \, b c e + 1122 \, {\left(c^{2} d + 2 \, b c e\right)} m^{2} + 2041 \, {\left(c^{2} d + 2 \, b c e\right)} m\right)} x^{9} + {\left({\left(2 \, b c d + {\left(b^{2} + 2 \, a c\right)} e\right)} m^{5} + 29 \, {\left(2 \, b c d + {\left(b^{2} + 2 \, a c\right)} e\right)} m^{4} + 302 \, {\left(2 \, b c d + {\left(b^{2} + 2 \, a c\right)} e\right)} m^{3} + 2970 \, b c d + 1366 \, {\left(2 \, b c d + {\left(b^{2} + 2 \, a c\right)} e\right)} m^{2} + 1485 \, {\left(b^{2} + 2 \, a c\right)} e + 2577 \, {\left(2 \, b c d + {\left(b^{2} + 2 \, a c\right)} e\right)} m\right)} x^{7} + {\left({\left(2 \, a b e + {\left(b^{2} + 2 \, a c\right)} d\right)} m^{5} + 31 \, {\left(2 \, a b e + {\left(b^{2} + 2 \, a c\right)} d\right)} m^{4} + 350 \, {\left(2 \, a b e + {\left(b^{2} + 2 \, a c\right)} d\right)} m^{3} + 4158 \, a b e + 1730 \, {\left(2 \, a b e + {\left(b^{2} + 2 \, a c\right)} d\right)} m^{2} + 2079 \, {\left(b^{2} + 2 \, a c\right)} d + 3489 \, {\left(2 \, a b e + {\left(b^{2} + 2 \, a c\right)} d\right)} m\right)} x^{5} + {\left({\left(2 \, a b d + a^{2} e\right)} m^{5} + 33 \, {\left(2 \, a b d + a^{2} e\right)} m^{4} + 406 \, {\left(2 \, a b d + a^{2} e\right)} m^{3} + 6930 \, a b d + 3465 \, a^{2} e + 2262 \, {\left(2 \, a b d + a^{2} e\right)} m^{2} + 5353 \, {\left(2 \, a b d + a^{2} e\right)} m\right)} x^{3} + {\left(a^{2} d m^{5} + 35 \, a^{2} d m^{4} + 470 \, a^{2} d m^{3} + 3010 \, a^{2} d m^{2} + 9129 \, a^{2} d m + 10395 \, a^{2} d\right)} x\right)} \left(f x\right)^{m}}{m^{6} + 36 \, m^{5} + 505 \, m^{4} + 3480 \, m^{3} + 12139 \, m^{2} + 19524 \, m + 10395}"," ",0,"((c^2*e*m^5 + 25*c^2*e*m^4 + 230*c^2*e*m^3 + 950*c^2*e*m^2 + 1689*c^2*e*m + 945*c^2*e)*x^11 + ((c^2*d + 2*b*c*e)*m^5 + 27*(c^2*d + 2*b*c*e)*m^4 + 262*(c^2*d + 2*b*c*e)*m^3 + 1155*c^2*d + 2310*b*c*e + 1122*(c^2*d + 2*b*c*e)*m^2 + 2041*(c^2*d + 2*b*c*e)*m)*x^9 + ((2*b*c*d + (b^2 + 2*a*c)*e)*m^5 + 29*(2*b*c*d + (b^2 + 2*a*c)*e)*m^4 + 302*(2*b*c*d + (b^2 + 2*a*c)*e)*m^3 + 2970*b*c*d + 1366*(2*b*c*d + (b^2 + 2*a*c)*e)*m^2 + 1485*(b^2 + 2*a*c)*e + 2577*(2*b*c*d + (b^2 + 2*a*c)*e)*m)*x^7 + ((2*a*b*e + (b^2 + 2*a*c)*d)*m^5 + 31*(2*a*b*e + (b^2 + 2*a*c)*d)*m^4 + 350*(2*a*b*e + (b^2 + 2*a*c)*d)*m^3 + 4158*a*b*e + 1730*(2*a*b*e + (b^2 + 2*a*c)*d)*m^2 + 2079*(b^2 + 2*a*c)*d + 3489*(2*a*b*e + (b^2 + 2*a*c)*d)*m)*x^5 + ((2*a*b*d + a^2*e)*m^5 + 33*(2*a*b*d + a^2*e)*m^4 + 406*(2*a*b*d + a^2*e)*m^3 + 6930*a*b*d + 3465*a^2*e + 2262*(2*a*b*d + a^2*e)*m^2 + 5353*(2*a*b*d + a^2*e)*m)*x^3 + (a^2*d*m^5 + 35*a^2*d*m^4 + 470*a^2*d*m^3 + 3010*a^2*d*m^2 + 9129*a^2*d*m + 10395*a^2*d)*x)*(f*x)^m/(m^6 + 36*m^5 + 505*m^4 + 3480*m^3 + 12139*m^2 + 19524*m + 10395)","B",0
222,1,171,0,0.717254," ","integrate((f*x)^m*(e*x^2+d)*(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{{\left({\left(c e m^{3} + 9 \, c e m^{2} + 23 \, c e m + 15 \, c e\right)} x^{7} + {\left({\left(c d + b e\right)} m^{3} + 11 \, {\left(c d + b e\right)} m^{2} + 21 \, c d + 21 \, b e + 31 \, {\left(c d + b e\right)} m\right)} x^{5} + {\left({\left(b d + a e\right)} m^{3} + 13 \, {\left(b d + a e\right)} m^{2} + 35 \, b d + 35 \, a e + 47 \, {\left(b d + a e\right)} m\right)} x^{3} + {\left(a d m^{3} + 15 \, a d m^{2} + 71 \, a d m + 105 \, a d\right)} x\right)} \left(f x\right)^{m}}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105}"," ",0,"((c*e*m^3 + 9*c*e*m^2 + 23*c*e*m + 15*c*e)*x^7 + ((c*d + b*e)*m^3 + 11*(c*d + b*e)*m^2 + 21*c*d + 21*b*e + 31*(c*d + b*e)*m)*x^5 + ((b*d + a*e)*m^3 + 13*(b*d + a*e)*m^2 + 35*b*d + 35*a*e + 47*(b*d + a*e)*m)*x^3 + (a*d*m^3 + 15*a*d*m^2 + 71*a*d*m + 105*a*d)*x)*(f*x)^m/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105)","B",0
223,0,0,0,0.837114," ","integrate((f*x)^m*(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{2} + d\right)} \left(f x\right)^{m}}{c x^{4} + b x^{2} + a}, x\right)"," ",0,"integral((e*x^2 + d)*(f*x)^m/(c*x^4 + b*x^2 + a), x)","F",0
224,0,0,0,1.189129," ","integrate((f*x)^m*(e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{2} + d\right)} \left(f x\right)^{m}}{c^{2} x^{8} + 2 \, b c x^{6} + {\left(b^{2} + 2 \, a c\right)} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((e*x^2 + d)*(f*x)^m/(c^2*x^8 + 2*b*c*x^6 + (b^2 + 2*a*c)*x^4 + 2*a*b*x^2 + a^2), x)","F",0
225,0,0,0,0.923182," ","integrate((f*x)^m*(e*x^2+d)*(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c e x^{6} + {\left(c d + b e\right)} x^{4} + {\left(b d + a e\right)} x^{2} + a d\right)} \sqrt{c x^{4} + b x^{2} + a} \left(f x\right)^{m}, x\right)"," ",0,"integral((c*e*x^6 + (c*d + b*e)*x^4 + (b*d + a*e)*x^2 + a*d)*sqrt(c*x^4 + b*x^2 + a)*(f*x)^m, x)","F",0
226,0,0,0,0.856469," ","integrate((f*x)^m*(e*x^2+d)*(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{4} + b x^{2} + a} {\left(e x^{2} + d\right)} \left(f x\right)^{m}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*(e*x^2 + d)*(f*x)^m, x)","F",0
227,0,0,0,1.020520," ","integrate((f*x)^m*(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{2} + d\right)} \left(f x\right)^{m}}{\sqrt{c x^{4} + b x^{2} + a}}, x\right)"," ",0,"integral((e*x^2 + d)*(f*x)^m/sqrt(c*x^4 + b*x^2 + a), x)","F",0
228,0,0,0,0.798407," ","integrate((f*x)^m*(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(e x^{2} + d\right)} \left(f x\right)^{m}}{c^{2} x^{8} + 2 \, b c x^{6} + {\left(b^{2} + 2 \, a c\right)} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*(e*x^2 + d)*(f*x)^m/(c^2*x^8 + 2*b*c*x^6 + (b^2 + 2*a*c)*x^4 + 2*a*b*x^2 + a^2), x)","F",0
229,1,277,0,11.000981," ","integrate(x^9/(e*x^2+d)/(c*x^4+a),x, algorithm=""fricas"")","\left[\frac{a c d e^{3} \sqrt{-\frac{a}{c}} \log\left(\frac{c x^{4} + 2 \, c x^{2} \sqrt{-\frac{a}{c}} - a}{c x^{4} + a}\right) - a^{2} e^{4} \log\left(c x^{4} + a\right) + 2 \, c^{2} d^{4} \log\left(e x^{2} + d\right) + {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)} x^{4} - 2 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x^{2}}{4 \, {\left(c^{3} d^{2} e^{3} + a c^{2} e^{5}\right)}}, \frac{2 \, a c d e^{3} \sqrt{\frac{a}{c}} \arctan\left(\frac{c x^{2} \sqrt{\frac{a}{c}}}{a}\right) - a^{2} e^{4} \log\left(c x^{4} + a\right) + 2 \, c^{2} d^{4} \log\left(e x^{2} + d\right) + {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)} x^{4} - 2 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x^{2}}{4 \, {\left(c^{3} d^{2} e^{3} + a c^{2} e^{5}\right)}}\right]"," ",0,"[1/4*(a*c*d*e^3*sqrt(-a/c)*log((c*x^4 + 2*c*x^2*sqrt(-a/c) - a)/(c*x^4 + a)) - a^2*e^4*log(c*x^4 + a) + 2*c^2*d^4*log(e*x^2 + d) + (c^2*d^2*e^2 + a*c*e^4)*x^4 - 2*(c^2*d^3*e + a*c*d*e^3)*x^2)/(c^3*d^2*e^3 + a*c^2*e^5), 1/4*(2*a*c*d*e^3*sqrt(a/c)*arctan(c*x^2*sqrt(a/c)/a) - a^2*e^4*log(c*x^4 + a) + 2*c^2*d^4*log(e*x^2 + d) + (c^2*d^2*e^2 + a*c*e^4)*x^4 - 2*(c^2*d^3*e + a*c*d*e^3)*x^2)/(c^3*d^2*e^3 + a*c^2*e^5)]","A",0
230,1,212,0,5.176028," ","integrate(x^7/(e*x^2+d)/(c*x^4+a),x, algorithm=""fricas"")","\left[\frac{a e^{3} \sqrt{-\frac{a}{c}} \log\left(\frac{c x^{4} - 2 \, c x^{2} \sqrt{-\frac{a}{c}} - a}{c x^{4} + a}\right) - a d e^{2} \log\left(c x^{4} + a\right) - 2 \, c d^{3} \log\left(e x^{2} + d\right) + 2 \, {\left(c d^{2} e + a e^{3}\right)} x^{2}}{4 \, {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)}}, -\frac{2 \, a e^{3} \sqrt{\frac{a}{c}} \arctan\left(\frac{c x^{2} \sqrt{\frac{a}{c}}}{a}\right) + a d e^{2} \log\left(c x^{4} + a\right) + 2 \, c d^{3} \log\left(e x^{2} + d\right) - 2 \, {\left(c d^{2} e + a e^{3}\right)} x^{2}}{4 \, {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)}}\right]"," ",0,"[1/4*(a*e^3*sqrt(-a/c)*log((c*x^4 - 2*c*x^2*sqrt(-a/c) - a)/(c*x^4 + a)) - a*d*e^2*log(c*x^4 + a) - 2*c*d^3*log(e*x^2 + d) + 2*(c*d^2*e + a*e^3)*x^2)/(c^2*d^2*e^2 + a*c*e^4), -1/4*(2*a*e^3*sqrt(a/c)*arctan(c*x^2*sqrt(a/c)/a) + a*d*e^2*log(c*x^4 + a) + 2*c*d^3*log(e*x^2 + d) - 2*(c*d^2*e + a*e^3)*x^2)/(c^2*d^2*e^2 + a*c*e^4)]","A",0
231,1,170,0,2.919815," ","integrate(x^5/(e*x^2+d)/(c*x^4+a),x, algorithm=""fricas"")","\left[\frac{c d e \sqrt{-\frac{a}{c}} \log\left(\frac{c x^{4} - 2 \, c x^{2} \sqrt{-\frac{a}{c}} - a}{c x^{4} + a}\right) + a e^{2} \log\left(c x^{4} + a\right) + 2 \, c d^{2} \log\left(e x^{2} + d\right)}{4 \, {\left(c^{2} d^{2} e + a c e^{3}\right)}}, -\frac{2 \, c d e \sqrt{\frac{a}{c}} \arctan\left(\frac{c x^{2} \sqrt{\frac{a}{c}}}{a}\right) - a e^{2} \log\left(c x^{4} + a\right) - 2 \, c d^{2} \log\left(e x^{2} + d\right)}{4 \, {\left(c^{2} d^{2} e + a c e^{3}\right)}}\right]"," ",0,"[1/4*(c*d*e*sqrt(-a/c)*log((c*x^4 - 2*c*x^2*sqrt(-a/c) - a)/(c*x^4 + a)) + a*e^2*log(c*x^4 + a) + 2*c*d^2*log(e*x^2 + d))/(c^2*d^2*e + a*c*e^3), -1/4*(2*c*d*e*sqrt(a/c)*arctan(c*x^2*sqrt(a/c)/a) - a*e^2*log(c*x^4 + a) - 2*c*d^2*log(e*x^2 + d))/(c^2*d^2*e + a*c*e^3)]","A",0
232,1,145,0,1.331871," ","integrate(x^3/(e*x^2+d)/(c*x^4+a),x, algorithm=""fricas"")","\left[\frac{e \sqrt{-\frac{a}{c}} \log\left(\frac{c x^{4} + 2 \, c x^{2} \sqrt{-\frac{a}{c}} - a}{c x^{4} + a}\right) + d \log\left(c x^{4} + a\right) - 2 \, d \log\left(e x^{2} + d\right)}{4 \, {\left(c d^{2} + a e^{2}\right)}}, \frac{2 \, e \sqrt{\frac{a}{c}} \arctan\left(\frac{c x^{2} \sqrt{\frac{a}{c}}}{a}\right) + d \log\left(c x^{4} + a\right) - 2 \, d \log\left(e x^{2} + d\right)}{4 \, {\left(c d^{2} + a e^{2}\right)}}\right]"," ",0,"[1/4*(e*sqrt(-a/c)*log((c*x^4 + 2*c*x^2*sqrt(-a/c) - a)/(c*x^4 + a)) + d*log(c*x^4 + a) - 2*d*log(e*x^2 + d))/(c*d^2 + a*e^2), 1/4*(2*e*sqrt(a/c)*arctan(c*x^2*sqrt(a/c)/a) + d*log(c*x^4 + a) - 2*d*log(e*x^2 + d))/(c*d^2 + a*e^2)]","A",0
233,1,146,0,1.499645," ","integrate(x/(e*x^2+d)/(c*x^4+a),x, algorithm=""fricas"")","\left[\frac{d \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{4} + 2 \, a x^{2} \sqrt{-\frac{c}{a}} - a}{c x^{4} + a}\right) - e \log\left(c x^{4} + a\right) + 2 \, e \log\left(e x^{2} + d\right)}{4 \, {\left(c d^{2} + a e^{2}\right)}}, -\frac{2 \, d \sqrt{\frac{c}{a}} \arctan\left(\frac{a \sqrt{\frac{c}{a}}}{c x^{2}}\right) + e \log\left(c x^{4} + a\right) - 2 \, e \log\left(e x^{2} + d\right)}{4 \, {\left(c d^{2} + a e^{2}\right)}}\right]"," ",0,"[1/4*(d*sqrt(-c/a)*log((c*x^4 + 2*a*x^2*sqrt(-c/a) - a)/(c*x^4 + a)) - e*log(c*x^4 + a) + 2*e*log(e*x^2 + d))/(c*d^2 + a*e^2), -1/4*(2*d*sqrt(c/a)*arctan(a*sqrt(c/a)/(c*x^2)) + e*log(c*x^4 + a) - 2*e*log(e*x^2 + d))/(c*d^2 + a*e^2)]","A",0
234,1,201,0,16.718195," ","integrate(1/x/(e*x^2+d)/(c*x^4+a),x, algorithm=""fricas"")","\left[\frac{a d e \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{4} - 2 \, a x^{2} \sqrt{-\frac{c}{a}} - a}{c x^{4} + a}\right) - c d^{2} \log\left(c x^{4} + a\right) - 2 \, a e^{2} \log\left(e x^{2} + d\right) + 4 \, {\left(c d^{2} + a e^{2}\right)} \log\left(x\right)}{4 \, {\left(a c d^{3} + a^{2} d e^{2}\right)}}, \frac{2 \, a d e \sqrt{\frac{c}{a}} \arctan\left(\frac{a \sqrt{\frac{c}{a}}}{c x^{2}}\right) - c d^{2} \log\left(c x^{4} + a\right) - 2 \, a e^{2} \log\left(e x^{2} + d\right) + 4 \, {\left(c d^{2} + a e^{2}\right)} \log\left(x\right)}{4 \, {\left(a c d^{3} + a^{2} d e^{2}\right)}}\right]"," ",0,"[1/4*(a*d*e*sqrt(-c/a)*log((c*x^4 - 2*a*x^2*sqrt(-c/a) - a)/(c*x^4 + a)) - c*d^2*log(c*x^4 + a) - 2*a*e^2*log(e*x^2 + d) + 4*(c*d^2 + a*e^2)*log(x))/(a*c*d^3 + a^2*d*e^2), 1/4*(2*a*d*e*sqrt(c/a)*arctan(a*sqrt(c/a)/(c*x^2)) - c*d^2*log(c*x^4 + a) - 2*a*e^2*log(e*x^2 + d) + 4*(c*d^2 + a*e^2)*log(x))/(a*c*d^3 + a^2*d*e^2)]","A",0
235,1,265,0,101.424301," ","integrate(1/x^3/(e*x^2+d)/(c*x^4+a),x, algorithm=""fricas"")","\left[\frac{c d^{3} x^{2} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{4} - 2 \, a x^{2} \sqrt{-\frac{c}{a}} - a}{c x^{4} + a}\right) + c d^{2} e x^{2} \log\left(c x^{4} + a\right) + 2 \, a e^{3} x^{2} \log\left(e x^{2} + d\right) - 2 \, c d^{3} - 2 \, a d e^{2} - 4 \, {\left(c d^{2} e + a e^{3}\right)} x^{2} \log\left(x\right)}{4 \, {\left(a c d^{4} + a^{2} d^{2} e^{2}\right)} x^{2}}, \frac{2 \, c d^{3} x^{2} \sqrt{\frac{c}{a}} \arctan\left(\frac{a \sqrt{\frac{c}{a}}}{c x^{2}}\right) + c d^{2} e x^{2} \log\left(c x^{4} + a\right) + 2 \, a e^{3} x^{2} \log\left(e x^{2} + d\right) - 2 \, c d^{3} - 2 \, a d e^{2} - 4 \, {\left(c d^{2} e + a e^{3}\right)} x^{2} \log\left(x\right)}{4 \, {\left(a c d^{4} + a^{2} d^{2} e^{2}\right)} x^{2}}\right]"," ",0,"[1/4*(c*d^3*x^2*sqrt(-c/a)*log((c*x^4 - 2*a*x^2*sqrt(-c/a) - a)/(c*x^4 + a)) + c*d^2*e*x^2*log(c*x^4 + a) + 2*a*e^3*x^2*log(e*x^2 + d) - 2*c*d^3 - 2*a*d*e^2 - 4*(c*d^2*e + a*e^3)*x^2*log(x))/((a*c*d^4 + a^2*d^2*e^2)*x^2), 1/4*(2*c*d^3*x^2*sqrt(c/a)*arctan(a*sqrt(c/a)/(c*x^2)) + c*d^2*e*x^2*log(c*x^4 + a) + 2*a*e^3*x^2*log(e*x^2 + d) - 2*c*d^3 - 2*a*d*e^2 - 4*(c*d^2*e + a*e^3)*x^2*log(x))/((a*c*d^4 + a^2*d^2*e^2)*x^2)]","A",0
236,-1,0,0,0.000000," ","integrate(1/x^5/(e*x^2+d)/(c*x^4+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
237,1,4414,0,32.470408," ","integrate(x^8/(e*x^2+d)/(c*x^4+a),x, algorithm=""fricas"")","\left[\frac{6 \, c d^{3} \sqrt{-\frac{d}{e}} \log\left(\frac{e x^{2} + 2 \, e x \sqrt{-\frac{d}{e}} - d}{e x^{2} + d}\right) + 4 \, {\left(c d^{2} e + a e^{3}\right)} x^{3} - 3 \, {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)} \sqrt{\frac{2 \, a^{3} d e + {\left(c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}}{c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}} \log\left(-{\left(a^{3} c d^{2} - a^{4} e^{2}\right)} x + {\left(a^{2} c^{3} d^{3} - a^{3} c^{2} d e^{2} + {\left(c^{7} d^{4} e + 2 \, a c^{6} d^{2} e^{3} + a^{2} c^{5} e^{5}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}\right)} \sqrt{\frac{2 \, a^{3} d e + {\left(c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}}{c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}}\right) + 3 \, {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)} \sqrt{\frac{2 \, a^{3} d e + {\left(c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}}{c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}} \log\left(-{\left(a^{3} c d^{2} - a^{4} e^{2}\right)} x - {\left(a^{2} c^{3} d^{3} - a^{3} c^{2} d e^{2} + {\left(c^{7} d^{4} e + 2 \, a c^{6} d^{2} e^{3} + a^{2} c^{5} e^{5}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}\right)} \sqrt{\frac{2 \, a^{3} d e + {\left(c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}}{c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}}\right) - 3 \, {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)} \sqrt{\frac{2 \, a^{3} d e - {\left(c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}}{c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}} \log\left(-{\left(a^{3} c d^{2} - a^{4} e^{2}\right)} x + {\left(a^{2} c^{3} d^{3} - a^{3} c^{2} d e^{2} - {\left(c^{7} d^{4} e + 2 \, a c^{6} d^{2} e^{3} + a^{2} c^{5} e^{5}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}\right)} \sqrt{\frac{2 \, a^{3} d e - {\left(c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}}{c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}}\right) + 3 \, {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)} \sqrt{\frac{2 \, a^{3} d e - {\left(c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}}{c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}} \log\left(-{\left(a^{3} c d^{2} - a^{4} e^{2}\right)} x - {\left(a^{2} c^{3} d^{3} - a^{3} c^{2} d e^{2} - {\left(c^{7} d^{4} e + 2 \, a c^{6} d^{2} e^{3} + a^{2} c^{5} e^{5}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}\right)} \sqrt{\frac{2 \, a^{3} d e - {\left(c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}}{c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}}\right) - 12 \, {\left(c d^{3} + a d e^{2}\right)} x}{12 \, {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)}}, \frac{12 \, c d^{3} \sqrt{\frac{d}{e}} \arctan\left(\frac{e x \sqrt{\frac{d}{e}}}{d}\right) + 4 \, {\left(c d^{2} e + a e^{3}\right)} x^{3} - 3 \, {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)} \sqrt{\frac{2 \, a^{3} d e + {\left(c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}}{c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}} \log\left(-{\left(a^{3} c d^{2} - a^{4} e^{2}\right)} x + {\left(a^{2} c^{3} d^{3} - a^{3} c^{2} d e^{2} + {\left(c^{7} d^{4} e + 2 \, a c^{6} d^{2} e^{3} + a^{2} c^{5} e^{5}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}\right)} \sqrt{\frac{2 \, a^{3} d e + {\left(c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}}{c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}}\right) + 3 \, {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)} \sqrt{\frac{2 \, a^{3} d e + {\left(c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}}{c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}} \log\left(-{\left(a^{3} c d^{2} - a^{4} e^{2}\right)} x - {\left(a^{2} c^{3} d^{3} - a^{3} c^{2} d e^{2} + {\left(c^{7} d^{4} e + 2 \, a c^{6} d^{2} e^{3} + a^{2} c^{5} e^{5}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}\right)} \sqrt{\frac{2 \, a^{3} d e + {\left(c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}}{c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}}\right) - 3 \, {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)} \sqrt{\frac{2 \, a^{3} d e - {\left(c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}}{c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}} \log\left(-{\left(a^{3} c d^{2} - a^{4} e^{2}\right)} x + {\left(a^{2} c^{3} d^{3} - a^{3} c^{2} d e^{2} - {\left(c^{7} d^{4} e + 2 \, a c^{6} d^{2} e^{3} + a^{2} c^{5} e^{5}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}\right)} \sqrt{\frac{2 \, a^{3} d e - {\left(c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}}{c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}}\right) + 3 \, {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)} \sqrt{\frac{2 \, a^{3} d e - {\left(c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}}{c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}} \log\left(-{\left(a^{3} c d^{2} - a^{4} e^{2}\right)} x - {\left(a^{2} c^{3} d^{3} - a^{3} c^{2} d e^{2} - {\left(c^{7} d^{4} e + 2 \, a c^{6} d^{2} e^{3} + a^{2} c^{5} e^{5}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}\right)} \sqrt{\frac{2 \, a^{3} d e - {\left(c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}\right)} \sqrt{-\frac{a^{5} c^{2} d^{4} - 2 \, a^{6} c d^{2} e^{2} + a^{7} e^{4}}{c^{11} d^{8} + 4 \, a c^{10} d^{6} e^{2} + 6 \, a^{2} c^{9} d^{4} e^{4} + 4 \, a^{3} c^{8} d^{2} e^{6} + a^{4} c^{7} e^{8}}}}{c^{5} d^{4} + 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}}\right) - 12 \, {\left(c d^{3} + a d e^{2}\right)} x}{12 \, {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)}}\right]"," ",0,"[1/12*(6*c*d^3*sqrt(-d/e)*log((e*x^2 + 2*e*x*sqrt(-d/e) - d)/(e*x^2 + d)) + 4*(c*d^2*e + a*e^3)*x^3 - 3*(c^2*d^2*e^2 + a*c*e^4)*sqrt((2*a^3*d*e + (c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))/(c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4))*log(-(a^3*c*d^2 - a^4*e^2)*x + (a^2*c^3*d^3 - a^3*c^2*d*e^2 + (c^7*d^4*e + 2*a*c^6*d^2*e^3 + a^2*c^5*e^5)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))*sqrt((2*a^3*d*e + (c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))/(c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4))) + 3*(c^2*d^2*e^2 + a*c*e^4)*sqrt((2*a^3*d*e + (c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))/(c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4))*log(-(a^3*c*d^2 - a^4*e^2)*x - (a^2*c^3*d^3 - a^3*c^2*d*e^2 + (c^7*d^4*e + 2*a*c^6*d^2*e^3 + a^2*c^5*e^5)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))*sqrt((2*a^3*d*e + (c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))/(c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4))) - 3*(c^2*d^2*e^2 + a*c*e^4)*sqrt((2*a^3*d*e - (c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))/(c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4))*log(-(a^3*c*d^2 - a^4*e^2)*x + (a^2*c^3*d^3 - a^3*c^2*d*e^2 - (c^7*d^4*e + 2*a*c^6*d^2*e^3 + a^2*c^5*e^5)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))*sqrt((2*a^3*d*e - (c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))/(c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4))) + 3*(c^2*d^2*e^2 + a*c*e^4)*sqrt((2*a^3*d*e - (c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))/(c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4))*log(-(a^3*c*d^2 - a^4*e^2)*x - (a^2*c^3*d^3 - a^3*c^2*d*e^2 - (c^7*d^4*e + 2*a*c^6*d^2*e^3 + a^2*c^5*e^5)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))*sqrt((2*a^3*d*e - (c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))/(c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4))) - 12*(c*d^3 + a*d*e^2)*x)/(c^2*d^2*e^2 + a*c*e^4), 1/12*(12*c*d^3*sqrt(d/e)*arctan(e*x*sqrt(d/e)/d) + 4*(c*d^2*e + a*e^3)*x^3 - 3*(c^2*d^2*e^2 + a*c*e^4)*sqrt((2*a^3*d*e + (c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))/(c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4))*log(-(a^3*c*d^2 - a^4*e^2)*x + (a^2*c^3*d^3 - a^3*c^2*d*e^2 + (c^7*d^4*e + 2*a*c^6*d^2*e^3 + a^2*c^5*e^5)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))*sqrt((2*a^3*d*e + (c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))/(c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4))) + 3*(c^2*d^2*e^2 + a*c*e^4)*sqrt((2*a^3*d*e + (c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))/(c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4))*log(-(a^3*c*d^2 - a^4*e^2)*x - (a^2*c^3*d^3 - a^3*c^2*d*e^2 + (c^7*d^4*e + 2*a*c^6*d^2*e^3 + a^2*c^5*e^5)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))*sqrt((2*a^3*d*e + (c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))/(c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4))) - 3*(c^2*d^2*e^2 + a*c*e^4)*sqrt((2*a^3*d*e - (c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))/(c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4))*log(-(a^3*c*d^2 - a^4*e^2)*x + (a^2*c^3*d^3 - a^3*c^2*d*e^2 - (c^7*d^4*e + 2*a*c^6*d^2*e^3 + a^2*c^5*e^5)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))*sqrt((2*a^3*d*e - (c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))/(c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4))) + 3*(c^2*d^2*e^2 + a*c*e^4)*sqrt((2*a^3*d*e - (c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))/(c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4))*log(-(a^3*c*d^2 - a^4*e^2)*x - (a^2*c^3*d^3 - a^3*c^2*d*e^2 - (c^7*d^4*e + 2*a*c^6*d^2*e^3 + a^2*c^5*e^5)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))*sqrt((2*a^3*d*e - (c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)*sqrt(-(a^5*c^2*d^4 - 2*a^6*c*d^2*e^2 + a^7*e^4)/(c^11*d^8 + 4*a*c^10*d^6*e^2 + 6*a^2*c^9*d^4*e^4 + 4*a^3*c^8*d^2*e^6 + a^4*c^7*e^8)))/(c^5*d^4 + 2*a*c^4*d^2*e^2 + a^2*c^3*e^4))) - 12*(c*d^3 + a*d*e^2)*x)/(c^2*d^2*e^2 + a*c*e^4)]","B",0
238,1,4354,0,4.864221," ","integrate(x^6/(e*x^2+d)/(c*x^4+a),x, algorithm=""fricas"")","\left[\frac{2 \, c d^{2} \sqrt{-\frac{d}{e}} \log\left(\frac{e x^{2} - 2 \, e x \sqrt{-\frac{d}{e}} - d}{e x^{2} + d}\right) + {\left(c^{2} d^{2} e + a c e^{3}\right)} \sqrt{-\frac{2 \, a^{2} d e + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}}{c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}}} \log\left(-{\left(a^{2} c d^{2} - a^{3} e^{2}\right)} x + {\left(a^{2} c^{2} d^{2} e - a^{3} c e^{3} - {\left(c^{6} d^{5} + 2 \, a c^{5} d^{3} e^{2} + a^{2} c^{4} d e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}\right)} \sqrt{-\frac{2 \, a^{2} d e + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}}{c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}}}\right) - {\left(c^{2} d^{2} e + a c e^{3}\right)} \sqrt{-\frac{2 \, a^{2} d e + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}}{c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}}} \log\left(-{\left(a^{2} c d^{2} - a^{3} e^{2}\right)} x - {\left(a^{2} c^{2} d^{2} e - a^{3} c e^{3} - {\left(c^{6} d^{5} + 2 \, a c^{5} d^{3} e^{2} + a^{2} c^{4} d e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}\right)} \sqrt{-\frac{2 \, a^{2} d e + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}}{c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}}}\right) + {\left(c^{2} d^{2} e + a c e^{3}\right)} \sqrt{-\frac{2 \, a^{2} d e - {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}}{c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}}} \log\left(-{\left(a^{2} c d^{2} - a^{3} e^{2}\right)} x + {\left(a^{2} c^{2} d^{2} e - a^{3} c e^{3} + {\left(c^{6} d^{5} + 2 \, a c^{5} d^{3} e^{2} + a^{2} c^{4} d e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}\right)} \sqrt{-\frac{2 \, a^{2} d e - {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}}{c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}}}\right) - {\left(c^{2} d^{2} e + a c e^{3}\right)} \sqrt{-\frac{2 \, a^{2} d e - {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}}{c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}}} \log\left(-{\left(a^{2} c d^{2} - a^{3} e^{2}\right)} x - {\left(a^{2} c^{2} d^{2} e - a^{3} c e^{3} + {\left(c^{6} d^{5} + 2 \, a c^{5} d^{3} e^{2} + a^{2} c^{4} d e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}\right)} \sqrt{-\frac{2 \, a^{2} d e - {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}}{c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}}}\right) + 4 \, {\left(c d^{2} + a e^{2}\right)} x}{4 \, {\left(c^{2} d^{2} e + a c e^{3}\right)}}, -\frac{4 \, c d^{2} \sqrt{\frac{d}{e}} \arctan\left(\frac{e x \sqrt{\frac{d}{e}}}{d}\right) - {\left(c^{2} d^{2} e + a c e^{3}\right)} \sqrt{-\frac{2 \, a^{2} d e + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}}{c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}}} \log\left(-{\left(a^{2} c d^{2} - a^{3} e^{2}\right)} x + {\left(a^{2} c^{2} d^{2} e - a^{3} c e^{3} - {\left(c^{6} d^{5} + 2 \, a c^{5} d^{3} e^{2} + a^{2} c^{4} d e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}\right)} \sqrt{-\frac{2 \, a^{2} d e + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}}{c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}}}\right) + {\left(c^{2} d^{2} e + a c e^{3}\right)} \sqrt{-\frac{2 \, a^{2} d e + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}}{c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}}} \log\left(-{\left(a^{2} c d^{2} - a^{3} e^{2}\right)} x - {\left(a^{2} c^{2} d^{2} e - a^{3} c e^{3} - {\left(c^{6} d^{5} + 2 \, a c^{5} d^{3} e^{2} + a^{2} c^{4} d e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}\right)} \sqrt{-\frac{2 \, a^{2} d e + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}}{c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}}}\right) - {\left(c^{2} d^{2} e + a c e^{3}\right)} \sqrt{-\frac{2 \, a^{2} d e - {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}}{c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}}} \log\left(-{\left(a^{2} c d^{2} - a^{3} e^{2}\right)} x + {\left(a^{2} c^{2} d^{2} e - a^{3} c e^{3} + {\left(c^{6} d^{5} + 2 \, a c^{5} d^{3} e^{2} + a^{2} c^{4} d e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}\right)} \sqrt{-\frac{2 \, a^{2} d e - {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}}{c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}}}\right) + {\left(c^{2} d^{2} e + a c e^{3}\right)} \sqrt{-\frac{2 \, a^{2} d e - {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}}{c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}}} \log\left(-{\left(a^{2} c d^{2} - a^{3} e^{2}\right)} x - {\left(a^{2} c^{2} d^{2} e - a^{3} c e^{3} + {\left(c^{6} d^{5} + 2 \, a c^{5} d^{3} e^{2} + a^{2} c^{4} d e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}\right)} \sqrt{-\frac{2 \, a^{2} d e - {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} d^{4} - 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}{c^{9} d^{8} + 4 \, a c^{8} d^{6} e^{2} + 6 \, a^{2} c^{7} d^{4} e^{4} + 4 \, a^{3} c^{6} d^{2} e^{6} + a^{4} c^{5} e^{8}}}}{c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}}}\right) - 4 \, {\left(c d^{2} + a e^{2}\right)} x}{4 \, {\left(c^{2} d^{2} e + a c e^{3}\right)}}\right]"," ",0,"[1/4*(2*c*d^2*sqrt(-d/e)*log((e*x^2 - 2*e*x*sqrt(-d/e) - d)/(e*x^2 + d)) + (c^2*d^2*e + a*c*e^3)*sqrt(-(2*a^2*d*e + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))/(c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4))*log(-(a^2*c*d^2 - a^3*e^2)*x + (a^2*c^2*d^2*e - a^3*c*e^3 - (c^6*d^5 + 2*a*c^5*d^3*e^2 + a^2*c^4*d*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))*sqrt(-(2*a^2*d*e + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))/(c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4))) - (c^2*d^2*e + a*c*e^3)*sqrt(-(2*a^2*d*e + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))/(c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4))*log(-(a^2*c*d^2 - a^3*e^2)*x - (a^2*c^2*d^2*e - a^3*c*e^3 - (c^6*d^5 + 2*a*c^5*d^3*e^2 + a^2*c^4*d*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))*sqrt(-(2*a^2*d*e + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))/(c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4))) + (c^2*d^2*e + a*c*e^3)*sqrt(-(2*a^2*d*e - (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))/(c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4))*log(-(a^2*c*d^2 - a^3*e^2)*x + (a^2*c^2*d^2*e - a^3*c*e^3 + (c^6*d^5 + 2*a*c^5*d^3*e^2 + a^2*c^4*d*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))*sqrt(-(2*a^2*d*e - (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))/(c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4))) - (c^2*d^2*e + a*c*e^3)*sqrt(-(2*a^2*d*e - (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))/(c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4))*log(-(a^2*c*d^2 - a^3*e^2)*x - (a^2*c^2*d^2*e - a^3*c*e^3 + (c^6*d^5 + 2*a*c^5*d^3*e^2 + a^2*c^4*d*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))*sqrt(-(2*a^2*d*e - (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))/(c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4))) + 4*(c*d^2 + a*e^2)*x)/(c^2*d^2*e + a*c*e^3), -1/4*(4*c*d^2*sqrt(d/e)*arctan(e*x*sqrt(d/e)/d) - (c^2*d^2*e + a*c*e^3)*sqrt(-(2*a^2*d*e + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))/(c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4))*log(-(a^2*c*d^2 - a^3*e^2)*x + (a^2*c^2*d^2*e - a^3*c*e^3 - (c^6*d^5 + 2*a*c^5*d^3*e^2 + a^2*c^4*d*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))*sqrt(-(2*a^2*d*e + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))/(c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4))) + (c^2*d^2*e + a*c*e^3)*sqrt(-(2*a^2*d*e + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))/(c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4))*log(-(a^2*c*d^2 - a^3*e^2)*x - (a^2*c^2*d^2*e - a^3*c*e^3 - (c^6*d^5 + 2*a*c^5*d^3*e^2 + a^2*c^4*d*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))*sqrt(-(2*a^2*d*e + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))/(c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4))) - (c^2*d^2*e + a*c*e^3)*sqrt(-(2*a^2*d*e - (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))/(c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4))*log(-(a^2*c*d^2 - a^3*e^2)*x + (a^2*c^2*d^2*e - a^3*c*e^3 + (c^6*d^5 + 2*a*c^5*d^3*e^2 + a^2*c^4*d*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))*sqrt(-(2*a^2*d*e - (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))/(c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4))) + (c^2*d^2*e + a*c*e^3)*sqrt(-(2*a^2*d*e - (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))/(c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4))*log(-(a^2*c*d^2 - a^3*e^2)*x - (a^2*c^2*d^2*e - a^3*c*e^3 + (c^6*d^5 + 2*a*c^5*d^3*e^2 + a^2*c^4*d*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))*sqrt(-(2*a^2*d*e - (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*sqrt(-(a^3*c^2*d^4 - 2*a^4*c*d^2*e^2 + a^5*e^4)/(c^9*d^8 + 4*a*c^8*d^6*e^2 + 6*a^2*c^7*d^4*e^4 + 4*a^3*c^6*d^2*e^6 + a^4*c^5*e^8)))/(c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4))) - 4*(c*d^2 + a*e^2)*x)/(c^2*d^2*e + a*c*e^3)]","B",0
239,1,4040,0,1.764107," ","integrate(x^4/(e*x^2+d)/(c*x^4+a),x, algorithm=""fricas"")","\left[\frac{{\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, a d e + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}}{c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}} \log\left(-{\left(c d^{2} - a e^{2}\right)} x + {\left(c^{2} d^{3} - a c d e^{2} + {\left(c^{4} d^{4} e + 2 \, a c^{3} d^{2} e^{3} + a^{2} c^{2} e^{5}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}\right)} \sqrt{\frac{2 \, a d e + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}}{c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}}\right) - {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, a d e + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}}{c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}} \log\left(-{\left(c d^{2} - a e^{2}\right)} x - {\left(c^{2} d^{3} - a c d e^{2} + {\left(c^{4} d^{4} e + 2 \, a c^{3} d^{2} e^{3} + a^{2} c^{2} e^{5}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}\right)} \sqrt{\frac{2 \, a d e + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}}{c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}}\right) + {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, a d e - {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}}{c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}} \log\left(-{\left(c d^{2} - a e^{2}\right)} x + {\left(c^{2} d^{3} - a c d e^{2} - {\left(c^{4} d^{4} e + 2 \, a c^{3} d^{2} e^{3} + a^{2} c^{2} e^{5}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}\right)} \sqrt{\frac{2 \, a d e - {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}}{c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}}\right) - {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, a d e - {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}}{c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}} \log\left(-{\left(c d^{2} - a e^{2}\right)} x - {\left(c^{2} d^{3} - a c d e^{2} - {\left(c^{4} d^{4} e + 2 \, a c^{3} d^{2} e^{3} + a^{2} c^{2} e^{5}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}\right)} \sqrt{\frac{2 \, a d e - {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}}{c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}}\right) + 2 \, d \sqrt{-\frac{d}{e}} \log\left(\frac{e x^{2} + 2 \, e x \sqrt{-\frac{d}{e}} - d}{e x^{2} + d}\right)}{4 \, {\left(c d^{2} + a e^{2}\right)}}, \frac{4 \, d \sqrt{\frac{d}{e}} \arctan\left(\frac{e x \sqrt{\frac{d}{e}}}{d}\right) + {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, a d e + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}}{c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}} \log\left(-{\left(c d^{2} - a e^{2}\right)} x + {\left(c^{2} d^{3} - a c d e^{2} + {\left(c^{4} d^{4} e + 2 \, a c^{3} d^{2} e^{3} + a^{2} c^{2} e^{5}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}\right)} \sqrt{\frac{2 \, a d e + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}}{c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}}\right) - {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, a d e + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}}{c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}} \log\left(-{\left(c d^{2} - a e^{2}\right)} x - {\left(c^{2} d^{3} - a c d e^{2} + {\left(c^{4} d^{4} e + 2 \, a c^{3} d^{2} e^{3} + a^{2} c^{2} e^{5}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}\right)} \sqrt{\frac{2 \, a d e + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}}{c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}}\right) + {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, a d e - {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}}{c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}} \log\left(-{\left(c d^{2} - a e^{2}\right)} x + {\left(c^{2} d^{3} - a c d e^{2} - {\left(c^{4} d^{4} e + 2 \, a c^{3} d^{2} e^{3} + a^{2} c^{2} e^{5}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}\right)} \sqrt{\frac{2 \, a d e - {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}}{c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}}\right) - {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, a d e - {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}}{c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}} \log\left(-{\left(c d^{2} - a e^{2}\right)} x - {\left(c^{2} d^{3} - a c d e^{2} - {\left(c^{4} d^{4} e + 2 \, a c^{3} d^{2} e^{3} + a^{2} c^{2} e^{5}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}\right)} \sqrt{\frac{2 \, a d e - {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} \sqrt{-\frac{a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}}{c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}}\right)}{4 \, {\left(c d^{2} + a e^{2}\right)}}\right]"," ",0,"[1/4*((c*d^2 + a*e^2)*sqrt((2*a*d*e + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))/(c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4))*log(-(c*d^2 - a*e^2)*x + (c^2*d^3 - a*c*d*e^2 + (c^4*d^4*e + 2*a*c^3*d^2*e^3 + a^2*c^2*e^5)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))*sqrt((2*a*d*e + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))/(c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4))) - (c*d^2 + a*e^2)*sqrt((2*a*d*e + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))/(c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4))*log(-(c*d^2 - a*e^2)*x - (c^2*d^3 - a*c*d*e^2 + (c^4*d^4*e + 2*a*c^3*d^2*e^3 + a^2*c^2*e^5)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))*sqrt((2*a*d*e + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))/(c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4))) + (c*d^2 + a*e^2)*sqrt((2*a*d*e - (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))/(c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4))*log(-(c*d^2 - a*e^2)*x + (c^2*d^3 - a*c*d*e^2 - (c^4*d^4*e + 2*a*c^3*d^2*e^3 + a^2*c^2*e^5)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))*sqrt((2*a*d*e - (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))/(c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4))) - (c*d^2 + a*e^2)*sqrt((2*a*d*e - (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))/(c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4))*log(-(c*d^2 - a*e^2)*x - (c^2*d^3 - a*c*d*e^2 - (c^4*d^4*e + 2*a*c^3*d^2*e^3 + a^2*c^2*e^5)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))*sqrt((2*a*d*e - (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))/(c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4))) + 2*d*sqrt(-d/e)*log((e*x^2 + 2*e*x*sqrt(-d/e) - d)/(e*x^2 + d)))/(c*d^2 + a*e^2), 1/4*(4*d*sqrt(d/e)*arctan(e*x*sqrt(d/e)/d) + (c*d^2 + a*e^2)*sqrt((2*a*d*e + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))/(c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4))*log(-(c*d^2 - a*e^2)*x + (c^2*d^3 - a*c*d*e^2 + (c^4*d^4*e + 2*a*c^3*d^2*e^3 + a^2*c^2*e^5)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))*sqrt((2*a*d*e + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))/(c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4))) - (c*d^2 + a*e^2)*sqrt((2*a*d*e + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))/(c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4))*log(-(c*d^2 - a*e^2)*x - (c^2*d^3 - a*c*d*e^2 + (c^4*d^4*e + 2*a*c^3*d^2*e^3 + a^2*c^2*e^5)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))*sqrt((2*a*d*e + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))/(c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4))) + (c*d^2 + a*e^2)*sqrt((2*a*d*e - (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))/(c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4))*log(-(c*d^2 - a*e^2)*x + (c^2*d^3 - a*c*d*e^2 - (c^4*d^4*e + 2*a*c^3*d^2*e^3 + a^2*c^2*e^5)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))*sqrt((2*a*d*e - (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))/(c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4))) - (c*d^2 + a*e^2)*sqrt((2*a*d*e - (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))/(c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4))*log(-(c*d^2 - a*e^2)*x - (c^2*d^3 - a*c*d*e^2 - (c^4*d^4*e + 2*a*c^3*d^2*e^3 + a^2*c^2*e^5)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))*sqrt((2*a*d*e - (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*sqrt(-(a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)))/(c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4))))/(c*d^2 + a*e^2)]","B",0
240,1,3892,0,1.776446," ","integrate(x^2/(e*x^2+d)/(c*x^4+a),x, algorithm=""fricas"")","\left[-\frac{{\left(c d^{2} + a e^{2}\right)} \sqrt{-\frac{2 \, d e + {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}}} \log\left(-{\left(c d^{2} - a e^{2}\right)} x + {\left(a c d^{2} e - a^{2} e^{3} - {\left(a c^{3} d^{5} + 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}\right)} \sqrt{-\frac{2 \, d e + {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}}}\right) - {\left(c d^{2} + a e^{2}\right)} \sqrt{-\frac{2 \, d e + {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}}} \log\left(-{\left(c d^{2} - a e^{2}\right)} x - {\left(a c d^{2} e - a^{2} e^{3} - {\left(a c^{3} d^{5} + 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}\right)} \sqrt{-\frac{2 \, d e + {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}}}\right) + {\left(c d^{2} + a e^{2}\right)} \sqrt{-\frac{2 \, d e - {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}}} \log\left(-{\left(c d^{2} - a e^{2}\right)} x + {\left(a c d^{2} e - a^{2} e^{3} + {\left(a c^{3} d^{5} + 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}\right)} \sqrt{-\frac{2 \, d e - {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}}}\right) - {\left(c d^{2} + a e^{2}\right)} \sqrt{-\frac{2 \, d e - {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}}} \log\left(-{\left(c d^{2} - a e^{2}\right)} x - {\left(a c d^{2} e - a^{2} e^{3} + {\left(a c^{3} d^{5} + 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}\right)} \sqrt{-\frac{2 \, d e - {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}}}\right) - 2 \, \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right)}{4 \, {\left(c d^{2} + a e^{2}\right)}}, -\frac{{\left(c d^{2} + a e^{2}\right)} \sqrt{-\frac{2 \, d e + {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}}} \log\left(-{\left(c d^{2} - a e^{2}\right)} x + {\left(a c d^{2} e - a^{2} e^{3} - {\left(a c^{3} d^{5} + 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}\right)} \sqrt{-\frac{2 \, d e + {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}}}\right) - {\left(c d^{2} + a e^{2}\right)} \sqrt{-\frac{2 \, d e + {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}}} \log\left(-{\left(c d^{2} - a e^{2}\right)} x - {\left(a c d^{2} e - a^{2} e^{3} - {\left(a c^{3} d^{5} + 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}\right)} \sqrt{-\frac{2 \, d e + {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}}}\right) + {\left(c d^{2} + a e^{2}\right)} \sqrt{-\frac{2 \, d e - {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}}} \log\left(-{\left(c d^{2} - a e^{2}\right)} x + {\left(a c d^{2} e - a^{2} e^{3} + {\left(a c^{3} d^{5} + 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}\right)} \sqrt{-\frac{2 \, d e - {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}}}\right) - {\left(c d^{2} + a e^{2}\right)} \sqrt{-\frac{2 \, d e - {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}}} \log\left(-{\left(c d^{2} - a e^{2}\right)} x - {\left(a c d^{2} e - a^{2} e^{3} + {\left(a c^{3} d^{5} + 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}\right)} \sqrt{-\frac{2 \, d e - {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}}}\right) + 4 \, \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right)}{4 \, {\left(c d^{2} + a e^{2}\right)}}\right]"," ",0,"[-1/4*((c*d^2 + a*e^2)*sqrt(-(2*d*e + (c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4))*log(-(c*d^2 - a*e^2)*x + (a*c*d^2*e - a^2*e^3 - (a*c^3*d^5 + 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))*sqrt(-(2*d*e + (c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4))) - (c*d^2 + a*e^2)*sqrt(-(2*d*e + (c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4))*log(-(c*d^2 - a*e^2)*x - (a*c*d^2*e - a^2*e^3 - (a*c^3*d^5 + 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))*sqrt(-(2*d*e + (c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4))) + (c*d^2 + a*e^2)*sqrt(-(2*d*e - (c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4))*log(-(c*d^2 - a*e^2)*x + (a*c*d^2*e - a^2*e^3 + (a*c^3*d^5 + 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))*sqrt(-(2*d*e - (c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4))) - (c*d^2 + a*e^2)*sqrt(-(2*d*e - (c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4))*log(-(c*d^2 - a*e^2)*x - (a*c*d^2*e - a^2*e^3 + (a*c^3*d^5 + 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))*sqrt(-(2*d*e - (c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4))) - 2*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)))/(c*d^2 + a*e^2), -1/4*((c*d^2 + a*e^2)*sqrt(-(2*d*e + (c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4))*log(-(c*d^2 - a*e^2)*x + (a*c*d^2*e - a^2*e^3 - (a*c^3*d^5 + 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))*sqrt(-(2*d*e + (c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4))) - (c*d^2 + a*e^2)*sqrt(-(2*d*e + (c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4))*log(-(c*d^2 - a*e^2)*x - (a*c*d^2*e - a^2*e^3 - (a*c^3*d^5 + 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))*sqrt(-(2*d*e + (c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4))) + (c*d^2 + a*e^2)*sqrt(-(2*d*e - (c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4))*log(-(c*d^2 - a*e^2)*x + (a*c*d^2*e - a^2*e^3 + (a*c^3*d^5 + 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))*sqrt(-(2*d*e - (c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4))) - (c*d^2 + a*e^2)*sqrt(-(2*d*e - (c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4))*log(-(c*d^2 - a*e^2)*x - (a*c*d^2*e - a^2*e^3 + (a*c^3*d^5 + 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))*sqrt(-(2*d*e - (c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)))/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4))) + 4*sqrt(d*e)*arctan(sqrt(d*e)*x/d))/(c*d^2 + a*e^2)]","B",0
241,1,4084,0,3.199525," ","integrate(1/(e*x^2+d)/(c*x^4+a),x, algorithm=""fricas"")","\left[-\frac{{\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, c d e + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}} \log\left(-{\left(c^{2} d^{2} - a c e^{2}\right)} x + {\left(a c^{2} d^{3} - a^{2} c d e^{2} + {\left(a^{3} c^{2} d^{4} e + 2 \, a^{4} c d^{2} e^{3} + a^{5} e^{5}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right)} \sqrt{\frac{2 \, c d e + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}}\right) - {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, c d e + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}} \log\left(-{\left(c^{2} d^{2} - a c e^{2}\right)} x - {\left(a c^{2} d^{3} - a^{2} c d e^{2} + {\left(a^{3} c^{2} d^{4} e + 2 \, a^{4} c d^{2} e^{3} + a^{5} e^{5}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right)} \sqrt{\frac{2 \, c d e + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}}\right) + {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, c d e - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}} \log\left(-{\left(c^{2} d^{2} - a c e^{2}\right)} x + {\left(a c^{2} d^{3} - a^{2} c d e^{2} - {\left(a^{3} c^{2} d^{4} e + 2 \, a^{4} c d^{2} e^{3} + a^{5} e^{5}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right)} \sqrt{\frac{2 \, c d e - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}}\right) - {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, c d e - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}} \log\left(-{\left(c^{2} d^{2} - a c e^{2}\right)} x - {\left(a c^{2} d^{3} - a^{2} c d e^{2} - {\left(a^{3} c^{2} d^{4} e + 2 \, a^{4} c d^{2} e^{3} + a^{5} e^{5}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right)} \sqrt{\frac{2 \, c d e - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}}\right) - 2 \, e \sqrt{-\frac{e}{d}} \log\left(\frac{e x^{2} + 2 \, d x \sqrt{-\frac{e}{d}} - d}{e x^{2} + d}\right)}{4 \, {\left(c d^{2} + a e^{2}\right)}}, \frac{4 \, e \sqrt{\frac{e}{d}} \arctan\left(x \sqrt{\frac{e}{d}}\right) - {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, c d e + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}} \log\left(-{\left(c^{2} d^{2} - a c e^{2}\right)} x + {\left(a c^{2} d^{3} - a^{2} c d e^{2} + {\left(a^{3} c^{2} d^{4} e + 2 \, a^{4} c d^{2} e^{3} + a^{5} e^{5}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right)} \sqrt{\frac{2 \, c d e + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}}\right) + {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, c d e + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}} \log\left(-{\left(c^{2} d^{2} - a c e^{2}\right)} x - {\left(a c^{2} d^{3} - a^{2} c d e^{2} + {\left(a^{3} c^{2} d^{4} e + 2 \, a^{4} c d^{2} e^{3} + a^{5} e^{5}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right)} \sqrt{\frac{2 \, c d e + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}}\right) - {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, c d e - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}} \log\left(-{\left(c^{2} d^{2} - a c e^{2}\right)} x + {\left(a c^{2} d^{3} - a^{2} c d e^{2} - {\left(a^{3} c^{2} d^{4} e + 2 \, a^{4} c d^{2} e^{3} + a^{5} e^{5}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right)} \sqrt{\frac{2 \, c d e - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}}\right) + {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, c d e - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}} \log\left(-{\left(c^{2} d^{2} - a c e^{2}\right)} x - {\left(a c^{2} d^{3} - a^{2} c d e^{2} - {\left(a^{3} c^{2} d^{4} e + 2 \, a^{4} c d^{2} e^{3} + a^{5} e^{5}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right)} \sqrt{\frac{2 \, c d e - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}}\right)}{4 \, {\left(c d^{2} + a e^{2}\right)}}\right]"," ",0,"[-1/4*((c*d^2 + a*e^2)*sqrt((2*c*d*e + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))*log(-(c^2*d^2 - a*c*e^2)*x + (a*c^2*d^3 - a^2*c*d*e^2 + (a^3*c^2*d^4*e + 2*a^4*c*d^2*e^3 + a^5*e^5)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))*sqrt((2*c*d*e + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))) - (c*d^2 + a*e^2)*sqrt((2*c*d*e + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))*log(-(c^2*d^2 - a*c*e^2)*x - (a*c^2*d^3 - a^2*c*d*e^2 + (a^3*c^2*d^4*e + 2*a^4*c*d^2*e^3 + a^5*e^5)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))*sqrt((2*c*d*e + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))) + (c*d^2 + a*e^2)*sqrt((2*c*d*e - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))*log(-(c^2*d^2 - a*c*e^2)*x + (a*c^2*d^3 - a^2*c*d*e^2 - (a^3*c^2*d^4*e + 2*a^4*c*d^2*e^3 + a^5*e^5)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))*sqrt((2*c*d*e - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))) - (c*d^2 + a*e^2)*sqrt((2*c*d*e - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))*log(-(c^2*d^2 - a*c*e^2)*x - (a*c^2*d^3 - a^2*c*d*e^2 - (a^3*c^2*d^4*e + 2*a^4*c*d^2*e^3 + a^5*e^5)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))*sqrt((2*c*d*e - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))) - 2*e*sqrt(-e/d)*log((e*x^2 + 2*d*x*sqrt(-e/d) - d)/(e*x^2 + d)))/(c*d^2 + a*e^2), 1/4*(4*e*sqrt(e/d)*arctan(x*sqrt(e/d)) - (c*d^2 + a*e^2)*sqrt((2*c*d*e + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))*log(-(c^2*d^2 - a*c*e^2)*x + (a*c^2*d^3 - a^2*c*d*e^2 + (a^3*c^2*d^4*e + 2*a^4*c*d^2*e^3 + a^5*e^5)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))*sqrt((2*c*d*e + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))) + (c*d^2 + a*e^2)*sqrt((2*c*d*e + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))*log(-(c^2*d^2 - a*c*e^2)*x - (a*c^2*d^3 - a^2*c*d*e^2 + (a^3*c^2*d^4*e + 2*a^4*c*d^2*e^3 + a^5*e^5)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))*sqrt((2*c*d*e + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))) - (c*d^2 + a*e^2)*sqrt((2*c*d*e - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))*log(-(c^2*d^2 - a*c*e^2)*x + (a*c^2*d^3 - a^2*c*d*e^2 - (a^3*c^2*d^4*e + 2*a^4*c*d^2*e^3 + a^5*e^5)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))*sqrt((2*c*d*e - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))) + (c*d^2 + a*e^2)*sqrt((2*c*d*e - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))*log(-(c^2*d^2 - a*c*e^2)*x - (a*c^2*d^3 - a^2*c*d*e^2 - (a^3*c^2*d^4*e + 2*a^4*c*d^2*e^3 + a^5*e^5)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))*sqrt((2*c*d*e - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))))/(c*d^2 + a*e^2)]","B",0
242,1,4362,0,9.079630," ","integrate(1/x^2/(e*x^2+d)/(c*x^4+a),x, algorithm=""fricas"")","\left[\frac{2 \, a e^{2} x \sqrt{-\frac{e}{d}} \log\left(\frac{e x^{2} - 2 \, d x \sqrt{-\frac{e}{d}} - d}{e x^{2} + d}\right) + {\left(a c d^{3} + a^{2} d e^{2}\right)} x \sqrt{-\frac{2 \, c^{2} d e + {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}}{a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}}} \log\left(-{\left(c^{3} d^{2} - a c^{2} e^{2}\right)} x + {\left(a^{2} c^{2} d^{2} e - a^{3} c e^{3} - {\left(a^{4} c^{2} d^{5} + 2 \, a^{5} c d^{3} e^{2} + a^{6} d e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}\right)} \sqrt{-\frac{2 \, c^{2} d e + {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}}{a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}}}\right) - {\left(a c d^{3} + a^{2} d e^{2}\right)} x \sqrt{-\frac{2 \, c^{2} d e + {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}}{a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}}} \log\left(-{\left(c^{3} d^{2} - a c^{2} e^{2}\right)} x - {\left(a^{2} c^{2} d^{2} e - a^{3} c e^{3} - {\left(a^{4} c^{2} d^{5} + 2 \, a^{5} c d^{3} e^{2} + a^{6} d e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}\right)} \sqrt{-\frac{2 \, c^{2} d e + {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}}{a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}}}\right) + {\left(a c d^{3} + a^{2} d e^{2}\right)} x \sqrt{-\frac{2 \, c^{2} d e - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}}{a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}}} \log\left(-{\left(c^{3} d^{2} - a c^{2} e^{2}\right)} x + {\left(a^{2} c^{2} d^{2} e - a^{3} c e^{3} + {\left(a^{4} c^{2} d^{5} + 2 \, a^{5} c d^{3} e^{2} + a^{6} d e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}\right)} \sqrt{-\frac{2 \, c^{2} d e - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}}{a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}}}\right) - {\left(a c d^{3} + a^{2} d e^{2}\right)} x \sqrt{-\frac{2 \, c^{2} d e - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}}{a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}}} \log\left(-{\left(c^{3} d^{2} - a c^{2} e^{2}\right)} x - {\left(a^{2} c^{2} d^{2} e - a^{3} c e^{3} + {\left(a^{4} c^{2} d^{5} + 2 \, a^{5} c d^{3} e^{2} + a^{6} d e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}\right)} \sqrt{-\frac{2 \, c^{2} d e - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}}{a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}}}\right) - 4 \, c d^{2} - 4 \, a e^{2}}{4 \, {\left(a c d^{3} + a^{2} d e^{2}\right)} x}, -\frac{4 \, a e^{2} x \sqrt{\frac{e}{d}} \arctan\left(x \sqrt{\frac{e}{d}}\right) - {\left(a c d^{3} + a^{2} d e^{2}\right)} x \sqrt{-\frac{2 \, c^{2} d e + {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}}{a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}}} \log\left(-{\left(c^{3} d^{2} - a c^{2} e^{2}\right)} x + {\left(a^{2} c^{2} d^{2} e - a^{3} c e^{3} - {\left(a^{4} c^{2} d^{5} + 2 \, a^{5} c d^{3} e^{2} + a^{6} d e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}\right)} \sqrt{-\frac{2 \, c^{2} d e + {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}}{a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}}}\right) + {\left(a c d^{3} + a^{2} d e^{2}\right)} x \sqrt{-\frac{2 \, c^{2} d e + {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}}{a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}}} \log\left(-{\left(c^{3} d^{2} - a c^{2} e^{2}\right)} x - {\left(a^{2} c^{2} d^{2} e - a^{3} c e^{3} - {\left(a^{4} c^{2} d^{5} + 2 \, a^{5} c d^{3} e^{2} + a^{6} d e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}\right)} \sqrt{-\frac{2 \, c^{2} d e + {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}}{a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}}}\right) - {\left(a c d^{3} + a^{2} d e^{2}\right)} x \sqrt{-\frac{2 \, c^{2} d e - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}}{a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}}} \log\left(-{\left(c^{3} d^{2} - a c^{2} e^{2}\right)} x + {\left(a^{2} c^{2} d^{2} e - a^{3} c e^{3} + {\left(a^{4} c^{2} d^{5} + 2 \, a^{5} c d^{3} e^{2} + a^{6} d e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}\right)} \sqrt{-\frac{2 \, c^{2} d e - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}}{a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}}}\right) + {\left(a c d^{3} + a^{2} d e^{2}\right)} x \sqrt{-\frac{2 \, c^{2} d e - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}}{a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}}} \log\left(-{\left(c^{3} d^{2} - a c^{2} e^{2}\right)} x - {\left(a^{2} c^{2} d^{2} e - a^{3} c e^{3} + {\left(a^{4} c^{2} d^{5} + 2 \, a^{5} c d^{3} e^{2} + a^{6} d e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}\right)} \sqrt{-\frac{2 \, c^{2} d e - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \sqrt{-\frac{c^{5} d^{4} - 2 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}}{a^{5} c^{4} d^{8} + 4 \, a^{6} c^{3} d^{6} e^{2} + 6 \, a^{7} c^{2} d^{4} e^{4} + 4 \, a^{8} c d^{2} e^{6} + a^{9} e^{8}}}}{a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}}}\right) + 4 \, c d^{2} + 4 \, a e^{2}}{4 \, {\left(a c d^{3} + a^{2} d e^{2}\right)} x}\right]"," ",0,"[1/4*(2*a*e^2*x*sqrt(-e/d)*log((e*x^2 - 2*d*x*sqrt(-e/d) - d)/(e*x^2 + d)) + (a*c*d^3 + a^2*d*e^2)*x*sqrt(-(2*c^2*d*e + (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4))*log(-(c^3*d^2 - a*c^2*e^2)*x + (a^2*c^2*d^2*e - a^3*c*e^3 - (a^4*c^2*d^5 + 2*a^5*c*d^3*e^2 + a^6*d*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))*sqrt(-(2*c^2*d*e + (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4))) - (a*c*d^3 + a^2*d*e^2)*x*sqrt(-(2*c^2*d*e + (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4))*log(-(c^3*d^2 - a*c^2*e^2)*x - (a^2*c^2*d^2*e - a^3*c*e^3 - (a^4*c^2*d^5 + 2*a^5*c*d^3*e^2 + a^6*d*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))*sqrt(-(2*c^2*d*e + (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4))) + (a*c*d^3 + a^2*d*e^2)*x*sqrt(-(2*c^2*d*e - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4))*log(-(c^3*d^2 - a*c^2*e^2)*x + (a^2*c^2*d^2*e - a^3*c*e^3 + (a^4*c^2*d^5 + 2*a^5*c*d^3*e^2 + a^6*d*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))*sqrt(-(2*c^2*d*e - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4))) - (a*c*d^3 + a^2*d*e^2)*x*sqrt(-(2*c^2*d*e - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4))*log(-(c^3*d^2 - a*c^2*e^2)*x - (a^2*c^2*d^2*e - a^3*c*e^3 + (a^4*c^2*d^5 + 2*a^5*c*d^3*e^2 + a^6*d*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))*sqrt(-(2*c^2*d*e - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4))) - 4*c*d^2 - 4*a*e^2)/((a*c*d^3 + a^2*d*e^2)*x), -1/4*(4*a*e^2*x*sqrt(e/d)*arctan(x*sqrt(e/d)) - (a*c*d^3 + a^2*d*e^2)*x*sqrt(-(2*c^2*d*e + (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4))*log(-(c^3*d^2 - a*c^2*e^2)*x + (a^2*c^2*d^2*e - a^3*c*e^3 - (a^4*c^2*d^5 + 2*a^5*c*d^3*e^2 + a^6*d*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))*sqrt(-(2*c^2*d*e + (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4))) + (a*c*d^3 + a^2*d*e^2)*x*sqrt(-(2*c^2*d*e + (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4))*log(-(c^3*d^2 - a*c^2*e^2)*x - (a^2*c^2*d^2*e - a^3*c*e^3 - (a^4*c^2*d^5 + 2*a^5*c*d^3*e^2 + a^6*d*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))*sqrt(-(2*c^2*d*e + (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4))) - (a*c*d^3 + a^2*d*e^2)*x*sqrt(-(2*c^2*d*e - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4))*log(-(c^3*d^2 - a*c^2*e^2)*x + (a^2*c^2*d^2*e - a^3*c*e^3 + (a^4*c^2*d^5 + 2*a^5*c*d^3*e^2 + a^6*d*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))*sqrt(-(2*c^2*d*e - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4))) + (a*c*d^3 + a^2*d*e^2)*x*sqrt(-(2*c^2*d*e - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4))*log(-(c^3*d^2 - a*c^2*e^2)*x - (a^2*c^2*d^2*e - a^3*c*e^3 + (a^4*c^2*d^5 + 2*a^5*c*d^3*e^2 + a^6*d*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))*sqrt(-(2*c^2*d*e - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*sqrt(-(c^5*d^4 - 2*a*c^4*d^2*e^2 + a^2*c^3*e^4)/(a^5*c^4*d^8 + 4*a^6*c^3*d^6*e^2 + 6*a^7*c^2*d^4*e^4 + 4*a^8*c*d^2*e^6 + a^9*e^8)))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4))) + 4*c*d^2 + 4*a*e^2)/((a*c*d^3 + a^2*d*e^2)*x)]","B",0
243,1,4442,0,26.625400," ","integrate(1/x^4/(e*x^2+d)/(c*x^4+a),x, algorithm=""fricas"")","\left[\frac{6 \, a e^{3} x^{3} \sqrt{-\frac{e}{d}} \log\left(\frac{e x^{2} + 2 \, d x \sqrt{-\frac{e}{d}} - d}{e x^{2} + d}\right) + 3 \, {\left(a c d^{4} + a^{2} d^{2} e^{2}\right)} x^{3} \sqrt{\frac{2 \, c^{3} d e + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}}{a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}} \log\left(-{\left(c^{5} d^{2} - a c^{4} e^{2}\right)} x + {\left(a^{2} c^{4} d^{3} - a^{3} c^{3} d e^{2} + {\left(a^{6} c^{2} d^{4} e + 2 \, a^{7} c d^{2} e^{3} + a^{8} e^{5}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}\right)} \sqrt{\frac{2 \, c^{3} d e + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}}{a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}}\right) - 3 \, {\left(a c d^{4} + a^{2} d^{2} e^{2}\right)} x^{3} \sqrt{\frac{2 \, c^{3} d e + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}}{a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}} \log\left(-{\left(c^{5} d^{2} - a c^{4} e^{2}\right)} x - {\left(a^{2} c^{4} d^{3} - a^{3} c^{3} d e^{2} + {\left(a^{6} c^{2} d^{4} e + 2 \, a^{7} c d^{2} e^{3} + a^{8} e^{5}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}\right)} \sqrt{\frac{2 \, c^{3} d e + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}}{a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}}\right) + 3 \, {\left(a c d^{4} + a^{2} d^{2} e^{2}\right)} x^{3} \sqrt{\frac{2 \, c^{3} d e - {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}}{a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}} \log\left(-{\left(c^{5} d^{2} - a c^{4} e^{2}\right)} x + {\left(a^{2} c^{4} d^{3} - a^{3} c^{3} d e^{2} - {\left(a^{6} c^{2} d^{4} e + 2 \, a^{7} c d^{2} e^{3} + a^{8} e^{5}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}\right)} \sqrt{\frac{2 \, c^{3} d e - {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}}{a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}}\right) - 3 \, {\left(a c d^{4} + a^{2} d^{2} e^{2}\right)} x^{3} \sqrt{\frac{2 \, c^{3} d e - {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}}{a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}} \log\left(-{\left(c^{5} d^{2} - a c^{4} e^{2}\right)} x - {\left(a^{2} c^{4} d^{3} - a^{3} c^{3} d e^{2} - {\left(a^{6} c^{2} d^{4} e + 2 \, a^{7} c d^{2} e^{3} + a^{8} e^{5}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}\right)} \sqrt{\frac{2 \, c^{3} d e - {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}}{a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}}\right) - 4 \, c d^{3} - 4 \, a d e^{2} + 12 \, {\left(c d^{2} e + a e^{3}\right)} x^{2}}{12 \, {\left(a c d^{4} + a^{2} d^{2} e^{2}\right)} x^{3}}, \frac{12 \, a e^{3} x^{3} \sqrt{\frac{e}{d}} \arctan\left(x \sqrt{\frac{e}{d}}\right) + 3 \, {\left(a c d^{4} + a^{2} d^{2} e^{2}\right)} x^{3} \sqrt{\frac{2 \, c^{3} d e + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}}{a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}} \log\left(-{\left(c^{5} d^{2} - a c^{4} e^{2}\right)} x + {\left(a^{2} c^{4} d^{3} - a^{3} c^{3} d e^{2} + {\left(a^{6} c^{2} d^{4} e + 2 \, a^{7} c d^{2} e^{3} + a^{8} e^{5}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}\right)} \sqrt{\frac{2 \, c^{3} d e + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}}{a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}}\right) - 3 \, {\left(a c d^{4} + a^{2} d^{2} e^{2}\right)} x^{3} \sqrt{\frac{2 \, c^{3} d e + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}}{a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}} \log\left(-{\left(c^{5} d^{2} - a c^{4} e^{2}\right)} x - {\left(a^{2} c^{4} d^{3} - a^{3} c^{3} d e^{2} + {\left(a^{6} c^{2} d^{4} e + 2 \, a^{7} c d^{2} e^{3} + a^{8} e^{5}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}\right)} \sqrt{\frac{2 \, c^{3} d e + {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}}{a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}}\right) + 3 \, {\left(a c d^{4} + a^{2} d^{2} e^{2}\right)} x^{3} \sqrt{\frac{2 \, c^{3} d e - {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}}{a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}} \log\left(-{\left(c^{5} d^{2} - a c^{4} e^{2}\right)} x + {\left(a^{2} c^{4} d^{3} - a^{3} c^{3} d e^{2} - {\left(a^{6} c^{2} d^{4} e + 2 \, a^{7} c d^{2} e^{3} + a^{8} e^{5}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}\right)} \sqrt{\frac{2 \, c^{3} d e - {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}}{a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}}\right) - 3 \, {\left(a c d^{4} + a^{2} d^{2} e^{2}\right)} x^{3} \sqrt{\frac{2 \, c^{3} d e - {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}}{a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}} \log\left(-{\left(c^{5} d^{2} - a c^{4} e^{2}\right)} x - {\left(a^{2} c^{4} d^{3} - a^{3} c^{3} d e^{2} - {\left(a^{6} c^{2} d^{4} e + 2 \, a^{7} c d^{2} e^{3} + a^{8} e^{5}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}\right)} \sqrt{\frac{2 \, c^{3} d e - {\left(a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}\right)} \sqrt{-\frac{c^{7} d^{4} - 2 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}}{a^{7} c^{4} d^{8} + 4 \, a^{8} c^{3} d^{6} e^{2} + 6 \, a^{9} c^{2} d^{4} e^{4} + 4 \, a^{10} c d^{2} e^{6} + a^{11} e^{8}}}}{a^{3} c^{2} d^{4} + 2 \, a^{4} c d^{2} e^{2} + a^{5} e^{4}}}\right) - 4 \, c d^{3} - 4 \, a d e^{2} + 12 \, {\left(c d^{2} e + a e^{3}\right)} x^{2}}{12 \, {\left(a c d^{4} + a^{2} d^{2} e^{2}\right)} x^{3}}\right]"," ",0,"[1/12*(6*a*e^3*x^3*sqrt(-e/d)*log((e*x^2 + 2*d*x*sqrt(-e/d) - d)/(e*x^2 + d)) + 3*(a*c*d^4 + a^2*d^2*e^2)*x^3*sqrt((2*c^3*d*e + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))/(a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4))*log(-(c^5*d^2 - a*c^4*e^2)*x + (a^2*c^4*d^3 - a^3*c^3*d*e^2 + (a^6*c^2*d^4*e + 2*a^7*c*d^2*e^3 + a^8*e^5)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))*sqrt((2*c^3*d*e + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))/(a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4))) - 3*(a*c*d^4 + a^2*d^2*e^2)*x^3*sqrt((2*c^3*d*e + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))/(a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4))*log(-(c^5*d^2 - a*c^4*e^2)*x - (a^2*c^4*d^3 - a^3*c^3*d*e^2 + (a^6*c^2*d^4*e + 2*a^7*c*d^2*e^3 + a^8*e^5)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))*sqrt((2*c^3*d*e + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))/(a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4))) + 3*(a*c*d^4 + a^2*d^2*e^2)*x^3*sqrt((2*c^3*d*e - (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))/(a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4))*log(-(c^5*d^2 - a*c^4*e^2)*x + (a^2*c^4*d^3 - a^3*c^3*d*e^2 - (a^6*c^2*d^4*e + 2*a^7*c*d^2*e^3 + a^8*e^5)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))*sqrt((2*c^3*d*e - (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))/(a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4))) - 3*(a*c*d^4 + a^2*d^2*e^2)*x^3*sqrt((2*c^3*d*e - (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))/(a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4))*log(-(c^5*d^2 - a*c^4*e^2)*x - (a^2*c^4*d^3 - a^3*c^3*d*e^2 - (a^6*c^2*d^4*e + 2*a^7*c*d^2*e^3 + a^8*e^5)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))*sqrt((2*c^3*d*e - (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))/(a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4))) - 4*c*d^3 - 4*a*d*e^2 + 12*(c*d^2*e + a*e^3)*x^2)/((a*c*d^4 + a^2*d^2*e^2)*x^3), 1/12*(12*a*e^3*x^3*sqrt(e/d)*arctan(x*sqrt(e/d)) + 3*(a*c*d^4 + a^2*d^2*e^2)*x^3*sqrt((2*c^3*d*e + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))/(a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4))*log(-(c^5*d^2 - a*c^4*e^2)*x + (a^2*c^4*d^3 - a^3*c^3*d*e^2 + (a^6*c^2*d^4*e + 2*a^7*c*d^2*e^3 + a^8*e^5)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))*sqrt((2*c^3*d*e + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))/(a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4))) - 3*(a*c*d^4 + a^2*d^2*e^2)*x^3*sqrt((2*c^3*d*e + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))/(a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4))*log(-(c^5*d^2 - a*c^4*e^2)*x - (a^2*c^4*d^3 - a^3*c^3*d*e^2 + (a^6*c^2*d^4*e + 2*a^7*c*d^2*e^3 + a^8*e^5)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))*sqrt((2*c^3*d*e + (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))/(a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4))) + 3*(a*c*d^4 + a^2*d^2*e^2)*x^3*sqrt((2*c^3*d*e - (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))/(a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4))*log(-(c^5*d^2 - a*c^4*e^2)*x + (a^2*c^4*d^3 - a^3*c^3*d*e^2 - (a^6*c^2*d^4*e + 2*a^7*c*d^2*e^3 + a^8*e^5)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))*sqrt((2*c^3*d*e - (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))/(a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4))) - 3*(a*c*d^4 + a^2*d^2*e^2)*x^3*sqrt((2*c^3*d*e - (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))/(a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4))*log(-(c^5*d^2 - a*c^4*e^2)*x - (a^2*c^4*d^3 - a^3*c^3*d*e^2 - (a^6*c^2*d^4*e + 2*a^7*c*d^2*e^3 + a^8*e^5)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))*sqrt((2*c^3*d*e - (a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4)*sqrt(-(c^7*d^4 - 2*a*c^6*d^2*e^2 + a^2*c^5*e^4)/(a^7*c^4*d^8 + 4*a^8*c^3*d^6*e^2 + 6*a^9*c^2*d^4*e^4 + 4*a^10*c*d^2*e^6 + a^11*e^8)))/(a^3*c^2*d^4 + 2*a^4*c*d^2*e^2 + a^5*e^4))) - 4*c*d^3 - 4*a*d*e^2 + 12*(c*d^2*e + a*e^3)*x^2)/((a*c*d^4 + a^2*d^2*e^2)*x^3)]","B",0
244,1,555,0,35.277317," ","integrate(x^9/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a^{2} c d^{2} e^{2} + 2 \, a^{3} e^{4} + 2 \, {\left(a c^{2} d^{3} e + a^{2} c d e^{3}\right)} x^{2} + {\left(3 \, a c^{2} d^{3} e + a^{2} c d e^{3} + {\left(3 \, c^{3} d^{3} e + a c^{2} d e^{3}\right)} x^{4}\right)} \sqrt{-\frac{a}{c}} \log\left(\frac{c x^{4} - 2 \, c x^{2} \sqrt{-\frac{a}{c}} - a}{c x^{4} + a}\right) + 2 \, {\left(2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{4}\right)} \log\left(c x^{4} + a\right) + 4 \, {\left(c^{3} d^{4} x^{4} + a c^{2} d^{4}\right)} \log\left(e x^{2} + d\right)}{8 \, {\left(a c^{4} d^{4} e + 2 \, a^{2} c^{3} d^{2} e^{3} + a^{3} c^{2} e^{5} + {\left(c^{5} d^{4} e + 2 \, a c^{4} d^{2} e^{3} + a^{2} c^{3} e^{5}\right)} x^{4}\right)}}, \frac{a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(a c^{2} d^{3} e + a^{2} c d e^{3}\right)} x^{2} - {\left(3 \, a c^{2} d^{3} e + a^{2} c d e^{3} + {\left(3 \, c^{3} d^{3} e + a c^{2} d e^{3}\right)} x^{4}\right)} \sqrt{\frac{a}{c}} \arctan\left(\frac{c x^{2} \sqrt{\frac{a}{c}}}{a}\right) + {\left(2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{4}\right)} \log\left(c x^{4} + a\right) + 2 \, {\left(c^{3} d^{4} x^{4} + a c^{2} d^{4}\right)} \log\left(e x^{2} + d\right)}{4 \, {\left(a c^{4} d^{4} e + 2 \, a^{2} c^{3} d^{2} e^{3} + a^{3} c^{2} e^{5} + {\left(c^{5} d^{4} e + 2 \, a c^{4} d^{2} e^{3} + a^{2} c^{3} e^{5}\right)} x^{4}\right)}}\right]"," ",0,"[1/8*(2*a^2*c*d^2*e^2 + 2*a^3*e^4 + 2*(a*c^2*d^3*e + a^2*c*d*e^3)*x^2 + (3*a*c^2*d^3*e + a^2*c*d*e^3 + (3*c^3*d^3*e + a*c^2*d*e^3)*x^4)*sqrt(-a/c)*log((c*x^4 - 2*c*x^2*sqrt(-a/c) - a)/(c*x^4 + a)) + 2*(2*a^2*c*d^2*e^2 + a^3*e^4 + (2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^4)*log(c*x^4 + a) + 4*(c^3*d^4*x^4 + a*c^2*d^4)*log(e*x^2 + d))/(a*c^4*d^4*e + 2*a^2*c^3*d^2*e^3 + a^3*c^2*e^5 + (c^5*d^4*e + 2*a*c^4*d^2*e^3 + a^2*c^3*e^5)*x^4), 1/4*(a^2*c*d^2*e^2 + a^3*e^4 + (a*c^2*d^3*e + a^2*c*d*e^3)*x^2 - (3*a*c^2*d^3*e + a^2*c*d*e^3 + (3*c^3*d^3*e + a*c^2*d*e^3)*x^4)*sqrt(a/c)*arctan(c*x^2*sqrt(a/c)/a) + (2*a^2*c*d^2*e^2 + a^3*e^4 + (2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^4)*log(c*x^4 + a) + 2*(c^3*d^4*x^4 + a*c^2*d^4)*log(e*x^2 + d))/(a*c^4*d^4*e + 2*a^2*c^3*d^2*e^3 + a^3*c^2*e^5 + (c^5*d^4*e + 2*a*c^4*d^2*e^3 + a^2*c^3*e^5)*x^4)]","A",0
245,1,457,0,17.039338," ","integrate(x^7/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a c d^{3} + 2 \, a^{2} d e^{2} - 2 \, {\left(a c d^{2} e + a^{2} e^{3}\right)} x^{2} + {\left(3 \, a c d^{2} e + a^{2} e^{3} + {\left(3 \, c^{2} d^{2} e + a c e^{3}\right)} x^{4}\right)} \sqrt{-\frac{a}{c}} \log\left(\frac{c x^{4} + 2 \, c x^{2} \sqrt{-\frac{a}{c}} - a}{c x^{4} + a}\right) + 2 \, {\left(c^{2} d^{3} x^{4} + a c d^{3}\right)} \log\left(c x^{4} + a\right) - 4 \, {\left(c^{2} d^{3} x^{4} + a c d^{3}\right)} \log\left(e x^{2} + d\right)}{8 \, {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)}}, \frac{a c d^{3} + a^{2} d e^{2} - {\left(a c d^{2} e + a^{2} e^{3}\right)} x^{2} + {\left(3 \, a c d^{2} e + a^{2} e^{3} + {\left(3 \, c^{2} d^{2} e + a c e^{3}\right)} x^{4}\right)} \sqrt{\frac{a}{c}} \arctan\left(\frac{c x^{2} \sqrt{\frac{a}{c}}}{a}\right) + {\left(c^{2} d^{3} x^{4} + a c d^{3}\right)} \log\left(c x^{4} + a\right) - 2 \, {\left(c^{2} d^{3} x^{4} + a c d^{3}\right)} \log\left(e x^{2} + d\right)}{4 \, {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)}}\right]"," ",0,"[1/8*(2*a*c*d^3 + 2*a^2*d*e^2 - 2*(a*c*d^2*e + a^2*e^3)*x^2 + (3*a*c*d^2*e + a^2*e^3 + (3*c^2*d^2*e + a*c*e^3)*x^4)*sqrt(-a/c)*log((c*x^4 + 2*c*x^2*sqrt(-a/c) - a)/(c*x^4 + a)) + 2*(c^2*d^3*x^4 + a*c*d^3)*log(c*x^4 + a) - 4*(c^2*d^3*x^4 + a*c*d^3)*log(e*x^2 + d))/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4), 1/4*(a*c*d^3 + a^2*d*e^2 - (a*c*d^2*e + a^2*e^3)*x^2 + (3*a*c*d^2*e + a^2*e^3 + (3*c^2*d^2*e + a*c*e^3)*x^4)*sqrt(a/c)*arctan(c*x^2*sqrt(a/c)/a) + (c^2*d^3*x^4 + a*c*d^3)*log(c*x^4 + a) - 2*(c^2*d^3*x^4 + a*c*d^3)*log(e*x^2 + d))/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4)]","A",0
246,1,487,0,6.195286," ","integrate(x^5/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, a^{2} c d^{2} e + 2 \, a^{3} e^{3} + 2 \, {\left(a c^{2} d^{3} + a^{2} c d e^{2}\right)} x^{2} - {\left(a c d^{3} - a^{2} d e^{2} + {\left(c^{2} d^{3} - a c d e^{2}\right)} x^{4}\right)} \sqrt{-a c} \log\left(\frac{c x^{4} + 2 \, \sqrt{-a c} x^{2} - a}{c x^{4} + a}\right) + 2 \, {\left(a c^{2} d^{2} e x^{4} + a^{2} c d^{2} e\right)} \log\left(c x^{4} + a\right) - 4 \, {\left(a c^{2} d^{2} e x^{4} + a^{2} c d^{2} e\right)} \log\left(e x^{2} + d\right)}{8 \, {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4} + {\left(a c^{4} d^{4} + 2 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} x^{4}\right)}}, -\frac{a^{2} c d^{2} e + a^{3} e^{3} + {\left(a c^{2} d^{3} + a^{2} c d e^{2}\right)} x^{2} + {\left(a c d^{3} - a^{2} d e^{2} + {\left(c^{2} d^{3} - a c d e^{2}\right)} x^{4}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c}}{c x^{2}}\right) + {\left(a c^{2} d^{2} e x^{4} + a^{2} c d^{2} e\right)} \log\left(c x^{4} + a\right) - 2 \, {\left(a c^{2} d^{2} e x^{4} + a^{2} c d^{2} e\right)} \log\left(e x^{2} + d\right)}{4 \, {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4} + {\left(a c^{4} d^{4} + 2 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} x^{4}\right)}}\right]"," ",0,"[-1/8*(2*a^2*c*d^2*e + 2*a^3*e^3 + 2*(a*c^2*d^3 + a^2*c*d*e^2)*x^2 - (a*c*d^3 - a^2*d*e^2 + (c^2*d^3 - a*c*d*e^2)*x^4)*sqrt(-a*c)*log((c*x^4 + 2*sqrt(-a*c)*x^2 - a)/(c*x^4 + a)) + 2*(a*c^2*d^2*e*x^4 + a^2*c*d^2*e)*log(c*x^4 + a) - 4*(a*c^2*d^2*e*x^4 + a^2*c*d^2*e)*log(e*x^2 + d))/(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4 + (a*c^4*d^4 + 2*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*x^4), -1/4*(a^2*c*d^2*e + a^3*e^3 + (a*c^2*d^3 + a^2*c*d*e^2)*x^2 + (a*c*d^3 - a^2*d*e^2 + (c^2*d^3 - a*c*d*e^2)*x^4)*sqrt(a*c)*arctan(sqrt(a*c)/(c*x^2)) + (a*c^2*d^2*e*x^4 + a^2*c*d^2*e)*log(c*x^4 + a) - 2*(a*c^2*d^2*e*x^4 + a^2*c*d^2*e)*log(e*x^2 + d))/(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4 + (a*c^4*d^4 + 2*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*x^4)]","A",0
247,1,492,0,7.088477," ","integrate(x^3/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, a c^{2} d^{3} + 2 \, a^{2} c d e^{2} - 2 \, {\left(a c^{2} d^{2} e + a^{2} c e^{3}\right)} x^{2} - {\left(a c d^{2} e - a^{2} e^{3} + {\left(c^{2} d^{2} e - a c e^{3}\right)} x^{4}\right)} \sqrt{-a c} \log\left(\frac{c x^{4} - 2 \, \sqrt{-a c} x^{2} - a}{c x^{4} + a}\right) - 2 \, {\left(a c^{2} d e^{2} x^{4} + a^{2} c d e^{2}\right)} \log\left(c x^{4} + a\right) + 4 \, {\left(a c^{2} d e^{2} x^{4} + a^{2} c d e^{2}\right)} \log\left(e x^{2} + d\right)}{8 \, {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4} + {\left(a c^{4} d^{4} + 2 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} x^{4}\right)}}, -\frac{a c^{2} d^{3} + a^{2} c d e^{2} - {\left(a c^{2} d^{2} e + a^{2} c e^{3}\right)} x^{2} - {\left(a c d^{2} e - a^{2} e^{3} + {\left(c^{2} d^{2} e - a c e^{3}\right)} x^{4}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c}}{c x^{2}}\right) - {\left(a c^{2} d e^{2} x^{4} + a^{2} c d e^{2}\right)} \log\left(c x^{4} + a\right) + 2 \, {\left(a c^{2} d e^{2} x^{4} + a^{2} c d e^{2}\right)} \log\left(e x^{2} + d\right)}{4 \, {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4} + {\left(a c^{4} d^{4} + 2 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} x^{4}\right)}}\right]"," ",0,"[-1/8*(2*a*c^2*d^3 + 2*a^2*c*d*e^2 - 2*(a*c^2*d^2*e + a^2*c*e^3)*x^2 - (a*c*d^2*e - a^2*e^3 + (c^2*d^2*e - a*c*e^3)*x^4)*sqrt(-a*c)*log((c*x^4 - 2*sqrt(-a*c)*x^2 - a)/(c*x^4 + a)) - 2*(a*c^2*d*e^2*x^4 + a^2*c*d*e^2)*log(c*x^4 + a) + 4*(a*c^2*d*e^2*x^4 + a^2*c*d*e^2)*log(e*x^2 + d))/(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4 + (a*c^4*d^4 + 2*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*x^4), -1/4*(a*c^2*d^3 + a^2*c*d*e^2 - (a*c^2*d^2*e + a^2*c*e^3)*x^2 - (a*c*d^2*e - a^2*e^3 + (c^2*d^2*e - a*c*e^3)*x^4)*sqrt(a*c)*arctan(sqrt(a*c)/(c*x^2)) - (a*c^2*d*e^2*x^4 + a^2*c*d*e^2)*log(c*x^4 + a) + 2*(a*c^2*d*e^2*x^4 + a^2*c*d*e^2)*log(e*x^2 + d))/(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4 + (a*c^4*d^4 + 2*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*x^4)]","A",0
248,1,458,0,16.307738," ","integrate(x/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a c d^{2} e + 2 \, a^{2} e^{3} + 2 \, {\left(c^{2} d^{3} + a c d e^{2}\right)} x^{2} + {\left(a c d^{3} + 3 \, a^{2} d e^{2} + {\left(c^{2} d^{3} + 3 \, a c d e^{2}\right)} x^{4}\right)} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{4} + 2 \, a x^{2} \sqrt{-\frac{c}{a}} - a}{c x^{4} + a}\right) - 2 \, {\left(a c e^{3} x^{4} + a^{2} e^{3}\right)} \log\left(c x^{4} + a\right) + 4 \, {\left(a c e^{3} x^{4} + a^{2} e^{3}\right)} \log\left(e x^{2} + d\right)}{8 \, {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)}}, \frac{a c d^{2} e + a^{2} e^{3} + {\left(c^{2} d^{3} + a c d e^{2}\right)} x^{2} - {\left(a c d^{3} + 3 \, a^{2} d e^{2} + {\left(c^{2} d^{3} + 3 \, a c d e^{2}\right)} x^{4}\right)} \sqrt{\frac{c}{a}} \arctan\left(\frac{a \sqrt{\frac{c}{a}}}{c x^{2}}\right) - {\left(a c e^{3} x^{4} + a^{2} e^{3}\right)} \log\left(c x^{4} + a\right) + 2 \, {\left(a c e^{3} x^{4} + a^{2} e^{3}\right)} \log\left(e x^{2} + d\right)}{4 \, {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)}}\right]"," ",0,"[1/8*(2*a*c*d^2*e + 2*a^2*e^3 + 2*(c^2*d^3 + a*c*d*e^2)*x^2 + (a*c*d^3 + 3*a^2*d*e^2 + (c^2*d^3 + 3*a*c*d*e^2)*x^4)*sqrt(-c/a)*log((c*x^4 + 2*a*x^2*sqrt(-c/a) - a)/(c*x^4 + a)) - 2*(a*c*e^3*x^4 + a^2*e^3)*log(c*x^4 + a) + 4*(a*c*e^3*x^4 + a^2*e^3)*log(e*x^2 + d))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4), 1/4*(a*c*d^2*e + a^2*e^3 + (c^2*d^3 + a*c*d*e^2)*x^2 - (a*c*d^3 + 3*a^2*d*e^2 + (c^2*d^3 + 3*a*c*d*e^2)*x^4)*sqrt(c/a)*arctan(a*sqrt(c/a)/(c*x^2)) - (a*c*e^3*x^4 + a^2*e^3)*log(c*x^4 + a) + 2*(a*c*e^3*x^4 + a^2*e^3)*log(e*x^2 + d))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)]","A",0
249,-1,0,0,0.000000," ","integrate(1/x/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
250,-1,0,0,0.000000," ","integrate(1/x^3/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
251,-1,0,0,0.000000," ","integrate(1/x^5/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
252,1,9856,0,43.130095," ","integrate(x^8/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(a c d^{2} e + a^{2} e^{3}\right)} x^{3} - {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)} \sqrt{\frac{70 \, a c^{2} d^{5} e + 44 \, a^{2} c d^{3} e^{3} + 6 \, a^{3} d e^{5} + {\left(c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}} \log\left(-{\left(625 \, c^{4} d^{8} - 750 \, a c^{3} d^{6} e^{2} - 1376 \, a^{2} c^{2} d^{4} e^{4} - 594 \, a^{3} c d^{2} e^{6} - 81 \, a^{4} e^{8}\right)} x + {\left(125 \, c^{6} d^{9} - 170 \, a c^{5} d^{7} e^{2} - 244 \, a^{2} c^{4} d^{5} e^{4} - 86 \, a^{3} c^{3} d^{3} e^{6} - 9 \, a^{4} c^{2} d e^{8} + {\left(7 \, c^{10} d^{10} e + 31 \, a c^{9} d^{8} e^{3} + 54 \, a^{2} c^{8} d^{6} e^{5} + 46 \, a^{3} c^{7} d^{4} e^{7} + 19 \, a^{4} c^{6} d^{2} e^{9} + 3 \, a^{5} c^{5} e^{11}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}\right)} \sqrt{\frac{70 \, a c^{2} d^{5} e + 44 \, a^{2} c d^{3} e^{3} + 6 \, a^{3} d e^{5} + {\left(c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}\right) + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)} \sqrt{\frac{70 \, a c^{2} d^{5} e + 44 \, a^{2} c d^{3} e^{3} + 6 \, a^{3} d e^{5} + {\left(c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}} \log\left(-{\left(625 \, c^{4} d^{8} - 750 \, a c^{3} d^{6} e^{2} - 1376 \, a^{2} c^{2} d^{4} e^{4} - 594 \, a^{3} c d^{2} e^{6} - 81 \, a^{4} e^{8}\right)} x - {\left(125 \, c^{6} d^{9} - 170 \, a c^{5} d^{7} e^{2} - 244 \, a^{2} c^{4} d^{5} e^{4} - 86 \, a^{3} c^{3} d^{3} e^{6} - 9 \, a^{4} c^{2} d e^{8} + {\left(7 \, c^{10} d^{10} e + 31 \, a c^{9} d^{8} e^{3} + 54 \, a^{2} c^{8} d^{6} e^{5} + 46 \, a^{3} c^{7} d^{4} e^{7} + 19 \, a^{4} c^{6} d^{2} e^{9} + 3 \, a^{5} c^{5} e^{11}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}\right)} \sqrt{\frac{70 \, a c^{2} d^{5} e + 44 \, a^{2} c d^{3} e^{3} + 6 \, a^{3} d e^{5} + {\left(c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}\right) - {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)} \sqrt{\frac{70 \, a c^{2} d^{5} e + 44 \, a^{2} c d^{3} e^{3} + 6 \, a^{3} d e^{5} - {\left(c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}} \log\left(-{\left(625 \, c^{4} d^{8} - 750 \, a c^{3} d^{6} e^{2} - 1376 \, a^{2} c^{2} d^{4} e^{4} - 594 \, a^{3} c d^{2} e^{6} - 81 \, a^{4} e^{8}\right)} x + {\left(125 \, c^{6} d^{9} - 170 \, a c^{5} d^{7} e^{2} - 244 \, a^{2} c^{4} d^{5} e^{4} - 86 \, a^{3} c^{3} d^{3} e^{6} - 9 \, a^{4} c^{2} d e^{8} - {\left(7 \, c^{10} d^{10} e + 31 \, a c^{9} d^{8} e^{3} + 54 \, a^{2} c^{8} d^{6} e^{5} + 46 \, a^{3} c^{7} d^{4} e^{7} + 19 \, a^{4} c^{6} d^{2} e^{9} + 3 \, a^{5} c^{5} e^{11}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}\right)} \sqrt{\frac{70 \, a c^{2} d^{5} e + 44 \, a^{2} c d^{3} e^{3} + 6 \, a^{3} d e^{5} - {\left(c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}\right) + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)} \sqrt{\frac{70 \, a c^{2} d^{5} e + 44 \, a^{2} c d^{3} e^{3} + 6 \, a^{3} d e^{5} - {\left(c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}} \log\left(-{\left(625 \, c^{4} d^{8} - 750 \, a c^{3} d^{6} e^{2} - 1376 \, a^{2} c^{2} d^{4} e^{4} - 594 \, a^{3} c d^{2} e^{6} - 81 \, a^{4} e^{8}\right)} x - {\left(125 \, c^{6} d^{9} - 170 \, a c^{5} d^{7} e^{2} - 244 \, a^{2} c^{4} d^{5} e^{4} - 86 \, a^{3} c^{3} d^{3} e^{6} - 9 \, a^{4} c^{2} d e^{8} - {\left(7 \, c^{10} d^{10} e + 31 \, a c^{9} d^{8} e^{3} + 54 \, a^{2} c^{8} d^{6} e^{5} + 46 \, a^{3} c^{7} d^{4} e^{7} + 19 \, a^{4} c^{6} d^{2} e^{9} + 3 \, a^{5} c^{5} e^{11}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}\right)} \sqrt{\frac{70 \, a c^{2} d^{5} e + 44 \, a^{2} c d^{3} e^{3} + 6 \, a^{3} d e^{5} - {\left(c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}\right) - 8 \, {\left(c^{2} d^{3} x^{4} + a c d^{3}\right)} \sqrt{-\frac{d}{e}} \log\left(\frac{e x^{2} + 2 \, e x \sqrt{-\frac{d}{e}} - d}{e x^{2} + d}\right) - 4 \, {\left(a c d^{3} + a^{2} d e^{2}\right)} x}{16 \, {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)}}, -\frac{4 \, {\left(a c d^{2} e + a^{2} e^{3}\right)} x^{3} - 16 \, {\left(c^{2} d^{3} x^{4} + a c d^{3}\right)} \sqrt{\frac{d}{e}} \arctan\left(\frac{e x \sqrt{\frac{d}{e}}}{d}\right) - {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)} \sqrt{\frac{70 \, a c^{2} d^{5} e + 44 \, a^{2} c d^{3} e^{3} + 6 \, a^{3} d e^{5} + {\left(c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}} \log\left(-{\left(625 \, c^{4} d^{8} - 750 \, a c^{3} d^{6} e^{2} - 1376 \, a^{2} c^{2} d^{4} e^{4} - 594 \, a^{3} c d^{2} e^{6} - 81 \, a^{4} e^{8}\right)} x + {\left(125 \, c^{6} d^{9} - 170 \, a c^{5} d^{7} e^{2} - 244 \, a^{2} c^{4} d^{5} e^{4} - 86 \, a^{3} c^{3} d^{3} e^{6} - 9 \, a^{4} c^{2} d e^{8} + {\left(7 \, c^{10} d^{10} e + 31 \, a c^{9} d^{8} e^{3} + 54 \, a^{2} c^{8} d^{6} e^{5} + 46 \, a^{3} c^{7} d^{4} e^{7} + 19 \, a^{4} c^{6} d^{2} e^{9} + 3 \, a^{5} c^{5} e^{11}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}\right)} \sqrt{\frac{70 \, a c^{2} d^{5} e + 44 \, a^{2} c d^{3} e^{3} + 6 \, a^{3} d e^{5} + {\left(c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}\right) + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)} \sqrt{\frac{70 \, a c^{2} d^{5} e + 44 \, a^{2} c d^{3} e^{3} + 6 \, a^{3} d e^{5} + {\left(c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}} \log\left(-{\left(625 \, c^{4} d^{8} - 750 \, a c^{3} d^{6} e^{2} - 1376 \, a^{2} c^{2} d^{4} e^{4} - 594 \, a^{3} c d^{2} e^{6} - 81 \, a^{4} e^{8}\right)} x - {\left(125 \, c^{6} d^{9} - 170 \, a c^{5} d^{7} e^{2} - 244 \, a^{2} c^{4} d^{5} e^{4} - 86 \, a^{3} c^{3} d^{3} e^{6} - 9 \, a^{4} c^{2} d e^{8} + {\left(7 \, c^{10} d^{10} e + 31 \, a c^{9} d^{8} e^{3} + 54 \, a^{2} c^{8} d^{6} e^{5} + 46 \, a^{3} c^{7} d^{4} e^{7} + 19 \, a^{4} c^{6} d^{2} e^{9} + 3 \, a^{5} c^{5} e^{11}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}\right)} \sqrt{\frac{70 \, a c^{2} d^{5} e + 44 \, a^{2} c d^{3} e^{3} + 6 \, a^{3} d e^{5} + {\left(c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}\right) - {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)} \sqrt{\frac{70 \, a c^{2} d^{5} e + 44 \, a^{2} c d^{3} e^{3} + 6 \, a^{3} d e^{5} - {\left(c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}} \log\left(-{\left(625 \, c^{4} d^{8} - 750 \, a c^{3} d^{6} e^{2} - 1376 \, a^{2} c^{2} d^{4} e^{4} - 594 \, a^{3} c d^{2} e^{6} - 81 \, a^{4} e^{8}\right)} x + {\left(125 \, c^{6} d^{9} - 170 \, a c^{5} d^{7} e^{2} - 244 \, a^{2} c^{4} d^{5} e^{4} - 86 \, a^{3} c^{3} d^{3} e^{6} - 9 \, a^{4} c^{2} d e^{8} - {\left(7 \, c^{10} d^{10} e + 31 \, a c^{9} d^{8} e^{3} + 54 \, a^{2} c^{8} d^{6} e^{5} + 46 \, a^{3} c^{7} d^{4} e^{7} + 19 \, a^{4} c^{6} d^{2} e^{9} + 3 \, a^{5} c^{5} e^{11}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}\right)} \sqrt{\frac{70 \, a c^{2} d^{5} e + 44 \, a^{2} c d^{3} e^{3} + 6 \, a^{3} d e^{5} - {\left(c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}\right) + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)} \sqrt{\frac{70 \, a c^{2} d^{5} e + 44 \, a^{2} c d^{3} e^{3} + 6 \, a^{3} d e^{5} - {\left(c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}} \log\left(-{\left(625 \, c^{4} d^{8} - 750 \, a c^{3} d^{6} e^{2} - 1376 \, a^{2} c^{2} d^{4} e^{4} - 594 \, a^{3} c d^{2} e^{6} - 81 \, a^{4} e^{8}\right)} x - {\left(125 \, c^{6} d^{9} - 170 \, a c^{5} d^{7} e^{2} - 244 \, a^{2} c^{4} d^{5} e^{4} - 86 \, a^{3} c^{3} d^{3} e^{6} - 9 \, a^{4} c^{2} d e^{8} - {\left(7 \, c^{10} d^{10} e + 31 \, a c^{9} d^{8} e^{3} + 54 \, a^{2} c^{8} d^{6} e^{5} + 46 \, a^{3} c^{7} d^{4} e^{7} + 19 \, a^{4} c^{6} d^{2} e^{9} + 3 \, a^{5} c^{5} e^{11}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}\right)} \sqrt{\frac{70 \, a c^{2} d^{5} e + 44 \, a^{2} c d^{3} e^{3} + 6 \, a^{3} d e^{5} - {\left(c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}\right)} \sqrt{-\frac{625 \, a c^{6} d^{12} - 1950 \, a^{2} c^{5} d^{10} e^{2} - 529 \, a^{3} c^{4} d^{8} e^{4} + 2748 \, a^{4} c^{3} d^{6} e^{6} + 2383 \, a^{5} c^{2} d^{4} e^{8} + 738 \, a^{6} c d^{2} e^{10} + 81 \, a^{7} e^{12}}{c^{15} d^{16} + 8 \, a c^{14} d^{14} e^{2} + 28 \, a^{2} c^{13} d^{12} e^{4} + 56 \, a^{3} c^{12} d^{10} e^{6} + 70 \, a^{4} c^{11} d^{8} e^{8} + 56 \, a^{5} c^{10} d^{6} e^{10} + 28 \, a^{6} c^{9} d^{4} e^{12} + 8 \, a^{7} c^{8} d^{2} e^{14} + a^{8} c^{7} e^{16}}}}{c^{7} d^{8} + 4 \, a c^{6} d^{6} e^{2} + 6 \, a^{2} c^{5} d^{4} e^{4} + 4 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}}\right) - 4 \, {\left(a c d^{3} + a^{2} d e^{2}\right)} x}{16 \, {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)}}\right]"," ",0,"[-1/16*(4*(a*c*d^2*e + a^2*e^3)*x^3 - (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4)*sqrt((70*a*c^2*d^5*e + 44*a^2*c*d^3*e^3 + 6*a^3*d*e^5 + (c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8))*log(-(625*c^4*d^8 - 750*a*c^3*d^6*e^2 - 1376*a^2*c^2*d^4*e^4 - 594*a^3*c*d^2*e^6 - 81*a^4*e^8)*x + (125*c^6*d^9 - 170*a*c^5*d^7*e^2 - 244*a^2*c^4*d^5*e^4 - 86*a^3*c^3*d^3*e^6 - 9*a^4*c^2*d*e^8 + (7*c^10*d^10*e + 31*a*c^9*d^8*e^3 + 54*a^2*c^8*d^6*e^5 + 46*a^3*c^7*d^4*e^7 + 19*a^4*c^6*d^2*e^9 + 3*a^5*c^5*e^11)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))*sqrt((70*a*c^2*d^5*e + 44*a^2*c*d^3*e^3 + 6*a^3*d*e^5 + (c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8))) + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4)*sqrt((70*a*c^2*d^5*e + 44*a^2*c*d^3*e^3 + 6*a^3*d*e^5 + (c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8))*log(-(625*c^4*d^8 - 750*a*c^3*d^6*e^2 - 1376*a^2*c^2*d^4*e^4 - 594*a^3*c*d^2*e^6 - 81*a^4*e^8)*x - (125*c^6*d^9 - 170*a*c^5*d^7*e^2 - 244*a^2*c^4*d^5*e^4 - 86*a^3*c^3*d^3*e^6 - 9*a^4*c^2*d*e^8 + (7*c^10*d^10*e + 31*a*c^9*d^8*e^3 + 54*a^2*c^8*d^6*e^5 + 46*a^3*c^7*d^4*e^7 + 19*a^4*c^6*d^2*e^9 + 3*a^5*c^5*e^11)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))*sqrt((70*a*c^2*d^5*e + 44*a^2*c*d^3*e^3 + 6*a^3*d*e^5 + (c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8))) - (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4)*sqrt((70*a*c^2*d^5*e + 44*a^2*c*d^3*e^3 + 6*a^3*d*e^5 - (c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8))*log(-(625*c^4*d^8 - 750*a*c^3*d^6*e^2 - 1376*a^2*c^2*d^4*e^4 - 594*a^3*c*d^2*e^6 - 81*a^4*e^8)*x + (125*c^6*d^9 - 170*a*c^5*d^7*e^2 - 244*a^2*c^4*d^5*e^4 - 86*a^3*c^3*d^3*e^6 - 9*a^4*c^2*d*e^8 - (7*c^10*d^10*e + 31*a*c^9*d^8*e^3 + 54*a^2*c^8*d^6*e^5 + 46*a^3*c^7*d^4*e^7 + 19*a^4*c^6*d^2*e^9 + 3*a^5*c^5*e^11)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))*sqrt((70*a*c^2*d^5*e + 44*a^2*c*d^3*e^3 + 6*a^3*d*e^5 - (c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8))) + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4)*sqrt((70*a*c^2*d^5*e + 44*a^2*c*d^3*e^3 + 6*a^3*d*e^5 - (c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8))*log(-(625*c^4*d^8 - 750*a*c^3*d^6*e^2 - 1376*a^2*c^2*d^4*e^4 - 594*a^3*c*d^2*e^6 - 81*a^4*e^8)*x - (125*c^6*d^9 - 170*a*c^5*d^7*e^2 - 244*a^2*c^4*d^5*e^4 - 86*a^3*c^3*d^3*e^6 - 9*a^4*c^2*d*e^8 - (7*c^10*d^10*e + 31*a*c^9*d^8*e^3 + 54*a^2*c^8*d^6*e^5 + 46*a^3*c^7*d^4*e^7 + 19*a^4*c^6*d^2*e^9 + 3*a^5*c^5*e^11)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))*sqrt((70*a*c^2*d^5*e + 44*a^2*c*d^3*e^3 + 6*a^3*d*e^5 - (c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8))) - 8*(c^2*d^3*x^4 + a*c*d^3)*sqrt(-d/e)*log((e*x^2 + 2*e*x*sqrt(-d/e) - d)/(e*x^2 + d)) - 4*(a*c*d^3 + a^2*d*e^2)*x)/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4), -1/16*(4*(a*c*d^2*e + a^2*e^3)*x^3 - 16*(c^2*d^3*x^4 + a*c*d^3)*sqrt(d/e)*arctan(e*x*sqrt(d/e)/d) - (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4)*sqrt((70*a*c^2*d^5*e + 44*a^2*c*d^3*e^3 + 6*a^3*d*e^5 + (c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8))*log(-(625*c^4*d^8 - 750*a*c^3*d^6*e^2 - 1376*a^2*c^2*d^4*e^4 - 594*a^3*c*d^2*e^6 - 81*a^4*e^8)*x + (125*c^6*d^9 - 170*a*c^5*d^7*e^2 - 244*a^2*c^4*d^5*e^4 - 86*a^3*c^3*d^3*e^6 - 9*a^4*c^2*d*e^8 + (7*c^10*d^10*e + 31*a*c^9*d^8*e^3 + 54*a^2*c^8*d^6*e^5 + 46*a^3*c^7*d^4*e^7 + 19*a^4*c^6*d^2*e^9 + 3*a^5*c^5*e^11)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))*sqrt((70*a*c^2*d^5*e + 44*a^2*c*d^3*e^3 + 6*a^3*d*e^5 + (c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8))) + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4)*sqrt((70*a*c^2*d^5*e + 44*a^2*c*d^3*e^3 + 6*a^3*d*e^5 + (c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8))*log(-(625*c^4*d^8 - 750*a*c^3*d^6*e^2 - 1376*a^2*c^2*d^4*e^4 - 594*a^3*c*d^2*e^6 - 81*a^4*e^8)*x - (125*c^6*d^9 - 170*a*c^5*d^7*e^2 - 244*a^2*c^4*d^5*e^4 - 86*a^3*c^3*d^3*e^6 - 9*a^4*c^2*d*e^8 + (7*c^10*d^10*e + 31*a*c^9*d^8*e^3 + 54*a^2*c^8*d^6*e^5 + 46*a^3*c^7*d^4*e^7 + 19*a^4*c^6*d^2*e^9 + 3*a^5*c^5*e^11)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))*sqrt((70*a*c^2*d^5*e + 44*a^2*c*d^3*e^3 + 6*a^3*d*e^5 + (c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8))) - (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4)*sqrt((70*a*c^2*d^5*e + 44*a^2*c*d^3*e^3 + 6*a^3*d*e^5 - (c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8))*log(-(625*c^4*d^8 - 750*a*c^3*d^6*e^2 - 1376*a^2*c^2*d^4*e^4 - 594*a^3*c*d^2*e^6 - 81*a^4*e^8)*x + (125*c^6*d^9 - 170*a*c^5*d^7*e^2 - 244*a^2*c^4*d^5*e^4 - 86*a^3*c^3*d^3*e^6 - 9*a^4*c^2*d*e^8 - (7*c^10*d^10*e + 31*a*c^9*d^8*e^3 + 54*a^2*c^8*d^6*e^5 + 46*a^3*c^7*d^4*e^7 + 19*a^4*c^6*d^2*e^9 + 3*a^5*c^5*e^11)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))*sqrt((70*a*c^2*d^5*e + 44*a^2*c*d^3*e^3 + 6*a^3*d*e^5 - (c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8))) + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4)*sqrt((70*a*c^2*d^5*e + 44*a^2*c*d^3*e^3 + 6*a^3*d*e^5 - (c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8))*log(-(625*c^4*d^8 - 750*a*c^3*d^6*e^2 - 1376*a^2*c^2*d^4*e^4 - 594*a^3*c*d^2*e^6 - 81*a^4*e^8)*x - (125*c^6*d^9 - 170*a*c^5*d^7*e^2 - 244*a^2*c^4*d^5*e^4 - 86*a^3*c^3*d^3*e^6 - 9*a^4*c^2*d*e^8 - (7*c^10*d^10*e + 31*a*c^9*d^8*e^3 + 54*a^2*c^8*d^6*e^5 + 46*a^3*c^7*d^4*e^7 + 19*a^4*c^6*d^2*e^9 + 3*a^5*c^5*e^11)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))*sqrt((70*a*c^2*d^5*e + 44*a^2*c*d^3*e^3 + 6*a^3*d*e^5 - (c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)*sqrt(-(625*a*c^6*d^12 - 1950*a^2*c^5*d^10*e^2 - 529*a^3*c^4*d^8*e^4 + 2748*a^4*c^3*d^6*e^6 + 2383*a^5*c^2*d^4*e^8 + 738*a^6*c*d^2*e^10 + 81*a^7*e^12)/(c^15*d^16 + 8*a*c^14*d^14*e^2 + 28*a^2*c^13*d^12*e^4 + 56*a^3*c^12*d^10*e^6 + 70*a^4*c^11*d^8*e^8 + 56*a^5*c^10*d^6*e^10 + 28*a^6*c^9*d^4*e^12 + 8*a^7*c^8*d^2*e^14 + a^8*c^7*e^16)))/(c^7*d^8 + 4*a*c^6*d^6*e^2 + 6*a^2*c^5*d^4*e^4 + 4*a^3*c^4*d^2*e^6 + a^4*c^3*e^8))) - 4*(a*c*d^3 + a^2*d*e^2)*x)/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4)]","B",0
253,1,9822,0,27.276899," ","integrate(x^6/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(c^{2} d^{3} + a c d e^{2}\right)} x^{3} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)} \sqrt{-\frac{30 \, c^{2} d^{5} e - 4 \, a c d^{3} e^{3} - 2 \, a^{2} d e^{5} + {\left(c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}}{c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}}} \log\left(-{\left(81 \, c^{4} d^{8} - 270 \, a c^{3} d^{6} e^{2} - 112 \, a^{2} c^{2} d^{4} e^{4} - 18 \, a^{3} c d^{2} e^{6} - a^{4} e^{8}\right)} x + {\left(45 \, a c^{5} d^{8} e - 146 \, a^{2} c^{4} d^{6} e^{3} - 76 \, a^{3} c^{3} d^{4} e^{5} - 14 \, a^{4} c^{2} d^{2} e^{7} - a^{5} c e^{9} - {\left(3 \, a c^{9} d^{11} + 11 \, a^{2} c^{8} d^{9} e^{2} + 14 \, a^{3} c^{7} d^{7} e^{4} + 6 \, a^{4} c^{6} d^{5} e^{6} - a^{5} c^{5} d^{3} e^{8} - a^{6} c^{4} d e^{10}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}\right)} \sqrt{-\frac{30 \, c^{2} d^{5} e - 4 \, a c d^{3} e^{3} - 2 \, a^{2} d e^{5} + {\left(c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}}{c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}}}\right) - {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)} \sqrt{-\frac{30 \, c^{2} d^{5} e - 4 \, a c d^{3} e^{3} - 2 \, a^{2} d e^{5} + {\left(c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}}{c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}}} \log\left(-{\left(81 \, c^{4} d^{8} - 270 \, a c^{3} d^{6} e^{2} - 112 \, a^{2} c^{2} d^{4} e^{4} - 18 \, a^{3} c d^{2} e^{6} - a^{4} e^{8}\right)} x - {\left(45 \, a c^{5} d^{8} e - 146 \, a^{2} c^{4} d^{6} e^{3} - 76 \, a^{3} c^{3} d^{4} e^{5} - 14 \, a^{4} c^{2} d^{2} e^{7} - a^{5} c e^{9} - {\left(3 \, a c^{9} d^{11} + 11 \, a^{2} c^{8} d^{9} e^{2} + 14 \, a^{3} c^{7} d^{7} e^{4} + 6 \, a^{4} c^{6} d^{5} e^{6} - a^{5} c^{5} d^{3} e^{8} - a^{6} c^{4} d e^{10}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}\right)} \sqrt{-\frac{30 \, c^{2} d^{5} e - 4 \, a c d^{3} e^{3} - 2 \, a^{2} d e^{5} + {\left(c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}}{c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}}}\right) + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)} \sqrt{-\frac{30 \, c^{2} d^{5} e - 4 \, a c d^{3} e^{3} - 2 \, a^{2} d e^{5} - {\left(c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}}{c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}}} \log\left(-{\left(81 \, c^{4} d^{8} - 270 \, a c^{3} d^{6} e^{2} - 112 \, a^{2} c^{2} d^{4} e^{4} - 18 \, a^{3} c d^{2} e^{6} - a^{4} e^{8}\right)} x + {\left(45 \, a c^{5} d^{8} e - 146 \, a^{2} c^{4} d^{6} e^{3} - 76 \, a^{3} c^{3} d^{4} e^{5} - 14 \, a^{4} c^{2} d^{2} e^{7} - a^{5} c e^{9} + {\left(3 \, a c^{9} d^{11} + 11 \, a^{2} c^{8} d^{9} e^{2} + 14 \, a^{3} c^{7} d^{7} e^{4} + 6 \, a^{4} c^{6} d^{5} e^{6} - a^{5} c^{5} d^{3} e^{8} - a^{6} c^{4} d e^{10}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}\right)} \sqrt{-\frac{30 \, c^{2} d^{5} e - 4 \, a c d^{3} e^{3} - 2 \, a^{2} d e^{5} - {\left(c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}}{c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}}}\right) - {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)} \sqrt{-\frac{30 \, c^{2} d^{5} e - 4 \, a c d^{3} e^{3} - 2 \, a^{2} d e^{5} - {\left(c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}}{c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}}} \log\left(-{\left(81 \, c^{4} d^{8} - 270 \, a c^{3} d^{6} e^{2} - 112 \, a^{2} c^{2} d^{4} e^{4} - 18 \, a^{3} c d^{2} e^{6} - a^{4} e^{8}\right)} x - {\left(45 \, a c^{5} d^{8} e - 146 \, a^{2} c^{4} d^{6} e^{3} - 76 \, a^{3} c^{3} d^{4} e^{5} - 14 \, a^{4} c^{2} d^{2} e^{7} - a^{5} c e^{9} + {\left(3 \, a c^{9} d^{11} + 11 \, a^{2} c^{8} d^{9} e^{2} + 14 \, a^{3} c^{7} d^{7} e^{4} + 6 \, a^{4} c^{6} d^{5} e^{6} - a^{5} c^{5} d^{3} e^{8} - a^{6} c^{4} d e^{10}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}\right)} \sqrt{-\frac{30 \, c^{2} d^{5} e - 4 \, a c d^{3} e^{3} - 2 \, a^{2} d e^{5} - {\left(c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}}{c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}}}\right) - 8 \, {\left(c^{2} d^{2} x^{4} + a c d^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 4 \, {\left(a c d^{2} e + a^{2} e^{3}\right)} x}{16 \, {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)}}, -\frac{4 \, {\left(c^{2} d^{3} + a c d e^{2}\right)} x^{3} + 16 \, {\left(c^{2} d^{2} x^{4} + a c d^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)} \sqrt{-\frac{30 \, c^{2} d^{5} e - 4 \, a c d^{3} e^{3} - 2 \, a^{2} d e^{5} + {\left(c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}}{c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}}} \log\left(-{\left(81 \, c^{4} d^{8} - 270 \, a c^{3} d^{6} e^{2} - 112 \, a^{2} c^{2} d^{4} e^{4} - 18 \, a^{3} c d^{2} e^{6} - a^{4} e^{8}\right)} x + {\left(45 \, a c^{5} d^{8} e - 146 \, a^{2} c^{4} d^{6} e^{3} - 76 \, a^{3} c^{3} d^{4} e^{5} - 14 \, a^{4} c^{2} d^{2} e^{7} - a^{5} c e^{9} - {\left(3 \, a c^{9} d^{11} + 11 \, a^{2} c^{8} d^{9} e^{2} + 14 \, a^{3} c^{7} d^{7} e^{4} + 6 \, a^{4} c^{6} d^{5} e^{6} - a^{5} c^{5} d^{3} e^{8} - a^{6} c^{4} d e^{10}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}\right)} \sqrt{-\frac{30 \, c^{2} d^{5} e - 4 \, a c d^{3} e^{3} - 2 \, a^{2} d e^{5} + {\left(c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}}{c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}}}\right) - {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)} \sqrt{-\frac{30 \, c^{2} d^{5} e - 4 \, a c d^{3} e^{3} - 2 \, a^{2} d e^{5} + {\left(c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}}{c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}}} \log\left(-{\left(81 \, c^{4} d^{8} - 270 \, a c^{3} d^{6} e^{2} - 112 \, a^{2} c^{2} d^{4} e^{4} - 18 \, a^{3} c d^{2} e^{6} - a^{4} e^{8}\right)} x - {\left(45 \, a c^{5} d^{8} e - 146 \, a^{2} c^{4} d^{6} e^{3} - 76 \, a^{3} c^{3} d^{4} e^{5} - 14 \, a^{4} c^{2} d^{2} e^{7} - a^{5} c e^{9} - {\left(3 \, a c^{9} d^{11} + 11 \, a^{2} c^{8} d^{9} e^{2} + 14 \, a^{3} c^{7} d^{7} e^{4} + 6 \, a^{4} c^{6} d^{5} e^{6} - a^{5} c^{5} d^{3} e^{8} - a^{6} c^{4} d e^{10}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}\right)} \sqrt{-\frac{30 \, c^{2} d^{5} e - 4 \, a c d^{3} e^{3} - 2 \, a^{2} d e^{5} + {\left(c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}}{c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}}}\right) + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)} \sqrt{-\frac{30 \, c^{2} d^{5} e - 4 \, a c d^{3} e^{3} - 2 \, a^{2} d e^{5} - {\left(c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}}{c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}}} \log\left(-{\left(81 \, c^{4} d^{8} - 270 \, a c^{3} d^{6} e^{2} - 112 \, a^{2} c^{2} d^{4} e^{4} - 18 \, a^{3} c d^{2} e^{6} - a^{4} e^{8}\right)} x + {\left(45 \, a c^{5} d^{8} e - 146 \, a^{2} c^{4} d^{6} e^{3} - 76 \, a^{3} c^{3} d^{4} e^{5} - 14 \, a^{4} c^{2} d^{2} e^{7} - a^{5} c e^{9} + {\left(3 \, a c^{9} d^{11} + 11 \, a^{2} c^{8} d^{9} e^{2} + 14 \, a^{3} c^{7} d^{7} e^{4} + 6 \, a^{4} c^{6} d^{5} e^{6} - a^{5} c^{5} d^{3} e^{8} - a^{6} c^{4} d e^{10}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}\right)} \sqrt{-\frac{30 \, c^{2} d^{5} e - 4 \, a c d^{3} e^{3} - 2 \, a^{2} d e^{5} - {\left(c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}}{c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}}}\right) - {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)} \sqrt{-\frac{30 \, c^{2} d^{5} e - 4 \, a c d^{3} e^{3} - 2 \, a^{2} d e^{5} - {\left(c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}}{c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}}} \log\left(-{\left(81 \, c^{4} d^{8} - 270 \, a c^{3} d^{6} e^{2} - 112 \, a^{2} c^{2} d^{4} e^{4} - 18 \, a^{3} c d^{2} e^{6} - a^{4} e^{8}\right)} x - {\left(45 \, a c^{5} d^{8} e - 146 \, a^{2} c^{4} d^{6} e^{3} - 76 \, a^{3} c^{3} d^{4} e^{5} - 14 \, a^{4} c^{2} d^{2} e^{7} - a^{5} c e^{9} + {\left(3 \, a c^{9} d^{11} + 11 \, a^{2} c^{8} d^{9} e^{2} + 14 \, a^{3} c^{7} d^{7} e^{4} + 6 \, a^{4} c^{6} d^{5} e^{6} - a^{5} c^{5} d^{3} e^{8} - a^{6} c^{4} d e^{10}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}\right)} \sqrt{-\frac{30 \, c^{2} d^{5} e - 4 \, a c d^{3} e^{3} - 2 \, a^{2} d e^{5} - {\left(c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}\right)} \sqrt{-\frac{81 \, c^{6} d^{12} - 558 \, a c^{5} d^{10} e^{2} + 799 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 143 \, a^{4} c^{2} d^{4} e^{8} + 18 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a c^{13} d^{16} + 8 \, a^{2} c^{12} d^{14} e^{2} + 28 \, a^{3} c^{11} d^{12} e^{4} + 56 \, a^{4} c^{10} d^{10} e^{6} + 70 \, a^{5} c^{9} d^{8} e^{8} + 56 \, a^{6} c^{8} d^{6} e^{10} + 28 \, a^{7} c^{7} d^{4} e^{12} + 8 \, a^{8} c^{6} d^{2} e^{14} + a^{9} c^{5} e^{16}}}}{c^{6} d^{8} + 4 \, a c^{5} d^{6} e^{2} + 6 \, a^{2} c^{4} d^{4} e^{4} + 4 \, a^{3} c^{3} d^{2} e^{6} + a^{4} c^{2} e^{8}}}\right) + 4 \, {\left(a c d^{2} e + a^{2} e^{3}\right)} x}{16 \, {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4}\right)}}\right]"," ",0,"[-1/16*(4*(c^2*d^3 + a*c*d*e^2)*x^3 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4)*sqrt(-(30*c^2*d^5*e - 4*a*c*d^3*e^3 - 2*a^2*d*e^5 + (c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))/(c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8))*log(-(81*c^4*d^8 - 270*a*c^3*d^6*e^2 - 112*a^2*c^2*d^4*e^4 - 18*a^3*c*d^2*e^6 - a^4*e^8)*x + (45*a*c^5*d^8*e - 146*a^2*c^4*d^6*e^3 - 76*a^3*c^3*d^4*e^5 - 14*a^4*c^2*d^2*e^7 - a^5*c*e^9 - (3*a*c^9*d^11 + 11*a^2*c^8*d^9*e^2 + 14*a^3*c^7*d^7*e^4 + 6*a^4*c^6*d^5*e^6 - a^5*c^5*d^3*e^8 - a^6*c^4*d*e^10)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))*sqrt(-(30*c^2*d^5*e - 4*a*c*d^3*e^3 - 2*a^2*d*e^5 + (c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))/(c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8))) - (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4)*sqrt(-(30*c^2*d^5*e - 4*a*c*d^3*e^3 - 2*a^2*d*e^5 + (c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))/(c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8))*log(-(81*c^4*d^8 - 270*a*c^3*d^6*e^2 - 112*a^2*c^2*d^4*e^4 - 18*a^3*c*d^2*e^6 - a^4*e^8)*x - (45*a*c^5*d^8*e - 146*a^2*c^4*d^6*e^3 - 76*a^3*c^3*d^4*e^5 - 14*a^4*c^2*d^2*e^7 - a^5*c*e^9 - (3*a*c^9*d^11 + 11*a^2*c^8*d^9*e^2 + 14*a^3*c^7*d^7*e^4 + 6*a^4*c^6*d^5*e^6 - a^5*c^5*d^3*e^8 - a^6*c^4*d*e^10)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))*sqrt(-(30*c^2*d^5*e - 4*a*c*d^3*e^3 - 2*a^2*d*e^5 + (c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))/(c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8))) + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4)*sqrt(-(30*c^2*d^5*e - 4*a*c*d^3*e^3 - 2*a^2*d*e^5 - (c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))/(c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8))*log(-(81*c^4*d^8 - 270*a*c^3*d^6*e^2 - 112*a^2*c^2*d^4*e^4 - 18*a^3*c*d^2*e^6 - a^4*e^8)*x + (45*a*c^5*d^8*e - 146*a^2*c^4*d^6*e^3 - 76*a^3*c^3*d^4*e^5 - 14*a^4*c^2*d^2*e^7 - a^5*c*e^9 + (3*a*c^9*d^11 + 11*a^2*c^8*d^9*e^2 + 14*a^3*c^7*d^7*e^4 + 6*a^4*c^6*d^5*e^6 - a^5*c^5*d^3*e^8 - a^6*c^4*d*e^10)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))*sqrt(-(30*c^2*d^5*e - 4*a*c*d^3*e^3 - 2*a^2*d*e^5 - (c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))/(c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8))) - (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4)*sqrt(-(30*c^2*d^5*e - 4*a*c*d^3*e^3 - 2*a^2*d*e^5 - (c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))/(c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8))*log(-(81*c^4*d^8 - 270*a*c^3*d^6*e^2 - 112*a^2*c^2*d^4*e^4 - 18*a^3*c*d^2*e^6 - a^4*e^8)*x - (45*a*c^5*d^8*e - 146*a^2*c^4*d^6*e^3 - 76*a^3*c^3*d^4*e^5 - 14*a^4*c^2*d^2*e^7 - a^5*c*e^9 + (3*a*c^9*d^11 + 11*a^2*c^8*d^9*e^2 + 14*a^3*c^7*d^7*e^4 + 6*a^4*c^6*d^5*e^6 - a^5*c^5*d^3*e^8 - a^6*c^4*d*e^10)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))*sqrt(-(30*c^2*d^5*e - 4*a*c*d^3*e^3 - 2*a^2*d*e^5 - (c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))/(c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8))) - 8*(c^2*d^2*x^4 + a*c*d^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 4*(a*c*d^2*e + a^2*e^3)*x)/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4), -1/16*(4*(c^2*d^3 + a*c*d*e^2)*x^3 + 16*(c^2*d^2*x^4 + a*c*d^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4)*sqrt(-(30*c^2*d^5*e - 4*a*c*d^3*e^3 - 2*a^2*d*e^5 + (c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))/(c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8))*log(-(81*c^4*d^8 - 270*a*c^3*d^6*e^2 - 112*a^2*c^2*d^4*e^4 - 18*a^3*c*d^2*e^6 - a^4*e^8)*x + (45*a*c^5*d^8*e - 146*a^2*c^4*d^6*e^3 - 76*a^3*c^3*d^4*e^5 - 14*a^4*c^2*d^2*e^7 - a^5*c*e^9 - (3*a*c^9*d^11 + 11*a^2*c^8*d^9*e^2 + 14*a^3*c^7*d^7*e^4 + 6*a^4*c^6*d^5*e^6 - a^5*c^5*d^3*e^8 - a^6*c^4*d*e^10)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))*sqrt(-(30*c^2*d^5*e - 4*a*c*d^3*e^3 - 2*a^2*d*e^5 + (c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))/(c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8))) - (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4)*sqrt(-(30*c^2*d^5*e - 4*a*c*d^3*e^3 - 2*a^2*d*e^5 + (c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))/(c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8))*log(-(81*c^4*d^8 - 270*a*c^3*d^6*e^2 - 112*a^2*c^2*d^4*e^4 - 18*a^3*c*d^2*e^6 - a^4*e^8)*x - (45*a*c^5*d^8*e - 146*a^2*c^4*d^6*e^3 - 76*a^3*c^3*d^4*e^5 - 14*a^4*c^2*d^2*e^7 - a^5*c*e^9 - (3*a*c^9*d^11 + 11*a^2*c^8*d^9*e^2 + 14*a^3*c^7*d^7*e^4 + 6*a^4*c^6*d^5*e^6 - a^5*c^5*d^3*e^8 - a^6*c^4*d*e^10)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))*sqrt(-(30*c^2*d^5*e - 4*a*c*d^3*e^3 - 2*a^2*d*e^5 + (c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))/(c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8))) + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4)*sqrt(-(30*c^2*d^5*e - 4*a*c*d^3*e^3 - 2*a^2*d*e^5 - (c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))/(c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8))*log(-(81*c^4*d^8 - 270*a*c^3*d^6*e^2 - 112*a^2*c^2*d^4*e^4 - 18*a^3*c*d^2*e^6 - a^4*e^8)*x + (45*a*c^5*d^8*e - 146*a^2*c^4*d^6*e^3 - 76*a^3*c^3*d^4*e^5 - 14*a^4*c^2*d^2*e^7 - a^5*c*e^9 + (3*a*c^9*d^11 + 11*a^2*c^8*d^9*e^2 + 14*a^3*c^7*d^7*e^4 + 6*a^4*c^6*d^5*e^6 - a^5*c^5*d^3*e^8 - a^6*c^4*d*e^10)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))*sqrt(-(30*c^2*d^5*e - 4*a*c*d^3*e^3 - 2*a^2*d*e^5 - (c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))/(c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8))) - (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4)*sqrt(-(30*c^2*d^5*e - 4*a*c*d^3*e^3 - 2*a^2*d*e^5 - (c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))/(c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8))*log(-(81*c^4*d^8 - 270*a*c^3*d^6*e^2 - 112*a^2*c^2*d^4*e^4 - 18*a^3*c*d^2*e^6 - a^4*e^8)*x - (45*a*c^5*d^8*e - 146*a^2*c^4*d^6*e^3 - 76*a^3*c^3*d^4*e^5 - 14*a^4*c^2*d^2*e^7 - a^5*c*e^9 + (3*a*c^9*d^11 + 11*a^2*c^8*d^9*e^2 + 14*a^3*c^7*d^7*e^4 + 6*a^4*c^6*d^5*e^6 - a^5*c^5*d^3*e^8 - a^6*c^4*d*e^10)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))*sqrt(-(30*c^2*d^5*e - 4*a*c*d^3*e^3 - 2*a^2*d*e^5 - (c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8)*sqrt(-(81*c^6*d^12 - 558*a*c^5*d^10*e^2 + 799*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 143*a^4*c^2*d^4*e^8 + 18*a^5*c*d^2*e^10 + a^6*e^12)/(a*c^13*d^16 + 8*a^2*c^12*d^14*e^2 + 28*a^3*c^11*d^12*e^4 + 56*a^4*c^10*d^10*e^6 + 70*a^5*c^9*d^8*e^8 + 56*a^6*c^8*d^6*e^10 + 28*a^7*c^7*d^4*e^12 + 8*a^8*c^6*d^2*e^14 + a^9*c^5*e^16)))/(c^6*d^8 + 4*a*c^5*d^6*e^2 + 6*a^2*c^4*d^4*e^4 + 4*a^3*c^3*d^2*e^6 + a^4*c^2*e^8))) + 4*(a*c*d^2*e + a^2*e^3)*x)/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4)]","B",0
254,1,9678,0,24.279674," ","integrate(x^4/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(c d^{2} e + a e^{3}\right)} x^{3} - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} + {\left(a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}} \log\left(-{\left(c^{4} d^{8} - 14 \, a c^{3} d^{6} e^{2} + 14 \, a^{3} c d^{2} e^{6} - a^{4} e^{8}\right)} x + {\left(a c^{5} d^{9} - 18 \, a^{2} c^{4} d^{7} e^{2} + 60 \, a^{3} c^{3} d^{5} e^{4} - 46 \, a^{4} c^{2} d^{3} e^{6} + 3 \, a^{5} c d e^{8} + {\left(3 \, a^{3} c^{7} d^{10} e + 11 \, a^{4} c^{6} d^{8} e^{3} + 14 \, a^{5} c^{5} d^{6} e^{5} + 6 \, a^{6} c^{4} d^{4} e^{7} - a^{7} c^{3} d^{2} e^{9} - a^{8} c^{2} e^{11}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}\right)} \sqrt{\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} + {\left(a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}\right) + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} + {\left(a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}} \log\left(-{\left(c^{4} d^{8} - 14 \, a c^{3} d^{6} e^{2} + 14 \, a^{3} c d^{2} e^{6} - a^{4} e^{8}\right)} x - {\left(a c^{5} d^{9} - 18 \, a^{2} c^{4} d^{7} e^{2} + 60 \, a^{3} c^{3} d^{5} e^{4} - 46 \, a^{4} c^{2} d^{3} e^{6} + 3 \, a^{5} c d e^{8} + {\left(3 \, a^{3} c^{7} d^{10} e + 11 \, a^{4} c^{6} d^{8} e^{3} + 14 \, a^{5} c^{5} d^{6} e^{5} + 6 \, a^{6} c^{4} d^{4} e^{7} - a^{7} c^{3} d^{2} e^{9} - a^{8} c^{2} e^{11}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}\right)} \sqrt{\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} + {\left(a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}\right) - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} - {\left(a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}} \log\left(-{\left(c^{4} d^{8} - 14 \, a c^{3} d^{6} e^{2} + 14 \, a^{3} c d^{2} e^{6} - a^{4} e^{8}\right)} x + {\left(a c^{5} d^{9} - 18 \, a^{2} c^{4} d^{7} e^{2} + 60 \, a^{3} c^{3} d^{5} e^{4} - 46 \, a^{4} c^{2} d^{3} e^{6} + 3 \, a^{5} c d e^{8} - {\left(3 \, a^{3} c^{7} d^{10} e + 11 \, a^{4} c^{6} d^{8} e^{3} + 14 \, a^{5} c^{5} d^{6} e^{5} + 6 \, a^{6} c^{4} d^{4} e^{7} - a^{7} c^{3} d^{2} e^{9} - a^{8} c^{2} e^{11}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}\right)} \sqrt{\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} - {\left(a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}\right) + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} - {\left(a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}} \log\left(-{\left(c^{4} d^{8} - 14 \, a c^{3} d^{6} e^{2} + 14 \, a^{3} c d^{2} e^{6} - a^{4} e^{8}\right)} x - {\left(a c^{5} d^{9} - 18 \, a^{2} c^{4} d^{7} e^{2} + 60 \, a^{3} c^{3} d^{5} e^{4} - 46 \, a^{4} c^{2} d^{3} e^{6} + 3 \, a^{5} c d e^{8} - {\left(3 \, a^{3} c^{7} d^{10} e + 11 \, a^{4} c^{6} d^{8} e^{3} + 14 \, a^{5} c^{5} d^{6} e^{5} + 6 \, a^{6} c^{4} d^{4} e^{7} - a^{7} c^{3} d^{2} e^{9} - a^{8} c^{2} e^{11}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}\right)} \sqrt{\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} - {\left(a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}\right) + 8 \, {\left(c d e x^{4} + a d e\right)} \sqrt{-d e} \log\left(\frac{e x^{2} + 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) - 4 \, {\left(c d^{3} + a d e^{2}\right)} x}{16 \, {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{4}\right)}}, \frac{4 \, {\left(c d^{2} e + a e^{3}\right)} x^{3} + 16 \, {\left(c d e x^{4} + a d e\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} + {\left(a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}} \log\left(-{\left(c^{4} d^{8} - 14 \, a c^{3} d^{6} e^{2} + 14 \, a^{3} c d^{2} e^{6} - a^{4} e^{8}\right)} x + {\left(a c^{5} d^{9} - 18 \, a^{2} c^{4} d^{7} e^{2} + 60 \, a^{3} c^{3} d^{5} e^{4} - 46 \, a^{4} c^{2} d^{3} e^{6} + 3 \, a^{5} c d e^{8} + {\left(3 \, a^{3} c^{7} d^{10} e + 11 \, a^{4} c^{6} d^{8} e^{3} + 14 \, a^{5} c^{5} d^{6} e^{5} + 6 \, a^{6} c^{4} d^{4} e^{7} - a^{7} c^{3} d^{2} e^{9} - a^{8} c^{2} e^{11}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}\right)} \sqrt{\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} + {\left(a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}\right) + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} + {\left(a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}} \log\left(-{\left(c^{4} d^{8} - 14 \, a c^{3} d^{6} e^{2} + 14 \, a^{3} c d^{2} e^{6} - a^{4} e^{8}\right)} x - {\left(a c^{5} d^{9} - 18 \, a^{2} c^{4} d^{7} e^{2} + 60 \, a^{3} c^{3} d^{5} e^{4} - 46 \, a^{4} c^{2} d^{3} e^{6} + 3 \, a^{5} c d e^{8} + {\left(3 \, a^{3} c^{7} d^{10} e + 11 \, a^{4} c^{6} d^{8} e^{3} + 14 \, a^{5} c^{5} d^{6} e^{5} + 6 \, a^{6} c^{4} d^{4} e^{7} - a^{7} c^{3} d^{2} e^{9} - a^{8} c^{2} e^{11}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}\right)} \sqrt{\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} + {\left(a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}\right) - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} - {\left(a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}} \log\left(-{\left(c^{4} d^{8} - 14 \, a c^{3} d^{6} e^{2} + 14 \, a^{3} c d^{2} e^{6} - a^{4} e^{8}\right)} x + {\left(a c^{5} d^{9} - 18 \, a^{2} c^{4} d^{7} e^{2} + 60 \, a^{3} c^{3} d^{5} e^{4} - 46 \, a^{4} c^{2} d^{3} e^{6} + 3 \, a^{5} c d e^{8} - {\left(3 \, a^{3} c^{7} d^{10} e + 11 \, a^{4} c^{6} d^{8} e^{3} + 14 \, a^{5} c^{5} d^{6} e^{5} + 6 \, a^{6} c^{4} d^{4} e^{7} - a^{7} c^{3} d^{2} e^{9} - a^{8} c^{2} e^{11}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}\right)} \sqrt{\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} - {\left(a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}\right) + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} - {\left(a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}} \log\left(-{\left(c^{4} d^{8} - 14 \, a c^{3} d^{6} e^{2} + 14 \, a^{3} c d^{2} e^{6} - a^{4} e^{8}\right)} x - {\left(a c^{5} d^{9} - 18 \, a^{2} c^{4} d^{7} e^{2} + 60 \, a^{3} c^{3} d^{5} e^{4} - 46 \, a^{4} c^{2} d^{3} e^{6} + 3 \, a^{5} c d e^{8} - {\left(3 \, a^{3} c^{7} d^{10} e + 11 \, a^{4} c^{6} d^{8} e^{3} + 14 \, a^{5} c^{5} d^{6} e^{5} + 6 \, a^{6} c^{4} d^{4} e^{7} - a^{7} c^{3} d^{2} e^{9} - a^{8} c^{2} e^{11}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}\right)} \sqrt{\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} - {\left(a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{11} d^{16} + 8 \, a^{4} c^{10} d^{14} e^{2} + 28 \, a^{5} c^{9} d^{12} e^{4} + 56 \, a^{6} c^{8} d^{10} e^{6} + 70 \, a^{7} c^{7} d^{8} e^{8} + 56 \, a^{8} c^{6} d^{6} e^{10} + 28 \, a^{9} c^{5} d^{4} e^{12} + 8 \, a^{10} c^{4} d^{2} e^{14} + a^{11} c^{3} e^{16}}}}{a c^{5} d^{8} + 4 \, a^{2} c^{4} d^{6} e^{2} + 6 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} + a^{5} c e^{8}}}\right) - 4 \, {\left(c d^{3} + a d e^{2}\right)} x}{16 \, {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{4}\right)}}\right]"," ",0,"[1/16*(4*(c*d^2*e + a*e^3)*x^3 - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^4)*sqrt((6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 + (a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8))*log(-(c^4*d^8 - 14*a*c^3*d^6*e^2 + 14*a^3*c*d^2*e^6 - a^4*e^8)*x + (a*c^5*d^9 - 18*a^2*c^4*d^7*e^2 + 60*a^3*c^3*d^5*e^4 - 46*a^4*c^2*d^3*e^6 + 3*a^5*c*d*e^8 + (3*a^3*c^7*d^10*e + 11*a^4*c^6*d^8*e^3 + 14*a^5*c^5*d^6*e^5 + 6*a^6*c^4*d^4*e^7 - a^7*c^3*d^2*e^9 - a^8*c^2*e^11)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))*sqrt((6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 + (a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8))) + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^4)*sqrt((6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 + (a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8))*log(-(c^4*d^8 - 14*a*c^3*d^6*e^2 + 14*a^3*c*d^2*e^6 - a^4*e^8)*x - (a*c^5*d^9 - 18*a^2*c^4*d^7*e^2 + 60*a^3*c^3*d^5*e^4 - 46*a^4*c^2*d^3*e^6 + 3*a^5*c*d*e^8 + (3*a^3*c^7*d^10*e + 11*a^4*c^6*d^8*e^3 + 14*a^5*c^5*d^6*e^5 + 6*a^6*c^4*d^4*e^7 - a^7*c^3*d^2*e^9 - a^8*c^2*e^11)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))*sqrt((6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 + (a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8))) - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^4)*sqrt((6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 - (a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8))*log(-(c^4*d^8 - 14*a*c^3*d^6*e^2 + 14*a^3*c*d^2*e^6 - a^4*e^8)*x + (a*c^5*d^9 - 18*a^2*c^4*d^7*e^2 + 60*a^3*c^3*d^5*e^4 - 46*a^4*c^2*d^3*e^6 + 3*a^5*c*d*e^8 - (3*a^3*c^7*d^10*e + 11*a^4*c^6*d^8*e^3 + 14*a^5*c^5*d^6*e^5 + 6*a^6*c^4*d^4*e^7 - a^7*c^3*d^2*e^9 - a^8*c^2*e^11)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))*sqrt((6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 - (a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8))) + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^4)*sqrt((6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 - (a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8))*log(-(c^4*d^8 - 14*a*c^3*d^6*e^2 + 14*a^3*c*d^2*e^6 - a^4*e^8)*x - (a*c^5*d^9 - 18*a^2*c^4*d^7*e^2 + 60*a^3*c^3*d^5*e^4 - 46*a^4*c^2*d^3*e^6 + 3*a^5*c*d*e^8 - (3*a^3*c^7*d^10*e + 11*a^4*c^6*d^8*e^3 + 14*a^5*c^5*d^6*e^5 + 6*a^6*c^4*d^4*e^7 - a^7*c^3*d^2*e^9 - a^8*c^2*e^11)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))*sqrt((6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 - (a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8))) + 8*(c*d*e*x^4 + a*d*e)*sqrt(-d*e)*log((e*x^2 + 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) - 4*(c*d^3 + a*d*e^2)*x)/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^4), 1/16*(4*(c*d^2*e + a*e^3)*x^3 + 16*(c*d*e*x^4 + a*d*e)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^4)*sqrt((6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 + (a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8))*log(-(c^4*d^8 - 14*a*c^3*d^6*e^2 + 14*a^3*c*d^2*e^6 - a^4*e^8)*x + (a*c^5*d^9 - 18*a^2*c^4*d^7*e^2 + 60*a^3*c^3*d^5*e^4 - 46*a^4*c^2*d^3*e^6 + 3*a^5*c*d*e^8 + (3*a^3*c^7*d^10*e + 11*a^4*c^6*d^8*e^3 + 14*a^5*c^5*d^6*e^5 + 6*a^6*c^4*d^4*e^7 - a^7*c^3*d^2*e^9 - a^8*c^2*e^11)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))*sqrt((6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 + (a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8))) + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^4)*sqrt((6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 + (a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8))*log(-(c^4*d^8 - 14*a*c^3*d^6*e^2 + 14*a^3*c*d^2*e^6 - a^4*e^8)*x - (a*c^5*d^9 - 18*a^2*c^4*d^7*e^2 + 60*a^3*c^3*d^5*e^4 - 46*a^4*c^2*d^3*e^6 + 3*a^5*c*d*e^8 + (3*a^3*c^7*d^10*e + 11*a^4*c^6*d^8*e^3 + 14*a^5*c^5*d^6*e^5 + 6*a^6*c^4*d^4*e^7 - a^7*c^3*d^2*e^9 - a^8*c^2*e^11)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))*sqrt((6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 + (a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8))) - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^4)*sqrt((6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 - (a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8))*log(-(c^4*d^8 - 14*a*c^3*d^6*e^2 + 14*a^3*c*d^2*e^6 - a^4*e^8)*x + (a*c^5*d^9 - 18*a^2*c^4*d^7*e^2 + 60*a^3*c^3*d^5*e^4 - 46*a^4*c^2*d^3*e^6 + 3*a^5*c*d*e^8 - (3*a^3*c^7*d^10*e + 11*a^4*c^6*d^8*e^3 + 14*a^5*c^5*d^6*e^5 + 6*a^6*c^4*d^4*e^7 - a^7*c^3*d^2*e^9 - a^8*c^2*e^11)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))*sqrt((6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 - (a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8))) + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^4)*sqrt((6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 - (a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8))*log(-(c^4*d^8 - 14*a*c^3*d^6*e^2 + 14*a^3*c*d^2*e^6 - a^4*e^8)*x - (a*c^5*d^9 - 18*a^2*c^4*d^7*e^2 + 60*a^3*c^3*d^5*e^4 - 46*a^4*c^2*d^3*e^6 + 3*a^5*c*d*e^8 - (3*a^3*c^7*d^10*e + 11*a^4*c^6*d^8*e^3 + 14*a^5*c^5*d^6*e^5 + 6*a^6*c^4*d^4*e^7 - a^7*c^3*d^2*e^9 - a^8*c^2*e^11)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))*sqrt((6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 - (a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^11*d^16 + 8*a^4*c^10*d^14*e^2 + 28*a^5*c^9*d^12*e^4 + 56*a^6*c^8*d^10*e^6 + 70*a^7*c^7*d^8*e^8 + 56*a^8*c^6*d^6*e^10 + 28*a^9*c^5*d^4*e^12 + 8*a^10*c^4*d^2*e^14 + a^11*c^3*e^16)))/(a*c^5*d^8 + 4*a^2*c^4*d^6*e^2 + 6*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 + a^5*c*e^8))) - 4*(c*d^3 + a*d*e^2)*x)/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^4)]","B",0
255,1,9774,0,26.340018," ","integrate(x^2/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(c^{2} d^{3} + a c d e^{2}\right)} x^{3} + {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} - 30 \, a^{2} d e^{5} + {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}}{a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}}} \log\left(-{\left(c^{4} d^{8} + 18 \, a c^{3} d^{6} e^{2} + 112 \, a^{2} c^{2} d^{4} e^{4} + 270 \, a^{3} c d^{2} e^{6} - 81 \, a^{4} e^{8}\right)} x + {\left(a^{2} c^{4} d^{8} e + 6 \, a^{3} c^{3} d^{6} e^{3} + 4 \, a^{4} c^{2} d^{4} e^{5} - 102 \, a^{5} c d^{2} e^{7} + 27 \, a^{6} e^{9} - {\left(a^{4} c^{6} d^{11} + 9 \, a^{5} c^{5} d^{9} e^{2} + 26 \, a^{6} c^{4} d^{7} e^{4} + 34 \, a^{7} c^{3} d^{5} e^{6} + 21 \, a^{8} c^{2} d^{3} e^{8} + 5 \, a^{9} c d e^{10}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}\right)} \sqrt{\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} - 30 \, a^{2} d e^{5} + {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}}{a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}}}\right) - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} - 30 \, a^{2} d e^{5} + {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}}{a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}}} \log\left(-{\left(c^{4} d^{8} + 18 \, a c^{3} d^{6} e^{2} + 112 \, a^{2} c^{2} d^{4} e^{4} + 270 \, a^{3} c d^{2} e^{6} - 81 \, a^{4} e^{8}\right)} x - {\left(a^{2} c^{4} d^{8} e + 6 \, a^{3} c^{3} d^{6} e^{3} + 4 \, a^{4} c^{2} d^{4} e^{5} - 102 \, a^{5} c d^{2} e^{7} + 27 \, a^{6} e^{9} - {\left(a^{4} c^{6} d^{11} + 9 \, a^{5} c^{5} d^{9} e^{2} + 26 \, a^{6} c^{4} d^{7} e^{4} + 34 \, a^{7} c^{3} d^{5} e^{6} + 21 \, a^{8} c^{2} d^{3} e^{8} + 5 \, a^{9} c d e^{10}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}\right)} \sqrt{\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} - 30 \, a^{2} d e^{5} + {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}}{a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}}}\right) + {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} - 30 \, a^{2} d e^{5} - {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}}{a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}}} \log\left(-{\left(c^{4} d^{8} + 18 \, a c^{3} d^{6} e^{2} + 112 \, a^{2} c^{2} d^{4} e^{4} + 270 \, a^{3} c d^{2} e^{6} - 81 \, a^{4} e^{8}\right)} x + {\left(a^{2} c^{4} d^{8} e + 6 \, a^{3} c^{3} d^{6} e^{3} + 4 \, a^{4} c^{2} d^{4} e^{5} - 102 \, a^{5} c d^{2} e^{7} + 27 \, a^{6} e^{9} + {\left(a^{4} c^{6} d^{11} + 9 \, a^{5} c^{5} d^{9} e^{2} + 26 \, a^{6} c^{4} d^{7} e^{4} + 34 \, a^{7} c^{3} d^{5} e^{6} + 21 \, a^{8} c^{2} d^{3} e^{8} + 5 \, a^{9} c d e^{10}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}\right)} \sqrt{\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} - 30 \, a^{2} d e^{5} - {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}}{a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}}}\right) - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} - 30 \, a^{2} d e^{5} - {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}}{a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}}} \log\left(-{\left(c^{4} d^{8} + 18 \, a c^{3} d^{6} e^{2} + 112 \, a^{2} c^{2} d^{4} e^{4} + 270 \, a^{3} c d^{2} e^{6} - 81 \, a^{4} e^{8}\right)} x - {\left(a^{2} c^{4} d^{8} e + 6 \, a^{3} c^{3} d^{6} e^{3} + 4 \, a^{4} c^{2} d^{4} e^{5} - 102 \, a^{5} c d^{2} e^{7} + 27 \, a^{6} e^{9} + {\left(a^{4} c^{6} d^{11} + 9 \, a^{5} c^{5} d^{9} e^{2} + 26 \, a^{6} c^{4} d^{7} e^{4} + 34 \, a^{7} c^{3} d^{5} e^{6} + 21 \, a^{8} c^{2} d^{3} e^{8} + 5 \, a^{9} c d e^{10}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}\right)} \sqrt{\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} - 30 \, a^{2} d e^{5} - {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}}{a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}}}\right) + 8 \, {\left(a c e^{2} x^{4} + a^{2} e^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 4 \, {\left(a c d^{2} e + a^{2} e^{3}\right)} x}{16 \, {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)}}, \frac{4 \, {\left(c^{2} d^{3} + a c d e^{2}\right)} x^{3} - 16 \, {\left(a c e^{2} x^{4} + a^{2} e^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} - 30 \, a^{2} d e^{5} + {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}}{a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}}} \log\left(-{\left(c^{4} d^{8} + 18 \, a c^{3} d^{6} e^{2} + 112 \, a^{2} c^{2} d^{4} e^{4} + 270 \, a^{3} c d^{2} e^{6} - 81 \, a^{4} e^{8}\right)} x + {\left(a^{2} c^{4} d^{8} e + 6 \, a^{3} c^{3} d^{6} e^{3} + 4 \, a^{4} c^{2} d^{4} e^{5} - 102 \, a^{5} c d^{2} e^{7} + 27 \, a^{6} e^{9} - {\left(a^{4} c^{6} d^{11} + 9 \, a^{5} c^{5} d^{9} e^{2} + 26 \, a^{6} c^{4} d^{7} e^{4} + 34 \, a^{7} c^{3} d^{5} e^{6} + 21 \, a^{8} c^{2} d^{3} e^{8} + 5 \, a^{9} c d e^{10}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}\right)} \sqrt{\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} - 30 \, a^{2} d e^{5} + {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}}{a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}}}\right) - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} - 30 \, a^{2} d e^{5} + {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}}{a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}}} \log\left(-{\left(c^{4} d^{8} + 18 \, a c^{3} d^{6} e^{2} + 112 \, a^{2} c^{2} d^{4} e^{4} + 270 \, a^{3} c d^{2} e^{6} - 81 \, a^{4} e^{8}\right)} x - {\left(a^{2} c^{4} d^{8} e + 6 \, a^{3} c^{3} d^{6} e^{3} + 4 \, a^{4} c^{2} d^{4} e^{5} - 102 \, a^{5} c d^{2} e^{7} + 27 \, a^{6} e^{9} - {\left(a^{4} c^{6} d^{11} + 9 \, a^{5} c^{5} d^{9} e^{2} + 26 \, a^{6} c^{4} d^{7} e^{4} + 34 \, a^{7} c^{3} d^{5} e^{6} + 21 \, a^{8} c^{2} d^{3} e^{8} + 5 \, a^{9} c d e^{10}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}\right)} \sqrt{\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} - 30 \, a^{2} d e^{5} + {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}}{a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}}}\right) + {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} - 30 \, a^{2} d e^{5} - {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}}{a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}}} \log\left(-{\left(c^{4} d^{8} + 18 \, a c^{3} d^{6} e^{2} + 112 \, a^{2} c^{2} d^{4} e^{4} + 270 \, a^{3} c d^{2} e^{6} - 81 \, a^{4} e^{8}\right)} x + {\left(a^{2} c^{4} d^{8} e + 6 \, a^{3} c^{3} d^{6} e^{3} + 4 \, a^{4} c^{2} d^{4} e^{5} - 102 \, a^{5} c d^{2} e^{7} + 27 \, a^{6} e^{9} + {\left(a^{4} c^{6} d^{11} + 9 \, a^{5} c^{5} d^{9} e^{2} + 26 \, a^{6} c^{4} d^{7} e^{4} + 34 \, a^{7} c^{3} d^{5} e^{6} + 21 \, a^{8} c^{2} d^{3} e^{8} + 5 \, a^{9} c d e^{10}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}\right)} \sqrt{\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} - 30 \, a^{2} d e^{5} - {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}}{a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}}}\right) - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} - 30 \, a^{2} d e^{5} - {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}}{a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}}} \log\left(-{\left(c^{4} d^{8} + 18 \, a c^{3} d^{6} e^{2} + 112 \, a^{2} c^{2} d^{4} e^{4} + 270 \, a^{3} c d^{2} e^{6} - 81 \, a^{4} e^{8}\right)} x - {\left(a^{2} c^{4} d^{8} e + 6 \, a^{3} c^{3} d^{6} e^{3} + 4 \, a^{4} c^{2} d^{4} e^{5} - 102 \, a^{5} c d^{2} e^{7} + 27 \, a^{6} e^{9} + {\left(a^{4} c^{6} d^{11} + 9 \, a^{5} c^{5} d^{9} e^{2} + 26 \, a^{6} c^{4} d^{7} e^{4} + 34 \, a^{7} c^{3} d^{5} e^{6} + 21 \, a^{8} c^{2} d^{3} e^{8} + 5 \, a^{9} c d e^{10}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}\right)} \sqrt{\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} - 30 \, a^{2} d e^{5} - {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} \sqrt{-\frac{c^{6} d^{12} + 18 \, a c^{5} d^{10} e^{2} + 143 \, a^{2} c^{4} d^{8} e^{4} + 540 \, a^{3} c^{3} d^{6} e^{6} + 799 \, a^{4} c^{2} d^{4} e^{8} - 558 \, a^{5} c d^{2} e^{10} + 81 \, a^{6} e^{12}}{a^{5} c^{9} d^{16} + 8 \, a^{6} c^{8} d^{14} e^{2} + 28 \, a^{7} c^{7} d^{12} e^{4} + 56 \, a^{8} c^{6} d^{10} e^{6} + 70 \, a^{9} c^{5} d^{8} e^{8} + 56 \, a^{10} c^{4} d^{6} e^{10} + 28 \, a^{11} c^{3} d^{4} e^{12} + 8 \, a^{12} c^{2} d^{2} e^{14} + a^{13} c e^{16}}}}{a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}}}\right) + 4 \, {\left(a c d^{2} e + a^{2} e^{3}\right)} x}{16 \, {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)}}\right]"," ",0,"[1/16*(4*(c^2*d^3 + a*c*d*e^2)*x^3 + (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((2*c^2*d^5*e + 4*a*c*d^3*e^3 - 30*a^2*d*e^5 + (a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))/(a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8))*log(-(c^4*d^8 + 18*a*c^3*d^6*e^2 + 112*a^2*c^2*d^4*e^4 + 270*a^3*c*d^2*e^6 - 81*a^4*e^8)*x + (a^2*c^4*d^8*e + 6*a^3*c^3*d^6*e^3 + 4*a^4*c^2*d^4*e^5 - 102*a^5*c*d^2*e^7 + 27*a^6*e^9 - (a^4*c^6*d^11 + 9*a^5*c^5*d^9*e^2 + 26*a^6*c^4*d^7*e^4 + 34*a^7*c^3*d^5*e^6 + 21*a^8*c^2*d^3*e^8 + 5*a^9*c*d*e^10)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))*sqrt((2*c^2*d^5*e + 4*a*c*d^3*e^3 - 30*a^2*d*e^5 + (a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))/(a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8))) - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((2*c^2*d^5*e + 4*a*c*d^3*e^3 - 30*a^2*d*e^5 + (a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))/(a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8))*log(-(c^4*d^8 + 18*a*c^3*d^6*e^2 + 112*a^2*c^2*d^4*e^4 + 270*a^3*c*d^2*e^6 - 81*a^4*e^8)*x - (a^2*c^4*d^8*e + 6*a^3*c^3*d^6*e^3 + 4*a^4*c^2*d^4*e^5 - 102*a^5*c*d^2*e^7 + 27*a^6*e^9 - (a^4*c^6*d^11 + 9*a^5*c^5*d^9*e^2 + 26*a^6*c^4*d^7*e^4 + 34*a^7*c^3*d^5*e^6 + 21*a^8*c^2*d^3*e^8 + 5*a^9*c*d*e^10)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))*sqrt((2*c^2*d^5*e + 4*a*c*d^3*e^3 - 30*a^2*d*e^5 + (a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))/(a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8))) + (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((2*c^2*d^5*e + 4*a*c*d^3*e^3 - 30*a^2*d*e^5 - (a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))/(a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8))*log(-(c^4*d^8 + 18*a*c^3*d^6*e^2 + 112*a^2*c^2*d^4*e^4 + 270*a^3*c*d^2*e^6 - 81*a^4*e^8)*x + (a^2*c^4*d^8*e + 6*a^3*c^3*d^6*e^3 + 4*a^4*c^2*d^4*e^5 - 102*a^5*c*d^2*e^7 + 27*a^6*e^9 + (a^4*c^6*d^11 + 9*a^5*c^5*d^9*e^2 + 26*a^6*c^4*d^7*e^4 + 34*a^7*c^3*d^5*e^6 + 21*a^8*c^2*d^3*e^8 + 5*a^9*c*d*e^10)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))*sqrt((2*c^2*d^5*e + 4*a*c*d^3*e^3 - 30*a^2*d*e^5 - (a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))/(a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8))) - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((2*c^2*d^5*e + 4*a*c*d^3*e^3 - 30*a^2*d*e^5 - (a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))/(a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8))*log(-(c^4*d^8 + 18*a*c^3*d^6*e^2 + 112*a^2*c^2*d^4*e^4 + 270*a^3*c*d^2*e^6 - 81*a^4*e^8)*x - (a^2*c^4*d^8*e + 6*a^3*c^3*d^6*e^3 + 4*a^4*c^2*d^4*e^5 - 102*a^5*c*d^2*e^7 + 27*a^6*e^9 + (a^4*c^6*d^11 + 9*a^5*c^5*d^9*e^2 + 26*a^6*c^4*d^7*e^4 + 34*a^7*c^3*d^5*e^6 + 21*a^8*c^2*d^3*e^8 + 5*a^9*c*d*e^10)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))*sqrt((2*c^2*d^5*e + 4*a*c*d^3*e^3 - 30*a^2*d*e^5 - (a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))/(a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8))) + 8*(a*c*e^2*x^4 + a^2*e^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 4*(a*c*d^2*e + a^2*e^3)*x)/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4), 1/16*(4*(c^2*d^3 + a*c*d*e^2)*x^3 - 16*(a*c*e^2*x^4 + a^2*e^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((2*c^2*d^5*e + 4*a*c*d^3*e^3 - 30*a^2*d*e^5 + (a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))/(a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8))*log(-(c^4*d^8 + 18*a*c^3*d^6*e^2 + 112*a^2*c^2*d^4*e^4 + 270*a^3*c*d^2*e^6 - 81*a^4*e^8)*x + (a^2*c^4*d^8*e + 6*a^3*c^3*d^6*e^3 + 4*a^4*c^2*d^4*e^5 - 102*a^5*c*d^2*e^7 + 27*a^6*e^9 - (a^4*c^6*d^11 + 9*a^5*c^5*d^9*e^2 + 26*a^6*c^4*d^7*e^4 + 34*a^7*c^3*d^5*e^6 + 21*a^8*c^2*d^3*e^8 + 5*a^9*c*d*e^10)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))*sqrt((2*c^2*d^5*e + 4*a*c*d^3*e^3 - 30*a^2*d*e^5 + (a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))/(a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8))) - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((2*c^2*d^5*e + 4*a*c*d^3*e^3 - 30*a^2*d*e^5 + (a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))/(a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8))*log(-(c^4*d^8 + 18*a*c^3*d^6*e^2 + 112*a^2*c^2*d^4*e^4 + 270*a^3*c*d^2*e^6 - 81*a^4*e^8)*x - (a^2*c^4*d^8*e + 6*a^3*c^3*d^6*e^3 + 4*a^4*c^2*d^4*e^5 - 102*a^5*c*d^2*e^7 + 27*a^6*e^9 - (a^4*c^6*d^11 + 9*a^5*c^5*d^9*e^2 + 26*a^6*c^4*d^7*e^4 + 34*a^7*c^3*d^5*e^6 + 21*a^8*c^2*d^3*e^8 + 5*a^9*c*d*e^10)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))*sqrt((2*c^2*d^5*e + 4*a*c*d^3*e^3 - 30*a^2*d*e^5 + (a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))/(a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8))) + (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((2*c^2*d^5*e + 4*a*c*d^3*e^3 - 30*a^2*d*e^5 - (a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))/(a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8))*log(-(c^4*d^8 + 18*a*c^3*d^6*e^2 + 112*a^2*c^2*d^4*e^4 + 270*a^3*c*d^2*e^6 - 81*a^4*e^8)*x + (a^2*c^4*d^8*e + 6*a^3*c^3*d^6*e^3 + 4*a^4*c^2*d^4*e^5 - 102*a^5*c*d^2*e^7 + 27*a^6*e^9 + (a^4*c^6*d^11 + 9*a^5*c^5*d^9*e^2 + 26*a^6*c^4*d^7*e^4 + 34*a^7*c^3*d^5*e^6 + 21*a^8*c^2*d^3*e^8 + 5*a^9*c*d*e^10)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))*sqrt((2*c^2*d^5*e + 4*a*c*d^3*e^3 - 30*a^2*d*e^5 - (a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))/(a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8))) - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((2*c^2*d^5*e + 4*a*c*d^3*e^3 - 30*a^2*d*e^5 - (a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))/(a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8))*log(-(c^4*d^8 + 18*a*c^3*d^6*e^2 + 112*a^2*c^2*d^4*e^4 + 270*a^3*c*d^2*e^6 - 81*a^4*e^8)*x - (a^2*c^4*d^8*e + 6*a^3*c^3*d^6*e^3 + 4*a^4*c^2*d^4*e^5 - 102*a^5*c*d^2*e^7 + 27*a^6*e^9 + (a^4*c^6*d^11 + 9*a^5*c^5*d^9*e^2 + 26*a^6*c^4*d^7*e^4 + 34*a^7*c^3*d^5*e^6 + 21*a^8*c^2*d^3*e^8 + 5*a^9*c*d*e^10)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))*sqrt((2*c^2*d^5*e + 4*a*c*d^3*e^3 - 30*a^2*d*e^5 - (a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*sqrt(-(c^6*d^12 + 18*a*c^5*d^10*e^2 + 143*a^2*c^4*d^8*e^4 + 540*a^3*c^3*d^6*e^6 + 799*a^4*c^2*d^4*e^8 - 558*a^5*c*d^2*e^10 + 81*a^6*e^12)/(a^5*c^9*d^16 + 8*a^6*c^8*d^14*e^2 + 28*a^7*c^7*d^12*e^4 + 56*a^8*c^6*d^10*e^6 + 70*a^9*c^5*d^8*e^8 + 56*a^10*c^4*d^6*e^10 + 28*a^11*c^3*d^4*e^12 + 8*a^12*c^2*d^2*e^14 + a^13*c*e^16)))/(a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8))) + 4*(a*c*d^2*e + a^2*e^3)*x)/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)]","B",0
256,1,9892,0,41.284214," ","integrate(1/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(c^{2} d^{2} e + a c e^{3}\right)} x^{3} + {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} + {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}} \log\left(-{\left(81 \, c^{5} d^{8} + 594 \, a c^{4} d^{6} e^{2} + 1376 \, a^{2} c^{3} d^{4} e^{4} + 750 \, a^{3} c^{2} d^{2} e^{6} - 625 \, a^{4} c e^{8}\right)} x + {\left(27 \, a^{2} c^{5} d^{9} + 186 \, a^{3} c^{4} d^{7} e^{2} + 404 \, a^{4} c^{3} d^{5} e^{4} + 198 \, a^{5} c^{2} d^{3} e^{6} - 175 \, a^{6} c d e^{8} + {\left(a^{6} c^{5} d^{10} e + 9 \, a^{7} c^{4} d^{8} e^{3} + 26 \, a^{8} c^{3} d^{6} e^{5} + 34 \, a^{9} c^{2} d^{4} e^{7} + 21 \, a^{10} c d^{2} e^{9} + 5 \, a^{11} e^{11}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} + {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right) - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} + {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}} \log\left(-{\left(81 \, c^{5} d^{8} + 594 \, a c^{4} d^{6} e^{2} + 1376 \, a^{2} c^{3} d^{4} e^{4} + 750 \, a^{3} c^{2} d^{2} e^{6} - 625 \, a^{4} c e^{8}\right)} x - {\left(27 \, a^{2} c^{5} d^{9} + 186 \, a^{3} c^{4} d^{7} e^{2} + 404 \, a^{4} c^{3} d^{5} e^{4} + 198 \, a^{5} c^{2} d^{3} e^{6} - 175 \, a^{6} c d e^{8} + {\left(a^{6} c^{5} d^{10} e + 9 \, a^{7} c^{4} d^{8} e^{3} + 26 \, a^{8} c^{3} d^{6} e^{5} + 34 \, a^{9} c^{2} d^{4} e^{7} + 21 \, a^{10} c d^{2} e^{9} + 5 \, a^{11} e^{11}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} + {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right) + {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} - {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}} \log\left(-{\left(81 \, c^{5} d^{8} + 594 \, a c^{4} d^{6} e^{2} + 1376 \, a^{2} c^{3} d^{4} e^{4} + 750 \, a^{3} c^{2} d^{2} e^{6} - 625 \, a^{4} c e^{8}\right)} x + {\left(27 \, a^{2} c^{5} d^{9} + 186 \, a^{3} c^{4} d^{7} e^{2} + 404 \, a^{4} c^{3} d^{5} e^{4} + 198 \, a^{5} c^{2} d^{3} e^{6} - 175 \, a^{6} c d e^{8} - {\left(a^{6} c^{5} d^{10} e + 9 \, a^{7} c^{4} d^{8} e^{3} + 26 \, a^{8} c^{3} d^{6} e^{5} + 34 \, a^{9} c^{2} d^{4} e^{7} + 21 \, a^{10} c d^{2} e^{9} + 5 \, a^{11} e^{11}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} - {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right) - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} - {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}} \log\left(-{\left(81 \, c^{5} d^{8} + 594 \, a c^{4} d^{6} e^{2} + 1376 \, a^{2} c^{3} d^{4} e^{4} + 750 \, a^{3} c^{2} d^{2} e^{6} - 625 \, a^{4} c e^{8}\right)} x - {\left(27 \, a^{2} c^{5} d^{9} + 186 \, a^{3} c^{4} d^{7} e^{2} + 404 \, a^{4} c^{3} d^{5} e^{4} + 198 \, a^{5} c^{2} d^{3} e^{6} - 175 \, a^{6} c d e^{8} - {\left(a^{6} c^{5} d^{10} e + 9 \, a^{7} c^{4} d^{8} e^{3} + 26 \, a^{8} c^{3} d^{6} e^{5} + 34 \, a^{9} c^{2} d^{4} e^{7} + 21 \, a^{10} c d^{2} e^{9} + 5 \, a^{11} e^{11}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} - {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right) - 8 \, {\left(a c e^{3} x^{4} + a^{2} e^{3}\right)} \sqrt{-\frac{e}{d}} \log\left(\frac{e x^{2} + 2 \, d x \sqrt{-\frac{e}{d}} - d}{e x^{2} + d}\right) - 4 \, {\left(c^{2} d^{3} + a c d e^{2}\right)} x}{16 \, {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)}}, -\frac{4 \, {\left(c^{2} d^{2} e + a c e^{3}\right)} x^{3} - 16 \, {\left(a c e^{3} x^{4} + a^{2} e^{3}\right)} \sqrt{\frac{e}{d}} \arctan\left(x \sqrt{\frac{e}{d}}\right) + {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} + {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}} \log\left(-{\left(81 \, c^{5} d^{8} + 594 \, a c^{4} d^{6} e^{2} + 1376 \, a^{2} c^{3} d^{4} e^{4} + 750 \, a^{3} c^{2} d^{2} e^{6} - 625 \, a^{4} c e^{8}\right)} x + {\left(27 \, a^{2} c^{5} d^{9} + 186 \, a^{3} c^{4} d^{7} e^{2} + 404 \, a^{4} c^{3} d^{5} e^{4} + 198 \, a^{5} c^{2} d^{3} e^{6} - 175 \, a^{6} c d e^{8} + {\left(a^{6} c^{5} d^{10} e + 9 \, a^{7} c^{4} d^{8} e^{3} + 26 \, a^{8} c^{3} d^{6} e^{5} + 34 \, a^{9} c^{2} d^{4} e^{7} + 21 \, a^{10} c d^{2} e^{9} + 5 \, a^{11} e^{11}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} + {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right) - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} + {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}} \log\left(-{\left(81 \, c^{5} d^{8} + 594 \, a c^{4} d^{6} e^{2} + 1376 \, a^{2} c^{3} d^{4} e^{4} + 750 \, a^{3} c^{2} d^{2} e^{6} - 625 \, a^{4} c e^{8}\right)} x - {\left(27 \, a^{2} c^{5} d^{9} + 186 \, a^{3} c^{4} d^{7} e^{2} + 404 \, a^{4} c^{3} d^{5} e^{4} + 198 \, a^{5} c^{2} d^{3} e^{6} - 175 \, a^{6} c d e^{8} + {\left(a^{6} c^{5} d^{10} e + 9 \, a^{7} c^{4} d^{8} e^{3} + 26 \, a^{8} c^{3} d^{6} e^{5} + 34 \, a^{9} c^{2} d^{4} e^{7} + 21 \, a^{10} c d^{2} e^{9} + 5 \, a^{11} e^{11}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} + {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right) + {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} - {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}} \log\left(-{\left(81 \, c^{5} d^{8} + 594 \, a c^{4} d^{6} e^{2} + 1376 \, a^{2} c^{3} d^{4} e^{4} + 750 \, a^{3} c^{2} d^{2} e^{6} - 625 \, a^{4} c e^{8}\right)} x + {\left(27 \, a^{2} c^{5} d^{9} + 186 \, a^{3} c^{4} d^{7} e^{2} + 404 \, a^{4} c^{3} d^{5} e^{4} + 198 \, a^{5} c^{2} d^{3} e^{6} - 175 \, a^{6} c d e^{8} - {\left(a^{6} c^{5} d^{10} e + 9 \, a^{7} c^{4} d^{8} e^{3} + 26 \, a^{8} c^{3} d^{6} e^{5} + 34 \, a^{9} c^{2} d^{4} e^{7} + 21 \, a^{10} c d^{2} e^{9} + 5 \, a^{11} e^{11}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} - {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right) - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} - {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}} \log\left(-{\left(81 \, c^{5} d^{8} + 594 \, a c^{4} d^{6} e^{2} + 1376 \, a^{2} c^{3} d^{4} e^{4} + 750 \, a^{3} c^{2} d^{2} e^{6} - 625 \, a^{4} c e^{8}\right)} x - {\left(27 \, a^{2} c^{5} d^{9} + 186 \, a^{3} c^{4} d^{7} e^{2} + 404 \, a^{4} c^{3} d^{5} e^{4} + 198 \, a^{5} c^{2} d^{3} e^{6} - 175 \, a^{6} c d e^{8} - {\left(a^{6} c^{5} d^{10} e + 9 \, a^{7} c^{4} d^{8} e^{3} + 26 \, a^{8} c^{3} d^{6} e^{5} + 34 \, a^{9} c^{2} d^{4} e^{7} + 21 \, a^{10} c d^{2} e^{9} + 5 \, a^{11} e^{11}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} - {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right) - 4 \, {\left(c^{2} d^{3} + a c d e^{2}\right)} x}{16 \, {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)}}\right]"," ",0,"[-1/16*(4*(c^2*d^2*e + a*c*e^3)*x^3 + (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 + (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))*log(-(81*c^5*d^8 + 594*a*c^4*d^6*e^2 + 1376*a^2*c^3*d^4*e^4 + 750*a^3*c^2*d^2*e^6 - 625*a^4*c*e^8)*x + (27*a^2*c^5*d^9 + 186*a^3*c^4*d^7*e^2 + 404*a^4*c^3*d^5*e^4 + 198*a^5*c^2*d^3*e^6 - 175*a^6*c*d*e^8 + (a^6*c^5*d^10*e + 9*a^7*c^4*d^8*e^3 + 26*a^8*c^3*d^6*e^5 + 34*a^9*c^2*d^4*e^7 + 21*a^10*c*d^2*e^9 + 5*a^11*e^11)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 + (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))) - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 + (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))*log(-(81*c^5*d^8 + 594*a*c^4*d^6*e^2 + 1376*a^2*c^3*d^4*e^4 + 750*a^3*c^2*d^2*e^6 - 625*a^4*c*e^8)*x - (27*a^2*c^5*d^9 + 186*a^3*c^4*d^7*e^2 + 404*a^4*c^3*d^5*e^4 + 198*a^5*c^2*d^3*e^6 - 175*a^6*c*d*e^8 + (a^6*c^5*d^10*e + 9*a^7*c^4*d^8*e^3 + 26*a^8*c^3*d^6*e^5 + 34*a^9*c^2*d^4*e^7 + 21*a^10*c*d^2*e^9 + 5*a^11*e^11)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 + (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))) + (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 - (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))*log(-(81*c^5*d^8 + 594*a*c^4*d^6*e^2 + 1376*a^2*c^3*d^4*e^4 + 750*a^3*c^2*d^2*e^6 - 625*a^4*c*e^8)*x + (27*a^2*c^5*d^9 + 186*a^3*c^4*d^7*e^2 + 404*a^4*c^3*d^5*e^4 + 198*a^5*c^2*d^3*e^6 - 175*a^6*c*d*e^8 - (a^6*c^5*d^10*e + 9*a^7*c^4*d^8*e^3 + 26*a^8*c^3*d^6*e^5 + 34*a^9*c^2*d^4*e^7 + 21*a^10*c*d^2*e^9 + 5*a^11*e^11)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 - (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))) - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 - (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))*log(-(81*c^5*d^8 + 594*a*c^4*d^6*e^2 + 1376*a^2*c^3*d^4*e^4 + 750*a^3*c^2*d^2*e^6 - 625*a^4*c*e^8)*x - (27*a^2*c^5*d^9 + 186*a^3*c^4*d^7*e^2 + 404*a^4*c^3*d^5*e^4 + 198*a^5*c^2*d^3*e^6 - 175*a^6*c*d*e^8 - (a^6*c^5*d^10*e + 9*a^7*c^4*d^8*e^3 + 26*a^8*c^3*d^6*e^5 + 34*a^9*c^2*d^4*e^7 + 21*a^10*c*d^2*e^9 + 5*a^11*e^11)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 - (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))) - 8*(a*c*e^3*x^4 + a^2*e^3)*sqrt(-e/d)*log((e*x^2 + 2*d*x*sqrt(-e/d) - d)/(e*x^2 + d)) - 4*(c^2*d^3 + a*c*d*e^2)*x)/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4), -1/16*(4*(c^2*d^2*e + a*c*e^3)*x^3 - 16*(a*c*e^3*x^4 + a^2*e^3)*sqrt(e/d)*arctan(x*sqrt(e/d)) + (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 + (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))*log(-(81*c^5*d^8 + 594*a*c^4*d^6*e^2 + 1376*a^2*c^3*d^4*e^4 + 750*a^3*c^2*d^2*e^6 - 625*a^4*c*e^8)*x + (27*a^2*c^5*d^9 + 186*a^3*c^4*d^7*e^2 + 404*a^4*c^3*d^5*e^4 + 198*a^5*c^2*d^3*e^6 - 175*a^6*c*d*e^8 + (a^6*c^5*d^10*e + 9*a^7*c^4*d^8*e^3 + 26*a^8*c^3*d^6*e^5 + 34*a^9*c^2*d^4*e^7 + 21*a^10*c*d^2*e^9 + 5*a^11*e^11)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 + (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))) - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 + (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))*log(-(81*c^5*d^8 + 594*a*c^4*d^6*e^2 + 1376*a^2*c^3*d^4*e^4 + 750*a^3*c^2*d^2*e^6 - 625*a^4*c*e^8)*x - (27*a^2*c^5*d^9 + 186*a^3*c^4*d^7*e^2 + 404*a^4*c^3*d^5*e^4 + 198*a^5*c^2*d^3*e^6 - 175*a^6*c*d*e^8 + (a^6*c^5*d^10*e + 9*a^7*c^4*d^8*e^3 + 26*a^8*c^3*d^6*e^5 + 34*a^9*c^2*d^4*e^7 + 21*a^10*c*d^2*e^9 + 5*a^11*e^11)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 + (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))) + (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 - (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))*log(-(81*c^5*d^8 + 594*a*c^4*d^6*e^2 + 1376*a^2*c^3*d^4*e^4 + 750*a^3*c^2*d^2*e^6 - 625*a^4*c*e^8)*x + (27*a^2*c^5*d^9 + 186*a^3*c^4*d^7*e^2 + 404*a^4*c^3*d^5*e^4 + 198*a^5*c^2*d^3*e^6 - 175*a^6*c*d*e^8 - (a^6*c^5*d^10*e + 9*a^7*c^4*d^8*e^3 + 26*a^8*c^3*d^6*e^5 + 34*a^9*c^2*d^4*e^7 + 21*a^10*c*d^2*e^9 + 5*a^11*e^11)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 - (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))) - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 - (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))*log(-(81*c^5*d^8 + 594*a*c^4*d^6*e^2 + 1376*a^2*c^3*d^4*e^4 + 750*a^3*c^2*d^2*e^6 - 625*a^4*c*e^8)*x - (27*a^2*c^5*d^9 + 186*a^3*c^4*d^7*e^2 + 404*a^4*c^3*d^5*e^4 + 198*a^5*c^2*d^3*e^6 - 175*a^6*c*d*e^8 - (a^6*c^5*d^10*e + 9*a^7*c^4*d^8*e^3 + 26*a^8*c^3*d^6*e^5 + 34*a^9*c^2*d^4*e^7 + 21*a^10*c*d^2*e^9 + 5*a^11*e^11)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 - (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))) - 4*(c^2*d^3 + a*c*d*e^2)*x)/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)]","B",0
257,1,10188,0,111.346081," ","integrate(1/x^2/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""fricas"")","\left[-\frac{16 \, a c^{2} d^{4} + 32 \, a^{2} c d^{2} e^{2} + 16 \, a^{3} e^{4} + 4 \, {\left(5 \, c^{3} d^{4} + 9 \, a c^{2} d^{2} e^{2} + 4 \, a^{2} c e^{4}\right)} x^{4} + 4 \, {\left(a c^{2} d^{3} e + a^{2} c d e^{3}\right)} x^{2} - {\left({\left(a^{2} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4}\right)} x^{5} + {\left(a^{3} c^{2} d^{5} + 2 \, a^{4} c d^{3} e^{2} + a^{5} d e^{4}\right)} x\right)} \sqrt{-\frac{30 \, c^{4} d^{5} e + 124 \, a c^{3} d^{3} e^{3} + 126 \, a^{2} c^{2} d e^{5} + {\left(a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}}{a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}}} \log\left(-{\left(625 \, c^{6} d^{8} + 3250 \, a c^{5} d^{6} e^{2} + 4944 \, a^{2} c^{4} d^{4} e^{4} + 686 \, a^{3} c^{3} d^{2} e^{6} - 2401 \, a^{4} c^{2} e^{8}\right)} x + {\left(75 \, a^{3} c^{5} d^{8} e + 418 \, a^{4} c^{4} d^{6} e^{3} + 684 \, a^{5} c^{3} d^{4} e^{5} + 126 \, a^{6} c^{2} d^{2} e^{7} - 343 \, a^{7} c e^{9} - {\left(5 \, a^{7} c^{5} d^{11} + 29 \, a^{8} c^{4} d^{9} e^{2} + 66 \, a^{9} c^{3} d^{7} e^{4} + 74 \, a^{10} c^{2} d^{5} e^{6} + 41 \, a^{11} c d^{3} e^{8} + 9 \, a^{12} d e^{10}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}\right)} \sqrt{-\frac{30 \, c^{4} d^{5} e + 124 \, a c^{3} d^{3} e^{3} + 126 \, a^{2} c^{2} d e^{5} + {\left(a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}}{a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}}}\right) + {\left({\left(a^{2} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4}\right)} x^{5} + {\left(a^{3} c^{2} d^{5} + 2 \, a^{4} c d^{3} e^{2} + a^{5} d e^{4}\right)} x\right)} \sqrt{-\frac{30 \, c^{4} d^{5} e + 124 \, a c^{3} d^{3} e^{3} + 126 \, a^{2} c^{2} d e^{5} + {\left(a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}}{a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}}} \log\left(-{\left(625 \, c^{6} d^{8} + 3250 \, a c^{5} d^{6} e^{2} + 4944 \, a^{2} c^{4} d^{4} e^{4} + 686 \, a^{3} c^{3} d^{2} e^{6} - 2401 \, a^{4} c^{2} e^{8}\right)} x - {\left(75 \, a^{3} c^{5} d^{8} e + 418 \, a^{4} c^{4} d^{6} e^{3} + 684 \, a^{5} c^{3} d^{4} e^{5} + 126 \, a^{6} c^{2} d^{2} e^{7} - 343 \, a^{7} c e^{9} - {\left(5 \, a^{7} c^{5} d^{11} + 29 \, a^{8} c^{4} d^{9} e^{2} + 66 \, a^{9} c^{3} d^{7} e^{4} + 74 \, a^{10} c^{2} d^{5} e^{6} + 41 \, a^{11} c d^{3} e^{8} + 9 \, a^{12} d e^{10}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}\right)} \sqrt{-\frac{30 \, c^{4} d^{5} e + 124 \, a c^{3} d^{3} e^{3} + 126 \, a^{2} c^{2} d e^{5} + {\left(a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}}{a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}}}\right) - {\left({\left(a^{2} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4}\right)} x^{5} + {\left(a^{3} c^{2} d^{5} + 2 \, a^{4} c d^{3} e^{2} + a^{5} d e^{4}\right)} x\right)} \sqrt{-\frac{30 \, c^{4} d^{5} e + 124 \, a c^{3} d^{3} e^{3} + 126 \, a^{2} c^{2} d e^{5} - {\left(a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}}{a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}}} \log\left(-{\left(625 \, c^{6} d^{8} + 3250 \, a c^{5} d^{6} e^{2} + 4944 \, a^{2} c^{4} d^{4} e^{4} + 686 \, a^{3} c^{3} d^{2} e^{6} - 2401 \, a^{4} c^{2} e^{8}\right)} x + {\left(75 \, a^{3} c^{5} d^{8} e + 418 \, a^{4} c^{4} d^{6} e^{3} + 684 \, a^{5} c^{3} d^{4} e^{5} + 126 \, a^{6} c^{2} d^{2} e^{7} - 343 \, a^{7} c e^{9} + {\left(5 \, a^{7} c^{5} d^{11} + 29 \, a^{8} c^{4} d^{9} e^{2} + 66 \, a^{9} c^{3} d^{7} e^{4} + 74 \, a^{10} c^{2} d^{5} e^{6} + 41 \, a^{11} c d^{3} e^{8} + 9 \, a^{12} d e^{10}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}\right)} \sqrt{-\frac{30 \, c^{4} d^{5} e + 124 \, a c^{3} d^{3} e^{3} + 126 \, a^{2} c^{2} d e^{5} - {\left(a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}}{a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}}}\right) + {\left({\left(a^{2} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4}\right)} x^{5} + {\left(a^{3} c^{2} d^{5} + 2 \, a^{4} c d^{3} e^{2} + a^{5} d e^{4}\right)} x\right)} \sqrt{-\frac{30 \, c^{4} d^{5} e + 124 \, a c^{3} d^{3} e^{3} + 126 \, a^{2} c^{2} d e^{5} - {\left(a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}}{a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}}} \log\left(-{\left(625 \, c^{6} d^{8} + 3250 \, a c^{5} d^{6} e^{2} + 4944 \, a^{2} c^{4} d^{4} e^{4} + 686 \, a^{3} c^{3} d^{2} e^{6} - 2401 \, a^{4} c^{2} e^{8}\right)} x - {\left(75 \, a^{3} c^{5} d^{8} e + 418 \, a^{4} c^{4} d^{6} e^{3} + 684 \, a^{5} c^{3} d^{4} e^{5} + 126 \, a^{6} c^{2} d^{2} e^{7} - 343 \, a^{7} c e^{9} + {\left(5 \, a^{7} c^{5} d^{11} + 29 \, a^{8} c^{4} d^{9} e^{2} + 66 \, a^{9} c^{3} d^{7} e^{4} + 74 \, a^{10} c^{2} d^{5} e^{6} + 41 \, a^{11} c d^{3} e^{8} + 9 \, a^{12} d e^{10}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}\right)} \sqrt{-\frac{30 \, c^{4} d^{5} e + 124 \, a c^{3} d^{3} e^{3} + 126 \, a^{2} c^{2} d e^{5} - {\left(a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}}{a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}}}\right) - 8 \, {\left(a^{2} c e^{4} x^{5} + a^{3} e^{4} x\right)} \sqrt{-\frac{e}{d}} \log\left(\frac{e x^{2} - 2 \, d x \sqrt{-\frac{e}{d}} - d}{e x^{2} + d}\right)}{16 \, {\left({\left(a^{2} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4}\right)} x^{5} + {\left(a^{3} c^{2} d^{5} + 2 \, a^{4} c d^{3} e^{2} + a^{5} d e^{4}\right)} x\right)}}, -\frac{16 \, a c^{2} d^{4} + 32 \, a^{2} c d^{2} e^{2} + 16 \, a^{3} e^{4} + 4 \, {\left(5 \, c^{3} d^{4} + 9 \, a c^{2} d^{2} e^{2} + 4 \, a^{2} c e^{4}\right)} x^{4} + 4 \, {\left(a c^{2} d^{3} e + a^{2} c d e^{3}\right)} x^{2} + 16 \, {\left(a^{2} c e^{4} x^{5} + a^{3} e^{4} x\right)} \sqrt{\frac{e}{d}} \arctan\left(x \sqrt{\frac{e}{d}}\right) - {\left({\left(a^{2} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4}\right)} x^{5} + {\left(a^{3} c^{2} d^{5} + 2 \, a^{4} c d^{3} e^{2} + a^{5} d e^{4}\right)} x\right)} \sqrt{-\frac{30 \, c^{4} d^{5} e + 124 \, a c^{3} d^{3} e^{3} + 126 \, a^{2} c^{2} d e^{5} + {\left(a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}}{a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}}} \log\left(-{\left(625 \, c^{6} d^{8} + 3250 \, a c^{5} d^{6} e^{2} + 4944 \, a^{2} c^{4} d^{4} e^{4} + 686 \, a^{3} c^{3} d^{2} e^{6} - 2401 \, a^{4} c^{2} e^{8}\right)} x + {\left(75 \, a^{3} c^{5} d^{8} e + 418 \, a^{4} c^{4} d^{6} e^{3} + 684 \, a^{5} c^{3} d^{4} e^{5} + 126 \, a^{6} c^{2} d^{2} e^{7} - 343 \, a^{7} c e^{9} - {\left(5 \, a^{7} c^{5} d^{11} + 29 \, a^{8} c^{4} d^{9} e^{2} + 66 \, a^{9} c^{3} d^{7} e^{4} + 74 \, a^{10} c^{2} d^{5} e^{6} + 41 \, a^{11} c d^{3} e^{8} + 9 \, a^{12} d e^{10}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}\right)} \sqrt{-\frac{30 \, c^{4} d^{5} e + 124 \, a c^{3} d^{3} e^{3} + 126 \, a^{2} c^{2} d e^{5} + {\left(a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}}{a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}}}\right) + {\left({\left(a^{2} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4}\right)} x^{5} + {\left(a^{3} c^{2} d^{5} + 2 \, a^{4} c d^{3} e^{2} + a^{5} d e^{4}\right)} x\right)} \sqrt{-\frac{30 \, c^{4} d^{5} e + 124 \, a c^{3} d^{3} e^{3} + 126 \, a^{2} c^{2} d e^{5} + {\left(a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}}{a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}}} \log\left(-{\left(625 \, c^{6} d^{8} + 3250 \, a c^{5} d^{6} e^{2} + 4944 \, a^{2} c^{4} d^{4} e^{4} + 686 \, a^{3} c^{3} d^{2} e^{6} - 2401 \, a^{4} c^{2} e^{8}\right)} x - {\left(75 \, a^{3} c^{5} d^{8} e + 418 \, a^{4} c^{4} d^{6} e^{3} + 684 \, a^{5} c^{3} d^{4} e^{5} + 126 \, a^{6} c^{2} d^{2} e^{7} - 343 \, a^{7} c e^{9} - {\left(5 \, a^{7} c^{5} d^{11} + 29 \, a^{8} c^{4} d^{9} e^{2} + 66 \, a^{9} c^{3} d^{7} e^{4} + 74 \, a^{10} c^{2} d^{5} e^{6} + 41 \, a^{11} c d^{3} e^{8} + 9 \, a^{12} d e^{10}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}\right)} \sqrt{-\frac{30 \, c^{4} d^{5} e + 124 \, a c^{3} d^{3} e^{3} + 126 \, a^{2} c^{2} d e^{5} + {\left(a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}}{a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}}}\right) - {\left({\left(a^{2} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4}\right)} x^{5} + {\left(a^{3} c^{2} d^{5} + 2 \, a^{4} c d^{3} e^{2} + a^{5} d e^{4}\right)} x\right)} \sqrt{-\frac{30 \, c^{4} d^{5} e + 124 \, a c^{3} d^{3} e^{3} + 126 \, a^{2} c^{2} d e^{5} - {\left(a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}}{a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}}} \log\left(-{\left(625 \, c^{6} d^{8} + 3250 \, a c^{5} d^{6} e^{2} + 4944 \, a^{2} c^{4} d^{4} e^{4} + 686 \, a^{3} c^{3} d^{2} e^{6} - 2401 \, a^{4} c^{2} e^{8}\right)} x + {\left(75 \, a^{3} c^{5} d^{8} e + 418 \, a^{4} c^{4} d^{6} e^{3} + 684 \, a^{5} c^{3} d^{4} e^{5} + 126 \, a^{6} c^{2} d^{2} e^{7} - 343 \, a^{7} c e^{9} + {\left(5 \, a^{7} c^{5} d^{11} + 29 \, a^{8} c^{4} d^{9} e^{2} + 66 \, a^{9} c^{3} d^{7} e^{4} + 74 \, a^{10} c^{2} d^{5} e^{6} + 41 \, a^{11} c d^{3} e^{8} + 9 \, a^{12} d e^{10}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}\right)} \sqrt{-\frac{30 \, c^{4} d^{5} e + 124 \, a c^{3} d^{3} e^{3} + 126 \, a^{2} c^{2} d e^{5} - {\left(a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}}{a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}}}\right) + {\left({\left(a^{2} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4}\right)} x^{5} + {\left(a^{3} c^{2} d^{5} + 2 \, a^{4} c d^{3} e^{2} + a^{5} d e^{4}\right)} x\right)} \sqrt{-\frac{30 \, c^{4} d^{5} e + 124 \, a c^{3} d^{3} e^{3} + 126 \, a^{2} c^{2} d e^{5} - {\left(a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}}{a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}}} \log\left(-{\left(625 \, c^{6} d^{8} + 3250 \, a c^{5} d^{6} e^{2} + 4944 \, a^{2} c^{4} d^{4} e^{4} + 686 \, a^{3} c^{3} d^{2} e^{6} - 2401 \, a^{4} c^{2} e^{8}\right)} x - {\left(75 \, a^{3} c^{5} d^{8} e + 418 \, a^{4} c^{4} d^{6} e^{3} + 684 \, a^{5} c^{3} d^{4} e^{5} + 126 \, a^{6} c^{2} d^{2} e^{7} - 343 \, a^{7} c e^{9} + {\left(5 \, a^{7} c^{5} d^{11} + 29 \, a^{8} c^{4} d^{9} e^{2} + 66 \, a^{9} c^{3} d^{7} e^{4} + 74 \, a^{10} c^{2} d^{5} e^{6} + 41 \, a^{11} c d^{3} e^{8} + 9 \, a^{12} d e^{10}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}\right)} \sqrt{-\frac{30 \, c^{4} d^{5} e + 124 \, a c^{3} d^{3} e^{3} + 126 \, a^{2} c^{2} d e^{5} - {\left(a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}\right)} \sqrt{-\frac{625 \, c^{9} d^{12} + 4050 \, a c^{8} d^{10} e^{2} + 8511 \, a^{2} c^{7} d^{8} e^{4} + 3868 \, a^{3} c^{6} d^{6} e^{6} - 6417 \, a^{4} c^{5} d^{4} e^{8} - 3822 \, a^{5} c^{4} d^{2} e^{10} + 2401 \, a^{6} c^{3} e^{12}}{a^{9} c^{8} d^{16} + 8 \, a^{10} c^{7} d^{14} e^{2} + 28 \, a^{11} c^{6} d^{12} e^{4} + 56 \, a^{12} c^{5} d^{10} e^{6} + 70 \, a^{13} c^{4} d^{8} e^{8} + 56 \, a^{14} c^{3} d^{6} e^{10} + 28 \, a^{15} c^{2} d^{4} e^{12} + 8 \, a^{16} c d^{2} e^{14} + a^{17} e^{16}}}}{a^{4} c^{4} d^{8} + 4 \, a^{5} c^{3} d^{6} e^{2} + 6 \, a^{6} c^{2} d^{4} e^{4} + 4 \, a^{7} c d^{2} e^{6} + a^{8} e^{8}}}\right)}{16 \, {\left({\left(a^{2} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4}\right)} x^{5} + {\left(a^{3} c^{2} d^{5} + 2 \, a^{4} c d^{3} e^{2} + a^{5} d e^{4}\right)} x\right)}}\right]"," ",0,"[-1/16*(16*a*c^2*d^4 + 32*a^2*c*d^2*e^2 + 16*a^3*e^4 + 4*(5*c^3*d^4 + 9*a*c^2*d^2*e^2 + 4*a^2*c*e^4)*x^4 + 4*(a*c^2*d^3*e + a^2*c*d*e^3)*x^2 - ((a^2*c^3*d^5 + 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4)*x^5 + (a^3*c^2*d^5 + 2*a^4*c*d^3*e^2 + a^5*d*e^4)*x)*sqrt(-(30*c^4*d^5*e + 124*a*c^3*d^3*e^3 + 126*a^2*c^2*d*e^5 + (a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))/(a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8))*log(-(625*c^6*d^8 + 3250*a*c^5*d^6*e^2 + 4944*a^2*c^4*d^4*e^4 + 686*a^3*c^3*d^2*e^6 - 2401*a^4*c^2*e^8)*x + (75*a^3*c^5*d^8*e + 418*a^4*c^4*d^6*e^3 + 684*a^5*c^3*d^4*e^5 + 126*a^6*c^2*d^2*e^7 - 343*a^7*c*e^9 - (5*a^7*c^5*d^11 + 29*a^8*c^4*d^9*e^2 + 66*a^9*c^3*d^7*e^4 + 74*a^10*c^2*d^5*e^6 + 41*a^11*c*d^3*e^8 + 9*a^12*d*e^10)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))*sqrt(-(30*c^4*d^5*e + 124*a*c^3*d^3*e^3 + 126*a^2*c^2*d*e^5 + (a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))/(a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8))) + ((a^2*c^3*d^5 + 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4)*x^5 + (a^3*c^2*d^5 + 2*a^4*c*d^3*e^2 + a^5*d*e^4)*x)*sqrt(-(30*c^4*d^5*e + 124*a*c^3*d^3*e^3 + 126*a^2*c^2*d*e^5 + (a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))/(a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8))*log(-(625*c^6*d^8 + 3250*a*c^5*d^6*e^2 + 4944*a^2*c^4*d^4*e^4 + 686*a^3*c^3*d^2*e^6 - 2401*a^4*c^2*e^8)*x - (75*a^3*c^5*d^8*e + 418*a^4*c^4*d^6*e^3 + 684*a^5*c^3*d^4*e^5 + 126*a^6*c^2*d^2*e^7 - 343*a^7*c*e^9 - (5*a^7*c^5*d^11 + 29*a^8*c^4*d^9*e^2 + 66*a^9*c^3*d^7*e^4 + 74*a^10*c^2*d^5*e^6 + 41*a^11*c*d^3*e^8 + 9*a^12*d*e^10)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))*sqrt(-(30*c^4*d^5*e + 124*a*c^3*d^3*e^3 + 126*a^2*c^2*d*e^5 + (a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))/(a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8))) - ((a^2*c^3*d^5 + 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4)*x^5 + (a^3*c^2*d^5 + 2*a^4*c*d^3*e^2 + a^5*d*e^4)*x)*sqrt(-(30*c^4*d^5*e + 124*a*c^3*d^3*e^3 + 126*a^2*c^2*d*e^5 - (a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))/(a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8))*log(-(625*c^6*d^8 + 3250*a*c^5*d^6*e^2 + 4944*a^2*c^4*d^4*e^4 + 686*a^3*c^3*d^2*e^6 - 2401*a^4*c^2*e^8)*x + (75*a^3*c^5*d^8*e + 418*a^4*c^4*d^6*e^3 + 684*a^5*c^3*d^4*e^5 + 126*a^6*c^2*d^2*e^7 - 343*a^7*c*e^9 + (5*a^7*c^5*d^11 + 29*a^8*c^4*d^9*e^2 + 66*a^9*c^3*d^7*e^4 + 74*a^10*c^2*d^5*e^6 + 41*a^11*c*d^3*e^8 + 9*a^12*d*e^10)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))*sqrt(-(30*c^4*d^5*e + 124*a*c^3*d^3*e^3 + 126*a^2*c^2*d*e^5 - (a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))/(a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8))) + ((a^2*c^3*d^5 + 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4)*x^5 + (a^3*c^2*d^5 + 2*a^4*c*d^3*e^2 + a^5*d*e^4)*x)*sqrt(-(30*c^4*d^5*e + 124*a*c^3*d^3*e^3 + 126*a^2*c^2*d*e^5 - (a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))/(a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8))*log(-(625*c^6*d^8 + 3250*a*c^5*d^6*e^2 + 4944*a^2*c^4*d^4*e^4 + 686*a^3*c^3*d^2*e^6 - 2401*a^4*c^2*e^8)*x - (75*a^3*c^5*d^8*e + 418*a^4*c^4*d^6*e^3 + 684*a^5*c^3*d^4*e^5 + 126*a^6*c^2*d^2*e^7 - 343*a^7*c*e^9 + (5*a^7*c^5*d^11 + 29*a^8*c^4*d^9*e^2 + 66*a^9*c^3*d^7*e^4 + 74*a^10*c^2*d^5*e^6 + 41*a^11*c*d^3*e^8 + 9*a^12*d*e^10)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))*sqrt(-(30*c^4*d^5*e + 124*a*c^3*d^3*e^3 + 126*a^2*c^2*d*e^5 - (a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))/(a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8))) - 8*(a^2*c*e^4*x^5 + a^3*e^4*x)*sqrt(-e/d)*log((e*x^2 - 2*d*x*sqrt(-e/d) - d)/(e*x^2 + d)))/((a^2*c^3*d^5 + 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4)*x^5 + (a^3*c^2*d^5 + 2*a^4*c*d^3*e^2 + a^5*d*e^4)*x), -1/16*(16*a*c^2*d^4 + 32*a^2*c*d^2*e^2 + 16*a^3*e^4 + 4*(5*c^3*d^4 + 9*a*c^2*d^2*e^2 + 4*a^2*c*e^4)*x^4 + 4*(a*c^2*d^3*e + a^2*c*d*e^3)*x^2 + 16*(a^2*c*e^4*x^5 + a^3*e^4*x)*sqrt(e/d)*arctan(x*sqrt(e/d)) - ((a^2*c^3*d^5 + 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4)*x^5 + (a^3*c^2*d^5 + 2*a^4*c*d^3*e^2 + a^5*d*e^4)*x)*sqrt(-(30*c^4*d^5*e + 124*a*c^3*d^3*e^3 + 126*a^2*c^2*d*e^5 + (a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))/(a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8))*log(-(625*c^6*d^8 + 3250*a*c^5*d^6*e^2 + 4944*a^2*c^4*d^4*e^4 + 686*a^3*c^3*d^2*e^6 - 2401*a^4*c^2*e^8)*x + (75*a^3*c^5*d^8*e + 418*a^4*c^4*d^6*e^3 + 684*a^5*c^3*d^4*e^5 + 126*a^6*c^2*d^2*e^7 - 343*a^7*c*e^9 - (5*a^7*c^5*d^11 + 29*a^8*c^4*d^9*e^2 + 66*a^9*c^3*d^7*e^4 + 74*a^10*c^2*d^5*e^6 + 41*a^11*c*d^3*e^8 + 9*a^12*d*e^10)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))*sqrt(-(30*c^4*d^5*e + 124*a*c^3*d^3*e^3 + 126*a^2*c^2*d*e^5 + (a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))/(a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8))) + ((a^2*c^3*d^5 + 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4)*x^5 + (a^3*c^2*d^5 + 2*a^4*c*d^3*e^2 + a^5*d*e^4)*x)*sqrt(-(30*c^4*d^5*e + 124*a*c^3*d^3*e^3 + 126*a^2*c^2*d*e^5 + (a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))/(a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8))*log(-(625*c^6*d^8 + 3250*a*c^5*d^6*e^2 + 4944*a^2*c^4*d^4*e^4 + 686*a^3*c^3*d^2*e^6 - 2401*a^4*c^2*e^8)*x - (75*a^3*c^5*d^8*e + 418*a^4*c^4*d^6*e^3 + 684*a^5*c^3*d^4*e^5 + 126*a^6*c^2*d^2*e^7 - 343*a^7*c*e^9 - (5*a^7*c^5*d^11 + 29*a^8*c^4*d^9*e^2 + 66*a^9*c^3*d^7*e^4 + 74*a^10*c^2*d^5*e^6 + 41*a^11*c*d^3*e^8 + 9*a^12*d*e^10)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))*sqrt(-(30*c^4*d^5*e + 124*a*c^3*d^3*e^3 + 126*a^2*c^2*d*e^5 + (a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))/(a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8))) - ((a^2*c^3*d^5 + 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4)*x^5 + (a^3*c^2*d^5 + 2*a^4*c*d^3*e^2 + a^5*d*e^4)*x)*sqrt(-(30*c^4*d^5*e + 124*a*c^3*d^3*e^3 + 126*a^2*c^2*d*e^5 - (a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))/(a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8))*log(-(625*c^6*d^8 + 3250*a*c^5*d^6*e^2 + 4944*a^2*c^4*d^4*e^4 + 686*a^3*c^3*d^2*e^6 - 2401*a^4*c^2*e^8)*x + (75*a^3*c^5*d^8*e + 418*a^4*c^4*d^6*e^3 + 684*a^5*c^3*d^4*e^5 + 126*a^6*c^2*d^2*e^7 - 343*a^7*c*e^9 + (5*a^7*c^5*d^11 + 29*a^8*c^4*d^9*e^2 + 66*a^9*c^3*d^7*e^4 + 74*a^10*c^2*d^5*e^6 + 41*a^11*c*d^3*e^8 + 9*a^12*d*e^10)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))*sqrt(-(30*c^4*d^5*e + 124*a*c^3*d^3*e^3 + 126*a^2*c^2*d*e^5 - (a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))/(a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8))) + ((a^2*c^3*d^5 + 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4)*x^5 + (a^3*c^2*d^5 + 2*a^4*c*d^3*e^2 + a^5*d*e^4)*x)*sqrt(-(30*c^4*d^5*e + 124*a*c^3*d^3*e^3 + 126*a^2*c^2*d*e^5 - (a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))/(a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8))*log(-(625*c^6*d^8 + 3250*a*c^5*d^6*e^2 + 4944*a^2*c^4*d^4*e^4 + 686*a^3*c^3*d^2*e^6 - 2401*a^4*c^2*e^8)*x - (75*a^3*c^5*d^8*e + 418*a^4*c^4*d^6*e^3 + 684*a^5*c^3*d^4*e^5 + 126*a^6*c^2*d^2*e^7 - 343*a^7*c*e^9 + (5*a^7*c^5*d^11 + 29*a^8*c^4*d^9*e^2 + 66*a^9*c^3*d^7*e^4 + 74*a^10*c^2*d^5*e^6 + 41*a^11*c*d^3*e^8 + 9*a^12*d*e^10)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))*sqrt(-(30*c^4*d^5*e + 124*a*c^3*d^3*e^3 + 126*a^2*c^2*d*e^5 - (a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8)*sqrt(-(625*c^9*d^12 + 4050*a*c^8*d^10*e^2 + 8511*a^2*c^7*d^8*e^4 + 3868*a^3*c^6*d^6*e^6 - 6417*a^4*c^5*d^4*e^8 - 3822*a^5*c^4*d^2*e^10 + 2401*a^6*c^3*e^12)/(a^9*c^8*d^16 + 8*a^10*c^7*d^14*e^2 + 28*a^11*c^6*d^12*e^4 + 56*a^12*c^5*d^10*e^6 + 70*a^13*c^4*d^8*e^8 + 56*a^14*c^3*d^6*e^10 + 28*a^15*c^2*d^4*e^12 + 8*a^16*c*d^2*e^14 + a^17*e^16)))/(a^4*c^4*d^8 + 4*a^5*c^3*d^6*e^2 + 6*a^6*c^2*d^4*e^4 + 4*a^7*c*d^2*e^6 + a^8*e^8))))/((a^2*c^3*d^5 + 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4)*x^5 + (a^3*c^2*d^5 + 2*a^4*c*d^3*e^2 + a^5*d*e^4)*x)]","B",0
258,-1,0,0,0.000000," ","integrate(1/x^4/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
259,0,0,0,1.029033," ","integrate(x^2/(x^2+1)/(x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 1} x^{2}}{x^{6} + x^{4} + x^{2} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + 1)*x^2/(x^6 + x^4 + x^2 + 1), x)","F",0
260,0,0,0,1.331606," ","integrate(x^2/(-x^2+1)/(x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{4} + 1} x^{2}}{x^{6} - x^{4} + x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(x^4 + 1)*x^2/(x^6 - x^4 + x^2 - 1), x)","F",0
261,0,0,0,1.043896," ","integrate(x^2/(x^2+1)/(-x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 1} x^{2}}{x^{6} + x^{4} - x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-x^4 + 1)*x^2/(x^6 + x^4 - x^2 - 1), x)","F",0
262,0,0,0,1.171742," ","integrate(x^2/(-x^2+1)/(-x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + 1} x^{2}}{x^{6} - x^{4} - x^{2} + 1}, x\right)"," ",0,"integral(sqrt(-x^4 + 1)*x^2/(x^6 - x^4 - x^2 + 1), x)","F",0
263,0,0,0,1.086014," ","integrate(x^2/(x^2+1)/(x^4-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} - 1} x^{2}}{x^{6} + x^{4} - x^{2} - 1}, x\right)"," ",0,"integral(sqrt(x^4 - 1)*x^2/(x^6 + x^4 - x^2 - 1), x)","F",0
264,0,0,0,1.053588," ","integrate(x^2/(-x^2+1)/(x^4-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{4} - 1} x^{2}}{x^{6} - x^{4} - x^{2} + 1}, x\right)"," ",0,"integral(-sqrt(x^4 - 1)*x^2/(x^6 - x^4 - x^2 + 1), x)","F",0
265,0,0,0,1.240026," ","integrate(x^2/(x^2+1)/(-x^4-1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{8} \, \sqrt{2} \log\left(\frac{\sqrt{2} x + \sqrt{-x^{4} - 1}}{x^{2} + 1}\right) + \frac{1}{8} \, \sqrt{2} \log\left(-\frac{\sqrt{2} x - \sqrt{-x^{4} - 1}}{x^{2} + 1}\right) + {\rm integral}\left(-\frac{\sqrt{-x^{4} - 1}}{2 \, {\left(x^{4} + 1\right)}}, x\right)"," ",0,"-1/8*sqrt(2)*log((sqrt(2)*x + sqrt(-x^4 - 1))/(x^2 + 1)) + 1/8*sqrt(2)*log(-(sqrt(2)*x - sqrt(-x^4 - 1))/(x^2 + 1)) + integral(-1/2*sqrt(-x^4 - 1)/(x^4 + 1), x)","F",0
266,0,0,0,1.139080," ","integrate(x^2/(-x^2+1)/(-x^4-1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{8} i \, \sqrt{2} \log\left(\frac{i \, \sqrt{2} x + \sqrt{-x^{4} - 1}}{x^{2} - 1}\right) + \frac{1}{8} i \, \sqrt{2} \log\left(\frac{-i \, \sqrt{2} x + \sqrt{-x^{4} - 1}}{x^{2} - 1}\right) + {\rm integral}\left(\frac{\sqrt{-x^{4} - 1}}{2 \, {\left(x^{4} + 1\right)}}, x\right)"," ",0,"-1/8*I*sqrt(2)*log((I*sqrt(2)*x + sqrt(-x^4 - 1))/(x^2 - 1)) + 1/8*I*sqrt(2)*log((-I*sqrt(2)*x + sqrt(-x^4 - 1))/(x^2 - 1)) + integral(1/2*sqrt(-x^4 - 1)/(x^4 + 1), x)","F",0
267,1,206,0,0.854823," ","integrate(x^2*(d*x^2+c)^(1/2)*((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b c^{3} - 2 \, a c^{2} d\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 2 \, {\left(8 \, b d^{3} x^{5} + 2 \, {\left(b c d^{2} + 6 \, a d^{3}\right)} x^{3} - 3 \, {\left(b c^{2} d - 2 \, a c d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{96 \, d^{3}}, -\frac{3 \, {\left(b c^{3} - 2 \, a c^{2} d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(8 \, b d^{3} x^{5} + 2 \, {\left(b c d^{2} + 6 \, a d^{3}\right)} x^{3} - 3 \, {\left(b c^{2} d - 2 \, a c d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{48 \, d^{3}}\right]"," ",0,"[-1/96*(3*(b*c^3 - 2*a*c^2*d)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 2*(8*b*d^3*x^5 + 2*(b*c*d^2 + 6*a*d^3)*x^3 - 3*(b*c^2*d - 2*a*c*d^2)*x)*sqrt(d*x^2 + c))/d^3, -1/48*(3*(b*c^3 - 2*a*c^2*d)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (8*b*d^3*x^5 + 2*(b*c*d^2 + 6*a*d^3)*x^3 - 3*(b*c^2*d - 2*a*c*d^2)*x)*sqrt(d*x^2 + c))/d^3]","A",0
268,1,50,0,0.603734," ","integrate(x*(d*x^2+c)^(1/2)*((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, b d^{2} x^{4} - 2 \, b c^{2} + 5 \, a c d + {\left(b c d + 5 \, a d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{15 \, d^{2}}"," ",0,"1/15*(3*b*d^2*x^4 - 2*b*c^2 + 5*a*c*d + (b*c*d + 5*a*d^2)*x^2)*sqrt(d*x^2 + c)/d^2","A",0
269,1,155,0,0.941931," ","integrate((d*x^2+c)^(1/2)*((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b c^{2} - 4 \, a c d\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 2 \, {\left(2 \, b d^{2} x^{3} + {\left(b c d + 4 \, a d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{16 \, d^{2}}, \frac{{\left(b c^{2} - 4 \, a c d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(2 \, b d^{2} x^{3} + {\left(b c d + 4 \, a d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{8 \, d^{2}}\right]"," ",0,"[-1/16*((b*c^2 - 4*a*c*d)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 2*(2*b*d^2*x^3 + (b*c*d + 4*a*d^2)*x)*sqrt(d*x^2 + c))/d^2, 1/8*((b*c^2 - 4*a*c*d)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (2*b*d^2*x^3 + (b*c*d + 4*a*d^2)*x)*sqrt(d*x^2 + c))/d^2]","A",0
270,1,123,0,0.949530," ","integrate((d*x^2+c)^(1/2)*((b*x^2+a)^2)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{3 \, a \sqrt{c} d \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(b d x^{2} + b c + 3 \, a d\right)} \sqrt{d x^{2} + c}}{6 \, d}, \frac{3 \, a \sqrt{-c} d \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(b d x^{2} + b c + 3 \, a d\right)} \sqrt{d x^{2} + c}}{3 \, d}\right]"," ",0,"[1/6*(3*a*sqrt(c)*d*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(b*d*x^2 + b*c + 3*a*d)*sqrt(d*x^2 + c))/d, 1/3*(3*a*sqrt(-c)*d*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (b*d*x^2 + b*c + 3*a*d)*sqrt(d*x^2 + c))/d]","A",0
271,1,134,0,0.883439," ","integrate((d*x^2+c)^(1/2)*((b*x^2+a)^2)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{{\left(b c + 2 \, a d\right)} \sqrt{d} x \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(b d x^{2} - 2 \, a d\right)} \sqrt{d x^{2} + c}}{4 \, d x}, -\frac{{\left(b c + 2 \, a d\right)} \sqrt{-d} x \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(b d x^{2} - 2 \, a d\right)} \sqrt{d x^{2} + c}}{2 \, d x}\right]"," ",0,"[1/4*((b*c + 2*a*d)*sqrt(d)*x*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(b*d*x^2 - 2*a*d)*sqrt(d*x^2 + c))/(d*x), -1/2*((b*c + 2*a*d)*sqrt(-d)*x*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (b*d*x^2 - 2*a*d)*sqrt(d*x^2 + c))/(d*x)]","A",0
272,1,141,0,0.869011," ","integrate((d*x^2+c)^(1/2)*((b*x^2+a)^2)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, b c + a d\right)} \sqrt{c} x^{2} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(2 \, b c x^{2} - a c\right)} \sqrt{d x^{2} + c}}{4 \, c x^{2}}, \frac{{\left(2 \, b c + a d\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(2 \, b c x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, c x^{2}}\right]"," ",0,"[1/4*((2*b*c + a*d)*sqrt(c)*x^2*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(2*b*c*x^2 - a*c)*sqrt(d*x^2 + c))/(c*x^2), 1/2*((2*b*c + a*d)*sqrt(-c)*x^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (2*b*c*x^2 - a*c)*sqrt(d*x^2 + c))/(c*x^2)]","A",0
273,1,79,0,0.831188," ","integrate(x^3*(e*x^2+d)^2*(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{1}{12} x^{12} e^{2} c + \frac{1}{5} x^{10} e d c + \frac{1}{10} x^{10} e^{2} b + \frac{1}{8} x^{8} d^{2} c + \frac{1}{4} x^{8} e d b + \frac{1}{8} x^{8} e^{2} a + \frac{1}{6} x^{6} d^{2} b + \frac{1}{3} x^{6} e d a + \frac{1}{4} x^{4} d^{2} a"," ",0,"1/12*x^12*e^2*c + 1/5*x^10*e*d*c + 1/10*x^10*e^2*b + 1/8*x^8*d^2*c + 1/4*x^8*e*d*b + 1/8*x^8*e^2*a + 1/6*x^6*d^2*b + 1/3*x^6*e*d*a + 1/4*x^4*d^2*a","A",0
274,1,79,0,0.790029," ","integrate(x^2*(e*x^2+d)^2*(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{1}{11} x^{11} e^{2} c + \frac{2}{9} x^{9} e d c + \frac{1}{9} x^{9} e^{2} b + \frac{1}{7} x^{7} d^{2} c + \frac{2}{7} x^{7} e d b + \frac{1}{7} x^{7} e^{2} a + \frac{1}{5} x^{5} d^{2} b + \frac{2}{5} x^{5} e d a + \frac{1}{3} x^{3} d^{2} a"," ",0,"1/11*x^11*e^2*c + 2/9*x^9*e*d*c + 1/9*x^9*e^2*b + 1/7*x^7*d^2*c + 2/7*x^7*e*d*b + 1/7*x^7*e^2*a + 1/5*x^5*d^2*b + 2/5*x^5*e*d*a + 1/3*x^3*d^2*a","A",0
275,1,79,0,0.809493," ","integrate(x*(e*x^2+d)^2*(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{1}{10} x^{10} e^{2} c + \frac{1}{4} x^{8} e d c + \frac{1}{8} x^{8} e^{2} b + \frac{1}{6} x^{6} d^{2} c + \frac{1}{3} x^{6} e d b + \frac{1}{6} x^{6} e^{2} a + \frac{1}{4} x^{4} d^{2} b + \frac{1}{2} x^{4} e d a + \frac{1}{2} x^{2} d^{2} a"," ",0,"1/10*x^10*e^2*c + 1/4*x^8*e*d*c + 1/8*x^8*e^2*b + 1/6*x^6*d^2*c + 1/3*x^6*e*d*b + 1/6*x^6*e^2*a + 1/4*x^4*d^2*b + 1/2*x^4*e*d*a + 1/2*x^2*d^2*a","A",0
276,1,76,0,0.518252," ","integrate((e*x^2+d)^2*(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{2} c + \frac{2}{7} x^{7} e d c + \frac{1}{7} x^{7} e^{2} b + \frac{1}{5} x^{5} d^{2} c + \frac{2}{5} x^{5} e d b + \frac{1}{5} x^{5} e^{2} a + \frac{1}{3} x^{3} d^{2} b + \frac{2}{3} x^{3} e d a + x d^{2} a"," ",0,"1/9*x^9*e^2*c + 2/7*x^7*e*d*c + 1/7*x^7*e^2*b + 1/5*x^5*d^2*c + 2/5*x^5*e*d*b + 1/5*x^5*e^2*a + 1/3*x^3*d^2*b + 2/3*x^3*e*d*a + x*d^2*a","A",0
277,1,70,0,0.897066," ","integrate((e*x^2+d)^2*(c*x^4+b*x^2+a)/x,x, algorithm=""fricas"")","\frac{1}{8} \, c e^{2} x^{8} + \frac{1}{6} \, {\left(2 \, c d e + b e^{2}\right)} x^{6} + \frac{1}{4} \, {\left(c d^{2} + 2 \, b d e + a e^{2}\right)} x^{4} + a d^{2} \log\left(x\right) + \frac{1}{2} \, {\left(b d^{2} + 2 \, a d e\right)} x^{2}"," ",0,"1/8*c*e^2*x^8 + 1/6*(2*c*d*e + b*e^2)*x^6 + 1/4*(c*d^2 + 2*b*d*e + a*e^2)*x^4 + a*d^2*log(x) + 1/2*(b*d^2 + 2*a*d*e)*x^2","A",0
278,1,74,0,0.844581," ","integrate((e*x^2+d)^2*(c*x^4+b*x^2+a)/x^2,x, algorithm=""fricas"")","\frac{15 \, c e^{2} x^{8} + 21 \, {\left(2 \, c d e + b e^{2}\right)} x^{6} + 35 \, {\left(c d^{2} + 2 \, b d e + a e^{2}\right)} x^{4} - 105 \, a d^{2} + 105 \, {\left(b d^{2} + 2 \, a d e\right)} x^{2}}{105 \, x}"," ",0,"1/105*(15*c*e^2*x^8 + 21*(2*c*d*e + b*e^2)*x^6 + 35*(c*d^2 + 2*b*d*e + a*e^2)*x^4 - 105*a*d^2 + 105*(b*d^2 + 2*a*d*e)*x^2)/x","A",0
279,1,76,0,0.891273," ","integrate((e*x^2+d)^2*(c*x^4+b*x^2+a)/x^3,x, algorithm=""fricas"")","\frac{2 \, c e^{2} x^{8} + 3 \, {\left(2 \, c d e + b e^{2}\right)} x^{6} + 6 \, {\left(c d^{2} + 2 \, b d e + a e^{2}\right)} x^{4} + 12 \, {\left(b d^{2} + 2 \, a d e\right)} x^{2} \log\left(x\right) - 6 \, a d^{2}}{12 \, x^{2}}"," ",0,"1/12*(2*c*e^2*x^8 + 3*(2*c*d*e + b*e^2)*x^6 + 6*(c*d^2 + 2*b*d*e + a*e^2)*x^4 + 12*(b*d^2 + 2*a*d*e)*x^2*log(x) - 6*a*d^2)/x^2","A",0
280,1,426,0,0.985764," ","integrate(x^6*(c*x^4+b*x^2+a)/(e*x^2+d)^2,x, algorithm=""fricas"")","\left[\frac{60 \, c e^{4} x^{9} - 12 \, {\left(9 \, c d e^{3} - 7 \, b e^{4}\right)} x^{7} + 28 \, {\left(9 \, c d^{2} e^{2} - 7 \, b d e^{3} + 5 \, a e^{4}\right)} x^{5} - 140 \, {\left(9 \, c d^{3} e - 7 \, b d^{2} e^{2} + 5 \, a d e^{3}\right)} x^{3} + 105 \, {\left(9 \, c d^{4} - 7 \, b d^{3} e + 5 \, a d^{2} e^{2} + {\left(9 \, c d^{3} e - 7 \, b d^{2} e^{2} + 5 \, a d e^{3}\right)} x^{2}\right)} \sqrt{-\frac{d}{e}} \log\left(\frac{e x^{2} + 2 \, e x \sqrt{-\frac{d}{e}} - d}{e x^{2} + d}\right) - 210 \, {\left(9 \, c d^{4} - 7 \, b d^{3} e + 5 \, a d^{2} e^{2}\right)} x}{420 \, {\left(e^{6} x^{2} + d e^{5}\right)}}, \frac{30 \, c e^{4} x^{9} - 6 \, {\left(9 \, c d e^{3} - 7 \, b e^{4}\right)} x^{7} + 14 \, {\left(9 \, c d^{2} e^{2} - 7 \, b d e^{3} + 5 \, a e^{4}\right)} x^{5} - 70 \, {\left(9 \, c d^{3} e - 7 \, b d^{2} e^{2} + 5 \, a d e^{3}\right)} x^{3} + 105 \, {\left(9 \, c d^{4} - 7 \, b d^{3} e + 5 \, a d^{2} e^{2} + {\left(9 \, c d^{3} e - 7 \, b d^{2} e^{2} + 5 \, a d e^{3}\right)} x^{2}\right)} \sqrt{\frac{d}{e}} \arctan\left(\frac{e x \sqrt{\frac{d}{e}}}{d}\right) - 105 \, {\left(9 \, c d^{4} - 7 \, b d^{3} e + 5 \, a d^{2} e^{2}\right)} x}{210 \, {\left(e^{6} x^{2} + d e^{5}\right)}}\right]"," ",0,"[1/420*(60*c*e^4*x^9 - 12*(9*c*d*e^3 - 7*b*e^4)*x^7 + 28*(9*c*d^2*e^2 - 7*b*d*e^3 + 5*a*e^4)*x^5 - 140*(9*c*d^3*e - 7*b*d^2*e^2 + 5*a*d*e^3)*x^3 + 105*(9*c*d^4 - 7*b*d^3*e + 5*a*d^2*e^2 + (9*c*d^3*e - 7*b*d^2*e^2 + 5*a*d*e^3)*x^2)*sqrt(-d/e)*log((e*x^2 + 2*e*x*sqrt(-d/e) - d)/(e*x^2 + d)) - 210*(9*c*d^4 - 7*b*d^3*e + 5*a*d^2*e^2)*x)/(e^6*x^2 + d*e^5), 1/210*(30*c*e^4*x^9 - 6*(9*c*d*e^3 - 7*b*e^4)*x^7 + 14*(9*c*d^2*e^2 - 7*b*d*e^3 + 5*a*e^4)*x^5 - 70*(9*c*d^3*e - 7*b*d^2*e^2 + 5*a*d*e^3)*x^3 + 105*(9*c*d^4 - 7*b*d^3*e + 5*a*d^2*e^2 + (9*c*d^3*e - 7*b*d^2*e^2 + 5*a*d*e^3)*x^2)*sqrt(d/e)*arctan(e*x*sqrt(d/e)/d) - 105*(9*c*d^4 - 7*b*d^3*e + 5*a*d^2*e^2)*x)/(e^6*x^2 + d*e^5)]","A",0
281,1,350,0,0.992689," ","integrate(x^4*(c*x^4+b*x^2+a)/(e*x^2+d)^2,x, algorithm=""fricas"")","\left[\frac{12 \, c e^{3} x^{7} - 4 \, {\left(7 \, c d e^{2} - 5 \, b e^{3}\right)} x^{5} + 20 \, {\left(7 \, c d^{2} e - 5 \, b d e^{2} + 3 \, a e^{3}\right)} x^{3} + 15 \, {\left(7 \, c d^{3} - 5 \, b d^{2} e + 3 \, a d e^{2} + {\left(7 \, c d^{2} e - 5 \, b d e^{2} + 3 \, a e^{3}\right)} x^{2}\right)} \sqrt{-\frac{d}{e}} \log\left(\frac{e x^{2} - 2 \, e x \sqrt{-\frac{d}{e}} - d}{e x^{2} + d}\right) + 30 \, {\left(7 \, c d^{3} - 5 \, b d^{2} e + 3 \, a d e^{2}\right)} x}{60 \, {\left(e^{5} x^{2} + d e^{4}\right)}}, \frac{6 \, c e^{3} x^{7} - 2 \, {\left(7 \, c d e^{2} - 5 \, b e^{3}\right)} x^{5} + 10 \, {\left(7 \, c d^{2} e - 5 \, b d e^{2} + 3 \, a e^{3}\right)} x^{3} - 15 \, {\left(7 \, c d^{3} - 5 \, b d^{2} e + 3 \, a d e^{2} + {\left(7 \, c d^{2} e - 5 \, b d e^{2} + 3 \, a e^{3}\right)} x^{2}\right)} \sqrt{\frac{d}{e}} \arctan\left(\frac{e x \sqrt{\frac{d}{e}}}{d}\right) + 15 \, {\left(7 \, c d^{3} - 5 \, b d^{2} e + 3 \, a d e^{2}\right)} x}{30 \, {\left(e^{5} x^{2} + d e^{4}\right)}}\right]"," ",0,"[1/60*(12*c*e^3*x^7 - 4*(7*c*d*e^2 - 5*b*e^3)*x^5 + 20*(7*c*d^2*e - 5*b*d*e^2 + 3*a*e^3)*x^3 + 15*(7*c*d^3 - 5*b*d^2*e + 3*a*d*e^2 + (7*c*d^2*e - 5*b*d*e^2 + 3*a*e^3)*x^2)*sqrt(-d/e)*log((e*x^2 - 2*e*x*sqrt(-d/e) - d)/(e*x^2 + d)) + 30*(7*c*d^3 - 5*b*d^2*e + 3*a*d*e^2)*x)/(e^5*x^2 + d*e^4), 1/30*(6*c*e^3*x^7 - 2*(7*c*d*e^2 - 5*b*e^3)*x^5 + 10*(7*c*d^2*e - 5*b*d*e^2 + 3*a*e^3)*x^3 - 15*(7*c*d^3 - 5*b*d^2*e + 3*a*d*e^2 + (7*c*d^2*e - 5*b*d*e^2 + 3*a*e^3)*x^2)*sqrt(d/e)*arctan(e*x*sqrt(d/e)/d) + 15*(7*c*d^3 - 5*b*d^2*e + 3*a*d*e^2)*x)/(e^5*x^2 + d*e^4)]","A",0
282,1,302,0,1.028935," ","integrate(x^2*(c*x^4+b*x^2+a)/(e*x^2+d)^2,x, algorithm=""fricas"")","\left[\frac{4 \, c d e^{3} x^{5} - 4 \, {\left(5 \, c d^{2} e^{2} - 3 \, b d e^{3}\right)} x^{3} - 3 \, {\left(5 \, c d^{3} - 3 \, b d^{2} e + a d e^{2} + {\left(5 \, c d^{2} e - 3 \, b d e^{2} + a e^{3}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) - 6 \, {\left(5 \, c d^{3} e - 3 \, b d^{2} e^{2} + a d e^{3}\right)} x}{12 \, {\left(d e^{5} x^{2} + d^{2} e^{4}\right)}}, \frac{2 \, c d e^{3} x^{5} - 2 \, {\left(5 \, c d^{2} e^{2} - 3 \, b d e^{3}\right)} x^{3} + 3 \, {\left(5 \, c d^{3} - 3 \, b d^{2} e + a d e^{2} + {\left(5 \, c d^{2} e - 3 \, b d e^{2} + a e^{3}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) - 3 \, {\left(5 \, c d^{3} e - 3 \, b d^{2} e^{2} + a d e^{3}\right)} x}{6 \, {\left(d e^{5} x^{2} + d^{2} e^{4}\right)}}\right]"," ",0,"[1/12*(4*c*d*e^3*x^5 - 4*(5*c*d^2*e^2 - 3*b*d*e^3)*x^3 - 3*(5*c*d^3 - 3*b*d^2*e + a*d*e^2 + (5*c*d^2*e - 3*b*d*e^2 + a*e^3)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) - 6*(5*c*d^3*e - 3*b*d^2*e^2 + a*d*e^3)*x)/(d*e^5*x^2 + d^2*e^4), 1/6*(2*c*d*e^3*x^5 - 2*(5*c*d^2*e^2 - 3*b*d*e^3)*x^3 + 3*(5*c*d^3 - 3*b*d^2*e + a*d*e^2 + (5*c*d^2*e - 3*b*d*e^2 + a*e^3)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) - 3*(5*c*d^3*e - 3*b*d^2*e^2 + a*d*e^3)*x)/(d*e^5*x^2 + d^2*e^4)]","A",0
283,1,268,0,1.084594," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^2,x, algorithm=""fricas"")","\left[\frac{4 \, c d^{2} e^{2} x^{3} + {\left(3 \, c d^{3} - b d^{2} e - a d e^{2} + {\left(3 \, c d^{2} e - b d e^{2} - a e^{3}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 2 \, {\left(3 \, c d^{3} e - b d^{2} e^{2} + a d e^{3}\right)} x}{4 \, {\left(d^{2} e^{4} x^{2} + d^{3} e^{3}\right)}}, \frac{2 \, c d^{2} e^{2} x^{3} - {\left(3 \, c d^{3} - b d^{2} e - a d e^{2} + {\left(3 \, c d^{2} e - b d e^{2} - a e^{3}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + {\left(3 \, c d^{3} e - b d^{2} e^{2} + a d e^{3}\right)} x}{2 \, {\left(d^{2} e^{4} x^{2} + d^{3} e^{3}\right)}}\right]"," ",0,"[1/4*(4*c*d^2*e^2*x^3 + (3*c*d^3 - b*d^2*e - a*d*e^2 + (3*c*d^2*e - b*d*e^2 - a*e^3)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 2*(3*c*d^3*e - b*d^2*e^2 + a*d*e^3)*x)/(d^2*e^4*x^2 + d^3*e^3), 1/2*(2*c*d^2*e^2*x^3 - (3*c*d^3 - b*d^2*e - a*d*e^2 + (3*c*d^2*e - b*d*e^2 - a*e^3)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + (3*c*d^3*e - b*d^2*e^2 + a*d*e^3)*x)/(d^2*e^4*x^2 + d^3*e^3)]","A",0
284,1,267,0,0.899438," ","integrate((c*x^4+b*x^2+a)/x^2/(e*x^2+d)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a d^{2} e^{2} + 2 \, {\left(c d^{3} e - b d^{2} e^{2} + 3 \, a d e^{3}\right)} x^{2} - {\left({\left(c d^{2} e + b d e^{2} - 3 \, a e^{3}\right)} x^{3} + {\left(c d^{3} + b d^{2} e - 3 \, a d e^{2}\right)} x\right)} \sqrt{-d e} \log\left(\frac{e x^{2} + 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right)}{4 \, {\left(d^{3} e^{3} x^{3} + d^{4} e^{2} x\right)}}, -\frac{2 \, a d^{2} e^{2} + {\left(c d^{3} e - b d^{2} e^{2} + 3 \, a d e^{3}\right)} x^{2} - {\left({\left(c d^{2} e + b d e^{2} - 3 \, a e^{3}\right)} x^{3} + {\left(c d^{3} + b d^{2} e - 3 \, a d e^{2}\right)} x\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right)}{2 \, {\left(d^{3} e^{3} x^{3} + d^{4} e^{2} x\right)}}\right]"," ",0,"[-1/4*(4*a*d^2*e^2 + 2*(c*d^3*e - b*d^2*e^2 + 3*a*d*e^3)*x^2 - ((c*d^2*e + b*d*e^2 - 3*a*e^3)*x^3 + (c*d^3 + b*d^2*e - 3*a*d*e^2)*x)*sqrt(-d*e)*log((e*x^2 + 2*sqrt(-d*e)*x - d)/(e*x^2 + d)))/(d^3*e^3*x^3 + d^4*e^2*x), -1/2*(2*a*d^2*e^2 + (c*d^3*e - b*d^2*e^2 + 3*a*d*e^3)*x^2 - ((c*d^2*e + b*d*e^2 - 3*a*e^3)*x^3 + (c*d^3 + b*d^2*e - 3*a*d*e^2)*x)*sqrt(d*e)*arctan(sqrt(d*e)*x/d))/(d^3*e^3*x^3 + d^4*e^2*x)]","A",0
285,1,316,0,0.882466," ","integrate((c*x^4+b*x^2+a)/x^4/(e*x^2+d)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a d^{3} e - 6 \, {\left(c d^{3} e - 3 \, b d^{2} e^{2} + 5 \, a d e^{3}\right)} x^{4} + 4 \, {\left(3 \, b d^{3} e - 5 \, a d^{2} e^{2}\right)} x^{2} + 3 \, {\left({\left(c d^{2} e - 3 \, b d e^{2} + 5 \, a e^{3}\right)} x^{5} + {\left(c d^{3} - 3 \, b d^{2} e + 5 \, a d e^{2}\right)} x^{3}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right)}{12 \, {\left(d^{4} e^{2} x^{5} + d^{5} e x^{3}\right)}}, -\frac{2 \, a d^{3} e - 3 \, {\left(c d^{3} e - 3 \, b d^{2} e^{2} + 5 \, a d e^{3}\right)} x^{4} + 2 \, {\left(3 \, b d^{3} e - 5 \, a d^{2} e^{2}\right)} x^{2} - 3 \, {\left({\left(c d^{2} e - 3 \, b d e^{2} + 5 \, a e^{3}\right)} x^{5} + {\left(c d^{3} - 3 \, b d^{2} e + 5 \, a d e^{2}\right)} x^{3}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right)}{6 \, {\left(d^{4} e^{2} x^{5} + d^{5} e x^{3}\right)}}\right]"," ",0,"[-1/12*(4*a*d^3*e - 6*(c*d^3*e - 3*b*d^2*e^2 + 5*a*d*e^3)*x^4 + 4*(3*b*d^3*e - 5*a*d^2*e^2)*x^2 + 3*((c*d^2*e - 3*b*d*e^2 + 5*a*e^3)*x^5 + (c*d^3 - 3*b*d^2*e + 5*a*d*e^2)*x^3)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)))/(d^4*e^2*x^5 + d^5*e*x^3), -1/6*(2*a*d^3*e - 3*(c*d^3*e - 3*b*d^2*e^2 + 5*a*d*e^3)*x^4 + 2*(3*b*d^3*e - 5*a*d^2*e^2)*x^2 - 3*((c*d^2*e - 3*b*d*e^2 + 5*a*e^3)*x^5 + (c*d^3 - 3*b*d^2*e + 5*a*d*e^2)*x^3)*sqrt(d*e)*arctan(sqrt(d*e)*x/d))/(d^4*e^2*x^5 + d^5*e*x^3)]","A",0
286,1,360,0,0.858487," ","integrate((c*x^4+b*x^2+a)/x^6/(e*x^2+d)^2,x, algorithm=""fricas"")","\left[-\frac{30 \, {\left(3 \, c d^{2} e - 5 \, b d e^{2} + 7 \, a e^{3}\right)} x^{6} + 20 \, {\left(3 \, c d^{3} - 5 \, b d^{2} e + 7 \, a d e^{2}\right)} x^{4} + 12 \, a d^{3} + 4 \, {\left(5 \, b d^{3} - 7 \, a d^{2} e\right)} x^{2} - 15 \, {\left({\left(3 \, c d^{2} e - 5 \, b d e^{2} + 7 \, a e^{3}\right)} x^{7} + {\left(3 \, c d^{3} - 5 \, b d^{2} e + 7 \, a d e^{2}\right)} x^{5}\right)} \sqrt{-\frac{e}{d}} \log\left(\frac{e x^{2} - 2 \, d x \sqrt{-\frac{e}{d}} - d}{e x^{2} + d}\right)}{60 \, {\left(d^{4} e x^{7} + d^{5} x^{5}\right)}}, -\frac{15 \, {\left(3 \, c d^{2} e - 5 \, b d e^{2} + 7 \, a e^{3}\right)} x^{6} + 10 \, {\left(3 \, c d^{3} - 5 \, b d^{2} e + 7 \, a d e^{2}\right)} x^{4} + 6 \, a d^{3} + 2 \, {\left(5 \, b d^{3} - 7 \, a d^{2} e\right)} x^{2} + 15 \, {\left({\left(3 \, c d^{2} e - 5 \, b d e^{2} + 7 \, a e^{3}\right)} x^{7} + {\left(3 \, c d^{3} - 5 \, b d^{2} e + 7 \, a d e^{2}\right)} x^{5}\right)} \sqrt{\frac{e}{d}} \arctan\left(x \sqrt{\frac{e}{d}}\right)}{30 \, {\left(d^{4} e x^{7} + d^{5} x^{5}\right)}}\right]"," ",0,"[-1/60*(30*(3*c*d^2*e - 5*b*d*e^2 + 7*a*e^3)*x^6 + 20*(3*c*d^3 - 5*b*d^2*e + 7*a*d*e^2)*x^4 + 12*a*d^3 + 4*(5*b*d^3 - 7*a*d^2*e)*x^2 - 15*((3*c*d^2*e - 5*b*d*e^2 + 7*a*e^3)*x^7 + (3*c*d^3 - 5*b*d^2*e + 7*a*d*e^2)*x^5)*sqrt(-e/d)*log((e*x^2 - 2*d*x*sqrt(-e/d) - d)/(e*x^2 + d)))/(d^4*e*x^7 + d^5*x^5), -1/30*(15*(3*c*d^2*e - 5*b*d*e^2 + 7*a*e^3)*x^6 + 10*(3*c*d^3 - 5*b*d^2*e + 7*a*d*e^2)*x^4 + 6*a*d^3 + 2*(5*b*d^3 - 7*a*d^2*e)*x^2 + 15*((3*c*d^2*e - 5*b*d*e^2 + 7*a*e^3)*x^7 + (3*c*d^3 - 5*b*d^2*e + 7*a*d*e^2)*x^5)*sqrt(e/d)*arctan(x*sqrt(e/d)))/(d^4*e*x^7 + d^5*x^5)]","A",0
287,1,436,0,0.916814," ","integrate((c*x^4+b*x^2+a)/x^8/(e*x^2+d)^2,x, algorithm=""fricas"")","\left[\frac{210 \, {\left(5 \, c d^{2} e^{2} - 7 \, b d e^{3} + 9 \, a e^{4}\right)} x^{8} + 140 \, {\left(5 \, c d^{3} e - 7 \, b d^{2} e^{2} + 9 \, a d e^{3}\right)} x^{6} - 60 \, a d^{4} - 28 \, {\left(5 \, c d^{4} - 7 \, b d^{3} e + 9 \, a d^{2} e^{2}\right)} x^{4} - 12 \, {\left(7 \, b d^{4} - 9 \, a d^{3} e\right)} x^{2} + 105 \, {\left({\left(5 \, c d^{2} e^{2} - 7 \, b d e^{3} + 9 \, a e^{4}\right)} x^{9} + {\left(5 \, c d^{3} e - 7 \, b d^{2} e^{2} + 9 \, a d e^{3}\right)} x^{7}\right)} \sqrt{-\frac{e}{d}} \log\left(\frac{e x^{2} + 2 \, d x \sqrt{-\frac{e}{d}} - d}{e x^{2} + d}\right)}{420 \, {\left(d^{5} e x^{9} + d^{6} x^{7}\right)}}, \frac{105 \, {\left(5 \, c d^{2} e^{2} - 7 \, b d e^{3} + 9 \, a e^{4}\right)} x^{8} + 70 \, {\left(5 \, c d^{3} e - 7 \, b d^{2} e^{2} + 9 \, a d e^{3}\right)} x^{6} - 30 \, a d^{4} - 14 \, {\left(5 \, c d^{4} - 7 \, b d^{3} e + 9 \, a d^{2} e^{2}\right)} x^{4} - 6 \, {\left(7 \, b d^{4} - 9 \, a d^{3} e\right)} x^{2} + 105 \, {\left({\left(5 \, c d^{2} e^{2} - 7 \, b d e^{3} + 9 \, a e^{4}\right)} x^{9} + {\left(5 \, c d^{3} e - 7 \, b d^{2} e^{2} + 9 \, a d e^{3}\right)} x^{7}\right)} \sqrt{\frac{e}{d}} \arctan\left(x \sqrt{\frac{e}{d}}\right)}{210 \, {\left(d^{5} e x^{9} + d^{6} x^{7}\right)}}\right]"," ",0,"[1/420*(210*(5*c*d^2*e^2 - 7*b*d*e^3 + 9*a*e^4)*x^8 + 140*(5*c*d^3*e - 7*b*d^2*e^2 + 9*a*d*e^3)*x^6 - 60*a*d^4 - 28*(5*c*d^4 - 7*b*d^3*e + 9*a*d^2*e^2)*x^4 - 12*(7*b*d^4 - 9*a*d^3*e)*x^2 + 105*((5*c*d^2*e^2 - 7*b*d*e^3 + 9*a*e^4)*x^9 + (5*c*d^3*e - 7*b*d^2*e^2 + 9*a*d*e^3)*x^7)*sqrt(-e/d)*log((e*x^2 + 2*d*x*sqrt(-e/d) - d)/(e*x^2 + d)))/(d^5*e*x^9 + d^6*x^7), 1/210*(105*(5*c*d^2*e^2 - 7*b*d*e^3 + 9*a*e^4)*x^8 + 70*(5*c*d^3*e - 7*b*d^2*e^2 + 9*a*d*e^3)*x^6 - 30*a*d^4 - 14*(5*c*d^4 - 7*b*d^3*e + 9*a*d^2*e^2)*x^4 - 6*(7*b*d^4 - 9*a*d^3*e)*x^2 + 105*((5*c*d^2*e^2 - 7*b*d*e^3 + 9*a*e^4)*x^9 + (5*c*d^3*e - 7*b*d^2*e^2 + 9*a*d*e^3)*x^7)*sqrt(e/d)*arctan(x*sqrt(e/d)))/(d^5*e*x^9 + d^6*x^7)]","A",0
288,1,504,0,0.726977," ","integrate(x^6*(c*x^4+b*x^2+a)/(e*x^2+d)^3,x, algorithm=""fricas"")","\left[\frac{48 \, c e^{4} x^{9} - 16 \, {\left(9 \, c d e^{3} - 5 \, b e^{4}\right)} x^{7} + 16 \, {\left(63 \, c d^{2} e^{2} - 35 \, b d e^{3} + 15 \, a e^{4}\right)} x^{5} + 50 \, {\left(63 \, c d^{3} e - 35 \, b d^{2} e^{2} + 15 \, a d e^{3}\right)} x^{3} + 15 \, {\left(63 \, c d^{4} - 35 \, b d^{3} e + 15 \, a d^{2} e^{2} + {\left(63 \, c d^{2} e^{2} - 35 \, b d e^{3} + 15 \, a e^{4}\right)} x^{4} + 2 \, {\left(63 \, c d^{3} e - 35 \, b d^{2} e^{2} + 15 \, a d e^{3}\right)} x^{2}\right)} \sqrt{-\frac{d}{e}} \log\left(\frac{e x^{2} - 2 \, e x \sqrt{-\frac{d}{e}} - d}{e x^{2} + d}\right) + 30 \, {\left(63 \, c d^{4} - 35 \, b d^{3} e + 15 \, a d^{2} e^{2}\right)} x}{240 \, {\left(e^{7} x^{4} + 2 \, d e^{6} x^{2} + d^{2} e^{5}\right)}}, \frac{24 \, c e^{4} x^{9} - 8 \, {\left(9 \, c d e^{3} - 5 \, b e^{4}\right)} x^{7} + 8 \, {\left(63 \, c d^{2} e^{2} - 35 \, b d e^{3} + 15 \, a e^{4}\right)} x^{5} + 25 \, {\left(63 \, c d^{3} e - 35 \, b d^{2} e^{2} + 15 \, a d e^{3}\right)} x^{3} - 15 \, {\left(63 \, c d^{4} - 35 \, b d^{3} e + 15 \, a d^{2} e^{2} + {\left(63 \, c d^{2} e^{2} - 35 \, b d e^{3} + 15 \, a e^{4}\right)} x^{4} + 2 \, {\left(63 \, c d^{3} e - 35 \, b d^{2} e^{2} + 15 \, a d e^{3}\right)} x^{2}\right)} \sqrt{\frac{d}{e}} \arctan\left(\frac{e x \sqrt{\frac{d}{e}}}{d}\right) + 15 \, {\left(63 \, c d^{4} - 35 \, b d^{3} e + 15 \, a d^{2} e^{2}\right)} x}{120 \, {\left(e^{7} x^{4} + 2 \, d e^{6} x^{2} + d^{2} e^{5}\right)}}\right]"," ",0,"[1/240*(48*c*e^4*x^9 - 16*(9*c*d*e^3 - 5*b*e^4)*x^7 + 16*(63*c*d^2*e^2 - 35*b*d*e^3 + 15*a*e^4)*x^5 + 50*(63*c*d^3*e - 35*b*d^2*e^2 + 15*a*d*e^3)*x^3 + 15*(63*c*d^4 - 35*b*d^3*e + 15*a*d^2*e^2 + (63*c*d^2*e^2 - 35*b*d*e^3 + 15*a*e^4)*x^4 + 2*(63*c*d^3*e - 35*b*d^2*e^2 + 15*a*d*e^3)*x^2)*sqrt(-d/e)*log((e*x^2 - 2*e*x*sqrt(-d/e) - d)/(e*x^2 + d)) + 30*(63*c*d^4 - 35*b*d^3*e + 15*a*d^2*e^2)*x)/(e^7*x^4 + 2*d*e^6*x^2 + d^2*e^5), 1/120*(24*c*e^4*x^9 - 8*(9*c*d*e^3 - 5*b*e^4)*x^7 + 8*(63*c*d^2*e^2 - 35*b*d*e^3 + 15*a*e^4)*x^5 + 25*(63*c*d^3*e - 35*b*d^2*e^2 + 15*a*d*e^3)*x^3 - 15*(63*c*d^4 - 35*b*d^3*e + 15*a*d^2*e^2 + (63*c*d^2*e^2 - 35*b*d*e^3 + 15*a*e^4)*x^4 + 2*(63*c*d^3*e - 35*b*d^2*e^2 + 15*a*d*e^3)*x^2)*sqrt(d/e)*arctan(e*x*sqrt(d/e)/d) + 15*(63*c*d^4 - 35*b*d^3*e + 15*a*d^2*e^2)*x)/(e^7*x^4 + 2*d*e^6*x^2 + d^2*e^5)]","A",0
289,1,462,0,0.607814," ","integrate(x^4*(c*x^4+b*x^2+a)/(e*x^2+d)^3,x, algorithm=""fricas"")","\left[\frac{16 \, c d e^{4} x^{7} - 16 \, {\left(7 \, c d^{2} e^{3} - 3 \, b d e^{4}\right)} x^{5} - 10 \, {\left(35 \, c d^{3} e^{2} - 15 \, b d^{2} e^{3} + 3 \, a d e^{4}\right)} x^{3} - 3 \, {\left(35 \, c d^{4} - 15 \, b d^{3} e + 3 \, a d^{2} e^{2} + {\left(35 \, c d^{2} e^{2} - 15 \, b d e^{3} + 3 \, a e^{4}\right)} x^{4} + 2 \, {\left(35 \, c d^{3} e - 15 \, b d^{2} e^{2} + 3 \, a d e^{3}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) - 6 \, {\left(35 \, c d^{4} e - 15 \, b d^{3} e^{2} + 3 \, a d^{2} e^{3}\right)} x}{48 \, {\left(d e^{7} x^{4} + 2 \, d^{2} e^{6} x^{2} + d^{3} e^{5}\right)}}, \frac{8 \, c d e^{4} x^{7} - 8 \, {\left(7 \, c d^{2} e^{3} - 3 \, b d e^{4}\right)} x^{5} - 5 \, {\left(35 \, c d^{3} e^{2} - 15 \, b d^{2} e^{3} + 3 \, a d e^{4}\right)} x^{3} + 3 \, {\left(35 \, c d^{4} - 15 \, b d^{3} e + 3 \, a d^{2} e^{2} + {\left(35 \, c d^{2} e^{2} - 15 \, b d e^{3} + 3 \, a e^{4}\right)} x^{4} + 2 \, {\left(35 \, c d^{3} e - 15 \, b d^{2} e^{2} + 3 \, a d e^{3}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) - 3 \, {\left(35 \, c d^{4} e - 15 \, b d^{3} e^{2} + 3 \, a d^{2} e^{3}\right)} x}{24 \, {\left(d e^{7} x^{4} + 2 \, d^{2} e^{6} x^{2} + d^{3} e^{5}\right)}}\right]"," ",0,"[1/48*(16*c*d*e^4*x^7 - 16*(7*c*d^2*e^3 - 3*b*d*e^4)*x^5 - 10*(35*c*d^3*e^2 - 15*b*d^2*e^3 + 3*a*d*e^4)*x^3 - 3*(35*c*d^4 - 15*b*d^3*e + 3*a*d^2*e^2 + (35*c*d^2*e^2 - 15*b*d*e^3 + 3*a*e^4)*x^4 + 2*(35*c*d^3*e - 15*b*d^2*e^2 + 3*a*d*e^3)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) - 6*(35*c*d^4*e - 15*b*d^3*e^2 + 3*a*d^2*e^3)*x)/(d*e^7*x^4 + 2*d^2*e^6*x^2 + d^3*e^5), 1/24*(8*c*d*e^4*x^7 - 8*(7*c*d^2*e^3 - 3*b*d*e^4)*x^5 - 5*(35*c*d^3*e^2 - 15*b*d^2*e^3 + 3*a*d*e^4)*x^3 + 3*(35*c*d^4 - 15*b*d^3*e + 3*a*d^2*e^2 + (35*c*d^2*e^2 - 15*b*d*e^3 + 3*a*e^4)*x^4 + 2*(35*c*d^3*e - 15*b*d^2*e^2 + 3*a*d*e^3)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) - 3*(35*c*d^4*e - 15*b*d^3*e^2 + 3*a*d^2*e^3)*x)/(d*e^7*x^4 + 2*d^2*e^6*x^2 + d^3*e^5)]","A",0
290,1,421,0,0.579255," ","integrate(x^2*(c*x^4+b*x^2+a)/(e*x^2+d)^3,x, algorithm=""fricas"")","\left[\frac{16 \, c d^{2} e^{3} x^{5} + 2 \, {\left(25 \, c d^{3} e^{2} - 5 \, b d^{2} e^{3} + a d e^{4}\right)} x^{3} + {\left(15 \, c d^{4} - 3 \, b d^{3} e - a d^{2} e^{2} + {\left(15 \, c d^{2} e^{2} - 3 \, b d e^{3} - a e^{4}\right)} x^{4} + 2 \, {\left(15 \, c d^{3} e - 3 \, b d^{2} e^{2} - a d e^{3}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 2 \, {\left(15 \, c d^{4} e - 3 \, b d^{3} e^{2} - a d^{2} e^{3}\right)} x}{16 \, {\left(d^{2} e^{6} x^{4} + 2 \, d^{3} e^{5} x^{2} + d^{4} e^{4}\right)}}, \frac{8 \, c d^{2} e^{3} x^{5} + {\left(25 \, c d^{3} e^{2} - 5 \, b d^{2} e^{3} + a d e^{4}\right)} x^{3} - {\left(15 \, c d^{4} - 3 \, b d^{3} e - a d^{2} e^{2} + {\left(15 \, c d^{2} e^{2} - 3 \, b d e^{3} - a e^{4}\right)} x^{4} + 2 \, {\left(15 \, c d^{3} e - 3 \, b d^{2} e^{2} - a d e^{3}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + {\left(15 \, c d^{4} e - 3 \, b d^{3} e^{2} - a d^{2} e^{3}\right)} x}{8 \, {\left(d^{2} e^{6} x^{4} + 2 \, d^{3} e^{5} x^{2} + d^{4} e^{4}\right)}}\right]"," ",0,"[1/16*(16*c*d^2*e^3*x^5 + 2*(25*c*d^3*e^2 - 5*b*d^2*e^3 + a*d*e^4)*x^3 + (15*c*d^4 - 3*b*d^3*e - a*d^2*e^2 + (15*c*d^2*e^2 - 3*b*d*e^3 - a*e^4)*x^4 + 2*(15*c*d^3*e - 3*b*d^2*e^2 - a*d*e^3)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 2*(15*c*d^4*e - 3*b*d^3*e^2 - a*d^2*e^3)*x)/(d^2*e^6*x^4 + 2*d^3*e^5*x^2 + d^4*e^4), 1/8*(8*c*d^2*e^3*x^5 + (25*c*d^3*e^2 - 5*b*d^2*e^3 + a*d*e^4)*x^3 - (15*c*d^4 - 3*b*d^3*e - a*d^2*e^2 + (15*c*d^2*e^2 - 3*b*d*e^3 - a*e^4)*x^4 + 2*(15*c*d^3*e - 3*b*d^2*e^2 - a*d*e^3)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + (15*c*d^4*e - 3*b*d^3*e^2 - a*d^2*e^3)*x)/(d^2*e^6*x^4 + 2*d^3*e^5*x^2 + d^4*e^4)]","A",0
291,1,391,0,0.646576," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(5 \, c d^{3} e^{2} - b d^{2} e^{3} - 3 \, a d e^{4}\right)} x^{3} + {\left(3 \, c d^{4} + b d^{3} e + 3 \, a d^{2} e^{2} + {\left(3 \, c d^{2} e^{2} + b d e^{3} + 3 \, a e^{4}\right)} x^{4} + 2 \, {\left(3 \, c d^{3} e + b d^{2} e^{2} + 3 \, a d e^{3}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 2 \, {\left(3 \, c d^{4} e + b d^{3} e^{2} - 5 \, a d^{2} e^{3}\right)} x}{16 \, {\left(d^{3} e^{5} x^{4} + 2 \, d^{4} e^{4} x^{2} + d^{5} e^{3}\right)}}, -\frac{{\left(5 \, c d^{3} e^{2} - b d^{2} e^{3} - 3 \, a d e^{4}\right)} x^{3} - {\left(3 \, c d^{4} + b d^{3} e + 3 \, a d^{2} e^{2} + {\left(3 \, c d^{2} e^{2} + b d e^{3} + 3 \, a e^{4}\right)} x^{4} + 2 \, {\left(3 \, c d^{3} e + b d^{2} e^{2} + 3 \, a d e^{3}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + {\left(3 \, c d^{4} e + b d^{3} e^{2} - 5 \, a d^{2} e^{3}\right)} x}{8 \, {\left(d^{3} e^{5} x^{4} + 2 \, d^{4} e^{4} x^{2} + d^{5} e^{3}\right)}}\right]"," ",0,"[-1/16*(2*(5*c*d^3*e^2 - b*d^2*e^3 - 3*a*d*e^4)*x^3 + (3*c*d^4 + b*d^3*e + 3*a*d^2*e^2 + (3*c*d^2*e^2 + b*d*e^3 + 3*a*e^4)*x^4 + 2*(3*c*d^3*e + b*d^2*e^2 + 3*a*d*e^3)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 2*(3*c*d^4*e + b*d^3*e^2 - 5*a*d^2*e^3)*x)/(d^3*e^5*x^4 + 2*d^4*e^4*x^2 + d^5*e^3), -1/8*((5*c*d^3*e^2 - b*d^2*e^3 - 3*a*d*e^4)*x^3 - (3*c*d^4 + b*d^3*e + 3*a*d^2*e^2 + (3*c*d^2*e^2 + b*d*e^3 + 3*a*e^4)*x^4 + 2*(3*c*d^3*e + b*d^2*e^2 + 3*a*d*e^3)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + (3*c*d^4*e + b*d^3*e^2 - 5*a*d^2*e^3)*x)/(d^3*e^5*x^4 + 2*d^4*e^4*x^2 + d^5*e^3)]","A",0
292,1,421,0,0.666173," ","integrate((c*x^4+b*x^2+a)/x^2/(e*x^2+d)^3,x, algorithm=""fricas"")","\left[-\frac{16 \, a d^{3} e^{2} - 2 \, {\left(c d^{3} e^{2} + 3 \, b d^{2} e^{3} - 15 \, a d e^{4}\right)} x^{4} + 2 \, {\left(c d^{4} e - 5 \, b d^{3} e^{2} + 25 \, a d^{2} e^{3}\right)} x^{2} - {\left({\left(c d^{2} e^{2} + 3 \, b d e^{3} - 15 \, a e^{4}\right)} x^{5} + 2 \, {\left(c d^{3} e + 3 \, b d^{2} e^{2} - 15 \, a d e^{3}\right)} x^{3} + {\left(c d^{4} + 3 \, b d^{3} e - 15 \, a d^{2} e^{2}\right)} x\right)} \sqrt{-d e} \log\left(\frac{e x^{2} + 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right)}{16 \, {\left(d^{4} e^{4} x^{5} + 2 \, d^{5} e^{3} x^{3} + d^{6} e^{2} x\right)}}, -\frac{8 \, a d^{3} e^{2} - {\left(c d^{3} e^{2} + 3 \, b d^{2} e^{3} - 15 \, a d e^{4}\right)} x^{4} + {\left(c d^{4} e - 5 \, b d^{3} e^{2} + 25 \, a d^{2} e^{3}\right)} x^{2} - {\left({\left(c d^{2} e^{2} + 3 \, b d e^{3} - 15 \, a e^{4}\right)} x^{5} + 2 \, {\left(c d^{3} e + 3 \, b d^{2} e^{2} - 15 \, a d e^{3}\right)} x^{3} + {\left(c d^{4} + 3 \, b d^{3} e - 15 \, a d^{2} e^{2}\right)} x\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right)}{8 \, {\left(d^{4} e^{4} x^{5} + 2 \, d^{5} e^{3} x^{3} + d^{6} e^{2} x\right)}}\right]"," ",0,"[-1/16*(16*a*d^3*e^2 - 2*(c*d^3*e^2 + 3*b*d^2*e^3 - 15*a*d*e^4)*x^4 + 2*(c*d^4*e - 5*b*d^3*e^2 + 25*a*d^2*e^3)*x^2 - ((c*d^2*e^2 + 3*b*d*e^3 - 15*a*e^4)*x^5 + 2*(c*d^3*e + 3*b*d^2*e^2 - 15*a*d*e^3)*x^3 + (c*d^4 + 3*b*d^3*e - 15*a*d^2*e^2)*x)*sqrt(-d*e)*log((e*x^2 + 2*sqrt(-d*e)*x - d)/(e*x^2 + d)))/(d^4*e^4*x^5 + 2*d^5*e^3*x^3 + d^6*e^2*x), -1/8*(8*a*d^3*e^2 - (c*d^3*e^2 + 3*b*d^2*e^3 - 15*a*d*e^4)*x^4 + (c*d^4*e - 5*b*d^3*e^2 + 25*a*d^2*e^3)*x^2 - ((c*d^2*e^2 + 3*b*d*e^3 - 15*a*e^4)*x^5 + 2*(c*d^3*e + 3*b*d^2*e^2 - 15*a*d*e^3)*x^3 + (c*d^4 + 3*b*d^3*e - 15*a*d^2*e^2)*x)*sqrt(d*e)*arctan(sqrt(d*e)*x/d))/(d^4*e^4*x^5 + 2*d^5*e^3*x^3 + d^6*e^2*x)]","A",0
293,1,476,0,0.781493," ","integrate((c*x^4+b*x^2+a)/x^4/(e*x^2+d)^3,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(3 \, c d^{3} e^{2} - 15 \, b d^{2} e^{3} + 35 \, a d e^{4}\right)} x^{6} - 16 \, a d^{4} e + 10 \, {\left(3 \, c d^{4} e - 15 \, b d^{3} e^{2} + 35 \, a d^{2} e^{3}\right)} x^{4} - 16 \, {\left(3 \, b d^{4} e - 7 \, a d^{3} e^{2}\right)} x^{2} - 3 \, {\left({\left(3 \, c d^{2} e^{2} - 15 \, b d e^{3} + 35 \, a e^{4}\right)} x^{7} + 2 \, {\left(3 \, c d^{3} e - 15 \, b d^{2} e^{2} + 35 \, a d e^{3}\right)} x^{5} + {\left(3 \, c d^{4} - 15 \, b d^{3} e + 35 \, a d^{2} e^{2}\right)} x^{3}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right)}{48 \, {\left(d^{5} e^{3} x^{7} + 2 \, d^{6} e^{2} x^{5} + d^{7} e x^{3}\right)}}, \frac{3 \, {\left(3 \, c d^{3} e^{2} - 15 \, b d^{2} e^{3} + 35 \, a d e^{4}\right)} x^{6} - 8 \, a d^{4} e + 5 \, {\left(3 \, c d^{4} e - 15 \, b d^{3} e^{2} + 35 \, a d^{2} e^{3}\right)} x^{4} - 8 \, {\left(3 \, b d^{4} e - 7 \, a d^{3} e^{2}\right)} x^{2} + 3 \, {\left({\left(3 \, c d^{2} e^{2} - 15 \, b d e^{3} + 35 \, a e^{4}\right)} x^{7} + 2 \, {\left(3 \, c d^{3} e - 15 \, b d^{2} e^{2} + 35 \, a d e^{3}\right)} x^{5} + {\left(3 \, c d^{4} - 15 \, b d^{3} e + 35 \, a d^{2} e^{2}\right)} x^{3}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right)}{24 \, {\left(d^{5} e^{3} x^{7} + 2 \, d^{6} e^{2} x^{5} + d^{7} e x^{3}\right)}}\right]"," ",0,"[1/48*(6*(3*c*d^3*e^2 - 15*b*d^2*e^3 + 35*a*d*e^4)*x^6 - 16*a*d^4*e + 10*(3*c*d^4*e - 15*b*d^3*e^2 + 35*a*d^2*e^3)*x^4 - 16*(3*b*d^4*e - 7*a*d^3*e^2)*x^2 - 3*((3*c*d^2*e^2 - 15*b*d*e^3 + 35*a*e^4)*x^7 + 2*(3*c*d^3*e - 15*b*d^2*e^2 + 35*a*d*e^3)*x^5 + (3*c*d^4 - 15*b*d^3*e + 35*a*d^2*e^2)*x^3)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)))/(d^5*e^3*x^7 + 2*d^6*e^2*x^5 + d^7*e*x^3), 1/24*(3*(3*c*d^3*e^2 - 15*b*d^2*e^3 + 35*a*d*e^4)*x^6 - 8*a*d^4*e + 5*(3*c*d^4*e - 15*b*d^3*e^2 + 35*a*d^2*e^3)*x^4 - 8*(3*b*d^4*e - 7*a*d^3*e^2)*x^2 + 3*((3*c*d^2*e^2 - 15*b*d*e^3 + 35*a*e^4)*x^7 + 2*(3*c*d^3*e - 15*b*d^2*e^2 + 35*a*d*e^3)*x^5 + (3*c*d^4 - 15*b*d^3*e + 35*a*d^2*e^2)*x^3)*sqrt(d*e)*arctan(sqrt(d*e)*x/d))/(d^5*e^3*x^7 + 2*d^6*e^2*x^5 + d^7*e*x^3)]","A",0
294,1,514,0,0.702946," ","integrate((c*x^4+b*x^2+a)/x^6/(e*x^2+d)^3,x, algorithm=""fricas"")","\left[-\frac{30 \, {\left(15 \, c d^{2} e^{2} - 35 \, b d e^{3} + 63 \, a e^{4}\right)} x^{8} + 50 \, {\left(15 \, c d^{3} e - 35 \, b d^{2} e^{2} + 63 \, a d e^{3}\right)} x^{6} + 48 \, a d^{4} + 16 \, {\left(15 \, c d^{4} - 35 \, b d^{3} e + 63 \, a d^{2} e^{2}\right)} x^{4} + 16 \, {\left(5 \, b d^{4} - 9 \, a d^{3} e\right)} x^{2} - 15 \, {\left({\left(15 \, c d^{2} e^{2} - 35 \, b d e^{3} + 63 \, a e^{4}\right)} x^{9} + 2 \, {\left(15 \, c d^{3} e - 35 \, b d^{2} e^{2} + 63 \, a d e^{3}\right)} x^{7} + {\left(15 \, c d^{4} - 35 \, b d^{3} e + 63 \, a d^{2} e^{2}\right)} x^{5}\right)} \sqrt{-\frac{e}{d}} \log\left(\frac{e x^{2} - 2 \, d x \sqrt{-\frac{e}{d}} - d}{e x^{2} + d}\right)}{240 \, {\left(d^{5} e^{2} x^{9} + 2 \, d^{6} e x^{7} + d^{7} x^{5}\right)}}, -\frac{15 \, {\left(15 \, c d^{2} e^{2} - 35 \, b d e^{3} + 63 \, a e^{4}\right)} x^{8} + 25 \, {\left(15 \, c d^{3} e - 35 \, b d^{2} e^{2} + 63 \, a d e^{3}\right)} x^{6} + 24 \, a d^{4} + 8 \, {\left(15 \, c d^{4} - 35 \, b d^{3} e + 63 \, a d^{2} e^{2}\right)} x^{4} + 8 \, {\left(5 \, b d^{4} - 9 \, a d^{3} e\right)} x^{2} + 15 \, {\left({\left(15 \, c d^{2} e^{2} - 35 \, b d e^{3} + 63 \, a e^{4}\right)} x^{9} + 2 \, {\left(15 \, c d^{3} e - 35 \, b d^{2} e^{2} + 63 \, a d e^{3}\right)} x^{7} + {\left(15 \, c d^{4} - 35 \, b d^{3} e + 63 \, a d^{2} e^{2}\right)} x^{5}\right)} \sqrt{\frac{e}{d}} \arctan\left(x \sqrt{\frac{e}{d}}\right)}{120 \, {\left(d^{5} e^{2} x^{9} + 2 \, d^{6} e x^{7} + d^{7} x^{5}\right)}}\right]"," ",0,"[-1/240*(30*(15*c*d^2*e^2 - 35*b*d*e^3 + 63*a*e^4)*x^8 + 50*(15*c*d^3*e - 35*b*d^2*e^2 + 63*a*d*e^3)*x^6 + 48*a*d^4 + 16*(15*c*d^4 - 35*b*d^3*e + 63*a*d^2*e^2)*x^4 + 16*(5*b*d^4 - 9*a*d^3*e)*x^2 - 15*((15*c*d^2*e^2 - 35*b*d*e^3 + 63*a*e^4)*x^9 + 2*(15*c*d^3*e - 35*b*d^2*e^2 + 63*a*d*e^3)*x^7 + (15*c*d^4 - 35*b*d^3*e + 63*a*d^2*e^2)*x^5)*sqrt(-e/d)*log((e*x^2 - 2*d*x*sqrt(-e/d) - d)/(e*x^2 + d)))/(d^5*e^2*x^9 + 2*d^6*e*x^7 + d^7*x^5), -1/120*(15*(15*c*d^2*e^2 - 35*b*d*e^3 + 63*a*e^4)*x^8 + 25*(15*c*d^3*e - 35*b*d^2*e^2 + 63*a*d*e^3)*x^6 + 24*a*d^4 + 8*(15*c*d^4 - 35*b*d^3*e + 63*a*d^2*e^2)*x^4 + 8*(5*b*d^4 - 9*a*d^3*e)*x^2 + 15*((15*c*d^2*e^2 - 35*b*d*e^3 + 63*a*e^4)*x^9 + 2*(15*c*d^3*e - 35*b*d^2*e^2 + 63*a*d*e^3)*x^7 + (15*c*d^4 - 35*b*d^3*e + 63*a*d^2*e^2)*x^5)*sqrt(e/d)*arctan(x*sqrt(e/d)))/(d^5*e^2*x^9 + 2*d^6*e*x^7 + d^7*x^5)]","A",0
295,-1,0,0,0.000000," ","integrate(x^9/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
296,-1,0,0,0.000000," ","integrate(x^7/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
297,1,421,0,128.564389," ","integrate(x^5/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} \log\left(e x^{2} + d\right) + {\left(a b e^{2} - {\left(b^{2} - 2 \, a c\right)} d e\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right) - {\left({\left(b^{3} - 4 \, a b c\right)} d e - {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e - {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} e^{3}\right)}}, \frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} \log\left(e x^{2} + d\right) + 2 \, {\left(a b e^{2} - {\left(b^{2} - 2 \, a c\right)} d e\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left({\left(b^{3} - 4 \, a b c\right)} d e - {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \log\left(c x^{4} + b x^{2} + a\right)}{4 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e - {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} e^{3}\right)}}\right]"," ",0,"[1/4*(2*(b^2*c - 4*a*c^2)*d^2*log(e*x^2 + d) + (a*b*e^2 - (b^2 - 2*a*c)*d*e)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)) - ((b^3 - 4*a*b*c)*d*e - (a*b^2 - 4*a^2*c)*e^2)*log(c*x^4 + b*x^2 + a))/((b^2*c^2 - 4*a*c^3)*d^2*e - (b^3*c - 4*a*b*c^2)*d*e^2 + (a*b^2*c - 4*a^2*c^2)*e^3), 1/4*(2*(b^2*c - 4*a*c^2)*d^2*log(e*x^2 + d) + 2*(a*b*e^2 - (b^2 - 2*a*c)*d*e)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - ((b^3 - 4*a*b*c)*d*e - (a*b^2 - 4*a^2*c)*e^2)*log(c*x^4 + b*x^2 + a))/((b^2*c^2 - 4*a*c^3)*d^2*e - (b^3*c - 4*a*b*c^2)*d*e^2 + (a*b^2*c - 4*a^2*c^2)*e^3)]","A",0
298,1,321,0,37.368660," ","integrate(x^3/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} - 4 \, a c\right)} d \log\left(c x^{4} + b x^{2} + a\right) - 2 \, {\left(b^{2} - 4 \, a c\right)} d \log\left(e x^{2} + d\right) - \sqrt{b^{2} - 4 \, a c} {\left(b d - 2 \, a e\right)} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c - {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right)}{4 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)}}, \frac{{\left(b^{2} - 4 \, a c\right)} d \log\left(c x^{4} + b x^{2} + a\right) - 2 \, {\left(b^{2} - 4 \, a c\right)} d \log\left(e x^{2} + d\right) + 2 \, \sqrt{-b^{2} + 4 \, a c} {\left(b d - 2 \, a e\right)} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right)}{4 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)}}\right]"," ",0,"[1/4*((b^2 - 4*a*c)*d*log(c*x^4 + b*x^2 + a) - 2*(b^2 - 4*a*c)*d*log(e*x^2 + d) - sqrt(b^2 - 4*a*c)*(b*d - 2*a*e)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c - (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2), 1/4*((b^2 - 4*a*c)*d*log(c*x^4 + b*x^2 + a) - 2*(b^2 - 4*a*c)*d*log(e*x^2 + d) + 2*sqrt(-b^2 + 4*a*c)*(b*d - 2*a*e)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)]","A",0
299,1,321,0,26.754940," ","integrate(x/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 4 \, a c\right)} e \log\left(c x^{4} + b x^{2} + a\right) - 2 \, {\left(b^{2} - 4 \, a c\right)} e \log\left(e x^{2} + d\right) + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c d - b e\right)} \log\left(\frac{2 \, c^{2} x^{4} + 2 \, b c x^{2} + b^{2} - 2 \, a c + {\left(2 \, c x^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{4} + b x^{2} + a}\right)}{4 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)}}, -\frac{{\left(b^{2} - 4 \, a c\right)} e \log\left(c x^{4} + b x^{2} + a\right) - 2 \, {\left(b^{2} - 4 \, a c\right)} e \log\left(e x^{2} + d\right) + 2 \, \sqrt{-b^{2} + 4 \, a c} {\left(2 \, c d - b e\right)} \arctan\left(-\frac{{\left(2 \, c x^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right)}{4 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)}}\right]"," ",0,"[-1/4*((b^2 - 4*a*c)*e*log(c*x^4 + b*x^2 + a) - 2*(b^2 - 4*a*c)*e*log(e*x^2 + d) + sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*log((2*c^2*x^4 + 2*b*c*x^2 + b^2 - 2*a*c + (2*c*x^2 + b)*sqrt(b^2 - 4*a*c))/(c*x^4 + b*x^2 + a)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2), -1/4*((b^2 - 4*a*c)*e*log(c*x^4 + b*x^2 + a) - 2*(b^2 - 4*a*c)*e*log(e*x^2 + d) + 2*sqrt(-b^2 + 4*a*c)*(2*c*d - b*e)*arctan(-(2*c*x^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)]","A",0
300,-1,0,0,0.000000," ","integrate(1/x/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
301,-1,0,0,0.000000," ","integrate(1/x^3/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
302,-1,0,0,0.000000," ","integrate(1/x^5/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
303,-1,0,0,0.000000," ","integrate(x^8/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
304,-1,0,0,0.000000," ","integrate(x^6/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
305,1,15553,0,9.248500," ","integrate(x^4/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{1}{2}} {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}}} \log\left(-2 \, {\left(2 \, a^{2} b d e - a^{3} e^{2} - {\left(a b^{2} - a^{2} c\right)} d^{2}\right)} x + \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{3} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{2} - {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} - 2 \, {\left(b^{4} c^{2} - 3 \, a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{4} e + {\left(b^{5} c + 2 \, a b^{3} c^{2} - 24 \, a^{2} b c^{3}\right)} d^{3} e^{2} - 4 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{2} e^{3} + 5 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{4} - 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{5}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}\right)} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}}}\right) - \sqrt{\frac{1}{2}} {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}}} \log\left(-2 \, {\left(2 \, a^{2} b d e - a^{3} e^{2} - {\left(a b^{2} - a^{2} c\right)} d^{2}\right)} x - \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{3} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{2} - {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} - 2 \, {\left(b^{4} c^{2} - 3 \, a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{4} e + {\left(b^{5} c + 2 \, a b^{3} c^{2} - 24 \, a^{2} b c^{3}\right)} d^{3} e^{2} - 4 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{2} e^{3} + 5 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{4} - 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{5}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}\right)} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}}}\right) + \sqrt{\frac{1}{2}} {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}}} \log\left(-2 \, {\left(2 \, a^{2} b d e - a^{3} e^{2} - {\left(a b^{2} - a^{2} c\right)} d^{2}\right)} x + \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{3} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{2} + {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} - 2 \, {\left(b^{4} c^{2} - 3 \, a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{4} e + {\left(b^{5} c + 2 \, a b^{3} c^{2} - 24 \, a^{2} b c^{3}\right)} d^{3} e^{2} - 4 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{2} e^{3} + 5 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{4} - 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{5}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}\right)} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}}}\right) - \sqrt{\frac{1}{2}} {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}}} \log\left(-2 \, {\left(2 \, a^{2} b d e - a^{3} e^{2} - {\left(a b^{2} - a^{2} c\right)} d^{2}\right)} x - \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{3} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{2} + {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} - 2 \, {\left(b^{4} c^{2} - 3 \, a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{4} e + {\left(b^{5} c + 2 \, a b^{3} c^{2} - 24 \, a^{2} b c^{3}\right)} d^{3} e^{2} - 4 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{2} e^{3} + 5 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{4} - 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{5}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}\right)} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}}}\right) + d \sqrt{-\frac{d}{e}} \log\left(\frac{e x^{2} + 2 \, e x \sqrt{-\frac{d}{e}} - d}{e x^{2} + d}\right)}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)}}, \frac{\sqrt{\frac{1}{2}} {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}}} \log\left(-2 \, {\left(2 \, a^{2} b d e - a^{3} e^{2} - {\left(a b^{2} - a^{2} c\right)} d^{2}\right)} x + \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{3} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{2} - {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} - 2 \, {\left(b^{4} c^{2} - 3 \, a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{4} e + {\left(b^{5} c + 2 \, a b^{3} c^{2} - 24 \, a^{2} b c^{3}\right)} d^{3} e^{2} - 4 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{2} e^{3} + 5 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{4} - 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{5}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}\right)} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}}}\right) - \sqrt{\frac{1}{2}} {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}}} \log\left(-2 \, {\left(2 \, a^{2} b d e - a^{3} e^{2} - {\left(a b^{2} - a^{2} c\right)} d^{2}\right)} x - \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{3} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{2} - {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} - 2 \, {\left(b^{4} c^{2} - 3 \, a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{4} e + {\left(b^{5} c + 2 \, a b^{3} c^{2} - 24 \, a^{2} b c^{3}\right)} d^{3} e^{2} - 4 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{2} e^{3} + 5 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{4} - 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{5}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}\right)} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}}}\right) + \sqrt{\frac{1}{2}} {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}}} \log\left(-2 \, {\left(2 \, a^{2} b d e - a^{3} e^{2} - {\left(a b^{2} - a^{2} c\right)} d^{2}\right)} x + \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{3} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{2} + {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} - 2 \, {\left(b^{4} c^{2} - 3 \, a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{4} e + {\left(b^{5} c + 2 \, a b^{3} c^{2} - 24 \, a^{2} b c^{3}\right)} d^{3} e^{2} - 4 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{2} e^{3} + 5 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{4} - 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{5}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}\right)} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}}}\right) - \sqrt{\frac{1}{2}} {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}}} \log\left(-2 \, {\left(2 \, a^{2} b d e - a^{3} e^{2} - {\left(a b^{2} - a^{2} c\right)} d^{2}\right)} x - \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{3} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{2} + {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} - 2 \, {\left(b^{4} c^{2} - 3 \, a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{4} e + {\left(b^{5} c + 2 \, a b^{3} c^{2} - 24 \, a^{2} b c^{3}\right)} d^{3} e^{2} - 4 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{2} e^{3} + 5 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{4} - 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{5}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}\right)} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{8} - 4 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{4} - 10 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c^{3} - a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{5} e^{3} + {\left(b^{6} c^{2} + 8 \, a b^{4} c^{3} - 42 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} c^{2} - a^{2} b^{3} c^{3} - 12 \, a^{3} b c^{4}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} c^{2} - 10 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{7} + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} e^{8}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}}}\right) + 2 \, d \sqrt{\frac{d}{e}} \arctan\left(\frac{e x \sqrt{\frac{d}{e}}}{d}\right)}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)}}\right]"," ",0,"[1/2*(sqrt(1/2)*(c*d^2 - b*d*e + a*e^2)*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))/((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4))*log(-2*(2*a^2*b*d*e - a^3*e^2 - (a*b^2 - a^2*c)*d^2)*x + sqrt(1/2)*((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^3 - 2*(a*b^3 - 4*a^2*b*c)*d^2*e + (a^2*b^2 - 4*a^3*c)*d*e^2 - ((b^3*c^3 - 4*a*b*c^4)*d^5 - 2*(b^4*c^2 - 3*a*b^2*c^3 - 4*a^2*c^4)*d^4*e + (b^5*c + 2*a*b^3*c^2 - 24*a^2*b*c^3)*d^3*e^2 - 4*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^2*e^3 + 5*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^4 - 2*(a^3*b^2*c - 4*a^4*c^2)*e^5)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))/((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4))) - sqrt(1/2)*(c*d^2 - b*d*e + a*e^2)*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))/((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4))*log(-2*(2*a^2*b*d*e - a^3*e^2 - (a*b^2 - a^2*c)*d^2)*x - sqrt(1/2)*((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^3 - 2*(a*b^3 - 4*a^2*b*c)*d^2*e + (a^2*b^2 - 4*a^3*c)*d*e^2 - ((b^3*c^3 - 4*a*b*c^4)*d^5 - 2*(b^4*c^2 - 3*a*b^2*c^3 - 4*a^2*c^4)*d^4*e + (b^5*c + 2*a*b^3*c^2 - 24*a^2*b*c^3)*d^3*e^2 - 4*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^2*e^3 + 5*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^4 - 2*(a^3*b^2*c - 4*a^4*c^2)*e^5)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))/((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4))) + sqrt(1/2)*(c*d^2 - b*d*e + a*e^2)*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e - ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))/((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4))*log(-2*(2*a^2*b*d*e - a^3*e^2 - (a*b^2 - a^2*c)*d^2)*x + sqrt(1/2)*((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^3 - 2*(a*b^3 - 4*a^2*b*c)*d^2*e + (a^2*b^2 - 4*a^3*c)*d*e^2 + ((b^3*c^3 - 4*a*b*c^4)*d^5 - 2*(b^4*c^2 - 3*a*b^2*c^3 - 4*a^2*c^4)*d^4*e + (b^5*c + 2*a*b^3*c^2 - 24*a^2*b*c^3)*d^3*e^2 - 4*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^2*e^3 + 5*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^4 - 2*(a^3*b^2*c - 4*a^4*c^2)*e^5)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e - ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))/((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4))) - sqrt(1/2)*(c*d^2 - b*d*e + a*e^2)*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e - ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))/((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4))*log(-2*(2*a^2*b*d*e - a^3*e^2 - (a*b^2 - a^2*c)*d^2)*x - sqrt(1/2)*((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^3 - 2*(a*b^3 - 4*a^2*b*c)*d^2*e + (a^2*b^2 - 4*a^3*c)*d*e^2 + ((b^3*c^3 - 4*a*b*c^4)*d^5 - 2*(b^4*c^2 - 3*a*b^2*c^3 - 4*a^2*c^4)*d^4*e + (b^5*c + 2*a*b^3*c^2 - 24*a^2*b*c^3)*d^3*e^2 - 4*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^2*e^3 + 5*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^4 - 2*(a^3*b^2*c - 4*a^4*c^2)*e^5)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e - ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))/((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4))) + d*sqrt(-d/e)*log((e*x^2 + 2*e*x*sqrt(-d/e) - d)/(e*x^2 + d)))/(c*d^2 - b*d*e + a*e^2), 1/2*(sqrt(1/2)*(c*d^2 - b*d*e + a*e^2)*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))/((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4))*log(-2*(2*a^2*b*d*e - a^3*e^2 - (a*b^2 - a^2*c)*d^2)*x + sqrt(1/2)*((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^3 - 2*(a*b^3 - 4*a^2*b*c)*d^2*e + (a^2*b^2 - 4*a^3*c)*d*e^2 - ((b^3*c^3 - 4*a*b*c^4)*d^5 - 2*(b^4*c^2 - 3*a*b^2*c^3 - 4*a^2*c^4)*d^4*e + (b^5*c + 2*a*b^3*c^2 - 24*a^2*b*c^3)*d^3*e^2 - 4*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^2*e^3 + 5*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^4 - 2*(a^3*b^2*c - 4*a^4*c^2)*e^5)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))/((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4))) - sqrt(1/2)*(c*d^2 - b*d*e + a*e^2)*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))/((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4))*log(-2*(2*a^2*b*d*e - a^3*e^2 - (a*b^2 - a^2*c)*d^2)*x - sqrt(1/2)*((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^3 - 2*(a*b^3 - 4*a^2*b*c)*d^2*e + (a^2*b^2 - 4*a^3*c)*d*e^2 - ((b^3*c^3 - 4*a*b*c^4)*d^5 - 2*(b^4*c^2 - 3*a*b^2*c^3 - 4*a^2*c^4)*d^4*e + (b^5*c + 2*a*b^3*c^2 - 24*a^2*b*c^3)*d^3*e^2 - 4*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^2*e^3 + 5*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^4 - 2*(a^3*b^2*c - 4*a^4*c^2)*e^5)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))/((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4))) + sqrt(1/2)*(c*d^2 - b*d*e + a*e^2)*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e - ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))/((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4))*log(-2*(2*a^2*b*d*e - a^3*e^2 - (a*b^2 - a^2*c)*d^2)*x + sqrt(1/2)*((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^3 - 2*(a*b^3 - 4*a^2*b*c)*d^2*e + (a^2*b^2 - 4*a^3*c)*d*e^2 + ((b^3*c^3 - 4*a*b*c^4)*d^5 - 2*(b^4*c^2 - 3*a*b^2*c^3 - 4*a^2*c^4)*d^4*e + (b^5*c + 2*a*b^3*c^2 - 24*a^2*b*c^3)*d^3*e^2 - 4*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^2*e^3 + 5*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^4 - 2*(a^3*b^2*c - 4*a^4*c^2)*e^5)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e - ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))/((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4))) - sqrt(1/2)*(c*d^2 - b*d*e + a*e^2)*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e - ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))/((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4))*log(-2*(2*a^2*b*d*e - a^3*e^2 - (a*b^2 - a^2*c)*d^2)*x - sqrt(1/2)*((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^3 - 2*(a*b^3 - 4*a^2*b*c)*d^2*e + (a^2*b^2 - 4*a^3*c)*d*e^2 + ((b^3*c^3 - 4*a*b*c^4)*d^5 - 2*(b^4*c^2 - 3*a*b^2*c^3 - 4*a^2*c^4)*d^4*e + (b^5*c + 2*a*b^3*c^2 - 24*a^2*b*c^3)*d^3*e^2 - 4*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^2*e^3 + 5*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^4 - 2*(a^3*b^2*c - 4*a^4*c^2)*e^5)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e - ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/((b^2*c^6 - 4*a*c^7)*d^8 - 4*(b^3*c^5 - 4*a*b*c^6)*d^7*e + 2*(3*b^4*c^4 - 10*a*b^2*c^5 - 8*a^2*c^6)*d^6*e^2 - 4*(b^5*c^3 - a*b^3*c^4 - 12*a^2*b*c^5)*d^5*e^3 + (b^6*c^2 + 8*a*b^4*c^3 - 42*a^2*b^2*c^4 - 24*a^3*c^5)*d^4*e^4 - 4*(a*b^5*c^2 - a^2*b^3*c^3 - 12*a^3*b*c^4)*d^3*e^5 + 2*(3*a^2*b^4*c^2 - 10*a^3*b^2*c^3 - 8*a^4*c^4)*d^2*e^6 - 4*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^7 + (a^4*b^2*c^2 - 4*a^5*c^3)*e^8)))/((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4))) + 2*d*sqrt(d/e)*arctan(e*x*sqrt(d/e)/d))/(c*d^2 - b*d*e + a*e^2)]","B",0
306,1,12269,0,3.759540," ","integrate(x^2/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{1}{2}} {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} \log\left(-2 \, {\left(c^{2} d^{2} - a c e^{2}\right)} x + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e - {\left(a b^{2} - 4 \, a^{2} c\right)} e^{3} - {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{5} - 5 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} e + 4 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{2} e^{3} + 2 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{4} - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{5}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}\right) - \sqrt{\frac{1}{2}} {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} \log\left(-2 \, {\left(c^{2} d^{2} - a c e^{2}\right)} x - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e - {\left(a b^{2} - 4 \, a^{2} c\right)} e^{3} - {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{5} - 5 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} e + 4 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{2} e^{3} + 2 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{4} - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{5}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}\right) + \sqrt{\frac{1}{2}} {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} - {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} \log\left(-2 \, {\left(c^{2} d^{2} - a c e^{2}\right)} x + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e - {\left(a b^{2} - 4 \, a^{2} c\right)} e^{3} + {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{5} - 5 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} e + 4 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{2} e^{3} + 2 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{4} - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{5}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} - {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}\right) - \sqrt{\frac{1}{2}} {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} - {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} \log\left(-2 \, {\left(c^{2} d^{2} - a c e^{2}\right)} x - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e - {\left(a b^{2} - 4 \, a^{2} c\right)} e^{3} + {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{5} - 5 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} e + 4 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{2} e^{3} + 2 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{4} - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{5}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} - {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}\right) + \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right)}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)}}, \frac{\sqrt{\frac{1}{2}} {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} \log\left(-2 \, {\left(c^{2} d^{2} - a c e^{2}\right)} x + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e - {\left(a b^{2} - 4 \, a^{2} c\right)} e^{3} - {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{5} - 5 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} e + 4 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{2} e^{3} + 2 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{4} - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{5}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}\right) - \sqrt{\frac{1}{2}} {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} \log\left(-2 \, {\left(c^{2} d^{2} - a c e^{2}\right)} x - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e - {\left(a b^{2} - 4 \, a^{2} c\right)} e^{3} - {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{5} - 5 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} e + 4 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{2} e^{3} + 2 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{4} - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{5}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}\right) + \sqrt{\frac{1}{2}} {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} - {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} \log\left(-2 \, {\left(c^{2} d^{2} - a c e^{2}\right)} x + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e - {\left(a b^{2} - 4 \, a^{2} c\right)} e^{3} + {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{5} - 5 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} e + 4 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{2} e^{3} + 2 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{4} - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{5}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} - {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}\right) - \sqrt{\frac{1}{2}} {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} - {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} \log\left(-2 \, {\left(c^{2} d^{2} - a c e^{2}\right)} x - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e - {\left(a b^{2} - 4 \, a^{2} c\right)} e^{3} + {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{5} - 5 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} e + 4 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{2} e^{3} + 2 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{4} - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{5}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} - {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} e + 2 \, {\left(3 \, b^{4} c^{2} - 10 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{6} e^{2} - 4 \, {\left(b^{5} c - a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d^{5} e^{3} + {\left(b^{6} + 8 \, a b^{4} c - 42 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{4} e^{4} - 4 \, {\left(a b^{5} - a^{2} b^{3} c - 12 \, a^{3} b c^{2}\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{4} - 10 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{7} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{8}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}\right) - 2 \, \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right)}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)}}\right]"," ",0,"[1/2*(sqrt(1/2)*(c*d^2 - b*d*e + a*e^2)*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 + ((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*log(-2*(c^2*d^2 - a*c*e^2)*x + sqrt(1/2)*((b^2*c - 4*a*c^2)*d^2*e - (a*b^2 - 4*a^2*c)*e^3 - (2*(b^2*c^3 - 4*a*c^4)*d^5 - 5*(b^3*c^2 - 4*a*b*c^3)*d^4*e + 4*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^3*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^2*e^3 + 2*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d*e^4 - (a^2*b^3 - 4*a^3*b*c)*e^5)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 + ((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))) - sqrt(1/2)*(c*d^2 - b*d*e + a*e^2)*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 + ((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*log(-2*(c^2*d^2 - a*c*e^2)*x - sqrt(1/2)*((b^2*c - 4*a*c^2)*d^2*e - (a*b^2 - 4*a^2*c)*e^3 - (2*(b^2*c^3 - 4*a*c^4)*d^5 - 5*(b^3*c^2 - 4*a*b*c^3)*d^4*e + 4*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^3*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^2*e^3 + 2*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d*e^4 - (a^2*b^3 - 4*a^3*b*c)*e^5)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 + ((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))) + sqrt(1/2)*(c*d^2 - b*d*e + a*e^2)*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 - ((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*log(-2*(c^2*d^2 - a*c*e^2)*x + sqrt(1/2)*((b^2*c - 4*a*c^2)*d^2*e - (a*b^2 - 4*a^2*c)*e^3 + (2*(b^2*c^3 - 4*a*c^4)*d^5 - 5*(b^3*c^2 - 4*a*b*c^3)*d^4*e + 4*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^3*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^2*e^3 + 2*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d*e^4 - (a^2*b^3 - 4*a^3*b*c)*e^5)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 - ((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))) - sqrt(1/2)*(c*d^2 - b*d*e + a*e^2)*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 - ((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*log(-2*(c^2*d^2 - a*c*e^2)*x - sqrt(1/2)*((b^2*c - 4*a*c^2)*d^2*e - (a*b^2 - 4*a^2*c)*e^3 + (2*(b^2*c^3 - 4*a*c^4)*d^5 - 5*(b^3*c^2 - 4*a*b*c^3)*d^4*e + 4*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^3*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^2*e^3 + 2*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d*e^4 - (a^2*b^3 - 4*a^3*b*c)*e^5)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 - ((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))) + sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)))/(c*d^2 - b*d*e + a*e^2), 1/2*(sqrt(1/2)*(c*d^2 - b*d*e + a*e^2)*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 + ((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*log(-2*(c^2*d^2 - a*c*e^2)*x + sqrt(1/2)*((b^2*c - 4*a*c^2)*d^2*e - (a*b^2 - 4*a^2*c)*e^3 - (2*(b^2*c^3 - 4*a*c^4)*d^5 - 5*(b^3*c^2 - 4*a*b*c^3)*d^4*e + 4*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^3*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^2*e^3 + 2*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d*e^4 - (a^2*b^3 - 4*a^3*b*c)*e^5)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 + ((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))) - sqrt(1/2)*(c*d^2 - b*d*e + a*e^2)*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 + ((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*log(-2*(c^2*d^2 - a*c*e^2)*x - sqrt(1/2)*((b^2*c - 4*a*c^2)*d^2*e - (a*b^2 - 4*a^2*c)*e^3 - (2*(b^2*c^3 - 4*a*c^4)*d^5 - 5*(b^3*c^2 - 4*a*b*c^3)*d^4*e + 4*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^3*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^2*e^3 + 2*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d*e^4 - (a^2*b^3 - 4*a^3*b*c)*e^5)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 + ((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))) + sqrt(1/2)*(c*d^2 - b*d*e + a*e^2)*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 - ((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*log(-2*(c^2*d^2 - a*c*e^2)*x + sqrt(1/2)*((b^2*c - 4*a*c^2)*d^2*e - (a*b^2 - 4*a^2*c)*e^3 + (2*(b^2*c^3 - 4*a*c^4)*d^5 - 5*(b^3*c^2 - 4*a*b*c^3)*d^4*e + 4*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^3*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^2*e^3 + 2*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d*e^4 - (a^2*b^3 - 4*a^3*b*c)*e^5)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 - ((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))) - sqrt(1/2)*(c*d^2 - b*d*e + a*e^2)*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 - ((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*log(-2*(c^2*d^2 - a*c*e^2)*x - sqrt(1/2)*((b^2*c - 4*a*c^2)*d^2*e - (a*b^2 - 4*a^2*c)*e^3 + (2*(b^2*c^3 - 4*a*c^4)*d^5 - 5*(b^3*c^2 - 4*a*b*c^3)*d^4*e + 4*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^3*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^2*e^3 + 2*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d*e^4 - (a^2*b^3 - 4*a^3*b*c)*e^5)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 - ((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/((b^2*c^4 - 4*a*c^5)*d^8 - 4*(b^3*c^3 - 4*a*b*c^4)*d^7*e + 2*(3*b^4*c^2 - 10*a*b^2*c^3 - 8*a^2*c^4)*d^6*e^2 - 4*(b^5*c - a*b^3*c^2 - 12*a^2*b*c^3)*d^5*e^3 + (b^6 + 8*a*b^4*c - 42*a^2*b^2*c^2 - 24*a^3*c^3)*d^4*e^4 - 4*(a*b^5 - a^2*b^3*c - 12*a^3*b*c^2)*d^3*e^5 + 2*(3*a^2*b^4 - 10*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 4*(a^3*b^3 - 4*a^4*b*c)*d*e^7 + (a^4*b^2 - 4*a^5*c)*e^8)))/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))) - 2*sqrt(d*e)*arctan(sqrt(d*e)*x/d))/(c*d^2 - b*d*e + a*e^2)]","B",0
307,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
308,-1,0,0,0.000000," ","integrate(1/x^2/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
309,-1,0,0,0.000000," ","integrate(1/x^4/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
310,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)/(c*x^4+b*x^2+a)/(f*x)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
311,-1,0,0,0.000000," ","integrate(x^5*(c*x^4+b*x^2+a)^(1/2)/(e*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
312,1,1231,0,56.149901," ","integrate(x^3*(c*x^4+b*x^2+a)^(1/2)/(e*x^2+d),x, algorithm=""fricas"")","\left[\frac{8 \, \sqrt{c d^{2} - b d e + a e^{2}} c^{2} d \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) + {\left(8 \, c^{2} d^{2} - 4 \, b c d e - {\left(b^{2} - 4 \, a c\right)} e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(2 \, c^{2} e^{2} x^{2} - 4 \, c^{2} d e + b c e^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{32 \, c^{2} e^{3}}, -\frac{16 \, \sqrt{-c d^{2} + b d e - a e^{2}} c^{2} d \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) - {\left(8 \, c^{2} d^{2} - 4 \, b c d e - {\left(b^{2} - 4 \, a c\right)} e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(2 \, c^{2} e^{2} x^{2} - 4 \, c^{2} d e + b c e^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{32 \, c^{2} e^{3}}, \frac{4 \, \sqrt{c d^{2} - b d e + a e^{2}} c^{2} d \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) - {\left(8 \, c^{2} d^{2} - 4 \, b c d e - {\left(b^{2} - 4 \, a c\right)} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) + 2 \, {\left(2 \, c^{2} e^{2} x^{2} - 4 \, c^{2} d e + b c e^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{16 \, c^{2} e^{3}}, -\frac{8 \, \sqrt{-c d^{2} + b d e - a e^{2}} c^{2} d \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) + {\left(8 \, c^{2} d^{2} - 4 \, b c d e - {\left(b^{2} - 4 \, a c\right)} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) - 2 \, {\left(2 \, c^{2} e^{2} x^{2} - 4 \, c^{2} d e + b c e^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{16 \, c^{2} e^{3}}\right]"," ",0,"[1/32*(8*sqrt(c*d^2 - b*d*e + a*e^2)*c^2*d*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 - 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) + (8*c^2*d^2 - 4*b*c*d*e - (b^2 - 4*a*c)*e^2)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + 4*(2*c^2*e^2*x^2 - 4*c^2*d*e + b*c*e^2)*sqrt(c*x^4 + b*x^2 + a))/(c^2*e^3), -1/32*(16*sqrt(-c*d^2 + b*d*e - a*e^2)*c^2*d*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) - (8*c^2*d^2 - 4*b*c*d*e - (b^2 - 4*a*c)*e^2)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) - 4*(2*c^2*e^2*x^2 - 4*c^2*d*e + b*c*e^2)*sqrt(c*x^4 + b*x^2 + a))/(c^2*e^3), 1/16*(4*sqrt(c*d^2 - b*d*e + a*e^2)*c^2*d*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 - 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) - (8*c^2*d^2 - 4*b*c*d*e - (b^2 - 4*a*c)*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + 2*(2*c^2*e^2*x^2 - 4*c^2*d*e + b*c*e^2)*sqrt(c*x^4 + b*x^2 + a))/(c^2*e^3), -1/16*(8*sqrt(-c*d^2 + b*d*e - a*e^2)*c^2*d*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) + (8*c^2*d^2 - 4*b*c*d*e - (b^2 - 4*a*c)*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) - 2*(2*c^2*e^2*x^2 - 4*c^2*d*e + b*c*e^2)*sqrt(c*x^4 + b*x^2 + a))/(c^2*e^3)]","A",0
313,1,1050,0,4.093227," ","integrate(x*(c*x^4+b*x^2+a)^(1/2)/(e*x^2+d),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{c x^{4} + b x^{2} + a} c e - {\left(2 \, c d - b e\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} c \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right)}{8 \, c e^{2}}, \frac{2 \, \sqrt{c x^{4} + b x^{2} + a} c e + {\left(2 \, c d - b e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) + \sqrt{c d^{2} - b d e + a e^{2}} c \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right)}{4 \, c e^{2}}, \frac{4 \, \sqrt{c x^{4} + b x^{2} + a} c e + 4 \, \sqrt{-c d^{2} + b d e - a e^{2}} c \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) - {\left(2 \, c d - b e\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right)}{8 \, c e^{2}}, \frac{2 \, \sqrt{c x^{4} + b x^{2} + a} c e + 2 \, \sqrt{-c d^{2} + b d e - a e^{2}} c \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) + {\left(2 \, c d - b e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right)}{4 \, c e^{2}}\right]"," ",0,"[1/8*(4*sqrt(c*x^4 + b*x^2 + a)*c*e - (2*c*d - b*e)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + 2*sqrt(c*d^2 - b*d*e + a*e^2)*c*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)))/(c*e^2), 1/4*(2*sqrt(c*x^4 + b*x^2 + a)*c*e + (2*c*d - b*e)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + sqrt(c*d^2 - b*d*e + a*e^2)*c*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)))/(c*e^2), 1/8*(4*sqrt(c*x^4 + b*x^2 + a)*c*e + 4*sqrt(-c*d^2 + b*d*e - a*e^2)*c*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) - (2*c*d - b*e)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c))/(c*e^2), 1/4*(2*sqrt(c*x^4 + b*x^2 + a)*c*e + 2*sqrt(-c*d^2 + b*d*e - a*e^2)*c*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) + (2*c*d - b*e)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)))/(c*e^2)]","A",0
314,-1,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(1/2)/x/(e*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
315,1,1094,0,2.362919," ","integrate((c*x^4+b*x^2+a)^(1/2)/x^3/(e*x^2+d),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{c d^{2} - b d e + a e^{2}} a x^{2} \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) - {\left(b d - 2 \, a e\right)} \sqrt{a} x^{2} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{4} + 8 \, a b x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{4}}\right) - 4 \, \sqrt{c x^{4} + b x^{2} + a} a d}{8 \, a d^{2} x^{2}}, \frac{4 \, \sqrt{-c d^{2} + b d e - a e^{2}} a x^{2} \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) - {\left(b d - 2 \, a e\right)} \sqrt{a} x^{2} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{4} + 8 \, a b x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{4}}\right) - 4 \, \sqrt{c x^{4} + b x^{2} + a} a d}{8 \, a d^{2} x^{2}}, \frac{{\left(b d - 2 \, a e\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{4} + a b x^{2} + a^{2}\right)}}\right) + \sqrt{c d^{2} - b d e + a e^{2}} a x^{2} \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) - 2 \, \sqrt{c x^{4} + b x^{2} + a} a d}{4 \, a d^{2} x^{2}}, \frac{2 \, \sqrt{-c d^{2} + b d e - a e^{2}} a x^{2} \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) + {\left(b d - 2 \, a e\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{4} + a b x^{2} + a^{2}\right)}}\right) - 2 \, \sqrt{c x^{4} + b x^{2} + a} a d}{4 \, a d^{2} x^{2}}\right]"," ",0,"[1/8*(2*sqrt(c*d^2 - b*d*e + a*e^2)*a*x^2*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) - (b*d - 2*a*e)*sqrt(a)*x^2*log(-((b^2 + 4*a*c)*x^4 + 8*a*b*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(a) + 8*a^2)/x^4) - 4*sqrt(c*x^4 + b*x^2 + a)*a*d)/(a*d^2*x^2), 1/8*(4*sqrt(-c*d^2 + b*d*e - a*e^2)*a*x^2*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) - (b*d - 2*a*e)*sqrt(a)*x^2*log(-((b^2 + 4*a*c)*x^4 + 8*a*b*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(a) + 8*a^2)/x^4) - 4*sqrt(c*x^4 + b*x^2 + a)*a*d)/(a*d^2*x^2), 1/4*((b*d - 2*a*e)*sqrt(-a)*x^2*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(-a)/(a*c*x^4 + a*b*x^2 + a^2)) + sqrt(c*d^2 - b*d*e + a*e^2)*a*x^2*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) - 2*sqrt(c*x^4 + b*x^2 + a)*a*d)/(a*d^2*x^2), 1/4*(2*sqrt(-c*d^2 + b*d*e - a*e^2)*a*x^2*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) + (b*d - 2*a*e)*sqrt(-a)*x^2*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(-a)/(a*c*x^4 + a*b*x^2 + a^2)) - 2*sqrt(c*x^4 + b*x^2 + a)*a*d)/(a*d^2*x^2)]","A",0
316,0,0,0,1.507493," ","integrate(x^4*(2*x^4+2*x^2+1)^(1/2)/(2*x^2+3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1} x^{4}}{2 \, x^{2} + 3}, x\right)"," ",0,"integral(sqrt(2*x^4 + 2*x^2 + 1)*x^4/(2*x^2 + 3), x)","F",0
317,0,0,0,0.988834," ","integrate(x^2*(2*x^4+2*x^2+1)^(1/2)/(2*x^2+3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1} x^{2}}{2 \, x^{2} + 3}, x\right)"," ",0,"integral(sqrt(2*x^4 + 2*x^2 + 1)*x^2/(2*x^2 + 3), x)","F",0
318,0,0,0,1.107608," ","integrate((2*x^4+2*x^2+1)^(1/2)/(2*x^2+3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1}}{2 \, x^{2} + 3}, x\right)"," ",0,"integral(sqrt(2*x^4 + 2*x^2 + 1)/(2*x^2 + 3), x)","F",0
319,0,0,0,1.297974," ","integrate((2*x^4+2*x^2+1)^(1/2)/x^2/(2*x^2+3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1}}{2 \, x^{4} + 3 \, x^{2}}, x\right)"," ",0,"integral(sqrt(2*x^4 + 2*x^2 + 1)/(2*x^4 + 3*x^2), x)","F",0
320,0,0,0,1.194402," ","integrate((2*x^4+2*x^2+1)^(1/2)/x^4/(2*x^2+3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1}}{2 \, x^{6} + 3 \, x^{4}}, x\right)"," ",0,"integral(sqrt(2*x^4 + 2*x^2 + 1)/(2*x^6 + 3*x^4), x)","F",0
321,0,0,0,1.126386," ","integrate((2*x^4+2*x^2+1)^(1/2)/x^6/(2*x^2+3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1}}{2 \, x^{8} + 3 \, x^{6}}, x\right)"," ",0,"integral(sqrt(2*x^4 + 2*x^2 + 1)/(2*x^8 + 3*x^6), x)","F",0
322,-1,0,0,0.000000," ","integrate(x^5*(c*x^4+b*x^2+a)^(3/2)/(e*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
323,-1,0,0,0.000000," ","integrate(x^3*(c*x^4+b*x^2+a)^(3/2)/(e*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
324,-1,0,0,0.000000," ","integrate(x*(c*x^4+b*x^2+a)^(3/2)/(e*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
325,-1,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(3/2)/x/(e*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
326,-1,0,0,0.000000," ","integrate((c*x^4+b*x^2+a)^(3/2)/x^3/(e*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
327,0,0,0,1.558536," ","integrate(x^2*(2*x^4+2*x^2+1)^(3/2)/(-2*x^2+3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(2 \, x^{6} + 2 \, x^{4} + x^{2}\right)} \sqrt{2 \, x^{4} + 2 \, x^{2} + 1}}{2 \, x^{2} - 3}, x\right)"," ",0,"integral(-(2*x^6 + 2*x^4 + x^2)*sqrt(2*x^4 + 2*x^2 + 1)/(2*x^2 - 3), x)","F",0
328,0,0,0,1.733580," ","integrate((2*x^4+2*x^2+1)^(3/2)/(-2*x^2+3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(2 \, x^{4} + 2 \, x^{2} + 1\right)}^{\frac{3}{2}}}{2 \, x^{2} - 3}, x\right)"," ",0,"integral(-(2*x^4 + 2*x^2 + 1)^(3/2)/(2*x^2 - 3), x)","F",0
329,0,0,0,1.645110," ","integrate((2*x^4+2*x^2+1)^(3/2)/x^2/(-2*x^2+3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(2 \, x^{4} + 2 \, x^{2} + 1\right)}^{\frac{3}{2}}}{2 \, x^{4} - 3 \, x^{2}}, x\right)"," ",0,"integral(-(2*x^4 + 2*x^2 + 1)^(3/2)/(2*x^4 - 3*x^2), x)","F",0
330,0,0,0,1.616078," ","integrate((2*x^4+2*x^2+1)^(3/2)/x^4/(-2*x^2+3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(2 \, x^{4} + 2 \, x^{2} + 1\right)}^{\frac{3}{2}}}{2 \, x^{6} - 3 \, x^{4}}, x\right)"," ",0,"integral(-(2*x^4 + 2*x^2 + 1)^(3/2)/(2*x^6 - 3*x^4), x)","F",0
331,0,0,0,1.488976," ","integrate((2*x^4+2*x^2+1)^(3/2)/x^6/(-2*x^2+3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(2 \, x^{4} + 2 \, x^{2} + 1\right)}^{\frac{3}{2}}}{2 \, x^{8} - 3 \, x^{6}}, x\right)"," ",0,"integral(-(2*x^4 + 2*x^2 + 1)^(3/2)/(2*x^8 - 3*x^6), x)","F",0
332,1,1364,0,58.184300," ","integrate(x^5/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{c d^{2} - b d e + a e^{2}} c^{2} d^{2} \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) + {\left(2 \, c^{2} d^{3} - b c d^{2} e + a b e^{3} - {\left(b^{2} - 2 \, a c\right)} d e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)} \sqrt{c x^{4} + b x^{2} + a}}{8 \, {\left(c^{3} d^{2} e^{2} - b c^{2} d e^{3} + a c^{2} e^{4}\right)}}, \frac{4 \, \sqrt{-c d^{2} + b d e - a e^{2}} c^{2} d^{2} \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) + {\left(2 \, c^{2} d^{3} - b c d^{2} e + a b e^{3} - {\left(b^{2} - 2 \, a c\right)} d e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)} \sqrt{c x^{4} + b x^{2} + a}}{8 \, {\left(c^{3} d^{2} e^{2} - b c^{2} d e^{3} + a c^{2} e^{4}\right)}}, \frac{\sqrt{c d^{2} - b d e + a e^{2}} c^{2} d^{2} \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) + {\left(2 \, c^{2} d^{3} - b c d^{2} e + a b e^{3} - {\left(b^{2} - 2 \, a c\right)} d e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) + 2 \, {\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)} \sqrt{c x^{4} + b x^{2} + a}}{4 \, {\left(c^{3} d^{2} e^{2} - b c^{2} d e^{3} + a c^{2} e^{4}\right)}}, \frac{2 \, \sqrt{-c d^{2} + b d e - a e^{2}} c^{2} d^{2} \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) + {\left(2 \, c^{2} d^{3} - b c d^{2} e + a b e^{3} - {\left(b^{2} - 2 \, a c\right)} d e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) + 2 \, {\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)} \sqrt{c x^{4} + b x^{2} + a}}{4 \, {\left(c^{3} d^{2} e^{2} - b c^{2} d e^{3} + a c^{2} e^{4}\right)}}\right]"," ",0,"[1/8*(2*sqrt(c*d^2 - b*d*e + a*e^2)*c^2*d^2*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) + (2*c^2*d^3 - b*c*d^2*e + a*b*e^3 - (b^2 - 2*a*c)*d*e^2)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 + 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + 4*(c^2*d^2*e - b*c*d*e^2 + a*c*e^3)*sqrt(c*x^4 + b*x^2 + a))/(c^3*d^2*e^2 - b*c^2*d*e^3 + a*c^2*e^4), 1/8*(4*sqrt(-c*d^2 + b*d*e - a*e^2)*c^2*d^2*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) + (2*c^2*d^3 - b*c*d^2*e + a*b*e^3 - (b^2 - 2*a*c)*d*e^2)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 + 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + 4*(c^2*d^2*e - b*c*d*e^2 + a*c*e^3)*sqrt(c*x^4 + b*x^2 + a))/(c^3*d^2*e^2 - b*c^2*d*e^3 + a*c^2*e^4), 1/4*(sqrt(c*d^2 - b*d*e + a*e^2)*c^2*d^2*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) + (2*c^2*d^3 - b*c*d^2*e + a*b*e^3 - (b^2 - 2*a*c)*d*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + 2*(c^2*d^2*e - b*c*d*e^2 + a*c*e^3)*sqrt(c*x^4 + b*x^2 + a))/(c^3*d^2*e^2 - b*c^2*d*e^3 + a*c^2*e^4), 1/4*(2*sqrt(-c*d^2 + b*d*e - a*e^2)*c^2*d^2*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) + (2*c^2*d^3 - b*c*d^2*e + a*b*e^3 - (b^2 - 2*a*c)*d*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + 2*(c^2*d^2*e - b*c*d*e^2 + a*c*e^3)*sqrt(c*x^4 + b*x^2 + a))/(c^3*d^2*e^2 - b*c^2*d*e^3 + a*c^2*e^4)]","B",0
333,1,1084,0,4.113163," ","integrate(x^3/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{c d^{2} - b d e + a e^{2}} c d \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) + {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right)}{4 \, {\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)}}, -\frac{2 \, \sqrt{-c d^{2} + b d e - a e^{2}} c d \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) - {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right)}{4 \, {\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)}}, \frac{\sqrt{c d^{2} - b d e + a e^{2}} c d \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) - 2 \, {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right)}{4 \, {\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)}}, -\frac{\sqrt{-c d^{2} + b d e - a e^{2}} c d \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) + {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right)}{2 \, {\left(c^{2} d^{2} e - b c d e^{2} + a c e^{3}\right)}}\right]"," ",0,"[1/4*(sqrt(c*d^2 - b*d*e + a*e^2)*c*d*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 - 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) + (c*d^2 - b*d*e + a*e^2)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c))/(c^2*d^2*e - b*c*d*e^2 + a*c*e^3), -1/4*(2*sqrt(-c*d^2 + b*d*e - a*e^2)*c*d*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) - (c*d^2 - b*d*e + a*e^2)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c))/(c^2*d^2*e - b*c*d*e^2 + a*c*e^3), 1/4*(sqrt(c*d^2 - b*d*e + a*e^2)*c*d*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 - 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) - 2*(c*d^2 - b*d*e + a*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)))/(c^2*d^2*e - b*c*d*e^2 + a*c*e^3), -1/2*(sqrt(-c*d^2 + b*d*e - a*e^2)*c*d*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) + (c*d^2 - b*d*e + a*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)))/(c^2*d^2*e - b*c*d*e^2 + a*c*e^3)]","B",0
334,1,357,0,1.190403," ","integrate(x/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right)}{4 \, \sqrt{c d^{2} - b d e + a e^{2}}}, \frac{\sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right)}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)}}\right]"," ",0,"[1/4*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2))/sqrt(c*d^2 - b*d*e + a*e^2), 1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2))/(c*d^2 - b*d*e + a*e^2)]","B",0
335,1,1097,0,1.742328," ","integrate(1/x/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{c d^{2} - b d e + a e^{2}} a e \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) + {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{a} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{4} + 8 \, a b x^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{4}}\right)}{4 \, {\left(a c d^{3} - a b d^{2} e + a^{2} d e^{2}\right)}}, -\frac{2 \, \sqrt{-c d^{2} + b d e - a e^{2}} a e \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) - {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{a} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{4} + 8 \, a b x^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{4}}\right)}{4 \, {\left(a c d^{3} - a b d^{2} e + a^{2} d e^{2}\right)}}, \frac{\sqrt{c d^{2} - b d e + a e^{2}} a e \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) + 2 \, {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{4} + a b x^{2} + a^{2}\right)}}\right)}{4 \, {\left(a c d^{3} - a b d^{2} e + a^{2} d e^{2}\right)}}, -\frac{\sqrt{-c d^{2} + b d e - a e^{2}} a e \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) - {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{4} + a b x^{2} + a^{2}\right)}}\right)}{2 \, {\left(a c d^{3} - a b d^{2} e + a^{2} d e^{2}\right)}}\right]"," ",0,"[1/4*(sqrt(c*d^2 - b*d*e + a*e^2)*a*e*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 - 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) + (c*d^2 - b*d*e + a*e^2)*sqrt(a)*log(-((b^2 + 4*a*c)*x^4 + 8*a*b*x^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(a) + 8*a^2)/x^4))/(a*c*d^3 - a*b*d^2*e + a^2*d*e^2), -1/4*(2*sqrt(-c*d^2 + b*d*e - a*e^2)*a*e*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) - (c*d^2 - b*d*e + a*e^2)*sqrt(a)*log(-((b^2 + 4*a*c)*x^4 + 8*a*b*x^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(a) + 8*a^2)/x^4))/(a*c*d^3 - a*b*d^2*e + a^2*d*e^2), 1/4*(sqrt(c*d^2 - b*d*e + a*e^2)*a*e*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 - 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) + 2*(c*d^2 - b*d*e + a*e^2)*sqrt(-a)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(-a)/(a*c*x^4 + a*b*x^2 + a^2)))/(a*c*d^3 - a*b*d^2*e + a^2*d*e^2), -1/2*(sqrt(-c*d^2 + b*d*e - a*e^2)*a*e*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) - (c*d^2 - b*d*e + a*e^2)*sqrt(-a)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(-a)/(a*c*x^4 + a*b*x^2 + a^2)))/(a*c*d^3 - a*b*d^2*e + a^2*d*e^2)]","B",0
336,1,1414,0,2.780726," ","integrate(1/x^3/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{2} e^{2} x^{2} \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) + {\left(b c d^{3} - a b d e^{2} + 2 \, a^{2} e^{3} - {\left(b^{2} - 2 \, a c\right)} d^{2} e\right)} \sqrt{a} x^{2} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{4} + 8 \, a b x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{4}}\right) - 4 \, {\left(a c d^{3} - a b d^{2} e + a^{2} d e^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{8 \, {\left(a^{2} c d^{4} - a^{2} b d^{3} e + a^{3} d^{2} e^{2}\right)} x^{2}}, \frac{4 \, \sqrt{-c d^{2} + b d e - a e^{2}} a^{2} e^{2} x^{2} \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) + {\left(b c d^{3} - a b d e^{2} + 2 \, a^{2} e^{3} - {\left(b^{2} - 2 \, a c\right)} d^{2} e\right)} \sqrt{a} x^{2} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{4} + 8 \, a b x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{4}}\right) - 4 \, {\left(a c d^{3} - a b d^{2} e + a^{2} d e^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{8 \, {\left(a^{2} c d^{4} - a^{2} b d^{3} e + a^{3} d^{2} e^{2}\right)} x^{2}}, \frac{\sqrt{c d^{2} - b d e + a e^{2}} a^{2} e^{2} x^{2} \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) - {\left(b c d^{3} - a b d e^{2} + 2 \, a^{2} e^{3} - {\left(b^{2} - 2 \, a c\right)} d^{2} e\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{4} + a b x^{2} + a^{2}\right)}}\right) - 2 \, {\left(a c d^{3} - a b d^{2} e + a^{2} d e^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{4 \, {\left(a^{2} c d^{4} - a^{2} b d^{3} e + a^{3} d^{2} e^{2}\right)} x^{2}}, \frac{2 \, \sqrt{-c d^{2} + b d e - a e^{2}} a^{2} e^{2} x^{2} \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) - {\left(b c d^{3} - a b d e^{2} + 2 \, a^{2} e^{3} - {\left(b^{2} - 2 \, a c\right)} d^{2} e\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{4} + a b x^{2} + a^{2}\right)}}\right) - 2 \, {\left(a c d^{3} - a b d^{2} e + a^{2} d e^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{4 \, {\left(a^{2} c d^{4} - a^{2} b d^{3} e + a^{3} d^{2} e^{2}\right)} x^{2}}\right]"," ",0,"[1/8*(2*sqrt(c*d^2 - b*d*e + a*e^2)*a^2*e^2*x^2*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) + (b*c*d^3 - a*b*d*e^2 + 2*a^2*e^3 - (b^2 - 2*a*c)*d^2*e)*sqrt(a)*x^2*log(-((b^2 + 4*a*c)*x^4 + 8*a*b*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(a) + 8*a^2)/x^4) - 4*(a*c*d^3 - a*b*d^2*e + a^2*d*e^2)*sqrt(c*x^4 + b*x^2 + a))/((a^2*c*d^4 - a^2*b*d^3*e + a^3*d^2*e^2)*x^2), 1/8*(4*sqrt(-c*d^2 + b*d*e - a*e^2)*a^2*e^2*x^2*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) + (b*c*d^3 - a*b*d*e^2 + 2*a^2*e^3 - (b^2 - 2*a*c)*d^2*e)*sqrt(a)*x^2*log(-((b^2 + 4*a*c)*x^4 + 8*a*b*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(a) + 8*a^2)/x^4) - 4*(a*c*d^3 - a*b*d^2*e + a^2*d*e^2)*sqrt(c*x^4 + b*x^2 + a))/((a^2*c*d^4 - a^2*b*d^3*e + a^3*d^2*e^2)*x^2), 1/4*(sqrt(c*d^2 - b*d*e + a*e^2)*a^2*e^2*x^2*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) - (b*c*d^3 - a*b*d*e^2 + 2*a^2*e^3 - (b^2 - 2*a*c)*d^2*e)*sqrt(-a)*x^2*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(-a)/(a*c*x^4 + a*b*x^2 + a^2)) - 2*(a*c*d^3 - a*b*d^2*e + a^2*d*e^2)*sqrt(c*x^4 + b*x^2 + a))/((a^2*c*d^4 - a^2*b*d^3*e + a^3*d^2*e^2)*x^2), 1/4*(2*sqrt(-c*d^2 + b*d*e - a*e^2)*a^2*e^2*x^2*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) - (b*c*d^3 - a*b*d*e^2 + 2*a^2*e^3 - (b^2 - 2*a*c)*d^2*e)*sqrt(-a)*x^2*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(-a)/(a*c*x^4 + a*b*x^2 + a^2)) - 2*(a*c*d^3 - a*b*d^2*e + a^2*d*e^2)*sqrt(c*x^4 + b*x^2 + a))/((a^2*c*d^4 - a^2*b*d^3*e + a^3*d^2*e^2)*x^2)]","A",0
337,0,0,0,1.363608," ","integrate(x^4/(2*x^2+3)/(2*x^4+2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1} x^{4}}{4 \, x^{6} + 10 \, x^{4} + 8 \, x^{2} + 3}, x\right)"," ",0,"integral(sqrt(2*x^4 + 2*x^2 + 1)*x^4/(4*x^6 + 10*x^4 + 8*x^2 + 3), x)","F",0
338,0,0,0,1.394660," ","integrate(x^2/(2*x^2+3)/(2*x^4+2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1} x^{2}}{4 \, x^{6} + 10 \, x^{4} + 8 \, x^{2} + 3}, x\right)"," ",0,"integral(sqrt(2*x^4 + 2*x^2 + 1)*x^2/(4*x^6 + 10*x^4 + 8*x^2 + 3), x)","F",0
339,0,0,0,1.123697," ","integrate(1/(2*x^2+3)/(2*x^4+2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1}}{4 \, x^{6} + 10 \, x^{4} + 8 \, x^{2} + 3}, x\right)"," ",0,"integral(sqrt(2*x^4 + 2*x^2 + 1)/(4*x^6 + 10*x^4 + 8*x^2 + 3), x)","F",0
340,0,0,0,1.281285," ","integrate(1/x^2/(2*x^2+3)/(2*x^4+2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1}}{4 \, x^{8} + 10 \, x^{6} + 8 \, x^{4} + 3 \, x^{2}}, x\right)"," ",0,"integral(sqrt(2*x^4 + 2*x^2 + 1)/(4*x^8 + 10*x^6 + 8*x^4 + 3*x^2), x)","F",0
341,0,0,0,1.116527," ","integrate(1/x^4/(2*x^2+3)/(2*x^4+2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1}}{4 \, x^{10} + 10 \, x^{8} + 8 \, x^{6} + 3 \, x^{4}}, x\right)"," ",0,"integral(sqrt(2*x^4 + 2*x^2 + 1)/(4*x^10 + 10*x^8 + 8*x^6 + 3*x^4), x)","F",0
342,1,4901,0,172.623922," ","integrate(x^7/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{4} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} x^{4} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} x^{2} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3}\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) - 4 \, {\left(a^{3} b c e^{4} - {\left(a b^{2} c^{2} - 2 \, a^{2} c^{3}\right)} d^{3} e + {\left(a b^{3} c - a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{2} c - a^{3} c^{2}\right)} d e^{3} - {\left({\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{3} e - {\left(b^{4} c - 2 \, a b^{2} c^{2} - 2 \, a^{2} c^{3}\right)} d^{2} e^{2} + {\left(2 \, a b^{3} c - 5 \, a^{2} b c^{2}\right)} d e^{3} - {\left(a^{2} b^{2} c - 2 \, a^{3} c^{2}\right)} e^{4}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{4 \, {\left({\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{4} e - 2 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{3} e^{2} + {\left(a b^{4} c^{2} - 2 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d^{2} e^{3} - 2 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d e^{4} + {\left(a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} e^{5} + {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{4} e - 2 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{3} e^{2} + {\left(b^{4} c^{3} - 2 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{2} e^{3} - 2 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d e^{4} + {\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} e^{5}\right)} x^{4} + {\left({\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{4} e - 2 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{3} e^{2} + {\left(b^{5} c^{2} - 2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4}\right)} d^{2} e^{3} - 2 \, {\left(a b^{4} c^{2} - 4 \, a^{2} b^{2} c^{3}\right)} d e^{4} + {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e^{5}\right)} x^{2}\right)}}, -\frac{2 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} x^{4} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} x^{2} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3}\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) - {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{4} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{4} - 8 \, b c x^{2} - b^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(a^{3} b c e^{4} - {\left(a b^{2} c^{2} - 2 \, a^{2} c^{3}\right)} d^{3} e + {\left(a b^{3} c - a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{2} c - a^{3} c^{2}\right)} d e^{3} - {\left({\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{3} e - {\left(b^{4} c - 2 \, a b^{2} c^{2} - 2 \, a^{2} c^{3}\right)} d^{2} e^{2} + {\left(2 \, a b^{3} c - 5 \, a^{2} b c^{2}\right)} d e^{3} - {\left(a^{2} b^{2} c - 2 \, a^{3} c^{2}\right)} e^{4}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{4 \, {\left({\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{4} e - 2 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{3} e^{2} + {\left(a b^{4} c^{2} - 2 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d^{2} e^{3} - 2 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d e^{4} + {\left(a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} e^{5} + {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{4} e - 2 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{3} e^{2} + {\left(b^{4} c^{3} - 2 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{2} e^{3} - 2 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d e^{4} + {\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} e^{5}\right)} x^{4} + {\left({\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{4} e - 2 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{3} e^{2} + {\left(b^{5} c^{2} - 2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4}\right)} d^{2} e^{3} - 2 \, {\left(a b^{4} c^{2} - 4 \, a^{2} b^{2} c^{3}\right)} d e^{4} + {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e^{5}\right)} x^{2}\right)}}, -\frac{2 \, {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{4} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} x^{4} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} x^{2} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3}\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) + 4 \, {\left(a^{3} b c e^{4} - {\left(a b^{2} c^{2} - 2 \, a^{2} c^{3}\right)} d^{3} e + {\left(a b^{3} c - a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{2} c - a^{3} c^{2}\right)} d e^{3} - {\left({\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{3} e - {\left(b^{4} c - 2 \, a b^{2} c^{2} - 2 \, a^{2} c^{3}\right)} d^{2} e^{2} + {\left(2 \, a b^{3} c - 5 \, a^{2} b c^{2}\right)} d e^{3} - {\left(a^{2} b^{2} c - 2 \, a^{3} c^{2}\right)} e^{4}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{4 \, {\left({\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{4} e - 2 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{3} e^{2} + {\left(a b^{4} c^{2} - 2 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d^{2} e^{3} - 2 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d e^{4} + {\left(a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} e^{5} + {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{4} e - 2 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{3} e^{2} + {\left(b^{4} c^{3} - 2 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{2} e^{3} - 2 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d e^{4} + {\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} e^{5}\right)} x^{4} + {\left({\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{4} e - 2 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{3} e^{2} + {\left(b^{5} c^{2} - 2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4}\right)} d^{2} e^{3} - 2 \, {\left(a b^{4} c^{2} - 4 \, a^{2} b^{2} c^{3}\right)} d e^{4} + {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e^{5}\right)} x^{2}\right)}}, -\frac{{\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} x^{4} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} x^{2} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3}\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) + {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{4} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(2 \, c x^{2} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{4} + b c x^{2} + a c\right)}}\right) + 2 \, {\left(a^{3} b c e^{4} - {\left(a b^{2} c^{2} - 2 \, a^{2} c^{3}\right)} d^{3} e + {\left(a b^{3} c - a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{2} c - a^{3} c^{2}\right)} d e^{3} - {\left({\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{3} e - {\left(b^{4} c - 2 \, a b^{2} c^{2} - 2 \, a^{2} c^{3}\right)} d^{2} e^{2} + {\left(2 \, a b^{3} c - 5 \, a^{2} b c^{2}\right)} d e^{3} - {\left(a^{2} b^{2} c - 2 \, a^{3} c^{2}\right)} e^{4}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{2 \, {\left({\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{4} e - 2 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{3} e^{2} + {\left(a b^{4} c^{2} - 2 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d^{2} e^{3} - 2 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d e^{4} + {\left(a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} e^{5} + {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{4} e - 2 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{3} e^{2} + {\left(b^{4} c^{3} - 2 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{2} e^{3} - 2 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d e^{4} + {\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} e^{5}\right)} x^{4} + {\left({\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{4} e - 2 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{3} e^{2} + {\left(b^{5} c^{2} - 2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4}\right)} d^{2} e^{3} - 2 \, {\left(a b^{4} c^{2} - 4 \, a^{2} b^{2} c^{3}\right)} d e^{4} + {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e^{5}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^4 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x^2)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + ((b^2*c^3 - 4*a*c^4)*d^3*x^4 + (b^3*c^2 - 4*a*b*c^3)*d^3*x^2 + (a*b^2*c^2 - 4*a^2*c^3)*d^3)*sqrt(c*d^2 - b*d*e + a*e^2)*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 - 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) - 4*(a^3*b*c*e^4 - (a*b^2*c^2 - 2*a^2*c^3)*d^3*e + (a*b^3*c - a^2*b*c^2)*d^2*e^2 - 2*(a^2*b^2*c - a^3*c^2)*d*e^3 - ((b^3*c^2 - 3*a*b*c^3)*d^3*e - (b^4*c - 2*a*b^2*c^2 - 2*a^2*c^3)*d^2*e^2 + (2*a*b^3*c - 5*a^2*b*c^2)*d*e^3 - (a^2*b^2*c - 2*a^3*c^2)*e^4)*x^2)*sqrt(c*x^4 + b*x^2 + a))/((a*b^2*c^4 - 4*a^2*c^5)*d^4*e - 2*(a*b^3*c^3 - 4*a^2*b*c^4)*d^3*e^2 + (a*b^4*c^2 - 2*a^2*b^2*c^3 - 8*a^3*c^4)*d^2*e^3 - 2*(a^2*b^3*c^2 - 4*a^3*b*c^3)*d*e^4 + (a^3*b^2*c^2 - 4*a^4*c^3)*e^5 + ((b^2*c^5 - 4*a*c^6)*d^4*e - 2*(b^3*c^4 - 4*a*b*c^5)*d^3*e^2 + (b^4*c^3 - 2*a*b^2*c^4 - 8*a^2*c^5)*d^2*e^3 - 2*(a*b^3*c^3 - 4*a^2*b*c^4)*d*e^4 + (a^2*b^2*c^3 - 4*a^3*c^4)*e^5)*x^4 + ((b^3*c^4 - 4*a*b*c^5)*d^4*e - 2*(b^4*c^3 - 4*a*b^2*c^4)*d^3*e^2 + (b^5*c^2 - 2*a*b^3*c^3 - 8*a^2*b*c^4)*d^2*e^3 - 2*(a*b^4*c^2 - 4*a^2*b^2*c^3)*d*e^4 + (a^2*b^3*c^2 - 4*a^3*b*c^3)*e^5)*x^2), -1/4*(2*((b^2*c^3 - 4*a*c^4)*d^3*x^4 + (b^3*c^2 - 4*a*b*c^3)*d^3*x^2 + (a*b^2*c^2 - 4*a^2*c^3)*d^3)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) - ((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^4 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x^2)*sqrt(c)*log(-8*c^2*x^4 - 8*b*c*x^2 - b^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(c) - 4*a*c) + 4*(a^3*b*c*e^4 - (a*b^2*c^2 - 2*a^2*c^3)*d^3*e + (a*b^3*c - a^2*b*c^2)*d^2*e^2 - 2*(a^2*b^2*c - a^3*c^2)*d*e^3 - ((b^3*c^2 - 3*a*b*c^3)*d^3*e - (b^4*c - 2*a*b^2*c^2 - 2*a^2*c^3)*d^2*e^2 + (2*a*b^3*c - 5*a^2*b*c^2)*d*e^3 - (a^2*b^2*c - 2*a^3*c^2)*e^4)*x^2)*sqrt(c*x^4 + b*x^2 + a))/((a*b^2*c^4 - 4*a^2*c^5)*d^4*e - 2*(a*b^3*c^3 - 4*a^2*b*c^4)*d^3*e^2 + (a*b^4*c^2 - 2*a^2*b^2*c^3 - 8*a^3*c^4)*d^2*e^3 - 2*(a^2*b^3*c^2 - 4*a^3*b*c^3)*d*e^4 + (a^3*b^2*c^2 - 4*a^4*c^3)*e^5 + ((b^2*c^5 - 4*a*c^6)*d^4*e - 2*(b^3*c^4 - 4*a*b*c^5)*d^3*e^2 + (b^4*c^3 - 2*a*b^2*c^4 - 8*a^2*c^5)*d^2*e^3 - 2*(a*b^3*c^3 - 4*a^2*b*c^4)*d*e^4 + (a^2*b^2*c^3 - 4*a^3*c^4)*e^5)*x^4 + ((b^3*c^4 - 4*a*b*c^5)*d^4*e - 2*(b^4*c^3 - 4*a*b^2*c^4)*d^3*e^2 + (b^5*c^2 - 2*a*b^3*c^3 - 8*a^2*b*c^4)*d^2*e^3 - 2*(a*b^4*c^2 - 4*a^2*b^2*c^3)*d*e^4 + (a^2*b^3*c^2 - 4*a^3*b*c^3)*e^5)*x^2), -1/4*(2*((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^4 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) - ((b^2*c^3 - 4*a*c^4)*d^3*x^4 + (b^3*c^2 - 4*a*b*c^3)*d^3*x^2 + (a*b^2*c^2 - 4*a^2*c^3)*d^3)*sqrt(c*d^2 - b*d*e + a*e^2)*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 - 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) + 4*(a^3*b*c*e^4 - (a*b^2*c^2 - 2*a^2*c^3)*d^3*e + (a*b^3*c - a^2*b*c^2)*d^2*e^2 - 2*(a^2*b^2*c - a^3*c^2)*d*e^3 - ((b^3*c^2 - 3*a*b*c^3)*d^3*e - (b^4*c - 2*a*b^2*c^2 - 2*a^2*c^3)*d^2*e^2 + (2*a*b^3*c - 5*a^2*b*c^2)*d*e^3 - (a^2*b^2*c - 2*a^3*c^2)*e^4)*x^2)*sqrt(c*x^4 + b*x^2 + a))/((a*b^2*c^4 - 4*a^2*c^5)*d^4*e - 2*(a*b^3*c^3 - 4*a^2*b*c^4)*d^3*e^2 + (a*b^4*c^2 - 2*a^2*b^2*c^3 - 8*a^3*c^4)*d^2*e^3 - 2*(a^2*b^3*c^2 - 4*a^3*b*c^3)*d*e^4 + (a^3*b^2*c^2 - 4*a^4*c^3)*e^5 + ((b^2*c^5 - 4*a*c^6)*d^4*e - 2*(b^3*c^4 - 4*a*b*c^5)*d^3*e^2 + (b^4*c^3 - 2*a*b^2*c^4 - 8*a^2*c^5)*d^2*e^3 - 2*(a*b^3*c^3 - 4*a^2*b*c^4)*d*e^4 + (a^2*b^2*c^3 - 4*a^3*c^4)*e^5)*x^4 + ((b^3*c^4 - 4*a*b*c^5)*d^4*e - 2*(b^4*c^3 - 4*a*b^2*c^4)*d^3*e^2 + (b^5*c^2 - 2*a*b^3*c^3 - 8*a^2*b*c^4)*d^2*e^3 - 2*(a*b^4*c^2 - 4*a^2*b^2*c^3)*d*e^4 + (a^2*b^3*c^2 - 4*a^3*b*c^3)*e^5)*x^2), -1/2*(((b^2*c^3 - 4*a*c^4)*d^3*x^4 + (b^3*c^2 - 4*a*b*c^3)*d^3*x^2 + (a*b^2*c^2 - 4*a^2*c^3)*d^3)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) + ((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^4 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(2*c*x^2 + b)*sqrt(-c)/(c^2*x^4 + b*c*x^2 + a*c)) + 2*(a^3*b*c*e^4 - (a*b^2*c^2 - 2*a^2*c^3)*d^3*e + (a*b^3*c - a^2*b*c^2)*d^2*e^2 - 2*(a^2*b^2*c - a^3*c^2)*d*e^3 - ((b^3*c^2 - 3*a*b*c^3)*d^3*e - (b^4*c - 2*a*b^2*c^2 - 2*a^2*c^3)*d^2*e^2 + (2*a*b^3*c - 5*a^2*b*c^2)*d*e^3 - (a^2*b^2*c - 2*a^3*c^2)*e^4)*x^2)*sqrt(c*x^4 + b*x^2 + a))/((a*b^2*c^4 - 4*a^2*c^5)*d^4*e - 2*(a*b^3*c^3 - 4*a^2*b*c^4)*d^3*e^2 + (a*b^4*c^2 - 2*a^2*b^2*c^3 - 8*a^3*c^4)*d^2*e^3 - 2*(a^2*b^3*c^2 - 4*a^3*b*c^3)*d*e^4 + (a^3*b^2*c^2 - 4*a^4*c^3)*e^5 + ((b^2*c^5 - 4*a*c^6)*d^4*e - 2*(b^3*c^4 - 4*a*b*c^5)*d^3*e^2 + (b^4*c^3 - 2*a*b^2*c^4 - 8*a^2*c^5)*d^2*e^3 - 2*(a*b^3*c^3 - 4*a^2*b*c^4)*d*e^4 + (a^2*b^2*c^3 - 4*a^3*c^4)*e^5)*x^4 + ((b^3*c^4 - 4*a*b*c^5)*d^4*e - 2*(b^4*c^3 - 4*a*b^2*c^4)*d^3*e^2 + (b^5*c^2 - 2*a*b^3*c^3 - 8*a^2*b*c^4)*d^2*e^3 - 2*(a*b^4*c^2 - 4*a^2*b^2*c^3)*d*e^4 + (a^2*b^3*c^2 - 4*a^3*b*c^3)*e^5)*x^2)]","B",0
343,1,1381,0,2.200594," ","integrate(x^5/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} x^{4} + {\left(b^{3} - 4 \, a b c\right)} d^{2} x^{2} + {\left(a b^{2} - 4 \, a^{2} c\right)} d^{2}\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) - 4 \, {\left(a b c d^{3} + 3 \, a^{2} b d e^{2} - 2 \, a^{3} e^{3} - {\left(a b^{2} + 2 \, a^{2} c\right)} d^{2} e - {\left(a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} + {\left(b^{3} - a b c\right)} d^{2} e - 2 \, {\left(a b^{2} - a^{2} c\right)} d e^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{4 \, {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{4} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x^{2}\right)}}, \frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} x^{4} + {\left(b^{3} - 4 \, a b c\right)} d^{2} x^{2} + {\left(a b^{2} - 4 \, a^{2} c\right)} d^{2}\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(a b c d^{3} + 3 \, a^{2} b d e^{2} - 2 \, a^{3} e^{3} - {\left(a b^{2} + 2 \, a^{2} c\right)} d^{2} e - {\left(a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} + {\left(b^{3} - a b c\right)} d^{2} e - 2 \, {\left(a b^{2} - a^{2} c\right)} d e^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{2 \, {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{4} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(((b^2*c - 4*a*c^2)*d^2*x^4 + (b^3 - 4*a*b*c)*d^2*x^2 + (a*b^2 - 4*a^2*c)*d^2)*sqrt(c*d^2 - b*d*e + a*e^2)*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) - 4*(a*b*c*d^3 + 3*a^2*b*d*e^2 - 2*a^3*e^3 - (a*b^2 + 2*a^2*c)*d^2*e - (a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3 + (b^3 - a*b*c)*d^2*e - 2*(a*b^2 - a^2*c)*d*e^2)*x^2)*sqrt(c*x^4 + b*x^2 + a))/((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^4 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x^2), 1/2*(((b^2*c - 4*a*c^2)*d^2*x^4 + (b^3 - 4*a*b*c)*d^2*x^2 + (a*b^2 - 4*a^2*c)*d^2)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) - 2*(a*b*c*d^3 + 3*a^2*b*d*e^2 - 2*a^3*e^3 - (a*b^2 + 2*a^2*c)*d^2*e - (a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3 + (b^3 - a*b*c)*d^2*e - 2*(a*b^2 - a^2*c)*d*e^2)*x^2)*sqrt(c*x^4 + b*x^2 + a))/((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^4 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x^2)]","B",0
344,1,1349,0,2.245163," ","integrate(x^3/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} d e x^{4} + {\left(b^{3} - 4 \, a b c\right)} d e x^{2} + {\left(a b^{2} - 4 \, a^{2} c\right)} d e\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) + 4 \, {\left(2 \, a c^{2} d^{3} - 3 \, a b c d^{2} e - a^{2} b e^{3} + {\left(a b^{2} + 2 \, a^{2} c\right)} d e^{2} + {\left(b c^{2} d^{3} + 3 \, a b c d e^{2} - 2 \, a^{2} c e^{3} - {\left(b^{2} c + 2 \, a c^{2}\right)} d^{2} e\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{4 \, {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{4} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x^{2}\right)}}, -\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} d e x^{4} + {\left(b^{3} - 4 \, a b c\right)} d e x^{2} + {\left(a b^{2} - 4 \, a^{2} c\right)} d e\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(2 \, a c^{2} d^{3} - 3 \, a b c d^{2} e - a^{2} b e^{3} + {\left(a b^{2} + 2 \, a^{2} c\right)} d e^{2} + {\left(b c^{2} d^{3} + 3 \, a b c d e^{2} - 2 \, a^{2} c e^{3} - {\left(b^{2} c + 2 \, a c^{2}\right)} d^{2} e\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{2 \, {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{4} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(((b^2*c - 4*a*c^2)*d*e*x^4 + (b^3 - 4*a*b*c)*d*e*x^2 + (a*b^2 - 4*a^2*c)*d*e)*sqrt(c*d^2 - b*d*e + a*e^2)*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 - 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) + 4*(2*a*c^2*d^3 - 3*a*b*c*d^2*e - a^2*b*e^3 + (a*b^2 + 2*a^2*c)*d*e^2 + (b*c^2*d^3 + 3*a*b*c*d*e^2 - 2*a^2*c*e^3 - (b^2*c + 2*a*c^2)*d^2*e)*x^2)*sqrt(c*x^4 + b*x^2 + a))/((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^4 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x^2), -1/2*(((b^2*c - 4*a*c^2)*d*e*x^4 + (b^3 - 4*a*b*c)*d*e*x^2 + (a*b^2 - 4*a^2*c)*d*e)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) - 2*(2*a*c^2*d^3 - 3*a*b*c*d^2*e - a^2*b*e^3 + (a*b^2 + 2*a^2*c)*d*e^2 + (b*c^2*d^3 + 3*a*b*c*d*e^2 - 2*a^2*c*e^3 - (b^2*c + 2*a*c^2)*d^2*e)*x^2)*sqrt(c*x^4 + b*x^2 + a))/((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^4 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x^2)]","B",0
345,1,1379,0,2.490709," ","integrate(x/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} x^{4} + {\left(b^{3} - 4 \, a b c\right)} e^{2} x^{2} + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) - 4 \, {\left(b c^{2} d^{3} - 2 \, {\left(b^{2} c - a c^{2}\right)} d^{2} e + {\left(b^{3} - a b c\right)} d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} + {\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e - a b c e^{3} + {\left(b^{2} c + 2 \, a c^{2}\right)} d e^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{4 \, {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{4} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x^{2}\right)}}, \frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} x^{4} + {\left(b^{3} - 4 \, a b c\right)} e^{2} x^{2} + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(b c^{2} d^{3} - 2 \, {\left(b^{2} c - a c^{2}\right)} d^{2} e + {\left(b^{3} - a b c\right)} d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} + {\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e - a b c e^{3} + {\left(b^{2} c + 2 \, a c^{2}\right)} d e^{2}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{2 \, {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{4} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(((b^2*c - 4*a*c^2)*e^2*x^4 + (b^3 - 4*a*b*c)*e^2*x^2 + (a*b^2 - 4*a^2*c)*e^2)*sqrt(c*d^2 - b*d*e + a*e^2)*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) - 4*(b*c^2*d^3 - 2*(b^2*c - a*c^2)*d^2*e + (b^3 - a*b*c)*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 + (2*c^3*d^3 - 3*b*c^2*d^2*e - a*b*c*e^3 + (b^2*c + 2*a*c^2)*d*e^2)*x^2)*sqrt(c*x^4 + b*x^2 + a))/((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^4 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x^2), 1/2*(((b^2*c - 4*a*c^2)*e^2*x^4 + (b^3 - 4*a*b*c)*e^2*x^2 + (a*b^2 - 4*a^2*c)*e^2)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) - 2*(b*c^2*d^3 - 2*(b^2*c - a*c^2)*d^2*e + (b^3 - a*b*c)*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 + (2*c^3*d^3 - 3*b*c^2*d^2*e - a*b*c*e^3 + (b^2*c + 2*a*c^2)*d*e^2)*x^2)*sqrt(c*x^4 + b*x^2 + a))/((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^4 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x^2)]","B",0
346,1,4909,0,10.493563," ","integrate(1/x/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{3} x^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{3} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{3}\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) + {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{4} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x^{2}\right)} \sqrt{a} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{4} + 8 \, a b x^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{4}}\right) + 4 \, {\left({\left(a b^{2} c^{2} - 2 \, a^{2} c^{3}\right)} d^{4} - {\left(2 \, a b^{3} c - 5 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 2 \, a^{3} c^{2}\right)} d^{2} e^{2} - {\left(a^{2} b^{3} - 3 \, a^{3} b c\right)} d e^{3} + {\left(a b c^{3} d^{4} - 2 \, {\left(a b^{2} c^{2} - a^{2} c^{3}\right)} d^{3} e + {\left(a b^{3} c - a^{2} b c^{2}\right)} d^{2} e^{2} - {\left(a^{2} b^{2} c - 2 \, a^{3} c^{2}\right)} d e^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{4 \, {\left({\left(a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} d^{5} - 2 \, {\left(a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d^{4} e + {\left(a^{3} b^{4} - 2 \, a^{4} b^{2} c - 8 \, a^{5} c^{2}\right)} d^{3} e^{2} - 2 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d^{2} e^{3} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} d e^{4} + {\left({\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d^{5} - 2 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d^{4} e + {\left(a^{2} b^{4} c - 2 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} d^{3} e^{2} - 2 \, {\left(a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d^{2} e^{3} + {\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} d e^{4}\right)} x^{4} + {\left({\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d^{5} - 2 \, {\left(a^{2} b^{4} c - 4 \, a^{3} b^{2} c^{2}\right)} d^{4} e + {\left(a^{2} b^{5} - 2 \, a^{3} b^{3} c - 8 \, a^{4} b c^{2}\right)} d^{3} e^{2} - 2 \, {\left(a^{3} b^{4} - 4 \, a^{4} b^{2} c\right)} d^{2} e^{3} + {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d e^{4}\right)} x^{2}\right)}}, -\frac{2 \, {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{3} x^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{3} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{3}\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) - {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{4} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x^{2}\right)} \sqrt{a} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{4} + 8 \, a b x^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{4}}\right) - 4 \, {\left({\left(a b^{2} c^{2} - 2 \, a^{2} c^{3}\right)} d^{4} - {\left(2 \, a b^{3} c - 5 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 2 \, a^{3} c^{2}\right)} d^{2} e^{2} - {\left(a^{2} b^{3} - 3 \, a^{3} b c\right)} d e^{3} + {\left(a b c^{3} d^{4} - 2 \, {\left(a b^{2} c^{2} - a^{2} c^{3}\right)} d^{3} e + {\left(a b^{3} c - a^{2} b c^{2}\right)} d^{2} e^{2} - {\left(a^{2} b^{2} c - 2 \, a^{3} c^{2}\right)} d e^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{4 \, {\left({\left(a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} d^{5} - 2 \, {\left(a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d^{4} e + {\left(a^{3} b^{4} - 2 \, a^{4} b^{2} c - 8 \, a^{5} c^{2}\right)} d^{3} e^{2} - 2 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d^{2} e^{3} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} d e^{4} + {\left({\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d^{5} - 2 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d^{4} e + {\left(a^{2} b^{4} c - 2 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} d^{3} e^{2} - 2 \, {\left(a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d^{2} e^{3} + {\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} d e^{4}\right)} x^{4} + {\left({\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d^{5} - 2 \, {\left(a^{2} b^{4} c - 4 \, a^{3} b^{2} c^{2}\right)} d^{4} e + {\left(a^{2} b^{5} - 2 \, a^{3} b^{3} c - 8 \, a^{4} b c^{2}\right)} d^{3} e^{2} - 2 \, {\left(a^{3} b^{4} - 4 \, a^{4} b^{2} c\right)} d^{2} e^{3} + {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d e^{4}\right)} x^{2}\right)}}, \frac{2 \, {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{4} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{4} + a b x^{2} + a^{2}\right)}}\right) + {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{3} x^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{3} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{3}\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} - 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) + 4 \, {\left({\left(a b^{2} c^{2} - 2 \, a^{2} c^{3}\right)} d^{4} - {\left(2 \, a b^{3} c - 5 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 2 \, a^{3} c^{2}\right)} d^{2} e^{2} - {\left(a^{2} b^{3} - 3 \, a^{3} b c\right)} d e^{3} + {\left(a b c^{3} d^{4} - 2 \, {\left(a b^{2} c^{2} - a^{2} c^{3}\right)} d^{3} e + {\left(a b^{3} c - a^{2} b c^{2}\right)} d^{2} e^{2} - {\left(a^{2} b^{2} c - 2 \, a^{3} c^{2}\right)} d e^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{4 \, {\left({\left(a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} d^{5} - 2 \, {\left(a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d^{4} e + {\left(a^{3} b^{4} - 2 \, a^{4} b^{2} c - 8 \, a^{5} c^{2}\right)} d^{3} e^{2} - 2 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d^{2} e^{3} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} d e^{4} + {\left({\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d^{5} - 2 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d^{4} e + {\left(a^{2} b^{4} c - 2 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} d^{3} e^{2} - 2 \, {\left(a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d^{2} e^{3} + {\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} d e^{4}\right)} x^{4} + {\left({\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d^{5} - 2 \, {\left(a^{2} b^{4} c - 4 \, a^{3} b^{2} c^{2}\right)} d^{4} e + {\left(a^{2} b^{5} - 2 \, a^{3} b^{3} c - 8 \, a^{4} b c^{2}\right)} d^{3} e^{2} - 2 \, {\left(a^{3} b^{4} - 4 \, a^{4} b^{2} c\right)} d^{2} e^{3} + {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d e^{4}\right)} x^{2}\right)}}, -\frac{{\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{3} x^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{3} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{3}\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) - {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{4} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{4} + a b x^{2} + a^{2}\right)}}\right) - 2 \, {\left({\left(a b^{2} c^{2} - 2 \, a^{2} c^{3}\right)} d^{4} - {\left(2 \, a b^{3} c - 5 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 2 \, a^{3} c^{2}\right)} d^{2} e^{2} - {\left(a^{2} b^{3} - 3 \, a^{3} b c\right)} d e^{3} + {\left(a b c^{3} d^{4} - 2 \, {\left(a b^{2} c^{2} - a^{2} c^{3}\right)} d^{3} e + {\left(a b^{3} c - a^{2} b c^{2}\right)} d^{2} e^{2} - {\left(a^{2} b^{2} c - 2 \, a^{3} c^{2}\right)} d e^{3}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{2 \, {\left({\left(a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} d^{5} - 2 \, {\left(a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d^{4} e + {\left(a^{3} b^{4} - 2 \, a^{4} b^{2} c - 8 \, a^{5} c^{2}\right)} d^{3} e^{2} - 2 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d^{2} e^{3} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} d e^{4} + {\left({\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d^{5} - 2 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d^{4} e + {\left(a^{2} b^{4} c - 2 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} d^{3} e^{2} - 2 \, {\left(a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d^{2} e^{3} + {\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} d e^{4}\right)} x^{4} + {\left({\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d^{5} - 2 \, {\left(a^{2} b^{4} c - 4 \, a^{3} b^{2} c^{2}\right)} d^{4} e + {\left(a^{2} b^{5} - 2 \, a^{3} b^{3} c - 8 \, a^{4} b c^{2}\right)} d^{3} e^{2} - 2 \, {\left(a^{3} b^{4} - 4 \, a^{4} b^{2} c\right)} d^{2} e^{3} + {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(((a^2*b^2*c - 4*a^3*c^2)*e^3*x^4 + (a^2*b^3 - 4*a^3*b*c)*e^3*x^2 + (a^3*b^2 - 4*a^4*c)*e^3)*sqrt(c*d^2 - b*d*e + a*e^2)*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 - 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) + ((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^4 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x^2)*sqrt(a)*log(-((b^2 + 4*a*c)*x^4 + 8*a*b*x^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(a) + 8*a^2)/x^4) + 4*((a*b^2*c^2 - 2*a^2*c^3)*d^4 - (2*a*b^3*c - 5*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 2*a^3*c^2)*d^2*e^2 - (a^2*b^3 - 3*a^3*b*c)*d*e^3 + (a*b*c^3*d^4 - 2*(a*b^2*c^2 - a^2*c^3)*d^3*e + (a*b^3*c - a^2*b*c^2)*d^2*e^2 - (a^2*b^2*c - 2*a^3*c^2)*d*e^3)*x^2)*sqrt(c*x^4 + b*x^2 + a))/((a^3*b^2*c^2 - 4*a^4*c^3)*d^5 - 2*(a^3*b^3*c - 4*a^4*b*c^2)*d^4*e + (a^3*b^4 - 2*a^4*b^2*c - 8*a^5*c^2)*d^3*e^2 - 2*(a^4*b^3 - 4*a^5*b*c)*d^2*e^3 + (a^5*b^2 - 4*a^6*c)*d*e^4 + ((a^2*b^2*c^3 - 4*a^3*c^4)*d^5 - 2*(a^2*b^3*c^2 - 4*a^3*b*c^3)*d^4*e + (a^2*b^4*c - 2*a^3*b^2*c^2 - 8*a^4*c^3)*d^3*e^2 - 2*(a^3*b^3*c - 4*a^4*b*c^2)*d^2*e^3 + (a^4*b^2*c - 4*a^5*c^2)*d*e^4)*x^4 + ((a^2*b^3*c^2 - 4*a^3*b*c^3)*d^5 - 2*(a^2*b^4*c - 4*a^3*b^2*c^2)*d^4*e + (a^2*b^5 - 2*a^3*b^3*c - 8*a^4*b*c^2)*d^3*e^2 - 2*(a^3*b^4 - 4*a^4*b^2*c)*d^2*e^3 + (a^4*b^3 - 4*a^5*b*c)*d*e^4)*x^2), -1/4*(2*((a^2*b^2*c - 4*a^3*c^2)*e^3*x^4 + (a^2*b^3 - 4*a^3*b*c)*e^3*x^2 + (a^3*b^2 - 4*a^4*c)*e^3)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) - ((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^4 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x^2)*sqrt(a)*log(-((b^2 + 4*a*c)*x^4 + 8*a*b*x^2 - 4*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(a) + 8*a^2)/x^4) - 4*((a*b^2*c^2 - 2*a^2*c^3)*d^4 - (2*a*b^3*c - 5*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 2*a^3*c^2)*d^2*e^2 - (a^2*b^3 - 3*a^3*b*c)*d*e^3 + (a*b*c^3*d^4 - 2*(a*b^2*c^2 - a^2*c^3)*d^3*e + (a*b^3*c - a^2*b*c^2)*d^2*e^2 - (a^2*b^2*c - 2*a^3*c^2)*d*e^3)*x^2)*sqrt(c*x^4 + b*x^2 + a))/((a^3*b^2*c^2 - 4*a^4*c^3)*d^5 - 2*(a^3*b^3*c - 4*a^4*b*c^2)*d^4*e + (a^3*b^4 - 2*a^4*b^2*c - 8*a^5*c^2)*d^3*e^2 - 2*(a^4*b^3 - 4*a^5*b*c)*d^2*e^3 + (a^5*b^2 - 4*a^6*c)*d*e^4 + ((a^2*b^2*c^3 - 4*a^3*c^4)*d^5 - 2*(a^2*b^3*c^2 - 4*a^3*b*c^3)*d^4*e + (a^2*b^4*c - 2*a^3*b^2*c^2 - 8*a^4*c^3)*d^3*e^2 - 2*(a^3*b^3*c - 4*a^4*b*c^2)*d^2*e^3 + (a^4*b^2*c - 4*a^5*c^2)*d*e^4)*x^4 + ((a^2*b^3*c^2 - 4*a^3*b*c^3)*d^5 - 2*(a^2*b^4*c - 4*a^3*b^2*c^2)*d^4*e + (a^2*b^5 - 2*a^3*b^3*c - 8*a^4*b*c^2)*d^3*e^2 - 2*(a^3*b^4 - 4*a^4*b^2*c)*d^2*e^3 + (a^4*b^3 - 4*a^5*b*c)*d*e^4)*x^2), 1/4*(2*((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^4 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x^2)*sqrt(-a)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(-a)/(a*c*x^4 + a*b*x^2 + a^2)) + ((a^2*b^2*c - 4*a^3*c^2)*e^3*x^4 + (a^2*b^3 - 4*a^3*b*c)*e^3*x^2 + (a^3*b^2 - 4*a^4*c)*e^3)*sqrt(c*d^2 - b*d*e + a*e^2)*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 - 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) + 4*((a*b^2*c^2 - 2*a^2*c^3)*d^4 - (2*a*b^3*c - 5*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 2*a^3*c^2)*d^2*e^2 - (a^2*b^3 - 3*a^3*b*c)*d*e^3 + (a*b*c^3*d^4 - 2*(a*b^2*c^2 - a^2*c^3)*d^3*e + (a*b^3*c - a^2*b*c^2)*d^2*e^2 - (a^2*b^2*c - 2*a^3*c^2)*d*e^3)*x^2)*sqrt(c*x^4 + b*x^2 + a))/((a^3*b^2*c^2 - 4*a^4*c^3)*d^5 - 2*(a^3*b^3*c - 4*a^4*b*c^2)*d^4*e + (a^3*b^4 - 2*a^4*b^2*c - 8*a^5*c^2)*d^3*e^2 - 2*(a^4*b^3 - 4*a^5*b*c)*d^2*e^3 + (a^5*b^2 - 4*a^6*c)*d*e^4 + ((a^2*b^2*c^3 - 4*a^3*c^4)*d^5 - 2*(a^2*b^3*c^2 - 4*a^3*b*c^3)*d^4*e + (a^2*b^4*c - 2*a^3*b^2*c^2 - 8*a^4*c^3)*d^3*e^2 - 2*(a^3*b^3*c - 4*a^4*b*c^2)*d^2*e^3 + (a^4*b^2*c - 4*a^5*c^2)*d*e^4)*x^4 + ((a^2*b^3*c^2 - 4*a^3*b*c^3)*d^5 - 2*(a^2*b^4*c - 4*a^3*b^2*c^2)*d^4*e + (a^2*b^5 - 2*a^3*b^3*c - 8*a^4*b*c^2)*d^3*e^2 - 2*(a^3*b^4 - 4*a^4*b^2*c)*d^2*e^3 + (a^4*b^3 - 4*a^5*b*c)*d*e^4)*x^2), -1/2*(((a^2*b^2*c - 4*a^3*c^2)*e^3*x^4 + (a^2*b^3 - 4*a^3*b*c)*e^3*x^2 + (a^3*b^2 - 4*a^4*c)*e^3)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) - ((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^4 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x^2)*sqrt(-a)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(-a)/(a*c*x^4 + a*b*x^2 + a^2)) - 2*((a*b^2*c^2 - 2*a^2*c^3)*d^4 - (2*a*b^3*c - 5*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 2*a^3*c^2)*d^2*e^2 - (a^2*b^3 - 3*a^3*b*c)*d*e^3 + (a*b*c^3*d^4 - 2*(a*b^2*c^2 - a^2*c^3)*d^3*e + (a*b^3*c - a^2*b*c^2)*d^2*e^2 - (a^2*b^2*c - 2*a^3*c^2)*d*e^3)*x^2)*sqrt(c*x^4 + b*x^2 + a))/((a^3*b^2*c^2 - 4*a^4*c^3)*d^5 - 2*(a^3*b^3*c - 4*a^4*b*c^2)*d^4*e + (a^3*b^4 - 2*a^4*b^2*c - 8*a^5*c^2)*d^3*e^2 - 2*(a^4*b^3 - 4*a^5*b*c)*d^2*e^3 + (a^5*b^2 - 4*a^6*c)*d*e^4 + ((a^2*b^2*c^3 - 4*a^3*c^4)*d^5 - 2*(a^2*b^3*c^2 - 4*a^3*b*c^3)*d^4*e + (a^2*b^4*c - 2*a^3*b^2*c^2 - 8*a^4*c^3)*d^3*e^2 - 2*(a^3*b^3*c - 4*a^4*b*c^2)*d^2*e^3 + (a^4*b^2*c - 4*a^5*c^2)*d*e^4)*x^4 + ((a^2*b^3*c^2 - 4*a^3*b*c^3)*d^5 - 2*(a^2*b^4*c - 4*a^3*b^2*c^2)*d^4*e + (a^2*b^5 - 2*a^3*b^3*c - 8*a^4*b*c^2)*d^3*e^2 - 2*(a^3*b^4 - 4*a^4*b^2*c)*d^2*e^3 + (a^4*b^3 - 4*a^5*b*c)*d*e^4)*x^2)]","B",0
347,1,6486,0,22.940611," ","integrate(1/x^3/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{4} x^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{4} x^{4} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4} x^{2}\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) + {\left({\left(3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} - 2 \, {\left(3 \, b^{4} c^{2} - 13 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{4} e + {\left(3 \, b^{5} c - 10 \, a b^{3} c^{2} - 8 \, a^{2} b c^{3}\right)} d^{3} e^{2} - 4 \, {\left(a b^{4} c - 5 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} d^{2} e^{3} - {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{4} + 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{5}\right)} x^{6} + {\left(3 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3}\right)} d^{5} - 2 \, {\left(3 \, b^{5} c - 13 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d^{4} e + {\left(3 \, b^{6} - 10 \, a b^{4} c - 8 \, a^{2} b^{2} c^{2}\right)} d^{3} e^{2} - 4 \, {\left(a b^{5} - 5 \, a^{2} b^{3} c + 4 \, a^{3} b c^{2}\right)} d^{2} e^{3} - {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c\right)} d e^{4} + 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{5}\right)} x^{4} + {\left(3 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{5} - 2 \, {\left(3 \, a b^{4} c - 13 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} d^{4} e + {\left(3 \, a b^{5} - 10 \, a^{2} b^{3} c - 8 \, a^{3} b c^{2}\right)} d^{3} e^{2} - 4 \, {\left(a^{2} b^{4} - 5 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d^{2} e^{3} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{4} + 2 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{5}\right)} x^{2}\right)} \sqrt{a} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{4} + 8 \, a b x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{4}}\right) - 4 \, {\left({\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{5} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{4} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{3} e^{2} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2} e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d e^{4} + {\left({\left(3 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{5} - 6 \, {\left(a b^{3} c^{2} - 3 \, a^{2} b c^{3}\right)} d^{4} e + 3 \, {\left(a b^{4} c - 2 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{3} e^{2} - 2 \, {\left(2 \, a^{2} b^{3} c - 7 \, a^{3} b c^{2}\right)} d^{2} e^{3} + {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d e^{4}\right)} x^{4} + {\left({\left(3 \, a b^{3} c^{2} - 10 \, a^{2} b c^{3}\right)} d^{5} - 2 \, {\left(3 \, a b^{4} c - 11 \, a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d^{4} e + {\left(3 \, a b^{5} - 8 \, a^{2} b^{3} c - 10 \, a^{3} b c^{2}\right)} d^{3} e^{2} - 4 \, {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{2} e^{3} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{4}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{8 \, {\left({\left({\left(a^{3} b^{2} c^{3} - 4 \, a^{4} c^{4}\right)} d^{6} - 2 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d^{5} e + {\left(a^{3} b^{4} c - 2 \, a^{4} b^{2} c^{2} - 8 \, a^{5} c^{3}\right)} d^{4} e^{2} - 2 \, {\left(a^{4} b^{3} c - 4 \, a^{5} b c^{2}\right)} d^{3} e^{3} + {\left(a^{5} b^{2} c - 4 \, a^{6} c^{2}\right)} d^{2} e^{4}\right)} x^{6} + {\left({\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d^{6} - 2 \, {\left(a^{3} b^{4} c - 4 \, a^{4} b^{2} c^{2}\right)} d^{5} e + {\left(a^{3} b^{5} - 2 \, a^{4} b^{3} c - 8 \, a^{5} b c^{2}\right)} d^{4} e^{2} - 2 \, {\left(a^{4} b^{4} - 4 \, a^{5} b^{2} c\right)} d^{3} e^{3} + {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d^{2} e^{4}\right)} x^{4} + {\left({\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{6} - 2 \, {\left(a^{4} b^{3} c - 4 \, a^{5} b c^{2}\right)} d^{5} e + {\left(a^{4} b^{4} - 2 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{4} e^{2} - 2 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d^{3} e^{3} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} d^{2} e^{4}\right)} x^{2}\right)}}, \frac{4 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{4} x^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{4} x^{4} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4} x^{2}\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) + {\left({\left(3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} - 2 \, {\left(3 \, b^{4} c^{2} - 13 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{4} e + {\left(3 \, b^{5} c - 10 \, a b^{3} c^{2} - 8 \, a^{2} b c^{3}\right)} d^{3} e^{2} - 4 \, {\left(a b^{4} c - 5 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} d^{2} e^{3} - {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{4} + 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{5}\right)} x^{6} + {\left(3 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3}\right)} d^{5} - 2 \, {\left(3 \, b^{5} c - 13 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d^{4} e + {\left(3 \, b^{6} - 10 \, a b^{4} c - 8 \, a^{2} b^{2} c^{2}\right)} d^{3} e^{2} - 4 \, {\left(a b^{5} - 5 \, a^{2} b^{3} c + 4 \, a^{3} b c^{2}\right)} d^{2} e^{3} - {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c\right)} d e^{4} + 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{5}\right)} x^{4} + {\left(3 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{5} - 2 \, {\left(3 \, a b^{4} c - 13 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} d^{4} e + {\left(3 \, a b^{5} - 10 \, a^{2} b^{3} c - 8 \, a^{3} b c^{2}\right)} d^{3} e^{2} - 4 \, {\left(a^{2} b^{4} - 5 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d^{2} e^{3} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{4} + 2 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{5}\right)} x^{2}\right)} \sqrt{a} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{4} + 8 \, a b x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{4}}\right) - 4 \, {\left({\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{5} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{4} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{3} e^{2} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2} e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d e^{4} + {\left({\left(3 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{5} - 6 \, {\left(a b^{3} c^{2} - 3 \, a^{2} b c^{3}\right)} d^{4} e + 3 \, {\left(a b^{4} c - 2 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{3} e^{2} - 2 \, {\left(2 \, a^{2} b^{3} c - 7 \, a^{3} b c^{2}\right)} d^{2} e^{3} + {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d e^{4}\right)} x^{4} + {\left({\left(3 \, a b^{3} c^{2} - 10 \, a^{2} b c^{3}\right)} d^{5} - 2 \, {\left(3 \, a b^{4} c - 11 \, a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d^{4} e + {\left(3 \, a b^{5} - 8 \, a^{2} b^{3} c - 10 \, a^{3} b c^{2}\right)} d^{3} e^{2} - 4 \, {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{2} e^{3} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{4}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{8 \, {\left({\left({\left(a^{3} b^{2} c^{3} - 4 \, a^{4} c^{4}\right)} d^{6} - 2 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d^{5} e + {\left(a^{3} b^{4} c - 2 \, a^{4} b^{2} c^{2} - 8 \, a^{5} c^{3}\right)} d^{4} e^{2} - 2 \, {\left(a^{4} b^{3} c - 4 \, a^{5} b c^{2}\right)} d^{3} e^{3} + {\left(a^{5} b^{2} c - 4 \, a^{6} c^{2}\right)} d^{2} e^{4}\right)} x^{6} + {\left({\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d^{6} - 2 \, {\left(a^{3} b^{4} c - 4 \, a^{4} b^{2} c^{2}\right)} d^{5} e + {\left(a^{3} b^{5} - 2 \, a^{4} b^{3} c - 8 \, a^{5} b c^{2}\right)} d^{4} e^{2} - 2 \, {\left(a^{4} b^{4} - 4 \, a^{5} b^{2} c\right)} d^{3} e^{3} + {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d^{2} e^{4}\right)} x^{4} + {\left({\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{6} - 2 \, {\left(a^{4} b^{3} c - 4 \, a^{5} b c^{2}\right)} d^{5} e + {\left(a^{4} b^{4} - 2 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{4} e^{2} - 2 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d^{3} e^{3} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} d^{2} e^{4}\right)} x^{2}\right)}}, -\frac{{\left({\left(3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} - 2 \, {\left(3 \, b^{4} c^{2} - 13 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{4} e + {\left(3 \, b^{5} c - 10 \, a b^{3} c^{2} - 8 \, a^{2} b c^{3}\right)} d^{3} e^{2} - 4 \, {\left(a b^{4} c - 5 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} d^{2} e^{3} - {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{4} + 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{5}\right)} x^{6} + {\left(3 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3}\right)} d^{5} - 2 \, {\left(3 \, b^{5} c - 13 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d^{4} e + {\left(3 \, b^{6} - 10 \, a b^{4} c - 8 \, a^{2} b^{2} c^{2}\right)} d^{3} e^{2} - 4 \, {\left(a b^{5} - 5 \, a^{2} b^{3} c + 4 \, a^{3} b c^{2}\right)} d^{2} e^{3} - {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c\right)} d e^{4} + 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{5}\right)} x^{4} + {\left(3 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{5} - 2 \, {\left(3 \, a b^{4} c - 13 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} d^{4} e + {\left(3 \, a b^{5} - 10 \, a^{2} b^{3} c - 8 \, a^{3} b c^{2}\right)} d^{3} e^{2} - 4 \, {\left(a^{2} b^{4} - 5 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d^{2} e^{3} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{4} + 2 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{5}\right)} x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{4} + a b x^{2} + a^{2}\right)}}\right) - {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{4} x^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{4} x^{4} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4} x^{2}\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{4} - 8 \, a b d e + 8 \, a^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d^{2} + 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x^{2} + 4 \, \sqrt{c x^{4} + b x^{2} + a} \sqrt{c d^{2} - b d e + a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) + 2 \, {\left({\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{5} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{4} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{3} e^{2} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2} e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d e^{4} + {\left({\left(3 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{5} - 6 \, {\left(a b^{3} c^{2} - 3 \, a^{2} b c^{3}\right)} d^{4} e + 3 \, {\left(a b^{4} c - 2 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{3} e^{2} - 2 \, {\left(2 \, a^{2} b^{3} c - 7 \, a^{3} b c^{2}\right)} d^{2} e^{3} + {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d e^{4}\right)} x^{4} + {\left({\left(3 \, a b^{3} c^{2} - 10 \, a^{2} b c^{3}\right)} d^{5} - 2 \, {\left(3 \, a b^{4} c - 11 \, a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d^{4} e + {\left(3 \, a b^{5} - 8 \, a^{2} b^{3} c - 10 \, a^{3} b c^{2}\right)} d^{3} e^{2} - 4 \, {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{2} e^{3} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{4}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{4 \, {\left({\left({\left(a^{3} b^{2} c^{3} - 4 \, a^{4} c^{4}\right)} d^{6} - 2 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d^{5} e + {\left(a^{3} b^{4} c - 2 \, a^{4} b^{2} c^{2} - 8 \, a^{5} c^{3}\right)} d^{4} e^{2} - 2 \, {\left(a^{4} b^{3} c - 4 \, a^{5} b c^{2}\right)} d^{3} e^{3} + {\left(a^{5} b^{2} c - 4 \, a^{6} c^{2}\right)} d^{2} e^{4}\right)} x^{6} + {\left({\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d^{6} - 2 \, {\left(a^{3} b^{4} c - 4 \, a^{4} b^{2} c^{2}\right)} d^{5} e + {\left(a^{3} b^{5} - 2 \, a^{4} b^{3} c - 8 \, a^{5} b c^{2}\right)} d^{4} e^{2} - 2 \, {\left(a^{4} b^{4} - 4 \, a^{5} b^{2} c\right)} d^{3} e^{3} + {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d^{2} e^{4}\right)} x^{4} + {\left({\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{6} - 2 \, {\left(a^{4} b^{3} c - 4 \, a^{5} b c^{2}\right)} d^{5} e + {\left(a^{4} b^{4} - 2 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{4} e^{2} - 2 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d^{3} e^{3} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} d^{2} e^{4}\right)} x^{2}\right)}}, \frac{2 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{4} x^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{4} x^{4} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4} x^{2}\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} \sqrt{-c d^{2} + b d e - a e^{2}} {\left({\left(2 \, c d - b e\right)} x^{2} + b d - 2 \, a e\right)}}{2 \, {\left({\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{4} + a c d^{2} - a b d e + a^{2} e^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x^{2}\right)}}\right) - {\left({\left(3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} - 2 \, {\left(3 \, b^{4} c^{2} - 13 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{4} e + {\left(3 \, b^{5} c - 10 \, a b^{3} c^{2} - 8 \, a^{2} b c^{3}\right)} d^{3} e^{2} - 4 \, {\left(a b^{4} c - 5 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} d^{2} e^{3} - {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{4} + 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{5}\right)} x^{6} + {\left(3 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3}\right)} d^{5} - 2 \, {\left(3 \, b^{5} c - 13 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d^{4} e + {\left(3 \, b^{6} - 10 \, a b^{4} c - 8 \, a^{2} b^{2} c^{2}\right)} d^{3} e^{2} - 4 \, {\left(a b^{5} - 5 \, a^{2} b^{3} c + 4 \, a^{3} b c^{2}\right)} d^{2} e^{3} - {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c\right)} d e^{4} + 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{5}\right)} x^{4} + {\left(3 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{5} - 2 \, {\left(3 \, a b^{4} c - 13 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} d^{4} e + {\left(3 \, a b^{5} - 10 \, a^{2} b^{3} c - 8 \, a^{3} b c^{2}\right)} d^{3} e^{2} - 4 \, {\left(a^{2} b^{4} - 5 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d^{2} e^{3} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{4} + 2 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{5}\right)} x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(b x^{2} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{4} + a b x^{2} + a^{2}\right)}}\right) - 2 \, {\left({\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{5} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{4} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{3} e^{2} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2} e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d e^{4} + {\left({\left(3 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{5} - 6 \, {\left(a b^{3} c^{2} - 3 \, a^{2} b c^{3}\right)} d^{4} e + 3 \, {\left(a b^{4} c - 2 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{3} e^{2} - 2 \, {\left(2 \, a^{2} b^{3} c - 7 \, a^{3} b c^{2}\right)} d^{2} e^{3} + {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d e^{4}\right)} x^{4} + {\left({\left(3 \, a b^{3} c^{2} - 10 \, a^{2} b c^{3}\right)} d^{5} - 2 \, {\left(3 \, a b^{4} c - 11 \, a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d^{4} e + {\left(3 \, a b^{5} - 8 \, a^{2} b^{3} c - 10 \, a^{3} b c^{2}\right)} d^{3} e^{2} - 4 \, {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{2} e^{3} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{4}\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{4 \, {\left({\left({\left(a^{3} b^{2} c^{3} - 4 \, a^{4} c^{4}\right)} d^{6} - 2 \, {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d^{5} e + {\left(a^{3} b^{4} c - 2 \, a^{4} b^{2} c^{2} - 8 \, a^{5} c^{3}\right)} d^{4} e^{2} - 2 \, {\left(a^{4} b^{3} c - 4 \, a^{5} b c^{2}\right)} d^{3} e^{3} + {\left(a^{5} b^{2} c - 4 \, a^{6} c^{2}\right)} d^{2} e^{4}\right)} x^{6} + {\left({\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d^{6} - 2 \, {\left(a^{3} b^{4} c - 4 \, a^{4} b^{2} c^{2}\right)} d^{5} e + {\left(a^{3} b^{5} - 2 \, a^{4} b^{3} c - 8 \, a^{5} b c^{2}\right)} d^{4} e^{2} - 2 \, {\left(a^{4} b^{4} - 4 \, a^{5} b^{2} c\right)} d^{3} e^{3} + {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d^{2} e^{4}\right)} x^{4} + {\left({\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{6} - 2 \, {\left(a^{4} b^{3} c - 4 \, a^{5} b c^{2}\right)} d^{5} e + {\left(a^{4} b^{4} - 2 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{4} e^{2} - 2 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d^{3} e^{3} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} d^{2} e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/8*(2*((a^3*b^2*c - 4*a^4*c^2)*e^4*x^6 + (a^3*b^3 - 4*a^4*b*c)*e^4*x^4 + (a^4*b^2 - 4*a^5*c)*e^4*x^2)*sqrt(c*d^2 - b*d*e + a*e^2)*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) + ((3*(b^3*c^3 - 4*a*b*c^4)*d^5 - 2*(3*b^4*c^2 - 13*a*b^2*c^3 + 4*a^2*c^4)*d^4*e + (3*b^5*c - 10*a*b^3*c^2 - 8*a^2*b*c^3)*d^3*e^2 - 4*(a*b^4*c - 5*a^2*b^2*c^2 + 4*a^3*c^3)*d^2*e^3 - (a^2*b^3*c - 4*a^3*b*c^2)*d*e^4 + 2*(a^3*b^2*c - 4*a^4*c^2)*e^5)*x^6 + (3*(b^4*c^2 - 4*a*b^2*c^3)*d^5 - 2*(3*b^5*c - 13*a*b^3*c^2 + 4*a^2*b*c^3)*d^4*e + (3*b^6 - 10*a*b^4*c - 8*a^2*b^2*c^2)*d^3*e^2 - 4*(a*b^5 - 5*a^2*b^3*c + 4*a^3*b*c^2)*d^2*e^3 - (a^2*b^4 - 4*a^3*b^2*c)*d*e^4 + 2*(a^3*b^3 - 4*a^4*b*c)*e^5)*x^4 + (3*(a*b^3*c^2 - 4*a^2*b*c^3)*d^5 - 2*(3*a*b^4*c - 13*a^2*b^2*c^2 + 4*a^3*c^3)*d^4*e + (3*a*b^5 - 10*a^2*b^3*c - 8*a^3*b*c^2)*d^3*e^2 - 4*(a^2*b^4 - 5*a^3*b^2*c + 4*a^4*c^2)*d^2*e^3 - (a^3*b^3 - 4*a^4*b*c)*d*e^4 + 2*(a^4*b^2 - 4*a^5*c)*e^5)*x^2)*sqrt(a)*log(-((b^2 + 4*a*c)*x^4 + 8*a*b*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(a) + 8*a^2)/x^4) - 4*((a^2*b^2*c^2 - 4*a^3*c^3)*d^5 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^4*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^3*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d^2*e^3 + (a^4*b^2 - 4*a^5*c)*d*e^4 + ((3*a*b^2*c^3 - 8*a^2*c^4)*d^5 - 6*(a*b^3*c^2 - 3*a^2*b*c^3)*d^4*e + 3*(a*b^4*c - 2*a^2*b^2*c^2 - 4*a^3*c^3)*d^3*e^2 - 2*(2*a^2*b^3*c - 7*a^3*b*c^2)*d^2*e^3 + (a^3*b^2*c - 4*a^4*c^2)*d*e^4)*x^4 + ((3*a*b^3*c^2 - 10*a^2*b*c^3)*d^5 - 2*(3*a*b^4*c - 11*a^2*b^2*c^2 + 2*a^3*c^3)*d^4*e + (3*a*b^5 - 8*a^2*b^3*c - 10*a^3*b*c^2)*d^3*e^2 - 4*(a^2*b^4 - 4*a^3*b^2*c + a^4*c^2)*d^2*e^3 + (a^3*b^3 - 4*a^4*b*c)*d*e^4)*x^2)*sqrt(c*x^4 + b*x^2 + a))/(((a^3*b^2*c^3 - 4*a^4*c^4)*d^6 - 2*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d^5*e + (a^3*b^4*c - 2*a^4*b^2*c^2 - 8*a^5*c^3)*d^4*e^2 - 2*(a^4*b^3*c - 4*a^5*b*c^2)*d^3*e^3 + (a^5*b^2*c - 4*a^6*c^2)*d^2*e^4)*x^6 + ((a^3*b^3*c^2 - 4*a^4*b*c^3)*d^6 - 2*(a^3*b^4*c - 4*a^4*b^2*c^2)*d^5*e + (a^3*b^5 - 2*a^4*b^3*c - 8*a^5*b*c^2)*d^4*e^2 - 2*(a^4*b^4 - 4*a^5*b^2*c)*d^3*e^3 + (a^5*b^3 - 4*a^6*b*c)*d^2*e^4)*x^4 + ((a^4*b^2*c^2 - 4*a^5*c^3)*d^6 - 2*(a^4*b^3*c - 4*a^5*b*c^2)*d^5*e + (a^4*b^4 - 2*a^5*b^2*c - 8*a^6*c^2)*d^4*e^2 - 2*(a^5*b^3 - 4*a^6*b*c)*d^3*e^3 + (a^6*b^2 - 4*a^7*c)*d^2*e^4)*x^2), 1/8*(4*((a^3*b^2*c - 4*a^4*c^2)*e^4*x^6 + (a^3*b^3 - 4*a^4*b*c)*e^4*x^4 + (a^4*b^2 - 4*a^5*c)*e^4*x^2)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) + ((3*(b^3*c^3 - 4*a*b*c^4)*d^5 - 2*(3*b^4*c^2 - 13*a*b^2*c^3 + 4*a^2*c^4)*d^4*e + (3*b^5*c - 10*a*b^3*c^2 - 8*a^2*b*c^3)*d^3*e^2 - 4*(a*b^4*c - 5*a^2*b^2*c^2 + 4*a^3*c^3)*d^2*e^3 - (a^2*b^3*c - 4*a^3*b*c^2)*d*e^4 + 2*(a^3*b^2*c - 4*a^4*c^2)*e^5)*x^6 + (3*(b^4*c^2 - 4*a*b^2*c^3)*d^5 - 2*(3*b^5*c - 13*a*b^3*c^2 + 4*a^2*b*c^3)*d^4*e + (3*b^6 - 10*a*b^4*c - 8*a^2*b^2*c^2)*d^3*e^2 - 4*(a*b^5 - 5*a^2*b^3*c + 4*a^3*b*c^2)*d^2*e^3 - (a^2*b^4 - 4*a^3*b^2*c)*d*e^4 + 2*(a^3*b^3 - 4*a^4*b*c)*e^5)*x^4 + (3*(a*b^3*c^2 - 4*a^2*b*c^3)*d^5 - 2*(3*a*b^4*c - 13*a^2*b^2*c^2 + 4*a^3*c^3)*d^4*e + (3*a*b^5 - 10*a^2*b^3*c - 8*a^3*b*c^2)*d^3*e^2 - 4*(a^2*b^4 - 5*a^3*b^2*c + 4*a^4*c^2)*d^2*e^3 - (a^3*b^3 - 4*a^4*b*c)*d*e^4 + 2*(a^4*b^2 - 4*a^5*c)*e^5)*x^2)*sqrt(a)*log(-((b^2 + 4*a*c)*x^4 + 8*a*b*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(a) + 8*a^2)/x^4) - 4*((a^2*b^2*c^2 - 4*a^3*c^3)*d^5 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^4*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^3*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d^2*e^3 + (a^4*b^2 - 4*a^5*c)*d*e^4 + ((3*a*b^2*c^3 - 8*a^2*c^4)*d^5 - 6*(a*b^3*c^2 - 3*a^2*b*c^3)*d^4*e + 3*(a*b^4*c - 2*a^2*b^2*c^2 - 4*a^3*c^3)*d^3*e^2 - 2*(2*a^2*b^3*c - 7*a^3*b*c^2)*d^2*e^3 + (a^3*b^2*c - 4*a^4*c^2)*d*e^4)*x^4 + ((3*a*b^3*c^2 - 10*a^2*b*c^3)*d^5 - 2*(3*a*b^4*c - 11*a^2*b^2*c^2 + 2*a^3*c^3)*d^4*e + (3*a*b^5 - 8*a^2*b^3*c - 10*a^3*b*c^2)*d^3*e^2 - 4*(a^2*b^4 - 4*a^3*b^2*c + a^4*c^2)*d^2*e^3 + (a^3*b^3 - 4*a^4*b*c)*d*e^4)*x^2)*sqrt(c*x^4 + b*x^2 + a))/(((a^3*b^2*c^3 - 4*a^4*c^4)*d^6 - 2*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d^5*e + (a^3*b^4*c - 2*a^4*b^2*c^2 - 8*a^5*c^3)*d^4*e^2 - 2*(a^4*b^3*c - 4*a^5*b*c^2)*d^3*e^3 + (a^5*b^2*c - 4*a^6*c^2)*d^2*e^4)*x^6 + ((a^3*b^3*c^2 - 4*a^4*b*c^3)*d^6 - 2*(a^3*b^4*c - 4*a^4*b^2*c^2)*d^5*e + (a^3*b^5 - 2*a^4*b^3*c - 8*a^5*b*c^2)*d^4*e^2 - 2*(a^4*b^4 - 4*a^5*b^2*c)*d^3*e^3 + (a^5*b^3 - 4*a^6*b*c)*d^2*e^4)*x^4 + ((a^4*b^2*c^2 - 4*a^5*c^3)*d^6 - 2*(a^4*b^3*c - 4*a^5*b*c^2)*d^5*e + (a^4*b^4 - 2*a^5*b^2*c - 8*a^6*c^2)*d^4*e^2 - 2*(a^5*b^3 - 4*a^6*b*c)*d^3*e^3 + (a^6*b^2 - 4*a^7*c)*d^2*e^4)*x^2), -1/4*(((3*(b^3*c^3 - 4*a*b*c^4)*d^5 - 2*(3*b^4*c^2 - 13*a*b^2*c^3 + 4*a^2*c^4)*d^4*e + (3*b^5*c - 10*a*b^3*c^2 - 8*a^2*b*c^3)*d^3*e^2 - 4*(a*b^4*c - 5*a^2*b^2*c^2 + 4*a^3*c^3)*d^2*e^3 - (a^2*b^3*c - 4*a^3*b*c^2)*d*e^4 + 2*(a^3*b^2*c - 4*a^4*c^2)*e^5)*x^6 + (3*(b^4*c^2 - 4*a*b^2*c^3)*d^5 - 2*(3*b^5*c - 13*a*b^3*c^2 + 4*a^2*b*c^3)*d^4*e + (3*b^6 - 10*a*b^4*c - 8*a^2*b^2*c^2)*d^3*e^2 - 4*(a*b^5 - 5*a^2*b^3*c + 4*a^3*b*c^2)*d^2*e^3 - (a^2*b^4 - 4*a^3*b^2*c)*d*e^4 + 2*(a^3*b^3 - 4*a^4*b*c)*e^5)*x^4 + (3*(a*b^3*c^2 - 4*a^2*b*c^3)*d^5 - 2*(3*a*b^4*c - 13*a^2*b^2*c^2 + 4*a^3*c^3)*d^4*e + (3*a*b^5 - 10*a^2*b^3*c - 8*a^3*b*c^2)*d^3*e^2 - 4*(a^2*b^4 - 5*a^3*b^2*c + 4*a^4*c^2)*d^2*e^3 - (a^3*b^3 - 4*a^4*b*c)*d*e^4 + 2*(a^4*b^2 - 4*a^5*c)*e^5)*x^2)*sqrt(-a)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(-a)/(a*c*x^4 + a*b*x^2 + a^2)) - ((a^3*b^2*c - 4*a^4*c^2)*e^4*x^6 + (a^3*b^3 - 4*a^4*b*c)*e^4*x^4 + (a^4*b^2 - 4*a^5*c)*e^4*x^2)*sqrt(c*d^2 - b*d*e + a*e^2)*log(-((8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^4 - 8*a*b*d*e + 8*a^2*e^2 + (b^2 + 4*a*c)*d^2 + 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x^2 + 4*sqrt(c*x^4 + b*x^2 + a)*sqrt(c*d^2 - b*d*e + a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e))/(e^2*x^4 + 2*d*e*x^2 + d^2)) + 2*((a^2*b^2*c^2 - 4*a^3*c^3)*d^5 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^4*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^3*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d^2*e^3 + (a^4*b^2 - 4*a^5*c)*d*e^4 + ((3*a*b^2*c^3 - 8*a^2*c^4)*d^5 - 6*(a*b^3*c^2 - 3*a^2*b*c^3)*d^4*e + 3*(a*b^4*c - 2*a^2*b^2*c^2 - 4*a^3*c^3)*d^3*e^2 - 2*(2*a^2*b^3*c - 7*a^3*b*c^2)*d^2*e^3 + (a^3*b^2*c - 4*a^4*c^2)*d*e^4)*x^4 + ((3*a*b^3*c^2 - 10*a^2*b*c^3)*d^5 - 2*(3*a*b^4*c - 11*a^2*b^2*c^2 + 2*a^3*c^3)*d^4*e + (3*a*b^5 - 8*a^2*b^3*c - 10*a^3*b*c^2)*d^3*e^2 - 4*(a^2*b^4 - 4*a^3*b^2*c + a^4*c^2)*d^2*e^3 + (a^3*b^3 - 4*a^4*b*c)*d*e^4)*x^2)*sqrt(c*x^4 + b*x^2 + a))/(((a^3*b^2*c^3 - 4*a^4*c^4)*d^6 - 2*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d^5*e + (a^3*b^4*c - 2*a^4*b^2*c^2 - 8*a^5*c^3)*d^4*e^2 - 2*(a^4*b^3*c - 4*a^5*b*c^2)*d^3*e^3 + (a^5*b^2*c - 4*a^6*c^2)*d^2*e^4)*x^6 + ((a^3*b^3*c^2 - 4*a^4*b*c^3)*d^6 - 2*(a^3*b^4*c - 4*a^4*b^2*c^2)*d^5*e + (a^3*b^5 - 2*a^4*b^3*c - 8*a^5*b*c^2)*d^4*e^2 - 2*(a^4*b^4 - 4*a^5*b^2*c)*d^3*e^3 + (a^5*b^3 - 4*a^6*b*c)*d^2*e^4)*x^4 + ((a^4*b^2*c^2 - 4*a^5*c^3)*d^6 - 2*(a^4*b^3*c - 4*a^5*b*c^2)*d^5*e + (a^4*b^4 - 2*a^5*b^2*c - 8*a^6*c^2)*d^4*e^2 - 2*(a^5*b^3 - 4*a^6*b*c)*d^3*e^3 + (a^6*b^2 - 4*a^7*c)*d^2*e^4)*x^2), 1/4*(2*((a^3*b^2*c - 4*a^4*c^2)*e^4*x^6 + (a^3*b^3 - 4*a^4*b*c)*e^4*x^4 + (a^4*b^2 - 4*a^5*c)*e^4*x^2)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(c*x^4 + b*x^2 + a)*sqrt(-c*d^2 + b*d*e - a*e^2)*((2*c*d - b*e)*x^2 + b*d - 2*a*e)/((c^2*d^2 - b*c*d*e + a*c*e^2)*x^4 + a*c*d^2 - a*b*d*e + a^2*e^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x^2)) - ((3*(b^3*c^3 - 4*a*b*c^4)*d^5 - 2*(3*b^4*c^2 - 13*a*b^2*c^3 + 4*a^2*c^4)*d^4*e + (3*b^5*c - 10*a*b^3*c^2 - 8*a^2*b*c^3)*d^3*e^2 - 4*(a*b^4*c - 5*a^2*b^2*c^2 + 4*a^3*c^3)*d^2*e^3 - (a^2*b^3*c - 4*a^3*b*c^2)*d*e^4 + 2*(a^3*b^2*c - 4*a^4*c^2)*e^5)*x^6 + (3*(b^4*c^2 - 4*a*b^2*c^3)*d^5 - 2*(3*b^5*c - 13*a*b^3*c^2 + 4*a^2*b*c^3)*d^4*e + (3*b^6 - 10*a*b^4*c - 8*a^2*b^2*c^2)*d^3*e^2 - 4*(a*b^5 - 5*a^2*b^3*c + 4*a^3*b*c^2)*d^2*e^3 - (a^2*b^4 - 4*a^3*b^2*c)*d*e^4 + 2*(a^3*b^3 - 4*a^4*b*c)*e^5)*x^4 + (3*(a*b^3*c^2 - 4*a^2*b*c^3)*d^5 - 2*(3*a*b^4*c - 13*a^2*b^2*c^2 + 4*a^3*c^3)*d^4*e + (3*a*b^5 - 10*a^2*b^3*c - 8*a^3*b*c^2)*d^3*e^2 - 4*(a^2*b^4 - 5*a^3*b^2*c + 4*a^4*c^2)*d^2*e^3 - (a^3*b^3 - 4*a^4*b*c)*d*e^4 + 2*(a^4*b^2 - 4*a^5*c)*e^5)*x^2)*sqrt(-a)*arctan(1/2*sqrt(c*x^4 + b*x^2 + a)*(b*x^2 + 2*a)*sqrt(-a)/(a*c*x^4 + a*b*x^2 + a^2)) - 2*((a^2*b^2*c^2 - 4*a^3*c^3)*d^5 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^4*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^3*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d^2*e^3 + (a^4*b^2 - 4*a^5*c)*d*e^4 + ((3*a*b^2*c^3 - 8*a^2*c^4)*d^5 - 6*(a*b^3*c^2 - 3*a^2*b*c^3)*d^4*e + 3*(a*b^4*c - 2*a^2*b^2*c^2 - 4*a^3*c^3)*d^3*e^2 - 2*(2*a^2*b^3*c - 7*a^3*b*c^2)*d^2*e^3 + (a^3*b^2*c - 4*a^4*c^2)*d*e^4)*x^4 + ((3*a*b^3*c^2 - 10*a^2*b*c^3)*d^5 - 2*(3*a*b^4*c - 11*a^2*b^2*c^2 + 2*a^3*c^3)*d^4*e + (3*a*b^5 - 8*a^2*b^3*c - 10*a^3*b*c^2)*d^3*e^2 - 4*(a^2*b^4 - 4*a^3*b^2*c + a^4*c^2)*d^2*e^3 + (a^3*b^3 - 4*a^4*b*c)*d*e^4)*x^2)*sqrt(c*x^4 + b*x^2 + a))/(((a^3*b^2*c^3 - 4*a^4*c^4)*d^6 - 2*(a^3*b^3*c^2 - 4*a^4*b*c^3)*d^5*e + (a^3*b^4*c - 2*a^4*b^2*c^2 - 8*a^5*c^3)*d^4*e^2 - 2*(a^4*b^3*c - 4*a^5*b*c^2)*d^3*e^3 + (a^5*b^2*c - 4*a^6*c^2)*d^2*e^4)*x^6 + ((a^3*b^3*c^2 - 4*a^4*b*c^3)*d^6 - 2*(a^3*b^4*c - 4*a^4*b^2*c^2)*d^5*e + (a^3*b^5 - 2*a^4*b^3*c - 8*a^5*b*c^2)*d^4*e^2 - 2*(a^4*b^4 - 4*a^5*b^2*c)*d^3*e^3 + (a^5*b^3 - 4*a^6*b*c)*d^2*e^4)*x^4 + ((a^4*b^2*c^2 - 4*a^5*c^3)*d^6 - 2*(a^4*b^3*c - 4*a^5*b*c^2)*d^5*e + (a^4*b^4 - 2*a^5*b^2*c - 8*a^6*c^2)*d^4*e^2 - 2*(a^5*b^3 - 4*a^6*b*c)*d^3*e^3 + (a^6*b^2 - 4*a^7*c)*d^2*e^4)*x^2)]","B",0
348,0,0,0,1.011820," ","integrate(x^8/(2*x^2+3)/(2*x^4+2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1} x^{8}}{8 \, x^{10} + 28 \, x^{8} + 40 \, x^{6} + 32 \, x^{4} + 14 \, x^{2} + 3}, x\right)"," ",0,"integral(sqrt(2*x^4 + 2*x^2 + 1)*x^8/(8*x^10 + 28*x^8 + 40*x^6 + 32*x^4 + 14*x^2 + 3), x)","F",0
349,0,0,0,1.274782," ","integrate(x^6/(2*x^2+3)/(2*x^4+2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1} x^{6}}{8 \, x^{10} + 28 \, x^{8} + 40 \, x^{6} + 32 \, x^{4} + 14 \, x^{2} + 3}, x\right)"," ",0,"integral(sqrt(2*x^4 + 2*x^2 + 1)*x^6/(8*x^10 + 28*x^8 + 40*x^6 + 32*x^4 + 14*x^2 + 3), x)","F",0
350,0,0,0,1.353067," ","integrate(x^4/(2*x^2+3)/(2*x^4+2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1} x^{4}}{8 \, x^{10} + 28 \, x^{8} + 40 \, x^{6} + 32 \, x^{4} + 14 \, x^{2} + 3}, x\right)"," ",0,"integral(sqrt(2*x^4 + 2*x^2 + 1)*x^4/(8*x^10 + 28*x^8 + 40*x^6 + 32*x^4 + 14*x^2 + 3), x)","F",0
351,0,0,0,1.148389," ","integrate(x^2/(2*x^2+3)/(2*x^4+2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1} x^{2}}{8 \, x^{10} + 28 \, x^{8} + 40 \, x^{6} + 32 \, x^{4} + 14 \, x^{2} + 3}, x\right)"," ",0,"integral(sqrt(2*x^4 + 2*x^2 + 1)*x^2/(8*x^10 + 28*x^8 + 40*x^6 + 32*x^4 + 14*x^2 + 3), x)","F",0
352,0,0,0,0.929284," ","integrate(1/(2*x^2+3)/(2*x^4+2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1}}{8 \, x^{10} + 28 \, x^{8} + 40 \, x^{6} + 32 \, x^{4} + 14 \, x^{2} + 3}, x\right)"," ",0,"integral(sqrt(2*x^4 + 2*x^2 + 1)/(8*x^10 + 28*x^8 + 40*x^6 + 32*x^4 + 14*x^2 + 3), x)","F",0
353,0,0,0,1.323109," ","integrate(1/x^2/(2*x^2+3)/(2*x^4+2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, x^{4} + 2 \, x^{2} + 1}}{8 \, x^{12} + 28 \, x^{10} + 40 \, x^{8} + 32 \, x^{6} + 14 \, x^{4} + 3 \, x^{2}}, x\right)"," ",0,"integral(sqrt(2*x^4 + 2*x^2 + 1)/(8*x^12 + 28*x^10 + 40*x^8 + 32*x^6 + 14*x^4 + 3*x^2), x)","F",0
354,-1,0,0,0.000000," ","integrate(x^7*(e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
355,-1,0,0,0.000000," ","integrate(x^5*(e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
356,1,2435,0,138.367171," ","integrate(x^3*(e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} c \sqrt{\frac{{\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(\frac{2 \, a b^{2} c d^{2} - 2 \, a b^{3} d e + 2 \, {\left(a^{2} b^{2} - a^{3} c\right)} e^{2} + {\left(a b^{2} c d e - {\left(a b^{3} - a^{2} b c\right)} e^{2}\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d - {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e - {\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{\frac{{\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} - {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} e x^{2} + 2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c \sqrt{\frac{{\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(\frac{2 \, a b^{2} c d^{2} - 2 \, a b^{3} d e + 2 \, {\left(a^{2} b^{2} - a^{3} c\right)} e^{2} + {\left(a b^{2} c d e - {\left(a b^{3} - a^{2} b c\right)} e^{2}\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d - {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e - {\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{\frac{{\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} - {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} e x^{2} + 2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{x^{2}}\right) + \sqrt{\frac{1}{2}} c \sqrt{\frac{{\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(\frac{2 \, a b^{2} c d^{2} - 2 \, a b^{3} d e + 2 \, {\left(a^{2} b^{2} - a^{3} c\right)} e^{2} + {\left(a b^{2} c d e - {\left(a b^{3} - a^{2} b c\right)} e^{2}\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d - {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e + {\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{\frac{{\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} + {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} e x^{2} + 2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c \sqrt{\frac{{\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(\frac{2 \, a b^{2} c d^{2} - 2 \, a b^{3} d e + 2 \, {\left(a^{2} b^{2} - a^{3} c\right)} e^{2} + {\left(a b^{2} c d e - {\left(a b^{3} - a^{2} b c\right)} e^{2}\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d - {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e + {\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{\frac{{\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} + {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} e x^{2} + 2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d\right)} \sqrt{\frac{b^{2} c^{2} d^{2} - 2 \, {\left(b^{3} c - a b c^{2}\right)} d e + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{x^{2}}\right) + 4 \, \sqrt{e x^{2} + d}}{4 \, c}"," ",0,"1/4*(sqrt(1/2)*c*sqrt(((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e + (b^2*c^3 - 4*a*c^4)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log((2*a*b^2*c*d^2 - 2*a*b^3*d*e + 2*(a^2*b^2 - a^3*c)*e^2 + (a*b^2*c*d*e - (a*b^3 - a^2*b*c)*e^2)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^4*c - 4*a*b^2*c^2)*d - (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e - (b^4*c^3 - 6*a*b^2*c^4 + 8*a^2*c^5)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e + (b^2*c^3 - 4*a*c^4)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) - ((a*b^2*c^3 - 4*a^2*c^4)*e*x^2 + 2*(a*b^2*c^3 - 4*a^2*c^4)*d)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))/x^2) - sqrt(1/2)*c*sqrt(((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e + (b^2*c^3 - 4*a*c^4)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log((2*a*b^2*c*d^2 - 2*a*b^3*d*e + 2*(a^2*b^2 - a^3*c)*e^2 + (a*b^2*c*d*e - (a*b^3 - a^2*b*c)*e^2)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^4*c - 4*a*b^2*c^2)*d - (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e - (b^4*c^3 - 6*a*b^2*c^4 + 8*a^2*c^5)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e + (b^2*c^3 - 4*a*c^4)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) - ((a*b^2*c^3 - 4*a^2*c^4)*e*x^2 + 2*(a*b^2*c^3 - 4*a^2*c^4)*d)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))/x^2) + sqrt(1/2)*c*sqrt(((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e - (b^2*c^3 - 4*a*c^4)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log((2*a*b^2*c*d^2 - 2*a*b^3*d*e + 2*(a^2*b^2 - a^3*c)*e^2 + (a*b^2*c*d*e - (a*b^3 - a^2*b*c)*e^2)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^4*c - 4*a*b^2*c^2)*d - (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e + (b^4*c^3 - 6*a*b^2*c^4 + 8*a^2*c^5)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e - (b^2*c^3 - 4*a*c^4)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) + ((a*b^2*c^3 - 4*a^2*c^4)*e*x^2 + 2*(a*b^2*c^3 - 4*a^2*c^4)*d)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))/x^2) - sqrt(1/2)*c*sqrt(((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e - (b^2*c^3 - 4*a*c^4)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log((2*a*b^2*c*d^2 - 2*a*b^3*d*e + 2*(a^2*b^2 - a^3*c)*e^2 + (a*b^2*c*d*e - (a*b^3 - a^2*b*c)*e^2)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^4*c - 4*a*b^2*c^2)*d - (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e + (b^4*c^3 - 6*a*b^2*c^4 + 8*a^2*c^5)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e - (b^2*c^3 - 4*a*c^4)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) + ((a*b^2*c^3 - 4*a^2*c^4)*e*x^2 + 2*(a*b^2*c^3 - 4*a^2*c^4)*d)*sqrt((b^2*c^2*d^2 - 2*(b^3*c - a*b*c^2)*d*e + (b^4 - 2*a*b^2*c + a^2*c^2)*e^2)/(b^2*c^6 - 4*a*c^7)))/x^2) + 4*sqrt(e*x^2 + d))/c","B",0
357,1,1085,0,21.448542," ","integrate(x*(e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{\frac{2 \, c d - b e + {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} \log\left(\frac{b e^{2} x^{2} + 2 \, b d e - 2 \, a e^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{2} - 4 \, a c\right)} e + {\left(b^{3} c - 4 \, a b c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}\right)} \sqrt{\frac{2 \, c d - b e + {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e x^{2} + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{x^{2}}\right) + \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{\frac{2 \, c d - b e + {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} \log\left(\frac{b e^{2} x^{2} + 2 \, b d e - 2 \, a e^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{2} - 4 \, a c\right)} e + {\left(b^{3} c - 4 \, a b c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}\right)} \sqrt{\frac{2 \, c d - b e + {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e x^{2} + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{x^{2}}\right) - \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{\frac{2 \, c d - b e - {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} \log\left(\frac{b e^{2} x^{2} + 2 \, b d e - 2 \, a e^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{2} - 4 \, a c\right)} e - {\left(b^{3} c - 4 \, a b c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}\right)} \sqrt{\frac{2 \, c d - b e - {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} - {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e x^{2} + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{x^{2}}\right) + \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{\frac{2 \, c d - b e - {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} \log\left(\frac{b e^{2} x^{2} + 2 \, b d e - 2 \, a e^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{2} - 4 \, a c\right)} e - {\left(b^{3} c - 4 \, a b c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}\right)} \sqrt{\frac{2 \, c d - b e - {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} - {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e x^{2} + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{x^{2}}\right)"," ",0,"-1/4*sqrt(1/2)*sqrt((2*c*d - b*e + (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2))*log((b*e^2*x^2 + 2*b*d*e - 2*a*e^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^2 - 4*a*c)*e + (b^3*c - 4*a*b*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))*sqrt((2*c*d - b*e + (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2)) + ((b^2*c - 4*a*c^2)*e*x^2 + 2*(b^2*c - 4*a*c^2)*d)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/x^2) + 1/4*sqrt(1/2)*sqrt((2*c*d - b*e + (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2))*log((b*e^2*x^2 + 2*b*d*e - 2*a*e^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^2 - 4*a*c)*e + (b^3*c - 4*a*b*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))*sqrt((2*c*d - b*e + (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2)) + ((b^2*c - 4*a*c^2)*e*x^2 + 2*(b^2*c - 4*a*c^2)*d)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/x^2) - 1/4*sqrt(1/2)*sqrt((2*c*d - b*e - (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2))*log((b*e^2*x^2 + 2*b*d*e - 2*a*e^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^2 - 4*a*c)*e - (b^3*c - 4*a*b*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))*sqrt((2*c*d - b*e - (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2)) - ((b^2*c - 4*a*c^2)*e*x^2 + 2*(b^2*c - 4*a*c^2)*d)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/x^2) + 1/4*sqrt(1/2)*sqrt((2*c*d - b*e - (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2))*log((b*e^2*x^2 + 2*b*d*e - 2*a*e^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^2 - 4*a*c)*e - (b^3*c - 4*a*b*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))*sqrt((2*c*d - b*e - (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2)) - ((b^2*c - 4*a*c^2)*e*x^2 + 2*(b^2*c - 4*a*c^2)*d)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/x^2)","B",0
358,-1,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)/x/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
359,-1,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)/x^3/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
360,-1,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)/x^5/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
361,1,6534,0,104.324271," ","integrate(x^4*(e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{1}{2}} c^{2} e \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}} \log\left(\frac{{\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d x^{2} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}} + 2 \, {\left(a^{2} b^{2} c - a^{3} c^{2}\right)} d^{2} - 2 \, {\left(a^{2} b^{3} - 2 \, a^{3} b c\right)} d e - {\left({\left(a b^{3} c - a^{2} b c^{2}\right)} d^{2} - {\left(a b^{4} + 2 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e + 4 \, {\left(a^{2} b^{3} - 2 \, a^{3} b c\right)} e^{2}\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{4} c^{4} - 6 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} x \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}} - {\left({\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d - {\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} e\right)} x\right)} \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c^{2} e \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}} \log\left(\frac{{\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d x^{2} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}} + 2 \, {\left(a^{2} b^{2} c - a^{3} c^{2}\right)} d^{2} - 2 \, {\left(a^{2} b^{3} - 2 \, a^{3} b c\right)} d e - {\left({\left(a b^{3} c - a^{2} b c^{2}\right)} d^{2} - {\left(a b^{4} + 2 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e + 4 \, {\left(a^{2} b^{3} - 2 \, a^{3} b c\right)} e^{2}\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{4} c^{4} - 6 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} x \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}} - {\left({\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d - {\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} e\right)} x\right)} \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}}}{x^{2}}\right) + \sqrt{\frac{1}{2}} c^{2} e \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}} \log\left(-\frac{{\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d x^{2} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}} - 2 \, {\left(a^{2} b^{2} c - a^{3} c^{2}\right)} d^{2} + 2 \, {\left(a^{2} b^{3} - 2 \, a^{3} b c\right)} d e + {\left({\left(a b^{3} c - a^{2} b c^{2}\right)} d^{2} - {\left(a b^{4} + 2 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e + 4 \, {\left(a^{2} b^{3} - 2 \, a^{3} b c\right)} e^{2}\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{4} c^{4} - 6 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} x \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}} + {\left({\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d - {\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} e\right)} x\right)} \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c^{2} e \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}} \log\left(-\frac{{\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d x^{2} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}} - 2 \, {\left(a^{2} b^{2} c - a^{3} c^{2}\right)} d^{2} + 2 \, {\left(a^{2} b^{3} - 2 \, a^{3} b c\right)} d e + {\left({\left(a b^{3} c - a^{2} b c^{2}\right)} d^{2} - {\left(a b^{4} + 2 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e + 4 \, {\left(a^{2} b^{3} - 2 \, a^{3} b c\right)} e^{2}\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{4} c^{4} - 6 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} x \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}} + {\left({\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d - {\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} e\right)} x\right)} \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}}}{x^{2}}\right) + 2 \, \sqrt{e x^{2} + d} c e x - {\left(c d - 2 \, b e\right)} \sqrt{e} \log\left(-2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right)}{4 \, c^{2} e}, \frac{\sqrt{\frac{1}{2}} c^{2} e \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}} \log\left(\frac{{\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d x^{2} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}} + 2 \, {\left(a^{2} b^{2} c - a^{3} c^{2}\right)} d^{2} - 2 \, {\left(a^{2} b^{3} - 2 \, a^{3} b c\right)} d e - {\left({\left(a b^{3} c - a^{2} b c^{2}\right)} d^{2} - {\left(a b^{4} + 2 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e + 4 \, {\left(a^{2} b^{3} - 2 \, a^{3} b c\right)} e^{2}\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{4} c^{4} - 6 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} x \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}} - {\left({\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d - {\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} e\right)} x\right)} \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c^{2} e \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}} \log\left(\frac{{\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d x^{2} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}} + 2 \, {\left(a^{2} b^{2} c - a^{3} c^{2}\right)} d^{2} - 2 \, {\left(a^{2} b^{3} - 2 \, a^{3} b c\right)} d e - {\left({\left(a b^{3} c - a^{2} b c^{2}\right)} d^{2} - {\left(a b^{4} + 2 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e + 4 \, {\left(a^{2} b^{3} - 2 \, a^{3} b c\right)} e^{2}\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{4} c^{4} - 6 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} x \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}} - {\left({\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d - {\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} e\right)} x\right)} \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}}}{x^{2}}\right) + \sqrt{\frac{1}{2}} c^{2} e \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}} \log\left(-\frac{{\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d x^{2} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}} - 2 \, {\left(a^{2} b^{2} c - a^{3} c^{2}\right)} d^{2} + 2 \, {\left(a^{2} b^{3} - 2 \, a^{3} b c\right)} d e + {\left({\left(a b^{3} c - a^{2} b c^{2}\right)} d^{2} - {\left(a b^{4} + 2 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e + 4 \, {\left(a^{2} b^{3} - 2 \, a^{3} b c\right)} e^{2}\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{4} c^{4} - 6 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} x \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}} + {\left({\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d - {\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} e\right)} x\right)} \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c^{2} e \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}} \log\left(-\frac{{\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d x^{2} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}} - 2 \, {\left(a^{2} b^{2} c - a^{3} c^{2}\right)} d^{2} + 2 \, {\left(a^{2} b^{3} - 2 \, a^{3} b c\right)} d e + {\left({\left(a b^{3} c - a^{2} b c^{2}\right)} d^{2} - {\left(a b^{4} + 2 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e + 4 \, {\left(a^{2} b^{3} - 2 \, a^{3} b c\right)} e^{2}\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{4} c^{4} - 6 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} x \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}} + {\left({\left(b^{5} c - 5 \, a b^{3} c^{2} + 4 \, a^{2} b c^{3}\right)} d - {\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} e\right)} x\right)} \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}}}{x^{2}}\right) + 2 \, \sqrt{e x^{2} + d} c e x - 2 \, {\left(c d - 2 \, b e\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{4 \, c^{2} e}\right]"," ",0,"[1/4*(sqrt(1/2)*c^2*e*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e + (b^2*c^4 - 4*a*c^5)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5))*log(((a*b^2*c^4 - 4*a^2*c^5)*d*x^2*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)) + 2*(a^2*b^2*c - a^3*c^2)*d^2 - 2*(a^2*b^3 - 2*a^3*b*c)*d*e - ((a*b^3*c - a^2*b*c^2)*d^2 - (a*b^4 + 2*a^2*b^2*c - 4*a^3*c^2)*d*e + 4*(a^2*b^3 - 2*a^3*b*c)*e^2)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^4*c^4 - 6*a*b^2*c^5 + 8*a^2*c^6)*x*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)) - ((b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d - (b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*e)*x)*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e + (b^2*c^4 - 4*a*c^5)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5)))/x^2) - sqrt(1/2)*c^2*e*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e + (b^2*c^4 - 4*a*c^5)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5))*log(((a*b^2*c^4 - 4*a^2*c^5)*d*x^2*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)) + 2*(a^2*b^2*c - a^3*c^2)*d^2 - 2*(a^2*b^3 - 2*a^3*b*c)*d*e - ((a*b^3*c - a^2*b*c^2)*d^2 - (a*b^4 + 2*a^2*b^2*c - 4*a^3*c^2)*d*e + 4*(a^2*b^3 - 2*a^3*b*c)*e^2)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^4*c^4 - 6*a*b^2*c^5 + 8*a^2*c^6)*x*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)) - ((b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d - (b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*e)*x)*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e + (b^2*c^4 - 4*a*c^5)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5)))/x^2) + sqrt(1/2)*c^2*e*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e - (b^2*c^4 - 4*a*c^5)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5))*log(-((a*b^2*c^4 - 4*a^2*c^5)*d*x^2*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)) - 2*(a^2*b^2*c - a^3*c^2)*d^2 + 2*(a^2*b^3 - 2*a^3*b*c)*d*e + ((a*b^3*c - a^2*b*c^2)*d^2 - (a*b^4 + 2*a^2*b^2*c - 4*a^3*c^2)*d*e + 4*(a^2*b^3 - 2*a^3*b*c)*e^2)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^4*c^4 - 6*a*b^2*c^5 + 8*a^2*c^6)*x*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)) + ((b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d - (b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*e)*x)*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e - (b^2*c^4 - 4*a*c^5)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5)))/x^2) - sqrt(1/2)*c^2*e*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e - (b^2*c^4 - 4*a*c^5)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5))*log(-((a*b^2*c^4 - 4*a^2*c^5)*d*x^2*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)) - 2*(a^2*b^2*c - a^3*c^2)*d^2 + 2*(a^2*b^3 - 2*a^3*b*c)*d*e + ((a*b^3*c - a^2*b*c^2)*d^2 - (a*b^4 + 2*a^2*b^2*c - 4*a^3*c^2)*d*e + 4*(a^2*b^3 - 2*a^3*b*c)*e^2)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^4*c^4 - 6*a*b^2*c^5 + 8*a^2*c^6)*x*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)) + ((b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d - (b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*e)*x)*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e - (b^2*c^4 - 4*a*c^5)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5)))/x^2) + 2*sqrt(e*x^2 + d)*c*e*x - (c*d - 2*b*e)*sqrt(e)*log(-2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x - d))/(c^2*e), 1/4*(sqrt(1/2)*c^2*e*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e + (b^2*c^4 - 4*a*c^5)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5))*log(((a*b^2*c^4 - 4*a^2*c^5)*d*x^2*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)) + 2*(a^2*b^2*c - a^3*c^2)*d^2 - 2*(a^2*b^3 - 2*a^3*b*c)*d*e - ((a*b^3*c - a^2*b*c^2)*d^2 - (a*b^4 + 2*a^2*b^2*c - 4*a^3*c^2)*d*e + 4*(a^2*b^3 - 2*a^3*b*c)*e^2)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^4*c^4 - 6*a*b^2*c^5 + 8*a^2*c^6)*x*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)) - ((b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d - (b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*e)*x)*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e + (b^2*c^4 - 4*a*c^5)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5)))/x^2) - sqrt(1/2)*c^2*e*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e + (b^2*c^4 - 4*a*c^5)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5))*log(((a*b^2*c^4 - 4*a^2*c^5)*d*x^2*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)) + 2*(a^2*b^2*c - a^3*c^2)*d^2 - 2*(a^2*b^3 - 2*a^3*b*c)*d*e - ((a*b^3*c - a^2*b*c^2)*d^2 - (a*b^4 + 2*a^2*b^2*c - 4*a^3*c^2)*d*e + 4*(a^2*b^3 - 2*a^3*b*c)*e^2)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^4*c^4 - 6*a*b^2*c^5 + 8*a^2*c^6)*x*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)) - ((b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d - (b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*e)*x)*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e + (b^2*c^4 - 4*a*c^5)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5)))/x^2) + sqrt(1/2)*c^2*e*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e - (b^2*c^4 - 4*a*c^5)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5))*log(-((a*b^2*c^4 - 4*a^2*c^5)*d*x^2*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)) - 2*(a^2*b^2*c - a^3*c^2)*d^2 + 2*(a^2*b^3 - 2*a^3*b*c)*d*e + ((a*b^3*c - a^2*b*c^2)*d^2 - (a*b^4 + 2*a^2*b^2*c - 4*a^3*c^2)*d*e + 4*(a^2*b^3 - 2*a^3*b*c)*e^2)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^4*c^4 - 6*a*b^2*c^5 + 8*a^2*c^6)*x*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)) + ((b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d - (b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*e)*x)*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e - (b^2*c^4 - 4*a*c^5)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5)))/x^2) - sqrt(1/2)*c^2*e*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e - (b^2*c^4 - 4*a*c^5)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5))*log(-((a*b^2*c^4 - 4*a^2*c^5)*d*x^2*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)) - 2*(a^2*b^2*c - a^3*c^2)*d^2 + 2*(a^2*b^3 - 2*a^3*b*c)*d*e + ((a*b^3*c - a^2*b*c^2)*d^2 - (a*b^4 + 2*a^2*b^2*c - 4*a^3*c^2)*d*e + 4*(a^2*b^3 - 2*a^3*b*c)*e^2)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^4*c^4 - 6*a*b^2*c^5 + 8*a^2*c^6)*x*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)) + ((b^5*c - 5*a*b^3*c^2 + 4*a^2*b*c^3)*d - (b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*e)*x)*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e - (b^2*c^4 - 4*a*c^5)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5)))/x^2) + 2*sqrt(e*x^2 + d)*c*e*x - 2*(c*d - 2*b*e)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)))/(c^2*e)]","B",0
362,1,3260,0,13.843641," ","integrate(x^2*(e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{\sqrt{\frac{1}{2}} c \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \log\left(-\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d x^{2} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} + 2 \, a c d^{2} - 2 \, a b d e - {\left(b c d^{2} + 4 \, a b e^{2} - {\left(b^{2} + 4 \, a c\right)} d e\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} - {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} x\right)} \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \log\left(-\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d x^{2} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} + 2 \, a c d^{2} - 2 \, a b d e - {\left(b c d^{2} + 4 \, a b e^{2} - {\left(b^{2} + 4 \, a c\right)} d e\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} - {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} x\right)} \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}}}{x^{2}}\right) + \sqrt{\frac{1}{2}} c \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \log\left(\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d x^{2} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} - 2 \, a c d^{2} + 2 \, a b d e + {\left(b c d^{2} + 4 \, a b e^{2} - {\left(b^{2} + 4 \, a c\right)} d e\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} x\right)} \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \log\left(\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d x^{2} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} - 2 \, a c d^{2} + 2 \, a b d e + {\left(b c d^{2} + 4 \, a b e^{2} - {\left(b^{2} + 4 \, a c\right)} d e\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} x\right)} \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}}}{x^{2}}\right) - 2 \, \sqrt{e} \log\left(-2 \, e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right)}{4 \, c}, -\frac{\sqrt{\frac{1}{2}} c \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \log\left(-\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d x^{2} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} + 2 \, a c d^{2} - 2 \, a b d e - {\left(b c d^{2} + 4 \, a b e^{2} - {\left(b^{2} + 4 \, a c\right)} d e\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} - {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} x\right)} \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \log\left(-\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d x^{2} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} + 2 \, a c d^{2} - 2 \, a b d e - {\left(b c d^{2} + 4 \, a b e^{2} - {\left(b^{2} + 4 \, a c\right)} d e\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} - {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} x\right)} \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}}}{x^{2}}\right) + \sqrt{\frac{1}{2}} c \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \log\left(\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d x^{2} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} - 2 \, a c d^{2} + 2 \, a b d e + {\left(b c d^{2} + 4 \, a b e^{2} - {\left(b^{2} + 4 \, a c\right)} d e\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} x\right)} \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \log\left(\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d x^{2} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} - 2 \, a c d^{2} + 2 \, a b d e + {\left(b c d^{2} + 4 \, a b e^{2} - {\left(b^{2} + 4 \, a c\right)} d e\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} x\right)} \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}}}{x^{2}}\right) + 4 \, \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{4 \, c}\right]"," ",0,"[-1/4*(sqrt(1/2)*c*sqrt(-(b*c*d - (b^2 - 2*a*c)*e + (b^2*c^2 - 4*a*c^3)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*log(-((b^2*c^2 - 4*a*c^3)*d*x^2*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)) + 2*a*c*d^2 - 2*a*b*d*e - (b*c*d^2 + 4*a*b*e^2 - (b^2 + 4*a*c)*d*e)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^3*c^2 - 4*a*b*c^3)*x*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)) - ((b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*x)*sqrt(-(b*c*d - (b^2 - 2*a*c)*e + (b^2*c^2 - 4*a*c^3)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3)))/x^2) - sqrt(1/2)*c*sqrt(-(b*c*d - (b^2 - 2*a*c)*e + (b^2*c^2 - 4*a*c^3)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*log(-((b^2*c^2 - 4*a*c^3)*d*x^2*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)) + 2*a*c*d^2 - 2*a*b*d*e - (b*c*d^2 + 4*a*b*e^2 - (b^2 + 4*a*c)*d*e)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^3*c^2 - 4*a*b*c^3)*x*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)) - ((b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*x)*sqrt(-(b*c*d - (b^2 - 2*a*c)*e + (b^2*c^2 - 4*a*c^3)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3)))/x^2) + sqrt(1/2)*c*sqrt(-(b*c*d - (b^2 - 2*a*c)*e - (b^2*c^2 - 4*a*c^3)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*log(((b^2*c^2 - 4*a*c^3)*d*x^2*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)) - 2*a*c*d^2 + 2*a*b*d*e + (b*c*d^2 + 4*a*b*e^2 - (b^2 + 4*a*c)*d*e)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^3*c^2 - 4*a*b*c^3)*x*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)) + ((b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*x)*sqrt(-(b*c*d - (b^2 - 2*a*c)*e - (b^2*c^2 - 4*a*c^3)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3)))/x^2) - sqrt(1/2)*c*sqrt(-(b*c*d - (b^2 - 2*a*c)*e - (b^2*c^2 - 4*a*c^3)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*log(((b^2*c^2 - 4*a*c^3)*d*x^2*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)) - 2*a*c*d^2 + 2*a*b*d*e + (b*c*d^2 + 4*a*b*e^2 - (b^2 + 4*a*c)*d*e)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^3*c^2 - 4*a*b*c^3)*x*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)) + ((b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*x)*sqrt(-(b*c*d - (b^2 - 2*a*c)*e - (b^2*c^2 - 4*a*c^3)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3)))/x^2) - 2*sqrt(e)*log(-2*e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(e)*x - d))/c, -1/4*(sqrt(1/2)*c*sqrt(-(b*c*d - (b^2 - 2*a*c)*e + (b^2*c^2 - 4*a*c^3)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*log(-((b^2*c^2 - 4*a*c^3)*d*x^2*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)) + 2*a*c*d^2 - 2*a*b*d*e - (b*c*d^2 + 4*a*b*e^2 - (b^2 + 4*a*c)*d*e)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^3*c^2 - 4*a*b*c^3)*x*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)) - ((b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*x)*sqrt(-(b*c*d - (b^2 - 2*a*c)*e + (b^2*c^2 - 4*a*c^3)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3)))/x^2) - sqrt(1/2)*c*sqrt(-(b*c*d - (b^2 - 2*a*c)*e + (b^2*c^2 - 4*a*c^3)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*log(-((b^2*c^2 - 4*a*c^3)*d*x^2*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)) + 2*a*c*d^2 - 2*a*b*d*e - (b*c*d^2 + 4*a*b*e^2 - (b^2 + 4*a*c)*d*e)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^3*c^2 - 4*a*b*c^3)*x*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)) - ((b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*x)*sqrt(-(b*c*d - (b^2 - 2*a*c)*e + (b^2*c^2 - 4*a*c^3)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3)))/x^2) + sqrt(1/2)*c*sqrt(-(b*c*d - (b^2 - 2*a*c)*e - (b^2*c^2 - 4*a*c^3)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*log(((b^2*c^2 - 4*a*c^3)*d*x^2*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)) - 2*a*c*d^2 + 2*a*b*d*e + (b*c*d^2 + 4*a*b*e^2 - (b^2 + 4*a*c)*d*e)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^3*c^2 - 4*a*b*c^3)*x*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)) + ((b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*x)*sqrt(-(b*c*d - (b^2 - 2*a*c)*e - (b^2*c^2 - 4*a*c^3)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3)))/x^2) - sqrt(1/2)*c*sqrt(-(b*c*d - (b^2 - 2*a*c)*e - (b^2*c^2 - 4*a*c^3)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*log(((b^2*c^2 - 4*a*c^3)*d*x^2*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)) - 2*a*c*d^2 + 2*a*b*d*e + (b*c*d^2 + 4*a*b*e^2 - (b^2 + 4*a*c)*d*e)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((b^3*c^2 - 4*a*b*c^3)*x*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)) + ((b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*x)*sqrt(-(b*c*d - (b^2 - 2*a*c)*e - (b^2*c^2 - 4*a*c^3)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3)))/x^2) + 4*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)))/c]","B",0
363,1,985,0,3.343104," ","integrate((e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b d - 2 \, a e + {\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{d^{2}}{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}} \log\left(-\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} d \sqrt{\frac{d^{2}}{a^{2} b^{2} - 4 \, a^{3} c}} x^{2} + 4 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{e x^{2} + d} \sqrt{\frac{d^{2}}{a^{2} b^{2} - 4 \, a^{3} c}} x \sqrt{-\frac{b d - 2 \, a e + {\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{d^{2}}{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}} - 2 \, a d^{2} + {\left(b d^{2} - 4 \, a d e\right)} x^{2}}{x^{2}}\right) - \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b d - 2 \, a e + {\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{d^{2}}{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}} \log\left(-\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} d \sqrt{\frac{d^{2}}{a^{2} b^{2} - 4 \, a^{3} c}} x^{2} - 4 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{e x^{2} + d} \sqrt{\frac{d^{2}}{a^{2} b^{2} - 4 \, a^{3} c}} x \sqrt{-\frac{b d - 2 \, a e + {\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{d^{2}}{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}} - 2 \, a d^{2} + {\left(b d^{2} - 4 \, a d e\right)} x^{2}}{x^{2}}\right) + \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b d - 2 \, a e - {\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{d^{2}}{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}} \log\left(\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} d \sqrt{\frac{d^{2}}{a^{2} b^{2} - 4 \, a^{3} c}} x^{2} + 4 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{e x^{2} + d} \sqrt{\frac{d^{2}}{a^{2} b^{2} - 4 \, a^{3} c}} x \sqrt{-\frac{b d - 2 \, a e - {\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{d^{2}}{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}} + 2 \, a d^{2} - {\left(b d^{2} - 4 \, a d e\right)} x^{2}}{x^{2}}\right) - \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b d - 2 \, a e - {\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{d^{2}}{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}} \log\left(\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} d \sqrt{\frac{d^{2}}{a^{2} b^{2} - 4 \, a^{3} c}} x^{2} - 4 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{e x^{2} + d} \sqrt{\frac{d^{2}}{a^{2} b^{2} - 4 \, a^{3} c}} x \sqrt{-\frac{b d - 2 \, a e - {\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{d^{2}}{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}} + 2 \, a d^{2} - {\left(b d^{2} - 4 \, a d e\right)} x^{2}}{x^{2}}\right)"," ",0,"1/4*sqrt(1/2)*sqrt(-(b*d - 2*a*e + (a*b^2 - 4*a^2*c)*sqrt(d^2/(a^2*b^2 - 4*a^3*c)))/(a*b^2 - 4*a^2*c))*log(-((a*b^2 - 4*a^2*c)*d*sqrt(d^2/(a^2*b^2 - 4*a^3*c))*x^2 + 4*sqrt(1/2)*(a^2*b^2 - 4*a^3*c)*sqrt(e*x^2 + d)*sqrt(d^2/(a^2*b^2 - 4*a^3*c))*x*sqrt(-(b*d - 2*a*e + (a*b^2 - 4*a^2*c)*sqrt(d^2/(a^2*b^2 - 4*a^3*c)))/(a*b^2 - 4*a^2*c)) - 2*a*d^2 + (b*d^2 - 4*a*d*e)*x^2)/x^2) - 1/4*sqrt(1/2)*sqrt(-(b*d - 2*a*e + (a*b^2 - 4*a^2*c)*sqrt(d^2/(a^2*b^2 - 4*a^3*c)))/(a*b^2 - 4*a^2*c))*log(-((a*b^2 - 4*a^2*c)*d*sqrt(d^2/(a^2*b^2 - 4*a^3*c))*x^2 - 4*sqrt(1/2)*(a^2*b^2 - 4*a^3*c)*sqrt(e*x^2 + d)*sqrt(d^2/(a^2*b^2 - 4*a^3*c))*x*sqrt(-(b*d - 2*a*e + (a*b^2 - 4*a^2*c)*sqrt(d^2/(a^2*b^2 - 4*a^3*c)))/(a*b^2 - 4*a^2*c)) - 2*a*d^2 + (b*d^2 - 4*a*d*e)*x^2)/x^2) + 1/4*sqrt(1/2)*sqrt(-(b*d - 2*a*e - (a*b^2 - 4*a^2*c)*sqrt(d^2/(a^2*b^2 - 4*a^3*c)))/(a*b^2 - 4*a^2*c))*log(((a*b^2 - 4*a^2*c)*d*sqrt(d^2/(a^2*b^2 - 4*a^3*c))*x^2 + 4*sqrt(1/2)*(a^2*b^2 - 4*a^3*c)*sqrt(e*x^2 + d)*sqrt(d^2/(a^2*b^2 - 4*a^3*c))*x*sqrt(-(b*d - 2*a*e - (a*b^2 - 4*a^2*c)*sqrt(d^2/(a^2*b^2 - 4*a^3*c)))/(a*b^2 - 4*a^2*c)) + 2*a*d^2 - (b*d^2 - 4*a*d*e)*x^2)/x^2) - 1/4*sqrt(1/2)*sqrt(-(b*d - 2*a*e - (a*b^2 - 4*a^2*c)*sqrt(d^2/(a^2*b^2 - 4*a^3*c)))/(a*b^2 - 4*a^2*c))*log(((a*b^2 - 4*a^2*c)*d*sqrt(d^2/(a^2*b^2 - 4*a^3*c))*x^2 - 4*sqrt(1/2)*(a^2*b^2 - 4*a^3*c)*sqrt(e*x^2 + d)*sqrt(d^2/(a^2*b^2 - 4*a^3*c))*x*sqrt(-(b*d - 2*a*e - (a*b^2 - 4*a^2*c)*sqrt(d^2/(a^2*b^2 - 4*a^3*c)))/(a*b^2 - 4*a^2*c)) + 2*a*d^2 - (b*d^2 - 4*a*d*e)*x^2)/x^2)","B",0
364,1,2402,0,7.224176," ","integrate((e*x^2+d)^(1/2)/x^2/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} a x \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(\frac{2 \, a^{2} b c d e + {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d x^{2} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{a^{6} b^{2} - 4 \, a^{7} c}} - 2 \, {\left(a b^{2} c - a^{2} c^{2}\right)} d^{2} + {\left(4 \, a^{2} b c e^{2} + {\left(b^{3} c - a b c^{2}\right)} d^{2} - {\left(5 \, a b^{2} c - 4 \, a^{2} c^{2}\right)} d e\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} x \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{a^{6} b^{2} - 4 \, a^{7} c}} - {\left({\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e\right)} x\right)} \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} a x \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(\frac{2 \, a^{2} b c d e + {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d x^{2} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{a^{6} b^{2} - 4 \, a^{7} c}} - 2 \, {\left(a b^{2} c - a^{2} c^{2}\right)} d^{2} + {\left(4 \, a^{2} b c e^{2} + {\left(b^{3} c - a b c^{2}\right)} d^{2} - {\left(5 \, a b^{2} c - 4 \, a^{2} c^{2}\right)} d e\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} x \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{a^{6} b^{2} - 4 \, a^{7} c}} - {\left({\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e\right)} x\right)} \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} a x \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(\frac{2 \, a^{2} b c d e - {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d x^{2} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{a^{6} b^{2} - 4 \, a^{7} c}} - 2 \, {\left(a b^{2} c - a^{2} c^{2}\right)} d^{2} + {\left(4 \, a^{2} b c e^{2} + {\left(b^{3} c - a b c^{2}\right)} d^{2} - {\left(5 \, a b^{2} c - 4 \, a^{2} c^{2}\right)} d e\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} x \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{a^{6} b^{2} - 4 \, a^{7} c}} + {\left({\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e\right)} x\right)} \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}}{x^{2}}\right) + \sqrt{\frac{1}{2}} a x \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(\frac{2 \, a^{2} b c d e - {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d x^{2} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{a^{6} b^{2} - 4 \, a^{7} c}} - 2 \, {\left(a b^{2} c - a^{2} c^{2}\right)} d^{2} + {\left(4 \, a^{2} b c e^{2} + {\left(b^{3} c - a b c^{2}\right)} d^{2} - {\left(5 \, a b^{2} c - 4 \, a^{2} c^{2}\right)} d e\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} x \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{a^{6} b^{2} - 4 \, a^{7} c}} + {\left({\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e\right)} x\right)} \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}}{x^{2}}\right) + 4 \, \sqrt{e x^{2} + d}}{4 \, a x}"," ",0,"-1/4*(sqrt(1/2)*a*x*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e + (a^3*b^2 - 4*a^4*c)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log((2*a^2*b*c*d*e + (a^3*b^2*c - 4*a^4*c^2)*d*x^2*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/(a^6*b^2 - 4*a^7*c)) - 2*(a*b^2*c - a^2*c^2)*d^2 + (4*a^2*b*c*e^2 + (b^3*c - a*b*c^2)*d^2 - (5*a*b^2*c - 4*a^2*c^2)*d*e)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((a^4*b^3 - 4*a^5*b*c)*x*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/(a^6*b^2 - 4*a^7*c)) - ((a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*d - (a^2*b^3 - 4*a^3*b*c)*e)*x)*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e + (a^3*b^2 - 4*a^4*c)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c)))/x^2) - sqrt(1/2)*a*x*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e + (a^3*b^2 - 4*a^4*c)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log((2*a^2*b*c*d*e + (a^3*b^2*c - 4*a^4*c^2)*d*x^2*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/(a^6*b^2 - 4*a^7*c)) - 2*(a*b^2*c - a^2*c^2)*d^2 + (4*a^2*b*c*e^2 + (b^3*c - a*b*c^2)*d^2 - (5*a*b^2*c - 4*a^2*c^2)*d*e)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((a^4*b^3 - 4*a^5*b*c)*x*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/(a^6*b^2 - 4*a^7*c)) - ((a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*d - (a^2*b^3 - 4*a^3*b*c)*e)*x)*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e + (a^3*b^2 - 4*a^4*c)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c)))/x^2) - sqrt(1/2)*a*x*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e - (a^3*b^2 - 4*a^4*c)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log((2*a^2*b*c*d*e - (a^3*b^2*c - 4*a^4*c^2)*d*x^2*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/(a^6*b^2 - 4*a^7*c)) - 2*(a*b^2*c - a^2*c^2)*d^2 + (4*a^2*b*c*e^2 + (b^3*c - a*b*c^2)*d^2 - (5*a*b^2*c - 4*a^2*c^2)*d*e)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((a^4*b^3 - 4*a^5*b*c)*x*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/(a^6*b^2 - 4*a^7*c)) + ((a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*d - (a^2*b^3 - 4*a^3*b*c)*e)*x)*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e - (a^3*b^2 - 4*a^4*c)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c)))/x^2) + sqrt(1/2)*a*x*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e - (a^3*b^2 - 4*a^4*c)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log((2*a^2*b*c*d*e - (a^3*b^2*c - 4*a^4*c^2)*d*x^2*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/(a^6*b^2 - 4*a^7*c)) - 2*(a*b^2*c - a^2*c^2)*d^2 + (4*a^2*b*c*e^2 + (b^3*c - a*b*c^2)*d^2 - (5*a*b^2*c - 4*a^2*c^2)*d*e)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((a^4*b^3 - 4*a^5*b*c)*x*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/(a^6*b^2 - 4*a^7*c)) + ((a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*d - (a^2*b^3 - 4*a^3*b*c)*e)*x)*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e - (a^3*b^2 - 4*a^4*c)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c)))/x^2) + 4*sqrt(e*x^2 + d))/(a*x)","B",0
365,1,4095,0,31.157389," ","integrate((e*x^2+d)^(1/2)/x^4/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{1}{2}} a^{2} d x^{3} \sqrt{-\frac{{\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} d - {\left(a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} e - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{{\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{2} - 2 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d e + {\left(a^{2} b^{6} - 4 \, a^{3} b^{4} c + 4 \, a^{4} b^{2} c^{2}\right)} e^{2}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} \log\left(\frac{{\left(a^{5} b^{2} c^{2} - 4 \, a^{6} c^{3}\right)} d x^{2} \sqrt{\frac{{\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{2} - 2 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d e + {\left(a^{2} b^{6} - 4 \, a^{3} b^{4} c + 4 \, a^{4} b^{2} c^{2}\right)} e^{2}}{a^{10} b^{2} - 4 \, a^{11} c}} + 2 \, {\left(a b^{4} c^{2} - 3 \, a^{2} b^{2} c^{3} + a^{3} c^{4}\right)} d^{2} - 2 \, {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b c^{3}\right)} d e - {\left({\left(b^{5} c^{2} - 3 \, a b^{3} c^{3} + a^{2} b c^{4}\right)} d^{2} - {\left(5 \, a b^{4} c^{2} - 14 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d e + 4 \, {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b c^{3}\right)} e^{2}\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(a^{6} b^{4} - 6 \, a^{7} b^{2} c + 8 \, a^{8} c^{2}\right)} x \sqrt{\frac{{\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{2} - 2 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d e + {\left(a^{2} b^{6} - 4 \, a^{3} b^{4} c + 4 \, a^{4} b^{2} c^{2}\right)} e^{2}}{a^{10} b^{2} - 4 \, a^{11} c}} + {\left({\left(a b^{7} - 7 \, a^{2} b^{5} c + 13 \, a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d - {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 8 \, a^{4} b^{2} c^{2}\right)} e\right)} x\right)} \sqrt{-\frac{{\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} d - {\left(a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} e - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{{\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{2} - 2 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d e + {\left(a^{2} b^{6} - 4 \, a^{3} b^{4} c + 4 \, a^{4} b^{2} c^{2}\right)} e^{2}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}}}{x^{2}}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} d x^{3} \sqrt{-\frac{{\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} d - {\left(a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} e - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{{\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{2} - 2 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d e + {\left(a^{2} b^{6} - 4 \, a^{3} b^{4} c + 4 \, a^{4} b^{2} c^{2}\right)} e^{2}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} \log\left(\frac{{\left(a^{5} b^{2} c^{2} - 4 \, a^{6} c^{3}\right)} d x^{2} \sqrt{\frac{{\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{2} - 2 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d e + {\left(a^{2} b^{6} - 4 \, a^{3} b^{4} c + 4 \, a^{4} b^{2} c^{2}\right)} e^{2}}{a^{10} b^{2} - 4 \, a^{11} c}} + 2 \, {\left(a b^{4} c^{2} - 3 \, a^{2} b^{2} c^{3} + a^{3} c^{4}\right)} d^{2} - 2 \, {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b c^{3}\right)} d e - {\left({\left(b^{5} c^{2} - 3 \, a b^{3} c^{3} + a^{2} b c^{4}\right)} d^{2} - {\left(5 \, a b^{4} c^{2} - 14 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d e + 4 \, {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b c^{3}\right)} e^{2}\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(a^{6} b^{4} - 6 \, a^{7} b^{2} c + 8 \, a^{8} c^{2}\right)} x \sqrt{\frac{{\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{2} - 2 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d e + {\left(a^{2} b^{6} - 4 \, a^{3} b^{4} c + 4 \, a^{4} b^{2} c^{2}\right)} e^{2}}{a^{10} b^{2} - 4 \, a^{11} c}} + {\left({\left(a b^{7} - 7 \, a^{2} b^{5} c + 13 \, a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d - {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 8 \, a^{4} b^{2} c^{2}\right)} e\right)} x\right)} \sqrt{-\frac{{\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} d - {\left(a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} e - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{{\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{2} - 2 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d e + {\left(a^{2} b^{6} - 4 \, a^{3} b^{4} c + 4 \, a^{4} b^{2} c^{2}\right)} e^{2}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}}}{x^{2}}\right) + 3 \, \sqrt{\frac{1}{2}} a^{2} d x^{3} \sqrt{-\frac{{\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} d - {\left(a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} e + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{{\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{2} - 2 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d e + {\left(a^{2} b^{6} - 4 \, a^{3} b^{4} c + 4 \, a^{4} b^{2} c^{2}\right)} e^{2}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} \log\left(-\frac{{\left(a^{5} b^{2} c^{2} - 4 \, a^{6} c^{3}\right)} d x^{2} \sqrt{\frac{{\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{2} - 2 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d e + {\left(a^{2} b^{6} - 4 \, a^{3} b^{4} c + 4 \, a^{4} b^{2} c^{2}\right)} e^{2}}{a^{10} b^{2} - 4 \, a^{11} c}} - 2 \, {\left(a b^{4} c^{2} - 3 \, a^{2} b^{2} c^{3} + a^{3} c^{4}\right)} d^{2} + 2 \, {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b c^{3}\right)} d e + {\left({\left(b^{5} c^{2} - 3 \, a b^{3} c^{3} + a^{2} b c^{4}\right)} d^{2} - {\left(5 \, a b^{4} c^{2} - 14 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d e + 4 \, {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b c^{3}\right)} e^{2}\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(a^{6} b^{4} - 6 \, a^{7} b^{2} c + 8 \, a^{8} c^{2}\right)} x \sqrt{\frac{{\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{2} - 2 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d e + {\left(a^{2} b^{6} - 4 \, a^{3} b^{4} c + 4 \, a^{4} b^{2} c^{2}\right)} e^{2}}{a^{10} b^{2} - 4 \, a^{11} c}} - {\left({\left(a b^{7} - 7 \, a^{2} b^{5} c + 13 \, a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d - {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 8 \, a^{4} b^{2} c^{2}\right)} e\right)} x\right)} \sqrt{-\frac{{\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} d - {\left(a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} e + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{{\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{2} - 2 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d e + {\left(a^{2} b^{6} - 4 \, a^{3} b^{4} c + 4 \, a^{4} b^{2} c^{2}\right)} e^{2}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}}}{x^{2}}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} d x^{3} \sqrt{-\frac{{\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} d - {\left(a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} e + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{{\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{2} - 2 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d e + {\left(a^{2} b^{6} - 4 \, a^{3} b^{4} c + 4 \, a^{4} b^{2} c^{2}\right)} e^{2}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} \log\left(-\frac{{\left(a^{5} b^{2} c^{2} - 4 \, a^{6} c^{3}\right)} d x^{2} \sqrt{\frac{{\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{2} - 2 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d e + {\left(a^{2} b^{6} - 4 \, a^{3} b^{4} c + 4 \, a^{4} b^{2} c^{2}\right)} e^{2}}{a^{10} b^{2} - 4 \, a^{11} c}} - 2 \, {\left(a b^{4} c^{2} - 3 \, a^{2} b^{2} c^{3} + a^{3} c^{4}\right)} d^{2} + 2 \, {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b c^{3}\right)} d e + {\left({\left(b^{5} c^{2} - 3 \, a b^{3} c^{3} + a^{2} b c^{4}\right)} d^{2} - {\left(5 \, a b^{4} c^{2} - 14 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d e + 4 \, {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b c^{3}\right)} e^{2}\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(a^{6} b^{4} - 6 \, a^{7} b^{2} c + 8 \, a^{8} c^{2}\right)} x \sqrt{\frac{{\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{2} - 2 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d e + {\left(a^{2} b^{6} - 4 \, a^{3} b^{4} c + 4 \, a^{4} b^{2} c^{2}\right)} e^{2}}{a^{10} b^{2} - 4 \, a^{11} c}} - {\left({\left(a b^{7} - 7 \, a^{2} b^{5} c + 13 \, a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d - {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 8 \, a^{4} b^{2} c^{2}\right)} e\right)} x\right)} \sqrt{-\frac{{\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} d - {\left(a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} e + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{{\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{2} - 2 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d e + {\left(a^{2} b^{6} - 4 \, a^{3} b^{4} c + 4 \, a^{4} b^{2} c^{2}\right)} e^{2}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}}}{x^{2}}\right) + 4 \, {\left({\left(3 \, b d - a e\right)} x^{2} - a d\right)} \sqrt{e x^{2} + d}}{12 \, a^{2} d x^{3}}"," ",0,"1/12*(3*sqrt(1/2)*a^2*d*x^3*sqrt(-((b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*d - (a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2)*e - (a^5*b^2 - 4*a^6*c)*sqrt(((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^2 - 2*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d*e + (a^2*b^6 - 4*a^3*b^4*c + 4*a^4*b^2*c^2)*e^2)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))*log(((a^5*b^2*c^2 - 4*a^6*c^3)*d*x^2*sqrt(((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^2 - 2*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d*e + (a^2*b^6 - 4*a^3*b^4*c + 4*a^4*b^2*c^2)*e^2)/(a^10*b^2 - 4*a^11*c)) + 2*(a*b^4*c^2 - 3*a^2*b^2*c^3 + a^3*c^4)*d^2 - 2*(a^2*b^3*c^2 - 2*a^3*b*c^3)*d*e - ((b^5*c^2 - 3*a*b^3*c^3 + a^2*b*c^4)*d^2 - (5*a*b^4*c^2 - 14*a^2*b^2*c^3 + 4*a^3*c^4)*d*e + 4*(a^2*b^3*c^2 - 2*a^3*b*c^3)*e^2)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((a^6*b^4 - 6*a^7*b^2*c + 8*a^8*c^2)*x*sqrt(((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^2 - 2*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d*e + (a^2*b^6 - 4*a^3*b^4*c + 4*a^4*b^2*c^2)*e^2)/(a^10*b^2 - 4*a^11*c)) + ((a*b^7 - 7*a^2*b^5*c + 13*a^3*b^3*c^2 - 4*a^4*b*c^3)*d - (a^2*b^6 - 6*a^3*b^4*c + 8*a^4*b^2*c^2)*e)*x)*sqrt(-((b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*d - (a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2)*e - (a^5*b^2 - 4*a^6*c)*sqrt(((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^2 - 2*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d*e + (a^2*b^6 - 4*a^3*b^4*c + 4*a^4*b^2*c^2)*e^2)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c)))/x^2) - 3*sqrt(1/2)*a^2*d*x^3*sqrt(-((b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*d - (a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2)*e - (a^5*b^2 - 4*a^6*c)*sqrt(((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^2 - 2*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d*e + (a^2*b^6 - 4*a^3*b^4*c + 4*a^4*b^2*c^2)*e^2)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))*log(((a^5*b^2*c^2 - 4*a^6*c^3)*d*x^2*sqrt(((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^2 - 2*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d*e + (a^2*b^6 - 4*a^3*b^4*c + 4*a^4*b^2*c^2)*e^2)/(a^10*b^2 - 4*a^11*c)) + 2*(a*b^4*c^2 - 3*a^2*b^2*c^3 + a^3*c^4)*d^2 - 2*(a^2*b^3*c^2 - 2*a^3*b*c^3)*d*e - ((b^5*c^2 - 3*a*b^3*c^3 + a^2*b*c^4)*d^2 - (5*a*b^4*c^2 - 14*a^2*b^2*c^3 + 4*a^3*c^4)*d*e + 4*(a^2*b^3*c^2 - 2*a^3*b*c^3)*e^2)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((a^6*b^4 - 6*a^7*b^2*c + 8*a^8*c^2)*x*sqrt(((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^2 - 2*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d*e + (a^2*b^6 - 4*a^3*b^4*c + 4*a^4*b^2*c^2)*e^2)/(a^10*b^2 - 4*a^11*c)) + ((a*b^7 - 7*a^2*b^5*c + 13*a^3*b^3*c^2 - 4*a^4*b*c^3)*d - (a^2*b^6 - 6*a^3*b^4*c + 8*a^4*b^2*c^2)*e)*x)*sqrt(-((b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*d - (a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2)*e - (a^5*b^2 - 4*a^6*c)*sqrt(((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^2 - 2*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d*e + (a^2*b^6 - 4*a^3*b^4*c + 4*a^4*b^2*c^2)*e^2)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c)))/x^2) + 3*sqrt(1/2)*a^2*d*x^3*sqrt(-((b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*d - (a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2)*e + (a^5*b^2 - 4*a^6*c)*sqrt(((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^2 - 2*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d*e + (a^2*b^6 - 4*a^3*b^4*c + 4*a^4*b^2*c^2)*e^2)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))*log(-((a^5*b^2*c^2 - 4*a^6*c^3)*d*x^2*sqrt(((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^2 - 2*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d*e + (a^2*b^6 - 4*a^3*b^4*c + 4*a^4*b^2*c^2)*e^2)/(a^10*b^2 - 4*a^11*c)) - 2*(a*b^4*c^2 - 3*a^2*b^2*c^3 + a^3*c^4)*d^2 + 2*(a^2*b^3*c^2 - 2*a^3*b*c^3)*d*e + ((b^5*c^2 - 3*a*b^3*c^3 + a^2*b*c^4)*d^2 - (5*a*b^4*c^2 - 14*a^2*b^2*c^3 + 4*a^3*c^4)*d*e + 4*(a^2*b^3*c^2 - 2*a^3*b*c^3)*e^2)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((a^6*b^4 - 6*a^7*b^2*c + 8*a^8*c^2)*x*sqrt(((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^2 - 2*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d*e + (a^2*b^6 - 4*a^3*b^4*c + 4*a^4*b^2*c^2)*e^2)/(a^10*b^2 - 4*a^11*c)) - ((a*b^7 - 7*a^2*b^5*c + 13*a^3*b^3*c^2 - 4*a^4*b*c^3)*d - (a^2*b^6 - 6*a^3*b^4*c + 8*a^4*b^2*c^2)*e)*x)*sqrt(-((b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*d - (a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2)*e + (a^5*b^2 - 4*a^6*c)*sqrt(((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^2 - 2*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d*e + (a^2*b^6 - 4*a^3*b^4*c + 4*a^4*b^2*c^2)*e^2)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c)))/x^2) - 3*sqrt(1/2)*a^2*d*x^3*sqrt(-((b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*d - (a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2)*e + (a^5*b^2 - 4*a^6*c)*sqrt(((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^2 - 2*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d*e + (a^2*b^6 - 4*a^3*b^4*c + 4*a^4*b^2*c^2)*e^2)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))*log(-((a^5*b^2*c^2 - 4*a^6*c^3)*d*x^2*sqrt(((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^2 - 2*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d*e + (a^2*b^6 - 4*a^3*b^4*c + 4*a^4*b^2*c^2)*e^2)/(a^10*b^2 - 4*a^11*c)) - 2*(a*b^4*c^2 - 3*a^2*b^2*c^3 + a^3*c^4)*d^2 + 2*(a^2*b^3*c^2 - 2*a^3*b*c^3)*d*e + ((b^5*c^2 - 3*a*b^3*c^3 + a^2*b*c^4)*d^2 - (5*a*b^4*c^2 - 14*a^2*b^2*c^3 + 4*a^3*c^4)*d*e + 4*(a^2*b^3*c^2 - 2*a^3*b*c^3)*e^2)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((a^6*b^4 - 6*a^7*b^2*c + 8*a^8*c^2)*x*sqrt(((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^2 - 2*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d*e + (a^2*b^6 - 4*a^3*b^4*c + 4*a^4*b^2*c^2)*e^2)/(a^10*b^2 - 4*a^11*c)) - ((a*b^7 - 7*a^2*b^5*c + 13*a^3*b^3*c^2 - 4*a^4*b*c^3)*d - (a^2*b^6 - 6*a^3*b^4*c + 8*a^4*b^2*c^2)*e)*x)*sqrt(-((b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*d - (a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2)*e + (a^5*b^2 - 4*a^6*c)*sqrt(((b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^2 - 2*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d*e + (a^2*b^6 - 4*a^3*b^4*c + 4*a^4*b^2*c^2)*e^2)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c)))/x^2) + 4*((3*b*d - a*e)*x^2 - a*d)*sqrt(e*x^2 + d))/(a^2*d*x^3)","B",0
366,1,5773,0,77.192251," ","integrate((e*x^2+d)^(1/2)/x^6/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{\frac{1}{2}} a^{3} d^{2} x^{5} \sqrt{-\frac{{\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} d - {\left(a b^{6} - 6 \, a^{2} b^{4} c + 9 \, a^{3} b^{2} c^{2} - 2 \, a^{4} c^{3}\right)} e - {\left(a^{7} b^{2} - 4 \, a^{8} c\right)} \sqrt{\frac{{\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} d^{2} - 2 \, {\left(a b^{11} - 9 \, a^{2} b^{9} c + 29 \, a^{3} b^{7} c^{2} - 40 \, a^{4} b^{5} c^{3} + 22 \, a^{5} b^{3} c^{4} - 3 \, a^{6} b c^{5}\right)} d e + {\left(a^{2} b^{10} - 8 \, a^{3} b^{8} c + 22 \, a^{4} b^{6} c^{2} - 24 \, a^{5} b^{4} c^{3} + 9 \, a^{6} b^{2} c^{4}\right)} e^{2}}{a^{14} b^{2} - 4 \, a^{15} c}}}{a^{7} b^{2} - 4 \, a^{8} c}} \log\left(-\frac{{\left(a^{7} b^{2} c^{3} - 4 \, a^{8} c^{4}\right)} d x^{2} \sqrt{\frac{{\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} d^{2} - 2 \, {\left(a b^{11} - 9 \, a^{2} b^{9} c + 29 \, a^{3} b^{7} c^{2} - 40 \, a^{4} b^{5} c^{3} + 22 \, a^{5} b^{3} c^{4} - 3 \, a^{6} b c^{5}\right)} d e + {\left(a^{2} b^{10} - 8 \, a^{3} b^{8} c + 22 \, a^{4} b^{6} c^{2} - 24 \, a^{5} b^{4} c^{3} + 9 \, a^{6} b^{2} c^{4}\right)} e^{2}}{a^{14} b^{2} - 4 \, a^{15} c}} + 2 \, {\left(a b^{6} c^{3} - 5 \, a^{2} b^{4} c^{4} + 6 \, a^{3} b^{2} c^{5} - a^{4} c^{6}\right)} d^{2} - 2 \, {\left(a^{2} b^{5} c^{3} - 4 \, a^{3} b^{3} c^{4} + 3 \, a^{4} b c^{5}\right)} d e - {\left({\left(b^{7} c^{3} - 5 \, a b^{5} c^{4} + 6 \, a^{2} b^{3} c^{5} - a^{3} b c^{6}\right)} d^{2} - {\left(5 \, a b^{6} c^{3} - 24 \, a^{2} b^{4} c^{4} + 27 \, a^{3} b^{2} c^{5} - 4 \, a^{4} c^{6}\right)} d e + 4 \, {\left(a^{2} b^{5} c^{3} - 4 \, a^{3} b^{3} c^{4} + 3 \, a^{4} b c^{5}\right)} e^{2}\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(a^{8} b^{5} - 7 \, a^{9} b^{3} c + 12 \, a^{10} b c^{2}\right)} x \sqrt{\frac{{\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} d^{2} - 2 \, {\left(a b^{11} - 9 \, a^{2} b^{9} c + 29 \, a^{3} b^{7} c^{2} - 40 \, a^{4} b^{5} c^{3} + 22 \, a^{5} b^{3} c^{4} - 3 \, a^{6} b c^{5}\right)} d e + {\left(a^{2} b^{10} - 8 \, a^{3} b^{8} c + 22 \, a^{4} b^{6} c^{2} - 24 \, a^{5} b^{4} c^{3} + 9 \, a^{6} b^{2} c^{4}\right)} e^{2}}{a^{14} b^{2} - 4 \, a^{15} c}} + {\left({\left(a b^{10} - 10 \, a^{2} b^{8} c + 35 \, a^{3} b^{6} c^{2} - 51 \, a^{4} b^{4} c^{3} + 29 \, a^{5} b^{2} c^{4} - 4 \, a^{6} c^{5}\right)} d - {\left(a^{2} b^{9} - 9 \, a^{3} b^{7} c + 27 \, a^{4} b^{5} c^{2} - 31 \, a^{5} b^{3} c^{3} + 12 \, a^{6} b c^{4}\right)} e\right)} x\right)} \sqrt{-\frac{{\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} d - {\left(a b^{6} - 6 \, a^{2} b^{4} c + 9 \, a^{3} b^{2} c^{2} - 2 \, a^{4} c^{3}\right)} e - {\left(a^{7} b^{2} - 4 \, a^{8} c\right)} \sqrt{\frac{{\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} d^{2} - 2 \, {\left(a b^{11} - 9 \, a^{2} b^{9} c + 29 \, a^{3} b^{7} c^{2} - 40 \, a^{4} b^{5} c^{3} + 22 \, a^{5} b^{3} c^{4} - 3 \, a^{6} b c^{5}\right)} d e + {\left(a^{2} b^{10} - 8 \, a^{3} b^{8} c + 22 \, a^{4} b^{6} c^{2} - 24 \, a^{5} b^{4} c^{3} + 9 \, a^{6} b^{2} c^{4}\right)} e^{2}}{a^{14} b^{2} - 4 \, a^{15} c}}}{a^{7} b^{2} - 4 \, a^{8} c}}}{x^{2}}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} d^{2} x^{5} \sqrt{-\frac{{\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} d - {\left(a b^{6} - 6 \, a^{2} b^{4} c + 9 \, a^{3} b^{2} c^{2} - 2 \, a^{4} c^{3}\right)} e - {\left(a^{7} b^{2} - 4 \, a^{8} c\right)} \sqrt{\frac{{\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} d^{2} - 2 \, {\left(a b^{11} - 9 \, a^{2} b^{9} c + 29 \, a^{3} b^{7} c^{2} - 40 \, a^{4} b^{5} c^{3} + 22 \, a^{5} b^{3} c^{4} - 3 \, a^{6} b c^{5}\right)} d e + {\left(a^{2} b^{10} - 8 \, a^{3} b^{8} c + 22 \, a^{4} b^{6} c^{2} - 24 \, a^{5} b^{4} c^{3} + 9 \, a^{6} b^{2} c^{4}\right)} e^{2}}{a^{14} b^{2} - 4 \, a^{15} c}}}{a^{7} b^{2} - 4 \, a^{8} c}} \log\left(-\frac{{\left(a^{7} b^{2} c^{3} - 4 \, a^{8} c^{4}\right)} d x^{2} \sqrt{\frac{{\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} d^{2} - 2 \, {\left(a b^{11} - 9 \, a^{2} b^{9} c + 29 \, a^{3} b^{7} c^{2} - 40 \, a^{4} b^{5} c^{3} + 22 \, a^{5} b^{3} c^{4} - 3 \, a^{6} b c^{5}\right)} d e + {\left(a^{2} b^{10} - 8 \, a^{3} b^{8} c + 22 \, a^{4} b^{6} c^{2} - 24 \, a^{5} b^{4} c^{3} + 9 \, a^{6} b^{2} c^{4}\right)} e^{2}}{a^{14} b^{2} - 4 \, a^{15} c}} + 2 \, {\left(a b^{6} c^{3} - 5 \, a^{2} b^{4} c^{4} + 6 \, a^{3} b^{2} c^{5} - a^{4} c^{6}\right)} d^{2} - 2 \, {\left(a^{2} b^{5} c^{3} - 4 \, a^{3} b^{3} c^{4} + 3 \, a^{4} b c^{5}\right)} d e - {\left({\left(b^{7} c^{3} - 5 \, a b^{5} c^{4} + 6 \, a^{2} b^{3} c^{5} - a^{3} b c^{6}\right)} d^{2} - {\left(5 \, a b^{6} c^{3} - 24 \, a^{2} b^{4} c^{4} + 27 \, a^{3} b^{2} c^{5} - 4 \, a^{4} c^{6}\right)} d e + 4 \, {\left(a^{2} b^{5} c^{3} - 4 \, a^{3} b^{3} c^{4} + 3 \, a^{4} b c^{5}\right)} e^{2}\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(a^{8} b^{5} - 7 \, a^{9} b^{3} c + 12 \, a^{10} b c^{2}\right)} x \sqrt{\frac{{\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} d^{2} - 2 \, {\left(a b^{11} - 9 \, a^{2} b^{9} c + 29 \, a^{3} b^{7} c^{2} - 40 \, a^{4} b^{5} c^{3} + 22 \, a^{5} b^{3} c^{4} - 3 \, a^{6} b c^{5}\right)} d e + {\left(a^{2} b^{10} - 8 \, a^{3} b^{8} c + 22 \, a^{4} b^{6} c^{2} - 24 \, a^{5} b^{4} c^{3} + 9 \, a^{6} b^{2} c^{4}\right)} e^{2}}{a^{14} b^{2} - 4 \, a^{15} c}} + {\left({\left(a b^{10} - 10 \, a^{2} b^{8} c + 35 \, a^{3} b^{6} c^{2} - 51 \, a^{4} b^{4} c^{3} + 29 \, a^{5} b^{2} c^{4} - 4 \, a^{6} c^{5}\right)} d - {\left(a^{2} b^{9} - 9 \, a^{3} b^{7} c + 27 \, a^{4} b^{5} c^{2} - 31 \, a^{5} b^{3} c^{3} + 12 \, a^{6} b c^{4}\right)} e\right)} x\right)} \sqrt{-\frac{{\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} d - {\left(a b^{6} - 6 \, a^{2} b^{4} c + 9 \, a^{3} b^{2} c^{2} - 2 \, a^{4} c^{3}\right)} e - {\left(a^{7} b^{2} - 4 \, a^{8} c\right)} \sqrt{\frac{{\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} d^{2} - 2 \, {\left(a b^{11} - 9 \, a^{2} b^{9} c + 29 \, a^{3} b^{7} c^{2} - 40 \, a^{4} b^{5} c^{3} + 22 \, a^{5} b^{3} c^{4} - 3 \, a^{6} b c^{5}\right)} d e + {\left(a^{2} b^{10} - 8 \, a^{3} b^{8} c + 22 \, a^{4} b^{6} c^{2} - 24 \, a^{5} b^{4} c^{3} + 9 \, a^{6} b^{2} c^{4}\right)} e^{2}}{a^{14} b^{2} - 4 \, a^{15} c}}}{a^{7} b^{2} - 4 \, a^{8} c}}}{x^{2}}\right) + 15 \, \sqrt{\frac{1}{2}} a^{3} d^{2} x^{5} \sqrt{-\frac{{\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} d - {\left(a b^{6} - 6 \, a^{2} b^{4} c + 9 \, a^{3} b^{2} c^{2} - 2 \, a^{4} c^{3}\right)} e + {\left(a^{7} b^{2} - 4 \, a^{8} c\right)} \sqrt{\frac{{\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} d^{2} - 2 \, {\left(a b^{11} - 9 \, a^{2} b^{9} c + 29 \, a^{3} b^{7} c^{2} - 40 \, a^{4} b^{5} c^{3} + 22 \, a^{5} b^{3} c^{4} - 3 \, a^{6} b c^{5}\right)} d e + {\left(a^{2} b^{10} - 8 \, a^{3} b^{8} c + 22 \, a^{4} b^{6} c^{2} - 24 \, a^{5} b^{4} c^{3} + 9 \, a^{6} b^{2} c^{4}\right)} e^{2}}{a^{14} b^{2} - 4 \, a^{15} c}}}{a^{7} b^{2} - 4 \, a^{8} c}} \log\left(\frac{{\left(a^{7} b^{2} c^{3} - 4 \, a^{8} c^{4}\right)} d x^{2} \sqrt{\frac{{\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} d^{2} - 2 \, {\left(a b^{11} - 9 \, a^{2} b^{9} c + 29 \, a^{3} b^{7} c^{2} - 40 \, a^{4} b^{5} c^{3} + 22 \, a^{5} b^{3} c^{4} - 3 \, a^{6} b c^{5}\right)} d e + {\left(a^{2} b^{10} - 8 \, a^{3} b^{8} c + 22 \, a^{4} b^{6} c^{2} - 24 \, a^{5} b^{4} c^{3} + 9 \, a^{6} b^{2} c^{4}\right)} e^{2}}{a^{14} b^{2} - 4 \, a^{15} c}} - 2 \, {\left(a b^{6} c^{3} - 5 \, a^{2} b^{4} c^{4} + 6 \, a^{3} b^{2} c^{5} - a^{4} c^{6}\right)} d^{2} + 2 \, {\left(a^{2} b^{5} c^{3} - 4 \, a^{3} b^{3} c^{4} + 3 \, a^{4} b c^{5}\right)} d e + {\left({\left(b^{7} c^{3} - 5 \, a b^{5} c^{4} + 6 \, a^{2} b^{3} c^{5} - a^{3} b c^{6}\right)} d^{2} - {\left(5 \, a b^{6} c^{3} - 24 \, a^{2} b^{4} c^{4} + 27 \, a^{3} b^{2} c^{5} - 4 \, a^{4} c^{6}\right)} d e + 4 \, {\left(a^{2} b^{5} c^{3} - 4 \, a^{3} b^{3} c^{4} + 3 \, a^{4} b c^{5}\right)} e^{2}\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(a^{8} b^{5} - 7 \, a^{9} b^{3} c + 12 \, a^{10} b c^{2}\right)} x \sqrt{\frac{{\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} d^{2} - 2 \, {\left(a b^{11} - 9 \, a^{2} b^{9} c + 29 \, a^{3} b^{7} c^{2} - 40 \, a^{4} b^{5} c^{3} + 22 \, a^{5} b^{3} c^{4} - 3 \, a^{6} b c^{5}\right)} d e + {\left(a^{2} b^{10} - 8 \, a^{3} b^{8} c + 22 \, a^{4} b^{6} c^{2} - 24 \, a^{5} b^{4} c^{3} + 9 \, a^{6} b^{2} c^{4}\right)} e^{2}}{a^{14} b^{2} - 4 \, a^{15} c}} - {\left({\left(a b^{10} - 10 \, a^{2} b^{8} c + 35 \, a^{3} b^{6} c^{2} - 51 \, a^{4} b^{4} c^{3} + 29 \, a^{5} b^{2} c^{4} - 4 \, a^{6} c^{5}\right)} d - {\left(a^{2} b^{9} - 9 \, a^{3} b^{7} c + 27 \, a^{4} b^{5} c^{2} - 31 \, a^{5} b^{3} c^{3} + 12 \, a^{6} b c^{4}\right)} e\right)} x\right)} \sqrt{-\frac{{\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} d - {\left(a b^{6} - 6 \, a^{2} b^{4} c + 9 \, a^{3} b^{2} c^{2} - 2 \, a^{4} c^{3}\right)} e + {\left(a^{7} b^{2} - 4 \, a^{8} c\right)} \sqrt{\frac{{\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} d^{2} - 2 \, {\left(a b^{11} - 9 \, a^{2} b^{9} c + 29 \, a^{3} b^{7} c^{2} - 40 \, a^{4} b^{5} c^{3} + 22 \, a^{5} b^{3} c^{4} - 3 \, a^{6} b c^{5}\right)} d e + {\left(a^{2} b^{10} - 8 \, a^{3} b^{8} c + 22 \, a^{4} b^{6} c^{2} - 24 \, a^{5} b^{4} c^{3} + 9 \, a^{6} b^{2} c^{4}\right)} e^{2}}{a^{14} b^{2} - 4 \, a^{15} c}}}{a^{7} b^{2} - 4 \, a^{8} c}}}{x^{2}}\right) - 15 \, \sqrt{\frac{1}{2}} a^{3} d^{2} x^{5} \sqrt{-\frac{{\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} d - {\left(a b^{6} - 6 \, a^{2} b^{4} c + 9 \, a^{3} b^{2} c^{2} - 2 \, a^{4} c^{3}\right)} e + {\left(a^{7} b^{2} - 4 \, a^{8} c\right)} \sqrt{\frac{{\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} d^{2} - 2 \, {\left(a b^{11} - 9 \, a^{2} b^{9} c + 29 \, a^{3} b^{7} c^{2} - 40 \, a^{4} b^{5} c^{3} + 22 \, a^{5} b^{3} c^{4} - 3 \, a^{6} b c^{5}\right)} d e + {\left(a^{2} b^{10} - 8 \, a^{3} b^{8} c + 22 \, a^{4} b^{6} c^{2} - 24 \, a^{5} b^{4} c^{3} + 9 \, a^{6} b^{2} c^{4}\right)} e^{2}}{a^{14} b^{2} - 4 \, a^{15} c}}}{a^{7} b^{2} - 4 \, a^{8} c}} \log\left(\frac{{\left(a^{7} b^{2} c^{3} - 4 \, a^{8} c^{4}\right)} d x^{2} \sqrt{\frac{{\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} d^{2} - 2 \, {\left(a b^{11} - 9 \, a^{2} b^{9} c + 29 \, a^{3} b^{7} c^{2} - 40 \, a^{4} b^{5} c^{3} + 22 \, a^{5} b^{3} c^{4} - 3 \, a^{6} b c^{5}\right)} d e + {\left(a^{2} b^{10} - 8 \, a^{3} b^{8} c + 22 \, a^{4} b^{6} c^{2} - 24 \, a^{5} b^{4} c^{3} + 9 \, a^{6} b^{2} c^{4}\right)} e^{2}}{a^{14} b^{2} - 4 \, a^{15} c}} - 2 \, {\left(a b^{6} c^{3} - 5 \, a^{2} b^{4} c^{4} + 6 \, a^{3} b^{2} c^{5} - a^{4} c^{6}\right)} d^{2} + 2 \, {\left(a^{2} b^{5} c^{3} - 4 \, a^{3} b^{3} c^{4} + 3 \, a^{4} b c^{5}\right)} d e + {\left({\left(b^{7} c^{3} - 5 \, a b^{5} c^{4} + 6 \, a^{2} b^{3} c^{5} - a^{3} b c^{6}\right)} d^{2} - {\left(5 \, a b^{6} c^{3} - 24 \, a^{2} b^{4} c^{4} + 27 \, a^{3} b^{2} c^{5} - 4 \, a^{4} c^{6}\right)} d e + 4 \, {\left(a^{2} b^{5} c^{3} - 4 \, a^{3} b^{3} c^{4} + 3 \, a^{4} b c^{5}\right)} e^{2}\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(a^{8} b^{5} - 7 \, a^{9} b^{3} c + 12 \, a^{10} b c^{2}\right)} x \sqrt{\frac{{\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} d^{2} - 2 \, {\left(a b^{11} - 9 \, a^{2} b^{9} c + 29 \, a^{3} b^{7} c^{2} - 40 \, a^{4} b^{5} c^{3} + 22 \, a^{5} b^{3} c^{4} - 3 \, a^{6} b c^{5}\right)} d e + {\left(a^{2} b^{10} - 8 \, a^{3} b^{8} c + 22 \, a^{4} b^{6} c^{2} - 24 \, a^{5} b^{4} c^{3} + 9 \, a^{6} b^{2} c^{4}\right)} e^{2}}{a^{14} b^{2} - 4 \, a^{15} c}} - {\left({\left(a b^{10} - 10 \, a^{2} b^{8} c + 35 \, a^{3} b^{6} c^{2} - 51 \, a^{4} b^{4} c^{3} + 29 \, a^{5} b^{2} c^{4} - 4 \, a^{6} c^{5}\right)} d - {\left(a^{2} b^{9} - 9 \, a^{3} b^{7} c + 27 \, a^{4} b^{5} c^{2} - 31 \, a^{5} b^{3} c^{3} + 12 \, a^{6} b c^{4}\right)} e\right)} x\right)} \sqrt{-\frac{{\left(b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3}\right)} d - {\left(a b^{6} - 6 \, a^{2} b^{4} c + 9 \, a^{3} b^{2} c^{2} - 2 \, a^{4} c^{3}\right)} e + {\left(a^{7} b^{2} - 4 \, a^{8} c\right)} \sqrt{\frac{{\left(b^{12} - 10 \, a b^{10} c + 37 \, a^{2} b^{8} c^{2} - 62 \, a^{3} b^{6} c^{3} + 46 \, a^{4} b^{4} c^{4} - 12 \, a^{5} b^{2} c^{5} + a^{6} c^{6}\right)} d^{2} - 2 \, {\left(a b^{11} - 9 \, a^{2} b^{9} c + 29 \, a^{3} b^{7} c^{2} - 40 \, a^{4} b^{5} c^{3} + 22 \, a^{5} b^{3} c^{4} - 3 \, a^{6} b c^{5}\right)} d e + {\left(a^{2} b^{10} - 8 \, a^{3} b^{8} c + 22 \, a^{4} b^{6} c^{2} - 24 \, a^{5} b^{4} c^{3} + 9 \, a^{6} b^{2} c^{4}\right)} e^{2}}{a^{14} b^{2} - 4 \, a^{15} c}}}{a^{7} b^{2} - 4 \, a^{8} c}}}{x^{2}}\right) - 4 \, {\left({\left(5 \, a b d e + 2 \, a^{2} e^{2} - 15 \, {\left(b^{2} - a c\right)} d^{2}\right)} x^{4} - 3 \, a^{2} d^{2} + {\left(5 \, a b d^{2} - a^{2} d e\right)} x^{2}\right)} \sqrt{e x^{2} + d}}{60 \, a^{3} d^{2} x^{5}}"," ",0,"-1/60*(15*sqrt(1/2)*a^3*d^2*x^5*sqrt(-((b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*d - (a*b^6 - 6*a^2*b^4*c + 9*a^3*b^2*c^2 - 2*a^4*c^3)*e - (a^7*b^2 - 4*a^8*c)*sqrt(((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*d^2 - 2*(a*b^11 - 9*a^2*b^9*c + 29*a^3*b^7*c^2 - 40*a^4*b^5*c^3 + 22*a^5*b^3*c^4 - 3*a^6*b*c^5)*d*e + (a^2*b^10 - 8*a^3*b^8*c + 22*a^4*b^6*c^2 - 24*a^5*b^4*c^3 + 9*a^6*b^2*c^4)*e^2)/(a^14*b^2 - 4*a^15*c)))/(a^7*b^2 - 4*a^8*c))*log(-((a^7*b^2*c^3 - 4*a^8*c^4)*d*x^2*sqrt(((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*d^2 - 2*(a*b^11 - 9*a^2*b^9*c + 29*a^3*b^7*c^2 - 40*a^4*b^5*c^3 + 22*a^5*b^3*c^4 - 3*a^6*b*c^5)*d*e + (a^2*b^10 - 8*a^3*b^8*c + 22*a^4*b^6*c^2 - 24*a^5*b^4*c^3 + 9*a^6*b^2*c^4)*e^2)/(a^14*b^2 - 4*a^15*c)) + 2*(a*b^6*c^3 - 5*a^2*b^4*c^4 + 6*a^3*b^2*c^5 - a^4*c^6)*d^2 - 2*(a^2*b^5*c^3 - 4*a^3*b^3*c^4 + 3*a^4*b*c^5)*d*e - ((b^7*c^3 - 5*a*b^5*c^4 + 6*a^2*b^3*c^5 - a^3*b*c^6)*d^2 - (5*a*b^6*c^3 - 24*a^2*b^4*c^4 + 27*a^3*b^2*c^5 - 4*a^4*c^6)*d*e + 4*(a^2*b^5*c^3 - 4*a^3*b^3*c^4 + 3*a^4*b*c^5)*e^2)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((a^8*b^5 - 7*a^9*b^3*c + 12*a^10*b*c^2)*x*sqrt(((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*d^2 - 2*(a*b^11 - 9*a^2*b^9*c + 29*a^3*b^7*c^2 - 40*a^4*b^5*c^3 + 22*a^5*b^3*c^4 - 3*a^6*b*c^5)*d*e + (a^2*b^10 - 8*a^3*b^8*c + 22*a^4*b^6*c^2 - 24*a^5*b^4*c^3 + 9*a^6*b^2*c^4)*e^2)/(a^14*b^2 - 4*a^15*c)) + ((a*b^10 - 10*a^2*b^8*c + 35*a^3*b^6*c^2 - 51*a^4*b^4*c^3 + 29*a^5*b^2*c^4 - 4*a^6*c^5)*d - (a^2*b^9 - 9*a^3*b^7*c + 27*a^4*b^5*c^2 - 31*a^5*b^3*c^3 + 12*a^6*b*c^4)*e)*x)*sqrt(-((b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*d - (a*b^6 - 6*a^2*b^4*c + 9*a^3*b^2*c^2 - 2*a^4*c^3)*e - (a^7*b^2 - 4*a^8*c)*sqrt(((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*d^2 - 2*(a*b^11 - 9*a^2*b^9*c + 29*a^3*b^7*c^2 - 40*a^4*b^5*c^3 + 22*a^5*b^3*c^4 - 3*a^6*b*c^5)*d*e + (a^2*b^10 - 8*a^3*b^8*c + 22*a^4*b^6*c^2 - 24*a^5*b^4*c^3 + 9*a^6*b^2*c^4)*e^2)/(a^14*b^2 - 4*a^15*c)))/(a^7*b^2 - 4*a^8*c)))/x^2) - 15*sqrt(1/2)*a^3*d^2*x^5*sqrt(-((b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*d - (a*b^6 - 6*a^2*b^4*c + 9*a^3*b^2*c^2 - 2*a^4*c^3)*e - (a^7*b^2 - 4*a^8*c)*sqrt(((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*d^2 - 2*(a*b^11 - 9*a^2*b^9*c + 29*a^3*b^7*c^2 - 40*a^4*b^5*c^3 + 22*a^5*b^3*c^4 - 3*a^6*b*c^5)*d*e + (a^2*b^10 - 8*a^3*b^8*c + 22*a^4*b^6*c^2 - 24*a^5*b^4*c^3 + 9*a^6*b^2*c^4)*e^2)/(a^14*b^2 - 4*a^15*c)))/(a^7*b^2 - 4*a^8*c))*log(-((a^7*b^2*c^3 - 4*a^8*c^4)*d*x^2*sqrt(((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*d^2 - 2*(a*b^11 - 9*a^2*b^9*c + 29*a^3*b^7*c^2 - 40*a^4*b^5*c^3 + 22*a^5*b^3*c^4 - 3*a^6*b*c^5)*d*e + (a^2*b^10 - 8*a^3*b^8*c + 22*a^4*b^6*c^2 - 24*a^5*b^4*c^3 + 9*a^6*b^2*c^4)*e^2)/(a^14*b^2 - 4*a^15*c)) + 2*(a*b^6*c^3 - 5*a^2*b^4*c^4 + 6*a^3*b^2*c^5 - a^4*c^6)*d^2 - 2*(a^2*b^5*c^3 - 4*a^3*b^3*c^4 + 3*a^4*b*c^5)*d*e - ((b^7*c^3 - 5*a*b^5*c^4 + 6*a^2*b^3*c^5 - a^3*b*c^6)*d^2 - (5*a*b^6*c^3 - 24*a^2*b^4*c^4 + 27*a^3*b^2*c^5 - 4*a^4*c^6)*d*e + 4*(a^2*b^5*c^3 - 4*a^3*b^3*c^4 + 3*a^4*b*c^5)*e^2)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((a^8*b^5 - 7*a^9*b^3*c + 12*a^10*b*c^2)*x*sqrt(((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*d^2 - 2*(a*b^11 - 9*a^2*b^9*c + 29*a^3*b^7*c^2 - 40*a^4*b^5*c^3 + 22*a^5*b^3*c^4 - 3*a^6*b*c^5)*d*e + (a^2*b^10 - 8*a^3*b^8*c + 22*a^4*b^6*c^2 - 24*a^5*b^4*c^3 + 9*a^6*b^2*c^4)*e^2)/(a^14*b^2 - 4*a^15*c)) + ((a*b^10 - 10*a^2*b^8*c + 35*a^3*b^6*c^2 - 51*a^4*b^4*c^3 + 29*a^5*b^2*c^4 - 4*a^6*c^5)*d - (a^2*b^9 - 9*a^3*b^7*c + 27*a^4*b^5*c^2 - 31*a^5*b^3*c^3 + 12*a^6*b*c^4)*e)*x)*sqrt(-((b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*d - (a*b^6 - 6*a^2*b^4*c + 9*a^3*b^2*c^2 - 2*a^4*c^3)*e - (a^7*b^2 - 4*a^8*c)*sqrt(((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*d^2 - 2*(a*b^11 - 9*a^2*b^9*c + 29*a^3*b^7*c^2 - 40*a^4*b^5*c^3 + 22*a^5*b^3*c^4 - 3*a^6*b*c^5)*d*e + (a^2*b^10 - 8*a^3*b^8*c + 22*a^4*b^6*c^2 - 24*a^5*b^4*c^3 + 9*a^6*b^2*c^4)*e^2)/(a^14*b^2 - 4*a^15*c)))/(a^7*b^2 - 4*a^8*c)))/x^2) + 15*sqrt(1/2)*a^3*d^2*x^5*sqrt(-((b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*d - (a*b^6 - 6*a^2*b^4*c + 9*a^3*b^2*c^2 - 2*a^4*c^3)*e + (a^7*b^2 - 4*a^8*c)*sqrt(((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*d^2 - 2*(a*b^11 - 9*a^2*b^9*c + 29*a^3*b^7*c^2 - 40*a^4*b^5*c^3 + 22*a^5*b^3*c^4 - 3*a^6*b*c^5)*d*e + (a^2*b^10 - 8*a^3*b^8*c + 22*a^4*b^6*c^2 - 24*a^5*b^4*c^3 + 9*a^6*b^2*c^4)*e^2)/(a^14*b^2 - 4*a^15*c)))/(a^7*b^2 - 4*a^8*c))*log(((a^7*b^2*c^3 - 4*a^8*c^4)*d*x^2*sqrt(((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*d^2 - 2*(a*b^11 - 9*a^2*b^9*c + 29*a^3*b^7*c^2 - 40*a^4*b^5*c^3 + 22*a^5*b^3*c^4 - 3*a^6*b*c^5)*d*e + (a^2*b^10 - 8*a^3*b^8*c + 22*a^4*b^6*c^2 - 24*a^5*b^4*c^3 + 9*a^6*b^2*c^4)*e^2)/(a^14*b^2 - 4*a^15*c)) - 2*(a*b^6*c^3 - 5*a^2*b^4*c^4 + 6*a^3*b^2*c^5 - a^4*c^6)*d^2 + 2*(a^2*b^5*c^3 - 4*a^3*b^3*c^4 + 3*a^4*b*c^5)*d*e + ((b^7*c^3 - 5*a*b^5*c^4 + 6*a^2*b^3*c^5 - a^3*b*c^6)*d^2 - (5*a*b^6*c^3 - 24*a^2*b^4*c^4 + 27*a^3*b^2*c^5 - 4*a^4*c^6)*d*e + 4*(a^2*b^5*c^3 - 4*a^3*b^3*c^4 + 3*a^4*b*c^5)*e^2)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((a^8*b^5 - 7*a^9*b^3*c + 12*a^10*b*c^2)*x*sqrt(((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*d^2 - 2*(a*b^11 - 9*a^2*b^9*c + 29*a^3*b^7*c^2 - 40*a^4*b^5*c^3 + 22*a^5*b^3*c^4 - 3*a^6*b*c^5)*d*e + (a^2*b^10 - 8*a^3*b^8*c + 22*a^4*b^6*c^2 - 24*a^5*b^4*c^3 + 9*a^6*b^2*c^4)*e^2)/(a^14*b^2 - 4*a^15*c)) - ((a*b^10 - 10*a^2*b^8*c + 35*a^3*b^6*c^2 - 51*a^4*b^4*c^3 + 29*a^5*b^2*c^4 - 4*a^6*c^5)*d - (a^2*b^9 - 9*a^3*b^7*c + 27*a^4*b^5*c^2 - 31*a^5*b^3*c^3 + 12*a^6*b*c^4)*e)*x)*sqrt(-((b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*d - (a*b^6 - 6*a^2*b^4*c + 9*a^3*b^2*c^2 - 2*a^4*c^3)*e + (a^7*b^2 - 4*a^8*c)*sqrt(((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*d^2 - 2*(a*b^11 - 9*a^2*b^9*c + 29*a^3*b^7*c^2 - 40*a^4*b^5*c^3 + 22*a^5*b^3*c^4 - 3*a^6*b*c^5)*d*e + (a^2*b^10 - 8*a^3*b^8*c + 22*a^4*b^6*c^2 - 24*a^5*b^4*c^3 + 9*a^6*b^2*c^4)*e^2)/(a^14*b^2 - 4*a^15*c)))/(a^7*b^2 - 4*a^8*c)))/x^2) - 15*sqrt(1/2)*a^3*d^2*x^5*sqrt(-((b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*d - (a*b^6 - 6*a^2*b^4*c + 9*a^3*b^2*c^2 - 2*a^4*c^3)*e + (a^7*b^2 - 4*a^8*c)*sqrt(((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*d^2 - 2*(a*b^11 - 9*a^2*b^9*c + 29*a^3*b^7*c^2 - 40*a^4*b^5*c^3 + 22*a^5*b^3*c^4 - 3*a^6*b*c^5)*d*e + (a^2*b^10 - 8*a^3*b^8*c + 22*a^4*b^6*c^2 - 24*a^5*b^4*c^3 + 9*a^6*b^2*c^4)*e^2)/(a^14*b^2 - 4*a^15*c)))/(a^7*b^2 - 4*a^8*c))*log(((a^7*b^2*c^3 - 4*a^8*c^4)*d*x^2*sqrt(((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*d^2 - 2*(a*b^11 - 9*a^2*b^9*c + 29*a^3*b^7*c^2 - 40*a^4*b^5*c^3 + 22*a^5*b^3*c^4 - 3*a^6*b*c^5)*d*e + (a^2*b^10 - 8*a^3*b^8*c + 22*a^4*b^6*c^2 - 24*a^5*b^4*c^3 + 9*a^6*b^2*c^4)*e^2)/(a^14*b^2 - 4*a^15*c)) - 2*(a*b^6*c^3 - 5*a^2*b^4*c^4 + 6*a^3*b^2*c^5 - a^4*c^6)*d^2 + 2*(a^2*b^5*c^3 - 4*a^3*b^3*c^4 + 3*a^4*b*c^5)*d*e + ((b^7*c^3 - 5*a*b^5*c^4 + 6*a^2*b^3*c^5 - a^3*b*c^6)*d^2 - (5*a*b^6*c^3 - 24*a^2*b^4*c^4 + 27*a^3*b^2*c^5 - 4*a^4*c^6)*d*e + 4*(a^2*b^5*c^3 - 4*a^3*b^3*c^4 + 3*a^4*b*c^5)*e^2)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((a^8*b^5 - 7*a^9*b^3*c + 12*a^10*b*c^2)*x*sqrt(((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*d^2 - 2*(a*b^11 - 9*a^2*b^9*c + 29*a^3*b^7*c^2 - 40*a^4*b^5*c^3 + 22*a^5*b^3*c^4 - 3*a^6*b*c^5)*d*e + (a^2*b^10 - 8*a^3*b^8*c + 22*a^4*b^6*c^2 - 24*a^5*b^4*c^3 + 9*a^6*b^2*c^4)*e^2)/(a^14*b^2 - 4*a^15*c)) - ((a*b^10 - 10*a^2*b^8*c + 35*a^3*b^6*c^2 - 51*a^4*b^4*c^3 + 29*a^5*b^2*c^4 - 4*a^6*c^5)*d - (a^2*b^9 - 9*a^3*b^7*c + 27*a^4*b^5*c^2 - 31*a^5*b^3*c^3 + 12*a^6*b*c^4)*e)*x)*sqrt(-((b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3)*d - (a*b^6 - 6*a^2*b^4*c + 9*a^3*b^2*c^2 - 2*a^4*c^3)*e + (a^7*b^2 - 4*a^8*c)*sqrt(((b^12 - 10*a*b^10*c + 37*a^2*b^8*c^2 - 62*a^3*b^6*c^3 + 46*a^4*b^4*c^4 - 12*a^5*b^2*c^5 + a^6*c^6)*d^2 - 2*(a*b^11 - 9*a^2*b^9*c + 29*a^3*b^7*c^2 - 40*a^4*b^5*c^3 + 22*a^5*b^3*c^4 - 3*a^6*b*c^5)*d*e + (a^2*b^10 - 8*a^3*b^8*c + 22*a^4*b^6*c^2 - 24*a^5*b^4*c^3 + 9*a^6*b^2*c^4)*e^2)/(a^14*b^2 - 4*a^15*c)))/(a^7*b^2 - 4*a^8*c)))/x^2) - 4*((5*a*b*d*e + 2*a^2*e^2 - 15*(b^2 - a*c)*d^2)*x^4 - 3*a^2*d^2 + (5*a*b*d^2 - a^2*d*e)*x^2)*sqrt(e*x^2 + d))/(a^3*d^2*x^5)","B",0
367,-1,0,0,0.000000," ","integrate(x^3*(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
368,-1,0,0,0.000000," ","integrate(x*(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
369,-1,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)/x/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
370,-1,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)/x^3/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
371,-1,0,0,0.000000," ","integrate(x^4*(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
372,-1,0,0,0.000000," ","integrate(x^2*(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
373,1,7721,0,99.050798," ","integrate((e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{1}{2}} c \sqrt{-\frac{b c^{2} d^{3} - 6 \, a c^{2} d^{2} e + 3 \, a b c d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} - {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}} \log\left(\frac{2 \, a c^{3} d^{6} - 2 \, a b c^{2} d^{5} e - 4 \, a^{2} c^{2} d^{4} e^{2} + 8 \, a^{2} b c d^{3} e^{3} + 2 \, a^{3} b d e^{5} - 2 \, {\left(a^{2} b^{2} + 3 \, a^{3} c\right)} d^{2} e^{4} + {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{3} - {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} e + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}} - {\left(b c^{3} d^{6} + 2 \, a b c^{2} d^{4} e^{2} - 4 \, a^{3} b e^{6} - {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{5} e + 4 \, {\left(a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} e^{3} - {\left(a b^{3} + 19 \, a^{2} b c\right)} d^{2} e^{4} + {\left(5 \, a^{2} b^{2} + 12 \, a^{3} c\right)} d e^{5}\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(2 \, {\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d - {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e\right)} x \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}} + {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} e - 3 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x\right)} \sqrt{-\frac{b c^{2} d^{3} - 6 \, a c^{2} d^{2} e + 3 \, a b c d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} - {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c \sqrt{-\frac{b c^{2} d^{3} - 6 \, a c^{2} d^{2} e + 3 \, a b c d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} - {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}} \log\left(\frac{2 \, a c^{3} d^{6} - 2 \, a b c^{2} d^{5} e - 4 \, a^{2} c^{2} d^{4} e^{2} + 8 \, a^{2} b c d^{3} e^{3} + 2 \, a^{3} b d e^{5} - 2 \, {\left(a^{2} b^{2} + 3 \, a^{3} c\right)} d^{2} e^{4} + {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{3} - {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} e + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}} - {\left(b c^{3} d^{6} + 2 \, a b c^{2} d^{4} e^{2} - 4 \, a^{3} b e^{6} - {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{5} e + 4 \, {\left(a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} e^{3} - {\left(a b^{3} + 19 \, a^{2} b c\right)} d^{2} e^{4} + {\left(5 \, a^{2} b^{2} + 12 \, a^{3} c\right)} d e^{5}\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(2 \, {\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d - {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e\right)} x \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}} + {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} e - 3 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x\right)} \sqrt{-\frac{b c^{2} d^{3} - 6 \, a c^{2} d^{2} e + 3 \, a b c d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} - {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c \sqrt{-\frac{b c^{2} d^{3} - 6 \, a c^{2} d^{2} e + 3 \, a b c d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}} \log\left(\frac{2 \, a c^{3} d^{6} - 2 \, a b c^{2} d^{5} e - 4 \, a^{2} c^{2} d^{4} e^{2} + 8 \, a^{2} b c d^{3} e^{3} + 2 \, a^{3} b d e^{5} - 2 \, {\left(a^{2} b^{2} + 3 \, a^{3} c\right)} d^{2} e^{4} - {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{3} - {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} e + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}} - {\left(b c^{3} d^{6} + 2 \, a b c^{2} d^{4} e^{2} - 4 \, a^{3} b e^{6} - {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{5} e + 4 \, {\left(a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} e^{3} - {\left(a b^{3} + 19 \, a^{2} b c\right)} d^{2} e^{4} + {\left(5 \, a^{2} b^{2} + 12 \, a^{3} c\right)} d e^{5}\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(2 \, {\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d - {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e\right)} x \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}} - {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} e - 3 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x\right)} \sqrt{-\frac{b c^{2} d^{3} - 6 \, a c^{2} d^{2} e + 3 \, a b c d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}}}{x^{2}}\right) + \sqrt{\frac{1}{2}} c \sqrt{-\frac{b c^{2} d^{3} - 6 \, a c^{2} d^{2} e + 3 \, a b c d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}} \log\left(\frac{2 \, a c^{3} d^{6} - 2 \, a b c^{2} d^{5} e - 4 \, a^{2} c^{2} d^{4} e^{2} + 8 \, a^{2} b c d^{3} e^{3} + 2 \, a^{3} b d e^{5} - 2 \, {\left(a^{2} b^{2} + 3 \, a^{3} c\right)} d^{2} e^{4} - {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{3} - {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} e + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}} - {\left(b c^{3} d^{6} + 2 \, a b c^{2} d^{4} e^{2} - 4 \, a^{3} b e^{6} - {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{5} e + 4 \, {\left(a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} e^{3} - {\left(a b^{3} + 19 \, a^{2} b c\right)} d^{2} e^{4} + {\left(5 \, a^{2} b^{2} + 12 \, a^{3} c\right)} d e^{5}\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(2 \, {\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d - {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e\right)} x \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}} - {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} e - 3 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x\right)} \sqrt{-\frac{b c^{2} d^{3} - 6 \, a c^{2} d^{2} e + 3 \, a b c d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}}}{x^{2}}\right) + 2 \, e^{\frac{3}{2}} \log\left(-2 \, e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right)}{4 \, c}, \frac{\sqrt{\frac{1}{2}} c \sqrt{-\frac{b c^{2} d^{3} - 6 \, a c^{2} d^{2} e + 3 \, a b c d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} - {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}} \log\left(\frac{2 \, a c^{3} d^{6} - 2 \, a b c^{2} d^{5} e - 4 \, a^{2} c^{2} d^{4} e^{2} + 8 \, a^{2} b c d^{3} e^{3} + 2 \, a^{3} b d e^{5} - 2 \, {\left(a^{2} b^{2} + 3 \, a^{3} c\right)} d^{2} e^{4} + {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{3} - {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} e + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}} - {\left(b c^{3} d^{6} + 2 \, a b c^{2} d^{4} e^{2} - 4 \, a^{3} b e^{6} - {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{5} e + 4 \, {\left(a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} e^{3} - {\left(a b^{3} + 19 \, a^{2} b c\right)} d^{2} e^{4} + {\left(5 \, a^{2} b^{2} + 12 \, a^{3} c\right)} d e^{5}\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(2 \, {\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d - {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e\right)} x \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}} + {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} e - 3 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x\right)} \sqrt{-\frac{b c^{2} d^{3} - 6 \, a c^{2} d^{2} e + 3 \, a b c d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} - {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c \sqrt{-\frac{b c^{2} d^{3} - 6 \, a c^{2} d^{2} e + 3 \, a b c d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} - {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}} \log\left(\frac{2 \, a c^{3} d^{6} - 2 \, a b c^{2} d^{5} e - 4 \, a^{2} c^{2} d^{4} e^{2} + 8 \, a^{2} b c d^{3} e^{3} + 2 \, a^{3} b d e^{5} - 2 \, {\left(a^{2} b^{2} + 3 \, a^{3} c\right)} d^{2} e^{4} + {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{3} - {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} e + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}} - {\left(b c^{3} d^{6} + 2 \, a b c^{2} d^{4} e^{2} - 4 \, a^{3} b e^{6} - {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{5} e + 4 \, {\left(a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} e^{3} - {\left(a b^{3} + 19 \, a^{2} b c\right)} d^{2} e^{4} + {\left(5 \, a^{2} b^{2} + 12 \, a^{3} c\right)} d e^{5}\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(2 \, {\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d - {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e\right)} x \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}} + {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} e - 3 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x\right)} \sqrt{-\frac{b c^{2} d^{3} - 6 \, a c^{2} d^{2} e + 3 \, a b c d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} - {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c \sqrt{-\frac{b c^{2} d^{3} - 6 \, a c^{2} d^{2} e + 3 \, a b c d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}} \log\left(\frac{2 \, a c^{3} d^{6} - 2 \, a b c^{2} d^{5} e - 4 \, a^{2} c^{2} d^{4} e^{2} + 8 \, a^{2} b c d^{3} e^{3} + 2 \, a^{3} b d e^{5} - 2 \, {\left(a^{2} b^{2} + 3 \, a^{3} c\right)} d^{2} e^{4} - {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{3} - {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} e + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}} - {\left(b c^{3} d^{6} + 2 \, a b c^{2} d^{4} e^{2} - 4 \, a^{3} b e^{6} - {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{5} e + 4 \, {\left(a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} e^{3} - {\left(a b^{3} + 19 \, a^{2} b c\right)} d^{2} e^{4} + {\left(5 \, a^{2} b^{2} + 12 \, a^{3} c\right)} d e^{5}\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(2 \, {\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d - {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e\right)} x \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}} - {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} e - 3 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x\right)} \sqrt{-\frac{b c^{2} d^{3} - 6 \, a c^{2} d^{2} e + 3 \, a b c d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}}}{x^{2}}\right) + \sqrt{\frac{1}{2}} c \sqrt{-\frac{b c^{2} d^{3} - 6 \, a c^{2} d^{2} e + 3 \, a b c d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}} \log\left(\frac{2 \, a c^{3} d^{6} - 2 \, a b c^{2} d^{5} e - 4 \, a^{2} c^{2} d^{4} e^{2} + 8 \, a^{2} b c d^{3} e^{3} + 2 \, a^{3} b d e^{5} - 2 \, {\left(a^{2} b^{2} + 3 \, a^{3} c\right)} d^{2} e^{4} - {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{3} - {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} e + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}} - {\left(b c^{3} d^{6} + 2 \, a b c^{2} d^{4} e^{2} - 4 \, a^{3} b e^{6} - {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{5} e + 4 \, {\left(a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} e^{3} - {\left(a b^{3} + 19 \, a^{2} b c\right)} d^{2} e^{4} + {\left(5 \, a^{2} b^{2} + 12 \, a^{3} c\right)} d e^{5}\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(2 \, {\left(a^{2} b^{2} c^{3} - 4 \, a^{3} c^{4}\right)} d - {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e\right)} x \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}} - {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} e - 3 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x\right)} \sqrt{-\frac{b c^{2} d^{3} - 6 \, a c^{2} d^{2} e + 3 \, a b c d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + 2 \, a b c^{2} d^{3} e^{3} + 9 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a^{2} b c d e^{5} + a^{2} b^{2} e^{6}}{a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}}}{x^{2}}\right) - 4 \, \sqrt{-e} e \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{4 \, c}\right]"," ",0,"[1/4*(sqrt(1/2)*c*sqrt(-(b*c^2*d^3 - 6*a*c^2*d^2*e + 3*a*b*c*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 - (a*b^2*c^2 - 4*a^2*c^3)*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)))/(a*b^2*c^2 - 4*a^2*c^3))*log((2*a*c^3*d^6 - 2*a*b*c^2*d^5*e - 4*a^2*c^2*d^4*e^2 + 8*a^2*b*c*d^3*e^3 + 2*a^3*b*d*e^5 - 2*(a^2*b^2 + 3*a^3*c)*d^2*e^4 + ((a*b^2*c^3 - 4*a^2*c^4)*d^3 - (a*b^3*c^2 - 4*a^2*b*c^3)*d^2*e + (a^2*b^2*c^2 - 4*a^3*c^3)*d*e^2)*x^2*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)) - (b*c^3*d^6 + 2*a*b*c^2*d^4*e^2 - 4*a^3*b*e^6 - (b^2*c^2 + 4*a*c^3)*d^5*e + 4*(a*b^2*c + 2*a^2*c^2)*d^3*e^3 - (a*b^3 + 19*a^2*b*c)*d^2*e^4 + (5*a^2*b^2 + 12*a^3*c)*d*e^5)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((2*(a^2*b^2*c^3 - 4*a^3*c^4)*d - (a^2*b^3*c^2 - 4*a^3*b*c^3)*e)*x*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)) + ((a*b^2*c^2 - 4*a^2*c^3)*d^3*e - 3*(a^2*b^2*c - 4*a^3*c^2)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x)*sqrt(-(b*c^2*d^3 - 6*a*c^2*d^2*e + 3*a*b*c*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 - (a*b^2*c^2 - 4*a^2*c^3)*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)))/(a*b^2*c^2 - 4*a^2*c^3)))/x^2) - sqrt(1/2)*c*sqrt(-(b*c^2*d^3 - 6*a*c^2*d^2*e + 3*a*b*c*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 - (a*b^2*c^2 - 4*a^2*c^3)*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)))/(a*b^2*c^2 - 4*a^2*c^3))*log((2*a*c^3*d^6 - 2*a*b*c^2*d^5*e - 4*a^2*c^2*d^4*e^2 + 8*a^2*b*c*d^3*e^3 + 2*a^3*b*d*e^5 - 2*(a^2*b^2 + 3*a^3*c)*d^2*e^4 + ((a*b^2*c^3 - 4*a^2*c^4)*d^3 - (a*b^3*c^2 - 4*a^2*b*c^3)*d^2*e + (a^2*b^2*c^2 - 4*a^3*c^3)*d*e^2)*x^2*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)) - (b*c^3*d^6 + 2*a*b*c^2*d^4*e^2 - 4*a^3*b*e^6 - (b^2*c^2 + 4*a*c^3)*d^5*e + 4*(a*b^2*c + 2*a^2*c^2)*d^3*e^3 - (a*b^3 + 19*a^2*b*c)*d^2*e^4 + (5*a^2*b^2 + 12*a^3*c)*d*e^5)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((2*(a^2*b^2*c^3 - 4*a^3*c^4)*d - (a^2*b^3*c^2 - 4*a^3*b*c^3)*e)*x*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)) + ((a*b^2*c^2 - 4*a^2*c^3)*d^3*e - 3*(a^2*b^2*c - 4*a^3*c^2)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x)*sqrt(-(b*c^2*d^3 - 6*a*c^2*d^2*e + 3*a*b*c*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 - (a*b^2*c^2 - 4*a^2*c^3)*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)))/(a*b^2*c^2 - 4*a^2*c^3)))/x^2) - sqrt(1/2)*c*sqrt(-(b*c^2*d^3 - 6*a*c^2*d^2*e + 3*a*b*c*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 + (a*b^2*c^2 - 4*a^2*c^3)*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)))/(a*b^2*c^2 - 4*a^2*c^3))*log((2*a*c^3*d^6 - 2*a*b*c^2*d^5*e - 4*a^2*c^2*d^4*e^2 + 8*a^2*b*c*d^3*e^3 + 2*a^3*b*d*e^5 - 2*(a^2*b^2 + 3*a^3*c)*d^2*e^4 - ((a*b^2*c^3 - 4*a^2*c^4)*d^3 - (a*b^3*c^2 - 4*a^2*b*c^3)*d^2*e + (a^2*b^2*c^2 - 4*a^3*c^3)*d*e^2)*x^2*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)) - (b*c^3*d^6 + 2*a*b*c^2*d^4*e^2 - 4*a^3*b*e^6 - (b^2*c^2 + 4*a*c^3)*d^5*e + 4*(a*b^2*c + 2*a^2*c^2)*d^3*e^3 - (a*b^3 + 19*a^2*b*c)*d^2*e^4 + (5*a^2*b^2 + 12*a^3*c)*d*e^5)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((2*(a^2*b^2*c^3 - 4*a^3*c^4)*d - (a^2*b^3*c^2 - 4*a^3*b*c^3)*e)*x*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)) - ((a*b^2*c^2 - 4*a^2*c^3)*d^3*e - 3*(a^2*b^2*c - 4*a^3*c^2)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x)*sqrt(-(b*c^2*d^3 - 6*a*c^2*d^2*e + 3*a*b*c*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 + (a*b^2*c^2 - 4*a^2*c^3)*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)))/(a*b^2*c^2 - 4*a^2*c^3)))/x^2) + sqrt(1/2)*c*sqrt(-(b*c^2*d^3 - 6*a*c^2*d^2*e + 3*a*b*c*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 + (a*b^2*c^2 - 4*a^2*c^3)*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)))/(a*b^2*c^2 - 4*a^2*c^3))*log((2*a*c^3*d^6 - 2*a*b*c^2*d^5*e - 4*a^2*c^2*d^4*e^2 + 8*a^2*b*c*d^3*e^3 + 2*a^3*b*d*e^5 - 2*(a^2*b^2 + 3*a^3*c)*d^2*e^4 - ((a*b^2*c^3 - 4*a^2*c^4)*d^3 - (a*b^3*c^2 - 4*a^2*b*c^3)*d^2*e + (a^2*b^2*c^2 - 4*a^3*c^3)*d*e^2)*x^2*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)) - (b*c^3*d^6 + 2*a*b*c^2*d^4*e^2 - 4*a^3*b*e^6 - (b^2*c^2 + 4*a*c^3)*d^5*e + 4*(a*b^2*c + 2*a^2*c^2)*d^3*e^3 - (a*b^3 + 19*a^2*b*c)*d^2*e^4 + (5*a^2*b^2 + 12*a^3*c)*d*e^5)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((2*(a^2*b^2*c^3 - 4*a^3*c^4)*d - (a^2*b^3*c^2 - 4*a^3*b*c^3)*e)*x*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)) - ((a*b^2*c^2 - 4*a^2*c^3)*d^3*e - 3*(a^2*b^2*c - 4*a^3*c^2)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x)*sqrt(-(b*c^2*d^3 - 6*a*c^2*d^2*e + 3*a*b*c*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 + (a*b^2*c^2 - 4*a^2*c^3)*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)))/(a*b^2*c^2 - 4*a^2*c^3)))/x^2) + 2*e^(3/2)*log(-2*e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(e)*x - d))/c, 1/4*(sqrt(1/2)*c*sqrt(-(b*c^2*d^3 - 6*a*c^2*d^2*e + 3*a*b*c*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 - (a*b^2*c^2 - 4*a^2*c^3)*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)))/(a*b^2*c^2 - 4*a^2*c^3))*log((2*a*c^3*d^6 - 2*a*b*c^2*d^5*e - 4*a^2*c^2*d^4*e^2 + 8*a^2*b*c*d^3*e^3 + 2*a^3*b*d*e^5 - 2*(a^2*b^2 + 3*a^3*c)*d^2*e^4 + ((a*b^2*c^3 - 4*a^2*c^4)*d^3 - (a*b^3*c^2 - 4*a^2*b*c^3)*d^2*e + (a^2*b^2*c^2 - 4*a^3*c^3)*d*e^2)*x^2*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)) - (b*c^3*d^6 + 2*a*b*c^2*d^4*e^2 - 4*a^3*b*e^6 - (b^2*c^2 + 4*a*c^3)*d^5*e + 4*(a*b^2*c + 2*a^2*c^2)*d^3*e^3 - (a*b^3 + 19*a^2*b*c)*d^2*e^4 + (5*a^2*b^2 + 12*a^3*c)*d*e^5)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((2*(a^2*b^2*c^3 - 4*a^3*c^4)*d - (a^2*b^3*c^2 - 4*a^3*b*c^3)*e)*x*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)) + ((a*b^2*c^2 - 4*a^2*c^3)*d^3*e - 3*(a^2*b^2*c - 4*a^3*c^2)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x)*sqrt(-(b*c^2*d^3 - 6*a*c^2*d^2*e + 3*a*b*c*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 - (a*b^2*c^2 - 4*a^2*c^3)*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)))/(a*b^2*c^2 - 4*a^2*c^3)))/x^2) - sqrt(1/2)*c*sqrt(-(b*c^2*d^3 - 6*a*c^2*d^2*e + 3*a*b*c*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 - (a*b^2*c^2 - 4*a^2*c^3)*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)))/(a*b^2*c^2 - 4*a^2*c^3))*log((2*a*c^3*d^6 - 2*a*b*c^2*d^5*e - 4*a^2*c^2*d^4*e^2 + 8*a^2*b*c*d^3*e^3 + 2*a^3*b*d*e^5 - 2*(a^2*b^2 + 3*a^3*c)*d^2*e^4 + ((a*b^2*c^3 - 4*a^2*c^4)*d^3 - (a*b^3*c^2 - 4*a^2*b*c^3)*d^2*e + (a^2*b^2*c^2 - 4*a^3*c^3)*d*e^2)*x^2*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)) - (b*c^3*d^6 + 2*a*b*c^2*d^4*e^2 - 4*a^3*b*e^6 - (b^2*c^2 + 4*a*c^3)*d^5*e + 4*(a*b^2*c + 2*a^2*c^2)*d^3*e^3 - (a*b^3 + 19*a^2*b*c)*d^2*e^4 + (5*a^2*b^2 + 12*a^3*c)*d*e^5)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((2*(a^2*b^2*c^3 - 4*a^3*c^4)*d - (a^2*b^3*c^2 - 4*a^3*b*c^3)*e)*x*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)) + ((a*b^2*c^2 - 4*a^2*c^3)*d^3*e - 3*(a^2*b^2*c - 4*a^3*c^2)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x)*sqrt(-(b*c^2*d^3 - 6*a*c^2*d^2*e + 3*a*b*c*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 - (a*b^2*c^2 - 4*a^2*c^3)*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)))/(a*b^2*c^2 - 4*a^2*c^3)))/x^2) - sqrt(1/2)*c*sqrt(-(b*c^2*d^3 - 6*a*c^2*d^2*e + 3*a*b*c*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 + (a*b^2*c^2 - 4*a^2*c^3)*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)))/(a*b^2*c^2 - 4*a^2*c^3))*log((2*a*c^3*d^6 - 2*a*b*c^2*d^5*e - 4*a^2*c^2*d^4*e^2 + 8*a^2*b*c*d^3*e^3 + 2*a^3*b*d*e^5 - 2*(a^2*b^2 + 3*a^3*c)*d^2*e^4 - ((a*b^2*c^3 - 4*a^2*c^4)*d^3 - (a*b^3*c^2 - 4*a^2*b*c^3)*d^2*e + (a^2*b^2*c^2 - 4*a^3*c^3)*d*e^2)*x^2*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)) - (b*c^3*d^6 + 2*a*b*c^2*d^4*e^2 - 4*a^3*b*e^6 - (b^2*c^2 + 4*a*c^3)*d^5*e + 4*(a*b^2*c + 2*a^2*c^2)*d^3*e^3 - (a*b^3 + 19*a^2*b*c)*d^2*e^4 + (5*a^2*b^2 + 12*a^3*c)*d*e^5)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((2*(a^2*b^2*c^3 - 4*a^3*c^4)*d - (a^2*b^3*c^2 - 4*a^3*b*c^3)*e)*x*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)) - ((a*b^2*c^2 - 4*a^2*c^3)*d^3*e - 3*(a^2*b^2*c - 4*a^3*c^2)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x)*sqrt(-(b*c^2*d^3 - 6*a*c^2*d^2*e + 3*a*b*c*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 + (a*b^2*c^2 - 4*a^2*c^3)*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)))/(a*b^2*c^2 - 4*a^2*c^3)))/x^2) + sqrt(1/2)*c*sqrt(-(b*c^2*d^3 - 6*a*c^2*d^2*e + 3*a*b*c*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 + (a*b^2*c^2 - 4*a^2*c^3)*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)))/(a*b^2*c^2 - 4*a^2*c^3))*log((2*a*c^3*d^6 - 2*a*b*c^2*d^5*e - 4*a^2*c^2*d^4*e^2 + 8*a^2*b*c*d^3*e^3 + 2*a^3*b*d*e^5 - 2*(a^2*b^2 + 3*a^3*c)*d^2*e^4 - ((a*b^2*c^3 - 4*a^2*c^4)*d^3 - (a*b^3*c^2 - 4*a^2*b*c^3)*d^2*e + (a^2*b^2*c^2 - 4*a^3*c^3)*d*e^2)*x^2*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)) - (b*c^3*d^6 + 2*a*b*c^2*d^4*e^2 - 4*a^3*b*e^6 - (b^2*c^2 + 4*a*c^3)*d^5*e + 4*(a*b^2*c + 2*a^2*c^2)*d^3*e^3 - (a*b^3 + 19*a^2*b*c)*d^2*e^4 + (5*a^2*b^2 + 12*a^3*c)*d*e^5)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((2*(a^2*b^2*c^3 - 4*a^3*c^4)*d - (a^2*b^3*c^2 - 4*a^3*b*c^3)*e)*x*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)) - ((a*b^2*c^2 - 4*a^2*c^3)*d^3*e - 3*(a^2*b^2*c - 4*a^3*c^2)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x)*sqrt(-(b*c^2*d^3 - 6*a*c^2*d^2*e + 3*a*b*c*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 + (a*b^2*c^2 - 4*a^2*c^3)*sqrt((c^4*d^6 - 6*a*c^3*d^4*e^2 + 2*a*b*c^2*d^3*e^3 + 9*a^2*c^2*d^2*e^4 - 6*a^2*b*c*d*e^5 + a^2*b^2*e^6)/(a^2*b^2*c^4 - 4*a^3*c^5)))/(a*b^2*c^2 - 4*a^2*c^3)))/x^2) - 4*sqrt(-e)*e*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)))/c]","B",0
374,1,4059,0,37.774121," ","integrate((e*x^2+d)^(3/2)/x^2/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} a x \sqrt{-\frac{3 \, a^{2} b d e^{2} - 2 \, a^{3} e^{3} + {\left(b^{3} - 3 \, a b c\right)} d^{3} - 3 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{2} e + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-\frac{18 \, a^{3} b d^{3} e^{3} - 9 \, a^{4} d^{2} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{3} - a^{2} b c\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(-\frac{12 \, a^{3} b d^{3} e^{3} - 6 \, a^{4} d^{2} e^{4} - 2 \, {\left(a b^{2} c - a^{2} c^{2}\right)} d^{6} + 2 \, {\left(a b^{3} + 2 \, a^{2} b c\right)} d^{5} e - 4 \, {\left(2 \, a^{2} b^{2} + a^{3} c\right)} d^{4} e^{2} + {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{3} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2} e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d e^{2}\right)} x^{2} \sqrt{-\frac{18 \, a^{3} b d^{3} e^{3} - 9 \, a^{4} d^{2} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{3} - a^{2} b c\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}} + {\left(27 \, a^{3} b d^{2} e^{4} - 12 \, a^{4} d e^{5} + {\left(b^{3} c - a b c^{2}\right)} d^{6} - {\left(b^{4} + 6 \, a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{5} e + 2 \, {\left(4 \, a b^{3} + 5 \, a^{2} b c\right)} d^{4} e^{2} - 2 \, {\left(11 \, a^{2} b^{2} + 4 \, a^{3} c\right)} d^{3} e^{3}\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left({\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d - 2 \, {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e\right)} x \sqrt{-\frac{18 \, a^{3} b d^{3} e^{3} - 9 \, a^{4} d^{2} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{3} - a^{2} b c\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}} - {\left({\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{3} e + 3 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{-\frac{3 \, a^{2} b d e^{2} - 2 \, a^{3} e^{3} + {\left(b^{3} - 3 \, a b c\right)} d^{3} - 3 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{2} e + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-\frac{18 \, a^{3} b d^{3} e^{3} - 9 \, a^{4} d^{2} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{3} - a^{2} b c\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} a x \sqrt{-\frac{3 \, a^{2} b d e^{2} - 2 \, a^{3} e^{3} + {\left(b^{3} - 3 \, a b c\right)} d^{3} - 3 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{2} e + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-\frac{18 \, a^{3} b d^{3} e^{3} - 9 \, a^{4} d^{2} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{3} - a^{2} b c\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(-\frac{12 \, a^{3} b d^{3} e^{3} - 6 \, a^{4} d^{2} e^{4} - 2 \, {\left(a b^{2} c - a^{2} c^{2}\right)} d^{6} + 2 \, {\left(a b^{3} + 2 \, a^{2} b c\right)} d^{5} e - 4 \, {\left(2 \, a^{2} b^{2} + a^{3} c\right)} d^{4} e^{2} + {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{3} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2} e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d e^{2}\right)} x^{2} \sqrt{-\frac{18 \, a^{3} b d^{3} e^{3} - 9 \, a^{4} d^{2} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{3} - a^{2} b c\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}} + {\left(27 \, a^{3} b d^{2} e^{4} - 12 \, a^{4} d e^{5} + {\left(b^{3} c - a b c^{2}\right)} d^{6} - {\left(b^{4} + 6 \, a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{5} e + 2 \, {\left(4 \, a b^{3} + 5 \, a^{2} b c\right)} d^{4} e^{2} - 2 \, {\left(11 \, a^{2} b^{2} + 4 \, a^{3} c\right)} d^{3} e^{3}\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left({\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d - 2 \, {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e\right)} x \sqrt{-\frac{18 \, a^{3} b d^{3} e^{3} - 9 \, a^{4} d^{2} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{3} - a^{2} b c\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}} - {\left({\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{3} e + 3 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{-\frac{3 \, a^{2} b d e^{2} - 2 \, a^{3} e^{3} + {\left(b^{3} - 3 \, a b c\right)} d^{3} - 3 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{2} e + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-\frac{18 \, a^{3} b d^{3} e^{3} - 9 \, a^{4} d^{2} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{3} - a^{2} b c\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} a x \sqrt{-\frac{3 \, a^{2} b d e^{2} - 2 \, a^{3} e^{3} + {\left(b^{3} - 3 \, a b c\right)} d^{3} - 3 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{2} e - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-\frac{18 \, a^{3} b d^{3} e^{3} - 9 \, a^{4} d^{2} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{3} - a^{2} b c\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(-\frac{12 \, a^{3} b d^{3} e^{3} - 6 \, a^{4} d^{2} e^{4} - 2 \, {\left(a b^{2} c - a^{2} c^{2}\right)} d^{6} + 2 \, {\left(a b^{3} + 2 \, a^{2} b c\right)} d^{5} e - 4 \, {\left(2 \, a^{2} b^{2} + a^{3} c\right)} d^{4} e^{2} - {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{3} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2} e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d e^{2}\right)} x^{2} \sqrt{-\frac{18 \, a^{3} b d^{3} e^{3} - 9 \, a^{4} d^{2} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{3} - a^{2} b c\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}} + {\left(27 \, a^{3} b d^{2} e^{4} - 12 \, a^{4} d e^{5} + {\left(b^{3} c - a b c^{2}\right)} d^{6} - {\left(b^{4} + 6 \, a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{5} e + 2 \, {\left(4 \, a b^{3} + 5 \, a^{2} b c\right)} d^{4} e^{2} - 2 \, {\left(11 \, a^{2} b^{2} + 4 \, a^{3} c\right)} d^{3} e^{3}\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left({\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d - 2 \, {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e\right)} x \sqrt{-\frac{18 \, a^{3} b d^{3} e^{3} - 9 \, a^{4} d^{2} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{3} - a^{2} b c\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}} + {\left({\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{3} e + 3 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{-\frac{3 \, a^{2} b d e^{2} - 2 \, a^{3} e^{3} + {\left(b^{3} - 3 \, a b c\right)} d^{3} - 3 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{2} e - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-\frac{18 \, a^{3} b d^{3} e^{3} - 9 \, a^{4} d^{2} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{3} - a^{2} b c\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}}{x^{2}}\right) + \sqrt{\frac{1}{2}} a x \sqrt{-\frac{3 \, a^{2} b d e^{2} - 2 \, a^{3} e^{3} + {\left(b^{3} - 3 \, a b c\right)} d^{3} - 3 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{2} e - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-\frac{18 \, a^{3} b d^{3} e^{3} - 9 \, a^{4} d^{2} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{3} - a^{2} b c\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(-\frac{12 \, a^{3} b d^{3} e^{3} - 6 \, a^{4} d^{2} e^{4} - 2 \, {\left(a b^{2} c - a^{2} c^{2}\right)} d^{6} + 2 \, {\left(a b^{3} + 2 \, a^{2} b c\right)} d^{5} e - 4 \, {\left(2 \, a^{2} b^{2} + a^{3} c\right)} d^{4} e^{2} - {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{3} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2} e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d e^{2}\right)} x^{2} \sqrt{-\frac{18 \, a^{3} b d^{3} e^{3} - 9 \, a^{4} d^{2} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{3} - a^{2} b c\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}} + {\left(27 \, a^{3} b d^{2} e^{4} - 12 \, a^{4} d e^{5} + {\left(b^{3} c - a b c^{2}\right)} d^{6} - {\left(b^{4} + 6 \, a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{5} e + 2 \, {\left(4 \, a b^{3} + 5 \, a^{2} b c\right)} d^{4} e^{2} - 2 \, {\left(11 \, a^{2} b^{2} + 4 \, a^{3} c\right)} d^{3} e^{3}\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left({\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d - 2 \, {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e\right)} x \sqrt{-\frac{18 \, a^{3} b d^{3} e^{3} - 9 \, a^{4} d^{2} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{3} - a^{2} b c\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}} + {\left({\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{3} e + 3 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{-\frac{3 \, a^{2} b d e^{2} - 2 \, a^{3} e^{3} + {\left(b^{3} - 3 \, a b c\right)} d^{3} - 3 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{2} e - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-\frac{18 \, a^{3} b d^{3} e^{3} - 9 \, a^{4} d^{2} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{6} + 6 \, {\left(a b^{3} - a^{2} b c\right)} d^{5} e - 3 \, {\left(5 \, a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}}{x^{2}}\right) + 4 \, \sqrt{e x^{2} + d} d}{4 \, a x}"," ",0,"-1/4*(sqrt(1/2)*a*x*sqrt(-(3*a^2*b*d*e^2 - 2*a^3*e^3 + (b^3 - 3*a*b*c)*d^3 - 3*(a*b^2 - 2*a^2*c)*d^2*e + (a^3*b^2 - 4*a^4*c)*sqrt(-(18*a^3*b*d^3*e^3 - 9*a^4*d^2*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^6 + 6*(a*b^3 - a^2*b*c)*d^5*e - 3*(5*a^2*b^2 - 2*a^3*c)*d^4*e^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log(-(12*a^3*b*d^3*e^3 - 6*a^4*d^2*e^4 - 2*(a*b^2*c - a^2*c^2)*d^6 + 2*(a*b^3 + 2*a^2*b*c)*d^5*e - 4*(2*a^2*b^2 + a^3*c)*d^4*e^2 + ((a^3*b^2*c - 4*a^4*c^2)*d^3 - (a^3*b^3 - 4*a^4*b*c)*d^2*e + (a^4*b^2 - 4*a^5*c)*d*e^2)*x^2*sqrt(-(18*a^3*b*d^3*e^3 - 9*a^4*d^2*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^6 + 6*(a*b^3 - a^2*b*c)*d^5*e - 3*(5*a^2*b^2 - 2*a^3*c)*d^4*e^2)/(a^6*b^2 - 4*a^7*c)) + (27*a^3*b*d^2*e^4 - 12*a^4*d*e^5 + (b^3*c - a*b*c^2)*d^6 - (b^4 + 6*a*b^2*c - 4*a^2*c^2)*d^5*e + 2*(4*a*b^3 + 5*a^2*b*c)*d^4*e^2 - 2*(11*a^2*b^2 + 4*a^3*c)*d^3*e^3)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*(((a^4*b^3 - 4*a^5*b*c)*d - 2*(a^5*b^2 - 4*a^6*c)*e)*x*sqrt(-(18*a^3*b*d^3*e^3 - 9*a^4*d^2*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^6 + 6*(a*b^3 - a^2*b*c)*d^5*e - 3*(5*a^2*b^2 - 2*a^3*c)*d^4*e^2)/(a^6*b^2 - 4*a^7*c)) - ((a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*d^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d^3*e + 3*(a^3*b^2 - 4*a^4*c)*d^2*e^2)*x)*sqrt(-(3*a^2*b*d*e^2 - 2*a^3*e^3 + (b^3 - 3*a*b*c)*d^3 - 3*(a*b^2 - 2*a^2*c)*d^2*e + (a^3*b^2 - 4*a^4*c)*sqrt(-(18*a^3*b*d^3*e^3 - 9*a^4*d^2*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^6 + 6*(a*b^3 - a^2*b*c)*d^5*e - 3*(5*a^2*b^2 - 2*a^3*c)*d^4*e^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c)))/x^2) - sqrt(1/2)*a*x*sqrt(-(3*a^2*b*d*e^2 - 2*a^3*e^3 + (b^3 - 3*a*b*c)*d^3 - 3*(a*b^2 - 2*a^2*c)*d^2*e + (a^3*b^2 - 4*a^4*c)*sqrt(-(18*a^3*b*d^3*e^3 - 9*a^4*d^2*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^6 + 6*(a*b^3 - a^2*b*c)*d^5*e - 3*(5*a^2*b^2 - 2*a^3*c)*d^4*e^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log(-(12*a^3*b*d^3*e^3 - 6*a^4*d^2*e^4 - 2*(a*b^2*c - a^2*c^2)*d^6 + 2*(a*b^3 + 2*a^2*b*c)*d^5*e - 4*(2*a^2*b^2 + a^3*c)*d^4*e^2 + ((a^3*b^2*c - 4*a^4*c^2)*d^3 - (a^3*b^3 - 4*a^4*b*c)*d^2*e + (a^4*b^2 - 4*a^5*c)*d*e^2)*x^2*sqrt(-(18*a^3*b*d^3*e^3 - 9*a^4*d^2*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^6 + 6*(a*b^3 - a^2*b*c)*d^5*e - 3*(5*a^2*b^2 - 2*a^3*c)*d^4*e^2)/(a^6*b^2 - 4*a^7*c)) + (27*a^3*b*d^2*e^4 - 12*a^4*d*e^5 + (b^3*c - a*b*c^2)*d^6 - (b^4 + 6*a*b^2*c - 4*a^2*c^2)*d^5*e + 2*(4*a*b^3 + 5*a^2*b*c)*d^4*e^2 - 2*(11*a^2*b^2 + 4*a^3*c)*d^3*e^3)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*(((a^4*b^3 - 4*a^5*b*c)*d - 2*(a^5*b^2 - 4*a^6*c)*e)*x*sqrt(-(18*a^3*b*d^3*e^3 - 9*a^4*d^2*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^6 + 6*(a*b^3 - a^2*b*c)*d^5*e - 3*(5*a^2*b^2 - 2*a^3*c)*d^4*e^2)/(a^6*b^2 - 4*a^7*c)) - ((a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*d^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d^3*e + 3*(a^3*b^2 - 4*a^4*c)*d^2*e^2)*x)*sqrt(-(3*a^2*b*d*e^2 - 2*a^3*e^3 + (b^3 - 3*a*b*c)*d^3 - 3*(a*b^2 - 2*a^2*c)*d^2*e + (a^3*b^2 - 4*a^4*c)*sqrt(-(18*a^3*b*d^3*e^3 - 9*a^4*d^2*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^6 + 6*(a*b^3 - a^2*b*c)*d^5*e - 3*(5*a^2*b^2 - 2*a^3*c)*d^4*e^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c)))/x^2) - sqrt(1/2)*a*x*sqrt(-(3*a^2*b*d*e^2 - 2*a^3*e^3 + (b^3 - 3*a*b*c)*d^3 - 3*(a*b^2 - 2*a^2*c)*d^2*e - (a^3*b^2 - 4*a^4*c)*sqrt(-(18*a^3*b*d^3*e^3 - 9*a^4*d^2*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^6 + 6*(a*b^3 - a^2*b*c)*d^5*e - 3*(5*a^2*b^2 - 2*a^3*c)*d^4*e^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log(-(12*a^3*b*d^3*e^3 - 6*a^4*d^2*e^4 - 2*(a*b^2*c - a^2*c^2)*d^6 + 2*(a*b^3 + 2*a^2*b*c)*d^5*e - 4*(2*a^2*b^2 + a^3*c)*d^4*e^2 - ((a^3*b^2*c - 4*a^4*c^2)*d^3 - (a^3*b^3 - 4*a^4*b*c)*d^2*e + (a^4*b^2 - 4*a^5*c)*d*e^2)*x^2*sqrt(-(18*a^3*b*d^3*e^3 - 9*a^4*d^2*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^6 + 6*(a*b^3 - a^2*b*c)*d^5*e - 3*(5*a^2*b^2 - 2*a^3*c)*d^4*e^2)/(a^6*b^2 - 4*a^7*c)) + (27*a^3*b*d^2*e^4 - 12*a^4*d*e^5 + (b^3*c - a*b*c^2)*d^6 - (b^4 + 6*a*b^2*c - 4*a^2*c^2)*d^5*e + 2*(4*a*b^3 + 5*a^2*b*c)*d^4*e^2 - 2*(11*a^2*b^2 + 4*a^3*c)*d^3*e^3)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*(((a^4*b^3 - 4*a^5*b*c)*d - 2*(a^5*b^2 - 4*a^6*c)*e)*x*sqrt(-(18*a^3*b*d^3*e^3 - 9*a^4*d^2*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^6 + 6*(a*b^3 - a^2*b*c)*d^5*e - 3*(5*a^2*b^2 - 2*a^3*c)*d^4*e^2)/(a^6*b^2 - 4*a^7*c)) + ((a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*d^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d^3*e + 3*(a^3*b^2 - 4*a^4*c)*d^2*e^2)*x)*sqrt(-(3*a^2*b*d*e^2 - 2*a^3*e^3 + (b^3 - 3*a*b*c)*d^3 - 3*(a*b^2 - 2*a^2*c)*d^2*e - (a^3*b^2 - 4*a^4*c)*sqrt(-(18*a^3*b*d^3*e^3 - 9*a^4*d^2*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^6 + 6*(a*b^3 - a^2*b*c)*d^5*e - 3*(5*a^2*b^2 - 2*a^3*c)*d^4*e^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c)))/x^2) + sqrt(1/2)*a*x*sqrt(-(3*a^2*b*d*e^2 - 2*a^3*e^3 + (b^3 - 3*a*b*c)*d^3 - 3*(a*b^2 - 2*a^2*c)*d^2*e - (a^3*b^2 - 4*a^4*c)*sqrt(-(18*a^3*b*d^3*e^3 - 9*a^4*d^2*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^6 + 6*(a*b^3 - a^2*b*c)*d^5*e - 3*(5*a^2*b^2 - 2*a^3*c)*d^4*e^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log(-(12*a^3*b*d^3*e^3 - 6*a^4*d^2*e^4 - 2*(a*b^2*c - a^2*c^2)*d^6 + 2*(a*b^3 + 2*a^2*b*c)*d^5*e - 4*(2*a^2*b^2 + a^3*c)*d^4*e^2 - ((a^3*b^2*c - 4*a^4*c^2)*d^3 - (a^3*b^3 - 4*a^4*b*c)*d^2*e + (a^4*b^2 - 4*a^5*c)*d*e^2)*x^2*sqrt(-(18*a^3*b*d^3*e^3 - 9*a^4*d^2*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^6 + 6*(a*b^3 - a^2*b*c)*d^5*e - 3*(5*a^2*b^2 - 2*a^3*c)*d^4*e^2)/(a^6*b^2 - 4*a^7*c)) + (27*a^3*b*d^2*e^4 - 12*a^4*d*e^5 + (b^3*c - a*b*c^2)*d^6 - (b^4 + 6*a*b^2*c - 4*a^2*c^2)*d^5*e + 2*(4*a*b^3 + 5*a^2*b*c)*d^4*e^2 - 2*(11*a^2*b^2 + 4*a^3*c)*d^3*e^3)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*(((a^4*b^3 - 4*a^5*b*c)*d - 2*(a^5*b^2 - 4*a^6*c)*e)*x*sqrt(-(18*a^3*b*d^3*e^3 - 9*a^4*d^2*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^6 + 6*(a*b^3 - a^2*b*c)*d^5*e - 3*(5*a^2*b^2 - 2*a^3*c)*d^4*e^2)/(a^6*b^2 - 4*a^7*c)) + ((a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*d^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d^3*e + 3*(a^3*b^2 - 4*a^4*c)*d^2*e^2)*x)*sqrt(-(3*a^2*b*d*e^2 - 2*a^3*e^3 + (b^3 - 3*a*b*c)*d^3 - 3*(a*b^2 - 2*a^2*c)*d^2*e - (a^3*b^2 - 4*a^4*c)*sqrt(-(18*a^3*b*d^3*e^3 - 9*a^4*d^2*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^6 + 6*(a*b^3 - a^2*b*c)*d^5*e - 3*(5*a^2*b^2 - 2*a^3*c)*d^4*e^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c)))/x^2) + 4*sqrt(e*x^2 + d)*d)/(a*x)","B",0
375,1,7830,0,149.195408," ","integrate((e*x^2+d)^(3/2)/x^4/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{1}{2}} a^{2} x^{3} \sqrt{-\frac{{\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} d^{3} - 3 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{2} e + 3 \, {\left(a^{2} b^{3} - 3 \, a^{3} b c\right)} d e^{2} - {\left(a^{3} b^{2} - 2 \, a^{4} c\right)} e^{3} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{a^{6} b^{2} e^{6} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{6} - 6 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d^{5} e + 3 \, {\left(5 \, a^{2} b^{6} - 20 \, a^{3} b^{4} c + 20 \, a^{4} b^{2} c^{2} - 2 \, a^{5} c^{3}\right)} d^{4} e^{2} - 2 \, {\left(10 \, a^{3} b^{5} - 30 \, a^{4} b^{3} c + 19 \, a^{5} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(5 \, a^{4} b^{4} - 10 \, a^{5} b^{2} c + 3 \, a^{6} c^{2}\right)} d^{2} e^{4} - 6 \, {\left(a^{5} b^{3} - a^{6} b c\right)} d e^{5}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} \log\left(\frac{2 \, a^{5} b c d e^{5} - 2 \, {\left(a b^{4} c^{2} - 3 \, a^{2} b^{2} c^{3} + a^{3} c^{4}\right)} d^{6} + 2 \, {\left(a b^{5} c - 5 \, a^{3} b c^{3}\right)} d^{5} e - 4 \, {\left(2 \, a^{2} b^{4} c - 3 \, a^{3} b^{2} c^{2} - a^{4} c^{3}\right)} d^{4} e^{2} + 4 \, {\left(3 \, a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d^{3} e^{3} - 2 \, {\left(4 \, a^{4} b^{2} c - 3 \, a^{5} c^{2}\right)} d^{2} e^{4} + {\left({\left(a^{5} b^{2} c^{2} - 4 \, a^{6} c^{3}\right)} d^{3} - {\left(a^{5} b^{3} c - 4 \, a^{6} b c^{2}\right)} d^{2} e + {\left(a^{6} b^{2} c - 4 \, a^{7} c^{2}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{a^{6} b^{2} e^{6} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{6} - 6 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d^{5} e + 3 \, {\left(5 \, a^{2} b^{6} - 20 \, a^{3} b^{4} c + 20 \, a^{4} b^{2} c^{2} - 2 \, a^{5} c^{3}\right)} d^{4} e^{2} - 2 \, {\left(10 \, a^{3} b^{5} - 30 \, a^{4} b^{3} c + 19 \, a^{5} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(5 \, a^{4} b^{4} - 10 \, a^{5} b^{2} c + 3 \, a^{6} c^{2}\right)} d^{2} e^{4} - 6 \, {\left(a^{5} b^{3} - a^{6} b c\right)} d e^{5}}{a^{10} b^{2} - 4 \, a^{11} c}} + {\left(4 \, a^{5} b c e^{6} + {\left(b^{5} c^{2} - 3 \, a b^{3} c^{3} + a^{2} b c^{4}\right)} d^{6} - {\left(b^{6} c + 4 \, a b^{4} c^{2} - 17 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d^{5} e + 2 \, {\left(4 \, a b^{5} c - 3 \, a^{2} b^{3} c^{2} - 11 \, a^{3} b c^{3}\right)} d^{4} e^{2} - 2 \, {\left(11 \, a^{2} b^{4} c - 16 \, a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} d^{3} e^{3} + 7 \, {\left(4 \, a^{3} b^{3} c - 5 \, a^{4} b c^{2}\right)} d^{2} e^{4} - {\left(17 \, a^{4} b^{2} c - 12 \, a^{5} c^{2}\right)} d e^{5}\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left({\left(a^{6} b^{4} - 6 \, a^{7} b^{2} c + 8 \, a^{8} c^{2}\right)} d - {\left(a^{7} b^{3} - 4 \, a^{8} b c\right)} e\right)} x \sqrt{\frac{a^{6} b^{2} e^{6} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{6} - 6 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d^{5} e + 3 \, {\left(5 \, a^{2} b^{6} - 20 \, a^{3} b^{4} c + 20 \, a^{4} b^{2} c^{2} - 2 \, a^{5} c^{3}\right)} d^{4} e^{2} - 2 \, {\left(10 \, a^{3} b^{5} - 30 \, a^{4} b^{3} c + 19 \, a^{5} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(5 \, a^{4} b^{4} - 10 \, a^{5} b^{2} c + 3 \, a^{6} c^{2}\right)} d^{2} e^{4} - 6 \, {\left(a^{5} b^{3} - a^{6} b c\right)} d e^{5}}{a^{10} b^{2} - 4 \, a^{11} c}} - {\left({\left(a b^{7} - 7 \, a^{2} b^{5} c + 13 \, a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d^{4} - {\left(4 \, a^{2} b^{6} - 25 \, a^{3} b^{4} c + 37 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{3} e + 3 \, {\left(2 \, a^{3} b^{5} - 11 \, a^{4} b^{3} c + 12 \, a^{5} b c^{2}\right)} d^{2} e^{2} - {\left(4 \, a^{4} b^{4} - 19 \, a^{5} b^{2} c + 12 \, a^{6} c^{2}\right)} d e^{3} + {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} e^{4}\right)} x\right)} \sqrt{-\frac{{\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} d^{3} - 3 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{2} e + 3 \, {\left(a^{2} b^{3} - 3 \, a^{3} b c\right)} d e^{2} - {\left(a^{3} b^{2} - 2 \, a^{4} c\right)} e^{3} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{a^{6} b^{2} e^{6} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{6} - 6 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d^{5} e + 3 \, {\left(5 \, a^{2} b^{6} - 20 \, a^{3} b^{4} c + 20 \, a^{4} b^{2} c^{2} - 2 \, a^{5} c^{3}\right)} d^{4} e^{2} - 2 \, {\left(10 \, a^{3} b^{5} - 30 \, a^{4} b^{3} c + 19 \, a^{5} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(5 \, a^{4} b^{4} - 10 \, a^{5} b^{2} c + 3 \, a^{6} c^{2}\right)} d^{2} e^{4} - 6 \, {\left(a^{5} b^{3} - a^{6} b c\right)} d e^{5}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}}}{x^{2}}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} x^{3} \sqrt{-\frac{{\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} d^{3} - 3 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{2} e + 3 \, {\left(a^{2} b^{3} - 3 \, a^{3} b c\right)} d e^{2} - {\left(a^{3} b^{2} - 2 \, a^{4} c\right)} e^{3} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{a^{6} b^{2} e^{6} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{6} - 6 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d^{5} e + 3 \, {\left(5 \, a^{2} b^{6} - 20 \, a^{3} b^{4} c + 20 \, a^{4} b^{2} c^{2} - 2 \, a^{5} c^{3}\right)} d^{4} e^{2} - 2 \, {\left(10 \, a^{3} b^{5} - 30 \, a^{4} b^{3} c + 19 \, a^{5} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(5 \, a^{4} b^{4} - 10 \, a^{5} b^{2} c + 3 \, a^{6} c^{2}\right)} d^{2} e^{4} - 6 \, {\left(a^{5} b^{3} - a^{6} b c\right)} d e^{5}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} \log\left(\frac{2 \, a^{5} b c d e^{5} - 2 \, {\left(a b^{4} c^{2} - 3 \, a^{2} b^{2} c^{3} + a^{3} c^{4}\right)} d^{6} + 2 \, {\left(a b^{5} c - 5 \, a^{3} b c^{3}\right)} d^{5} e - 4 \, {\left(2 \, a^{2} b^{4} c - 3 \, a^{3} b^{2} c^{2} - a^{4} c^{3}\right)} d^{4} e^{2} + 4 \, {\left(3 \, a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d^{3} e^{3} - 2 \, {\left(4 \, a^{4} b^{2} c - 3 \, a^{5} c^{2}\right)} d^{2} e^{4} + {\left({\left(a^{5} b^{2} c^{2} - 4 \, a^{6} c^{3}\right)} d^{3} - {\left(a^{5} b^{3} c - 4 \, a^{6} b c^{2}\right)} d^{2} e + {\left(a^{6} b^{2} c - 4 \, a^{7} c^{2}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{a^{6} b^{2} e^{6} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{6} - 6 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d^{5} e + 3 \, {\left(5 \, a^{2} b^{6} - 20 \, a^{3} b^{4} c + 20 \, a^{4} b^{2} c^{2} - 2 \, a^{5} c^{3}\right)} d^{4} e^{2} - 2 \, {\left(10 \, a^{3} b^{5} - 30 \, a^{4} b^{3} c + 19 \, a^{5} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(5 \, a^{4} b^{4} - 10 \, a^{5} b^{2} c + 3 \, a^{6} c^{2}\right)} d^{2} e^{4} - 6 \, {\left(a^{5} b^{3} - a^{6} b c\right)} d e^{5}}{a^{10} b^{2} - 4 \, a^{11} c}} + {\left(4 \, a^{5} b c e^{6} + {\left(b^{5} c^{2} - 3 \, a b^{3} c^{3} + a^{2} b c^{4}\right)} d^{6} - {\left(b^{6} c + 4 \, a b^{4} c^{2} - 17 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d^{5} e + 2 \, {\left(4 \, a b^{5} c - 3 \, a^{2} b^{3} c^{2} - 11 \, a^{3} b c^{3}\right)} d^{4} e^{2} - 2 \, {\left(11 \, a^{2} b^{4} c - 16 \, a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} d^{3} e^{3} + 7 \, {\left(4 \, a^{3} b^{3} c - 5 \, a^{4} b c^{2}\right)} d^{2} e^{4} - {\left(17 \, a^{4} b^{2} c - 12 \, a^{5} c^{2}\right)} d e^{5}\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left({\left(a^{6} b^{4} - 6 \, a^{7} b^{2} c + 8 \, a^{8} c^{2}\right)} d - {\left(a^{7} b^{3} - 4 \, a^{8} b c\right)} e\right)} x \sqrt{\frac{a^{6} b^{2} e^{6} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{6} - 6 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d^{5} e + 3 \, {\left(5 \, a^{2} b^{6} - 20 \, a^{3} b^{4} c + 20 \, a^{4} b^{2} c^{2} - 2 \, a^{5} c^{3}\right)} d^{4} e^{2} - 2 \, {\left(10 \, a^{3} b^{5} - 30 \, a^{4} b^{3} c + 19 \, a^{5} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(5 \, a^{4} b^{4} - 10 \, a^{5} b^{2} c + 3 \, a^{6} c^{2}\right)} d^{2} e^{4} - 6 \, {\left(a^{5} b^{3} - a^{6} b c\right)} d e^{5}}{a^{10} b^{2} - 4 \, a^{11} c}} - {\left({\left(a b^{7} - 7 \, a^{2} b^{5} c + 13 \, a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d^{4} - {\left(4 \, a^{2} b^{6} - 25 \, a^{3} b^{4} c + 37 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{3} e + 3 \, {\left(2 \, a^{3} b^{5} - 11 \, a^{4} b^{3} c + 12 \, a^{5} b c^{2}\right)} d^{2} e^{2} - {\left(4 \, a^{4} b^{4} - 19 \, a^{5} b^{2} c + 12 \, a^{6} c^{2}\right)} d e^{3} + {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} e^{4}\right)} x\right)} \sqrt{-\frac{{\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} d^{3} - 3 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{2} e + 3 \, {\left(a^{2} b^{3} - 3 \, a^{3} b c\right)} d e^{2} - {\left(a^{3} b^{2} - 2 \, a^{4} c\right)} e^{3} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{a^{6} b^{2} e^{6} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{6} - 6 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d^{5} e + 3 \, {\left(5 \, a^{2} b^{6} - 20 \, a^{3} b^{4} c + 20 \, a^{4} b^{2} c^{2} - 2 \, a^{5} c^{3}\right)} d^{4} e^{2} - 2 \, {\left(10 \, a^{3} b^{5} - 30 \, a^{4} b^{3} c + 19 \, a^{5} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(5 \, a^{4} b^{4} - 10 \, a^{5} b^{2} c + 3 \, a^{6} c^{2}\right)} d^{2} e^{4} - 6 \, {\left(a^{5} b^{3} - a^{6} b c\right)} d e^{5}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}}}{x^{2}}\right) - 3 \, \sqrt{\frac{1}{2}} a^{2} x^{3} \sqrt{-\frac{{\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} d^{3} - 3 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{2} e + 3 \, {\left(a^{2} b^{3} - 3 \, a^{3} b c\right)} d e^{2} - {\left(a^{3} b^{2} - 2 \, a^{4} c\right)} e^{3} - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{a^{6} b^{2} e^{6} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{6} - 6 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d^{5} e + 3 \, {\left(5 \, a^{2} b^{6} - 20 \, a^{3} b^{4} c + 20 \, a^{4} b^{2} c^{2} - 2 \, a^{5} c^{3}\right)} d^{4} e^{2} - 2 \, {\left(10 \, a^{3} b^{5} - 30 \, a^{4} b^{3} c + 19 \, a^{5} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(5 \, a^{4} b^{4} - 10 \, a^{5} b^{2} c + 3 \, a^{6} c^{2}\right)} d^{2} e^{4} - 6 \, {\left(a^{5} b^{3} - a^{6} b c\right)} d e^{5}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} \log\left(\frac{2 \, a^{5} b c d e^{5} - 2 \, {\left(a b^{4} c^{2} - 3 \, a^{2} b^{2} c^{3} + a^{3} c^{4}\right)} d^{6} + 2 \, {\left(a b^{5} c - 5 \, a^{3} b c^{3}\right)} d^{5} e - 4 \, {\left(2 \, a^{2} b^{4} c - 3 \, a^{3} b^{2} c^{2} - a^{4} c^{3}\right)} d^{4} e^{2} + 4 \, {\left(3 \, a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d^{3} e^{3} - 2 \, {\left(4 \, a^{4} b^{2} c - 3 \, a^{5} c^{2}\right)} d^{2} e^{4} - {\left({\left(a^{5} b^{2} c^{2} - 4 \, a^{6} c^{3}\right)} d^{3} - {\left(a^{5} b^{3} c - 4 \, a^{6} b c^{2}\right)} d^{2} e + {\left(a^{6} b^{2} c - 4 \, a^{7} c^{2}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{a^{6} b^{2} e^{6} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{6} - 6 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d^{5} e + 3 \, {\left(5 \, a^{2} b^{6} - 20 \, a^{3} b^{4} c + 20 \, a^{4} b^{2} c^{2} - 2 \, a^{5} c^{3}\right)} d^{4} e^{2} - 2 \, {\left(10 \, a^{3} b^{5} - 30 \, a^{4} b^{3} c + 19 \, a^{5} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(5 \, a^{4} b^{4} - 10 \, a^{5} b^{2} c + 3 \, a^{6} c^{2}\right)} d^{2} e^{4} - 6 \, {\left(a^{5} b^{3} - a^{6} b c\right)} d e^{5}}{a^{10} b^{2} - 4 \, a^{11} c}} + {\left(4 \, a^{5} b c e^{6} + {\left(b^{5} c^{2} - 3 \, a b^{3} c^{3} + a^{2} b c^{4}\right)} d^{6} - {\left(b^{6} c + 4 \, a b^{4} c^{2} - 17 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d^{5} e + 2 \, {\left(4 \, a b^{5} c - 3 \, a^{2} b^{3} c^{2} - 11 \, a^{3} b c^{3}\right)} d^{4} e^{2} - 2 \, {\left(11 \, a^{2} b^{4} c - 16 \, a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} d^{3} e^{3} + 7 \, {\left(4 \, a^{3} b^{3} c - 5 \, a^{4} b c^{2}\right)} d^{2} e^{4} - {\left(17 \, a^{4} b^{2} c - 12 \, a^{5} c^{2}\right)} d e^{5}\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left({\left(a^{6} b^{4} - 6 \, a^{7} b^{2} c + 8 \, a^{8} c^{2}\right)} d - {\left(a^{7} b^{3} - 4 \, a^{8} b c\right)} e\right)} x \sqrt{\frac{a^{6} b^{2} e^{6} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{6} - 6 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d^{5} e + 3 \, {\left(5 \, a^{2} b^{6} - 20 \, a^{3} b^{4} c + 20 \, a^{4} b^{2} c^{2} - 2 \, a^{5} c^{3}\right)} d^{4} e^{2} - 2 \, {\left(10 \, a^{3} b^{5} - 30 \, a^{4} b^{3} c + 19 \, a^{5} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(5 \, a^{4} b^{4} - 10 \, a^{5} b^{2} c + 3 \, a^{6} c^{2}\right)} d^{2} e^{4} - 6 \, {\left(a^{5} b^{3} - a^{6} b c\right)} d e^{5}}{a^{10} b^{2} - 4 \, a^{11} c}} + {\left({\left(a b^{7} - 7 \, a^{2} b^{5} c + 13 \, a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d^{4} - {\left(4 \, a^{2} b^{6} - 25 \, a^{3} b^{4} c + 37 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{3} e + 3 \, {\left(2 \, a^{3} b^{5} - 11 \, a^{4} b^{3} c + 12 \, a^{5} b c^{2}\right)} d^{2} e^{2} - {\left(4 \, a^{4} b^{4} - 19 \, a^{5} b^{2} c + 12 \, a^{6} c^{2}\right)} d e^{3} + {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} e^{4}\right)} x\right)} \sqrt{-\frac{{\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} d^{3} - 3 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{2} e + 3 \, {\left(a^{2} b^{3} - 3 \, a^{3} b c\right)} d e^{2} - {\left(a^{3} b^{2} - 2 \, a^{4} c\right)} e^{3} - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{a^{6} b^{2} e^{6} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{6} - 6 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d^{5} e + 3 \, {\left(5 \, a^{2} b^{6} - 20 \, a^{3} b^{4} c + 20 \, a^{4} b^{2} c^{2} - 2 \, a^{5} c^{3}\right)} d^{4} e^{2} - 2 \, {\left(10 \, a^{3} b^{5} - 30 \, a^{4} b^{3} c + 19 \, a^{5} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(5 \, a^{4} b^{4} - 10 \, a^{5} b^{2} c + 3 \, a^{6} c^{2}\right)} d^{2} e^{4} - 6 \, {\left(a^{5} b^{3} - a^{6} b c\right)} d e^{5}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}}}{x^{2}}\right) + 3 \, \sqrt{\frac{1}{2}} a^{2} x^{3} \sqrt{-\frac{{\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} d^{3} - 3 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{2} e + 3 \, {\left(a^{2} b^{3} - 3 \, a^{3} b c\right)} d e^{2} - {\left(a^{3} b^{2} - 2 \, a^{4} c\right)} e^{3} - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{a^{6} b^{2} e^{6} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{6} - 6 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d^{5} e + 3 \, {\left(5 \, a^{2} b^{6} - 20 \, a^{3} b^{4} c + 20 \, a^{4} b^{2} c^{2} - 2 \, a^{5} c^{3}\right)} d^{4} e^{2} - 2 \, {\left(10 \, a^{3} b^{5} - 30 \, a^{4} b^{3} c + 19 \, a^{5} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(5 \, a^{4} b^{4} - 10 \, a^{5} b^{2} c + 3 \, a^{6} c^{2}\right)} d^{2} e^{4} - 6 \, {\left(a^{5} b^{3} - a^{6} b c\right)} d e^{5}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}} \log\left(\frac{2 \, a^{5} b c d e^{5} - 2 \, {\left(a b^{4} c^{2} - 3 \, a^{2} b^{2} c^{3} + a^{3} c^{4}\right)} d^{6} + 2 \, {\left(a b^{5} c - 5 \, a^{3} b c^{3}\right)} d^{5} e - 4 \, {\left(2 \, a^{2} b^{4} c - 3 \, a^{3} b^{2} c^{2} - a^{4} c^{3}\right)} d^{4} e^{2} + 4 \, {\left(3 \, a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d^{3} e^{3} - 2 \, {\left(4 \, a^{4} b^{2} c - 3 \, a^{5} c^{2}\right)} d^{2} e^{4} - {\left({\left(a^{5} b^{2} c^{2} - 4 \, a^{6} c^{3}\right)} d^{3} - {\left(a^{5} b^{3} c - 4 \, a^{6} b c^{2}\right)} d^{2} e + {\left(a^{6} b^{2} c - 4 \, a^{7} c^{2}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{a^{6} b^{2} e^{6} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{6} - 6 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d^{5} e + 3 \, {\left(5 \, a^{2} b^{6} - 20 \, a^{3} b^{4} c + 20 \, a^{4} b^{2} c^{2} - 2 \, a^{5} c^{3}\right)} d^{4} e^{2} - 2 \, {\left(10 \, a^{3} b^{5} - 30 \, a^{4} b^{3} c + 19 \, a^{5} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(5 \, a^{4} b^{4} - 10 \, a^{5} b^{2} c + 3 \, a^{6} c^{2}\right)} d^{2} e^{4} - 6 \, {\left(a^{5} b^{3} - a^{6} b c\right)} d e^{5}}{a^{10} b^{2} - 4 \, a^{11} c}} + {\left(4 \, a^{5} b c e^{6} + {\left(b^{5} c^{2} - 3 \, a b^{3} c^{3} + a^{2} b c^{4}\right)} d^{6} - {\left(b^{6} c + 4 \, a b^{4} c^{2} - 17 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d^{5} e + 2 \, {\left(4 \, a b^{5} c - 3 \, a^{2} b^{3} c^{2} - 11 \, a^{3} b c^{3}\right)} d^{4} e^{2} - 2 \, {\left(11 \, a^{2} b^{4} c - 16 \, a^{3} b^{2} c^{2} - 4 \, a^{4} c^{3}\right)} d^{3} e^{3} + 7 \, {\left(4 \, a^{3} b^{3} c - 5 \, a^{4} b c^{2}\right)} d^{2} e^{4} - {\left(17 \, a^{4} b^{2} c - 12 \, a^{5} c^{2}\right)} d e^{5}\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left({\left(a^{6} b^{4} - 6 \, a^{7} b^{2} c + 8 \, a^{8} c^{2}\right)} d - {\left(a^{7} b^{3} - 4 \, a^{8} b c\right)} e\right)} x \sqrt{\frac{a^{6} b^{2} e^{6} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{6} - 6 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d^{5} e + 3 \, {\left(5 \, a^{2} b^{6} - 20 \, a^{3} b^{4} c + 20 \, a^{4} b^{2} c^{2} - 2 \, a^{5} c^{3}\right)} d^{4} e^{2} - 2 \, {\left(10 \, a^{3} b^{5} - 30 \, a^{4} b^{3} c + 19 \, a^{5} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(5 \, a^{4} b^{4} - 10 \, a^{5} b^{2} c + 3 \, a^{6} c^{2}\right)} d^{2} e^{4} - 6 \, {\left(a^{5} b^{3} - a^{6} b c\right)} d e^{5}}{a^{10} b^{2} - 4 \, a^{11} c}} + {\left({\left(a b^{7} - 7 \, a^{2} b^{5} c + 13 \, a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d^{4} - {\left(4 \, a^{2} b^{6} - 25 \, a^{3} b^{4} c + 37 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{3} e + 3 \, {\left(2 \, a^{3} b^{5} - 11 \, a^{4} b^{3} c + 12 \, a^{5} b c^{2}\right)} d^{2} e^{2} - {\left(4 \, a^{4} b^{4} - 19 \, a^{5} b^{2} c + 12 \, a^{6} c^{2}\right)} d e^{3} + {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} e^{4}\right)} x\right)} \sqrt{-\frac{{\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} d^{3} - 3 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{2} e + 3 \, {\left(a^{2} b^{3} - 3 \, a^{3} b c\right)} d e^{2} - {\left(a^{3} b^{2} - 2 \, a^{4} c\right)} e^{3} - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{a^{6} b^{2} e^{6} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} d^{6} - 6 \, {\left(a b^{7} - 5 \, a^{2} b^{5} c + 7 \, a^{3} b^{3} c^{2} - 2 \, a^{4} b c^{3}\right)} d^{5} e + 3 \, {\left(5 \, a^{2} b^{6} - 20 \, a^{3} b^{4} c + 20 \, a^{4} b^{2} c^{2} - 2 \, a^{5} c^{3}\right)} d^{4} e^{2} - 2 \, {\left(10 \, a^{3} b^{5} - 30 \, a^{4} b^{3} c + 19 \, a^{5} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(5 \, a^{4} b^{4} - 10 \, a^{5} b^{2} c + 3 \, a^{6} c^{2}\right)} d^{2} e^{4} - 6 \, {\left(a^{5} b^{3} - a^{6} b c\right)} d e^{5}}{a^{10} b^{2} - 4 \, a^{11} c}}}{a^{5} b^{2} - 4 \, a^{6} c}}}{x^{2}}\right) + 4 \, {\left({\left(3 \, b d - 4 \, a e\right)} x^{2} - a d\right)} \sqrt{e x^{2} + d}}{12 \, a^{2} x^{3}}"," ",0,"1/12*(3*sqrt(1/2)*a^2*x^3*sqrt(-((b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*d^3 - 3*(a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2)*d^2*e + 3*(a^2*b^3 - 3*a^3*b*c)*d*e^2 - (a^3*b^2 - 2*a^4*c)*e^3 + (a^5*b^2 - 4*a^6*c)*sqrt((a^6*b^2*e^6 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^6 - 6*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d^5*e + 3*(5*a^2*b^6 - 20*a^3*b^4*c + 20*a^4*b^2*c^2 - 2*a^5*c^3)*d^4*e^2 - 2*(10*a^3*b^5 - 30*a^4*b^3*c + 19*a^5*b*c^2)*d^3*e^3 + 3*(5*a^4*b^4 - 10*a^5*b^2*c + 3*a^6*c^2)*d^2*e^4 - 6*(a^5*b^3 - a^6*b*c)*d*e^5)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))*log((2*a^5*b*c*d*e^5 - 2*(a*b^4*c^2 - 3*a^2*b^2*c^3 + a^3*c^4)*d^6 + 2*(a*b^5*c - 5*a^3*b*c^3)*d^5*e - 4*(2*a^2*b^4*c - 3*a^3*b^2*c^2 - a^4*c^3)*d^4*e^2 + 4*(3*a^3*b^3*c - 4*a^4*b*c^2)*d^3*e^3 - 2*(4*a^4*b^2*c - 3*a^5*c^2)*d^2*e^4 + ((a^5*b^2*c^2 - 4*a^6*c^3)*d^3 - (a^5*b^3*c - 4*a^6*b*c^2)*d^2*e + (a^6*b^2*c - 4*a^7*c^2)*d*e^2)*x^2*sqrt((a^6*b^2*e^6 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^6 - 6*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d^5*e + 3*(5*a^2*b^6 - 20*a^3*b^4*c + 20*a^4*b^2*c^2 - 2*a^5*c^3)*d^4*e^2 - 2*(10*a^3*b^5 - 30*a^4*b^3*c + 19*a^5*b*c^2)*d^3*e^3 + 3*(5*a^4*b^4 - 10*a^5*b^2*c + 3*a^6*c^2)*d^2*e^4 - 6*(a^5*b^3 - a^6*b*c)*d*e^5)/(a^10*b^2 - 4*a^11*c)) + (4*a^5*b*c*e^6 + (b^5*c^2 - 3*a*b^3*c^3 + a^2*b*c^4)*d^6 - (b^6*c + 4*a*b^4*c^2 - 17*a^2*b^2*c^3 + 4*a^3*c^4)*d^5*e + 2*(4*a*b^5*c - 3*a^2*b^3*c^2 - 11*a^3*b*c^3)*d^4*e^2 - 2*(11*a^2*b^4*c - 16*a^3*b^2*c^2 - 4*a^4*c^3)*d^3*e^3 + 7*(4*a^3*b^3*c - 5*a^4*b*c^2)*d^2*e^4 - (17*a^4*b^2*c - 12*a^5*c^2)*d*e^5)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*(((a^6*b^4 - 6*a^7*b^2*c + 8*a^8*c^2)*d - (a^7*b^3 - 4*a^8*b*c)*e)*x*sqrt((a^6*b^2*e^6 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^6 - 6*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d^5*e + 3*(5*a^2*b^6 - 20*a^3*b^4*c + 20*a^4*b^2*c^2 - 2*a^5*c^3)*d^4*e^2 - 2*(10*a^3*b^5 - 30*a^4*b^3*c + 19*a^5*b*c^2)*d^3*e^3 + 3*(5*a^4*b^4 - 10*a^5*b^2*c + 3*a^6*c^2)*d^2*e^4 - 6*(a^5*b^3 - a^6*b*c)*d*e^5)/(a^10*b^2 - 4*a^11*c)) - ((a*b^7 - 7*a^2*b^5*c + 13*a^3*b^3*c^2 - 4*a^4*b*c^3)*d^4 - (4*a^2*b^6 - 25*a^3*b^4*c + 37*a^4*b^2*c^2 - 4*a^5*c^3)*d^3*e + 3*(2*a^3*b^5 - 11*a^4*b^3*c + 12*a^5*b*c^2)*d^2*e^2 - (4*a^4*b^4 - 19*a^5*b^2*c + 12*a^6*c^2)*d*e^3 + (a^5*b^3 - 4*a^6*b*c)*e^4)*x)*sqrt(-((b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*d^3 - 3*(a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2)*d^2*e + 3*(a^2*b^3 - 3*a^3*b*c)*d*e^2 - (a^3*b^2 - 2*a^4*c)*e^3 + (a^5*b^2 - 4*a^6*c)*sqrt((a^6*b^2*e^6 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^6 - 6*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d^5*e + 3*(5*a^2*b^6 - 20*a^3*b^4*c + 20*a^4*b^2*c^2 - 2*a^5*c^3)*d^4*e^2 - 2*(10*a^3*b^5 - 30*a^4*b^3*c + 19*a^5*b*c^2)*d^3*e^3 + 3*(5*a^4*b^4 - 10*a^5*b^2*c + 3*a^6*c^2)*d^2*e^4 - 6*(a^5*b^3 - a^6*b*c)*d*e^5)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c)))/x^2) - 3*sqrt(1/2)*a^2*x^3*sqrt(-((b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*d^3 - 3*(a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2)*d^2*e + 3*(a^2*b^3 - 3*a^3*b*c)*d*e^2 - (a^3*b^2 - 2*a^4*c)*e^3 + (a^5*b^2 - 4*a^6*c)*sqrt((a^6*b^2*e^6 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^6 - 6*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d^5*e + 3*(5*a^2*b^6 - 20*a^3*b^4*c + 20*a^4*b^2*c^2 - 2*a^5*c^3)*d^4*e^2 - 2*(10*a^3*b^5 - 30*a^4*b^3*c + 19*a^5*b*c^2)*d^3*e^3 + 3*(5*a^4*b^4 - 10*a^5*b^2*c + 3*a^6*c^2)*d^2*e^4 - 6*(a^5*b^3 - a^6*b*c)*d*e^5)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))*log((2*a^5*b*c*d*e^5 - 2*(a*b^4*c^2 - 3*a^2*b^2*c^3 + a^3*c^4)*d^6 + 2*(a*b^5*c - 5*a^3*b*c^3)*d^5*e - 4*(2*a^2*b^4*c - 3*a^3*b^2*c^2 - a^4*c^3)*d^4*e^2 + 4*(3*a^3*b^3*c - 4*a^4*b*c^2)*d^3*e^3 - 2*(4*a^4*b^2*c - 3*a^5*c^2)*d^2*e^4 + ((a^5*b^2*c^2 - 4*a^6*c^3)*d^3 - (a^5*b^3*c - 4*a^6*b*c^2)*d^2*e + (a^6*b^2*c - 4*a^7*c^2)*d*e^2)*x^2*sqrt((a^6*b^2*e^6 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^6 - 6*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d^5*e + 3*(5*a^2*b^6 - 20*a^3*b^4*c + 20*a^4*b^2*c^2 - 2*a^5*c^3)*d^4*e^2 - 2*(10*a^3*b^5 - 30*a^4*b^3*c + 19*a^5*b*c^2)*d^3*e^3 + 3*(5*a^4*b^4 - 10*a^5*b^2*c + 3*a^6*c^2)*d^2*e^4 - 6*(a^5*b^3 - a^6*b*c)*d*e^5)/(a^10*b^2 - 4*a^11*c)) + (4*a^5*b*c*e^6 + (b^5*c^2 - 3*a*b^3*c^3 + a^2*b*c^4)*d^6 - (b^6*c + 4*a*b^4*c^2 - 17*a^2*b^2*c^3 + 4*a^3*c^4)*d^5*e + 2*(4*a*b^5*c - 3*a^2*b^3*c^2 - 11*a^3*b*c^3)*d^4*e^2 - 2*(11*a^2*b^4*c - 16*a^3*b^2*c^2 - 4*a^4*c^3)*d^3*e^3 + 7*(4*a^3*b^3*c - 5*a^4*b*c^2)*d^2*e^4 - (17*a^4*b^2*c - 12*a^5*c^2)*d*e^5)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*(((a^6*b^4 - 6*a^7*b^2*c + 8*a^8*c^2)*d - (a^7*b^3 - 4*a^8*b*c)*e)*x*sqrt((a^6*b^2*e^6 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^6 - 6*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d^5*e + 3*(5*a^2*b^6 - 20*a^3*b^4*c + 20*a^4*b^2*c^2 - 2*a^5*c^3)*d^4*e^2 - 2*(10*a^3*b^5 - 30*a^4*b^3*c + 19*a^5*b*c^2)*d^3*e^3 + 3*(5*a^4*b^4 - 10*a^5*b^2*c + 3*a^6*c^2)*d^2*e^4 - 6*(a^5*b^3 - a^6*b*c)*d*e^5)/(a^10*b^2 - 4*a^11*c)) - ((a*b^7 - 7*a^2*b^5*c + 13*a^3*b^3*c^2 - 4*a^4*b*c^3)*d^4 - (4*a^2*b^6 - 25*a^3*b^4*c + 37*a^4*b^2*c^2 - 4*a^5*c^3)*d^3*e + 3*(2*a^3*b^5 - 11*a^4*b^3*c + 12*a^5*b*c^2)*d^2*e^2 - (4*a^4*b^4 - 19*a^5*b^2*c + 12*a^6*c^2)*d*e^3 + (a^5*b^3 - 4*a^6*b*c)*e^4)*x)*sqrt(-((b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*d^3 - 3*(a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2)*d^2*e + 3*(a^2*b^3 - 3*a^3*b*c)*d*e^2 - (a^3*b^2 - 2*a^4*c)*e^3 + (a^5*b^2 - 4*a^6*c)*sqrt((a^6*b^2*e^6 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^6 - 6*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d^5*e + 3*(5*a^2*b^6 - 20*a^3*b^4*c + 20*a^4*b^2*c^2 - 2*a^5*c^3)*d^4*e^2 - 2*(10*a^3*b^5 - 30*a^4*b^3*c + 19*a^5*b*c^2)*d^3*e^3 + 3*(5*a^4*b^4 - 10*a^5*b^2*c + 3*a^6*c^2)*d^2*e^4 - 6*(a^5*b^3 - a^6*b*c)*d*e^5)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c)))/x^2) - 3*sqrt(1/2)*a^2*x^3*sqrt(-((b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*d^3 - 3*(a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2)*d^2*e + 3*(a^2*b^3 - 3*a^3*b*c)*d*e^2 - (a^3*b^2 - 2*a^4*c)*e^3 - (a^5*b^2 - 4*a^6*c)*sqrt((a^6*b^2*e^6 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^6 - 6*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d^5*e + 3*(5*a^2*b^6 - 20*a^3*b^4*c + 20*a^4*b^2*c^2 - 2*a^5*c^3)*d^4*e^2 - 2*(10*a^3*b^5 - 30*a^4*b^3*c + 19*a^5*b*c^2)*d^3*e^3 + 3*(5*a^4*b^4 - 10*a^5*b^2*c + 3*a^6*c^2)*d^2*e^4 - 6*(a^5*b^3 - a^6*b*c)*d*e^5)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))*log((2*a^5*b*c*d*e^5 - 2*(a*b^4*c^2 - 3*a^2*b^2*c^3 + a^3*c^4)*d^6 + 2*(a*b^5*c - 5*a^3*b*c^3)*d^5*e - 4*(2*a^2*b^4*c - 3*a^3*b^2*c^2 - a^4*c^3)*d^4*e^2 + 4*(3*a^3*b^3*c - 4*a^4*b*c^2)*d^3*e^3 - 2*(4*a^4*b^2*c - 3*a^5*c^2)*d^2*e^4 - ((a^5*b^2*c^2 - 4*a^6*c^3)*d^3 - (a^5*b^3*c - 4*a^6*b*c^2)*d^2*e + (a^6*b^2*c - 4*a^7*c^2)*d*e^2)*x^2*sqrt((a^6*b^2*e^6 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^6 - 6*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d^5*e + 3*(5*a^2*b^6 - 20*a^3*b^4*c + 20*a^4*b^2*c^2 - 2*a^5*c^3)*d^4*e^2 - 2*(10*a^3*b^5 - 30*a^4*b^3*c + 19*a^5*b*c^2)*d^3*e^3 + 3*(5*a^4*b^4 - 10*a^5*b^2*c + 3*a^6*c^2)*d^2*e^4 - 6*(a^5*b^3 - a^6*b*c)*d*e^5)/(a^10*b^2 - 4*a^11*c)) + (4*a^5*b*c*e^6 + (b^5*c^2 - 3*a*b^3*c^3 + a^2*b*c^4)*d^6 - (b^6*c + 4*a*b^4*c^2 - 17*a^2*b^2*c^3 + 4*a^3*c^4)*d^5*e + 2*(4*a*b^5*c - 3*a^2*b^3*c^2 - 11*a^3*b*c^3)*d^4*e^2 - 2*(11*a^2*b^4*c - 16*a^3*b^2*c^2 - 4*a^4*c^3)*d^3*e^3 + 7*(4*a^3*b^3*c - 5*a^4*b*c^2)*d^2*e^4 - (17*a^4*b^2*c - 12*a^5*c^2)*d*e^5)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*(((a^6*b^4 - 6*a^7*b^2*c + 8*a^8*c^2)*d - (a^7*b^3 - 4*a^8*b*c)*e)*x*sqrt((a^6*b^2*e^6 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^6 - 6*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d^5*e + 3*(5*a^2*b^6 - 20*a^3*b^4*c + 20*a^4*b^2*c^2 - 2*a^5*c^3)*d^4*e^2 - 2*(10*a^3*b^5 - 30*a^4*b^3*c + 19*a^5*b*c^2)*d^3*e^3 + 3*(5*a^4*b^4 - 10*a^5*b^2*c + 3*a^6*c^2)*d^2*e^4 - 6*(a^5*b^3 - a^6*b*c)*d*e^5)/(a^10*b^2 - 4*a^11*c)) + ((a*b^7 - 7*a^2*b^5*c + 13*a^3*b^3*c^2 - 4*a^4*b*c^3)*d^4 - (4*a^2*b^6 - 25*a^3*b^4*c + 37*a^4*b^2*c^2 - 4*a^5*c^3)*d^3*e + 3*(2*a^3*b^5 - 11*a^4*b^3*c + 12*a^5*b*c^2)*d^2*e^2 - (4*a^4*b^4 - 19*a^5*b^2*c + 12*a^6*c^2)*d*e^3 + (a^5*b^3 - 4*a^6*b*c)*e^4)*x)*sqrt(-((b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*d^3 - 3*(a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2)*d^2*e + 3*(a^2*b^3 - 3*a^3*b*c)*d*e^2 - (a^3*b^2 - 2*a^4*c)*e^3 - (a^5*b^2 - 4*a^6*c)*sqrt((a^6*b^2*e^6 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^6 - 6*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d^5*e + 3*(5*a^2*b^6 - 20*a^3*b^4*c + 20*a^4*b^2*c^2 - 2*a^5*c^3)*d^4*e^2 - 2*(10*a^3*b^5 - 30*a^4*b^3*c + 19*a^5*b*c^2)*d^3*e^3 + 3*(5*a^4*b^4 - 10*a^5*b^2*c + 3*a^6*c^2)*d^2*e^4 - 6*(a^5*b^3 - a^6*b*c)*d*e^5)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c)))/x^2) + 3*sqrt(1/2)*a^2*x^3*sqrt(-((b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*d^3 - 3*(a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2)*d^2*e + 3*(a^2*b^3 - 3*a^3*b*c)*d*e^2 - (a^3*b^2 - 2*a^4*c)*e^3 - (a^5*b^2 - 4*a^6*c)*sqrt((a^6*b^2*e^6 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^6 - 6*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d^5*e + 3*(5*a^2*b^6 - 20*a^3*b^4*c + 20*a^4*b^2*c^2 - 2*a^5*c^3)*d^4*e^2 - 2*(10*a^3*b^5 - 30*a^4*b^3*c + 19*a^5*b*c^2)*d^3*e^3 + 3*(5*a^4*b^4 - 10*a^5*b^2*c + 3*a^6*c^2)*d^2*e^4 - 6*(a^5*b^3 - a^6*b*c)*d*e^5)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c))*log((2*a^5*b*c*d*e^5 - 2*(a*b^4*c^2 - 3*a^2*b^2*c^3 + a^3*c^4)*d^6 + 2*(a*b^5*c - 5*a^3*b*c^3)*d^5*e - 4*(2*a^2*b^4*c - 3*a^3*b^2*c^2 - a^4*c^3)*d^4*e^2 + 4*(3*a^3*b^3*c - 4*a^4*b*c^2)*d^3*e^3 - 2*(4*a^4*b^2*c - 3*a^5*c^2)*d^2*e^4 - ((a^5*b^2*c^2 - 4*a^6*c^3)*d^3 - (a^5*b^3*c - 4*a^6*b*c^2)*d^2*e + (a^6*b^2*c - 4*a^7*c^2)*d*e^2)*x^2*sqrt((a^6*b^2*e^6 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^6 - 6*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d^5*e + 3*(5*a^2*b^6 - 20*a^3*b^4*c + 20*a^4*b^2*c^2 - 2*a^5*c^3)*d^4*e^2 - 2*(10*a^3*b^5 - 30*a^4*b^3*c + 19*a^5*b*c^2)*d^3*e^3 + 3*(5*a^4*b^4 - 10*a^5*b^2*c + 3*a^6*c^2)*d^2*e^4 - 6*(a^5*b^3 - a^6*b*c)*d*e^5)/(a^10*b^2 - 4*a^11*c)) + (4*a^5*b*c*e^6 + (b^5*c^2 - 3*a*b^3*c^3 + a^2*b*c^4)*d^6 - (b^6*c + 4*a*b^4*c^2 - 17*a^2*b^2*c^3 + 4*a^3*c^4)*d^5*e + 2*(4*a*b^5*c - 3*a^2*b^3*c^2 - 11*a^3*b*c^3)*d^4*e^2 - 2*(11*a^2*b^4*c - 16*a^3*b^2*c^2 - 4*a^4*c^3)*d^3*e^3 + 7*(4*a^3*b^3*c - 5*a^4*b*c^2)*d^2*e^4 - (17*a^4*b^2*c - 12*a^5*c^2)*d*e^5)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*(((a^6*b^4 - 6*a^7*b^2*c + 8*a^8*c^2)*d - (a^7*b^3 - 4*a^8*b*c)*e)*x*sqrt((a^6*b^2*e^6 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^6 - 6*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d^5*e + 3*(5*a^2*b^6 - 20*a^3*b^4*c + 20*a^4*b^2*c^2 - 2*a^5*c^3)*d^4*e^2 - 2*(10*a^3*b^5 - 30*a^4*b^3*c + 19*a^5*b*c^2)*d^3*e^3 + 3*(5*a^4*b^4 - 10*a^5*b^2*c + 3*a^6*c^2)*d^2*e^4 - 6*(a^5*b^3 - a^6*b*c)*d*e^5)/(a^10*b^2 - 4*a^11*c)) + ((a*b^7 - 7*a^2*b^5*c + 13*a^3*b^3*c^2 - 4*a^4*b*c^3)*d^4 - (4*a^2*b^6 - 25*a^3*b^4*c + 37*a^4*b^2*c^2 - 4*a^5*c^3)*d^3*e + 3*(2*a^3*b^5 - 11*a^4*b^3*c + 12*a^5*b*c^2)*d^2*e^2 - (4*a^4*b^4 - 19*a^5*b^2*c + 12*a^6*c^2)*d*e^3 + (a^5*b^3 - 4*a^6*b*c)*e^4)*x)*sqrt(-((b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*d^3 - 3*(a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2)*d^2*e + 3*(a^2*b^3 - 3*a^3*b*c)*d*e^2 - (a^3*b^2 - 2*a^4*c)*e^3 - (a^5*b^2 - 4*a^6*c)*sqrt((a^6*b^2*e^6 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*d^6 - 6*(a*b^7 - 5*a^2*b^5*c + 7*a^3*b^3*c^2 - 2*a^4*b*c^3)*d^5*e + 3*(5*a^2*b^6 - 20*a^3*b^4*c + 20*a^4*b^2*c^2 - 2*a^5*c^3)*d^4*e^2 - 2*(10*a^3*b^5 - 30*a^4*b^3*c + 19*a^5*b*c^2)*d^3*e^3 + 3*(5*a^4*b^4 - 10*a^5*b^2*c + 3*a^6*c^2)*d^2*e^4 - 6*(a^5*b^3 - a^6*b*c)*d*e^5)/(a^10*b^2 - 4*a^11*c)))/(a^5*b^2 - 4*a^6*c)))/x^2) + 4*((3*b*d - 4*a*e)*x^2 - a*d)*sqrt(e*x^2 + d))/(a^2*x^3)","B",0
376,1,3615,0,16.821146," ","integrate(x^5*(-x^2+1)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{1}{2}} c^{2} \sqrt{\frac{b^{5} + 2 \, a^{2} c^{3} + {\left(5 \, a^{2} b - 4 \, a b^{2}\right)} c^{2} - {\left(5 \, a b^{3} - b^{4}\right)} c - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{8} + {\left(a^{4} - 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{4} - 2 \, {\left(3 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c^{3} + {\left(11 \, a^{2} b^{4} - 10 \, a b^{5} + b^{6}\right)} c^{2} - 2 \, {\left(3 \, a b^{6} - b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(-\frac{2 \, a^{3} b^{4} + {\left(a^{2} b^{2} c^{5} - 4 \, a^{3} c^{6}\right)} x^{2} \sqrt{\frac{b^{8} + {\left(a^{4} - 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{4} - 2 \, {\left(3 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c^{3} + {\left(11 \, a^{2} b^{4} - 10 \, a b^{5} + b^{6}\right)} c^{2} - 2 \, {\left(3 \, a b^{6} - b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}} + 2 \, {\left(a^{5} - 2 \, a^{4} b\right)} c^{2} + {\left(a^{2} b^{5} + {\left(a^{4} b - 2 \, a^{3} b^{2}\right)} c^{2} - {\left(3 \, a^{3} b^{3} - a^{2} b^{4}\right)} c\right)} x^{2} - 2 \, {\left(3 \, a^{4} b^{2} - a^{3} b^{3}\right)} c + \sqrt{\frac{1}{2}} {\left({\left(b^{5} c^{5} - 7 \, a b^{3} c^{6} + 12 \, a^{2} b c^{7}\right)} x^{2} \sqrt{\frac{b^{8} + {\left(a^{4} - 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{4} - 2 \, {\left(3 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c^{3} + {\left(11 \, a^{2} b^{4} - 10 \, a b^{5} + b^{6}\right)} c^{2} - 2 \, {\left(3 \, a b^{6} - b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}} + {\left(b^{8} + 4 \, {\left(a^{4} - 2 \, a^{3} b\right)} c^{4} - {\left(17 \, a^{3} b^{2} - 14 \, a^{2} b^{3}\right)} c^{3} + {\left(20 \, a^{2} b^{4} - 7 \, a b^{5}\right)} c^{2} - {\left(8 \, a b^{6} - b^{7}\right)} c\right)} x^{2}\right)} \sqrt{\frac{b^{5} + 2 \, a^{2} c^{3} + {\left(5 \, a^{2} b - 4 \, a b^{2}\right)} c^{2} - {\left(5 \, a b^{3} - b^{4}\right)} c - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{8} + {\left(a^{4} - 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{4} - 2 \, {\left(3 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c^{3} + {\left(11 \, a^{2} b^{4} - 10 \, a b^{5} + b^{6}\right)} c^{2} - 2 \, {\left(3 \, a b^{6} - b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} - 2 \, {\left(a^{3} b^{4} + {\left(a^{5} - 2 \, a^{4} b\right)} c^{2} - {\left(3 \, a^{4} b^{2} - a^{3} b^{3}\right)} c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) - 3 \, \sqrt{\frac{1}{2}} c^{2} \sqrt{\frac{b^{5} + 2 \, a^{2} c^{3} + {\left(5 \, a^{2} b - 4 \, a b^{2}\right)} c^{2} - {\left(5 \, a b^{3} - b^{4}\right)} c - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{8} + {\left(a^{4} - 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{4} - 2 \, {\left(3 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c^{3} + {\left(11 \, a^{2} b^{4} - 10 \, a b^{5} + b^{6}\right)} c^{2} - 2 \, {\left(3 \, a b^{6} - b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(-\frac{2 \, a^{3} b^{4} + {\left(a^{2} b^{2} c^{5} - 4 \, a^{3} c^{6}\right)} x^{2} \sqrt{\frac{b^{8} + {\left(a^{4} - 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{4} - 2 \, {\left(3 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c^{3} + {\left(11 \, a^{2} b^{4} - 10 \, a b^{5} + b^{6}\right)} c^{2} - 2 \, {\left(3 \, a b^{6} - b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}} + 2 \, {\left(a^{5} - 2 \, a^{4} b\right)} c^{2} + {\left(a^{2} b^{5} + {\left(a^{4} b - 2 \, a^{3} b^{2}\right)} c^{2} - {\left(3 \, a^{3} b^{3} - a^{2} b^{4}\right)} c\right)} x^{2} - 2 \, {\left(3 \, a^{4} b^{2} - a^{3} b^{3}\right)} c - \sqrt{\frac{1}{2}} {\left({\left(b^{5} c^{5} - 7 \, a b^{3} c^{6} + 12 \, a^{2} b c^{7}\right)} x^{2} \sqrt{\frac{b^{8} + {\left(a^{4} - 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{4} - 2 \, {\left(3 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c^{3} + {\left(11 \, a^{2} b^{4} - 10 \, a b^{5} + b^{6}\right)} c^{2} - 2 \, {\left(3 \, a b^{6} - b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}} + {\left(b^{8} + 4 \, {\left(a^{4} - 2 \, a^{3} b\right)} c^{4} - {\left(17 \, a^{3} b^{2} - 14 \, a^{2} b^{3}\right)} c^{3} + {\left(20 \, a^{2} b^{4} - 7 \, a b^{5}\right)} c^{2} - {\left(8 \, a b^{6} - b^{7}\right)} c\right)} x^{2}\right)} \sqrt{\frac{b^{5} + 2 \, a^{2} c^{3} + {\left(5 \, a^{2} b - 4 \, a b^{2}\right)} c^{2} - {\left(5 \, a b^{3} - b^{4}\right)} c - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{8} + {\left(a^{4} - 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{4} - 2 \, {\left(3 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c^{3} + {\left(11 \, a^{2} b^{4} - 10 \, a b^{5} + b^{6}\right)} c^{2} - 2 \, {\left(3 \, a b^{6} - b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} - 2 \, {\left(a^{3} b^{4} + {\left(a^{5} - 2 \, a^{4} b\right)} c^{2} - {\left(3 \, a^{4} b^{2} - a^{3} b^{3}\right)} c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) - 3 \, \sqrt{\frac{1}{2}} c^{2} \sqrt{\frac{b^{5} + 2 \, a^{2} c^{3} + {\left(5 \, a^{2} b - 4 \, a b^{2}\right)} c^{2} - {\left(5 \, a b^{3} - b^{4}\right)} c + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{8} + {\left(a^{4} - 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{4} - 2 \, {\left(3 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c^{3} + {\left(11 \, a^{2} b^{4} - 10 \, a b^{5} + b^{6}\right)} c^{2} - 2 \, {\left(3 \, a b^{6} - b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(-\frac{2 \, a^{3} b^{4} - {\left(a^{2} b^{2} c^{5} - 4 \, a^{3} c^{6}\right)} x^{2} \sqrt{\frac{b^{8} + {\left(a^{4} - 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{4} - 2 \, {\left(3 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c^{3} + {\left(11 \, a^{2} b^{4} - 10 \, a b^{5} + b^{6}\right)} c^{2} - 2 \, {\left(3 \, a b^{6} - b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}} + 2 \, {\left(a^{5} - 2 \, a^{4} b\right)} c^{2} + {\left(a^{2} b^{5} + {\left(a^{4} b - 2 \, a^{3} b^{2}\right)} c^{2} - {\left(3 \, a^{3} b^{3} - a^{2} b^{4}\right)} c\right)} x^{2} - 2 \, {\left(3 \, a^{4} b^{2} - a^{3} b^{3}\right)} c + \sqrt{\frac{1}{2}} {\left({\left(b^{5} c^{5} - 7 \, a b^{3} c^{6} + 12 \, a^{2} b c^{7}\right)} x^{2} \sqrt{\frac{b^{8} + {\left(a^{4} - 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{4} - 2 \, {\left(3 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c^{3} + {\left(11 \, a^{2} b^{4} - 10 \, a b^{5} + b^{6}\right)} c^{2} - 2 \, {\left(3 \, a b^{6} - b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}} - {\left(b^{8} + 4 \, {\left(a^{4} - 2 \, a^{3} b\right)} c^{4} - {\left(17 \, a^{3} b^{2} - 14 \, a^{2} b^{3}\right)} c^{3} + {\left(20 \, a^{2} b^{4} - 7 \, a b^{5}\right)} c^{2} - {\left(8 \, a b^{6} - b^{7}\right)} c\right)} x^{2}\right)} \sqrt{\frac{b^{5} + 2 \, a^{2} c^{3} + {\left(5 \, a^{2} b - 4 \, a b^{2}\right)} c^{2} - {\left(5 \, a b^{3} - b^{4}\right)} c + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{8} + {\left(a^{4} - 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{4} - 2 \, {\left(3 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c^{3} + {\left(11 \, a^{2} b^{4} - 10 \, a b^{5} + b^{6}\right)} c^{2} - 2 \, {\left(3 \, a b^{6} - b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} - 2 \, {\left(a^{3} b^{4} + {\left(a^{5} - 2 \, a^{4} b\right)} c^{2} - {\left(3 \, a^{4} b^{2} - a^{3} b^{3}\right)} c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) + 3 \, \sqrt{\frac{1}{2}} c^{2} \sqrt{\frac{b^{5} + 2 \, a^{2} c^{3} + {\left(5 \, a^{2} b - 4 \, a b^{2}\right)} c^{2} - {\left(5 \, a b^{3} - b^{4}\right)} c + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{8} + {\left(a^{4} - 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{4} - 2 \, {\left(3 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c^{3} + {\left(11 \, a^{2} b^{4} - 10 \, a b^{5} + b^{6}\right)} c^{2} - 2 \, {\left(3 \, a b^{6} - b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(-\frac{2 \, a^{3} b^{4} - {\left(a^{2} b^{2} c^{5} - 4 \, a^{3} c^{6}\right)} x^{2} \sqrt{\frac{b^{8} + {\left(a^{4} - 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{4} - 2 \, {\left(3 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c^{3} + {\left(11 \, a^{2} b^{4} - 10 \, a b^{5} + b^{6}\right)} c^{2} - 2 \, {\left(3 \, a b^{6} - b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}} + 2 \, {\left(a^{5} - 2 \, a^{4} b\right)} c^{2} + {\left(a^{2} b^{5} + {\left(a^{4} b - 2 \, a^{3} b^{2}\right)} c^{2} - {\left(3 \, a^{3} b^{3} - a^{2} b^{4}\right)} c\right)} x^{2} - 2 \, {\left(3 \, a^{4} b^{2} - a^{3} b^{3}\right)} c - \sqrt{\frac{1}{2}} {\left({\left(b^{5} c^{5} - 7 \, a b^{3} c^{6} + 12 \, a^{2} b c^{7}\right)} x^{2} \sqrt{\frac{b^{8} + {\left(a^{4} - 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{4} - 2 \, {\left(3 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c^{3} + {\left(11 \, a^{2} b^{4} - 10 \, a b^{5} + b^{6}\right)} c^{2} - 2 \, {\left(3 \, a b^{6} - b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}} - {\left(b^{8} + 4 \, {\left(a^{4} - 2 \, a^{3} b\right)} c^{4} - {\left(17 \, a^{3} b^{2} - 14 \, a^{2} b^{3}\right)} c^{3} + {\left(20 \, a^{2} b^{4} - 7 \, a b^{5}\right)} c^{2} - {\left(8 \, a b^{6} - b^{7}\right)} c\right)} x^{2}\right)} \sqrt{\frac{b^{5} + 2 \, a^{2} c^{3} + {\left(5 \, a^{2} b - 4 \, a b^{2}\right)} c^{2} - {\left(5 \, a b^{3} - b^{4}\right)} c + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{8} + {\left(a^{4} - 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{4} - 2 \, {\left(3 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c^{3} + {\left(11 \, a^{2} b^{4} - 10 \, a b^{5} + b^{6}\right)} c^{2} - 2 \, {\left(3 \, a b^{6} - b^{7}\right)} c}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} - 2 \, {\left(a^{3} b^{4} + {\left(a^{5} - 2 \, a^{4} b\right)} c^{2} - {\left(3 \, a^{4} b^{2} - a^{3} b^{3}\right)} c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) - 2 \, {\left(c x^{2} - 3 \, b - c\right)} \sqrt{-x^{2} + 1}}{6 \, c^{2}}"," ",0,"-1/6*(3*sqrt(1/2)*c^2*sqrt((b^5 + 2*a^2*c^3 + (5*a^2*b - 4*a*b^2)*c^2 - (5*a*b^3 - b^4)*c - (b^2*c^5 - 4*a*c^6)*sqrt((b^8 + (a^4 - 4*a^3*b + 4*a^2*b^2)*c^4 - 2*(3*a^3*b^2 - 7*a^2*b^3 + 2*a*b^4)*c^3 + (11*a^2*b^4 - 10*a*b^5 + b^6)*c^2 - 2*(3*a*b^6 - b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(-(2*a^3*b^4 + (a^2*b^2*c^5 - 4*a^3*c^6)*x^2*sqrt((b^8 + (a^4 - 4*a^3*b + 4*a^2*b^2)*c^4 - 2*(3*a^3*b^2 - 7*a^2*b^3 + 2*a*b^4)*c^3 + (11*a^2*b^4 - 10*a*b^5 + b^6)*c^2 - 2*(3*a*b^6 - b^7)*c)/(b^2*c^10 - 4*a*c^11)) + 2*(a^5 - 2*a^4*b)*c^2 + (a^2*b^5 + (a^4*b - 2*a^3*b^2)*c^2 - (3*a^3*b^3 - a^2*b^4)*c)*x^2 - 2*(3*a^4*b^2 - a^3*b^3)*c + sqrt(1/2)*((b^5*c^5 - 7*a*b^3*c^6 + 12*a^2*b*c^7)*x^2*sqrt((b^8 + (a^4 - 4*a^3*b + 4*a^2*b^2)*c^4 - 2*(3*a^3*b^2 - 7*a^2*b^3 + 2*a*b^4)*c^3 + (11*a^2*b^4 - 10*a*b^5 + b^6)*c^2 - 2*(3*a*b^6 - b^7)*c)/(b^2*c^10 - 4*a*c^11)) + (b^8 + 4*(a^4 - 2*a^3*b)*c^4 - (17*a^3*b^2 - 14*a^2*b^3)*c^3 + (20*a^2*b^4 - 7*a*b^5)*c^2 - (8*a*b^6 - b^7)*c)*x^2)*sqrt((b^5 + 2*a^2*c^3 + (5*a^2*b - 4*a*b^2)*c^2 - (5*a*b^3 - b^4)*c - (b^2*c^5 - 4*a*c^6)*sqrt((b^8 + (a^4 - 4*a^3*b + 4*a^2*b^2)*c^4 - 2*(3*a^3*b^2 - 7*a^2*b^3 + 2*a*b^4)*c^3 + (11*a^2*b^4 - 10*a*b^5 + b^6)*c^2 - 2*(3*a*b^6 - b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6)) - 2*(a^3*b^4 + (a^5 - 2*a^4*b)*c^2 - (3*a^4*b^2 - a^3*b^3)*c)*sqrt(-x^2 + 1))/x^2) - 3*sqrt(1/2)*c^2*sqrt((b^5 + 2*a^2*c^3 + (5*a^2*b - 4*a*b^2)*c^2 - (5*a*b^3 - b^4)*c - (b^2*c^5 - 4*a*c^6)*sqrt((b^8 + (a^4 - 4*a^3*b + 4*a^2*b^2)*c^4 - 2*(3*a^3*b^2 - 7*a^2*b^3 + 2*a*b^4)*c^3 + (11*a^2*b^4 - 10*a*b^5 + b^6)*c^2 - 2*(3*a*b^6 - b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(-(2*a^3*b^4 + (a^2*b^2*c^5 - 4*a^3*c^6)*x^2*sqrt((b^8 + (a^4 - 4*a^3*b + 4*a^2*b^2)*c^4 - 2*(3*a^3*b^2 - 7*a^2*b^3 + 2*a*b^4)*c^3 + (11*a^2*b^4 - 10*a*b^5 + b^6)*c^2 - 2*(3*a*b^6 - b^7)*c)/(b^2*c^10 - 4*a*c^11)) + 2*(a^5 - 2*a^4*b)*c^2 + (a^2*b^5 + (a^4*b - 2*a^3*b^2)*c^2 - (3*a^3*b^3 - a^2*b^4)*c)*x^2 - 2*(3*a^4*b^2 - a^3*b^3)*c - sqrt(1/2)*((b^5*c^5 - 7*a*b^3*c^6 + 12*a^2*b*c^7)*x^2*sqrt((b^8 + (a^4 - 4*a^3*b + 4*a^2*b^2)*c^4 - 2*(3*a^3*b^2 - 7*a^2*b^3 + 2*a*b^4)*c^3 + (11*a^2*b^4 - 10*a*b^5 + b^6)*c^2 - 2*(3*a*b^6 - b^7)*c)/(b^2*c^10 - 4*a*c^11)) + (b^8 + 4*(a^4 - 2*a^3*b)*c^4 - (17*a^3*b^2 - 14*a^2*b^3)*c^3 + (20*a^2*b^4 - 7*a*b^5)*c^2 - (8*a*b^6 - b^7)*c)*x^2)*sqrt((b^5 + 2*a^2*c^3 + (5*a^2*b - 4*a*b^2)*c^2 - (5*a*b^3 - b^4)*c - (b^2*c^5 - 4*a*c^6)*sqrt((b^8 + (a^4 - 4*a^3*b + 4*a^2*b^2)*c^4 - 2*(3*a^3*b^2 - 7*a^2*b^3 + 2*a*b^4)*c^3 + (11*a^2*b^4 - 10*a*b^5 + b^6)*c^2 - 2*(3*a*b^6 - b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6)) - 2*(a^3*b^4 + (a^5 - 2*a^4*b)*c^2 - (3*a^4*b^2 - a^3*b^3)*c)*sqrt(-x^2 + 1))/x^2) - 3*sqrt(1/2)*c^2*sqrt((b^5 + 2*a^2*c^3 + (5*a^2*b - 4*a*b^2)*c^2 - (5*a*b^3 - b^4)*c + (b^2*c^5 - 4*a*c^6)*sqrt((b^8 + (a^4 - 4*a^3*b + 4*a^2*b^2)*c^4 - 2*(3*a^3*b^2 - 7*a^2*b^3 + 2*a*b^4)*c^3 + (11*a^2*b^4 - 10*a*b^5 + b^6)*c^2 - 2*(3*a*b^6 - b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(-(2*a^3*b^4 - (a^2*b^2*c^5 - 4*a^3*c^6)*x^2*sqrt((b^8 + (a^4 - 4*a^3*b + 4*a^2*b^2)*c^4 - 2*(3*a^3*b^2 - 7*a^2*b^3 + 2*a*b^4)*c^3 + (11*a^2*b^4 - 10*a*b^5 + b^6)*c^2 - 2*(3*a*b^6 - b^7)*c)/(b^2*c^10 - 4*a*c^11)) + 2*(a^5 - 2*a^4*b)*c^2 + (a^2*b^5 + (a^4*b - 2*a^3*b^2)*c^2 - (3*a^3*b^3 - a^2*b^4)*c)*x^2 - 2*(3*a^4*b^2 - a^3*b^3)*c + sqrt(1/2)*((b^5*c^5 - 7*a*b^3*c^6 + 12*a^2*b*c^7)*x^2*sqrt((b^8 + (a^4 - 4*a^3*b + 4*a^2*b^2)*c^4 - 2*(3*a^3*b^2 - 7*a^2*b^3 + 2*a*b^4)*c^3 + (11*a^2*b^4 - 10*a*b^5 + b^6)*c^2 - 2*(3*a*b^6 - b^7)*c)/(b^2*c^10 - 4*a*c^11)) - (b^8 + 4*(a^4 - 2*a^3*b)*c^4 - (17*a^3*b^2 - 14*a^2*b^3)*c^3 + (20*a^2*b^4 - 7*a*b^5)*c^2 - (8*a*b^6 - b^7)*c)*x^2)*sqrt((b^5 + 2*a^2*c^3 + (5*a^2*b - 4*a*b^2)*c^2 - (5*a*b^3 - b^4)*c + (b^2*c^5 - 4*a*c^6)*sqrt((b^8 + (a^4 - 4*a^3*b + 4*a^2*b^2)*c^4 - 2*(3*a^3*b^2 - 7*a^2*b^3 + 2*a*b^4)*c^3 + (11*a^2*b^4 - 10*a*b^5 + b^6)*c^2 - 2*(3*a*b^6 - b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6)) - 2*(a^3*b^4 + (a^5 - 2*a^4*b)*c^2 - (3*a^4*b^2 - a^3*b^3)*c)*sqrt(-x^2 + 1))/x^2) + 3*sqrt(1/2)*c^2*sqrt((b^5 + 2*a^2*c^3 + (5*a^2*b - 4*a*b^2)*c^2 - (5*a*b^3 - b^4)*c + (b^2*c^5 - 4*a*c^6)*sqrt((b^8 + (a^4 - 4*a^3*b + 4*a^2*b^2)*c^4 - 2*(3*a^3*b^2 - 7*a^2*b^3 + 2*a*b^4)*c^3 + (11*a^2*b^4 - 10*a*b^5 + b^6)*c^2 - 2*(3*a*b^6 - b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(-(2*a^3*b^4 - (a^2*b^2*c^5 - 4*a^3*c^6)*x^2*sqrt((b^8 + (a^4 - 4*a^3*b + 4*a^2*b^2)*c^4 - 2*(3*a^3*b^2 - 7*a^2*b^3 + 2*a*b^4)*c^3 + (11*a^2*b^4 - 10*a*b^5 + b^6)*c^2 - 2*(3*a*b^6 - b^7)*c)/(b^2*c^10 - 4*a*c^11)) + 2*(a^5 - 2*a^4*b)*c^2 + (a^2*b^5 + (a^4*b - 2*a^3*b^2)*c^2 - (3*a^3*b^3 - a^2*b^4)*c)*x^2 - 2*(3*a^4*b^2 - a^3*b^3)*c - sqrt(1/2)*((b^5*c^5 - 7*a*b^3*c^6 + 12*a^2*b*c^7)*x^2*sqrt((b^8 + (a^4 - 4*a^3*b + 4*a^2*b^2)*c^4 - 2*(3*a^3*b^2 - 7*a^2*b^3 + 2*a*b^4)*c^3 + (11*a^2*b^4 - 10*a*b^5 + b^6)*c^2 - 2*(3*a*b^6 - b^7)*c)/(b^2*c^10 - 4*a*c^11)) - (b^8 + 4*(a^4 - 2*a^3*b)*c^4 - (17*a^3*b^2 - 14*a^2*b^3)*c^3 + (20*a^2*b^4 - 7*a*b^5)*c^2 - (8*a*b^6 - b^7)*c)*x^2)*sqrt((b^5 + 2*a^2*c^3 + (5*a^2*b - 4*a*b^2)*c^2 - (5*a*b^3 - b^4)*c + (b^2*c^5 - 4*a*c^6)*sqrt((b^8 + (a^4 - 4*a^3*b + 4*a^2*b^2)*c^4 - 2*(3*a^3*b^2 - 7*a^2*b^3 + 2*a*b^4)*c^3 + (11*a^2*b^4 - 10*a*b^5 + b^6)*c^2 - 2*(3*a*b^6 - b^7)*c)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6)) - 2*(a^3*b^4 + (a^5 - 2*a^4*b)*c^2 - (3*a^4*b^2 - a^3*b^3)*c)*sqrt(-x^2 + 1))/x^2) - 2*(c*x^2 - 3*b - c)*sqrt(-x^2 + 1))/c^2","B",0
377,1,2053,0,6.457077," ","integrate(x^3*(-x^2+1)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} c \sqrt{\frac{b^{3} - 2 \, a c^{2} - {\left(3 \, a b - b^{2}\right)} c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} + {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} - 2 \, {\left(a b^{2} - b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(\frac{2 \, a^{2} b^{2} + {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} x^{2} \sqrt{\frac{b^{4} + {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} - 2 \, {\left(a b^{2} - b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}} + {\left(a b^{3} - {\left(a^{2} b - a b^{2}\right)} c\right)} x^{2} - 2 \, {\left(a^{3} - a^{2} b\right)} c + \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} x^{2} \sqrt{\frac{b^{4} + {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} - 2 \, {\left(a b^{2} - b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}} + {\left(b^{5} + 4 \, {\left(a^{2} b - a b^{2}\right)} c^{2} - {\left(5 \, a b^{3} - b^{4}\right)} c\right)} x^{2}\right)} \sqrt{\frac{b^{3} - 2 \, a c^{2} - {\left(3 \, a b - b^{2}\right)} c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} + {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} - 2 \, {\left(a b^{2} - b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} - 2 \, {\left(a^{2} b^{2} - {\left(a^{3} - a^{2} b\right)} c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c \sqrt{\frac{b^{3} - 2 \, a c^{2} - {\left(3 \, a b - b^{2}\right)} c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} + {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} - 2 \, {\left(a b^{2} - b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(\frac{2 \, a^{2} b^{2} + {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} x^{2} \sqrt{\frac{b^{4} + {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} - 2 \, {\left(a b^{2} - b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}} + {\left(a b^{3} - {\left(a^{2} b - a b^{2}\right)} c\right)} x^{2} - 2 \, {\left(a^{3} - a^{2} b\right)} c - \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} x^{2} \sqrt{\frac{b^{4} + {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} - 2 \, {\left(a b^{2} - b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}} + {\left(b^{5} + 4 \, {\left(a^{2} b - a b^{2}\right)} c^{2} - {\left(5 \, a b^{3} - b^{4}\right)} c\right)} x^{2}\right)} \sqrt{\frac{b^{3} - 2 \, a c^{2} - {\left(3 \, a b - b^{2}\right)} c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} + {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} - 2 \, {\left(a b^{2} - b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} - 2 \, {\left(a^{2} b^{2} - {\left(a^{3} - a^{2} b\right)} c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c \sqrt{\frac{b^{3} - 2 \, a c^{2} - {\left(3 \, a b - b^{2}\right)} c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} + {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} - 2 \, {\left(a b^{2} - b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(\frac{2 \, a^{2} b^{2} - {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} x^{2} \sqrt{\frac{b^{4} + {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} - 2 \, {\left(a b^{2} - b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}} + {\left(a b^{3} - {\left(a^{2} b - a b^{2}\right)} c\right)} x^{2} - 2 \, {\left(a^{3} - a^{2} b\right)} c + \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} x^{2} \sqrt{\frac{b^{4} + {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} - 2 \, {\left(a b^{2} - b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}} - {\left(b^{5} + 4 \, {\left(a^{2} b - a b^{2}\right)} c^{2} - {\left(5 \, a b^{3} - b^{4}\right)} c\right)} x^{2}\right)} \sqrt{\frac{b^{3} - 2 \, a c^{2} - {\left(3 \, a b - b^{2}\right)} c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} + {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} - 2 \, {\left(a b^{2} - b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} - 2 \, {\left(a^{2} b^{2} - {\left(a^{3} - a^{2} b\right)} c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) + \sqrt{\frac{1}{2}} c \sqrt{\frac{b^{3} - 2 \, a c^{2} - {\left(3 \, a b - b^{2}\right)} c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} + {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} - 2 \, {\left(a b^{2} - b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(\frac{2 \, a^{2} b^{2} - {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} x^{2} \sqrt{\frac{b^{4} + {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} - 2 \, {\left(a b^{2} - b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}} + {\left(a b^{3} - {\left(a^{2} b - a b^{2}\right)} c\right)} x^{2} - 2 \, {\left(a^{3} - a^{2} b\right)} c - \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} x^{2} \sqrt{\frac{b^{4} + {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} - 2 \, {\left(a b^{2} - b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}} - {\left(b^{5} + 4 \, {\left(a^{2} b - a b^{2}\right)} c^{2} - {\left(5 \, a b^{3} - b^{4}\right)} c\right)} x^{2}\right)} \sqrt{\frac{b^{3} - 2 \, a c^{2} - {\left(3 \, a b - b^{2}\right)} c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} + {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} - 2 \, {\left(a b^{2} - b^{3}\right)} c}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} - 2 \, {\left(a^{2} b^{2} - {\left(a^{3} - a^{2} b\right)} c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) + 2 \, \sqrt{-x^{2} + 1}}{2 \, c}"," ",0,"1/2*(sqrt(1/2)*c*sqrt((b^3 - 2*a*c^2 - (3*a*b - b^2)*c - (b^2*c^3 - 4*a*c^4)*sqrt((b^4 + (a^2 - 2*a*b + b^2)*c^2 - 2*(a*b^2 - b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log((2*a^2*b^2 + (a*b^2*c^3 - 4*a^2*c^4)*x^2*sqrt((b^4 + (a^2 - 2*a*b + b^2)*c^2 - 2*(a*b^2 - b^3)*c)/(b^2*c^6 - 4*a*c^7)) + (a*b^3 - (a^2*b - a*b^2)*c)*x^2 - 2*(a^3 - a^2*b)*c + sqrt(1/2)*((b^4*c^3 - 6*a*b^2*c^4 + 8*a^2*c^5)*x^2*sqrt((b^4 + (a^2 - 2*a*b + b^2)*c^2 - 2*(a*b^2 - b^3)*c)/(b^2*c^6 - 4*a*c^7)) + (b^5 + 4*(a^2*b - a*b^2)*c^2 - (5*a*b^3 - b^4)*c)*x^2)*sqrt((b^3 - 2*a*c^2 - (3*a*b - b^2)*c - (b^2*c^3 - 4*a*c^4)*sqrt((b^4 + (a^2 - 2*a*b + b^2)*c^2 - 2*(a*b^2 - b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) - 2*(a^2*b^2 - (a^3 - a^2*b)*c)*sqrt(-x^2 + 1))/x^2) - sqrt(1/2)*c*sqrt((b^3 - 2*a*c^2 - (3*a*b - b^2)*c - (b^2*c^3 - 4*a*c^4)*sqrt((b^4 + (a^2 - 2*a*b + b^2)*c^2 - 2*(a*b^2 - b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log((2*a^2*b^2 + (a*b^2*c^3 - 4*a^2*c^4)*x^2*sqrt((b^4 + (a^2 - 2*a*b + b^2)*c^2 - 2*(a*b^2 - b^3)*c)/(b^2*c^6 - 4*a*c^7)) + (a*b^3 - (a^2*b - a*b^2)*c)*x^2 - 2*(a^3 - a^2*b)*c - sqrt(1/2)*((b^4*c^3 - 6*a*b^2*c^4 + 8*a^2*c^5)*x^2*sqrt((b^4 + (a^2 - 2*a*b + b^2)*c^2 - 2*(a*b^2 - b^3)*c)/(b^2*c^6 - 4*a*c^7)) + (b^5 + 4*(a^2*b - a*b^2)*c^2 - (5*a*b^3 - b^4)*c)*x^2)*sqrt((b^3 - 2*a*c^2 - (3*a*b - b^2)*c - (b^2*c^3 - 4*a*c^4)*sqrt((b^4 + (a^2 - 2*a*b + b^2)*c^2 - 2*(a*b^2 - b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) - 2*(a^2*b^2 - (a^3 - a^2*b)*c)*sqrt(-x^2 + 1))/x^2) - sqrt(1/2)*c*sqrt((b^3 - 2*a*c^2 - (3*a*b - b^2)*c + (b^2*c^3 - 4*a*c^4)*sqrt((b^4 + (a^2 - 2*a*b + b^2)*c^2 - 2*(a*b^2 - b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log((2*a^2*b^2 - (a*b^2*c^3 - 4*a^2*c^4)*x^2*sqrt((b^4 + (a^2 - 2*a*b + b^2)*c^2 - 2*(a*b^2 - b^3)*c)/(b^2*c^6 - 4*a*c^7)) + (a*b^3 - (a^2*b - a*b^2)*c)*x^2 - 2*(a^3 - a^2*b)*c + sqrt(1/2)*((b^4*c^3 - 6*a*b^2*c^4 + 8*a^2*c^5)*x^2*sqrt((b^4 + (a^2 - 2*a*b + b^2)*c^2 - 2*(a*b^2 - b^3)*c)/(b^2*c^6 - 4*a*c^7)) - (b^5 + 4*(a^2*b - a*b^2)*c^2 - (5*a*b^3 - b^4)*c)*x^2)*sqrt((b^3 - 2*a*c^2 - (3*a*b - b^2)*c + (b^2*c^3 - 4*a*c^4)*sqrt((b^4 + (a^2 - 2*a*b + b^2)*c^2 - 2*(a*b^2 - b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) - 2*(a^2*b^2 - (a^3 - a^2*b)*c)*sqrt(-x^2 + 1))/x^2) + sqrt(1/2)*c*sqrt((b^3 - 2*a*c^2 - (3*a*b - b^2)*c + (b^2*c^3 - 4*a*c^4)*sqrt((b^4 + (a^2 - 2*a*b + b^2)*c^2 - 2*(a*b^2 - b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log((2*a^2*b^2 - (a*b^2*c^3 - 4*a^2*c^4)*x^2*sqrt((b^4 + (a^2 - 2*a*b + b^2)*c^2 - 2*(a*b^2 - b^3)*c)/(b^2*c^6 - 4*a*c^7)) + (a*b^3 - (a^2*b - a*b^2)*c)*x^2 - 2*(a^3 - a^2*b)*c - sqrt(1/2)*((b^4*c^3 - 6*a*b^2*c^4 + 8*a^2*c^5)*x^2*sqrt((b^4 + (a^2 - 2*a*b + b^2)*c^2 - 2*(a*b^2 - b^3)*c)/(b^2*c^6 - 4*a*c^7)) - (b^5 + 4*(a^2*b - a*b^2)*c^2 - (5*a*b^3 - b^4)*c)*x^2)*sqrt((b^3 - 2*a*c^2 - (3*a*b - b^2)*c + (b^2*c^3 - 4*a*c^4)*sqrt((b^4 + (a^2 - 2*a*b + b^2)*c^2 - 2*(a*b^2 - b^3)*c)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) - 2*(a^2*b^2 - (a^3 - a^2*b)*c)*sqrt(-x^2 + 1))/x^2) + 2*sqrt(-x^2 + 1))/c","B",0
378,1,871,0,3.123204," ","integrate(x*(-x^2+1)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{\frac{b + 2 \, c - \frac{b^{2} c - 4 \, a c^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} \log\left(\frac{b x^{2} + \frac{{\left(b^{2} c - 4 \, a c^{2}\right)} x^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}} + \sqrt{\frac{1}{2}} {\left({\left(b^{2} - 4 \, a c\right)} x^{2} + \frac{{\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}\right)} \sqrt{\frac{b + 2 \, c - \frac{b^{2} c - 4 \, a c^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} - 2 \, \sqrt{-x^{2} + 1} a + 2 \, a}{x^{2}}\right) + \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{\frac{b + 2 \, c - \frac{b^{2} c - 4 \, a c^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} \log\left(\frac{b x^{2} + \frac{{\left(b^{2} c - 4 \, a c^{2}\right)} x^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}} - \sqrt{\frac{1}{2}} {\left({\left(b^{2} - 4 \, a c\right)} x^{2} + \frac{{\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}\right)} \sqrt{\frac{b + 2 \, c - \frac{b^{2} c - 4 \, a c^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} - 2 \, \sqrt{-x^{2} + 1} a + 2 \, a}{x^{2}}\right) - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{\frac{b + 2 \, c + \frac{b^{2} c - 4 \, a c^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} \log\left(\frac{b x^{2} - \frac{{\left(b^{2} c - 4 \, a c^{2}\right)} x^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}} + \sqrt{\frac{1}{2}} {\left({\left(b^{2} - 4 \, a c\right)} x^{2} - \frac{{\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}\right)} \sqrt{\frac{b + 2 \, c + \frac{b^{2} c - 4 \, a c^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} - 2 \, \sqrt{-x^{2} + 1} a + 2 \, a}{x^{2}}\right) + \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{\frac{b + 2 \, c + \frac{b^{2} c - 4 \, a c^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} \log\left(\frac{b x^{2} - \frac{{\left(b^{2} c - 4 \, a c^{2}\right)} x^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}} - \sqrt{\frac{1}{2}} {\left({\left(b^{2} - 4 \, a c\right)} x^{2} - \frac{{\left(b^{3} c - 4 \, a b c^{2}\right)} x^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}\right)} \sqrt{\frac{b + 2 \, c + \frac{b^{2} c - 4 \, a c^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} - 2 \, \sqrt{-x^{2} + 1} a + 2 \, a}{x^{2}}\right)"," ",0,"-1/2*sqrt(1/2)*sqrt((b + 2*c - (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2))*log((b*x^2 + (b^2*c - 4*a*c^2)*x^2/sqrt(b^2*c^2 - 4*a*c^3) + sqrt(1/2)*((b^2 - 4*a*c)*x^2 + (b^3*c - 4*a*b*c^2)*x^2/sqrt(b^2*c^2 - 4*a*c^3))*sqrt((b + 2*c - (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2)) - 2*sqrt(-x^2 + 1)*a + 2*a)/x^2) + 1/2*sqrt(1/2)*sqrt((b + 2*c - (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2))*log((b*x^2 + (b^2*c - 4*a*c^2)*x^2/sqrt(b^2*c^2 - 4*a*c^3) - sqrt(1/2)*((b^2 - 4*a*c)*x^2 + (b^3*c - 4*a*b*c^2)*x^2/sqrt(b^2*c^2 - 4*a*c^3))*sqrt((b + 2*c - (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2)) - 2*sqrt(-x^2 + 1)*a + 2*a)/x^2) - 1/2*sqrt(1/2)*sqrt((b + 2*c + (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2))*log((b*x^2 - (b^2*c - 4*a*c^2)*x^2/sqrt(b^2*c^2 - 4*a*c^3) + sqrt(1/2)*((b^2 - 4*a*c)*x^2 - (b^3*c - 4*a*b*c^2)*x^2/sqrt(b^2*c^2 - 4*a*c^3))*sqrt((b + 2*c + (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2)) - 2*sqrt(-x^2 + 1)*a + 2*a)/x^2) + 1/2*sqrt(1/2)*sqrt((b + 2*c + (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2))*log((b*x^2 - (b^2*c - 4*a*c^2)*x^2/sqrt(b^2*c^2 - 4*a*c^3) - sqrt(1/2)*((b^2 - 4*a*c)*x^2 - (b^3*c - 4*a*b*c^2)*x^2/sqrt(b^2*c^2 - 4*a*c^3))*sqrt((b + 2*c + (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2)) - 2*sqrt(-x^2 + 1)*a + 2*a)/x^2)","B",0
379,1,1232,0,11.647519," ","integrate((-x^2+1)^(1/2)/x/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} a \sqrt{\frac{a b + b^{2} - 2 \, a c + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{a^{2} + 2 \, a b + b^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x^{2} \sqrt{\frac{a^{2} + 2 \, a b + b^{2}}{a^{4} b^{2} - 4 \, a^{5} c}} \sqrt{\frac{a b + b^{2} - 2 \, a c + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{a^{2} + 2 \, a b + b^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x^{2} \sqrt{\frac{a^{2} + 2 \, a b + b^{2}}{a^{4} b^{2} - 4 \, a^{5} c}} + {\left(a b + b^{2}\right)} x^{2} + 2 \, a^{2} + 2 \, a b - 2 \, {\left(a^{2} + a b\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) - \sqrt{\frac{1}{2}} a \sqrt{\frac{a b + b^{2} - 2 \, a c + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{a^{2} + 2 \, a b + b^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} \log\left(-\frac{2 \, \sqrt{\frac{1}{2}} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x^{2} \sqrt{\frac{a^{2} + 2 \, a b + b^{2}}{a^{4} b^{2} - 4 \, a^{5} c}} \sqrt{\frac{a b + b^{2} - 2 \, a c + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{a^{2} + 2 \, a b + b^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} - {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x^{2} \sqrt{\frac{a^{2} + 2 \, a b + b^{2}}{a^{4} b^{2} - 4 \, a^{5} c}} - {\left(a b + b^{2}\right)} x^{2} - 2 \, a^{2} - 2 \, a b + 2 \, {\left(a^{2} + a b\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) + \sqrt{\frac{1}{2}} a \sqrt{\frac{a b + b^{2} - 2 \, a c - {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{a^{2} + 2 \, a b + b^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} \log\left(-\frac{2 \, \sqrt{\frac{1}{2}} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x^{2} \sqrt{\frac{a^{2} + 2 \, a b + b^{2}}{a^{4} b^{2} - 4 \, a^{5} c}} \sqrt{\frac{a b + b^{2} - 2 \, a c - {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{a^{2} + 2 \, a b + b^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x^{2} \sqrt{\frac{a^{2} + 2 \, a b + b^{2}}{a^{4} b^{2} - 4 \, a^{5} c}} - {\left(a b + b^{2}\right)} x^{2} - 2 \, a^{2} - 2 \, a b + 2 \, {\left(a^{2} + a b\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) - \sqrt{\frac{1}{2}} a \sqrt{\frac{a b + b^{2} - 2 \, a c - {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{a^{2} + 2 \, a b + b^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} \log\left(\frac{2 \, \sqrt{\frac{1}{2}} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x^{2} \sqrt{\frac{a^{2} + 2 \, a b + b^{2}}{a^{4} b^{2} - 4 \, a^{5} c}} \sqrt{\frac{a b + b^{2} - 2 \, a c - {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{a^{2} + 2 \, a b + b^{2}}{a^{4} b^{2} - 4 \, a^{5} c}}}{a^{2} b^{2} - 4 \, a^{3} c}} - {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x^{2} \sqrt{\frac{a^{2} + 2 \, a b + b^{2}}{a^{4} b^{2} - 4 \, a^{5} c}} + {\left(a b + b^{2}\right)} x^{2} + 2 \, a^{2} + 2 \, a b - 2 \, {\left(a^{2} + a b\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) + 2 \, \log\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)}{2 \, a}"," ",0,"1/2*(sqrt(1/2)*a*sqrt((a*b + b^2 - 2*a*c + (a^2*b^2 - 4*a^3*c)*sqrt((a^2 + 2*a*b + b^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c))*log((2*sqrt(1/2)*(a^3*b^2 - 4*a^4*c)*x^2*sqrt((a^2 + 2*a*b + b^2)/(a^4*b^2 - 4*a^5*c))*sqrt((a*b + b^2 - 2*a*c + (a^2*b^2 - 4*a^3*c)*sqrt((a^2 + 2*a*b + b^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c)) + (a^2*b^2 - 4*a^3*c)*x^2*sqrt((a^2 + 2*a*b + b^2)/(a^4*b^2 - 4*a^5*c)) + (a*b + b^2)*x^2 + 2*a^2 + 2*a*b - 2*(a^2 + a*b)*sqrt(-x^2 + 1))/x^2) - sqrt(1/2)*a*sqrt((a*b + b^2 - 2*a*c + (a^2*b^2 - 4*a^3*c)*sqrt((a^2 + 2*a*b + b^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c))*log(-(2*sqrt(1/2)*(a^3*b^2 - 4*a^4*c)*x^2*sqrt((a^2 + 2*a*b + b^2)/(a^4*b^2 - 4*a^5*c))*sqrt((a*b + b^2 - 2*a*c + (a^2*b^2 - 4*a^3*c)*sqrt((a^2 + 2*a*b + b^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c)) - (a^2*b^2 - 4*a^3*c)*x^2*sqrt((a^2 + 2*a*b + b^2)/(a^4*b^2 - 4*a^5*c)) - (a*b + b^2)*x^2 - 2*a^2 - 2*a*b + 2*(a^2 + a*b)*sqrt(-x^2 + 1))/x^2) + sqrt(1/2)*a*sqrt((a*b + b^2 - 2*a*c - (a^2*b^2 - 4*a^3*c)*sqrt((a^2 + 2*a*b + b^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c))*log(-(2*sqrt(1/2)*(a^3*b^2 - 4*a^4*c)*x^2*sqrt((a^2 + 2*a*b + b^2)/(a^4*b^2 - 4*a^5*c))*sqrt((a*b + b^2 - 2*a*c - (a^2*b^2 - 4*a^3*c)*sqrt((a^2 + 2*a*b + b^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c)) + (a^2*b^2 - 4*a^3*c)*x^2*sqrt((a^2 + 2*a*b + b^2)/(a^4*b^2 - 4*a^5*c)) - (a*b + b^2)*x^2 - 2*a^2 - 2*a*b + 2*(a^2 + a*b)*sqrt(-x^2 + 1))/x^2) - sqrt(1/2)*a*sqrt((a*b + b^2 - 2*a*c - (a^2*b^2 - 4*a^3*c)*sqrt((a^2 + 2*a*b + b^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c))*log((2*sqrt(1/2)*(a^3*b^2 - 4*a^4*c)*x^2*sqrt((a^2 + 2*a*b + b^2)/(a^4*b^2 - 4*a^5*c))*sqrt((a*b + b^2 - 2*a*c - (a^2*b^2 - 4*a^3*c)*sqrt((a^2 + 2*a*b + b^2)/(a^4*b^2 - 4*a^5*c)))/(a^2*b^2 - 4*a^3*c)) - (a^2*b^2 - 4*a^3*c)*x^2*sqrt((a^2 + 2*a*b + b^2)/(a^4*b^2 - 4*a^5*c)) + (a*b + b^2)*x^2 + 2*a^2 + 2*a*b - 2*(a^2 + a*b)*sqrt(-x^2 + 1))/x^2) + 2*log((sqrt(-x^2 + 1) - 1)/x))/a","B",0
380,1,2799,0,32.216506," ","integrate((-x^2+1)^(1/2)/x^3/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} a^{2} x^{2} \sqrt{\frac{a b^{3} + b^{4} + 2 \, a^{2} c^{2} - {\left(3 \, a^{2} b + 4 \, a b^{2}\right)} c - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{a^{2} b^{4} + 2 \, a b^{5} + b^{6} + {\left(a^{4} + 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} \log\left(\frac{{\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} x^{2} \sqrt{\frac{a^{2} b^{4} + 2 \, a b^{5} + b^{6} + {\left(a^{4} + 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c}{a^{8} b^{2} - 4 \, a^{9} c}} + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} c^{2} + {\left({\left(a^{2} b + 2 \, a b^{2}\right)} c^{2} - {\left(a b^{3} + b^{4}\right)} c\right)} x^{2} - 2 \, {\left(a^{2} b^{2} + a b^{3}\right)} c + \sqrt{\frac{1}{2}} {\left({\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} x^{2} \sqrt{\frac{a^{2} b^{4} + 2 \, a b^{5} + b^{6} + {\left(a^{4} + 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c}{a^{8} b^{2} - 4 \, a^{9} c}} + {\left(a^{2} b^{4} + a b^{5} + 4 \, {\left(a^{4} + 2 \, a^{3} b\right)} c^{2} - {\left(5 \, a^{3} b^{2} + 6 \, a^{2} b^{3}\right)} c\right)} x^{2}\right)} \sqrt{\frac{a b^{3} + b^{4} + 2 \, a^{2} c^{2} - {\left(3 \, a^{2} b + 4 \, a b^{2}\right)} c - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{a^{2} b^{4} + 2 \, a b^{5} + b^{6} + {\left(a^{4} + 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} - 2 \, {\left({\left(a^{3} + 2 \, a^{2} b\right)} c^{2} - {\left(a^{2} b^{2} + a b^{3}\right)} c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) - \sqrt{\frac{1}{2}} a^{2} x^{2} \sqrt{\frac{a b^{3} + b^{4} + 2 \, a^{2} c^{2} - {\left(3 \, a^{2} b + 4 \, a b^{2}\right)} c - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{a^{2} b^{4} + 2 \, a b^{5} + b^{6} + {\left(a^{4} + 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} \log\left(\frac{{\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} x^{2} \sqrt{\frac{a^{2} b^{4} + 2 \, a b^{5} + b^{6} + {\left(a^{4} + 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c}{a^{8} b^{2} - 4 \, a^{9} c}} + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} c^{2} + {\left({\left(a^{2} b + 2 \, a b^{2}\right)} c^{2} - {\left(a b^{3} + b^{4}\right)} c\right)} x^{2} - 2 \, {\left(a^{2} b^{2} + a b^{3}\right)} c - \sqrt{\frac{1}{2}} {\left({\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} x^{2} \sqrt{\frac{a^{2} b^{4} + 2 \, a b^{5} + b^{6} + {\left(a^{4} + 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c}{a^{8} b^{2} - 4 \, a^{9} c}} + {\left(a^{2} b^{4} + a b^{5} + 4 \, {\left(a^{4} + 2 \, a^{3} b\right)} c^{2} - {\left(5 \, a^{3} b^{2} + 6 \, a^{2} b^{3}\right)} c\right)} x^{2}\right)} \sqrt{\frac{a b^{3} + b^{4} + 2 \, a^{2} c^{2} - {\left(3 \, a^{2} b + 4 \, a b^{2}\right)} c - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{a^{2} b^{4} + 2 \, a b^{5} + b^{6} + {\left(a^{4} + 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} - 2 \, {\left({\left(a^{3} + 2 \, a^{2} b\right)} c^{2} - {\left(a^{2} b^{2} + a b^{3}\right)} c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) + \sqrt{\frac{1}{2}} a^{2} x^{2} \sqrt{\frac{a b^{3} + b^{4} + 2 \, a^{2} c^{2} - {\left(3 \, a^{2} b + 4 \, a b^{2}\right)} c + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{a^{2} b^{4} + 2 \, a b^{5} + b^{6} + {\left(a^{4} + 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} \log\left(-\frac{{\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} x^{2} \sqrt{\frac{a^{2} b^{4} + 2 \, a b^{5} + b^{6} + {\left(a^{4} + 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c}{a^{8} b^{2} - 4 \, a^{9} c}} - 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} c^{2} - {\left({\left(a^{2} b + 2 \, a b^{2}\right)} c^{2} - {\left(a b^{3} + b^{4}\right)} c\right)} x^{2} + 2 \, {\left(a^{2} b^{2} + a b^{3}\right)} c + \sqrt{\frac{1}{2}} {\left({\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} x^{2} \sqrt{\frac{a^{2} b^{4} + 2 \, a b^{5} + b^{6} + {\left(a^{4} + 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c}{a^{8} b^{2} - 4 \, a^{9} c}} - {\left(a^{2} b^{4} + a b^{5} + 4 \, {\left(a^{4} + 2 \, a^{3} b\right)} c^{2} - {\left(5 \, a^{3} b^{2} + 6 \, a^{2} b^{3}\right)} c\right)} x^{2}\right)} \sqrt{\frac{a b^{3} + b^{4} + 2 \, a^{2} c^{2} - {\left(3 \, a^{2} b + 4 \, a b^{2}\right)} c + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{a^{2} b^{4} + 2 \, a b^{5} + b^{6} + {\left(a^{4} + 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} + 2 \, {\left({\left(a^{3} + 2 \, a^{2} b\right)} c^{2} - {\left(a^{2} b^{2} + a b^{3}\right)} c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) - \sqrt{\frac{1}{2}} a^{2} x^{2} \sqrt{\frac{a b^{3} + b^{4} + 2 \, a^{2} c^{2} - {\left(3 \, a^{2} b + 4 \, a b^{2}\right)} c + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{a^{2} b^{4} + 2 \, a b^{5} + b^{6} + {\left(a^{4} + 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} \log\left(-\frac{{\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} x^{2} \sqrt{\frac{a^{2} b^{4} + 2 \, a b^{5} + b^{6} + {\left(a^{4} + 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c}{a^{8} b^{2} - 4 \, a^{9} c}} - 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} c^{2} - {\left({\left(a^{2} b + 2 \, a b^{2}\right)} c^{2} - {\left(a b^{3} + b^{4}\right)} c\right)} x^{2} + 2 \, {\left(a^{2} b^{2} + a b^{3}\right)} c - \sqrt{\frac{1}{2}} {\left({\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} x^{2} \sqrt{\frac{a^{2} b^{4} + 2 \, a b^{5} + b^{6} + {\left(a^{4} + 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c}{a^{8} b^{2} - 4 \, a^{9} c}} - {\left(a^{2} b^{4} + a b^{5} + 4 \, {\left(a^{4} + 2 \, a^{3} b\right)} c^{2} - {\left(5 \, a^{3} b^{2} + 6 \, a^{2} b^{3}\right)} c\right)} x^{2}\right)} \sqrt{\frac{a b^{3} + b^{4} + 2 \, a^{2} c^{2} - {\left(3 \, a^{2} b + 4 \, a b^{2}\right)} c + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{a^{2} b^{4} + 2 \, a b^{5} + b^{6} + {\left(a^{4} + 4 \, a^{3} b + 4 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 2 \, a b^{4}\right)} c}{a^{8} b^{2} - 4 \, a^{9} c}}}{a^{4} b^{2} - 4 \, a^{5} c}} + 2 \, {\left({\left(a^{3} + 2 \, a^{2} b\right)} c^{2} - {\left(a^{2} b^{2} + a b^{3}\right)} c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) + {\left(a + 2 \, b\right)} x^{2} \log\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right) + \sqrt{-x^{2} + 1} a}{2 \, a^{2} x^{2}}"," ",0,"-1/2*(sqrt(1/2)*a^2*x^2*sqrt((a*b^3 + b^4 + 2*a^2*c^2 - (3*a^2*b + 4*a*b^2)*c - (a^4*b^2 - 4*a^5*c)*sqrt((a^2*b^4 + 2*a*b^5 + b^6 + (a^4 + 4*a^3*b + 4*a^2*b^2)*c^2 - 2*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*c)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c))*log(((a^4*b^2*c - 4*a^5*c^2)*x^2*sqrt((a^2*b^4 + 2*a*b^5 + b^6 + (a^4 + 4*a^3*b + 4*a^2*b^2)*c^2 - 2*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*c)/(a^8*b^2 - 4*a^9*c)) + 2*(a^3 + 2*a^2*b)*c^2 + ((a^2*b + 2*a*b^2)*c^2 - (a*b^3 + b^4)*c)*x^2 - 2*(a^2*b^2 + a*b^3)*c + sqrt(1/2)*((a^5*b^3 - 4*a^6*b*c)*x^2*sqrt((a^2*b^4 + 2*a*b^5 + b^6 + (a^4 + 4*a^3*b + 4*a^2*b^2)*c^2 - 2*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*c)/(a^8*b^2 - 4*a^9*c)) + (a^2*b^4 + a*b^5 + 4*(a^4 + 2*a^3*b)*c^2 - (5*a^3*b^2 + 6*a^2*b^3)*c)*x^2)*sqrt((a*b^3 + b^4 + 2*a^2*c^2 - (3*a^2*b + 4*a*b^2)*c - (a^4*b^2 - 4*a^5*c)*sqrt((a^2*b^4 + 2*a*b^5 + b^6 + (a^4 + 4*a^3*b + 4*a^2*b^2)*c^2 - 2*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*c)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c)) - 2*((a^3 + 2*a^2*b)*c^2 - (a^2*b^2 + a*b^3)*c)*sqrt(-x^2 + 1))/x^2) - sqrt(1/2)*a^2*x^2*sqrt((a*b^3 + b^4 + 2*a^2*c^2 - (3*a^2*b + 4*a*b^2)*c - (a^4*b^2 - 4*a^5*c)*sqrt((a^2*b^4 + 2*a*b^5 + b^6 + (a^4 + 4*a^3*b + 4*a^2*b^2)*c^2 - 2*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*c)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c))*log(((a^4*b^2*c - 4*a^5*c^2)*x^2*sqrt((a^2*b^4 + 2*a*b^5 + b^6 + (a^4 + 4*a^3*b + 4*a^2*b^2)*c^2 - 2*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*c)/(a^8*b^2 - 4*a^9*c)) + 2*(a^3 + 2*a^2*b)*c^2 + ((a^2*b + 2*a*b^2)*c^2 - (a*b^3 + b^4)*c)*x^2 - 2*(a^2*b^2 + a*b^3)*c - sqrt(1/2)*((a^5*b^3 - 4*a^6*b*c)*x^2*sqrt((a^2*b^4 + 2*a*b^5 + b^6 + (a^4 + 4*a^3*b + 4*a^2*b^2)*c^2 - 2*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*c)/(a^8*b^2 - 4*a^9*c)) + (a^2*b^4 + a*b^5 + 4*(a^4 + 2*a^3*b)*c^2 - (5*a^3*b^2 + 6*a^2*b^3)*c)*x^2)*sqrt((a*b^3 + b^4 + 2*a^2*c^2 - (3*a^2*b + 4*a*b^2)*c - (a^4*b^2 - 4*a^5*c)*sqrt((a^2*b^4 + 2*a*b^5 + b^6 + (a^4 + 4*a^3*b + 4*a^2*b^2)*c^2 - 2*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*c)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c)) - 2*((a^3 + 2*a^2*b)*c^2 - (a^2*b^2 + a*b^3)*c)*sqrt(-x^2 + 1))/x^2) + sqrt(1/2)*a^2*x^2*sqrt((a*b^3 + b^4 + 2*a^2*c^2 - (3*a^2*b + 4*a*b^2)*c + (a^4*b^2 - 4*a^5*c)*sqrt((a^2*b^4 + 2*a*b^5 + b^6 + (a^4 + 4*a^3*b + 4*a^2*b^2)*c^2 - 2*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*c)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c))*log(-((a^4*b^2*c - 4*a^5*c^2)*x^2*sqrt((a^2*b^4 + 2*a*b^5 + b^6 + (a^4 + 4*a^3*b + 4*a^2*b^2)*c^2 - 2*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*c)/(a^8*b^2 - 4*a^9*c)) - 2*(a^3 + 2*a^2*b)*c^2 - ((a^2*b + 2*a*b^2)*c^2 - (a*b^3 + b^4)*c)*x^2 + 2*(a^2*b^2 + a*b^3)*c + sqrt(1/2)*((a^5*b^3 - 4*a^6*b*c)*x^2*sqrt((a^2*b^4 + 2*a*b^5 + b^6 + (a^4 + 4*a^3*b + 4*a^2*b^2)*c^2 - 2*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*c)/(a^8*b^2 - 4*a^9*c)) - (a^2*b^4 + a*b^5 + 4*(a^4 + 2*a^3*b)*c^2 - (5*a^3*b^2 + 6*a^2*b^3)*c)*x^2)*sqrt((a*b^3 + b^4 + 2*a^2*c^2 - (3*a^2*b + 4*a*b^2)*c + (a^4*b^2 - 4*a^5*c)*sqrt((a^2*b^4 + 2*a*b^5 + b^6 + (a^4 + 4*a^3*b + 4*a^2*b^2)*c^2 - 2*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*c)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c)) + 2*((a^3 + 2*a^2*b)*c^2 - (a^2*b^2 + a*b^3)*c)*sqrt(-x^2 + 1))/x^2) - sqrt(1/2)*a^2*x^2*sqrt((a*b^3 + b^4 + 2*a^2*c^2 - (3*a^2*b + 4*a*b^2)*c + (a^4*b^2 - 4*a^5*c)*sqrt((a^2*b^4 + 2*a*b^5 + b^6 + (a^4 + 4*a^3*b + 4*a^2*b^2)*c^2 - 2*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*c)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c))*log(-((a^4*b^2*c - 4*a^5*c^2)*x^2*sqrt((a^2*b^4 + 2*a*b^5 + b^6 + (a^4 + 4*a^3*b + 4*a^2*b^2)*c^2 - 2*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*c)/(a^8*b^2 - 4*a^9*c)) - 2*(a^3 + 2*a^2*b)*c^2 - ((a^2*b + 2*a*b^2)*c^2 - (a*b^3 + b^4)*c)*x^2 + 2*(a^2*b^2 + a*b^3)*c - sqrt(1/2)*((a^5*b^3 - 4*a^6*b*c)*x^2*sqrt((a^2*b^4 + 2*a*b^5 + b^6 + (a^4 + 4*a^3*b + 4*a^2*b^2)*c^2 - 2*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*c)/(a^8*b^2 - 4*a^9*c)) - (a^2*b^4 + a*b^5 + 4*(a^4 + 2*a^3*b)*c^2 - (5*a^3*b^2 + 6*a^2*b^3)*c)*x^2)*sqrt((a*b^3 + b^4 + 2*a^2*c^2 - (3*a^2*b + 4*a*b^2)*c + (a^4*b^2 - 4*a^5*c)*sqrt((a^2*b^4 + 2*a*b^5 + b^6 + (a^4 + 4*a^3*b + 4*a^2*b^2)*c^2 - 2*(a^3*b^2 + 3*a^2*b^3 + 2*a*b^4)*c)/(a^8*b^2 - 4*a^9*c)))/(a^4*b^2 - 4*a^5*c)) + 2*((a^3 + 2*a^2*b)*c^2 - (a^2*b^2 + a*b^3)*c)*sqrt(-x^2 + 1))/x^2) + (a + 2*b)*x^2*log((sqrt(-x^2 + 1) - 1)/x) + sqrt(-x^2 + 1)*a)/(a^2*x^2)","B",0
381,1,2860,0,4.252453," ","integrate(x^4*(-x^2+1)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} c^{2} \sqrt{-\frac{b^{4} + {\left(2 \, a^{2} - 3 \, a b\right)} c^{2} - {\left(4 \, a b^{2} - b^{3}\right)} c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{6} + a^{2} c^{4} + 2 \, {\left(2 \, a^{2} b - a b^{2}\right)} c^{3} + {\left(4 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} c^{2} - 2 \, {\left(2 \, a b^{4} - b^{5}\right)} c}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}} \log\left(-\frac{2 \, a^{2} b^{3} - 2 \, a^{3} c^{2} - 2 \, {\left(a^{2} b^{3} - a^{3} c^{2} - {\left(2 \, a^{3} b - a^{2} b^{2}\right)} c\right)} x^{2} - 2 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} c + \sqrt{\frac{1}{2}} {\left({\left(b^{6} + 4 \, a^{2} b c^{3} + {\left(8 \, a^{2} b^{2} - 5 \, a b^{3}\right)} c^{2} - {\left(6 \, a b^{4} - b^{5}\right)} c\right)} \sqrt{-x^{2} + 1} x - {\left(b^{6} + 4 \, a^{2} b c^{3} + {\left(8 \, a^{2} b^{2} - 5 \, a b^{3}\right)} c^{2} - {\left(6 \, a b^{4} - b^{5}\right)} c\right)} x - {\left({\left(b^{4} c^{4} - 6 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} \sqrt{-x^{2} + 1} x - {\left(b^{4} c^{4} - 6 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} x\right)} \sqrt{\frac{b^{6} + a^{2} c^{4} + 2 \, {\left(2 \, a^{2} b - a b^{2}\right)} c^{3} + {\left(4 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} c^{2} - 2 \, {\left(2 \, a b^{4} - b^{5}\right)} c}{b^{2} c^{8} - 4 \, a c^{9}}}\right)} \sqrt{-\frac{b^{4} + {\left(2 \, a^{2} - 3 \, a b\right)} c^{2} - {\left(4 \, a b^{2} - b^{3}\right)} c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{6} + a^{2} c^{4} + 2 \, {\left(2 \, a^{2} b - a b^{2}\right)} c^{3} + {\left(4 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} c^{2} - 2 \, {\left(2 \, a b^{4} - b^{5}\right)} c}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}} - 2 \, {\left(a^{2} b^{3} - a^{3} c^{2} - {\left(2 \, a^{3} b - a^{2} b^{2}\right)} c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c^{2} \sqrt{-\frac{b^{4} + {\left(2 \, a^{2} - 3 \, a b\right)} c^{2} - {\left(4 \, a b^{2} - b^{3}\right)} c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{6} + a^{2} c^{4} + 2 \, {\left(2 \, a^{2} b - a b^{2}\right)} c^{3} + {\left(4 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} c^{2} - 2 \, {\left(2 \, a b^{4} - b^{5}\right)} c}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}} \log\left(-\frac{2 \, a^{2} b^{3} - 2 \, a^{3} c^{2} - 2 \, {\left(a^{2} b^{3} - a^{3} c^{2} - {\left(2 \, a^{3} b - a^{2} b^{2}\right)} c\right)} x^{2} - 2 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} c - \sqrt{\frac{1}{2}} {\left({\left(b^{6} + 4 \, a^{2} b c^{3} + {\left(8 \, a^{2} b^{2} - 5 \, a b^{3}\right)} c^{2} - {\left(6 \, a b^{4} - b^{5}\right)} c\right)} \sqrt{-x^{2} + 1} x - {\left(b^{6} + 4 \, a^{2} b c^{3} + {\left(8 \, a^{2} b^{2} - 5 \, a b^{3}\right)} c^{2} - {\left(6 \, a b^{4} - b^{5}\right)} c\right)} x - {\left({\left(b^{4} c^{4} - 6 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} \sqrt{-x^{2} + 1} x - {\left(b^{4} c^{4} - 6 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} x\right)} \sqrt{\frac{b^{6} + a^{2} c^{4} + 2 \, {\left(2 \, a^{2} b - a b^{2}\right)} c^{3} + {\left(4 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} c^{2} - 2 \, {\left(2 \, a b^{4} - b^{5}\right)} c}{b^{2} c^{8} - 4 \, a c^{9}}}\right)} \sqrt{-\frac{b^{4} + {\left(2 \, a^{2} - 3 \, a b\right)} c^{2} - {\left(4 \, a b^{2} - b^{3}\right)} c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{6} + a^{2} c^{4} + 2 \, {\left(2 \, a^{2} b - a b^{2}\right)} c^{3} + {\left(4 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} c^{2} - 2 \, {\left(2 \, a b^{4} - b^{5}\right)} c}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}} - 2 \, {\left(a^{2} b^{3} - a^{3} c^{2} - {\left(2 \, a^{3} b - a^{2} b^{2}\right)} c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) + \sqrt{\frac{1}{2}} c^{2} \sqrt{-\frac{b^{4} + {\left(2 \, a^{2} - 3 \, a b\right)} c^{2} - {\left(4 \, a b^{2} - b^{3}\right)} c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{6} + a^{2} c^{4} + 2 \, {\left(2 \, a^{2} b - a b^{2}\right)} c^{3} + {\left(4 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} c^{2} - 2 \, {\left(2 \, a b^{4} - b^{5}\right)} c}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}} \log\left(-\frac{2 \, a^{2} b^{3} - 2 \, a^{3} c^{2} - 2 \, {\left(a^{2} b^{3} - a^{3} c^{2} - {\left(2 \, a^{3} b - a^{2} b^{2}\right)} c\right)} x^{2} - 2 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} c + \sqrt{\frac{1}{2}} {\left({\left(b^{6} + 4 \, a^{2} b c^{3} + {\left(8 \, a^{2} b^{2} - 5 \, a b^{3}\right)} c^{2} - {\left(6 \, a b^{4} - b^{5}\right)} c\right)} \sqrt{-x^{2} + 1} x - {\left(b^{6} + 4 \, a^{2} b c^{3} + {\left(8 \, a^{2} b^{2} - 5 \, a b^{3}\right)} c^{2} - {\left(6 \, a b^{4} - b^{5}\right)} c\right)} x + {\left({\left(b^{4} c^{4} - 6 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} \sqrt{-x^{2} + 1} x - {\left(b^{4} c^{4} - 6 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} x\right)} \sqrt{\frac{b^{6} + a^{2} c^{4} + 2 \, {\left(2 \, a^{2} b - a b^{2}\right)} c^{3} + {\left(4 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} c^{2} - 2 \, {\left(2 \, a b^{4} - b^{5}\right)} c}{b^{2} c^{8} - 4 \, a c^{9}}}\right)} \sqrt{-\frac{b^{4} + {\left(2 \, a^{2} - 3 \, a b\right)} c^{2} - {\left(4 \, a b^{2} - b^{3}\right)} c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{6} + a^{2} c^{4} + 2 \, {\left(2 \, a^{2} b - a b^{2}\right)} c^{3} + {\left(4 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} c^{2} - 2 \, {\left(2 \, a b^{4} - b^{5}\right)} c}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}} - 2 \, {\left(a^{2} b^{3} - a^{3} c^{2} - {\left(2 \, a^{3} b - a^{2} b^{2}\right)} c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c^{2} \sqrt{-\frac{b^{4} + {\left(2 \, a^{2} - 3 \, a b\right)} c^{2} - {\left(4 \, a b^{2} - b^{3}\right)} c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{6} + a^{2} c^{4} + 2 \, {\left(2 \, a^{2} b - a b^{2}\right)} c^{3} + {\left(4 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} c^{2} - 2 \, {\left(2 \, a b^{4} - b^{5}\right)} c}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}} \log\left(-\frac{2 \, a^{2} b^{3} - 2 \, a^{3} c^{2} - 2 \, {\left(a^{2} b^{3} - a^{3} c^{2} - {\left(2 \, a^{3} b - a^{2} b^{2}\right)} c\right)} x^{2} - 2 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} c - \sqrt{\frac{1}{2}} {\left({\left(b^{6} + 4 \, a^{2} b c^{3} + {\left(8 \, a^{2} b^{2} - 5 \, a b^{3}\right)} c^{2} - {\left(6 \, a b^{4} - b^{5}\right)} c\right)} \sqrt{-x^{2} + 1} x - {\left(b^{6} + 4 \, a^{2} b c^{3} + {\left(8 \, a^{2} b^{2} - 5 \, a b^{3}\right)} c^{2} - {\left(6 \, a b^{4} - b^{5}\right)} c\right)} x + {\left({\left(b^{4} c^{4} - 6 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} \sqrt{-x^{2} + 1} x - {\left(b^{4} c^{4} - 6 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} x\right)} \sqrt{\frac{b^{6} + a^{2} c^{4} + 2 \, {\left(2 \, a^{2} b - a b^{2}\right)} c^{3} + {\left(4 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} c^{2} - 2 \, {\left(2 \, a b^{4} - b^{5}\right)} c}{b^{2} c^{8} - 4 \, a c^{9}}}\right)} \sqrt{-\frac{b^{4} + {\left(2 \, a^{2} - 3 \, a b\right)} c^{2} - {\left(4 \, a b^{2} - b^{3}\right)} c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{6} + a^{2} c^{4} + 2 \, {\left(2 \, a^{2} b - a b^{2}\right)} c^{3} + {\left(4 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} c^{2} - 2 \, {\left(2 \, a b^{4} - b^{5}\right)} c}{b^{2} c^{8} - 4 \, a c^{9}}}}{b^{2} c^{4} - 4 \, a c^{5}}} - 2 \, {\left(a^{2} b^{3} - a^{3} c^{2} - {\left(2 \, a^{3} b - a^{2} b^{2}\right)} c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) - \sqrt{-x^{2} + 1} c x + 2 \, {\left(2 \, b + c\right)} \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)}{2 \, c^{2}}"," ",0,"-1/2*(sqrt(1/2)*c^2*sqrt(-(b^4 + (2*a^2 - 3*a*b)*c^2 - (4*a*b^2 - b^3)*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^6 + a^2*c^4 + 2*(2*a^2*b - a*b^2)*c^3 + (4*a^2*b^2 - 6*a*b^3 + b^4)*c^2 - 2*(2*a*b^4 - b^5)*c)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5))*log(-(2*a^2*b^3 - 2*a^3*c^2 - 2*(a^2*b^3 - a^3*c^2 - (2*a^3*b - a^2*b^2)*c)*x^2 - 2*(2*a^3*b - a^2*b^2)*c + sqrt(1/2)*((b^6 + 4*a^2*b*c^3 + (8*a^2*b^2 - 5*a*b^3)*c^2 - (6*a*b^4 - b^5)*c)*sqrt(-x^2 + 1)*x - (b^6 + 4*a^2*b*c^3 + (8*a^2*b^2 - 5*a*b^3)*c^2 - (6*a*b^4 - b^5)*c)*x - ((b^4*c^4 - 6*a*b^2*c^5 + 8*a^2*c^6)*sqrt(-x^2 + 1)*x - (b^4*c^4 - 6*a*b^2*c^5 + 8*a^2*c^6)*x)*sqrt((b^6 + a^2*c^4 + 2*(2*a^2*b - a*b^2)*c^3 + (4*a^2*b^2 - 6*a*b^3 + b^4)*c^2 - 2*(2*a*b^4 - b^5)*c)/(b^2*c^8 - 4*a*c^9)))*sqrt(-(b^4 + (2*a^2 - 3*a*b)*c^2 - (4*a*b^2 - b^3)*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^6 + a^2*c^4 + 2*(2*a^2*b - a*b^2)*c^3 + (4*a^2*b^2 - 6*a*b^3 + b^4)*c^2 - 2*(2*a*b^4 - b^5)*c)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5)) - 2*(a^2*b^3 - a^3*c^2 - (2*a^3*b - a^2*b^2)*c)*sqrt(-x^2 + 1))/x^2) - sqrt(1/2)*c^2*sqrt(-(b^4 + (2*a^2 - 3*a*b)*c^2 - (4*a*b^2 - b^3)*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^6 + a^2*c^4 + 2*(2*a^2*b - a*b^2)*c^3 + (4*a^2*b^2 - 6*a*b^3 + b^4)*c^2 - 2*(2*a*b^4 - b^5)*c)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5))*log(-(2*a^2*b^3 - 2*a^3*c^2 - 2*(a^2*b^3 - a^3*c^2 - (2*a^3*b - a^2*b^2)*c)*x^2 - 2*(2*a^3*b - a^2*b^2)*c - sqrt(1/2)*((b^6 + 4*a^2*b*c^3 + (8*a^2*b^2 - 5*a*b^3)*c^2 - (6*a*b^4 - b^5)*c)*sqrt(-x^2 + 1)*x - (b^6 + 4*a^2*b*c^3 + (8*a^2*b^2 - 5*a*b^3)*c^2 - (6*a*b^4 - b^5)*c)*x - ((b^4*c^4 - 6*a*b^2*c^5 + 8*a^2*c^6)*sqrt(-x^2 + 1)*x - (b^4*c^4 - 6*a*b^2*c^5 + 8*a^2*c^6)*x)*sqrt((b^6 + a^2*c^4 + 2*(2*a^2*b - a*b^2)*c^3 + (4*a^2*b^2 - 6*a*b^3 + b^4)*c^2 - 2*(2*a*b^4 - b^5)*c)/(b^2*c^8 - 4*a*c^9)))*sqrt(-(b^4 + (2*a^2 - 3*a*b)*c^2 - (4*a*b^2 - b^3)*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^6 + a^2*c^4 + 2*(2*a^2*b - a*b^2)*c^3 + (4*a^2*b^2 - 6*a*b^3 + b^4)*c^2 - 2*(2*a*b^4 - b^5)*c)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5)) - 2*(a^2*b^3 - a^3*c^2 - (2*a^3*b - a^2*b^2)*c)*sqrt(-x^2 + 1))/x^2) + sqrt(1/2)*c^2*sqrt(-(b^4 + (2*a^2 - 3*a*b)*c^2 - (4*a*b^2 - b^3)*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^6 + a^2*c^4 + 2*(2*a^2*b - a*b^2)*c^3 + (4*a^2*b^2 - 6*a*b^3 + b^4)*c^2 - 2*(2*a*b^4 - b^5)*c)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5))*log(-(2*a^2*b^3 - 2*a^3*c^2 - 2*(a^2*b^3 - a^3*c^2 - (2*a^3*b - a^2*b^2)*c)*x^2 - 2*(2*a^3*b - a^2*b^2)*c + sqrt(1/2)*((b^6 + 4*a^2*b*c^3 + (8*a^2*b^2 - 5*a*b^3)*c^2 - (6*a*b^4 - b^5)*c)*sqrt(-x^2 + 1)*x - (b^6 + 4*a^2*b*c^3 + (8*a^2*b^2 - 5*a*b^3)*c^2 - (6*a*b^4 - b^5)*c)*x + ((b^4*c^4 - 6*a*b^2*c^5 + 8*a^2*c^6)*sqrt(-x^2 + 1)*x - (b^4*c^4 - 6*a*b^2*c^5 + 8*a^2*c^6)*x)*sqrt((b^6 + a^2*c^4 + 2*(2*a^2*b - a*b^2)*c^3 + (4*a^2*b^2 - 6*a*b^3 + b^4)*c^2 - 2*(2*a*b^4 - b^5)*c)/(b^2*c^8 - 4*a*c^9)))*sqrt(-(b^4 + (2*a^2 - 3*a*b)*c^2 - (4*a*b^2 - b^3)*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^6 + a^2*c^4 + 2*(2*a^2*b - a*b^2)*c^3 + (4*a^2*b^2 - 6*a*b^3 + b^4)*c^2 - 2*(2*a*b^4 - b^5)*c)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5)) - 2*(a^2*b^3 - a^3*c^2 - (2*a^3*b - a^2*b^2)*c)*sqrt(-x^2 + 1))/x^2) - sqrt(1/2)*c^2*sqrt(-(b^4 + (2*a^2 - 3*a*b)*c^2 - (4*a*b^2 - b^3)*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^6 + a^2*c^4 + 2*(2*a^2*b - a*b^2)*c^3 + (4*a^2*b^2 - 6*a*b^3 + b^4)*c^2 - 2*(2*a*b^4 - b^5)*c)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5))*log(-(2*a^2*b^3 - 2*a^3*c^2 - 2*(a^2*b^3 - a^3*c^2 - (2*a^3*b - a^2*b^2)*c)*x^2 - 2*(2*a^3*b - a^2*b^2)*c - sqrt(1/2)*((b^6 + 4*a^2*b*c^3 + (8*a^2*b^2 - 5*a*b^3)*c^2 - (6*a*b^4 - b^5)*c)*sqrt(-x^2 + 1)*x - (b^6 + 4*a^2*b*c^3 + (8*a^2*b^2 - 5*a*b^3)*c^2 - (6*a*b^4 - b^5)*c)*x + ((b^4*c^4 - 6*a*b^2*c^5 + 8*a^2*c^6)*sqrt(-x^2 + 1)*x - (b^4*c^4 - 6*a*b^2*c^5 + 8*a^2*c^6)*x)*sqrt((b^6 + a^2*c^4 + 2*(2*a^2*b - a*b^2)*c^3 + (4*a^2*b^2 - 6*a*b^3 + b^4)*c^2 - 2*(2*a*b^4 - b^5)*c)/(b^2*c^8 - 4*a*c^9)))*sqrt(-(b^4 + (2*a^2 - 3*a*b)*c^2 - (4*a*b^2 - b^3)*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^6 + a^2*c^4 + 2*(2*a^2*b - a*b^2)*c^3 + (4*a^2*b^2 - 6*a*b^3 + b^4)*c^2 - 2*(2*a*b^4 - b^5)*c)/(b^2*c^8 - 4*a*c^9)))/(b^2*c^4 - 4*a*c^5)) - 2*(a^2*b^3 - a^3*c^2 - (2*a^3*b - a^2*b^2)*c)*sqrt(-x^2 + 1))/x^2) - sqrt(-x^2 + 1)*c*x + 2*(2*b + c)*arctan((sqrt(-x^2 + 1) - 1)/x))/c^2","B",0
382,1,1430,0,1.981891," ","integrate(x^2*(-x^2+1)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} c \sqrt{-\frac{b^{2} - {\left(2 \, a - b\right)} c + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2} + 2 \, b c + c^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \log\left(-\frac{2 \, {\left(a b + a c\right)} x^{2} - 2 \, a b - 2 \, a c + \sqrt{\frac{1}{2}} {\left({\left(b^{3} - 4 \, a c^{2} - {\left(4 \, a b - b^{2}\right)} c\right)} \sqrt{-x^{2} + 1} x - {\left(b^{3} - 4 \, a c^{2} - {\left(4 \, a b - b^{2}\right)} c\right)} x - {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} \sqrt{-x^{2} + 1} x - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)} \sqrt{\frac{b^{2} + 2 \, b c + c^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}\right)} \sqrt{-\frac{b^{2} - {\left(2 \, a - b\right)} c + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2} + 2 \, b c + c^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} + 2 \, {\left(a b + a c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c \sqrt{-\frac{b^{2} - {\left(2 \, a - b\right)} c + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2} + 2 \, b c + c^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \log\left(-\frac{2 \, {\left(a b + a c\right)} x^{2} - 2 \, a b - 2 \, a c - \sqrt{\frac{1}{2}} {\left({\left(b^{3} - 4 \, a c^{2} - {\left(4 \, a b - b^{2}\right)} c\right)} \sqrt{-x^{2} + 1} x - {\left(b^{3} - 4 \, a c^{2} - {\left(4 \, a b - b^{2}\right)} c\right)} x - {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} \sqrt{-x^{2} + 1} x - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)} \sqrt{\frac{b^{2} + 2 \, b c + c^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}\right)} \sqrt{-\frac{b^{2} - {\left(2 \, a - b\right)} c + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2} + 2 \, b c + c^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} + 2 \, {\left(a b + a c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) + \sqrt{\frac{1}{2}} c \sqrt{-\frac{b^{2} - {\left(2 \, a - b\right)} c - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2} + 2 \, b c + c^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \log\left(-\frac{2 \, {\left(a b + a c\right)} x^{2} - 2 \, a b - 2 \, a c + \sqrt{\frac{1}{2}} {\left({\left(b^{3} - 4 \, a c^{2} - {\left(4 \, a b - b^{2}\right)} c\right)} \sqrt{-x^{2} + 1} x - {\left(b^{3} - 4 \, a c^{2} - {\left(4 \, a b - b^{2}\right)} c\right)} x + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} \sqrt{-x^{2} + 1} x - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)} \sqrt{\frac{b^{2} + 2 \, b c + c^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}\right)} \sqrt{-\frac{b^{2} - {\left(2 \, a - b\right)} c - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2} + 2 \, b c + c^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} + 2 \, {\left(a b + a c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c \sqrt{-\frac{b^{2} - {\left(2 \, a - b\right)} c - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2} + 2 \, b c + c^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \log\left(-\frac{2 \, {\left(a b + a c\right)} x^{2} - 2 \, a b - 2 \, a c - \sqrt{\frac{1}{2}} {\left({\left(b^{3} - 4 \, a c^{2} - {\left(4 \, a b - b^{2}\right)} c\right)} \sqrt{-x^{2} + 1} x - {\left(b^{3} - 4 \, a c^{2} - {\left(4 \, a b - b^{2}\right)} c\right)} x + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} \sqrt{-x^{2} + 1} x - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)} \sqrt{\frac{b^{2} + 2 \, b c + c^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}\right)} \sqrt{-\frac{b^{2} - {\left(2 \, a - b\right)} c - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2} + 2 \, b c + c^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} + 2 \, {\left(a b + a c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) - 4 \, \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)}{2 \, c}"," ",0,"-1/2*(sqrt(1/2)*c*sqrt(-(b^2 - (2*a - b)*c + (b^2*c^2 - 4*a*c^3)*sqrt((b^2 + 2*b*c + c^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*log(-(2*(a*b + a*c)*x^2 - 2*a*b - 2*a*c + sqrt(1/2)*((b^3 - 4*a*c^2 - (4*a*b - b^2)*c)*sqrt(-x^2 + 1)*x - (b^3 - 4*a*c^2 - (4*a*b - b^2)*c)*x - ((b^3*c^2 - 4*a*b*c^3)*sqrt(-x^2 + 1)*x - (b^3*c^2 - 4*a*b*c^3)*x)*sqrt((b^2 + 2*b*c + c^2)/(b^2*c^4 - 4*a*c^5)))*sqrt(-(b^2 - (2*a - b)*c + (b^2*c^2 - 4*a*c^3)*sqrt((b^2 + 2*b*c + c^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3)) + 2*(a*b + a*c)*sqrt(-x^2 + 1))/x^2) - sqrt(1/2)*c*sqrt(-(b^2 - (2*a - b)*c + (b^2*c^2 - 4*a*c^3)*sqrt((b^2 + 2*b*c + c^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*log(-(2*(a*b + a*c)*x^2 - 2*a*b - 2*a*c - sqrt(1/2)*((b^3 - 4*a*c^2 - (4*a*b - b^2)*c)*sqrt(-x^2 + 1)*x - (b^3 - 4*a*c^2 - (4*a*b - b^2)*c)*x - ((b^3*c^2 - 4*a*b*c^3)*sqrt(-x^2 + 1)*x - (b^3*c^2 - 4*a*b*c^3)*x)*sqrt((b^2 + 2*b*c + c^2)/(b^2*c^4 - 4*a*c^5)))*sqrt(-(b^2 - (2*a - b)*c + (b^2*c^2 - 4*a*c^3)*sqrt((b^2 + 2*b*c + c^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3)) + 2*(a*b + a*c)*sqrt(-x^2 + 1))/x^2) + sqrt(1/2)*c*sqrt(-(b^2 - (2*a - b)*c - (b^2*c^2 - 4*a*c^3)*sqrt((b^2 + 2*b*c + c^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*log(-(2*(a*b + a*c)*x^2 - 2*a*b - 2*a*c + sqrt(1/2)*((b^3 - 4*a*c^2 - (4*a*b - b^2)*c)*sqrt(-x^2 + 1)*x - (b^3 - 4*a*c^2 - (4*a*b - b^2)*c)*x + ((b^3*c^2 - 4*a*b*c^3)*sqrt(-x^2 + 1)*x - (b^3*c^2 - 4*a*b*c^3)*x)*sqrt((b^2 + 2*b*c + c^2)/(b^2*c^4 - 4*a*c^5)))*sqrt(-(b^2 - (2*a - b)*c - (b^2*c^2 - 4*a*c^3)*sqrt((b^2 + 2*b*c + c^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3)) + 2*(a*b + a*c)*sqrt(-x^2 + 1))/x^2) - sqrt(1/2)*c*sqrt(-(b^2 - (2*a - b)*c - (b^2*c^2 - 4*a*c^3)*sqrt((b^2 + 2*b*c + c^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*log(-(2*(a*b + a*c)*x^2 - 2*a*b - 2*a*c - sqrt(1/2)*((b^3 - 4*a*c^2 - (4*a*b - b^2)*c)*sqrt(-x^2 + 1)*x - (b^3 - 4*a*c^2 - (4*a*b - b^2)*c)*x + ((b^3*c^2 - 4*a*b*c^3)*sqrt(-x^2 + 1)*x - (b^3*c^2 - 4*a*b*c^3)*x)*sqrt((b^2 + 2*b*c + c^2)/(b^2*c^4 - 4*a*c^5)))*sqrt(-(b^2 - (2*a - b)*c - (b^2*c^2 - 4*a*c^3)*sqrt((b^2 + 2*b*c + c^2)/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3)) + 2*(a*b + a*c)*sqrt(-x^2 + 1))/x^2) - 4*arctan((sqrt(-x^2 + 1) - 1)/x))/c","B",0
383,1,759,0,0.925413," ","integrate((-x^2+1)^(1/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{2 \, a + b + \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}} \log\left(-\frac{x^{2} + \frac{\sqrt{\frac{1}{2}} {\left({\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{-x^{2} + 1} x - {\left(a b^{2} - 4 \, a^{2} c\right)} x\right)} \sqrt{-\frac{2 \, a + b + \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}}}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}} + \sqrt{-x^{2} + 1} - 1}{x^{2}}\right) - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{2 \, a + b + \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}} \log\left(-\frac{x^{2} - \frac{\sqrt{\frac{1}{2}} {\left({\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{-x^{2} + 1} x - {\left(a b^{2} - 4 \, a^{2} c\right)} x\right)} \sqrt{-\frac{2 \, a + b + \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}}}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}} + \sqrt{-x^{2} + 1} - 1}{x^{2}}\right) - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{2 \, a + b - \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}} \log\left(-\frac{x^{2} + \frac{\sqrt{\frac{1}{2}} {\left({\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{-x^{2} + 1} x - {\left(a b^{2} - 4 \, a^{2} c\right)} x\right)} \sqrt{-\frac{2 \, a + b - \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}}}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}} + \sqrt{-x^{2} + 1} - 1}{x^{2}}\right) + \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{2 \, a + b - \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}} \log\left(-\frac{x^{2} - \frac{\sqrt{\frac{1}{2}} {\left({\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{-x^{2} + 1} x - {\left(a b^{2} - 4 \, a^{2} c\right)} x\right)} \sqrt{-\frac{2 \, a + b - \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}}}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}} + \sqrt{-x^{2} + 1} - 1}{x^{2}}\right)"," ",0,"1/2*sqrt(1/2)*sqrt(-(2*a + b + (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))*log(-(x^2 + sqrt(1/2)*((a*b^2 - 4*a^2*c)*sqrt(-x^2 + 1)*x - (a*b^2 - 4*a^2*c)*x)*sqrt(-(2*a + b + (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))/sqrt(a^2*b^2 - 4*a^3*c) + sqrt(-x^2 + 1) - 1)/x^2) - 1/2*sqrt(1/2)*sqrt(-(2*a + b + (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))*log(-(x^2 - sqrt(1/2)*((a*b^2 - 4*a^2*c)*sqrt(-x^2 + 1)*x - (a*b^2 - 4*a^2*c)*x)*sqrt(-(2*a + b + (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))/sqrt(a^2*b^2 - 4*a^3*c) + sqrt(-x^2 + 1) - 1)/x^2) - 1/2*sqrt(1/2)*sqrt(-(2*a + b - (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))*log(-(x^2 + sqrt(1/2)*((a*b^2 - 4*a^2*c)*sqrt(-x^2 + 1)*x - (a*b^2 - 4*a^2*c)*x)*sqrt(-(2*a + b - (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))/sqrt(a^2*b^2 - 4*a^3*c) + sqrt(-x^2 + 1) - 1)/x^2) + 1/2*sqrt(1/2)*sqrt(-(2*a + b - (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))*log(-(x^2 - sqrt(1/2)*((a*b^2 - 4*a^2*c)*sqrt(-x^2 + 1)*x - (a*b^2 - 4*a^2*c)*x)*sqrt(-(2*a + b - (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))/sqrt(a^2*b^2 - 4*a^3*c) + sqrt(-x^2 + 1) - 1)/x^2)","B",0
384,1,1998,0,1.417896," ","integrate((-x^2+1)^(1/2)/x^2/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} a x \sqrt{-\frac{a b^{2} + b^{3} - {\left(2 \, a^{2} + 3 \, a b\right)} c + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{a^{2} b^{2} + 2 \, a b^{3} + b^{4} + a^{2} c^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(\frac{2 \, a c^{2} - 2 \, {\left(a c^{2} - {\left(a b + b^{2}\right)} c\right)} x^{2} - 2 \, {\left(a b + b^{2}\right)} c + \sqrt{\frac{1}{2}} {\left({\left(a b^{3} + b^{4} + 4 \, a^{2} c^{2} - {\left(4 \, a^{2} b + 5 \, a b^{2}\right)} c\right)} \sqrt{-x^{2} + 1} x - {\left(a b^{3} + b^{4} + 4 \, a^{2} c^{2} - {\left(4 \, a^{2} b + 5 \, a b^{2}\right)} c\right)} x - {\left({\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} \sqrt{-x^{2} + 1} x - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x\right)} \sqrt{\frac{a^{2} b^{2} + 2 \, a b^{3} + b^{4} + a^{2} c^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{a b^{2} + b^{3} - {\left(2 \, a^{2} + 3 \, a b\right)} c + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{a^{2} b^{2} + 2 \, a b^{3} + b^{4} + a^{2} c^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} - 2 \, {\left(a c^{2} - {\left(a b + b^{2}\right)} c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) - \sqrt{\frac{1}{2}} a x \sqrt{-\frac{a b^{2} + b^{3} - {\left(2 \, a^{2} + 3 \, a b\right)} c + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{a^{2} b^{2} + 2 \, a b^{3} + b^{4} + a^{2} c^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(\frac{2 \, a c^{2} - 2 \, {\left(a c^{2} - {\left(a b + b^{2}\right)} c\right)} x^{2} - 2 \, {\left(a b + b^{2}\right)} c - \sqrt{\frac{1}{2}} {\left({\left(a b^{3} + b^{4} + 4 \, a^{2} c^{2} - {\left(4 \, a^{2} b + 5 \, a b^{2}\right)} c\right)} \sqrt{-x^{2} + 1} x - {\left(a b^{3} + b^{4} + 4 \, a^{2} c^{2} - {\left(4 \, a^{2} b + 5 \, a b^{2}\right)} c\right)} x - {\left({\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} \sqrt{-x^{2} + 1} x - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x\right)} \sqrt{\frac{a^{2} b^{2} + 2 \, a b^{3} + b^{4} + a^{2} c^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{a b^{2} + b^{3} - {\left(2 \, a^{2} + 3 \, a b\right)} c + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{a^{2} b^{2} + 2 \, a b^{3} + b^{4} + a^{2} c^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} - 2 \, {\left(a c^{2} - {\left(a b + b^{2}\right)} c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) + \sqrt{\frac{1}{2}} a x \sqrt{-\frac{a b^{2} + b^{3} - {\left(2 \, a^{2} + 3 \, a b\right)} c - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{a^{2} b^{2} + 2 \, a b^{3} + b^{4} + a^{2} c^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(\frac{2 \, a c^{2} - 2 \, {\left(a c^{2} - {\left(a b + b^{2}\right)} c\right)} x^{2} - 2 \, {\left(a b + b^{2}\right)} c + \sqrt{\frac{1}{2}} {\left({\left(a b^{3} + b^{4} + 4 \, a^{2} c^{2} - {\left(4 \, a^{2} b + 5 \, a b^{2}\right)} c\right)} \sqrt{-x^{2} + 1} x - {\left(a b^{3} + b^{4} + 4 \, a^{2} c^{2} - {\left(4 \, a^{2} b + 5 \, a b^{2}\right)} c\right)} x + {\left({\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} \sqrt{-x^{2} + 1} x - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x\right)} \sqrt{\frac{a^{2} b^{2} + 2 \, a b^{3} + b^{4} + a^{2} c^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{a b^{2} + b^{3} - {\left(2 \, a^{2} + 3 \, a b\right)} c - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{a^{2} b^{2} + 2 \, a b^{3} + b^{4} + a^{2} c^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} - 2 \, {\left(a c^{2} - {\left(a b + b^{2}\right)} c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) - \sqrt{\frac{1}{2}} a x \sqrt{-\frac{a b^{2} + b^{3} - {\left(2 \, a^{2} + 3 \, a b\right)} c - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{a^{2} b^{2} + 2 \, a b^{3} + b^{4} + a^{2} c^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(\frac{2 \, a c^{2} - 2 \, {\left(a c^{2} - {\left(a b + b^{2}\right)} c\right)} x^{2} - 2 \, {\left(a b + b^{2}\right)} c - \sqrt{\frac{1}{2}} {\left({\left(a b^{3} + b^{4} + 4 \, a^{2} c^{2} - {\left(4 \, a^{2} b + 5 \, a b^{2}\right)} c\right)} \sqrt{-x^{2} + 1} x - {\left(a b^{3} + b^{4} + 4 \, a^{2} c^{2} - {\left(4 \, a^{2} b + 5 \, a b^{2}\right)} c\right)} x + {\left({\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} \sqrt{-x^{2} + 1} x - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x\right)} \sqrt{\frac{a^{2} b^{2} + 2 \, a b^{3} + b^{4} + a^{2} c^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{a b^{2} + b^{3} - {\left(2 \, a^{2} + 3 \, a b\right)} c - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{a^{2} b^{2} + 2 \, a b^{3} + b^{4} + a^{2} c^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} c}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} - 2 \, {\left(a c^{2} - {\left(a b + b^{2}\right)} c\right)} \sqrt{-x^{2} + 1}}{x^{2}}\right) - 2 \, \sqrt{-x^{2} + 1}}{2 \, a x}"," ",0,"1/2*(sqrt(1/2)*a*x*sqrt(-(a*b^2 + b^3 - (2*a^2 + 3*a*b)*c + (a^3*b^2 - 4*a^4*c)*sqrt((a^2*b^2 + 2*a*b^3 + b^4 + a^2*c^2 - 2*(a^2*b + a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log((2*a*c^2 - 2*(a*c^2 - (a*b + b^2)*c)*x^2 - 2*(a*b + b^2)*c + sqrt(1/2)*((a*b^3 + b^4 + 4*a^2*c^2 - (4*a^2*b + 5*a*b^2)*c)*sqrt(-x^2 + 1)*x - (a*b^3 + b^4 + 4*a^2*c^2 - (4*a^2*b + 5*a*b^2)*c)*x - ((a^3*b^3 - 4*a^4*b*c)*sqrt(-x^2 + 1)*x - (a^3*b^3 - 4*a^4*b*c)*x)*sqrt((a^2*b^2 + 2*a*b^3 + b^4 + a^2*c^2 - 2*(a^2*b + a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(a*b^2 + b^3 - (2*a^2 + 3*a*b)*c + (a^3*b^2 - 4*a^4*c)*sqrt((a^2*b^2 + 2*a*b^3 + b^4 + a^2*c^2 - 2*(a^2*b + a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c)) - 2*(a*c^2 - (a*b + b^2)*c)*sqrt(-x^2 + 1))/x^2) - sqrt(1/2)*a*x*sqrt(-(a*b^2 + b^3 - (2*a^2 + 3*a*b)*c + (a^3*b^2 - 4*a^4*c)*sqrt((a^2*b^2 + 2*a*b^3 + b^4 + a^2*c^2 - 2*(a^2*b + a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log((2*a*c^2 - 2*(a*c^2 - (a*b + b^2)*c)*x^2 - 2*(a*b + b^2)*c - sqrt(1/2)*((a*b^3 + b^4 + 4*a^2*c^2 - (4*a^2*b + 5*a*b^2)*c)*sqrt(-x^2 + 1)*x - (a*b^3 + b^4 + 4*a^2*c^2 - (4*a^2*b + 5*a*b^2)*c)*x - ((a^3*b^3 - 4*a^4*b*c)*sqrt(-x^2 + 1)*x - (a^3*b^3 - 4*a^4*b*c)*x)*sqrt((a^2*b^2 + 2*a*b^3 + b^4 + a^2*c^2 - 2*(a^2*b + a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(a*b^2 + b^3 - (2*a^2 + 3*a*b)*c + (a^3*b^2 - 4*a^4*c)*sqrt((a^2*b^2 + 2*a*b^3 + b^4 + a^2*c^2 - 2*(a^2*b + a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c)) - 2*(a*c^2 - (a*b + b^2)*c)*sqrt(-x^2 + 1))/x^2) + sqrt(1/2)*a*x*sqrt(-(a*b^2 + b^3 - (2*a^2 + 3*a*b)*c - (a^3*b^2 - 4*a^4*c)*sqrt((a^2*b^2 + 2*a*b^3 + b^4 + a^2*c^2 - 2*(a^2*b + a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log((2*a*c^2 - 2*(a*c^2 - (a*b + b^2)*c)*x^2 - 2*(a*b + b^2)*c + sqrt(1/2)*((a*b^3 + b^4 + 4*a^2*c^2 - (4*a^2*b + 5*a*b^2)*c)*sqrt(-x^2 + 1)*x - (a*b^3 + b^4 + 4*a^2*c^2 - (4*a^2*b + 5*a*b^2)*c)*x + ((a^3*b^3 - 4*a^4*b*c)*sqrt(-x^2 + 1)*x - (a^3*b^3 - 4*a^4*b*c)*x)*sqrt((a^2*b^2 + 2*a*b^3 + b^4 + a^2*c^2 - 2*(a^2*b + a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(a*b^2 + b^3 - (2*a^2 + 3*a*b)*c - (a^3*b^2 - 4*a^4*c)*sqrt((a^2*b^2 + 2*a*b^3 + b^4 + a^2*c^2 - 2*(a^2*b + a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c)) - 2*(a*c^2 - (a*b + b^2)*c)*sqrt(-x^2 + 1))/x^2) - sqrt(1/2)*a*x*sqrt(-(a*b^2 + b^3 - (2*a^2 + 3*a*b)*c - (a^3*b^2 - 4*a^4*c)*sqrt((a^2*b^2 + 2*a*b^3 + b^4 + a^2*c^2 - 2*(a^2*b + a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log((2*a*c^2 - 2*(a*c^2 - (a*b + b^2)*c)*x^2 - 2*(a*b + b^2)*c - sqrt(1/2)*((a*b^3 + b^4 + 4*a^2*c^2 - (4*a^2*b + 5*a*b^2)*c)*sqrt(-x^2 + 1)*x - (a*b^3 + b^4 + 4*a^2*c^2 - (4*a^2*b + 5*a*b^2)*c)*x + ((a^3*b^3 - 4*a^4*b*c)*sqrt(-x^2 + 1)*x - (a^3*b^3 - 4*a^4*b*c)*x)*sqrt((a^2*b^2 + 2*a*b^3 + b^4 + a^2*c^2 - 2*(a^2*b + a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(a*b^2 + b^3 - (2*a^2 + 3*a*b)*c - (a^3*b^2 - 4*a^4*c)*sqrt((a^2*b^2 + 2*a*b^3 + b^4 + a^2*c^2 - 2*(a^2*b + a*b^2)*c)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c)) - 2*(a*c^2 - (a*b + b^2)*c)*sqrt(-x^2 + 1))/x^2) - 2*sqrt(-x^2 + 1))/(a*x)","B",0
385,1,290,0,1.071841," ","integrate(x^2*(-x^2+1)^(1/2)/(x^4+x^2-1),x, algorithm=""fricas"")","\frac{2}{5} \, \sqrt{5} \sqrt{\sqrt{5} + 2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{-x^{2} + 1} {\left(\sqrt{5} - 3\right)} + \sqrt{5} - 3\right)} \sqrt{\sqrt{5} + 2} \sqrt{\frac{x^{4} - 4 \, x^{2} - \sqrt{5} {\left(x^{4} - 2 \, x^{2}\right)} - 2 \, {\left(\sqrt{5} x^{2} - x^{2} + 2\right)} \sqrt{-x^{2} + 1} + 4}{x^{4}}} + 2 \, \sqrt{-x^{2} + 1} \sqrt{\sqrt{5} + 2} {\left(\sqrt{5} - 3\right)}}{4 \, x}\right) + \frac{1}{10} \, \sqrt{5} \sqrt{\sqrt{5} - 2} \log\left(-\frac{2 \, x^{2} + {\left(\sqrt{-x^{2} + 1} {\left(\sqrt{5} x + x\right)} - \sqrt{5} x - x\right)} \sqrt{\sqrt{5} - 2} + 2 \, \sqrt{-x^{2} + 1} - 2}{x^{2}}\right) - \frac{1}{10} \, \sqrt{5} \sqrt{\sqrt{5} - 2} \log\left(-\frac{2 \, x^{2} - {\left(\sqrt{-x^{2} + 1} {\left(\sqrt{5} x + x\right)} - \sqrt{5} x - x\right)} \sqrt{\sqrt{5} - 2} + 2 \, \sqrt{-x^{2} + 1} - 2}{x^{2}}\right) + 2 \, \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"2/5*sqrt(5)*sqrt(sqrt(5) + 2)*arctan(1/4*(sqrt(2)*(sqrt(-x^2 + 1)*(sqrt(5) - 3) + sqrt(5) - 3)*sqrt(sqrt(5) + 2)*sqrt((x^4 - 4*x^2 - sqrt(5)*(x^4 - 2*x^2) - 2*(sqrt(5)*x^2 - x^2 + 2)*sqrt(-x^2 + 1) + 4)/x^4) + 2*sqrt(-x^2 + 1)*sqrt(sqrt(5) + 2)*(sqrt(5) - 3))/x) + 1/10*sqrt(5)*sqrt(sqrt(5) - 2)*log(-(2*x^2 + (sqrt(-x^2 + 1)*(sqrt(5)*x + x) - sqrt(5)*x - x)*sqrt(sqrt(5) - 2) + 2*sqrt(-x^2 + 1) - 2)/x^2) - 1/10*sqrt(5)*sqrt(sqrt(5) - 2)*log(-(2*x^2 - (sqrt(-x^2 + 1)*(sqrt(5)*x + x) - sqrt(5)*x - x)*sqrt(sqrt(5) - 2) + 2*sqrt(-x^2 + 1) - 2)/x^2) + 2*arctan((sqrt(-x^2 + 1) - 1)/x)","B",0
386,-1,0,0,0.000000," ","integrate(x^8/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
387,-1,0,0,0.000000," ","integrate(x^6/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
388,1,11094,0,51.774374," ","integrate(x^4/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{1}{2}} c e \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}}} \log\left(\frac{2 \, a^{3} b d e + {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{3} - {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} e + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}} - 2 \, {\left(a^{2} b^{2} - a^{3} c\right)} d^{2} + {\left(4 \, a^{3} b e^{2} + {\left(a b^{3} - a^{2} b c\right)} d^{2} - {\left(5 \, a^{2} b^{2} - 4 \, a^{3} c\right)} d e\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left({\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} d^{3} - {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 4 \, a^{2} b c^{4}\right)} d^{2} e + 2 \, {\left(a b^{4} c^{2} - 5 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d e^{2} - {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e^{3}\right)} x \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}} + {\left({\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} d^{2} - {\left(2 \, a b^{4} - 9 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d e + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{2}\right)} x\right)} \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c e \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}}} \log\left(\frac{2 \, a^{3} b d e + {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{3} - {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} e + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}} - 2 \, {\left(a^{2} b^{2} - a^{3} c\right)} d^{2} + {\left(4 \, a^{3} b e^{2} + {\left(a b^{3} - a^{2} b c\right)} d^{2} - {\left(5 \, a^{2} b^{2} - 4 \, a^{3} c\right)} d e\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left({\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} d^{3} - {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 4 \, a^{2} b c^{4}\right)} d^{2} e + 2 \, {\left(a b^{4} c^{2} - 5 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d e^{2} - {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e^{3}\right)} x \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}} + {\left({\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} d^{2} - {\left(2 \, a b^{4} - 9 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d e + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{2}\right)} x\right)} \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c e \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}}} \log\left(\frac{2 \, a^{3} b d e - {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{3} - {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} e + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}} - 2 \, {\left(a^{2} b^{2} - a^{3} c\right)} d^{2} + {\left(4 \, a^{3} b e^{2} + {\left(a b^{3} - a^{2} b c\right)} d^{2} - {\left(5 \, a^{2} b^{2} - 4 \, a^{3} c\right)} d e\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left({\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} d^{3} - {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 4 \, a^{2} b c^{4}\right)} d^{2} e + 2 \, {\left(a b^{4} c^{2} - 5 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d e^{2} - {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e^{3}\right)} x \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}} - {\left({\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} d^{2} - {\left(2 \, a b^{4} - 9 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d e + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{2}\right)} x\right)} \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}}}}{x^{2}}\right) + \sqrt{\frac{1}{2}} c e \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}}} \log\left(\frac{2 \, a^{3} b d e - {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{3} - {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} e + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}} - 2 \, {\left(a^{2} b^{2} - a^{3} c\right)} d^{2} + {\left(4 \, a^{3} b e^{2} + {\left(a b^{3} - a^{2} b c\right)} d^{2} - {\left(5 \, a^{2} b^{2} - 4 \, a^{3} c\right)} d e\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left({\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} d^{3} - {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 4 \, a^{2} b c^{4}\right)} d^{2} e + 2 \, {\left(a b^{4} c^{2} - 5 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d e^{2} - {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e^{3}\right)} x \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}} - {\left({\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} d^{2} - {\left(2 \, a b^{4} - 9 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d e + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{2}\right)} x\right)} \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}}}}{x^{2}}\right) + 2 \, \sqrt{e} \log\left(-2 \, e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right)}{4 \, c e}, \frac{\sqrt{\frac{1}{2}} c e \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}}} \log\left(\frac{2 \, a^{3} b d e + {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{3} - {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} e + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}} - 2 \, {\left(a^{2} b^{2} - a^{3} c\right)} d^{2} + {\left(4 \, a^{3} b e^{2} + {\left(a b^{3} - a^{2} b c\right)} d^{2} - {\left(5 \, a^{2} b^{2} - 4 \, a^{3} c\right)} d e\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left({\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} d^{3} - {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 4 \, a^{2} b c^{4}\right)} d^{2} e + 2 \, {\left(a b^{4} c^{2} - 5 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d e^{2} - {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e^{3}\right)} x \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}} + {\left({\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} d^{2} - {\left(2 \, a b^{4} - 9 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d e + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{2}\right)} x\right)} \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c e \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}}} \log\left(\frac{2 \, a^{3} b d e + {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{3} - {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} e + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}} - 2 \, {\left(a^{2} b^{2} - a^{3} c\right)} d^{2} + {\left(4 \, a^{3} b e^{2} + {\left(a b^{3} - a^{2} b c\right)} d^{2} - {\left(5 \, a^{2} b^{2} - 4 \, a^{3} c\right)} d e\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left({\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} d^{3} - {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 4 \, a^{2} b c^{4}\right)} d^{2} e + 2 \, {\left(a b^{4} c^{2} - 5 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d e^{2} - {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e^{3}\right)} x \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}} + {\left({\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} d^{2} - {\left(2 \, a b^{4} - 9 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d e + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{2}\right)} x\right)} \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} c e \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}}} \log\left(\frac{2 \, a^{3} b d e - {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{3} - {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} e + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}} - 2 \, {\left(a^{2} b^{2} - a^{3} c\right)} d^{2} + {\left(4 \, a^{3} b e^{2} + {\left(a b^{3} - a^{2} b c\right)} d^{2} - {\left(5 \, a^{2} b^{2} - 4 \, a^{3} c\right)} d e\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left({\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} d^{3} - {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 4 \, a^{2} b c^{4}\right)} d^{2} e + 2 \, {\left(a b^{4} c^{2} - 5 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d e^{2} - {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e^{3}\right)} x \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}} - {\left({\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} d^{2} - {\left(2 \, a b^{4} - 9 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d e + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{2}\right)} x\right)} \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}}}}{x^{2}}\right) + \sqrt{\frac{1}{2}} c e \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}}} \log\left(\frac{2 \, a^{3} b d e - {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{3} - {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} e + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}} - 2 \, {\left(a^{2} b^{2} - a^{3} c\right)} d^{2} + {\left(4 \, a^{3} b e^{2} + {\left(a b^{3} - a^{2} b c\right)} d^{2} - {\left(5 \, a^{2} b^{2} - 4 \, a^{3} c\right)} d e\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left({\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} d^{3} - {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 4 \, a^{2} b c^{4}\right)} d^{2} e + 2 \, {\left(a b^{4} c^{2} - 5 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d e^{2} - {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e^{3}\right)} x \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}} - {\left({\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} d^{2} - {\left(2 \, a b^{4} - 9 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d e + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{2}\right)} x\right)} \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} d - {\left(a b^{2} - 2 \, a^{2} c\right)} e + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}\right)} \sqrt{\frac{a^{2} b^{2} e^{2} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{2} - 2 \, {\left(a b^{3} - a^{2} b c\right)} d e}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2}}}}{x^{2}}\right) - 4 \, \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{4 \, c e}\right]"," ",0,"[1/4*(sqrt(1/2)*c*e*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e - ((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)))/((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2))*log((2*a^3*b*d*e + ((a*b^2*c^3 - 4*a^2*c^4)*d^3 - (a*b^3*c^2 - 4*a^2*b*c^3)*d^2*e + (a^2*b^2*c^2 - 4*a^3*c^3)*d*e^2)*x^2*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)) - 2*(a^2*b^2 - a^3*c)*d^2 + (4*a^3*b*e^2 + (a*b^3 - a^2*b*c)*d^2 - (5*a^2*b^2 - 4*a^3*c)*d*e)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*(((b^4*c^3 - 6*a*b^2*c^4 + 8*a^2*c^5)*d^3 - (b^5*c^2 - 5*a*b^3*c^3 + 4*a^2*b*c^4)*d^2*e + 2*(a*b^4*c^2 - 5*a^2*b^2*c^3 + 4*a^3*c^4)*d*e^2 - (a^2*b^3*c^2 - 4*a^3*b*c^3)*e^3)*x*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)) + ((b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*d^2 - (2*a*b^4 - 9*a^2*b^2*c + 4*a^3*c^2)*d*e + (a^2*b^3 - 4*a^3*b*c)*e^2)*x)*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e - ((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)))/((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)))/x^2) - sqrt(1/2)*c*e*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e - ((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)))/((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2))*log((2*a^3*b*d*e + ((a*b^2*c^3 - 4*a^2*c^4)*d^3 - (a*b^3*c^2 - 4*a^2*b*c^3)*d^2*e + (a^2*b^2*c^2 - 4*a^3*c^3)*d*e^2)*x^2*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)) - 2*(a^2*b^2 - a^3*c)*d^2 + (4*a^3*b*e^2 + (a*b^3 - a^2*b*c)*d^2 - (5*a^2*b^2 - 4*a^3*c)*d*e)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*(((b^4*c^3 - 6*a*b^2*c^4 + 8*a^2*c^5)*d^3 - (b^5*c^2 - 5*a*b^3*c^3 + 4*a^2*b*c^4)*d^2*e + 2*(a*b^4*c^2 - 5*a^2*b^2*c^3 + 4*a^3*c^4)*d*e^2 - (a^2*b^3*c^2 - 4*a^3*b*c^3)*e^3)*x*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)) + ((b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*d^2 - (2*a*b^4 - 9*a^2*b^2*c + 4*a^3*c^2)*d*e + (a^2*b^3 - 4*a^3*b*c)*e^2)*x)*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e - ((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)))/((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)))/x^2) - sqrt(1/2)*c*e*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e + ((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)))/((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2))*log((2*a^3*b*d*e - ((a*b^2*c^3 - 4*a^2*c^4)*d^3 - (a*b^3*c^2 - 4*a^2*b*c^3)*d^2*e + (a^2*b^2*c^2 - 4*a^3*c^3)*d*e^2)*x^2*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)) - 2*(a^2*b^2 - a^3*c)*d^2 + (4*a^3*b*e^2 + (a*b^3 - a^2*b*c)*d^2 - (5*a^2*b^2 - 4*a^3*c)*d*e)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*(((b^4*c^3 - 6*a*b^2*c^4 + 8*a^2*c^5)*d^3 - (b^5*c^2 - 5*a*b^3*c^3 + 4*a^2*b*c^4)*d^2*e + 2*(a*b^4*c^2 - 5*a^2*b^2*c^3 + 4*a^3*c^4)*d*e^2 - (a^2*b^3*c^2 - 4*a^3*b*c^3)*e^3)*x*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)) - ((b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*d^2 - (2*a*b^4 - 9*a^2*b^2*c + 4*a^3*c^2)*d*e + (a^2*b^3 - 4*a^3*b*c)*e^2)*x)*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e + ((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)))/((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)))/x^2) + sqrt(1/2)*c*e*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e + ((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)))/((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2))*log((2*a^3*b*d*e - ((a*b^2*c^3 - 4*a^2*c^4)*d^3 - (a*b^3*c^2 - 4*a^2*b*c^3)*d^2*e + (a^2*b^2*c^2 - 4*a^3*c^3)*d*e^2)*x^2*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)) - 2*(a^2*b^2 - a^3*c)*d^2 + (4*a^3*b*e^2 + (a*b^3 - a^2*b*c)*d^2 - (5*a^2*b^2 - 4*a^3*c)*d*e)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*(((b^4*c^3 - 6*a*b^2*c^4 + 8*a^2*c^5)*d^3 - (b^5*c^2 - 5*a*b^3*c^3 + 4*a^2*b*c^4)*d^2*e + 2*(a*b^4*c^2 - 5*a^2*b^2*c^3 + 4*a^3*c^4)*d*e^2 - (a^2*b^3*c^2 - 4*a^3*b*c^3)*e^3)*x*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)) - ((b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*d^2 - (2*a*b^4 - 9*a^2*b^2*c + 4*a^3*c^2)*d*e + (a^2*b^3 - 4*a^3*b*c)*e^2)*x)*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e + ((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)))/((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)))/x^2) + 2*sqrt(e)*log(-2*e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(e)*x - d))/(c*e), 1/4*(sqrt(1/2)*c*e*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e - ((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)))/((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2))*log((2*a^3*b*d*e + ((a*b^2*c^3 - 4*a^2*c^4)*d^3 - (a*b^3*c^2 - 4*a^2*b*c^3)*d^2*e + (a^2*b^2*c^2 - 4*a^3*c^3)*d*e^2)*x^2*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)) - 2*(a^2*b^2 - a^3*c)*d^2 + (4*a^3*b*e^2 + (a*b^3 - a^2*b*c)*d^2 - (5*a^2*b^2 - 4*a^3*c)*d*e)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*(((b^4*c^3 - 6*a*b^2*c^4 + 8*a^2*c^5)*d^3 - (b^5*c^2 - 5*a*b^3*c^3 + 4*a^2*b*c^4)*d^2*e + 2*(a*b^4*c^2 - 5*a^2*b^2*c^3 + 4*a^3*c^4)*d*e^2 - (a^2*b^3*c^2 - 4*a^3*b*c^3)*e^3)*x*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)) + ((b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*d^2 - (2*a*b^4 - 9*a^2*b^2*c + 4*a^3*c^2)*d*e + (a^2*b^3 - 4*a^3*b*c)*e^2)*x)*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e - ((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)))/((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)))/x^2) - sqrt(1/2)*c*e*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e - ((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)))/((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2))*log((2*a^3*b*d*e + ((a*b^2*c^3 - 4*a^2*c^4)*d^3 - (a*b^3*c^2 - 4*a^2*b*c^3)*d^2*e + (a^2*b^2*c^2 - 4*a^3*c^3)*d*e^2)*x^2*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)) - 2*(a^2*b^2 - a^3*c)*d^2 + (4*a^3*b*e^2 + (a*b^3 - a^2*b*c)*d^2 - (5*a^2*b^2 - 4*a^3*c)*d*e)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*(((b^4*c^3 - 6*a*b^2*c^4 + 8*a^2*c^5)*d^3 - (b^5*c^2 - 5*a*b^3*c^3 + 4*a^2*b*c^4)*d^2*e + 2*(a*b^4*c^2 - 5*a^2*b^2*c^3 + 4*a^3*c^4)*d*e^2 - (a^2*b^3*c^2 - 4*a^3*b*c^3)*e^3)*x*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)) + ((b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*d^2 - (2*a*b^4 - 9*a^2*b^2*c + 4*a^3*c^2)*d*e + (a^2*b^3 - 4*a^3*b*c)*e^2)*x)*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e - ((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)))/((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)))/x^2) - sqrt(1/2)*c*e*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e + ((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)))/((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2))*log((2*a^3*b*d*e - ((a*b^2*c^3 - 4*a^2*c^4)*d^3 - (a*b^3*c^2 - 4*a^2*b*c^3)*d^2*e + (a^2*b^2*c^2 - 4*a^3*c^3)*d*e^2)*x^2*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)) - 2*(a^2*b^2 - a^3*c)*d^2 + (4*a^3*b*e^2 + (a*b^3 - a^2*b*c)*d^2 - (5*a^2*b^2 - 4*a^3*c)*d*e)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*(((b^4*c^3 - 6*a*b^2*c^4 + 8*a^2*c^5)*d^3 - (b^5*c^2 - 5*a*b^3*c^3 + 4*a^2*b*c^4)*d^2*e + 2*(a*b^4*c^2 - 5*a^2*b^2*c^3 + 4*a^3*c^4)*d*e^2 - (a^2*b^3*c^2 - 4*a^3*b*c^3)*e^3)*x*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)) - ((b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*d^2 - (2*a*b^4 - 9*a^2*b^2*c + 4*a^3*c^2)*d*e + (a^2*b^3 - 4*a^3*b*c)*e^2)*x)*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e + ((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)))/((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)))/x^2) + sqrt(1/2)*c*e*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e + ((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)))/((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2))*log((2*a^3*b*d*e - ((a*b^2*c^3 - 4*a^2*c^4)*d^3 - (a*b^3*c^2 - 4*a^2*b*c^3)*d^2*e + (a^2*b^2*c^2 - 4*a^3*c^3)*d*e^2)*x^2*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)) - 2*(a^2*b^2 - a^3*c)*d^2 + (4*a^3*b*e^2 + (a*b^3 - a^2*b*c)*d^2 - (5*a^2*b^2 - 4*a^3*c)*d*e)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*(((b^4*c^3 - 6*a*b^2*c^4 + 8*a^2*c^5)*d^3 - (b^5*c^2 - 5*a*b^3*c^3 + 4*a^2*b*c^4)*d^2*e + 2*(a*b^4*c^2 - 5*a^2*b^2*c^3 + 4*a^3*c^4)*d*e^2 - (a^2*b^3*c^2 - 4*a^3*b*c^3)*e^3)*x*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)) - ((b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*d^2 - (2*a*b^4 - 9*a^2*b^2*c + 4*a^3*c^2)*d*e + (a^2*b^3 - 4*a^3*b*c)*e^2)*x)*sqrt(-((b^3 - 3*a*b*c)*d - (a*b^2 - 2*a^2*c)*e + ((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)*sqrt((a^2*b^2*e^2 + (b^4 - 2*a*b^2*c + a^2*c^2)*d^2 - 2*(a*b^3 - a^2*b*c)*d*e)/((b^2*c^6 - 4*a*c^7)*d^4 - 2*(b^3*c^5 - 4*a*b*c^6)*d^3*e + (b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^2 - 2*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^3 + (a^2*b^2*c^4 - 4*a^3*c^5)*e^4)))/((b^2*c^3 - 4*a*c^4)*d^2 - (b^3*c^2 - 4*a*b*c^3)*d*e + (a*b^2*c^2 - 4*a^2*c^3)*e^2)))/x^2) - 4*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)))/(c*e)]","B",0
389,1,3395,0,12.713370," ","integrate(x^2/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b d - 2 \, a e + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{\frac{d^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}} \log\left(\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} - {\left(b^{3} - 4 \, a b c\right)} d^{2} e + {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{2}\right)} \sqrt{\frac{d^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} x^{2} + 2 \, a d^{2} - {\left(b d^{2} - 4 \, a d e\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} {\left({\left(b^{2} - 4 \, a c\right)} d^{2} x - {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} - {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e + 3 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{2} - 2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{3}\right)} \sqrt{\frac{d^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} x\right)} \sqrt{e x^{2} + d} \sqrt{-\frac{b d - 2 \, a e + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{\frac{d^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}}}{x^{2}}\right) - \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b d - 2 \, a e + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{\frac{d^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}} \log\left(\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} - {\left(b^{3} - 4 \, a b c\right)} d^{2} e + {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{2}\right)} \sqrt{\frac{d^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} x^{2} + 2 \, a d^{2} - {\left(b d^{2} - 4 \, a d e\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} {\left({\left(b^{2} - 4 \, a c\right)} d^{2} x - {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} - {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e + 3 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{2} - 2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{3}\right)} \sqrt{\frac{d^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} x\right)} \sqrt{e x^{2} + d} \sqrt{-\frac{b d - 2 \, a e + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{\frac{d^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}}}{x^{2}}\right) - \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b d - 2 \, a e - {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{\frac{d^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}} \log\left(-\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} - {\left(b^{3} - 4 \, a b c\right)} d^{2} e + {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{2}\right)} \sqrt{\frac{d^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} x^{2} - 2 \, a d^{2} + {\left(b d^{2} - 4 \, a d e\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} {\left({\left(b^{2} - 4 \, a c\right)} d^{2} x + {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} - {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e + 3 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{2} - 2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{3}\right)} \sqrt{\frac{d^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} x\right)} \sqrt{e x^{2} + d} \sqrt{-\frac{b d - 2 \, a e - {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{\frac{d^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}}}{x^{2}}\right) + \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b d - 2 \, a e - {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{\frac{d^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}} \log\left(-\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} - {\left(b^{3} - 4 \, a b c\right)} d^{2} e + {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{2}\right)} \sqrt{\frac{d^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} x^{2} - 2 \, a d^{2} + {\left(b d^{2} - 4 \, a d e\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} {\left({\left(b^{2} - 4 \, a c\right)} d^{2} x + {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} - {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e + 3 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{2} - 2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{3}\right)} \sqrt{\frac{d^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}} x\right)} \sqrt{e x^{2} + d} \sqrt{-\frac{b d - 2 \, a e - {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{\frac{d^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}}}{x^{2}}\right)"," ",0,"1/4*sqrt(1/2)*sqrt(-(b*d - 2*a*e + ((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)*sqrt(d^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))*log((((b^2*c - 4*a*c^2)*d^3 - (b^3 - 4*a*b*c)*d^2*e + (a*b^2 - 4*a^2*c)*d*e^2)*sqrt(d^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*x^2 + 2*a*d^2 - (b*d^2 - 4*a*d*e)*x^2 + 2*sqrt(1/2)*((b^2 - 4*a*c)*d^2*x - ((b^3*c - 4*a*b*c^2)*d^3 - (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e + 3*(a*b^3 - 4*a^2*b*c)*d*e^2 - 2*(a^2*b^2 - 4*a^3*c)*e^3)*sqrt(d^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*x)*sqrt(e*x^2 + d)*sqrt(-(b*d - 2*a*e + ((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)*sqrt(d^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)))/x^2) - 1/4*sqrt(1/2)*sqrt(-(b*d - 2*a*e + ((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)*sqrt(d^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))*log((((b^2*c - 4*a*c^2)*d^3 - (b^3 - 4*a*b*c)*d^2*e + (a*b^2 - 4*a^2*c)*d*e^2)*sqrt(d^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*x^2 + 2*a*d^2 - (b*d^2 - 4*a*d*e)*x^2 - 2*sqrt(1/2)*((b^2 - 4*a*c)*d^2*x - ((b^3*c - 4*a*b*c^2)*d^3 - (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e + 3*(a*b^3 - 4*a^2*b*c)*d*e^2 - 2*(a^2*b^2 - 4*a^3*c)*e^3)*sqrt(d^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*x)*sqrt(e*x^2 + d)*sqrt(-(b*d - 2*a*e + ((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)*sqrt(d^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)))/x^2) - 1/4*sqrt(1/2)*sqrt(-(b*d - 2*a*e - ((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)*sqrt(d^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))*log(-(((b^2*c - 4*a*c^2)*d^3 - (b^3 - 4*a*b*c)*d^2*e + (a*b^2 - 4*a^2*c)*d*e^2)*sqrt(d^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*x^2 - 2*a*d^2 + (b*d^2 - 4*a*d*e)*x^2 + 2*sqrt(1/2)*((b^2 - 4*a*c)*d^2*x + ((b^3*c - 4*a*b*c^2)*d^3 - (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e + 3*(a*b^3 - 4*a^2*b*c)*d*e^2 - 2*(a^2*b^2 - 4*a^3*c)*e^3)*sqrt(d^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*x)*sqrt(e*x^2 + d)*sqrt(-(b*d - 2*a*e - ((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)*sqrt(d^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)))/x^2) + 1/4*sqrt(1/2)*sqrt(-(b*d - 2*a*e - ((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)*sqrt(d^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))*log(-(((b^2*c - 4*a*c^2)*d^3 - (b^3 - 4*a*b*c)*d^2*e + (a*b^2 - 4*a^2*c)*d*e^2)*sqrt(d^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*x^2 - 2*a*d^2 + (b*d^2 - 4*a*d*e)*x^2 - 2*sqrt(1/2)*((b^2 - 4*a*c)*d^2*x + ((b^3*c - 4*a*b*c^2)*d^3 - (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e + 3*(a*b^3 - 4*a^2*b*c)*d*e^2 - 2*(a^2*b^2 - 4*a^3*c)*e^3)*sqrt(d^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4))*x)*sqrt(e*x^2 + d)*sqrt(-(b*d - 2*a*e - ((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)*sqrt(d^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)))/x^2)","B",0
390,1,4557,0,30.482607," ","integrate(1/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e - {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{2}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{{\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{3} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4}}}}{{\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{2}}} \log\left(-\frac{2 \, a c^{2} d^{2} - 2 \, a b c d e + {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} - {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{2} e + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{{\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{3} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4}}} - {\left(b c^{2} d^{2} + 4 \, a b c e^{2} - {\left(b^{2} c + 4 \, a c^{2}\right)} d e\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(2 \, {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{3} - 3 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{2} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d e^{2} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{3}\right)} x \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{{\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{3} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4}}} - {\left({\left(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)} x\right)} \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e - {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{2}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{{\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{3} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4}}}}{{\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{2}}}}{x^{2}}\right) - \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e - {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{2}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{{\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{3} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4}}}}{{\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{2}}} \log\left(-\frac{2 \, a c^{2} d^{2} - 2 \, a b c d e + {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} - {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{2} e + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{{\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{3} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4}}} - {\left(b c^{2} d^{2} + 4 \, a b c e^{2} - {\left(b^{2} c + 4 \, a c^{2}\right)} d e\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(2 \, {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{3} - 3 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{2} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d e^{2} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{3}\right)} x \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{{\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{3} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4}}} - {\left({\left(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)} x\right)} \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e - {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{2}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{{\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{3} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4}}}}{{\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{2}}}}{x^{2}}\right) - \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e + {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{2}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{{\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{3} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4}}}}{{\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{2}}} \log\left(-\frac{2 \, a c^{2} d^{2} - 2 \, a b c d e - {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} - {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{2} e + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{{\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{3} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4}}} - {\left(b c^{2} d^{2} + 4 \, a b c e^{2} - {\left(b^{2} c + 4 \, a c^{2}\right)} d e\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(2 \, {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{3} - 3 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{2} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d e^{2} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{3}\right)} x \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{{\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{3} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4}}} + {\left({\left(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)} x\right)} \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e + {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{2}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{{\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{3} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4}}}}{{\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{2}}}}{x^{2}}\right) + \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e + {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{2}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{{\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{3} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4}}}}{{\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{2}}} \log\left(-\frac{2 \, a c^{2} d^{2} - 2 \, a b c d e - {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{3} - {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{2} e + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{{\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{3} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4}}} - {\left(b c^{2} d^{2} + 4 \, a b c e^{2} - {\left(b^{2} c + 4 \, a c^{2}\right)} d e\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left(2 \, {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{3} - 3 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{2} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d e^{2} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{3}\right)} x \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{{\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{3} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4}}} + {\left({\left(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)} x\right)} \sqrt{-\frac{b c d - {\left(b^{2} - 2 \, a c\right)} e + {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{2}\right)} \sqrt{\frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}}{{\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{4} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{3} e + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{4}}}}{{\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{2}}}}{x^{2}}\right)"," ",0,"1/4*sqrt(1/2)*sqrt(-(b*c*d - (b^2 - 2*a*c)*e - ((a*b^2*c - 4*a^2*c^2)*d^2 - (a*b^3 - 4*a^2*b*c)*d*e + (a^2*b^2 - 4*a^3*c)*e^2)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/((a^2*b^2*c^2 - 4*a^3*c^3)*d^4 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^3*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^2*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4)))/((a*b^2*c - 4*a^2*c^2)*d^2 - (a*b^3 - 4*a^2*b*c)*d*e + (a^2*b^2 - 4*a^3*c)*e^2))*log(-(2*a*c^2*d^2 - 2*a*b*c*d*e + ((a*b^2*c^2 - 4*a^2*c^3)*d^3 - (a*b^3*c - 4*a^2*b*c^2)*d^2*e + (a^2*b^2*c - 4*a^3*c^2)*d*e^2)*x^2*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/((a^2*b^2*c^2 - 4*a^3*c^3)*d^4 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^3*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^2*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4)) - (b*c^2*d^2 + 4*a*b*c*e^2 - (b^2*c + 4*a*c^2)*d*e)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((2*(a^2*b^2*c^2 - 4*a^3*c^3)*d^3 - 3*(a^2*b^3*c - 4*a^3*b*c^2)*d^2*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d*e^2 - (a^3*b^3 - 4*a^4*b*c)*e^3)*x*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/((a^2*b^2*c^2 - 4*a^3*c^3)*d^4 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^3*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^2*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4)) - ((a*b^2*c - 4*a^2*c^2)*d*e - (a*b^3 - 4*a^2*b*c)*e^2)*x)*sqrt(-(b*c*d - (b^2 - 2*a*c)*e - ((a*b^2*c - 4*a^2*c^2)*d^2 - (a*b^3 - 4*a^2*b*c)*d*e + (a^2*b^2 - 4*a^3*c)*e^2)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/((a^2*b^2*c^2 - 4*a^3*c^3)*d^4 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^3*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^2*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4)))/((a*b^2*c - 4*a^2*c^2)*d^2 - (a*b^3 - 4*a^2*b*c)*d*e + (a^2*b^2 - 4*a^3*c)*e^2)))/x^2) - 1/4*sqrt(1/2)*sqrt(-(b*c*d - (b^2 - 2*a*c)*e - ((a*b^2*c - 4*a^2*c^2)*d^2 - (a*b^3 - 4*a^2*b*c)*d*e + (a^2*b^2 - 4*a^3*c)*e^2)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/((a^2*b^2*c^2 - 4*a^3*c^3)*d^4 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^3*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^2*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4)))/((a*b^2*c - 4*a^2*c^2)*d^2 - (a*b^3 - 4*a^2*b*c)*d*e + (a^2*b^2 - 4*a^3*c)*e^2))*log(-(2*a*c^2*d^2 - 2*a*b*c*d*e + ((a*b^2*c^2 - 4*a^2*c^3)*d^3 - (a*b^3*c - 4*a^2*b*c^2)*d^2*e + (a^2*b^2*c - 4*a^3*c^2)*d*e^2)*x^2*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/((a^2*b^2*c^2 - 4*a^3*c^3)*d^4 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^3*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^2*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4)) - (b*c^2*d^2 + 4*a*b*c*e^2 - (b^2*c + 4*a*c^2)*d*e)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((2*(a^2*b^2*c^2 - 4*a^3*c^3)*d^3 - 3*(a^2*b^3*c - 4*a^3*b*c^2)*d^2*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d*e^2 - (a^3*b^3 - 4*a^4*b*c)*e^3)*x*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/((a^2*b^2*c^2 - 4*a^3*c^3)*d^4 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^3*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^2*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4)) - ((a*b^2*c - 4*a^2*c^2)*d*e - (a*b^3 - 4*a^2*b*c)*e^2)*x)*sqrt(-(b*c*d - (b^2 - 2*a*c)*e - ((a*b^2*c - 4*a^2*c^2)*d^2 - (a*b^3 - 4*a^2*b*c)*d*e + (a^2*b^2 - 4*a^3*c)*e^2)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/((a^2*b^2*c^2 - 4*a^3*c^3)*d^4 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^3*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^2*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4)))/((a*b^2*c - 4*a^2*c^2)*d^2 - (a*b^3 - 4*a^2*b*c)*d*e + (a^2*b^2 - 4*a^3*c)*e^2)))/x^2) - 1/4*sqrt(1/2)*sqrt(-(b*c*d - (b^2 - 2*a*c)*e + ((a*b^2*c - 4*a^2*c^2)*d^2 - (a*b^3 - 4*a^2*b*c)*d*e + (a^2*b^2 - 4*a^3*c)*e^2)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/((a^2*b^2*c^2 - 4*a^3*c^3)*d^4 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^3*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^2*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4)))/((a*b^2*c - 4*a^2*c^2)*d^2 - (a*b^3 - 4*a^2*b*c)*d*e + (a^2*b^2 - 4*a^3*c)*e^2))*log(-(2*a*c^2*d^2 - 2*a*b*c*d*e - ((a*b^2*c^2 - 4*a^2*c^3)*d^3 - (a*b^3*c - 4*a^2*b*c^2)*d^2*e + (a^2*b^2*c - 4*a^3*c^2)*d*e^2)*x^2*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/((a^2*b^2*c^2 - 4*a^3*c^3)*d^4 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^3*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^2*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4)) - (b*c^2*d^2 + 4*a*b*c*e^2 - (b^2*c + 4*a*c^2)*d*e)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*((2*(a^2*b^2*c^2 - 4*a^3*c^3)*d^3 - 3*(a^2*b^3*c - 4*a^3*b*c^2)*d^2*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d*e^2 - (a^3*b^3 - 4*a^4*b*c)*e^3)*x*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/((a^2*b^2*c^2 - 4*a^3*c^3)*d^4 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^3*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^2*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4)) + ((a*b^2*c - 4*a^2*c^2)*d*e - (a*b^3 - 4*a^2*b*c)*e^2)*x)*sqrt(-(b*c*d - (b^2 - 2*a*c)*e + ((a*b^2*c - 4*a^2*c^2)*d^2 - (a*b^3 - 4*a^2*b*c)*d*e + (a^2*b^2 - 4*a^3*c)*e^2)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/((a^2*b^2*c^2 - 4*a^3*c^3)*d^4 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^3*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^2*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4)))/((a*b^2*c - 4*a^2*c^2)*d^2 - (a*b^3 - 4*a^2*b*c)*d*e + (a^2*b^2 - 4*a^3*c)*e^2)))/x^2) + 1/4*sqrt(1/2)*sqrt(-(b*c*d - (b^2 - 2*a*c)*e + ((a*b^2*c - 4*a^2*c^2)*d^2 - (a*b^3 - 4*a^2*b*c)*d*e + (a^2*b^2 - 4*a^3*c)*e^2)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/((a^2*b^2*c^2 - 4*a^3*c^3)*d^4 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^3*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^2*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4)))/((a*b^2*c - 4*a^2*c^2)*d^2 - (a*b^3 - 4*a^2*b*c)*d*e + (a^2*b^2 - 4*a^3*c)*e^2))*log(-(2*a*c^2*d^2 - 2*a*b*c*d*e - ((a*b^2*c^2 - 4*a^2*c^3)*d^3 - (a*b^3*c - 4*a^2*b*c^2)*d^2*e + (a^2*b^2*c - 4*a^3*c^2)*d*e^2)*x^2*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/((a^2*b^2*c^2 - 4*a^3*c^3)*d^4 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^3*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^2*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4)) - (b*c^2*d^2 + 4*a*b*c*e^2 - (b^2*c + 4*a*c^2)*d*e)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*((2*(a^2*b^2*c^2 - 4*a^3*c^3)*d^3 - 3*(a^2*b^3*c - 4*a^3*b*c^2)*d^2*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d*e^2 - (a^3*b^3 - 4*a^4*b*c)*e^3)*x*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/((a^2*b^2*c^2 - 4*a^3*c^3)*d^4 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^3*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^2*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4)) + ((a*b^2*c - 4*a^2*c^2)*d*e - (a*b^3 - 4*a^2*b*c)*e^2)*x)*sqrt(-(b*c*d - (b^2 - 2*a*c)*e + ((a*b^2*c - 4*a^2*c^2)*d^2 - (a*b^3 - 4*a^2*b*c)*d*e + (a^2*b^2 - 4*a^3*c)*e^2)*sqrt((c^2*d^2 - 2*b*c*d*e + b^2*e^2)/((a^2*b^2*c^2 - 4*a^3*c^3)*d^4 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^3*e + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^2*e^2 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^3 + (a^4*b^2 - 4*a^5*c)*e^4)))/((a*b^2*c - 4*a^2*c^2)*d^2 - (a*b^3 - 4*a^2*b*c)*d*e + (a^2*b^2 - 4*a^3*c)*e^2)))/x^2)","B",0
391,1,6431,0,59.583289," ","integrate(1/x^2/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} a d x \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e - {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{2}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{{\left(a^{6} b^{2} c^{2} - 4 \, a^{7} c^{3}\right)} d^{4} - 2 \, {\left(a^{6} b^{3} c - 4 \, a^{7} b c^{2}\right)} d^{3} e + {\left(a^{6} b^{4} - 2 \, a^{7} b^{2} c - 8 \, a^{8} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{7} b^{3} - 4 \, a^{8} b c\right)} d e^{3} + {\left(a^{8} b^{2} - 4 \, a^{9} c\right)} e^{4}}}}{{\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{2}}} \log\left(\frac{{\left({\left(a^{3} b^{2} c^{3} - 4 \, a^{4} c^{4}\right)} d^{3} - {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d^{2} e + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{{\left(a^{6} b^{2} c^{2} - 4 \, a^{7} c^{3}\right)} d^{4} - 2 \, {\left(a^{6} b^{3} c - 4 \, a^{7} b c^{2}\right)} d^{3} e + {\left(a^{6} b^{4} - 2 \, a^{7} b^{2} c - 8 \, a^{8} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{7} b^{3} - 4 \, a^{8} b c\right)} d e^{3} + {\left(a^{8} b^{2} - 4 \, a^{9} c\right)} e^{4}}} + 2 \, {\left(a b^{2} c^{3} - a^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d e - {\left({\left(b^{3} c^{3} - a b c^{4}\right)} d^{2} - {\left(b^{4} c^{2} + 2 \, a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d e + 4 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} e^{2}\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left({\left(a^{4} b^{3} c^{2} - 4 \, a^{5} b c^{3}\right)} d^{3} - 2 \, {\left(a^{4} b^{4} c - 5 \, a^{5} b^{2} c^{2} + 4 \, a^{6} c^{3}\right)} d^{2} e + {\left(a^{4} b^{5} - 5 \, a^{5} b^{3} c + 4 \, a^{6} b c^{2}\right)} d e^{2} - {\left(a^{5} b^{4} - 6 \, a^{6} b^{2} c + 8 \, a^{7} c^{2}\right)} e^{3}\right)} x \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{{\left(a^{6} b^{2} c^{2} - 4 \, a^{7} c^{3}\right)} d^{4} - 2 \, {\left(a^{6} b^{3} c - 4 \, a^{7} b c^{2}\right)} d^{3} e + {\left(a^{6} b^{4} - 2 \, a^{7} b^{2} c - 8 \, a^{8} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{7} b^{3} - 4 \, a^{8} b c\right)} d e^{3} + {\left(a^{8} b^{2} - 4 \, a^{9} c\right)} e^{4}}} + {\left({\left(a b^{4} c^{2} - 5 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d^{2} - {\left(2 \, a b^{5} c - 11 \, a^{2} b^{3} c^{2} + 12 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 8 \, a^{3} b^{2} c^{2}\right)} e^{2}\right)} x\right)} \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e - {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{2}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{{\left(a^{6} b^{2} c^{2} - 4 \, a^{7} c^{3}\right)} d^{4} - 2 \, {\left(a^{6} b^{3} c - 4 \, a^{7} b c^{2}\right)} d^{3} e + {\left(a^{6} b^{4} - 2 \, a^{7} b^{2} c - 8 \, a^{8} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{7} b^{3} - 4 \, a^{8} b c\right)} d e^{3} + {\left(a^{8} b^{2} - 4 \, a^{9} c\right)} e^{4}}}}{{\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{2}}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} a d x \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e - {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{2}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{{\left(a^{6} b^{2} c^{2} - 4 \, a^{7} c^{3}\right)} d^{4} - 2 \, {\left(a^{6} b^{3} c - 4 \, a^{7} b c^{2}\right)} d^{3} e + {\left(a^{6} b^{4} - 2 \, a^{7} b^{2} c - 8 \, a^{8} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{7} b^{3} - 4 \, a^{8} b c\right)} d e^{3} + {\left(a^{8} b^{2} - 4 \, a^{9} c\right)} e^{4}}}}{{\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{2}}} \log\left(\frac{{\left({\left(a^{3} b^{2} c^{3} - 4 \, a^{4} c^{4}\right)} d^{3} - {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d^{2} e + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{{\left(a^{6} b^{2} c^{2} - 4 \, a^{7} c^{3}\right)} d^{4} - 2 \, {\left(a^{6} b^{3} c - 4 \, a^{7} b c^{2}\right)} d^{3} e + {\left(a^{6} b^{4} - 2 \, a^{7} b^{2} c - 8 \, a^{8} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{7} b^{3} - 4 \, a^{8} b c\right)} d e^{3} + {\left(a^{8} b^{2} - 4 \, a^{9} c\right)} e^{4}}} + 2 \, {\left(a b^{2} c^{3} - a^{2} c^{4}\right)} d^{2} - 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d e - {\left({\left(b^{3} c^{3} - a b c^{4}\right)} d^{2} - {\left(b^{4} c^{2} + 2 \, a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d e + 4 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} e^{2}\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left({\left(a^{4} b^{3} c^{2} - 4 \, a^{5} b c^{3}\right)} d^{3} - 2 \, {\left(a^{4} b^{4} c - 5 \, a^{5} b^{2} c^{2} + 4 \, a^{6} c^{3}\right)} d^{2} e + {\left(a^{4} b^{5} - 5 \, a^{5} b^{3} c + 4 \, a^{6} b c^{2}\right)} d e^{2} - {\left(a^{5} b^{4} - 6 \, a^{6} b^{2} c + 8 \, a^{7} c^{2}\right)} e^{3}\right)} x \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{{\left(a^{6} b^{2} c^{2} - 4 \, a^{7} c^{3}\right)} d^{4} - 2 \, {\left(a^{6} b^{3} c - 4 \, a^{7} b c^{2}\right)} d^{3} e + {\left(a^{6} b^{4} - 2 \, a^{7} b^{2} c - 8 \, a^{8} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{7} b^{3} - 4 \, a^{8} b c\right)} d e^{3} + {\left(a^{8} b^{2} - 4 \, a^{9} c\right)} e^{4}}} + {\left({\left(a b^{4} c^{2} - 5 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d^{2} - {\left(2 \, a b^{5} c - 11 \, a^{2} b^{3} c^{2} + 12 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 8 \, a^{3} b^{2} c^{2}\right)} e^{2}\right)} x\right)} \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e - {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{2}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{{\left(a^{6} b^{2} c^{2} - 4 \, a^{7} c^{3}\right)} d^{4} - 2 \, {\left(a^{6} b^{3} c - 4 \, a^{7} b c^{2}\right)} d^{3} e + {\left(a^{6} b^{4} - 2 \, a^{7} b^{2} c - 8 \, a^{8} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{7} b^{3} - 4 \, a^{8} b c\right)} d e^{3} + {\left(a^{8} b^{2} - 4 \, a^{9} c\right)} e^{4}}}}{{\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{2}}}}{x^{2}}\right) + \sqrt{\frac{1}{2}} a d x \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e + {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{2}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{{\left(a^{6} b^{2} c^{2} - 4 \, a^{7} c^{3}\right)} d^{4} - 2 \, {\left(a^{6} b^{3} c - 4 \, a^{7} b c^{2}\right)} d^{3} e + {\left(a^{6} b^{4} - 2 \, a^{7} b^{2} c - 8 \, a^{8} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{7} b^{3} - 4 \, a^{8} b c\right)} d e^{3} + {\left(a^{8} b^{2} - 4 \, a^{9} c\right)} e^{4}}}}{{\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{2}}} \log\left(-\frac{{\left({\left(a^{3} b^{2} c^{3} - 4 \, a^{4} c^{4}\right)} d^{3} - {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d^{2} e + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{{\left(a^{6} b^{2} c^{2} - 4 \, a^{7} c^{3}\right)} d^{4} - 2 \, {\left(a^{6} b^{3} c - 4 \, a^{7} b c^{2}\right)} d^{3} e + {\left(a^{6} b^{4} - 2 \, a^{7} b^{2} c - 8 \, a^{8} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{7} b^{3} - 4 \, a^{8} b c\right)} d e^{3} + {\left(a^{8} b^{2} - 4 \, a^{9} c\right)} e^{4}}} - 2 \, {\left(a b^{2} c^{3} - a^{2} c^{4}\right)} d^{2} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d e + {\left({\left(b^{3} c^{3} - a b c^{4}\right)} d^{2} - {\left(b^{4} c^{2} + 2 \, a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d e + 4 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} e^{2}\right)} x^{2} + 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left({\left(a^{4} b^{3} c^{2} - 4 \, a^{5} b c^{3}\right)} d^{3} - 2 \, {\left(a^{4} b^{4} c - 5 \, a^{5} b^{2} c^{2} + 4 \, a^{6} c^{3}\right)} d^{2} e + {\left(a^{4} b^{5} - 5 \, a^{5} b^{3} c + 4 \, a^{6} b c^{2}\right)} d e^{2} - {\left(a^{5} b^{4} - 6 \, a^{6} b^{2} c + 8 \, a^{7} c^{2}\right)} e^{3}\right)} x \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{{\left(a^{6} b^{2} c^{2} - 4 \, a^{7} c^{3}\right)} d^{4} - 2 \, {\left(a^{6} b^{3} c - 4 \, a^{7} b c^{2}\right)} d^{3} e + {\left(a^{6} b^{4} - 2 \, a^{7} b^{2} c - 8 \, a^{8} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{7} b^{3} - 4 \, a^{8} b c\right)} d e^{3} + {\left(a^{8} b^{2} - 4 \, a^{9} c\right)} e^{4}}} - {\left({\left(a b^{4} c^{2} - 5 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d^{2} - {\left(2 \, a b^{5} c - 11 \, a^{2} b^{3} c^{2} + 12 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 8 \, a^{3} b^{2} c^{2}\right)} e^{2}\right)} x\right)} \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e + {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{2}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{{\left(a^{6} b^{2} c^{2} - 4 \, a^{7} c^{3}\right)} d^{4} - 2 \, {\left(a^{6} b^{3} c - 4 \, a^{7} b c^{2}\right)} d^{3} e + {\left(a^{6} b^{4} - 2 \, a^{7} b^{2} c - 8 \, a^{8} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{7} b^{3} - 4 \, a^{8} b c\right)} d e^{3} + {\left(a^{8} b^{2} - 4 \, a^{9} c\right)} e^{4}}}}{{\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{2}}}}{x^{2}}\right) - \sqrt{\frac{1}{2}} a d x \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e + {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{2}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{{\left(a^{6} b^{2} c^{2} - 4 \, a^{7} c^{3}\right)} d^{4} - 2 \, {\left(a^{6} b^{3} c - 4 \, a^{7} b c^{2}\right)} d^{3} e + {\left(a^{6} b^{4} - 2 \, a^{7} b^{2} c - 8 \, a^{8} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{7} b^{3} - 4 \, a^{8} b c\right)} d e^{3} + {\left(a^{8} b^{2} - 4 \, a^{9} c\right)} e^{4}}}}{{\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{2}}} \log\left(-\frac{{\left({\left(a^{3} b^{2} c^{3} - 4 \, a^{4} c^{4}\right)} d^{3} - {\left(a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d^{2} e + {\left(a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d e^{2}\right)} x^{2} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{{\left(a^{6} b^{2} c^{2} - 4 \, a^{7} c^{3}\right)} d^{4} - 2 \, {\left(a^{6} b^{3} c - 4 \, a^{7} b c^{2}\right)} d^{3} e + {\left(a^{6} b^{4} - 2 \, a^{7} b^{2} c - 8 \, a^{8} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{7} b^{3} - 4 \, a^{8} b c\right)} d e^{3} + {\left(a^{8} b^{2} - 4 \, a^{9} c\right)} e^{4}}} - 2 \, {\left(a b^{2} c^{3} - a^{2} c^{4}\right)} d^{2} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d e + {\left({\left(b^{3} c^{3} - a b c^{4}\right)} d^{2} - {\left(b^{4} c^{2} + 2 \, a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d e + 4 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} e^{2}\right)} x^{2} - 2 \, \sqrt{\frac{1}{2}} \sqrt{e x^{2} + d} {\left({\left({\left(a^{4} b^{3} c^{2} - 4 \, a^{5} b c^{3}\right)} d^{3} - 2 \, {\left(a^{4} b^{4} c - 5 \, a^{5} b^{2} c^{2} + 4 \, a^{6} c^{3}\right)} d^{2} e + {\left(a^{4} b^{5} - 5 \, a^{5} b^{3} c + 4 \, a^{6} b c^{2}\right)} d e^{2} - {\left(a^{5} b^{4} - 6 \, a^{6} b^{2} c + 8 \, a^{7} c^{2}\right)} e^{3}\right)} x \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{{\left(a^{6} b^{2} c^{2} - 4 \, a^{7} c^{3}\right)} d^{4} - 2 \, {\left(a^{6} b^{3} c - 4 \, a^{7} b c^{2}\right)} d^{3} e + {\left(a^{6} b^{4} - 2 \, a^{7} b^{2} c - 8 \, a^{8} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{7} b^{3} - 4 \, a^{8} b c\right)} d e^{3} + {\left(a^{8} b^{2} - 4 \, a^{9} c\right)} e^{4}}} - {\left({\left(a b^{4} c^{2} - 5 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d^{2} - {\left(2 \, a b^{5} c - 11 \, a^{2} b^{3} c^{2} + 12 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 8 \, a^{3} b^{2} c^{2}\right)} e^{2}\right)} x\right)} \sqrt{-\frac{{\left(b^{3} c - 3 \, a b c^{2}\right)} d - {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e + {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{2}\right)} \sqrt{\frac{{\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 2 \, {\left(b^{5} c - 3 \, a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e + {\left(b^{6} - 4 \, a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} e^{2}}{{\left(a^{6} b^{2} c^{2} - 4 \, a^{7} c^{3}\right)} d^{4} - 2 \, {\left(a^{6} b^{3} c - 4 \, a^{7} b c^{2}\right)} d^{3} e + {\left(a^{6} b^{4} - 2 \, a^{7} b^{2} c - 8 \, a^{8} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{7} b^{3} - 4 \, a^{8} b c\right)} d e^{3} + {\left(a^{8} b^{2} - 4 \, a^{9} c\right)} e^{4}}}}{{\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{2}}}}{x^{2}}\right) + 4 \, \sqrt{e x^{2} + d}}{4 \, a d x}"," ",0,"-1/4*(sqrt(1/2)*a*d*x*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e - ((a^3*b^2*c - 4*a^4*c^2)*d^2 - (a^3*b^3 - 4*a^4*b*c)*d*e + (a^4*b^2 - 4*a^5*c)*e^2)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/((a^6*b^2*c^2 - 4*a^7*c^3)*d^4 - 2*(a^6*b^3*c - 4*a^7*b*c^2)*d^3*e + (a^6*b^4 - 2*a^7*b^2*c - 8*a^8*c^2)*d^2*e^2 - 2*(a^7*b^3 - 4*a^8*b*c)*d*e^3 + (a^8*b^2 - 4*a^9*c)*e^4)))/((a^3*b^2*c - 4*a^4*c^2)*d^2 - (a^3*b^3 - 4*a^4*b*c)*d*e + (a^4*b^2 - 4*a^5*c)*e^2))*log((((a^3*b^2*c^3 - 4*a^4*c^4)*d^3 - (a^3*b^3*c^2 - 4*a^4*b*c^3)*d^2*e + (a^4*b^2*c^2 - 4*a^5*c^3)*d*e^2)*x^2*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/((a^6*b^2*c^2 - 4*a^7*c^3)*d^4 - 2*(a^6*b^3*c - 4*a^7*b*c^2)*d^3*e + (a^6*b^4 - 2*a^7*b^2*c - 8*a^8*c^2)*d^2*e^2 - 2*(a^7*b^3 - 4*a^8*b*c)*d*e^3 + (a^8*b^2 - 4*a^9*c)*e^4)) + 2*(a*b^2*c^3 - a^2*c^4)*d^2 - 2*(a*b^3*c^2 - 2*a^2*b*c^3)*d*e - ((b^3*c^3 - a*b*c^4)*d^2 - (b^4*c^2 + 2*a*b^2*c^3 - 4*a^2*c^4)*d*e + 4*(a*b^3*c^2 - 2*a^2*b*c^3)*e^2)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*(((a^4*b^3*c^2 - 4*a^5*b*c^3)*d^3 - 2*(a^4*b^4*c - 5*a^5*b^2*c^2 + 4*a^6*c^3)*d^2*e + (a^4*b^5 - 5*a^5*b^3*c + 4*a^6*b*c^2)*d*e^2 - (a^5*b^4 - 6*a^6*b^2*c + 8*a^7*c^2)*e^3)*x*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/((a^6*b^2*c^2 - 4*a^7*c^3)*d^4 - 2*(a^6*b^3*c - 4*a^7*b*c^2)*d^3*e + (a^6*b^4 - 2*a^7*b^2*c - 8*a^8*c^2)*d^2*e^2 - 2*(a^7*b^3 - 4*a^8*b*c)*d*e^3 + (a^8*b^2 - 4*a^9*c)*e^4)) + ((a*b^4*c^2 - 5*a^2*b^2*c^3 + 4*a^3*c^4)*d^2 - (2*a*b^5*c - 11*a^2*b^3*c^2 + 12*a^3*b*c^3)*d*e + (a*b^6 - 6*a^2*b^4*c + 8*a^3*b^2*c^2)*e^2)*x)*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e - ((a^3*b^2*c - 4*a^4*c^2)*d^2 - (a^3*b^3 - 4*a^4*b*c)*d*e + (a^4*b^2 - 4*a^5*c)*e^2)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/((a^6*b^2*c^2 - 4*a^7*c^3)*d^4 - 2*(a^6*b^3*c - 4*a^7*b*c^2)*d^3*e + (a^6*b^4 - 2*a^7*b^2*c - 8*a^8*c^2)*d^2*e^2 - 2*(a^7*b^3 - 4*a^8*b*c)*d*e^3 + (a^8*b^2 - 4*a^9*c)*e^4)))/((a^3*b^2*c - 4*a^4*c^2)*d^2 - (a^3*b^3 - 4*a^4*b*c)*d*e + (a^4*b^2 - 4*a^5*c)*e^2)))/x^2) - sqrt(1/2)*a*d*x*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e - ((a^3*b^2*c - 4*a^4*c^2)*d^2 - (a^3*b^3 - 4*a^4*b*c)*d*e + (a^4*b^2 - 4*a^5*c)*e^2)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/((a^6*b^2*c^2 - 4*a^7*c^3)*d^4 - 2*(a^6*b^3*c - 4*a^7*b*c^2)*d^3*e + (a^6*b^4 - 2*a^7*b^2*c - 8*a^8*c^2)*d^2*e^2 - 2*(a^7*b^3 - 4*a^8*b*c)*d*e^3 + (a^8*b^2 - 4*a^9*c)*e^4)))/((a^3*b^2*c - 4*a^4*c^2)*d^2 - (a^3*b^3 - 4*a^4*b*c)*d*e + (a^4*b^2 - 4*a^5*c)*e^2))*log((((a^3*b^2*c^3 - 4*a^4*c^4)*d^3 - (a^3*b^3*c^2 - 4*a^4*b*c^3)*d^2*e + (a^4*b^2*c^2 - 4*a^5*c^3)*d*e^2)*x^2*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/((a^6*b^2*c^2 - 4*a^7*c^3)*d^4 - 2*(a^6*b^3*c - 4*a^7*b*c^2)*d^3*e + (a^6*b^4 - 2*a^7*b^2*c - 8*a^8*c^2)*d^2*e^2 - 2*(a^7*b^3 - 4*a^8*b*c)*d*e^3 + (a^8*b^2 - 4*a^9*c)*e^4)) + 2*(a*b^2*c^3 - a^2*c^4)*d^2 - 2*(a*b^3*c^2 - 2*a^2*b*c^3)*d*e - ((b^3*c^3 - a*b*c^4)*d^2 - (b^4*c^2 + 2*a*b^2*c^3 - 4*a^2*c^4)*d*e + 4*(a*b^3*c^2 - 2*a^2*b*c^3)*e^2)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*(((a^4*b^3*c^2 - 4*a^5*b*c^3)*d^3 - 2*(a^4*b^4*c - 5*a^5*b^2*c^2 + 4*a^6*c^3)*d^2*e + (a^4*b^5 - 5*a^5*b^3*c + 4*a^6*b*c^2)*d*e^2 - (a^5*b^4 - 6*a^6*b^2*c + 8*a^7*c^2)*e^3)*x*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/((a^6*b^2*c^2 - 4*a^7*c^3)*d^4 - 2*(a^6*b^3*c - 4*a^7*b*c^2)*d^3*e + (a^6*b^4 - 2*a^7*b^2*c - 8*a^8*c^2)*d^2*e^2 - 2*(a^7*b^3 - 4*a^8*b*c)*d*e^3 + (a^8*b^2 - 4*a^9*c)*e^4)) + ((a*b^4*c^2 - 5*a^2*b^2*c^3 + 4*a^3*c^4)*d^2 - (2*a*b^5*c - 11*a^2*b^3*c^2 + 12*a^3*b*c^3)*d*e + (a*b^6 - 6*a^2*b^4*c + 8*a^3*b^2*c^2)*e^2)*x)*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e - ((a^3*b^2*c - 4*a^4*c^2)*d^2 - (a^3*b^3 - 4*a^4*b*c)*d*e + (a^4*b^2 - 4*a^5*c)*e^2)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/((a^6*b^2*c^2 - 4*a^7*c^3)*d^4 - 2*(a^6*b^3*c - 4*a^7*b*c^2)*d^3*e + (a^6*b^4 - 2*a^7*b^2*c - 8*a^8*c^2)*d^2*e^2 - 2*(a^7*b^3 - 4*a^8*b*c)*d*e^3 + (a^8*b^2 - 4*a^9*c)*e^4)))/((a^3*b^2*c - 4*a^4*c^2)*d^2 - (a^3*b^3 - 4*a^4*b*c)*d*e + (a^4*b^2 - 4*a^5*c)*e^2)))/x^2) + sqrt(1/2)*a*d*x*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e + ((a^3*b^2*c - 4*a^4*c^2)*d^2 - (a^3*b^3 - 4*a^4*b*c)*d*e + (a^4*b^2 - 4*a^5*c)*e^2)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/((a^6*b^2*c^2 - 4*a^7*c^3)*d^4 - 2*(a^6*b^3*c - 4*a^7*b*c^2)*d^3*e + (a^6*b^4 - 2*a^7*b^2*c - 8*a^8*c^2)*d^2*e^2 - 2*(a^7*b^3 - 4*a^8*b*c)*d*e^3 + (a^8*b^2 - 4*a^9*c)*e^4)))/((a^3*b^2*c - 4*a^4*c^2)*d^2 - (a^3*b^3 - 4*a^4*b*c)*d*e + (a^4*b^2 - 4*a^5*c)*e^2))*log(-(((a^3*b^2*c^3 - 4*a^4*c^4)*d^3 - (a^3*b^3*c^2 - 4*a^4*b*c^3)*d^2*e + (a^4*b^2*c^2 - 4*a^5*c^3)*d*e^2)*x^2*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/((a^6*b^2*c^2 - 4*a^7*c^3)*d^4 - 2*(a^6*b^3*c - 4*a^7*b*c^2)*d^3*e + (a^6*b^4 - 2*a^7*b^2*c - 8*a^8*c^2)*d^2*e^2 - 2*(a^7*b^3 - 4*a^8*b*c)*d*e^3 + (a^8*b^2 - 4*a^9*c)*e^4)) - 2*(a*b^2*c^3 - a^2*c^4)*d^2 + 2*(a*b^3*c^2 - 2*a^2*b*c^3)*d*e + ((b^3*c^3 - a*b*c^4)*d^2 - (b^4*c^2 + 2*a*b^2*c^3 - 4*a^2*c^4)*d*e + 4*(a*b^3*c^2 - 2*a^2*b*c^3)*e^2)*x^2 + 2*sqrt(1/2)*sqrt(e*x^2 + d)*(((a^4*b^3*c^2 - 4*a^5*b*c^3)*d^3 - 2*(a^4*b^4*c - 5*a^5*b^2*c^2 + 4*a^6*c^3)*d^2*e + (a^4*b^5 - 5*a^5*b^3*c + 4*a^6*b*c^2)*d*e^2 - (a^5*b^4 - 6*a^6*b^2*c + 8*a^7*c^2)*e^3)*x*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/((a^6*b^2*c^2 - 4*a^7*c^3)*d^4 - 2*(a^6*b^3*c - 4*a^7*b*c^2)*d^3*e + (a^6*b^4 - 2*a^7*b^2*c - 8*a^8*c^2)*d^2*e^2 - 2*(a^7*b^3 - 4*a^8*b*c)*d*e^3 + (a^8*b^2 - 4*a^9*c)*e^4)) - ((a*b^4*c^2 - 5*a^2*b^2*c^3 + 4*a^3*c^4)*d^2 - (2*a*b^5*c - 11*a^2*b^3*c^2 + 12*a^3*b*c^3)*d*e + (a*b^6 - 6*a^2*b^4*c + 8*a^3*b^2*c^2)*e^2)*x)*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e + ((a^3*b^2*c - 4*a^4*c^2)*d^2 - (a^3*b^3 - 4*a^4*b*c)*d*e + (a^4*b^2 - 4*a^5*c)*e^2)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/((a^6*b^2*c^2 - 4*a^7*c^3)*d^4 - 2*(a^6*b^3*c - 4*a^7*b*c^2)*d^3*e + (a^6*b^4 - 2*a^7*b^2*c - 8*a^8*c^2)*d^2*e^2 - 2*(a^7*b^3 - 4*a^8*b*c)*d*e^3 + (a^8*b^2 - 4*a^9*c)*e^4)))/((a^3*b^2*c - 4*a^4*c^2)*d^2 - (a^3*b^3 - 4*a^4*b*c)*d*e + (a^4*b^2 - 4*a^5*c)*e^2)))/x^2) - sqrt(1/2)*a*d*x*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e + ((a^3*b^2*c - 4*a^4*c^2)*d^2 - (a^3*b^3 - 4*a^4*b*c)*d*e + (a^4*b^2 - 4*a^5*c)*e^2)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/((a^6*b^2*c^2 - 4*a^7*c^3)*d^4 - 2*(a^6*b^3*c - 4*a^7*b*c^2)*d^3*e + (a^6*b^4 - 2*a^7*b^2*c - 8*a^8*c^2)*d^2*e^2 - 2*(a^7*b^3 - 4*a^8*b*c)*d*e^3 + (a^8*b^2 - 4*a^9*c)*e^4)))/((a^3*b^2*c - 4*a^4*c^2)*d^2 - (a^3*b^3 - 4*a^4*b*c)*d*e + (a^4*b^2 - 4*a^5*c)*e^2))*log(-(((a^3*b^2*c^3 - 4*a^4*c^4)*d^3 - (a^3*b^3*c^2 - 4*a^4*b*c^3)*d^2*e + (a^4*b^2*c^2 - 4*a^5*c^3)*d*e^2)*x^2*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/((a^6*b^2*c^2 - 4*a^7*c^3)*d^4 - 2*(a^6*b^3*c - 4*a^7*b*c^2)*d^3*e + (a^6*b^4 - 2*a^7*b^2*c - 8*a^8*c^2)*d^2*e^2 - 2*(a^7*b^3 - 4*a^8*b*c)*d*e^3 + (a^8*b^2 - 4*a^9*c)*e^4)) - 2*(a*b^2*c^3 - a^2*c^4)*d^2 + 2*(a*b^3*c^2 - 2*a^2*b*c^3)*d*e + ((b^3*c^3 - a*b*c^4)*d^2 - (b^4*c^2 + 2*a*b^2*c^3 - 4*a^2*c^4)*d*e + 4*(a*b^3*c^2 - 2*a^2*b*c^3)*e^2)*x^2 - 2*sqrt(1/2)*sqrt(e*x^2 + d)*(((a^4*b^3*c^2 - 4*a^5*b*c^3)*d^3 - 2*(a^4*b^4*c - 5*a^5*b^2*c^2 + 4*a^6*c^3)*d^2*e + (a^4*b^5 - 5*a^5*b^3*c + 4*a^6*b*c^2)*d*e^2 - (a^5*b^4 - 6*a^6*b^2*c + 8*a^7*c^2)*e^3)*x*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/((a^6*b^2*c^2 - 4*a^7*c^3)*d^4 - 2*(a^6*b^3*c - 4*a^7*b*c^2)*d^3*e + (a^6*b^4 - 2*a^7*b^2*c - 8*a^8*c^2)*d^2*e^2 - 2*(a^7*b^3 - 4*a^8*b*c)*d*e^3 + (a^8*b^2 - 4*a^9*c)*e^4)) - ((a*b^4*c^2 - 5*a^2*b^2*c^3 + 4*a^3*c^4)*d^2 - (2*a*b^5*c - 11*a^2*b^3*c^2 + 12*a^3*b*c^3)*d*e + (a*b^6 - 6*a^2*b^4*c + 8*a^3*b^2*c^2)*e^2)*x)*sqrt(-((b^3*c - 3*a*b*c^2)*d - (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e + ((a^3*b^2*c - 4*a^4*c^2)*d^2 - (a^3*b^3 - 4*a^4*b*c)*d*e + (a^4*b^2 - 4*a^5*c)*e^2)*sqrt(((b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^2 - 2*(b^5*c - 3*a*b^3*c^2 + 2*a^2*b*c^3)*d*e + (b^6 - 4*a*b^4*c + 4*a^2*b^2*c^2)*e^2)/((a^6*b^2*c^2 - 4*a^7*c^3)*d^4 - 2*(a^6*b^3*c - 4*a^7*b*c^2)*d^3*e + (a^6*b^4 - 2*a^7*b^2*c - 8*a^8*c^2)*d^2*e^2 - 2*(a^7*b^3 - 4*a^8*b*c)*d*e^3 + (a^8*b^2 - 4*a^9*c)*e^4)))/((a^3*b^2*c - 4*a^4*c^2)*d^2 - (a^3*b^3 - 4*a^4*b*c)*d*e + (a^4*b^2 - 4*a^5*c)*e^2)))/x^2) + 4*sqrt(e*x^2 + d))/(a*d*x)","B",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=""fricas"")","\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=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
394,-1,0,0,0.000000," ","integrate(x^6/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
395,-1,0,0,0.000000," ","integrate(x^4/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
396,-1,0,0,0.000000," ","integrate(x^2/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
397,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",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=""fricas"")","\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=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
400,0,0,0,1.266399," ","integrate((f*x)^m*(e*x^2+d)^q/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{2} + d\right)}^{q} \left(f x\right)^{m}}{c x^{4} + b x^{2} + a}, x\right)"," ",0,"integral((e*x^2 + d)^q*(f*x)^m/(c*x^4 + b*x^2 + a), x)","F",0
401,0,0,0,1.244583," ","integrate(x^7*(e*x^2+d)^q/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{2} + d\right)}^{q} x^{7}}{c x^{4} + b x^{2} + a}, x\right)"," ",0,"integral((e*x^2 + d)^q*x^7/(c*x^4 + b*x^2 + a), x)","F",0
402,0,0,0,1.327761," ","integrate(x^5*(e*x^2+d)^q/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{2} + d\right)}^{q} x^{5}}{c x^{4} + b x^{2} + a}, x\right)"," ",0,"integral((e*x^2 + d)^q*x^5/(c*x^4 + b*x^2 + a), x)","F",0
403,0,0,0,0.864632," ","integrate(x^3*(e*x^2+d)^q/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{2} + d\right)}^{q} x^{3}}{c x^{4} + b x^{2} + a}, x\right)"," ",0,"integral((e*x^2 + d)^q*x^3/(c*x^4 + b*x^2 + a), x)","F",0
404,0,0,0,0.920801," ","integrate(x*(e*x^2+d)^q/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{2} + d\right)}^{q} x}{c x^{4} + b x^{2} + a}, x\right)"," ",0,"integral((e*x^2 + d)^q*x/(c*x^4 + b*x^2 + a), x)","F",0
405,0,0,0,1.216636," ","integrate((e*x^2+d)^q/x/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{2} + d\right)}^{q}}{c x^{5} + b x^{3} + a x}, x\right)"," ",0,"integral((e*x^2 + d)^q/(c*x^5 + b*x^3 + a*x), x)","F",0
406,0,0,0,0.881555," ","integrate((e*x^2+d)^q/x^3/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{2} + d\right)}^{q}}{c x^{7} + b x^{5} + a x^{3}}, x\right)"," ",0,"integral((e*x^2 + d)^q/(c*x^7 + b*x^5 + a*x^3), x)","F",0
407,0,0,0,0.732445," ","integrate(x^6*(e*x^2+d)^q/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{2} + d\right)}^{q} x^{6}}{c x^{4} + b x^{2} + a}, x\right)"," ",0,"integral((e*x^2 + d)^q*x^6/(c*x^4 + b*x^2 + a), x)","F",0
408,0,0,0,0.977952," ","integrate(x^4*(e*x^2+d)^q/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{2} + d\right)}^{q} x^{4}}{c x^{4} + b x^{2} + a}, x\right)"," ",0,"integral((e*x^2 + d)^q*x^4/(c*x^4 + b*x^2 + a), x)","F",0
409,0,0,0,0.910428," ","integrate(x^2*(e*x^2+d)^q/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{2} + d\right)}^{q} x^{2}}{c x^{4} + b x^{2} + a}, x\right)"," ",0,"integral((e*x^2 + d)^q*x^2/(c*x^4 + b*x^2 + a), x)","F",0
410,0,0,0,0.920421," ","integrate((e*x^2+d)^q/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{2} + d\right)}^{q}}{c x^{4} + b x^{2} + a}, x\right)"," ",0,"integral((e*x^2 + d)^q/(c*x^4 + b*x^2 + a), x)","F",0
411,0,0,0,0.705774," ","integrate((e*x^2+d)^q/x^2/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{2} + d\right)}^{q}}{c x^{6} + b x^{4} + a x^{2}}, x\right)"," ",0,"integral((e*x^2 + d)^q/(c*x^6 + b*x^4 + a*x^2), x)","F",0
412,0,0,0,0.973822," ","integrate((e*x^2+d)^q/x^4/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{2} + d\right)}^{q}}{c x^{8} + b x^{6} + a x^{4}}, x\right)"," ",0,"integral((e*x^2 + d)^q/(c*x^8 + b*x^6 + a*x^4), x)","F",0
413,1,120,0,0.937274," ","integrate((1+1/c^2/x^2)^(1/2)/(-c^4*x^4+1)^(1/2),x, algorithm=""fricas"")","-\frac{\log\left(\frac{c^{2} x^{2} + \sqrt{-c^{4} x^{4} + 1} c x \sqrt{\frac{c^{2} x^{2} + 1}{c^{2} x^{2}}} + 1}{c^{2} x^{2} + 1}\right) - \log\left(-\frac{c^{2} x^{2} - \sqrt{-c^{4} x^{4} + 1} c x \sqrt{\frac{c^{2} x^{2} + 1}{c^{2} x^{2}}} + 1}{c^{2} x^{2} + 1}\right)}{2 \, c}"," ",0,"-1/2*(log((c^2*x^2 + sqrt(-c^4*x^4 + 1)*c*x*sqrt((c^2*x^2 + 1)/(c^2*x^2)) + 1)/(c^2*x^2 + 1)) - log(-(c^2*x^2 - sqrt(-c^4*x^4 + 1)*c*x*sqrt((c^2*x^2 + 1)/(c^2*x^2)) + 1)/(c^2*x^2 + 1)))/c","B",0
