1,1,53,0,1.973049," ","integrate((b*x^6+a*x^3)^(5/3),x, algorithm=""fricas"")","\frac{{\left(8 \, b^{3} x^{9} + 13 \, a b^{2} x^{6} + 2 \, a^{2} b x^{3} - 3 \, a^{3}\right)} {\left(b x^{6} + a x^{3}\right)}^{\frac{2}{3}}}{88 \, b^{2} x^{2}}"," ",0,"1/88*(8*b^3*x^9 + 13*a*b^2*x^6 + 2*a^2*b*x^3 - 3*a^3)*(b*x^6 + a*x^3)^(2/3)/(b^2*x^2)","A",0
2,1,28,0,1.907834," ","integrate((b*x^6+a*x^3)^(2/3),x, algorithm=""fricas"")","\frac{{\left(b x^{6} + a x^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}}{5 \, b x^{2}}"," ",0,"1/5*(b*x^6 + a*x^3)^(2/3)*(b*x^3 + a)/(b*x^2)","A",0
3,1,21,0,1.166587," ","integrate(1/(b*x^6+a*x^3)^(2/3),x, algorithm=""fricas"")","-\frac{{\left(b x^{6} + a x^{3}\right)}^{\frac{1}{3}}}{a x^{2}}"," ",0,"-(b*x^6 + a*x^3)^(1/3)/(a*x^2)","A",0
4,1,54,0,1.064074," ","integrate(1/(b*x^6+a*x^3)^(5/3),x, algorithm=""fricas"")","\frac{{\left(9 \, b^{2} x^{6} + 6 \, a b x^{3} - a^{2}\right)} {\left(b x^{6} + a x^{3}\right)}^{\frac{1}{3}}}{4 \, {\left(a^{3} b x^{8} + a^{4} x^{5}\right)}}"," ",0,"1/4*(9*b^2*x^6 + 6*a*b*x^3 - a^2)*(b*x^6 + a*x^3)^(1/3)/(a^3*b*x^8 + a^4*x^5)","A",0
5,1,46,0,1.545793," ","integrate(1/(x^6-x^3),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} x^{2} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + x^{2} \log\left(x^{2} + x + 1\right) - 2 \, x^{2} \log\left(x - 1\right) - 3}{6 \, x^{2}}"," ",0,"-1/6*(2*sqrt(3)*x^2*arctan(1/3*sqrt(3)*(2*x + 1)) + x^2*log(x^2 + x + 1) - 2*x^2*log(x - 1) - 3)/x^2","A",0
6,1,13,0,1.342097," ","integrate(x^5*((b*x^3+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{9} \, b x^{9} + \frac{1}{6} \, a x^{6}"," ",0,"1/9*b*x^9 + 1/6*a*x^6","A",0
7,1,13,0,1.328094," ","integrate(x^4*((b*x^3+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{8} \, b x^{8} + \frac{1}{5} \, a x^{5}"," ",0,"1/8*b*x^8 + 1/5*a*x^5","A",0
8,1,13,0,1.670588," ","integrate(x^3*((b*x^3+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{7} \, b x^{7} + \frac{1}{4} \, a x^{4}"," ",0,"1/7*b*x^7 + 1/4*a*x^4","A",0
9,1,13,0,1.666840," ","integrate(x^2*((b*x^3+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, b x^{6} + \frac{1}{3} \, a x^{3}"," ",0,"1/6*b*x^6 + 1/3*a*x^3","A",0
10,1,13,0,1.010480," ","integrate(x*((b*x^3+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{5} \, b x^{5} + \frac{1}{2} \, a x^{2}"," ",0,"1/5*b*x^5 + 1/2*a*x^2","A",0
11,1,10,0,1.061986," ","integrate(((b*x^3+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, b x^{4} + a x"," ",0,"1/4*b*x^4 + a*x","A",0
12,1,11,0,1.178677," ","integrate(((b*x^3+a)^2)^(1/2)/x,x, algorithm=""fricas"")","\frac{1}{3} \, b x^{3} + a \log\left(x\right)"," ",0,"1/3*b*x^3 + a*log(x)","A",0
13,1,14,0,1.072440," ","integrate(((b*x^3+a)^2)^(1/2)/x^2,x, algorithm=""fricas"")","\frac{b x^{3} - 2 \, a}{2 \, x}"," ",0,"1/2*(b*x^3 - 2*a)/x","A",0
14,1,15,0,1.531756," ","integrate(((b*x^3+a)^2)^(1/2)/x^3,x, algorithm=""fricas"")","\frac{2 \, b x^{3} - a}{2 \, x^{2}}"," ",0,"1/2*(2*b*x^3 - a)/x^2","A",0
15,1,17,0,0.885358," ","integrate(((b*x^3+a)^2)^(1/2)/x^4,x, algorithm=""fricas"")","\frac{3 \, b x^{3} \log\left(x\right) - a}{3 \, x^{3}}"," ",0,"1/3*(3*b*x^3*log(x) - a)/x^3","A",0
16,1,13,0,1.145456," ","integrate(((b*x^3+a)^2)^(1/2)/x^5,x, algorithm=""fricas"")","-\frac{4 \, b x^{3} + a}{4 \, x^{4}}"," ",0,"-1/4*(4*b*x^3 + a)/x^4","A",0
17,1,15,0,0.952710," ","integrate(((b*x^3+a)^2)^(1/2)/x^6,x, algorithm=""fricas"")","-\frac{5 \, b x^{3} + 2 \, a}{10 \, x^{5}}"," ",0,"-1/10*(5*b*x^3 + 2*a)/x^5","A",0
18,1,13,0,1.337691," ","integrate(((b*x^3+a)^2)^(1/2)/x^7,x, algorithm=""fricas"")","-\frac{2 \, b x^{3} + a}{6 \, x^{6}}"," ",0,"-1/6*(2*b*x^3 + a)/x^6","A",0
19,1,15,0,1.908840," ","integrate(((b*x^3+a)^2)^(1/2)/x^8,x, algorithm=""fricas"")","-\frac{7 \, b x^{3} + 4 \, a}{28 \, x^{7}}"," ",0,"-1/28*(7*b*x^3 + 4*a)/x^7","A",0
20,1,15,0,1.066129," ","integrate(((b*x^3+a)^2)^(1/2)/x^9,x, algorithm=""fricas"")","-\frac{8 \, b x^{3} + 5 \, a}{40 \, x^{8}}"," ",0,"-1/40*(8*b*x^3 + 5*a)/x^8","A",0
21,1,15,0,1.370433," ","integrate(((b*x^3+a)^2)^(1/2)/x^10,x, algorithm=""fricas"")","-\frac{3 \, b x^{3} + 2 \, a}{18 \, x^{9}}"," ",0,"-1/18*(3*b*x^3 + 2*a)/x^9","A",0
22,1,15,0,1.404154," ","integrate(((b*x^3+a)^2)^(1/2)/x^11,x, algorithm=""fricas"")","-\frac{10 \, b x^{3} + 7 \, a}{70 \, x^{10}}"," ",0,"-1/70*(10*b*x^3 + 7*a)/x^10","A",0
23,1,35,0,1.219575," ","integrate(x^9*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{19} \, b^{3} x^{19} + \frac{3}{16} \, a b^{2} x^{16} + \frac{3}{13} \, a^{2} b x^{13} + \frac{1}{10} \, a^{3} x^{10}"," ",0,"1/19*b^3*x^19 + 3/16*a*b^2*x^16 + 3/13*a^2*b*x^13 + 1/10*a^3*x^10","A",0
24,1,35,0,0.758613," ","integrate(x^8*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{18} \, b^{3} x^{18} + \frac{1}{5} \, a b^{2} x^{15} + \frac{1}{4} \, a^{2} b x^{12} + \frac{1}{9} \, a^{3} x^{9}"," ",0,"1/18*b^3*x^18 + 1/5*a*b^2*x^15 + 1/4*a^2*b*x^12 + 1/9*a^3*x^9","A",0
25,1,35,0,1.319832," ","integrate(x^7*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{17} \, b^{3} x^{17} + \frac{3}{14} \, a b^{2} x^{14} + \frac{3}{11} \, a^{2} b x^{11} + \frac{1}{8} \, a^{3} x^{8}"," ",0,"1/17*b^3*x^17 + 3/14*a*b^2*x^14 + 3/11*a^2*b*x^11 + 1/8*a^3*x^8","A",0
26,1,35,0,1.541978," ","integrate(x^6*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{16} \, b^{3} x^{16} + \frac{3}{13} \, a b^{2} x^{13} + \frac{3}{10} \, a^{2} b x^{10} + \frac{1}{7} \, a^{3} x^{7}"," ",0,"1/16*b^3*x^16 + 3/13*a*b^2*x^13 + 3/10*a^2*b*x^10 + 1/7*a^3*x^7","A",0
27,1,35,0,1.482291," ","integrate(x^5*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{15} \, b^{3} x^{15} + \frac{1}{4} \, a b^{2} x^{12} + \frac{1}{3} \, a^{2} b x^{9} + \frac{1}{6} \, a^{3} x^{6}"," ",0,"1/15*b^3*x^15 + 1/4*a*b^2*x^12 + 1/3*a^2*b*x^9 + 1/6*a^3*x^6","A",0
28,1,35,0,1.125180," ","integrate(x^4*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{14} \, b^{3} x^{14} + \frac{3}{11} \, a b^{2} x^{11} + \frac{3}{8} \, a^{2} b x^{8} + \frac{1}{5} \, a^{3} x^{5}"," ",0,"1/14*b^3*x^14 + 3/11*a*b^2*x^11 + 3/8*a^2*b*x^8 + 1/5*a^3*x^5","A",0
29,1,35,0,1.338424," ","integrate(x^3*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{13} \, b^{3} x^{13} + \frac{3}{10} \, a b^{2} x^{10} + \frac{3}{7} \, a^{2} b x^{7} + \frac{1}{4} \, a^{3} x^{4}"," ",0,"1/13*b^3*x^13 + 3/10*a*b^2*x^10 + 3/7*a^2*b*x^7 + 1/4*a^3*x^4","A",0
30,1,35,0,1.472692," ","integrate(x^2*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{12} \, b^{3} x^{12} + \frac{1}{3} \, a b^{2} x^{9} + \frac{1}{2} \, a^{2} b x^{6} + \frac{1}{3} \, a^{3} x^{3}"," ",0,"1/12*b^3*x^12 + 1/3*a*b^2*x^9 + 1/2*a^2*b*x^6 + 1/3*a^3*x^3","A",0
31,1,35,0,1.514554," ","integrate(x*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{11} \, b^{3} x^{11} + \frac{3}{8} \, a b^{2} x^{8} + \frac{3}{5} \, a^{2} b x^{5} + \frac{1}{2} \, a^{3} x^{2}"," ",0,"1/11*b^3*x^11 + 3/8*a*b^2*x^8 + 3/5*a^2*b*x^5 + 1/2*a^3*x^2","A",0
32,1,32,0,3.026206," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{10} \, b^{3} x^{10} + \frac{3}{7} \, a b^{2} x^{7} + \frac{3}{4} \, a^{2} b x^{4} + a^{3} x"," ",0,"1/10*b^3*x^10 + 3/7*a*b^2*x^7 + 3/4*a^2*b*x^4 + a^3*x","A",0
33,1,32,0,1.094562," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x,x, algorithm=""fricas"")","\frac{1}{9} \, b^{3} x^{9} + \frac{1}{2} \, a b^{2} x^{6} + a^{2} b x^{3} + a^{3} \log\left(x\right)"," ",0,"1/9*b^3*x^9 + 1/2*a*b^2*x^6 + a^2*b*x^3 + a^3*log(x)","A",0
34,1,37,0,1.381891," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^2,x, algorithm=""fricas"")","\frac{5 \, b^{3} x^{9} + 24 \, a b^{2} x^{6} + 60 \, a^{2} b x^{3} - 40 \, a^{3}}{40 \, x}"," ",0,"1/40*(5*b^3*x^9 + 24*a*b^2*x^6 + 60*a^2*b*x^3 - 40*a^3)/x","A",0
35,1,37,0,1.468883," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^3,x, algorithm=""fricas"")","\frac{4 \, b^{3} x^{9} + 21 \, a b^{2} x^{6} + 84 \, a^{2} b x^{3} - 14 \, a^{3}}{28 \, x^{2}}"," ",0,"1/28*(4*b^3*x^9 + 21*a*b^2*x^6 + 84*a^2*b*x^3 - 14*a^3)/x^2","A",0
36,1,38,0,1.174052," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^4,x, algorithm=""fricas"")","\frac{b^{3} x^{9} + 6 \, a b^{2} x^{6} + 18 \, a^{2} b x^{3} \log\left(x\right) - 2 \, a^{3}}{6 \, x^{3}}"," ",0,"1/6*(b^3*x^9 + 6*a*b^2*x^6 + 18*a^2*b*x^3*log(x) - 2*a^3)/x^3","A",0
37,1,37,0,1.152295," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^5,x, algorithm=""fricas"")","\frac{4 \, b^{3} x^{9} + 30 \, a b^{2} x^{6} - 60 \, a^{2} b x^{3} - 5 \, a^{3}}{20 \, x^{4}}"," ",0,"1/20*(4*b^3*x^9 + 30*a*b^2*x^6 - 60*a^2*b*x^3 - 5*a^3)/x^4","A",0
38,1,37,0,1.420371," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^6,x, algorithm=""fricas"")","\frac{5 \, b^{3} x^{9} + 60 \, a b^{2} x^{6} - 30 \, a^{2} b x^{3} - 4 \, a^{3}}{20 \, x^{5}}"," ",0,"1/20*(5*b^3*x^9 + 60*a*b^2*x^6 - 30*a^2*b*x^3 - 4*a^3)/x^5","A",0
39,1,39,0,1.299052," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^7,x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{9} + 18 \, a b^{2} x^{6} \log\left(x\right) - 6 \, a^{2} b x^{3} - a^{3}}{6 \, x^{6}}"," ",0,"1/6*(2*b^3*x^9 + 18*a*b^2*x^6*log(x) - 6*a^2*b*x^3 - a^3)/x^6","A",0
40,1,37,0,1.916678," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^8,x, algorithm=""fricas"")","\frac{14 \, b^{3} x^{9} - 84 \, a b^{2} x^{6} - 21 \, a^{2} b x^{3} - 4 \, a^{3}}{28 \, x^{7}}"," ",0,"1/28*(14*b^3*x^9 - 84*a*b^2*x^6 - 21*a^2*b*x^3 - 4*a^3)/x^7","A",0
41,1,37,0,1.255503," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^9,x, algorithm=""fricas"")","\frac{40 \, b^{3} x^{9} - 60 \, a b^{2} x^{6} - 24 \, a^{2} b x^{3} - 5 \, a^{3}}{40 \, x^{8}}"," ",0,"1/40*(40*b^3*x^9 - 60*a*b^2*x^6 - 24*a^2*b*x^3 - 5*a^3)/x^8","A",0
42,1,39,0,1.310850," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^10,x, algorithm=""fricas"")","\frac{18 \, b^{3} x^{9} \log\left(x\right) - 18 \, a b^{2} x^{6} - 9 \, a^{2} b x^{3} - 2 \, a^{3}}{18 \, x^{9}}"," ",0,"1/18*(18*b^3*x^9*log(x) - 18*a*b^2*x^6 - 9*a^2*b*x^3 - 2*a^3)/x^9","A",0
43,1,37,0,1.524951," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^11,x, algorithm=""fricas"")","-\frac{140 \, b^{3} x^{9} + 105 \, a b^{2} x^{6} + 60 \, a^{2} b x^{3} + 14 \, a^{3}}{140 \, x^{10}}"," ",0,"-1/140*(140*b^3*x^9 + 105*a*b^2*x^6 + 60*a^2*b*x^3 + 14*a^3)/x^10","A",0
44,1,37,0,1.191355," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^12,x, algorithm=""fricas"")","-\frac{220 \, b^{3} x^{9} + 264 \, a b^{2} x^{6} + 165 \, a^{2} b x^{3} + 40 \, a^{3}}{440 \, x^{11}}"," ",0,"-1/440*(220*b^3*x^9 + 264*a*b^2*x^6 + 165*a^2*b*x^3 + 40*a^3)/x^11","A",0
45,1,35,0,1.418635," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^13,x, algorithm=""fricas"")","-\frac{4 \, b^{3} x^{9} + 6 \, a b^{2} x^{6} + 4 \, a^{2} b x^{3} + a^{3}}{12 \, x^{12}}"," ",0,"-1/12*(4*b^3*x^9 + 6*a*b^2*x^6 + 4*a^2*b*x^3 + a^3)/x^12","A",0
46,1,37,0,1.364805," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^14,x, algorithm=""fricas"")","-\frac{455 \, b^{3} x^{9} + 780 \, a b^{2} x^{6} + 546 \, a^{2} b x^{3} + 140 \, a^{3}}{1820 \, x^{13}}"," ",0,"-1/1820*(455*b^3*x^9 + 780*a*b^2*x^6 + 546*a^2*b*x^3 + 140*a^3)/x^13","A",0
47,1,37,0,2.231736," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^15,x, algorithm=""fricas"")","-\frac{616 \, b^{3} x^{9} + 1155 \, a b^{2} x^{6} + 840 \, a^{2} b x^{3} + 220 \, a^{3}}{3080 \, x^{14}}"," ",0,"-1/3080*(616*b^3*x^9 + 1155*a*b^2*x^6 + 840*a^2*b*x^3 + 220*a^3)/x^14","A",0
48,1,37,0,0.850376," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^16,x, algorithm=""fricas"")","-\frac{10 \, b^{3} x^{9} + 20 \, a b^{2} x^{6} + 15 \, a^{2} b x^{3} + 4 \, a^{3}}{60 \, x^{15}}"," ",0,"-1/60*(10*b^3*x^9 + 20*a*b^2*x^6 + 15*a^2*b*x^3 + 4*a^3)/x^15","A",0
49,1,37,0,1.647760," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^17,x, algorithm=""fricas"")","-\frac{1040 \, b^{3} x^{9} + 2184 \, a b^{2} x^{6} + 1680 \, a^{2} b x^{3} + 455 \, a^{3}}{7280 \, x^{16}}"," ",0,"-1/7280*(1040*b^3*x^9 + 2184*a*b^2*x^6 + 1680*a^2*b*x^3 + 455*a^3)/x^16","A",0
50,1,57,0,0.976412," ","integrate(x^13*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{29} \, b^{5} x^{29} + \frac{5}{26} \, a b^{4} x^{26} + \frac{10}{23} \, a^{2} b^{3} x^{23} + \frac{1}{2} \, a^{3} b^{2} x^{20} + \frac{5}{17} \, a^{4} b x^{17} + \frac{1}{14} \, a^{5} x^{14}"," ",0,"1/29*b^5*x^29 + 5/26*a*b^4*x^26 + 10/23*a^2*b^3*x^23 + 1/2*a^3*b^2*x^20 + 5/17*a^4*b*x^17 + 1/14*a^5*x^14","A",0
51,1,57,0,1.987136," ","integrate(x^12*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{28} \, b^{5} x^{28} + \frac{1}{5} \, a b^{4} x^{25} + \frac{5}{11} \, a^{2} b^{3} x^{22} + \frac{10}{19} \, a^{3} b^{2} x^{19} + \frac{5}{16} \, a^{4} b x^{16} + \frac{1}{13} \, a^{5} x^{13}"," ",0,"1/28*b^5*x^28 + 1/5*a*b^4*x^25 + 5/11*a^2*b^3*x^22 + 10/19*a^3*b^2*x^19 + 5/16*a^4*b*x^16 + 1/13*a^5*x^13","A",0
52,1,57,0,1.450207," ","integrate(x^11*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{27} \, b^{5} x^{27} + \frac{5}{24} \, a b^{4} x^{24} + \frac{10}{21} \, a^{2} b^{3} x^{21} + \frac{5}{9} \, a^{3} b^{2} x^{18} + \frac{1}{3} \, a^{4} b x^{15} + \frac{1}{12} \, a^{5} x^{12}"," ",0,"1/27*b^5*x^27 + 5/24*a*b^4*x^24 + 10/21*a^2*b^3*x^21 + 5/9*a^3*b^2*x^18 + 1/3*a^4*b*x^15 + 1/12*a^5*x^12","A",0
53,1,57,0,1.556566," ","integrate(x^10*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{26} \, b^{5} x^{26} + \frac{5}{23} \, a b^{4} x^{23} + \frac{1}{2} \, a^{2} b^{3} x^{20} + \frac{10}{17} \, a^{3} b^{2} x^{17} + \frac{5}{14} \, a^{4} b x^{14} + \frac{1}{11} \, a^{5} x^{11}"," ",0,"1/26*b^5*x^26 + 5/23*a*b^4*x^23 + 1/2*a^2*b^3*x^20 + 10/17*a^3*b^2*x^17 + 5/14*a^4*b*x^14 + 1/11*a^5*x^11","A",0
54,1,57,0,1.139845," ","integrate(x^9*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{25} \, b^{5} x^{25} + \frac{5}{22} \, a b^{4} x^{22} + \frac{10}{19} \, a^{2} b^{3} x^{19} + \frac{5}{8} \, a^{3} b^{2} x^{16} + \frac{5}{13} \, a^{4} b x^{13} + \frac{1}{10} \, a^{5} x^{10}"," ",0,"1/25*b^5*x^25 + 5/22*a*b^4*x^22 + 10/19*a^2*b^3*x^19 + 5/8*a^3*b^2*x^16 + 5/13*a^4*b*x^13 + 1/10*a^5*x^10","A",0
55,1,57,0,1.149747," ","integrate(x^8*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{24} \, b^{5} x^{24} + \frac{5}{21} \, a b^{4} x^{21} + \frac{5}{9} \, a^{2} b^{3} x^{18} + \frac{2}{3} \, a^{3} b^{2} x^{15} + \frac{5}{12} \, a^{4} b x^{12} + \frac{1}{9} \, a^{5} x^{9}"," ",0,"1/24*b^5*x^24 + 5/21*a*b^4*x^21 + 5/9*a^2*b^3*x^18 + 2/3*a^3*b^2*x^15 + 5/12*a^4*b*x^12 + 1/9*a^5*x^9","A",0
56,1,57,0,1.141350," ","integrate(x^7*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{23} \, b^{5} x^{23} + \frac{1}{4} \, a b^{4} x^{20} + \frac{10}{17} \, a^{2} b^{3} x^{17} + \frac{5}{7} \, a^{3} b^{2} x^{14} + \frac{5}{11} \, a^{4} b x^{11} + \frac{1}{8} \, a^{5} x^{8}"," ",0,"1/23*b^5*x^23 + 1/4*a*b^4*x^20 + 10/17*a^2*b^3*x^17 + 5/7*a^3*b^2*x^14 + 5/11*a^4*b*x^11 + 1/8*a^5*x^8","A",0
57,1,57,0,1.053680," ","integrate(x^6*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{22} \, b^{5} x^{22} + \frac{5}{19} \, a b^{4} x^{19} + \frac{5}{8} \, a^{2} b^{3} x^{16} + \frac{10}{13} \, a^{3} b^{2} x^{13} + \frac{1}{2} \, a^{4} b x^{10} + \frac{1}{7} \, a^{5} x^{7}"," ",0,"1/22*b^5*x^22 + 5/19*a*b^4*x^19 + 5/8*a^2*b^3*x^16 + 10/13*a^3*b^2*x^13 + 1/2*a^4*b*x^10 + 1/7*a^5*x^7","A",0
58,1,57,0,1.125932," ","integrate(x^5*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{21} \, b^{5} x^{21} + \frac{5}{18} \, a b^{4} x^{18} + \frac{2}{3} \, a^{2} b^{3} x^{15} + \frac{5}{6} \, a^{3} b^{2} x^{12} + \frac{5}{9} \, a^{4} b x^{9} + \frac{1}{6} \, a^{5} x^{6}"," ",0,"1/21*b^5*x^21 + 5/18*a*b^4*x^18 + 2/3*a^2*b^3*x^15 + 5/6*a^3*b^2*x^12 + 5/9*a^4*b*x^9 + 1/6*a^5*x^6","A",0
59,1,57,0,1.328345," ","integrate(x^4*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{20} \, b^{5} x^{20} + \frac{5}{17} \, a b^{4} x^{17} + \frac{5}{7} \, a^{2} b^{3} x^{14} + \frac{10}{11} \, a^{3} b^{2} x^{11} + \frac{5}{8} \, a^{4} b x^{8} + \frac{1}{5} \, a^{5} x^{5}"," ",0,"1/20*b^5*x^20 + 5/17*a*b^4*x^17 + 5/7*a^2*b^3*x^14 + 10/11*a^3*b^2*x^11 + 5/8*a^4*b*x^8 + 1/5*a^5*x^5","A",0
60,1,56,0,1.157967," ","integrate(x^3*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{19} \, b^{5} x^{19} + \frac{5}{16} \, a b^{4} x^{16} + \frac{10}{13} \, a^{2} b^{3} x^{13} + a^{3} b^{2} x^{10} + \frac{5}{7} \, a^{4} b x^{7} + \frac{1}{4} \, a^{5} x^{4}"," ",0,"1/19*b^5*x^19 + 5/16*a*b^4*x^16 + 10/13*a^2*b^3*x^13 + a^3*b^2*x^10 + 5/7*a^4*b*x^7 + 1/4*a^5*x^4","A",0
61,1,57,0,0.938957," ","integrate(x^2*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{18} \, b^{5} x^{18} + \frac{1}{3} \, a b^{4} x^{15} + \frac{5}{6} \, a^{2} b^{3} x^{12} + \frac{10}{9} \, a^{3} b^{2} x^{9} + \frac{5}{6} \, a^{4} b x^{6} + \frac{1}{3} \, a^{5} x^{3}"," ",0,"1/18*b^5*x^18 + 1/3*a*b^4*x^15 + 5/6*a^2*b^3*x^12 + 10/9*a^3*b^2*x^9 + 5/6*a^4*b*x^6 + 1/3*a^5*x^3","A",0
62,1,56,0,0.813579," ","integrate(x*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{17} \, b^{5} x^{17} + \frac{5}{14} \, a b^{4} x^{14} + \frac{10}{11} \, a^{2} b^{3} x^{11} + \frac{5}{4} \, a^{3} b^{2} x^{8} + a^{4} b x^{5} + \frac{1}{2} \, a^{5} x^{2}"," ",0,"1/17*b^5*x^17 + 5/14*a*b^4*x^14 + 10/11*a^2*b^3*x^11 + 5/4*a^3*b^2*x^8 + a^4*b*x^5 + 1/2*a^5*x^2","A",0
63,1,53,0,1.287394," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{16} \, b^{5} x^{16} + \frac{5}{13} \, a b^{4} x^{13} + a^{2} b^{3} x^{10} + \frac{10}{7} \, a^{3} b^{2} x^{7} + \frac{5}{4} \, a^{4} b x^{4} + a^{5} x"," ",0,"1/16*b^5*x^16 + 5/13*a*b^4*x^13 + a^2*b^3*x^10 + 10/7*a^3*b^2*x^7 + 5/4*a^4*b*x^4 + a^5*x","A",0
64,1,55,0,1.169729," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x,x, algorithm=""fricas"")","\frac{1}{15} \, b^{5} x^{15} + \frac{5}{12} \, a b^{4} x^{12} + \frac{10}{9} \, a^{2} b^{3} x^{9} + \frac{5}{3} \, a^{3} b^{2} x^{6} + \frac{5}{3} \, a^{4} b x^{3} + a^{5} \log\left(x\right)"," ",0,"1/15*b^5*x^15 + 5/12*a*b^4*x^12 + 10/9*a^2*b^3*x^9 + 5/3*a^3*b^2*x^6 + 5/3*a^4*b*x^3 + a^5*log(x)","A",0
65,1,59,0,1.219172," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^2,x, algorithm=""fricas"")","\frac{22 \, b^{5} x^{15} + 140 \, a b^{4} x^{12} + 385 \, a^{2} b^{3} x^{9} + 616 \, a^{3} b^{2} x^{6} + 770 \, a^{4} b x^{3} - 308 \, a^{5}}{308 \, x}"," ",0,"1/308*(22*b^5*x^15 + 140*a*b^4*x^12 + 385*a^2*b^3*x^9 + 616*a^3*b^2*x^6 + 770*a^4*b*x^3 - 308*a^5)/x","A",0
66,1,59,0,1.217075," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^3,x, algorithm=""fricas"")","\frac{14 \, b^{5} x^{15} + 91 \, a b^{4} x^{12} + 260 \, a^{2} b^{3} x^{9} + 455 \, a^{3} b^{2} x^{6} + 910 \, a^{4} b x^{3} - 91 \, a^{5}}{182 \, x^{2}}"," ",0,"1/182*(14*b^5*x^15 + 91*a*b^4*x^12 + 260*a^2*b^3*x^9 + 455*a^3*b^2*x^6 + 910*a^4*b*x^3 - 91*a^5)/x^2","A",0
67,1,61,0,0.984604," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^4,x, algorithm=""fricas"")","\frac{3 \, b^{5} x^{15} + 20 \, a b^{4} x^{12} + 60 \, a^{2} b^{3} x^{9} + 120 \, a^{3} b^{2} x^{6} + 180 \, a^{4} b x^{3} \log\left(x\right) - 12 \, a^{5}}{36 \, x^{3}}"," ",0,"1/36*(3*b^5*x^15 + 20*a*b^4*x^12 + 60*a^2*b^3*x^9 + 120*a^3*b^2*x^6 + 180*a^4*b*x^3*log(x) - 12*a^5)/x^3","A",0
68,1,59,0,1.343068," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^5,x, algorithm=""fricas"")","\frac{8 \, b^{5} x^{15} + 55 \, a b^{4} x^{12} + 176 \, a^{2} b^{3} x^{9} + 440 \, a^{3} b^{2} x^{6} - 440 \, a^{4} b x^{3} - 22 \, a^{5}}{88 \, x^{4}}"," ",0,"1/88*(8*b^5*x^15 + 55*a*b^4*x^12 + 176*a^2*b^3*x^9 + 440*a^3*b^2*x^6 - 440*a^4*b*x^3 - 22*a^5)/x^4","A",0
69,1,59,0,0.714998," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^6,x, algorithm=""fricas"")","\frac{7 \, b^{5} x^{15} + 50 \, a b^{4} x^{12} + 175 \, a^{2} b^{3} x^{9} + 700 \, a^{3} b^{2} x^{6} - 175 \, a^{4} b x^{3} - 14 \, a^{5}}{70 \, x^{5}}"," ",0,"1/70*(7*b^5*x^15 + 50*a*b^4*x^12 + 175*a^2*b^3*x^9 + 700*a^3*b^2*x^6 - 175*a^4*b*x^3 - 14*a^5)/x^5","A",0
70,1,61,0,1.308593," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^7,x, algorithm=""fricas"")","\frac{2 \, b^{5} x^{15} + 15 \, a b^{4} x^{12} + 60 \, a^{2} b^{3} x^{9} + 180 \, a^{3} b^{2} x^{6} \log\left(x\right) - 30 \, a^{4} b x^{3} - 3 \, a^{5}}{18 \, x^{6}}"," ",0,"1/18*(2*b^5*x^15 + 15*a*b^4*x^12 + 60*a^2*b^3*x^9 + 180*a^3*b^2*x^6*log(x) - 30*a^4*b*x^3 - 3*a^5)/x^6","A",0
71,1,59,0,1.141545," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^8,x, algorithm=""fricas"")","\frac{7 \, b^{5} x^{15} + 56 \, a b^{4} x^{12} + 280 \, a^{2} b^{3} x^{9} - 560 \, a^{3} b^{2} x^{6} - 70 \, a^{4} b x^{3} - 8 \, a^{5}}{56 \, x^{7}}"," ",0,"1/56*(7*b^5*x^15 + 56*a*b^4*x^12 + 280*a^2*b^3*x^9 - 560*a^3*b^2*x^6 - 70*a^4*b*x^3 - 8*a^5)/x^7","A",0
72,1,59,0,1.285451," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^9,x, algorithm=""fricas"")","\frac{8 \, b^{5} x^{15} + 70 \, a b^{4} x^{12} + 560 \, a^{2} b^{3} x^{9} - 280 \, a^{3} b^{2} x^{6} - 56 \, a^{4} b x^{3} - 7 \, a^{5}}{56 \, x^{8}}"," ",0,"1/56*(8*b^5*x^15 + 70*a*b^4*x^12 + 560*a^2*b^3*x^9 - 280*a^3*b^2*x^6 - 56*a^4*b*x^3 - 7*a^5)/x^8","A",0
73,1,61,0,1.716486," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^10,x, algorithm=""fricas"")","\frac{3 \, b^{5} x^{15} + 30 \, a b^{4} x^{12} + 180 \, a^{2} b^{3} x^{9} \log\left(x\right) - 60 \, a^{3} b^{2} x^{6} - 15 \, a^{4} b x^{3} - 2 \, a^{5}}{18 \, x^{9}}"," ",0,"1/18*(3*b^5*x^15 + 30*a*b^4*x^12 + 180*a^2*b^3*x^9*log(x) - 60*a^3*b^2*x^6 - 15*a^4*b*x^3 - 2*a^5)/x^9","A",0
74,1,59,0,1.197145," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^11,x, algorithm=""fricas"")","\frac{14 \, b^{5} x^{15} + 175 \, a b^{4} x^{12} - 700 \, a^{2} b^{3} x^{9} - 175 \, a^{3} b^{2} x^{6} - 50 \, a^{4} b x^{3} - 7 \, a^{5}}{70 \, x^{10}}"," ",0,"1/70*(14*b^5*x^15 + 175*a*b^4*x^12 - 700*a^2*b^3*x^9 - 175*a^3*b^2*x^6 - 50*a^4*b*x^3 - 7*a^5)/x^10","A",0
75,1,59,0,1.079491," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^12,x, algorithm=""fricas"")","\frac{22 \, b^{5} x^{15} + 440 \, a b^{4} x^{12} - 440 \, a^{2} b^{3} x^{9} - 176 \, a^{3} b^{2} x^{6} - 55 \, a^{4} b x^{3} - 8 \, a^{5}}{88 \, x^{11}}"," ",0,"1/88*(22*b^5*x^15 + 440*a*b^4*x^12 - 440*a^2*b^3*x^9 - 176*a^3*b^2*x^6 - 55*a^4*b*x^3 - 8*a^5)/x^11","A",0
76,1,61,0,1.171551," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^13,x, algorithm=""fricas"")","\frac{12 \, b^{5} x^{15} + 180 \, a b^{4} x^{12} \log\left(x\right) - 120 \, a^{2} b^{3} x^{9} - 60 \, a^{3} b^{2} x^{6} - 20 \, a^{4} b x^{3} - 3 \, a^{5}}{36 \, x^{12}}"," ",0,"1/36*(12*b^5*x^15 + 180*a*b^4*x^12*log(x) - 120*a^2*b^3*x^9 - 60*a^3*b^2*x^6 - 20*a^4*b*x^3 - 3*a^5)/x^12","A",0
77,1,59,0,1.179288," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^14,x, algorithm=""fricas"")","\frac{91 \, b^{5} x^{15} - 910 \, a b^{4} x^{12} - 455 \, a^{2} b^{3} x^{9} - 260 \, a^{3} b^{2} x^{6} - 91 \, a^{4} b x^{3} - 14 \, a^{5}}{182 \, x^{13}}"," ",0,"1/182*(91*b^5*x^15 - 910*a*b^4*x^12 - 455*a^2*b^3*x^9 - 260*a^3*b^2*x^6 - 91*a^4*b*x^3 - 14*a^5)/x^13","A",0
78,1,59,0,0.677853," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^15,x, algorithm=""fricas"")","\frac{308 \, b^{5} x^{15} - 770 \, a b^{4} x^{12} - 616 \, a^{2} b^{3} x^{9} - 385 \, a^{3} b^{2} x^{6} - 140 \, a^{4} b x^{3} - 22 \, a^{5}}{308 \, x^{14}}"," ",0,"1/308*(308*b^5*x^15 - 770*a*b^4*x^12 - 616*a^2*b^3*x^9 - 385*a^3*b^2*x^6 - 140*a^4*b*x^3 - 22*a^5)/x^14","A",0
79,1,61,0,1.233546," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^16,x, algorithm=""fricas"")","\frac{180 \, b^{5} x^{15} \log\left(x\right) - 300 \, a b^{4} x^{12} - 300 \, a^{2} b^{3} x^{9} - 200 \, a^{3} b^{2} x^{6} - 75 \, a^{4} b x^{3} - 12 \, a^{5}}{180 \, x^{15}}"," ",0,"1/180*(180*b^5*x^15*log(x) - 300*a*b^4*x^12 - 300*a^2*b^3*x^9 - 200*a^3*b^2*x^6 - 75*a^4*b*x^3 - 12*a^5)/x^15","A",0
80,1,59,0,1.155534," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^17,x, algorithm=""fricas"")","-\frac{1456 \, b^{5} x^{15} + 1820 \, a b^{4} x^{12} + 2080 \, a^{2} b^{3} x^{9} + 1456 \, a^{3} b^{2} x^{6} + 560 \, a^{4} b x^{3} + 91 \, a^{5}}{1456 \, x^{16}}"," ",0,"-1/1456*(1456*b^5*x^15 + 1820*a*b^4*x^12 + 2080*a^2*b^3*x^9 + 1456*a^3*b^2*x^6 + 560*a^4*b*x^3 + 91*a^5)/x^16","A",0
81,1,59,0,1.205479," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^18,x, algorithm=""fricas"")","-\frac{2618 \, b^{5} x^{15} + 5236 \, a b^{4} x^{12} + 6545 \, a^{2} b^{3} x^{9} + 4760 \, a^{3} b^{2} x^{6} + 1870 \, a^{4} b x^{3} + 308 \, a^{5}}{5236 \, x^{17}}"," ",0,"-1/5236*(2618*b^5*x^15 + 5236*a*b^4*x^12 + 6545*a^2*b^3*x^9 + 4760*a^3*b^2*x^6 + 1870*a^4*b*x^3 + 308*a^5)/x^17","A",0
82,1,57,0,1.140562," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^19,x, algorithm=""fricas"")","-\frac{6 \, b^{5} x^{15} + 15 \, a b^{4} x^{12} + 20 \, a^{2} b^{3} x^{9} + 15 \, a^{3} b^{2} x^{6} + 6 \, a^{4} b x^{3} + a^{5}}{18 \, x^{18}}"," ",0,"-1/18*(6*b^5*x^15 + 15*a*b^4*x^12 + 20*a^2*b^3*x^9 + 15*a^3*b^2*x^6 + 6*a^4*b*x^3 + a^5)/x^18","B",0
83,1,59,0,1.100195," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^20,x, algorithm=""fricas"")","-\frac{6916 \, b^{5} x^{15} + 19760 \, a b^{4} x^{12} + 27664 \, a^{2} b^{3} x^{9} + 21280 \, a^{3} b^{2} x^{6} + 8645 \, a^{4} b x^{3} + 1456 \, a^{5}}{27664 \, x^{19}}"," ",0,"-1/27664*(6916*b^5*x^15 + 19760*a*b^4*x^12 + 27664*a^2*b^3*x^9 + 21280*a^3*b^2*x^6 + 8645*a^4*b*x^3 + 1456*a^5)/x^19","A",0
84,1,59,0,1.110728," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^21,x, algorithm=""fricas"")","-\frac{10472 \, b^{5} x^{15} + 32725 \, a b^{4} x^{12} + 47600 \, a^{2} b^{3} x^{9} + 37400 \, a^{3} b^{2} x^{6} + 15400 \, a^{4} b x^{3} + 2618 \, a^{5}}{52360 \, x^{20}}"," ",0,"-1/52360*(10472*b^5*x^15 + 32725*a*b^4*x^12 + 47600*a^2*b^3*x^9 + 37400*a^3*b^2*x^6 + 15400*a^4*b*x^3 + 2618*a^5)/x^20","A",0
85,1,59,0,1.018521," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^22,x, algorithm=""fricas"")","-\frac{21 \, b^{5} x^{15} + 70 \, a b^{4} x^{12} + 105 \, a^{2} b^{3} x^{9} + 84 \, a^{3} b^{2} x^{6} + 35 \, a^{4} b x^{3} + 6 \, a^{5}}{126 \, x^{21}}"," ",0,"-1/126*(21*b^5*x^15 + 70*a*b^4*x^12 + 105*a^2*b^3*x^9 + 84*a^3*b^2*x^6 + 35*a^4*b*x^3 + 6*a^5)/x^21","A",0
86,1,59,0,1.107034," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^23,x, algorithm=""fricas"")","-\frac{21736 \, b^{5} x^{15} + 76076 \, a b^{4} x^{12} + 117040 \, a^{2} b^{3} x^{9} + 95095 \, a^{3} b^{2} x^{6} + 40040 \, a^{4} b x^{3} + 6916 \, a^{5}}{152152 \, x^{22}}"," ",0,"-1/152152*(21736*b^5*x^15 + 76076*a*b^4*x^12 + 117040*a^2*b^3*x^9 + 95095*a^3*b^2*x^6 + 40040*a^4*b*x^3 + 6916*a^5)/x^22","A",0
87,1,59,0,1.094406," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^24,x, algorithm=""fricas"")","-\frac{30107 \, b^{5} x^{15} + 109480 \, a b^{4} x^{12} + 172040 \, a^{2} b^{3} x^{9} + 141680 \, a^{3} b^{2} x^{6} + 60214 \, a^{4} b x^{3} + 10472 \, a^{5}}{240856 \, x^{23}}"," ",0,"-1/240856*(30107*b^5*x^15 + 109480*a*b^4*x^12 + 172040*a^2*b^3*x^9 + 141680*a^3*b^2*x^6 + 60214*a^4*b*x^3 + 10472*a^5)/x^23","A",0
88,1,59,0,1.274854," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^25,x, algorithm=""fricas"")","-\frac{56 \, b^{5} x^{15} + 210 \, a b^{4} x^{12} + 336 \, a^{2} b^{3} x^{9} + 280 \, a^{3} b^{2} x^{6} + 120 \, a^{4} b x^{3} + 21 \, a^{5}}{504 \, x^{24}}"," ",0,"-1/504*(56*b^5*x^15 + 210*a*b^4*x^12 + 336*a^2*b^3*x^9 + 280*a^3*b^2*x^6 + 120*a^4*b*x^3 + 21*a^5)/x^24","A",0
89,1,123,0,0.853658," ","integrate(x^4/((b*x^3+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{3 \, x^{2} - 2 \, \sqrt{3} \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} - \sqrt{3} a}{3 \, a}\right) - \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x^{2} - b x \left(\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}} + a \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}}\right) + 2 \, \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x + b \left(\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}}\right)}{6 \, b}"," ",0,"1/6*(3*x^2 - 2*sqrt(3)*(a^2/b^2)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(a^2/b^2)^(1/3) - sqrt(3)*a)/a) - (a^2/b^2)^(1/3)*log(a*x^2 - b*x*(a^2/b^2)^(2/3) + a*(a^2/b^2)^(1/3)) + 2*(a^2/b^2)^(1/3)*log(a*x + b*(a^2/b^2)^(2/3)))/b","A",0
90,1,106,0,1.173516," ","integrate(x^3/((b*x^3+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(-\frac{a}{b}\right)^{\frac{2}{3}} - \sqrt{3} a}{3 \, a}\right) - \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right) + 2 \, \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x - \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right) + 6 \, x}{6 \, b}"," ",0,"1/6*(2*sqrt(3)*(-a/b)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(-a/b)^(2/3) - sqrt(3)*a)/a) - (-a/b)^(1/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3)) + 2*(-a/b)^(1/3)*log(x - (-a/b)^(1/3)) + 6*x)/b","A",0
91,1,13,0,1.072832," ","integrate(x^2/((b*x^3+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{\log\left(b x^{3} + a\right)}{3 \, b}"," ",0,"1/3*log(b*x^3 + a)/b","A",0
92,1,304,0,1.755126," ","integrate(x/((b*x^3+a)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a b \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} + a}\right) + \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{6 \, a b^{2}}, \frac{6 \, \sqrt{\frac{1}{3}} a b \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{6 \, a b^{2}}\right]"," ",0,"[1/6*(3*sqrt(1/3)*a*b*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*x^3 - a*b + 3*sqrt(1/3)*(a*b*x + 2*(-a*b^2)^(2/3)*x^2 + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*x)/(b*x^3 + a)) + (-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 2*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a*b^2), 1/6*(6*sqrt(1/3)*a*b*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*x + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + (-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 2*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a*b^2)]","A",0
93,1,299,0,1.312117," ","integrate(1/((b*x^3+a)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a b \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{6 \, a^{2} b}, \frac{6 \, \sqrt{\frac{1}{3}} a b \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{6 \, a^{2} b}\right]"," ",0,"[1/6*(3*sqrt(1/3)*a*b*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) - (a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 2*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^2*b), 1/6*(6*sqrt(1/3)*a*b*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - (a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 2*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^2*b)]","A",0
94,1,18,0,1.117707," ","integrate(1/x/((b*x^3+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{\log\left(b x^{3} + a\right) - 3 \, \log\left(x\right)}{3 \, a}"," ",0,"-1/3*(log(b*x^3 + a) - 3*log(x))/a","A",0
95,1,103,0,1.075436," ","integrate(1/x^2/((b*x^3+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} x \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(\frac{b}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + x \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x^{2} - a x \left(\frac{b}{a}\right)^{\frac{2}{3}} + a \left(\frac{b}{a}\right)^{\frac{1}{3}}\right) - 2 \, x \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x + a \left(\frac{b}{a}\right)^{\frac{2}{3}}\right) + 6}{6 \, a x}"," ",0,"-1/6*(2*sqrt(3)*x*(b/a)^(1/3)*arctan(2/3*sqrt(3)*x*(b/a)^(1/3) - 1/3*sqrt(3)) + x*(b/a)^(1/3)*log(b*x^2 - a*x*(b/a)^(2/3) + a*(b/a)^(1/3)) - 2*x*(b/a)^(1/3)*log(b*x + a*(b/a)^(2/3)) + 6)/(a*x)","A",0
96,1,143,0,1.297616," ","integrate(1/x^3/((b*x^3+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} x^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) - x^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} x^{2} + a b x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} + a^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right) + 2 \, x^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x - a \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) - 3}{6 \, a x^{2}}"," ",0,"1/6*(2*sqrt(3)*x^2*(-b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(-b^2/a^2)^(2/3) - sqrt(3)*b)/b) - x^2*(-b^2/a^2)^(1/3)*log(b^2*x^2 + a*b*x*(-b^2/a^2)^(1/3) + a^2*(-b^2/a^2)^(2/3)) + 2*x^2*(-b^2/a^2)^(1/3)*log(b*x - a*(-b^2/a^2)^(1/3)) - 3)/(a*x^2)","A",0
97,1,33,0,1.115697," ","integrate(1/x^4/((b*x^3+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{b x^{3} \log\left(b x^{3} + a\right) - 3 \, b x^{3} \log\left(x\right) - a}{3 \, a^{2} x^{3}}"," ",0,"1/3*(b*x^3*log(b*x^3 + a) - 3*b*x^3*log(x) - a)/(a^2*x^3)","A",0
98,1,512,0,1.379272," ","integrate(x^4/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{6 \, a b^{3} x^{5} - 3 \, a^{2} b^{2} x^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} + a}\right) + {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a^{2} b^{5} x^{6} + 2 \, a^{3} b^{4} x^{3} + a^{4} b^{3}\right)}}, \frac{6 \, a b^{3} x^{5} - 3 \, a^{2} b^{2} x^{2} + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a^{2} b^{5} x^{6} + 2 \, a^{3} b^{4} x^{3} + a^{4} b^{3}\right)}}\right]"," ",0,"[1/54*(6*a*b^3*x^5 - 3*a^2*b^2*x^2 + 3*sqrt(1/3)*(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*x^3 - a*b + 3*sqrt(1/3)*(a*b*x + 2*(-a*b^2)^(2/3)*x^2 + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*x)/(b*x^3 + a)) + (b^2*x^6 + 2*a*b*x^3 + a^2)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 2*(b^2*x^6 + 2*a*b*x^3 + a^2)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a^2*b^5*x^6 + 2*a^3*b^4*x^3 + a^4*b^3), 1/54*(6*a*b^3*x^5 - 3*a^2*b^2*x^2 + 6*sqrt(1/3)*(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*x + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + (b^2*x^6 + 2*a*b*x^3 + a^2)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 2*(b^2*x^6 + 2*a*b*x^3 + a^2)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a^2*b^5*x^6 + 2*a^3*b^4*x^3 + a^4*b^3)]","A",0
99,1,503,0,1.305660," ","integrate(x^3/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} b^{2} x^{4} - 6 \, a^{3} b x + 3 \, \sqrt{\frac{1}{3}} {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{54 \, {\left(a^{3} b^{4} x^{6} + 2 \, a^{4} b^{3} x^{3} + a^{5} b^{2}\right)}}, \frac{3 \, a^{2} b^{2} x^{4} - 6 \, a^{3} b x + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{54 \, {\left(a^{3} b^{4} x^{6} + 2 \, a^{4} b^{3} x^{3} + a^{5} b^{2}\right)}}\right]"," ",0,"[1/54*(3*a^2*b^2*x^4 - 6*a^3*b*x + 3*sqrt(1/3)*(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) - (b^2*x^6 + 2*a*b*x^3 + a^2)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 2*(b^2*x^6 + 2*a*b*x^3 + a^2)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^3*b^4*x^6 + 2*a^4*b^3*x^3 + a^5*b^2), 1/54*(3*a^2*b^2*x^4 - 6*a^3*b*x + 6*sqrt(1/3)*(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - (b^2*x^6 + 2*a*b*x^3 + a^2)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 2*(b^2*x^6 + 2*a*b*x^3 + a^2)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^3*b^4*x^6 + 2*a^4*b^3*x^3 + a^5*b^2)]","A",0
100,1,26,0,1.410362," ","integrate(x^2/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{1}{6 \, {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}}"," ",0,"-1/6/(b^3*x^6 + 2*a*b^2*x^3 + a^2*b)","A",0
101,1,514,0,0.736496," ","integrate(x/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{12 \, a b^{3} x^{5} + 21 \, a^{2} b^{2} x^{2} + 6 \, \sqrt{\frac{1}{3}} {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} + a}\right) + 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 4 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a^{3} b^{4} x^{6} + 2 \, a^{4} b^{3} x^{3} + a^{5} b^{2}\right)}}, \frac{12 \, a b^{3} x^{5} + 21 \, a^{2} b^{2} x^{2} + 12 \, \sqrt{\frac{1}{3}} {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 4 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a^{3} b^{4} x^{6} + 2 \, a^{4} b^{3} x^{3} + a^{5} b^{2}\right)}}\right]"," ",0,"[1/54*(12*a*b^3*x^5 + 21*a^2*b^2*x^2 + 6*sqrt(1/3)*(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*x^3 - a*b + 3*sqrt(1/3)*(a*b*x + 2*(-a*b^2)^(2/3)*x^2 + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*x)/(b*x^3 + a)) + 2*(b^2*x^6 + 2*a*b*x^3 + a^2)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 4*(b^2*x^6 + 2*a*b*x^3 + a^2)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a^3*b^4*x^6 + 2*a^4*b^3*x^3 + a^5*b^2), 1/54*(12*a*b^3*x^5 + 21*a^2*b^2*x^2 + 12*sqrt(1/3)*(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*x + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + 2*(b^2*x^6 + 2*a*b*x^3 + a^2)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 4*(b^2*x^6 + 2*a*b*x^3 + a^2)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a^3*b^4*x^6 + 2*a^4*b^3*x^3 + a^5*b^2)]","A",0
102,1,499,0,1.342985," ","integrate(1/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{2} b^{2} x^{4} + 24 \, a^{3} b x + 15 \, \sqrt{\frac{1}{3}} {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - 5 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 10 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{54 \, {\left(a^{4} b^{3} x^{6} + 2 \, a^{5} b^{2} x^{3} + a^{6} b\right)}}, \frac{15 \, a^{2} b^{2} x^{4} + 24 \, a^{3} b x + 30 \, \sqrt{\frac{1}{3}} {\left(a b^{3} x^{6} + 2 \, a^{2} b^{2} x^{3} + a^{3} b\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - 5 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 10 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{54 \, {\left(a^{4} b^{3} x^{6} + 2 \, a^{5} b^{2} x^{3} + a^{6} b\right)}}\right]"," ",0,"[1/54*(15*a^2*b^2*x^4 + 24*a^3*b*x + 15*sqrt(1/3)*(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) - 5*(b^2*x^6 + 2*a*b*x^3 + a^2)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 10*(b^2*x^6 + 2*a*b*x^3 + a^2)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^4*b^3*x^6 + 2*a^5*b^2*x^3 + a^6*b), 1/54*(15*a^2*b^2*x^4 + 24*a^3*b*x + 30*sqrt(1/3)*(a*b^3*x^6 + 2*a^2*b^2*x^3 + a^3*b)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - 5*(b^2*x^6 + 2*a*b*x^3 + a^2)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 10*(b^2*x^6 + 2*a*b*x^3 + a^2)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^4*b^3*x^6 + 2*a^5*b^2*x^3 + a^6*b)]","A",0
103,1,90,0,1.239792," ","integrate(1/x/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, a b x^{3} + 3 \, a^{2} - 2 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \log\left(b x^{3} + a\right) + 6 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \log\left(x\right)}{6 \, {\left(a^{3} b^{2} x^{6} + 2 \, a^{4} b x^{3} + a^{5}\right)}}"," ",0,"1/6*(2*a*b*x^3 + 3*a^2 - 2*(b^2*x^6 + 2*a*b*x^3 + a^2)*log(b*x^3 + a) + 6*(b^2*x^6 + 2*a*b*x^3 + a^2)*log(x))/(a^3*b^2*x^6 + 2*a^4*b*x^3 + a^5)","A",0
104,1,201,0,1.397473," ","integrate(1/x^2/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{84 \, b^{2} x^{6} + 147 \, a b x^{3} + 28 \, \sqrt{3} {\left(b^{2} x^{7} + 2 \, a b x^{4} + a^{2} x\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(\frac{b}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + 14 \, {\left(b^{2} x^{7} + 2 \, a b x^{4} + a^{2} x\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x^{2} - a x \left(\frac{b}{a}\right)^{\frac{2}{3}} + a \left(\frac{b}{a}\right)^{\frac{1}{3}}\right) - 28 \, {\left(b^{2} x^{7} + 2 \, a b x^{4} + a^{2} x\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x + a \left(\frac{b}{a}\right)^{\frac{2}{3}}\right) + 54 \, a^{2}}{54 \, {\left(a^{3} b^{2} x^{7} + 2 \, a^{4} b x^{4} + a^{5} x\right)}}"," ",0,"-1/54*(84*b^2*x^6 + 147*a*b*x^3 + 28*sqrt(3)*(b^2*x^7 + 2*a*b*x^4 + a^2*x)*(b/a)^(1/3)*arctan(2/3*sqrt(3)*x*(b/a)^(1/3) - 1/3*sqrt(3)) + 14*(b^2*x^7 + 2*a*b*x^4 + a^2*x)*(b/a)^(1/3)*log(b*x^2 - a*x*(b/a)^(2/3) + a*(b/a)^(1/3)) - 28*(b^2*x^7 + 2*a*b*x^4 + a^2*x)*(b/a)^(1/3)*log(b*x + a*(b/a)^(2/3)) + 54*a^2)/(a^3*b^2*x^7 + 2*a^4*b*x^4 + a^5*x)","A",0
105,1,242,0,1.397544," ","integrate(1/x^3/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{60 \, b^{2} x^{6} + 96 \, a b x^{3} - 40 \, \sqrt{3} {\left(b^{2} x^{8} + 2 \, a b x^{5} + a^{2} x^{2}\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) + 20 \, {\left(b^{2} x^{8} + 2 \, a b x^{5} + a^{2} x^{2}\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} x^{2} + a b x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} + a^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right) - 40 \, {\left(b^{2} x^{8} + 2 \, a b x^{5} + a^{2} x^{2}\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x - a \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) + 27 \, a^{2}}{54 \, {\left(a^{3} b^{2} x^{8} + 2 \, a^{4} b x^{5} + a^{5} x^{2}\right)}}"," ",0,"-1/54*(60*b^2*x^6 + 96*a*b*x^3 - 40*sqrt(3)*(b^2*x^8 + 2*a*b*x^5 + a^2*x^2)*(-b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(-b^2/a^2)^(2/3) - sqrt(3)*b)/b) + 20*(b^2*x^8 + 2*a*b*x^5 + a^2*x^2)*(-b^2/a^2)^(1/3)*log(b^2*x^2 + a*b*x*(-b^2/a^2)^(1/3) + a^2*(-b^2/a^2)^(2/3)) - 40*(b^2*x^8 + 2*a*b*x^5 + a^2*x^2)*(-b^2/a^2)^(1/3)*log(b*x - a*(-b^2/a^2)^(1/3)) + 27*a^2)/(a^3*b^2*x^8 + 2*a^4*b*x^5 + a^5*x^2)","A",0
106,1,119,0,1.266912," ","integrate(1/x^4/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{6 \, a b^{2} x^{6} + 9 \, a^{2} b x^{3} + 2 \, a^{3} - 6 \, {\left(b^{3} x^{9} + 2 \, a b^{2} x^{6} + a^{2} b x^{3}\right)} \log\left(b x^{3} + a\right) + 18 \, {\left(b^{3} x^{9} + 2 \, a b^{2} x^{6} + a^{2} b x^{3}\right)} \log\left(x\right)}{6 \, {\left(a^{4} b^{2} x^{9} + 2 \, a^{5} b x^{6} + a^{6} x^{3}\right)}}"," ",0,"-1/6*(6*a*b^2*x^6 + 9*a^2*b*x^3 + 2*a^3 - 6*(b^3*x^9 + 2*a*b^2*x^6 + a^2*b*x^3)*log(b*x^3 + a) + 18*(b^3*x^9 + 2*a*b^2*x^6 + a^2*b*x^3)*log(x))/(a^4*b^2*x^9 + 2*a^5*b*x^6 + a^6*x^3)","A",0
107,1,723,0,0.778676," ","integrate(x^6/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{30 \, a^{2} b^{4} x^{10} + 108 \, a^{3} b^{3} x^{7} - 225 \, a^{4} b^{2} x^{4} - 60 \, a^{5} b x + 30 \, \sqrt{\frac{1}{3}} {\left(a b^{5} x^{12} + 4 \, a^{2} b^{4} x^{9} + 6 \, a^{3} b^{3} x^{6} + 4 \, a^{4} b^{2} x^{3} + a^{5} b\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - 10 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 20 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{2916 \, {\left(a^{4} b^{7} x^{12} + 4 \, a^{5} b^{6} x^{9} + 6 \, a^{6} b^{5} x^{6} + 4 \, a^{7} b^{4} x^{3} + a^{8} b^{3}\right)}}, \frac{30 \, a^{2} b^{4} x^{10} + 108 \, a^{3} b^{3} x^{7} - 225 \, a^{4} b^{2} x^{4} - 60 \, a^{5} b x + 60 \, \sqrt{\frac{1}{3}} {\left(a b^{5} x^{12} + 4 \, a^{2} b^{4} x^{9} + 6 \, a^{3} b^{3} x^{6} + 4 \, a^{4} b^{2} x^{3} + a^{5} b\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - 10 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 20 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{2916 \, {\left(a^{4} b^{7} x^{12} + 4 \, a^{5} b^{6} x^{9} + 6 \, a^{6} b^{5} x^{6} + 4 \, a^{7} b^{4} x^{3} + a^{8} b^{3}\right)}}\right]"," ",0,"[1/2916*(30*a^2*b^4*x^10 + 108*a^3*b^3*x^7 - 225*a^4*b^2*x^4 - 60*a^5*b*x + 30*sqrt(1/3)*(a*b^5*x^12 + 4*a^2*b^4*x^9 + 6*a^3*b^3*x^6 + 4*a^4*b^2*x^3 + a^5*b)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) - 10*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 20*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^4*b^7*x^12 + 4*a^5*b^6*x^9 + 6*a^6*b^5*x^6 + 4*a^7*b^4*x^3 + a^8*b^3), 1/2916*(30*a^2*b^4*x^10 + 108*a^3*b^3*x^7 - 225*a^4*b^2*x^4 - 60*a^5*b*x + 60*sqrt(1/3)*(a*b^5*x^12 + 4*a^2*b^4*x^9 + 6*a^3*b^3*x^6 + 4*a^4*b^2*x^3 + a^5*b)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - 10*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 20*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^4*b^7*x^12 + 4*a^5*b^6*x^9 + 6*a^6*b^5*x^6 + 4*a^7*b^4*x^3 + a^8*b^3)]","A",0
108,1,58,0,1.181099," ","integrate(x^5/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{4 \, b x^{3} + a}{36 \, {\left(b^{6} x^{12} + 4 \, a b^{5} x^{9} + 6 \, a^{2} b^{4} x^{6} + 4 \, a^{3} b^{3} x^{3} + a^{4} b^{2}\right)}}"," ",0,"-1/36*(4*b*x^3 + a)/(b^6*x^12 + 4*a*b^5*x^9 + 6*a^2*b^4*x^6 + 4*a^3*b^3*x^3 + a^4*b^2)","A",0
109,1,734,0,1.302284," ","integrate(x^4/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{84 \, a b^{5} x^{11} + 315 \, a^{2} b^{4} x^{8} + 432 \, a^{3} b^{3} x^{5} - 42 \, a^{4} b^{2} x^{2} + 42 \, \sqrt{\frac{1}{3}} {\left(a b^{5} x^{12} + 4 \, a^{2} b^{4} x^{9} + 6 \, a^{3} b^{3} x^{6} + 4 \, a^{4} b^{2} x^{3} + a^{5} b\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} + a}\right) + 14 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 28 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{2916 \, {\left(a^{4} b^{7} x^{12} + 4 \, a^{5} b^{6} x^{9} + 6 \, a^{6} b^{5} x^{6} + 4 \, a^{7} b^{4} x^{3} + a^{8} b^{3}\right)}}, \frac{84 \, a b^{5} x^{11} + 315 \, a^{2} b^{4} x^{8} + 432 \, a^{3} b^{3} x^{5} - 42 \, a^{4} b^{2} x^{2} + 84 \, \sqrt{\frac{1}{3}} {\left(a b^{5} x^{12} + 4 \, a^{2} b^{4} x^{9} + 6 \, a^{3} b^{3} x^{6} + 4 \, a^{4} b^{2} x^{3} + a^{5} b\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + 14 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 28 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{2916 \, {\left(a^{4} b^{7} x^{12} + 4 \, a^{5} b^{6} x^{9} + 6 \, a^{6} b^{5} x^{6} + 4 \, a^{7} b^{4} x^{3} + a^{8} b^{3}\right)}}\right]"," ",0,"[1/2916*(84*a*b^5*x^11 + 315*a^2*b^4*x^8 + 432*a^3*b^3*x^5 - 42*a^4*b^2*x^2 + 42*sqrt(1/3)*(a*b^5*x^12 + 4*a^2*b^4*x^9 + 6*a^3*b^3*x^6 + 4*a^4*b^2*x^3 + a^5*b)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*x^3 - a*b + 3*sqrt(1/3)*(a*b*x + 2*(-a*b^2)^(2/3)*x^2 + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*x)/(b*x^3 + a)) + 14*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 28*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a^4*b^7*x^12 + 4*a^5*b^6*x^9 + 6*a^6*b^5*x^6 + 4*a^7*b^4*x^3 + a^8*b^3), 1/2916*(84*a*b^5*x^11 + 315*a^2*b^4*x^8 + 432*a^3*b^3*x^5 - 42*a^4*b^2*x^2 + 84*sqrt(1/3)*(a*b^5*x^12 + 4*a^2*b^4*x^9 + 6*a^3*b^3*x^6 + 4*a^4*b^2*x^3 + a^5*b)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*x + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + 14*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 28*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a^4*b^7*x^12 + 4*a^5*b^6*x^9 + 6*a^6*b^5*x^6 + 4*a^7*b^4*x^3 + a^8*b^3)]","A",0
110,1,723,0,1.229650," ","integrate(x^3/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{60 \, a^{2} b^{4} x^{10} + 216 \, a^{3} b^{3} x^{7} + 279 \, a^{4} b^{2} x^{4} - 120 \, a^{5} b x + 60 \, \sqrt{\frac{1}{3}} {\left(a b^{5} x^{12} + 4 \, a^{2} b^{4} x^{9} + 6 \, a^{3} b^{3} x^{6} + 4 \, a^{4} b^{2} x^{3} + a^{5} b\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - 20 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 40 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{2916 \, {\left(a^{5} b^{6} x^{12} + 4 \, a^{6} b^{5} x^{9} + 6 \, a^{7} b^{4} x^{6} + 4 \, a^{8} b^{3} x^{3} + a^{9} b^{2}\right)}}, \frac{60 \, a^{2} b^{4} x^{10} + 216 \, a^{3} b^{3} x^{7} + 279 \, a^{4} b^{2} x^{4} - 120 \, a^{5} b x + 120 \, \sqrt{\frac{1}{3}} {\left(a b^{5} x^{12} + 4 \, a^{2} b^{4} x^{9} + 6 \, a^{3} b^{3} x^{6} + 4 \, a^{4} b^{2} x^{3} + a^{5} b\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - 20 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 40 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{2916 \, {\left(a^{5} b^{6} x^{12} + 4 \, a^{6} b^{5} x^{9} + 6 \, a^{7} b^{4} x^{6} + 4 \, a^{8} b^{3} x^{3} + a^{9} b^{2}\right)}}\right]"," ",0,"[1/2916*(60*a^2*b^4*x^10 + 216*a^3*b^3*x^7 + 279*a^4*b^2*x^4 - 120*a^5*b*x + 60*sqrt(1/3)*(a*b^5*x^12 + 4*a^2*b^4*x^9 + 6*a^3*b^3*x^6 + 4*a^4*b^2*x^3 + a^5*b)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) - 20*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 40*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^5*b^6*x^12 + 4*a^6*b^5*x^9 + 6*a^7*b^4*x^6 + 4*a^8*b^3*x^3 + a^9*b^2), 1/2916*(60*a^2*b^4*x^10 + 216*a^3*b^3*x^7 + 279*a^4*b^2*x^4 - 120*a^5*b*x + 120*sqrt(1/3)*(a*b^5*x^12 + 4*a^2*b^4*x^9 + 6*a^3*b^3*x^6 + 4*a^4*b^2*x^3 + a^5*b)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - 20*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 40*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^5*b^6*x^12 + 4*a^6*b^5*x^9 + 6*a^7*b^4*x^6 + 4*a^8*b^3*x^3 + a^9*b^2)]","A",0
111,1,48,0,1.147117," ","integrate(x^2/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{1}{12 \, {\left(b^{5} x^{12} + 4 \, a b^{4} x^{9} + 6 \, a^{2} b^{3} x^{6} + 4 \, a^{3} b^{2} x^{3} + a^{4} b\right)}}"," ",0,"-1/12/(b^5*x^12 + 4*a*b^4*x^9 + 6*a^2*b^3*x^6 + 4*a^3*b^2*x^3 + a^4*b)","A",0
112,1,734,0,1.270329," ","integrate(x/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{420 \, a b^{5} x^{11} + 1575 \, a^{2} b^{4} x^{8} + 2160 \, a^{3} b^{3} x^{5} + 1248 \, a^{4} b^{2} x^{2} + 210 \, \sqrt{\frac{1}{3}} {\left(a b^{5} x^{12} + 4 \, a^{2} b^{4} x^{9} + 6 \, a^{3} b^{3} x^{6} + 4 \, a^{4} b^{2} x^{3} + a^{5} b\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} + a}\right) + 70 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 140 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{2916 \, {\left(a^{5} b^{6} x^{12} + 4 \, a^{6} b^{5} x^{9} + 6 \, a^{7} b^{4} x^{6} + 4 \, a^{8} b^{3} x^{3} + a^{9} b^{2}\right)}}, \frac{420 \, a b^{5} x^{11} + 1575 \, a^{2} b^{4} x^{8} + 2160 \, a^{3} b^{3} x^{5} + 1248 \, a^{4} b^{2} x^{2} + 420 \, \sqrt{\frac{1}{3}} {\left(a b^{5} x^{12} + 4 \, a^{2} b^{4} x^{9} + 6 \, a^{3} b^{3} x^{6} + 4 \, a^{4} b^{2} x^{3} + a^{5} b\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + 70 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 140 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{2916 \, {\left(a^{5} b^{6} x^{12} + 4 \, a^{6} b^{5} x^{9} + 6 \, a^{7} b^{4} x^{6} + 4 \, a^{8} b^{3} x^{3} + a^{9} b^{2}\right)}}\right]"," ",0,"[1/2916*(420*a*b^5*x^11 + 1575*a^2*b^4*x^8 + 2160*a^3*b^3*x^5 + 1248*a^4*b^2*x^2 + 210*sqrt(1/3)*(a*b^5*x^12 + 4*a^2*b^4*x^9 + 6*a^3*b^3*x^6 + 4*a^4*b^2*x^3 + a^5*b)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*x^3 - a*b + 3*sqrt(1/3)*(a*b*x + 2*(-a*b^2)^(2/3)*x^2 + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*x)/(b*x^3 + a)) + 70*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 140*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a^5*b^6*x^12 + 4*a^6*b^5*x^9 + 6*a^7*b^4*x^6 + 4*a^8*b^3*x^3 + a^9*b^2), 1/2916*(420*a*b^5*x^11 + 1575*a^2*b^4*x^8 + 2160*a^3*b^3*x^5 + 1248*a^4*b^2*x^2 + 420*sqrt(1/3)*(a*b^5*x^12 + 4*a^2*b^4*x^9 + 6*a^3*b^3*x^6 + 4*a^4*b^2*x^3 + a^5*b)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*x + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + 70*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 140*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a^5*b^6*x^12 + 4*a^6*b^5*x^9 + 6*a^7*b^4*x^6 + 4*a^8*b^3*x^3 + a^9*b^2)]","A",0
113,1,719,0,1.242591," ","integrate(1/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{660 \, a^{2} b^{4} x^{10} + 2376 \, a^{3} b^{3} x^{7} + 3069 \, a^{4} b^{2} x^{4} + 1596 \, a^{5} b x + 660 \, \sqrt{\frac{1}{3}} {\left(a b^{5} x^{12} + 4 \, a^{2} b^{4} x^{9} + 6 \, a^{3} b^{3} x^{6} + 4 \, a^{4} b^{2} x^{3} + a^{5} b\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - 220 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 440 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{2916 \, {\left(a^{6} b^{5} x^{12} + 4 \, a^{7} b^{4} x^{9} + 6 \, a^{8} b^{3} x^{6} + 4 \, a^{9} b^{2} x^{3} + a^{10} b\right)}}, \frac{660 \, a^{2} b^{4} x^{10} + 2376 \, a^{3} b^{3} x^{7} + 3069 \, a^{4} b^{2} x^{4} + 1596 \, a^{5} b x + 1320 \, \sqrt{\frac{1}{3}} {\left(a b^{5} x^{12} + 4 \, a^{2} b^{4} x^{9} + 6 \, a^{3} b^{3} x^{6} + 4 \, a^{4} b^{2} x^{3} + a^{5} b\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - 220 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 440 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{2916 \, {\left(a^{6} b^{5} x^{12} + 4 \, a^{7} b^{4} x^{9} + 6 \, a^{8} b^{3} x^{6} + 4 \, a^{9} b^{2} x^{3} + a^{10} b\right)}}\right]"," ",0,"[1/2916*(660*a^2*b^4*x^10 + 2376*a^3*b^3*x^7 + 3069*a^4*b^2*x^4 + 1596*a^5*b*x + 660*sqrt(1/3)*(a*b^5*x^12 + 4*a^2*b^4*x^9 + 6*a^3*b^3*x^6 + 4*a^4*b^2*x^3 + a^5*b)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) - 220*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 440*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^6*b^5*x^12 + 4*a^7*b^4*x^9 + 6*a^8*b^3*x^6 + 4*a^9*b^2*x^3 + a^10*b), 1/2916*(660*a^2*b^4*x^10 + 2376*a^3*b^3*x^7 + 3069*a^4*b^2*x^4 + 1596*a^5*b*x + 1320*sqrt(1/3)*(a*b^5*x^12 + 4*a^2*b^4*x^9 + 6*a^3*b^3*x^6 + 4*a^4*b^2*x^3 + a^5*b)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - 220*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 440*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)))/(a^6*b^5*x^12 + 4*a^7*b^4*x^9 + 6*a^8*b^3*x^6 + 4*a^9*b^2*x^3 + a^10*b)]","A",0
114,1,178,0,1.022236," ","integrate(1/x/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\frac{12 \, a b^{3} x^{9} + 42 \, a^{2} b^{2} x^{6} + 52 \, a^{3} b x^{3} + 25 \, a^{4} - 12 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \log\left(b x^{3} + a\right) + 36 \, {\left(b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}\right)} \log\left(x\right)}{36 \, {\left(a^{5} b^{4} x^{12} + 4 \, a^{6} b^{3} x^{9} + 6 \, a^{7} b^{2} x^{6} + 4 \, a^{8} b x^{3} + a^{9}\right)}}"," ",0,"1/36*(12*a*b^3*x^9 + 42*a^2*b^2*x^6 + 52*a^3*b*x^3 + 25*a^4 - 12*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*log(b*x^3 + a) + 36*(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4)*log(x))/(a^5*b^4*x^12 + 4*a^6*b^3*x^9 + 6*a^7*b^2*x^6 + 4*a^8*b*x^3 + a^9)","A",0
115,1,311,0,0.965631," ","integrate(1/x^2/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{5460 \, b^{4} x^{12} + 20475 \, a b^{3} x^{9} + 28080 \, a^{2} b^{2} x^{6} + 16224 \, a^{3} b x^{3} + 2916 \, a^{4} + 1820 \, \sqrt{3} {\left(b^{4} x^{13} + 4 \, a b^{3} x^{10} + 6 \, a^{2} b^{2} x^{7} + 4 \, a^{3} b x^{4} + a^{4} x\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(\frac{b}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + 910 \, {\left(b^{4} x^{13} + 4 \, a b^{3} x^{10} + 6 \, a^{2} b^{2} x^{7} + 4 \, a^{3} b x^{4} + a^{4} x\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x^{2} - a x \left(\frac{b}{a}\right)^{\frac{2}{3}} + a \left(\frac{b}{a}\right)^{\frac{1}{3}}\right) - 1820 \, {\left(b^{4} x^{13} + 4 \, a b^{3} x^{10} + 6 \, a^{2} b^{2} x^{7} + 4 \, a^{3} b x^{4} + a^{4} x\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x + a \left(\frac{b}{a}\right)^{\frac{2}{3}}\right)}{2916 \, {\left(a^{5} b^{4} x^{13} + 4 \, a^{6} b^{3} x^{10} + 6 \, a^{7} b^{2} x^{7} + 4 \, a^{8} b x^{4} + a^{9} x\right)}}"," ",0,"-1/2916*(5460*b^4*x^12 + 20475*a*b^3*x^9 + 28080*a^2*b^2*x^6 + 16224*a^3*b*x^3 + 2916*a^4 + 1820*sqrt(3)*(b^4*x^13 + 4*a*b^3*x^10 + 6*a^2*b^2*x^7 + 4*a^3*b*x^4 + a^4*x)*(b/a)^(1/3)*arctan(2/3*sqrt(3)*x*(b/a)^(1/3) - 1/3*sqrt(3)) + 910*(b^4*x^13 + 4*a*b^3*x^10 + 6*a^2*b^2*x^7 + 4*a^3*b*x^4 + a^4*x)*(b/a)^(1/3)*log(b*x^2 - a*x*(b/a)^(2/3) + a*(b/a)^(1/3)) - 1820*(b^4*x^13 + 4*a*b^3*x^10 + 6*a^2*b^2*x^7 + 4*a^3*b*x^4 + a^4*x)*(b/a)^(1/3)*log(b*x + a*(b/a)^(2/3)))/(a^5*b^4*x^13 + 4*a^6*b^3*x^10 + 6*a^7*b^2*x^7 + 4*a^8*b*x^4 + a^9*x)","A",0
116,1,352,0,1.304181," ","integrate(1/x^3/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{4620 \, b^{4} x^{12} + 16632 \, a b^{3} x^{9} + 21483 \, a^{2} b^{2} x^{6} + 11172 \, a^{3} b x^{3} + 1458 \, a^{4} - 3080 \, \sqrt{3} {\left(b^{4} x^{14} + 4 \, a b^{3} x^{11} + 6 \, a^{2} b^{2} x^{8} + 4 \, a^{3} b x^{5} + a^{4} x^{2}\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) + 1540 \, {\left(b^{4} x^{14} + 4 \, a b^{3} x^{11} + 6 \, a^{2} b^{2} x^{8} + 4 \, a^{3} b x^{5} + a^{4} x^{2}\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} x^{2} + a b x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} + a^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right) - 3080 \, {\left(b^{4} x^{14} + 4 \, a b^{3} x^{11} + 6 \, a^{2} b^{2} x^{8} + 4 \, a^{3} b x^{5} + a^{4} x^{2}\right)} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x - a \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right)}{2916 \, {\left(a^{5} b^{4} x^{14} + 4 \, a^{6} b^{3} x^{11} + 6 \, a^{7} b^{2} x^{8} + 4 \, a^{8} b x^{5} + a^{9} x^{2}\right)}}"," ",0,"-1/2916*(4620*b^4*x^12 + 16632*a*b^3*x^9 + 21483*a^2*b^2*x^6 + 11172*a^3*b*x^3 + 1458*a^4 - 3080*sqrt(3)*(b^4*x^14 + 4*a*b^3*x^11 + 6*a^2*b^2*x^8 + 4*a^3*b*x^5 + a^4*x^2)*(-b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(-b^2/a^2)^(2/3) - sqrt(3)*b)/b) + 1540*(b^4*x^14 + 4*a*b^3*x^11 + 6*a^2*b^2*x^8 + 4*a^3*b*x^5 + a^4*x^2)*(-b^2/a^2)^(1/3)*log(b^2*x^2 + a*b*x*(-b^2/a^2)^(1/3) + a^2*(-b^2/a^2)^(2/3)) - 3080*(b^4*x^14 + 4*a*b^3*x^11 + 6*a^2*b^2*x^8 + 4*a^3*b*x^5 + a^4*x^2)*(-b^2/a^2)^(1/3)*log(b*x - a*(-b^2/a^2)^(1/3)))/(a^5*b^4*x^14 + 4*a^6*b^3*x^11 + 6*a^7*b^2*x^8 + 4*a^8*b*x^5 + a^9*x^2)","A",0
117,1,207,0,1.266649," ","integrate(1/x^4/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{60 \, a b^{4} x^{12} + 210 \, a^{2} b^{3} x^{9} + 260 \, a^{3} b^{2} x^{6} + 125 \, a^{4} b x^{3} + 12 \, a^{5} - 60 \, {\left(b^{5} x^{15} + 4 \, a b^{4} x^{12} + 6 \, a^{2} b^{3} x^{9} + 4 \, a^{3} b^{2} x^{6} + a^{4} b x^{3}\right)} \log\left(b x^{3} + a\right) + 180 \, {\left(b^{5} x^{15} + 4 \, a b^{4} x^{12} + 6 \, a^{2} b^{3} x^{9} + 4 \, a^{3} b^{2} x^{6} + a^{4} b x^{3}\right)} \log\left(x\right)}{36 \, {\left(a^{6} b^{4} x^{15} + 4 \, a^{7} b^{3} x^{12} + 6 \, a^{8} b^{2} x^{9} + 4 \, a^{9} b x^{6} + a^{10} x^{3}\right)}}"," ",0,"-1/36*(60*a*b^4*x^12 + 210*a^2*b^3*x^9 + 260*a^3*b^2*x^6 + 125*a^4*b*x^3 + 12*a^5 - 60*(b^5*x^15 + 4*a*b^4*x^12 + 6*a^2*b^3*x^9 + 4*a^3*b^2*x^6 + a^4*b*x^3)*log(b*x^3 + a) + 180*(b^5*x^15 + 4*a*b^4*x^12 + 6*a^2*b^3*x^9 + 4*a^3*b^2*x^6 + a^4*b*x^3)*log(x))/(a^6*b^4*x^15 + 4*a^7*b^3*x^12 + 6*a^8*b^2*x^9 + 4*a^9*b*x^6 + a^10*x^3)","A",0
118,1,369,0,1.906260," ","integrate((d*x)^m*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left({\left(b^{5} m^{5} + 35 \, b^{5} m^{4} + 445 \, b^{5} m^{3} + 2485 \, b^{5} m^{2} + 5714 \, b^{5} m + 3640 \, b^{5}\right)} x^{16} + 5 \, {\left(a b^{4} m^{5} + 38 \, a b^{4} m^{4} + 511 \, a b^{4} m^{3} + 2962 \, a b^{4} m^{2} + 6968 \, a b^{4} m + 4480 \, a b^{4}\right)} x^{13} + 10 \, {\left(a^{2} b^{3} m^{5} + 41 \, a^{2} b^{3} m^{4} + 595 \, a^{2} b^{3} m^{3} + 3655 \, a^{2} b^{3} m^{2} + 8924 \, a^{2} b^{3} m + 5824 \, a^{2} b^{3}\right)} x^{10} + 10 \, {\left(a^{3} b^{2} m^{5} + 44 \, a^{3} b^{2} m^{4} + 697 \, a^{3} b^{2} m^{3} + 4726 \, a^{3} b^{2} m^{2} + 12392 \, a^{3} b^{2} m + 8320 \, a^{3} b^{2}\right)} x^{7} + 5 \, {\left(a^{4} b m^{5} + 47 \, a^{4} b m^{4} + 817 \, a^{4} b m^{3} + 6337 \, a^{4} b m^{2} + 20126 \, a^{4} b m + 14560 \, a^{4} b\right)} x^{4} + {\left(a^{5} m^{5} + 50 \, a^{5} m^{4} + 955 \, a^{5} m^{3} + 8650 \, a^{5} m^{2} + 36824 \, a^{5} m + 58240 \, a^{5}\right)} x\right)} \left(d x\right)^{m}}{m^{6} + 51 \, m^{5} + 1005 \, m^{4} + 9605 \, m^{3} + 45474 \, m^{2} + 95064 \, m + 58240}"," ",0,"((b^5*m^5 + 35*b^5*m^4 + 445*b^5*m^3 + 2485*b^5*m^2 + 5714*b^5*m + 3640*b^5)*x^16 + 5*(a*b^4*m^5 + 38*a*b^4*m^4 + 511*a*b^4*m^3 + 2962*a*b^4*m^2 + 6968*a*b^4*m + 4480*a*b^4)*x^13 + 10*(a^2*b^3*m^5 + 41*a^2*b^3*m^4 + 595*a^2*b^3*m^3 + 3655*a^2*b^3*m^2 + 8924*a^2*b^3*m + 5824*a^2*b^3)*x^10 + 10*(a^3*b^2*m^5 + 44*a^3*b^2*m^4 + 697*a^3*b^2*m^3 + 4726*a^3*b^2*m^2 + 12392*a^3*b^2*m + 8320*a^3*b^2)*x^7 + 5*(a^4*b*m^5 + 47*a^4*b*m^4 + 817*a^4*b*m^3 + 6337*a^4*b*m^2 + 20126*a^4*b*m + 14560*a^4*b)*x^4 + (a^5*m^5 + 50*a^5*m^4 + 955*a^5*m^3 + 8650*a^5*m^2 + 36824*a^5*m + 58240*a^5)*x)*(d*x)^m/(m^6 + 51*m^5 + 1005*m^4 + 9605*m^3 + 45474*m^2 + 95064*m + 58240)","A",0
119,1,159,0,1.197471," ","integrate((d*x)^m*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(b^{3} m^{3} + 12 \, b^{3} m^{2} + 39 \, b^{3} m + 28 \, b^{3}\right)} x^{10} + 3 \, {\left(a b^{2} m^{3} + 15 \, a b^{2} m^{2} + 54 \, a b^{2} m + 40 \, a b^{2}\right)} x^{7} + 3 \, {\left(a^{2} b m^{3} + 18 \, a^{2} b m^{2} + 87 \, a^{2} b m + 70 \, a^{2} b\right)} x^{4} + {\left(a^{3} m^{3} + 21 \, a^{3} m^{2} + 138 \, a^{3} m + 280 \, a^{3}\right)} x\right)} \left(d x\right)^{m}}{m^{4} + 22 \, m^{3} + 159 \, m^{2} + 418 \, m + 280}"," ",0,"((b^3*m^3 + 12*b^3*m^2 + 39*b^3*m + 28*b^3)*x^10 + 3*(a*b^2*m^3 + 15*a*b^2*m^2 + 54*a*b^2*m + 40*a*b^2)*x^7 + 3*(a^2*b*m^3 + 18*a^2*b*m^2 + 87*a^2*b*m + 70*a^2*b)*x^4 + (a^3*m^3 + 21*a^3*m^2 + 138*a^3*m + 280*a^3)*x)*(d*x)^m/(m^4 + 22*m^3 + 159*m^2 + 418*m + 280)","A",0
120,1,35,0,1.276777," ","integrate((d*x)^m*(b^2*x^6+2*a*b*x^3+a^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left({\left(b m + b\right)} x^{4} + {\left(a m + 4 \, a\right)} x\right)} \left(d x\right)^{m}}{m^{2} + 5 \, m + 4}"," ",0,"((b*m + b)*x^4 + (a*m + 4*a)*x)*(d*x)^m/(m^2 + 5*m + 4)","A",0
121,0,0,0,0.785385," ","integrate((d*x)^m/(b^2*x^6+2*a*b*x^3+a^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{\sqrt{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}}, x\right)"," ",0,"integral((d*x)^m/sqrt(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
122,0,0,0,1.020714," ","integrate((d*x)^m/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}} \left(d x\right)^{m}}{b^{4} x^{12} + 4 \, a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} + 4 \, a^{3} b x^{3} + a^{4}}, x\right)"," ",0,"integral(sqrt(b^2*x^6 + 2*a*b*x^3 + a^2)*(d*x)^m/(b^4*x^12 + 4*a*b^3*x^9 + 6*a^2*b^2*x^6 + 4*a^3*b*x^3 + a^4), x)","F",0
123,0,0,0,1.189282," ","integrate((d*x)^m/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}} \left(d x\right)^{m}}{b^{6} x^{18} + 6 \, a b^{5} x^{15} + 15 \, a^{2} b^{4} x^{12} + 20 \, a^{3} b^{3} x^{9} + 15 \, a^{4} b^{2} x^{6} + 6 \, a^{5} b x^{3} + a^{6}}, x\right)"," ",0,"integral(sqrt(b^2*x^6 + 2*a*b*x^3 + a^2)*(d*x)^m/(b^6*x^18 + 6*a*b^5*x^15 + 15*a^2*b^4*x^12 + 20*a^3*b^3*x^9 + 15*a^4*b^2*x^6 + 6*a^5*b*x^3 + a^6), x)","F",0
124,0,0,0,1.196125," ","integrate((d*x)^m*(b^2*x^6+2*a*b*x^3+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} \left(d x\right)^{m}, x\right)"," ",0,"integral((b^2*x^6 + 2*a*b*x^3 + a^2)^p*(d*x)^m, x)","F",0
125,1,163,0,1.168254," ","integrate(x^11*(b^2*x^6+2*a*b*x^3+a^2)^p,x, algorithm=""fricas"")","\frac{{\left({\left(4 \, b^{4} p^{3} + 12 \, b^{4} p^{2} + 11 \, b^{4} p + 3 \, b^{4}\right)} x^{12} + 2 \, {\left(2 \, a b^{3} p^{3} + 3 \, a b^{3} p^{2} + a b^{3} p\right)} x^{9} + 6 \, a^{3} b p x^{3} - 3 \, {\left(2 \, a^{2} b^{2} p^{2} + a^{2} b^{2} p\right)} x^{6} - 3 \, a^{4}\right)} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p}}{6 \, {\left(4 \, b^{4} p^{4} + 20 \, b^{4} p^{3} + 35 \, b^{4} p^{2} + 25 \, b^{4} p + 6 \, b^{4}\right)}}"," ",0,"1/6*((4*b^4*p^3 + 12*b^4*p^2 + 11*b^4*p + 3*b^4)*x^12 + 2*(2*a*b^3*p^3 + 3*a*b^3*p^2 + a*b^3*p)*x^9 + 6*a^3*b*p*x^3 - 3*(2*a^2*b^2*p^2 + a^2*b^2*p)*x^6 - 3*a^4)*(b^2*x^6 + 2*a*b*x^3 + a^2)^p/(4*b^4*p^4 + 20*b^4*p^3 + 35*b^4*p^2 + 25*b^4*p + 6*b^4)","A",0
126,1,108,0,1.129496," ","integrate(x^8*(b^2*x^6+2*a*b*x^3+a^2)^p,x, algorithm=""fricas"")","\frac{{\left({\left(2 \, b^{3} p^{2} + 3 \, b^{3} p + b^{3}\right)} x^{9} - 2 \, a^{2} b p x^{3} + {\left(2 \, a b^{2} p^{2} + a b^{2} p\right)} x^{6} + a^{3}\right)} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p}}{3 \, {\left(4 \, b^{3} p^{3} + 12 \, b^{3} p^{2} + 11 \, b^{3} p + 3 \, b^{3}\right)}}"," ",0,"1/3*((2*b^3*p^2 + 3*b^3*p + b^3)*x^9 - 2*a^2*b*p*x^3 + (2*a*b^2*p^2 + a*b^2*p)*x^6 + a^3)*(b^2*x^6 + 2*a*b*x^3 + a^2)^p/(4*b^3*p^3 + 12*b^3*p^2 + 11*b^3*p + 3*b^3)","A",0
127,1,70,0,1.116408," ","integrate(x^5*(b^2*x^6+2*a*b*x^3+a^2)^p,x, algorithm=""fricas"")","\frac{{\left({\left(2 \, b^{2} p + b^{2}\right)} x^{6} + 2 \, a b p x^{3} - a^{2}\right)} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p}}{6 \, {\left(2 \, b^{2} p^{2} + 3 \, b^{2} p + b^{2}\right)}}"," ",0,"1/6*((2*b^2*p + b^2)*x^6 + 2*a*b*p*x^3 - a^2)*(b^2*x^6 + 2*a*b*x^3 + a^2)^p/(2*b^2*p^2 + 3*b^2*p + b^2)","A",0
128,0,0,0,1.134917," ","integrate(x^4*(b^2*x^6+2*a*b*x^3+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} x^{4}, x\right)"," ",0,"integral((b^2*x^6 + 2*a*b*x^3 + a^2)^p*x^4, x)","F",0
129,0,0,0,1.179797," ","integrate(x^3*(b^2*x^6+2*a*b*x^3+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} x^{3}, x\right)"," ",0,"integral((b^2*x^6 + 2*a*b*x^3 + a^2)^p*x^3, x)","F",0
130,1,37,0,1.389402," ","integrate(x^2*(b^2*x^6+2*a*b*x^3+a^2)^p,x, algorithm=""fricas"")","\frac{{\left(b x^{3} + a\right)} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p}}{3 \, {\left(2 \, b p + b\right)}}"," ",0,"1/3*(b*x^3 + a)*(b^2*x^6 + 2*a*b*x^3 + a^2)^p/(2*b*p + b)","A",0
131,0,0,0,1.280990," ","integrate(x*(b^2*x^6+2*a*b*x^3+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p} x, x\right)"," ",0,"integral((b^2*x^6 + 2*a*b*x^3 + a^2)^p*x, x)","F",0
132,0,0,0,1.506175," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p}, x\right)"," ",0,"integral((b^2*x^6 + 2*a*b*x^3 + a^2)^p, x)","F",0
133,0,0,0,1.735288," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p}}{x}, x\right)"," ",0,"integral((b^2*x^6 + 2*a*b*x^3 + a^2)^p/x, x)","F",0
134,0,0,0,1.522660," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((b^2*x^6 + 2*a*b*x^3 + a^2)^p/x^2, x)","F",0
135,0,0,0,1.172984," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^p/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p}}{x^{3}}, x\right)"," ",0,"integral((b^2*x^6 + 2*a*b*x^3 + a^2)^p/x^3, x)","F",0
136,0,0,0,1.685909," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^p/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p}}{x^{4}}, x\right)"," ",0,"integral((b^2*x^6 + 2*a*b*x^3 + a^2)^p/x^4, x)","F",0
137,0,0,0,1.222479," ","integrate((b^2*x^6+2*a*b*x^3+a^2)^p/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}^{p}}{x^{5}}, x\right)"," ",0,"integral((b^2*x^6 + 2*a*b*x^3 + a^2)^p/x^5, x)","F",0
138,1,254,0,1.289744," ","integrate(x^8/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x^{3} - {\left(b^{2} - 2 \, a c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{6} + 2 \, b c x^{3} + b^{2} - 2 \, a c + {\left(2 \, c x^{3} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{6} + b x^{3} + a}\right) - {\left(b^{3} - 4 \, a b c\right)} \log\left(c x^{6} + b x^{3} + a\right)}{6 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}, \frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x^{3} - 2 \, {\left(b^{2} - 2 \, a c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{3} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left(b^{3} - 4 \, a b c\right)} \log\left(c x^{6} + b x^{3} + a\right)}{6 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}\right]"," ",0,"[1/6*(2*(b^2*c - 4*a*c^2)*x^3 - (b^2 - 2*a*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^6 + 2*b*c*x^3 + b^2 - 2*a*c + (2*c*x^3 + b)*sqrt(b^2 - 4*a*c))/(c*x^6 + b*x^3 + a)) - (b^3 - 4*a*b*c)*log(c*x^6 + b*x^3 + a))/(b^2*c^2 - 4*a*c^3), 1/6*(2*(b^2*c - 4*a*c^2)*x^3 - 2*(b^2 - 2*a*c)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^3 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - (b^3 - 4*a*b*c)*log(c*x^6 + b*x^3 + a))/(b^2*c^2 - 4*a*c^3)]","A",0
139,1,197,0,0.832803," ","integrate(x^5/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} - 4 \, a c} b \log\left(\frac{2 \, c^{2} x^{6} + 2 \, b c x^{3} + b^{2} - 2 \, a c + {\left(2 \, c x^{3} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{6} + b x^{3} + a}\right) + {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{6} + b x^{3} + a\right)}{6 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}, \frac{2 \, \sqrt{-b^{2} + 4 \, a c} b \arctan\left(-\frac{{\left(2 \, c x^{3} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) + {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{6} + b x^{3} + a\right)}{6 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\right]"," ",0,"[1/6*(sqrt(b^2 - 4*a*c)*b*log((2*c^2*x^6 + 2*b*c*x^3 + b^2 - 2*a*c + (2*c*x^3 + b)*sqrt(b^2 - 4*a*c))/(c*x^6 + b*x^3 + a)) + (b^2 - 4*a*c)*log(c*x^6 + b*x^3 + a))/(b^2*c - 4*a*c^2), 1/6*(2*sqrt(-b^2 + 4*a*c)*b*arctan(-(2*c*x^3 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) + (b^2 - 4*a*c)*log(c*x^6 + b*x^3 + a))/(b^2*c - 4*a*c^2)]","A",0
140,1,129,0,1.309067," ","integrate(x^2/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{2 \, c^{2} x^{6} + 2 \, b c x^{3} + b^{2} - 2 \, a c - {\left(2 \, c x^{3} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{6} + b x^{3} + a}\right)}{3 \, \sqrt{b^{2} - 4 \, a c}}, -\frac{2 \, \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{3} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right)}{3 \, {\left(b^{2} - 4 \, a c\right)}}\right]"," ",0,"[1/3*log((2*c^2*x^6 + 2*b*c*x^3 + b^2 - 2*a*c - (2*c*x^3 + b)*sqrt(b^2 - 4*a*c))/(c*x^6 + b*x^3 + a))/sqrt(b^2 - 4*a*c), -2/3*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^3 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c))/(b^2 - 4*a*c)]","A",0
141,1,223,0,1.407374," ","integrate(1/x/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} - 4 \, a c} b \log\left(\frac{2 \, c^{2} x^{6} + 2 \, b c x^{3} + b^{2} - 2 \, a c + {\left(2 \, c x^{3} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{6} + b x^{3} + a}\right) - {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{6} + b x^{3} + a\right) + 6 \, {\left(b^{2} - 4 \, a c\right)} \log\left(x\right)}{6 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}, \frac{2 \, \sqrt{-b^{2} + 4 \, a c} b \arctan\left(-\frac{{\left(2 \, c x^{3} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{6} + b x^{3} + a\right) + 6 \, {\left(b^{2} - 4 \, a c\right)} \log\left(x\right)}{6 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}\right]"," ",0,"[1/6*(sqrt(b^2 - 4*a*c)*b*log((2*c^2*x^6 + 2*b*c*x^3 + b^2 - 2*a*c + (2*c*x^3 + b)*sqrt(b^2 - 4*a*c))/(c*x^6 + b*x^3 + a)) - (b^2 - 4*a*c)*log(c*x^6 + b*x^3 + a) + 6*(b^2 - 4*a*c)*log(x))/(a*b^2 - 4*a^2*c), 1/6*(2*sqrt(-b^2 + 4*a*c)*b*arctan(-(2*c*x^3 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - (b^2 - 4*a*c)*log(c*x^6 + b*x^3 + a) + 6*(b^2 - 4*a*c)*log(x))/(a*b^2 - 4*a^2*c)]","A",0
142,1,293,0,1.381606," ","integrate(1/x^4/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 2 \, a c\right)} \sqrt{b^{2} - 4 \, a c} x^{3} \log\left(\frac{2 \, c^{2} x^{6} + 2 \, b c x^{3} + b^{2} - 2 \, a c + {\left(2 \, c x^{3} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{6} + b x^{3} + a}\right) - {\left(b^{3} - 4 \, a b c\right)} x^{3} \log\left(c x^{6} + b x^{3} + a\right) + 6 \, {\left(b^{3} - 4 \, a b c\right)} x^{3} \log\left(x\right) + 2 \, a b^{2} - 8 \, a^{2} c}{6 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x^{3}}, -\frac{2 \, {\left(b^{2} - 2 \, a c\right)} \sqrt{-b^{2} + 4 \, a c} x^{3} \arctan\left(-\frac{{\left(2 \, c x^{3} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left(b^{3} - 4 \, a b c\right)} x^{3} \log\left(c x^{6} + b x^{3} + a\right) + 6 \, {\left(b^{3} - 4 \, a b c\right)} x^{3} \log\left(x\right) + 2 \, a b^{2} - 8 \, a^{2} c}{6 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x^{3}}\right]"," ",0,"[-1/6*((b^2 - 2*a*c)*sqrt(b^2 - 4*a*c)*x^3*log((2*c^2*x^6 + 2*b*c*x^3 + b^2 - 2*a*c + (2*c*x^3 + b)*sqrt(b^2 - 4*a*c))/(c*x^6 + b*x^3 + a)) - (b^3 - 4*a*b*c)*x^3*log(c*x^6 + b*x^3 + a) + 6*(b^3 - 4*a*b*c)*x^3*log(x) + 2*a*b^2 - 8*a^2*c)/((a^2*b^2 - 4*a^3*c)*x^3), -1/6*(2*(b^2 - 2*a*c)*sqrt(-b^2 + 4*a*c)*x^3*arctan(-(2*c*x^3 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - (b^3 - 4*a*b*c)*x^3*log(c*x^6 + b*x^3 + a) + 6*(b^3 - 4*a*b*c)*x^3*log(x) + 2*a*b^2 - 8*a^2*c)/((a^2*b^2 - 4*a^3*c)*x^3)]","A",0
143,1,5601,0,4.091895," ","integrate(x^7/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} c \left(\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{2} c^{5} - 4 \, a c^{6}}\right)^{\frac{1}{3}} \arctan\left(-\frac{\left(\frac{1}{2}\right)^{\frac{5}{6}} {\left(\sqrt{3} {\left(b^{6} c^{5} - 10 \, a b^{4} c^{6} + 32 \, a^{2} b^{2} c^{7} - 32 \, a^{3} c^{8}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}} - \sqrt{3} {\left(b^{8} - 9 \, a b^{6} c + 25 \, a^{2} b^{4} c^{2} - 20 \, a^{3} b^{2} c^{3}\right)}\right)} \left(\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{2} c^{5} - 4 \, a c^{6}}\right)^{\frac{1}{3}} \sqrt{\frac{2 \, {\left(a^{3} b^{5} - 5 \, a^{4} b^{3} c + 5 \, a^{5} b c^{2}\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(b^{8} c^{5} - 13 \, a b^{6} c^{6} + 60 \, a^{2} b^{4} c^{7} - 112 \, a^{3} b^{2} c^{8} + 64 \, a^{4} c^{9}\right)} x \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}} - {\left(b^{10} - 12 \, a b^{8} c + 52 \, a^{2} b^{6} c^{2} - 95 \, a^{3} b^{4} c^{3} + 60 \, a^{4} b^{2} c^{4}\right)} x\right)} \left(\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{2} c^{5} - 4 \, a c^{6}}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(a^{2} b^{7} - 9 \, a^{3} b^{5} c + 25 \, a^{4} b^{3} c^{2} - 20 \, a^{5} b c^{3} - {\left(a^{2} b^{5} c^{5} - 8 \, a^{3} b^{3} c^{6} + 16 \, a^{4} b c^{7}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \left(\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{2} c^{5} - 4 \, a c^{6}}\right)^{\frac{1}{3}}}{a^{3} b^{5} - 5 \, a^{4} b^{3} c + 5 \, a^{5} b c^{2}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\sqrt{3} {\left(b^{6} c^{5} - 10 \, a b^{4} c^{6} + 32 \, a^{2} b^{2} c^{7} - 32 \, a^{3} c^{8}\right)} x \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}} - \sqrt{3} {\left(b^{8} - 9 \, a b^{6} c + 25 \, a^{2} b^{4} c^{2} - 20 \, a^{3} b^{2} c^{3}\right)} x\right)} \left(\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{2} c^{5} - 4 \, a c^{6}}\right)^{\frac{1}{3}} + \sqrt{3} {\left(a^{2} b^{5} - 5 \, a^{3} b^{3} c + 5 \, a^{4} b c^{2}\right)}}{3 \, {\left(a^{2} b^{5} - 5 \, a^{3} b^{3} c + 5 \, a^{4} b c^{2}\right)}}\right) - 4 \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} c \left(\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{2} c^{5} - 4 \, a c^{6}}\right)^{\frac{1}{3}} \arctan\left(-\frac{\left(\frac{1}{2}\right)^{\frac{5}{6}} {\left(\sqrt{3} {\left(b^{6} c^{5} - 10 \, a b^{4} c^{6} + 32 \, a^{2} b^{2} c^{7} - 32 \, a^{3} c^{8}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}} + \sqrt{3} {\left(b^{8} - 9 \, a b^{6} c + 25 \, a^{2} b^{4} c^{2} - 20 \, a^{3} b^{2} c^{3}\right)}\right)} \left(\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{2} c^{5} - 4 \, a c^{6}}\right)^{\frac{1}{3}} \sqrt{\frac{2 \, {\left(a^{3} b^{5} - 5 \, a^{4} b^{3} c + 5 \, a^{5} b c^{2}\right)} x^{2} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(b^{8} c^{5} - 13 \, a b^{6} c^{6} + 60 \, a^{2} b^{4} c^{7} - 112 \, a^{3} b^{2} c^{8} + 64 \, a^{4} c^{9}\right)} x \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}} + {\left(b^{10} - 12 \, a b^{8} c + 52 \, a^{2} b^{6} c^{2} - 95 \, a^{3} b^{4} c^{3} + 60 \, a^{4} b^{2} c^{4}\right)} x\right)} \left(\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{2} c^{5} - 4 \, a c^{6}}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(a^{2} b^{7} - 9 \, a^{3} b^{5} c + 25 \, a^{4} b^{3} c^{2} - 20 \, a^{5} b c^{3} + {\left(a^{2} b^{5} c^{5} - 8 \, a^{3} b^{3} c^{6} + 16 \, a^{4} b c^{7}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \left(\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{2} c^{5} - 4 \, a c^{6}}\right)^{\frac{1}{3}}}{a^{3} b^{5} - 5 \, a^{4} b^{3} c + 5 \, a^{5} b c^{2}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\sqrt{3} {\left(b^{6} c^{5} - 10 \, a b^{4} c^{6} + 32 \, a^{2} b^{2} c^{7} - 32 \, a^{3} c^{8}\right)} x \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}} + \sqrt{3} {\left(b^{8} - 9 \, a b^{6} c + 25 \, a^{2} b^{4} c^{2} - 20 \, a^{3} b^{2} c^{3}\right)} x\right)} \left(\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{2} c^{5} - 4 \, a c^{6}}\right)^{\frac{1}{3}} - \sqrt{3} {\left(a^{2} b^{5} - 5 \, a^{3} b^{3} c + 5 \, a^{4} b c^{2}\right)}}{3 \, {\left(a^{2} b^{5} - 5 \, a^{3} b^{3} c + 5 \, a^{4} b c^{2}\right)}}\right) + \left(\frac{1}{2}\right)^{\frac{1}{3}} c \left(\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{2} c^{5} - 4 \, a c^{6}}\right)^{\frac{1}{3}} \log\left(2 \, {\left(a^{3} b^{5} - 5 \, a^{4} b^{3} c + 5 \, a^{5} b c^{2}\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(b^{8} c^{5} - 13 \, a b^{6} c^{6} + 60 \, a^{2} b^{4} c^{7} - 112 \, a^{3} b^{2} c^{8} + 64 \, a^{4} c^{9}\right)} x \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}} - {\left(b^{10} - 12 \, a b^{8} c + 52 \, a^{2} b^{6} c^{2} - 95 \, a^{3} b^{4} c^{3} + 60 \, a^{4} b^{2} c^{4}\right)} x\right)} \left(\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{2} c^{5} - 4 \, a c^{6}}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(a^{2} b^{7} - 9 \, a^{3} b^{5} c + 25 \, a^{4} b^{3} c^{2} - 20 \, a^{5} b c^{3} - {\left(a^{2} b^{5} c^{5} - 8 \, a^{3} b^{3} c^{6} + 16 \, a^{4} b c^{7}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \left(\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{2} c^{5} - 4 \, a c^{6}}\right)^{\frac{1}{3}}\right) + \left(\frac{1}{2}\right)^{\frac{1}{3}} c \left(\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{2} c^{5} - 4 \, a c^{6}}\right)^{\frac{1}{3}} \log\left(2 \, {\left(a^{3} b^{5} - 5 \, a^{4} b^{3} c + 5 \, a^{5} b c^{2}\right)} x^{2} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(b^{8} c^{5} - 13 \, a b^{6} c^{6} + 60 \, a^{2} b^{4} c^{7} - 112 \, a^{3} b^{2} c^{8} + 64 \, a^{4} c^{9}\right)} x \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}} + {\left(b^{10} - 12 \, a b^{8} c + 52 \, a^{2} b^{6} c^{2} - 95 \, a^{3} b^{4} c^{3} + 60 \, a^{4} b^{2} c^{4}\right)} x\right)} \left(\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{2} c^{5} - 4 \, a c^{6}}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(a^{2} b^{7} - 9 \, a^{3} b^{5} c + 25 \, a^{4} b^{3} c^{2} - 20 \, a^{5} b c^{3} + {\left(a^{2} b^{5} c^{5} - 8 \, a^{3} b^{3} c^{6} + 16 \, a^{4} b c^{7}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \left(\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{2} c^{5} - 4 \, a c^{6}}\right)^{\frac{1}{3}}\right) - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} c \left(\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{2} c^{5} - 4 \, a c^{6}}\right)^{\frac{1}{3}} \log\left(\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{10} - 12 \, a b^{8} c + 52 \, a^{2} b^{6} c^{2} - 95 \, a^{3} b^{4} c^{3} + 60 \, a^{4} b^{2} c^{4} - {\left(b^{8} c^{5} - 13 \, a b^{6} c^{6} + 60 \, a^{2} b^{4} c^{7} - 112 \, a^{3} b^{2} c^{8} + 64 \, a^{4} c^{9}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \left(\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{2} c^{5} - 4 \, a c^{6}}\right)^{\frac{2}{3}} + 2 \, {\left(a^{3} b^{5} - 5 \, a^{4} b^{3} c + 5 \, a^{5} b c^{2}\right)} x\right) - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} c \left(\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{2} c^{5} - 4 \, a c^{6}}\right)^{\frac{1}{3}} \log\left(\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{10} - 12 \, a b^{8} c + 52 \, a^{2} b^{6} c^{2} - 95 \, a^{3} b^{4} c^{3} + 60 \, a^{4} b^{2} c^{4} + {\left(b^{8} c^{5} - 13 \, a b^{6} c^{6} + 60 \, a^{2} b^{4} c^{7} - 112 \, a^{3} b^{2} c^{8} + 64 \, a^{4} c^{9}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \left(\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{2} c^{5} - 4 \, a c^{6}}\right)^{\frac{2}{3}} + 2 \, {\left(a^{3} b^{5} - 5 \, a^{4} b^{3} c + 5 \, a^{5} b c^{2}\right)} x\right) - 3 \, x^{2}}{6 \, c}"," ",0,"-1/6*(4*sqrt(3)*(1/2)^(1/3)*c*((b^4 - 3*a*b^2*c + a^2*c^2 + (b^2*c^5 - 4*a*c^6)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^2*c^5 - 4*a*c^6))^(1/3)*arctan(-1/3*((1/2)^(5/6)*(sqrt(3)*(b^6*c^5 - 10*a*b^4*c^6 + 32*a^2*b^2*c^7 - 32*a^3*c^8)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)) - sqrt(3)*(b^8 - 9*a*b^6*c + 25*a^2*b^4*c^2 - 20*a^3*b^2*c^3))*((b^4 - 3*a*b^2*c + a^2*c^2 + (b^2*c^5 - 4*a*c^6)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^2*c^5 - 4*a*c^6))^(1/3)*sqrt((2*(a^3*b^5 - 5*a^4*b^3*c + 5*a^5*b*c^2)*x^2 + (1/2)^(2/3)*((b^8*c^5 - 13*a*b^6*c^6 + 60*a^2*b^4*c^7 - 112*a^3*b^2*c^8 + 64*a^4*c^9)*x*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)) - (b^10 - 12*a*b^8*c + 52*a^2*b^6*c^2 - 95*a^3*b^4*c^3 + 60*a^4*b^2*c^4)*x)*((b^4 - 3*a*b^2*c + a^2*c^2 + (b^2*c^5 - 4*a*c^6)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^2*c^5 - 4*a*c^6))^(2/3) - (1/2)^(1/3)*(a^2*b^7 - 9*a^3*b^5*c + 25*a^4*b^3*c^2 - 20*a^5*b*c^3 - (a^2*b^5*c^5 - 8*a^3*b^3*c^6 + 16*a^4*b*c^7)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*((b^4 - 3*a*b^2*c + a^2*c^2 + (b^2*c^5 - 4*a*c^6)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^2*c^5 - 4*a*c^6))^(1/3))/(a^3*b^5 - 5*a^4*b^3*c + 5*a^5*b*c^2)) - (1/2)^(1/3)*(sqrt(3)*(b^6*c^5 - 10*a*b^4*c^6 + 32*a^2*b^2*c^7 - 32*a^3*c^8)*x*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)) - sqrt(3)*(b^8 - 9*a*b^6*c + 25*a^2*b^4*c^2 - 20*a^3*b^2*c^3)*x)*((b^4 - 3*a*b^2*c + a^2*c^2 + (b^2*c^5 - 4*a*c^6)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^2*c^5 - 4*a*c^6))^(1/3) + sqrt(3)*(a^2*b^5 - 5*a^3*b^3*c + 5*a^4*b*c^2))/(a^2*b^5 - 5*a^3*b^3*c + 5*a^4*b*c^2)) - 4*sqrt(3)*(1/2)^(1/3)*c*((b^4 - 3*a*b^2*c + a^2*c^2 - (b^2*c^5 - 4*a*c^6)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^2*c^5 - 4*a*c^6))^(1/3)*arctan(-1/3*((1/2)^(5/6)*(sqrt(3)*(b^6*c^5 - 10*a*b^4*c^6 + 32*a^2*b^2*c^7 - 32*a^3*c^8)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)) + sqrt(3)*(b^8 - 9*a*b^6*c + 25*a^2*b^4*c^2 - 20*a^3*b^2*c^3))*((b^4 - 3*a*b^2*c + a^2*c^2 - (b^2*c^5 - 4*a*c^6)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^2*c^5 - 4*a*c^6))^(1/3)*sqrt((2*(a^3*b^5 - 5*a^4*b^3*c + 5*a^5*b*c^2)*x^2 - (1/2)^(2/3)*((b^8*c^5 - 13*a*b^6*c^6 + 60*a^2*b^4*c^7 - 112*a^3*b^2*c^8 + 64*a^4*c^9)*x*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)) + (b^10 - 12*a*b^8*c + 52*a^2*b^6*c^2 - 95*a^3*b^4*c^3 + 60*a^4*b^2*c^4)*x)*((b^4 - 3*a*b^2*c + a^2*c^2 - (b^2*c^5 - 4*a*c^6)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^2*c^5 - 4*a*c^6))^(2/3) - (1/2)^(1/3)*(a^2*b^7 - 9*a^3*b^5*c + 25*a^4*b^3*c^2 - 20*a^5*b*c^3 + (a^2*b^5*c^5 - 8*a^3*b^3*c^6 + 16*a^4*b*c^7)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*((b^4 - 3*a*b^2*c + a^2*c^2 - (b^2*c^5 - 4*a*c^6)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^2*c^5 - 4*a*c^6))^(1/3))/(a^3*b^5 - 5*a^4*b^3*c + 5*a^5*b*c^2)) - (1/2)^(1/3)*(sqrt(3)*(b^6*c^5 - 10*a*b^4*c^6 + 32*a^2*b^2*c^7 - 32*a^3*c^8)*x*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)) + sqrt(3)*(b^8 - 9*a*b^6*c + 25*a^2*b^4*c^2 - 20*a^3*b^2*c^3)*x)*((b^4 - 3*a*b^2*c + a^2*c^2 - (b^2*c^5 - 4*a*c^6)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^2*c^5 - 4*a*c^6))^(1/3) - sqrt(3)*(a^2*b^5 - 5*a^3*b^3*c + 5*a^4*b*c^2))/(a^2*b^5 - 5*a^3*b^3*c + 5*a^4*b*c^2)) + (1/2)^(1/3)*c*((b^4 - 3*a*b^2*c + a^2*c^2 + (b^2*c^5 - 4*a*c^6)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^2*c^5 - 4*a*c^6))^(1/3)*log(2*(a^3*b^5 - 5*a^4*b^3*c + 5*a^5*b*c^2)*x^2 + (1/2)^(2/3)*((b^8*c^5 - 13*a*b^6*c^6 + 60*a^2*b^4*c^7 - 112*a^3*b^2*c^8 + 64*a^4*c^9)*x*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)) - (b^10 - 12*a*b^8*c + 52*a^2*b^6*c^2 - 95*a^3*b^4*c^3 + 60*a^4*b^2*c^4)*x)*((b^4 - 3*a*b^2*c + a^2*c^2 + (b^2*c^5 - 4*a*c^6)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^2*c^5 - 4*a*c^6))^(2/3) - (1/2)^(1/3)*(a^2*b^7 - 9*a^3*b^5*c + 25*a^4*b^3*c^2 - 20*a^5*b*c^3 - (a^2*b^5*c^5 - 8*a^3*b^3*c^6 + 16*a^4*b*c^7)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*((b^4 - 3*a*b^2*c + a^2*c^2 + (b^2*c^5 - 4*a*c^6)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^2*c^5 - 4*a*c^6))^(1/3)) + (1/2)^(1/3)*c*((b^4 - 3*a*b^2*c + a^2*c^2 - (b^2*c^5 - 4*a*c^6)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^2*c^5 - 4*a*c^6))^(1/3)*log(2*(a^3*b^5 - 5*a^4*b^3*c + 5*a^5*b*c^2)*x^2 - (1/2)^(2/3)*((b^8*c^5 - 13*a*b^6*c^6 + 60*a^2*b^4*c^7 - 112*a^3*b^2*c^8 + 64*a^4*c^9)*x*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)) + (b^10 - 12*a*b^8*c + 52*a^2*b^6*c^2 - 95*a^3*b^4*c^3 + 60*a^4*b^2*c^4)*x)*((b^4 - 3*a*b^2*c + a^2*c^2 - (b^2*c^5 - 4*a*c^6)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^2*c^5 - 4*a*c^6))^(2/3) - (1/2)^(1/3)*(a^2*b^7 - 9*a^3*b^5*c + 25*a^4*b^3*c^2 - 20*a^5*b*c^3 + (a^2*b^5*c^5 - 8*a^3*b^3*c^6 + 16*a^4*b*c^7)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*((b^4 - 3*a*b^2*c + a^2*c^2 - (b^2*c^5 - 4*a*c^6)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^2*c^5 - 4*a*c^6))^(1/3)) - 2*(1/2)^(1/3)*c*((b^4 - 3*a*b^2*c + a^2*c^2 + (b^2*c^5 - 4*a*c^6)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^2*c^5 - 4*a*c^6))^(1/3)*log((1/2)^(2/3)*(b^10 - 12*a*b^8*c + 52*a^2*b^6*c^2 - 95*a^3*b^4*c^3 + 60*a^4*b^2*c^4 - (b^8*c^5 - 13*a*b^6*c^6 + 60*a^2*b^4*c^7 - 112*a^3*b^2*c^8 + 64*a^4*c^9)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*((b^4 - 3*a*b^2*c + a^2*c^2 + (b^2*c^5 - 4*a*c^6)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^2*c^5 - 4*a*c^6))^(2/3) + 2*(a^3*b^5 - 5*a^4*b^3*c + 5*a^5*b*c^2)*x) - 2*(1/2)^(1/3)*c*((b^4 - 3*a*b^2*c + a^2*c^2 - (b^2*c^5 - 4*a*c^6)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^2*c^5 - 4*a*c^6))^(1/3)*log((1/2)^(2/3)*(b^10 - 12*a*b^8*c + 52*a^2*b^6*c^2 - 95*a^3*b^4*c^3 + 60*a^4*b^2*c^4 + (b^8*c^5 - 13*a*b^6*c^6 + 60*a^2*b^4*c^7 - 112*a^3*b^2*c^8 + 64*a^4*c^9)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*((b^4 - 3*a*b^2*c + a^2*c^2 - (b^2*c^5 - 4*a*c^6)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^2*c^5 - 4*a*c^6))^(2/3) + 2*(a^3*b^5 - 5*a^4*b^3*c + 5*a^5*b*c^2)*x) - 3*x^2)/c","B",0
144,1,5260,0,3.184810," ","integrate(x^6/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} c \left(-\frac{b^{3} - 2 \, a b c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left(b^{8} c^{4} - 13 \, a b^{6} c^{5} + 60 \, a^{2} b^{4} c^{6} - 112 \, a^{3} b^{2} c^{7} + 64 \, a^{4} c^{8}\right)} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}} - \sqrt{3} {\left(b^{9} - 11 \, a b^{7} c + 42 \, a^{2} b^{5} c^{2} - 62 \, a^{3} b^{3} c^{3} + 24 \, a^{4} b c^{4}\right)} x\right)} \left(-\frac{b^{3} - 2 \, a b c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{6}} {\left(\sqrt{3} {\left(b^{8} c^{4} - 13 \, a b^{6} c^{5} + 60 \, a^{2} b^{4} c^{6} - 112 \, a^{3} b^{2} c^{7} + 64 \, a^{4} c^{8}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}} - \sqrt{3} {\left(b^{9} - 11 \, a b^{7} c + 42 \, a^{2} b^{5} c^{2} - 62 \, a^{3} b^{3} c^{3} + 24 \, a^{4} b c^{4}\right)}\right)} \left(-\frac{b^{3} - 2 \, a b c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{2}{3}} \sqrt{\frac{2 \, {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 2 \, a^{4} c^{2}\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{8} - 10 \, a b^{6} c + 34 \, a^{2} b^{4} c^{2} - 44 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} - {\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)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}\right)} \left(-\frac{b^{3} - 2 \, a b c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{2}{3}} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 16 \, a^{3} b c^{6}\right)} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}} - {\left(a b^{6} - 8 \, a^{2} b^{4} c + 18 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} x\right)} \left(-\frac{b^{3} - 2 \, a b c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}}}{a^{2} b^{4} - 4 \, a^{3} b^{2} c + 2 \, a^{4} c^{2}}} + 2 \, \sqrt{3} {\left(a^{3} b^{4} - 4 \, a^{4} b^{2} c + 2 \, a^{5} c^{2}\right)}}{6 \, {\left(a^{3} b^{4} - 4 \, a^{4} b^{2} c + 2 \, a^{5} c^{2}\right)}}\right) - 4 \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} c \left(-\frac{b^{3} - 2 \, a b c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left(b^{8} c^{4} - 13 \, a b^{6} c^{5} + 60 \, a^{2} b^{4} c^{6} - 112 \, a^{3} b^{2} c^{7} + 64 \, a^{4} c^{8}\right)} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}} + \sqrt{3} {\left(b^{9} - 11 \, a b^{7} c + 42 \, a^{2} b^{5} c^{2} - 62 \, a^{3} b^{3} c^{3} + 24 \, a^{4} b c^{4}\right)} x\right)} \left(-\frac{b^{3} - 2 \, a b c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{6}} {\left(\sqrt{3} {\left(b^{8} c^{4} - 13 \, a b^{6} c^{5} + 60 \, a^{2} b^{4} c^{6} - 112 \, a^{3} b^{2} c^{7} + 64 \, a^{4} c^{8}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}} + \sqrt{3} {\left(b^{9} - 11 \, a b^{7} c + 42 \, a^{2} b^{5} c^{2} - 62 \, a^{3} b^{3} c^{3} + 24 \, a^{4} b c^{4}\right)}\right)} \left(-\frac{b^{3} - 2 \, a b c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{2}{3}} \sqrt{\frac{2 \, {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 2 \, a^{4} c^{2}\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{8} - 10 \, a b^{6} c + 34 \, a^{2} b^{4} c^{2} - 44 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + {\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)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}\right)} \left(-\frac{b^{3} - 2 \, a b c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 16 \, a^{3} b c^{6}\right)} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}} + {\left(a b^{6} - 8 \, a^{2} b^{4} c + 18 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} x\right)} \left(-\frac{b^{3} - 2 \, a b c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}}}{a^{2} b^{4} - 4 \, a^{3} b^{2} c + 2 \, a^{4} c^{2}}} - 2 \, \sqrt{3} {\left(a^{3} b^{4} - 4 \, a^{4} b^{2} c + 2 \, a^{5} c^{2}\right)}}{6 \, {\left(a^{3} b^{4} - 4 \, a^{4} b^{2} c + 2 \, a^{5} c^{2}\right)}}\right) - \left(\frac{1}{2}\right)^{\frac{1}{3}} c \left(-\frac{b^{3} - 2 \, a b c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}} \log\left(2 \, {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 2 \, a^{4} c^{2}\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{8} - 10 \, a b^{6} c + 34 \, a^{2} b^{4} c^{2} - 44 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} - {\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)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}\right)} \left(-\frac{b^{3} - 2 \, a b c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{2}{3}} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 16 \, a^{3} b c^{6}\right)} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}} - {\left(a b^{6} - 8 \, a^{2} b^{4} c + 18 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} x\right)} \left(-\frac{b^{3} - 2 \, a b c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}}\right) - \left(\frac{1}{2}\right)^{\frac{1}{3}} c \left(-\frac{b^{3} - 2 \, a b c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}} \log\left(2 \, {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 2 \, a^{4} c^{2}\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{8} - 10 \, a b^{6} c + 34 \, a^{2} b^{4} c^{2} - 44 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + {\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)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}\right)} \left(-\frac{b^{3} - 2 \, a b c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 16 \, a^{3} b c^{6}\right)} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}} + {\left(a b^{6} - 8 \, a^{2} b^{4} c + 18 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} x\right)} \left(-\frac{b^{3} - 2 \, a b c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}}\right) + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} c \left(-\frac{b^{3} - 2 \, a b c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}} \log\left(2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} x + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{6} - 8 \, a b^{4} c + 18 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3} - {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}\right)} \left(-\frac{b^{3} - 2 \, a b c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}}\right) + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} c \left(-\frac{b^{3} - 2 \, a b c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}} \log\left(2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} x + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{6} - 8 \, a b^{4} c + 18 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3} + {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}\right)} \left(-\frac{b^{3} - 2 \, a b c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}}\right) + 6 \, x}{6 \, c}"," ",0,"1/6*(4*sqrt(3)*(1/2)^(1/3)*c*(-(b^3 - 2*a*b*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3)*arctan(-1/6*(2*(1/2)^(2/3)*(sqrt(3)*(b^8*c^4 - 13*a*b^6*c^5 + 60*a^2*b^4*c^6 - 112*a^3*b^2*c^7 + 64*a^4*c^8)*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)) - sqrt(3)*(b^9 - 11*a*b^7*c + 42*a^2*b^5*c^2 - 62*a^3*b^3*c^3 + 24*a^4*b*c^4)*x)*(-(b^3 - 2*a*b*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(2/3) - (1/2)^(1/6)*(sqrt(3)*(b^8*c^4 - 13*a*b^6*c^5 + 60*a^2*b^4*c^6 - 112*a^3*b^2*c^7 + 64*a^4*c^8)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)) - sqrt(3)*(b^9 - 11*a*b^7*c + 42*a^2*b^5*c^2 - 62*a^3*b^3*c^3 + 24*a^4*b*c^4))*(-(b^3 - 2*a*b*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(2/3)*sqrt((2*(a^2*b^4 - 4*a^3*b^2*c + 2*a^4*c^2)*x^2 + (1/2)^(2/3)*(b^8 - 10*a*b^6*c + 34*a^2*b^4*c^2 - 44*a^3*b^2*c^3 + 16*a^4*c^4 - (b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))*(-(b^3 - 2*a*b*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(2/3) + (1/2)^(1/3)*((a*b^5*c^4 - 8*a^2*b^3*c^5 + 16*a^3*b*c^6)*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)) - (a*b^6 - 8*a^2*b^4*c + 18*a^3*b^2*c^2 - 8*a^4*c^3)*x)*(-(b^3 - 2*a*b*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3))/(a^2*b^4 - 4*a^3*b^2*c + 2*a^4*c^2)) + 2*sqrt(3)*(a^3*b^4 - 4*a^4*b^2*c + 2*a^5*c^2))/(a^3*b^4 - 4*a^4*b^2*c + 2*a^5*c^2)) - 4*sqrt(3)*(1/2)^(1/3)*c*(-(b^3 - 2*a*b*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3)*arctan(-1/6*(2*(1/2)^(2/3)*(sqrt(3)*(b^8*c^4 - 13*a*b^6*c^5 + 60*a^2*b^4*c^6 - 112*a^3*b^2*c^7 + 64*a^4*c^8)*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)) + sqrt(3)*(b^9 - 11*a*b^7*c + 42*a^2*b^5*c^2 - 62*a^3*b^3*c^3 + 24*a^4*b*c^4)*x)*(-(b^3 - 2*a*b*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(2/3) - (1/2)^(1/6)*(sqrt(3)*(b^8*c^4 - 13*a*b^6*c^5 + 60*a^2*b^4*c^6 - 112*a^3*b^2*c^7 + 64*a^4*c^8)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)) + sqrt(3)*(b^9 - 11*a*b^7*c + 42*a^2*b^5*c^2 - 62*a^3*b^3*c^3 + 24*a^4*b*c^4))*(-(b^3 - 2*a*b*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(2/3)*sqrt((2*(a^2*b^4 - 4*a^3*b^2*c + 2*a^4*c^2)*x^2 + (1/2)^(2/3)*(b^8 - 10*a*b^6*c + 34*a^2*b^4*c^2 - 44*a^3*b^2*c^3 + 16*a^4*c^4 + (b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))*(-(b^3 - 2*a*b*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(2/3) - (1/2)^(1/3)*((a*b^5*c^4 - 8*a^2*b^3*c^5 + 16*a^3*b*c^6)*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)) + (a*b^6 - 8*a^2*b^4*c + 18*a^3*b^2*c^2 - 8*a^4*c^3)*x)*(-(b^3 - 2*a*b*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3))/(a^2*b^4 - 4*a^3*b^2*c + 2*a^4*c^2)) - 2*sqrt(3)*(a^3*b^4 - 4*a^4*b^2*c + 2*a^5*c^2))/(a^3*b^4 - 4*a^4*b^2*c + 2*a^5*c^2)) - (1/2)^(1/3)*c*(-(b^3 - 2*a*b*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3)*log(2*(a^2*b^4 - 4*a^3*b^2*c + 2*a^4*c^2)*x^2 + (1/2)^(2/3)*(b^8 - 10*a*b^6*c + 34*a^2*b^4*c^2 - 44*a^3*b^2*c^3 + 16*a^4*c^4 - (b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))*(-(b^3 - 2*a*b*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(2/3) + (1/2)^(1/3)*((a*b^5*c^4 - 8*a^2*b^3*c^5 + 16*a^3*b*c^6)*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)) - (a*b^6 - 8*a^2*b^4*c + 18*a^3*b^2*c^2 - 8*a^4*c^3)*x)*(-(b^3 - 2*a*b*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3)) - (1/2)^(1/3)*c*(-(b^3 - 2*a*b*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3)*log(2*(a^2*b^4 - 4*a^3*b^2*c + 2*a^4*c^2)*x^2 + (1/2)^(2/3)*(b^8 - 10*a*b^6*c + 34*a^2*b^4*c^2 - 44*a^3*b^2*c^3 + 16*a^4*c^4 + (b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))*(-(b^3 - 2*a*b*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(2/3) - (1/2)^(1/3)*((a*b^5*c^4 - 8*a^2*b^3*c^5 + 16*a^3*b*c^6)*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)) + (a*b^6 - 8*a^2*b^4*c + 18*a^3*b^2*c^2 - 8*a^4*c^3)*x)*(-(b^3 - 2*a*b*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3)) + 2*(1/2)^(1/3)*c*(-(b^3 - 2*a*b*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3)*log(2*(a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2)*x + (1/2)^(1/3)*(b^6 - 8*a*b^4*c + 18*a^2*b^2*c^2 - 8*a^3*c^3 - (b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))*(-(b^3 - 2*a*b*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3)) + 2*(1/2)^(1/3)*c*(-(b^3 - 2*a*b*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3)*log(2*(a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2)*x + (1/2)^(1/3)*(b^6 - 8*a*b^4*c + 18*a^2*b^2*c^2 - 8*a^3*c^3 + (b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))*(-(b^3 - 2*a*b*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3)) + 6*x)/c","B",0
145,1,3799,0,1.778486," ","integrate(x^4/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\frac{2}{3} \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} + b}{b^{2} c^{2} - 4 \, a c^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{\left(\frac{1}{2}\right)^{\frac{5}{6}} {\left(\sqrt{3} {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} - \sqrt{3} {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)}\right)} \sqrt{\frac{2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\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 \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} - {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} x\right)} \left(-\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} + b}{b^{2} c^{2} - 4 \, a c^{3}}\right)^{\frac{2}{3}} - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} \left(-\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} + b}{b^{2} c^{2} - 4 \, a c^{3}}\right)^{\frac{1}{3}}}{a b^{2} - 2 \, a^{2} c}} \left(-\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} + b}{b^{2} c^{2} - 4 \, a c^{3}}\right)^{\frac{1}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\sqrt{3} {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} - \sqrt{3} {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} x\right)} \left(-\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} + b}{b^{2} c^{2} - 4 \, a c^{3}}\right)^{\frac{1}{3}} - \sqrt{3} {\left(a b^{2} - 2 \, a^{2} c\right)}}{3 \, {\left(a b^{2} - 2 \, a^{2} c\right)}}\right) - \frac{2}{3} \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} - b}{b^{2} c^{2} - 4 \, a c^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{\left(\frac{1}{2}\right)^{\frac{5}{6}} {\left(\sqrt{3} {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} + \sqrt{3} {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)}\right)} \sqrt{\frac{2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} x^{2} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\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 \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} + {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} x\right)} \left(\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} - b}{b^{2} c^{2} - 4 \, a c^{3}}\right)^{\frac{2}{3}} + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} \left(\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} - b}{b^{2} c^{2} - 4 \, a c^{3}}\right)^{\frac{1}{3}}}{a b^{2} - 2 \, a^{2} c}} \left(\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} - b}{b^{2} c^{2} - 4 \, a c^{3}}\right)^{\frac{1}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\sqrt{3} {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} + \sqrt{3} {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} x\right)} \left(\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} - b}{b^{2} c^{2} - 4 \, a c^{3}}\right)^{\frac{1}{3}} + \sqrt{3} {\left(a b^{2} - 2 \, a^{2} c\right)}}{3 \, {\left(a b^{2} - 2 \, a^{2} c\right)}}\right) - \frac{1}{6} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} + b}{b^{2} c^{2} - 4 \, a c^{3}}\right)^{\frac{1}{3}} \log\left(-2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} x^{2} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\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 \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} - {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} x\right)} \left(-\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} + b}{b^{2} c^{2} - 4 \, a c^{3}}\right)^{\frac{2}{3}} + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} \left(-\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} + b}{b^{2} c^{2} - 4 \, a c^{3}}\right)^{\frac{1}{3}}\right) - \frac{1}{6} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} - b}{b^{2} c^{2} - 4 \, a c^{3}}\right)^{\frac{1}{3}} \log\left(-2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\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 \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} + {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} x\right)} \left(\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} - b}{b^{2} c^{2} - 4 \, a c^{3}}\right)^{\frac{2}{3}} - 2 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} \left(\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} - b}{b^{2} c^{2} - 4 \, a c^{3}}\right)^{\frac{1}{3}}\right) + \frac{1}{3} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} + b}{b^{2} c^{2} - 4 \, a c^{3}}\right)^{\frac{1}{3}} \log\left(-\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2} - {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}}\right)} \left(-\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} + b}{b^{2} c^{2} - 4 \, a c^{3}}\right)^{\frac{2}{3}} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} x\right) + \frac{1}{3} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} - b}{b^{2} c^{2} - 4 \, a c^{3}}\right)^{\frac{1}{3}} \log\left(-\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}}\right)} \left(\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}}} - b}{b^{2} c^{2} - 4 \, a c^{3}}\right)^{\frac{2}{3}} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} x\right)"," ",0,"2/3*sqrt(3)*(1/2)^(1/3)*(-((b^2*c^2 - 4*a*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) + b)/(b^2*c^2 - 4*a*c^3))^(1/3)*arctan(-1/3*((1/2)^(5/6)*(sqrt(3)*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) - sqrt(3)*(b^4 - 6*a*b^2*c + 8*a^2*c^2))*sqrt((2*(a*b^2 - 2*a^2*c)*x^2 + (1/2)^(2/3)*((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) - (b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*x)*(-((b^2*c^2 - 4*a*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) + b)/(b^2*c^2 - 4*a*c^3))^(2/3) - 2*(1/2)^(1/3)*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7))*(-((b^2*c^2 - 4*a*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) + b)/(b^2*c^2 - 4*a*c^3))^(1/3))/(a*b^2 - 2*a^2*c))*(-((b^2*c^2 - 4*a*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) + b)/(b^2*c^2 - 4*a*c^3))^(1/3) - (1/2)^(1/3)*(sqrt(3)*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) - sqrt(3)*(b^4 - 6*a*b^2*c + 8*a^2*c^2)*x)*(-((b^2*c^2 - 4*a*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) + b)/(b^2*c^2 - 4*a*c^3))^(1/3) - sqrt(3)*(a*b^2 - 2*a^2*c))/(a*b^2 - 2*a^2*c)) - 2/3*sqrt(3)*(1/2)^(1/3)*(((b^2*c^2 - 4*a*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) - b)/(b^2*c^2 - 4*a*c^3))^(1/3)*arctan(-1/3*((1/2)^(5/6)*(sqrt(3)*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) + sqrt(3)*(b^4 - 6*a*b^2*c + 8*a^2*c^2))*sqrt((2*(a*b^2 - 2*a^2*c)*x^2 - (1/2)^(2/3)*((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) + (b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*x)*(((b^2*c^2 - 4*a*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) - b)/(b^2*c^2 - 4*a*c^3))^(2/3) + 2*(1/2)^(1/3)*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7))*(((b^2*c^2 - 4*a*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) - b)/(b^2*c^2 - 4*a*c^3))^(1/3))/(a*b^2 - 2*a^2*c))*(((b^2*c^2 - 4*a*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) - b)/(b^2*c^2 - 4*a*c^3))^(1/3) - (1/2)^(1/3)*(sqrt(3)*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) + sqrt(3)*(b^4 - 6*a*b^2*c + 8*a^2*c^2)*x)*(((b^2*c^2 - 4*a*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) - b)/(b^2*c^2 - 4*a*c^3))^(1/3) + sqrt(3)*(a*b^2 - 2*a^2*c))/(a*b^2 - 2*a^2*c)) - 1/6*(1/2)^(1/3)*(-((b^2*c^2 - 4*a*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) + b)/(b^2*c^2 - 4*a*c^3))^(1/3)*log(-2*(a*b^2 - 2*a^2*c)*x^2 - (1/2)^(2/3)*((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) - (b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*x)*(-((b^2*c^2 - 4*a*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) + b)/(b^2*c^2 - 4*a*c^3))^(2/3) + 2*(1/2)^(1/3)*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7))*(-((b^2*c^2 - 4*a*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) + b)/(b^2*c^2 - 4*a*c^3))^(1/3)) - 1/6*(1/2)^(1/3)*(((b^2*c^2 - 4*a*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) - b)/(b^2*c^2 - 4*a*c^3))^(1/3)*log(-2*(a*b^2 - 2*a^2*c)*x^2 + (1/2)^(2/3)*((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) + (b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*x)*(((b^2*c^2 - 4*a*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) - b)/(b^2*c^2 - 4*a*c^3))^(2/3) - 2*(1/2)^(1/3)*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7))*(((b^2*c^2 - 4*a*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) - b)/(b^2*c^2 - 4*a*c^3))^(1/3)) + 1/3*(1/2)^(1/3)*(-((b^2*c^2 - 4*a*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) + b)/(b^2*c^2 - 4*a*c^3))^(1/3)*log(-(1/2)^(2/3)*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2 - (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)))*(-((b^2*c^2 - 4*a*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) + b)/(b^2*c^2 - 4*a*c^3))^(2/3) - 2*(a*b^2 - 2*a^2*c)*x) + 1/3*(1/2)^(1/3)*(((b^2*c^2 - 4*a*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) - b)/(b^2*c^2 - 4*a*c^3))^(1/3)*log(-(1/2)^(2/3)*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)))*(((b^2*c^2 - 4*a*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)) - b)/(b^2*c^2 - 4*a*c^3))^(2/3) - 2*(a*b^2 - 2*a^2*c)*x)","B",0
146,1,2551,0,1.485281," ","integrate(x^3/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","-\frac{2}{3} \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} + 1}{b^{2} c - 4 \, a c^{2}}\right)^{\frac{1}{3}} \arctan\left(-\frac{\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} - \sqrt{3} {\left(b^{4} - 4 \, a b^{2} c\right)}\right)} \left(\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} + 1}{b^{2} c - 4 \, a c^{2}}\right)^{\frac{2}{3}} \sqrt{-\frac{\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} x \left(\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} + 1}{b^{2} c - 4 \, a c^{2}}\right)^{\frac{1}{3}} - b x^{2} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{3} - 4 \, a b c\right)} \left(\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} + 1}{b^{2} c - 4 \, a c^{2}}\right)^{\frac{2}{3}}}{b}} - \sqrt{3} a b - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} x - \sqrt{3} {\left(b^{4} - 4 \, a b^{2} c\right)} x\right)} \left(\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} + 1}{b^{2} c - 4 \, a c^{2}}\right)^{\frac{2}{3}}}{3 \, a b}\right) + \frac{2}{3} \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} - 1}{b^{2} c - 4 \, a c^{2}}\right)^{\frac{1}{3}} \arctan\left(-\frac{\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} + \sqrt{3} {\left(b^{4} - 4 \, a b^{2} c\right)}\right)} \left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} - 1}{b^{2} c - 4 \, a c^{2}}\right)^{\frac{2}{3}} \sqrt{\frac{\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} x \left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} - 1}{b^{2} c - 4 \, a c^{2}}\right)^{\frac{1}{3}} + b x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{3} - 4 \, a b c\right)} \left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} - 1}{b^{2} c - 4 \, a c^{2}}\right)^{\frac{2}{3}}}{b}} + \sqrt{3} a b - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} x + \sqrt{3} {\left(b^{4} - 4 \, a b^{2} c\right)} x\right)} \left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} - 1}{b^{2} c - 4 \, a c^{2}}\right)^{\frac{2}{3}}}{3 \, a b}\right) - \frac{1}{6} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} + 1}{b^{2} c - 4 \, a c^{2}}\right)^{\frac{1}{3}} \log\left(-\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} x \left(\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} + 1}{b^{2} c - 4 \, a c^{2}}\right)^{\frac{1}{3}} + b x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{3} - 4 \, a b c\right)} \left(\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} + 1}{b^{2} c - 4 \, a c^{2}}\right)^{\frac{2}{3}}\right) - \frac{1}{6} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} - 1}{b^{2} c - 4 \, a c^{2}}\right)^{\frac{1}{3}} \log\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} x \left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} - 1}{b^{2} c - 4 \, a c^{2}}\right)^{\frac{1}{3}} + b x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{3} - 4 \, a b c\right)} \left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} - 1}{b^{2} c - 4 \, a c^{2}}\right)^{\frac{2}{3}}\right) + \frac{1}{3} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} + 1}{b^{2} c - 4 \, a c^{2}}\right)^{\frac{1}{3}} \log\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} \left(\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} + 1}{b^{2} c - 4 \, a c^{2}}\right)^{\frac{1}{3}} + b x\right) + \frac{1}{3} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} - 1}{b^{2} c - 4 \, a c^{2}}\right)^{\frac{1}{3}} \log\left(-\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} \left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{b^{2}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} - 1}{b^{2} c - 4 \, a c^{2}}\right)^{\frac{1}{3}} + b x\right)"," ",0,"-2/3*sqrt(3)*(1/2)^(1/3)*(((b^2*c - 4*a*c^2)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) + 1)/(b^2*c - 4*a*c^2))^(1/3)*arctan(-1/3*((1/2)^(2/3)*(sqrt(3)*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) - sqrt(3)*(b^4 - 4*a*b^2*c))*(((b^2*c - 4*a*c^2)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) + 1)/(b^2*c - 4*a*c^2))^(2/3)*sqrt(-((1/2)^(1/3)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*x*(((b^2*c - 4*a*c^2)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) + 1)/(b^2*c - 4*a*c^2))^(1/3) - b*x^2 - (1/2)^(2/3)*(b^3 - 4*a*b*c)*(((b^2*c - 4*a*c^2)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) + 1)/(b^2*c - 4*a*c^2))^(2/3))/b) - sqrt(3)*a*b - (1/2)^(2/3)*(sqrt(3)*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*x - sqrt(3)*(b^4 - 4*a*b^2*c)*x)*(((b^2*c - 4*a*c^2)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) + 1)/(b^2*c - 4*a*c^2))^(2/3))/(a*b)) + 2/3*sqrt(3)*(1/2)^(1/3)*(-((b^2*c - 4*a*c^2)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) - 1)/(b^2*c - 4*a*c^2))^(1/3)*arctan(-1/3*((1/2)^(2/3)*(sqrt(3)*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) + sqrt(3)*(b^4 - 4*a*b^2*c))*(-((b^2*c - 4*a*c^2)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) - 1)/(b^2*c - 4*a*c^2))^(2/3)*sqrt(((1/2)^(1/3)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*x*(-((b^2*c - 4*a*c^2)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) - 1)/(b^2*c - 4*a*c^2))^(1/3) + b*x^2 + (1/2)^(2/3)*(b^3 - 4*a*b*c)*(-((b^2*c - 4*a*c^2)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) - 1)/(b^2*c - 4*a*c^2))^(2/3))/b) + sqrt(3)*a*b - (1/2)^(2/3)*(sqrt(3)*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*x + sqrt(3)*(b^4 - 4*a*b^2*c)*x)*(-((b^2*c - 4*a*c^2)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) - 1)/(b^2*c - 4*a*c^2))^(2/3))/(a*b)) - 1/6*(1/2)^(1/3)*(((b^2*c - 4*a*c^2)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) + 1)/(b^2*c - 4*a*c^2))^(1/3)*log(-(1/2)^(1/3)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*x*(((b^2*c - 4*a*c^2)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) + 1)/(b^2*c - 4*a*c^2))^(1/3) + b*x^2 + (1/2)^(2/3)*(b^3 - 4*a*b*c)*(((b^2*c - 4*a*c^2)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) + 1)/(b^2*c - 4*a*c^2))^(2/3)) - 1/6*(1/2)^(1/3)*(-((b^2*c - 4*a*c^2)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) - 1)/(b^2*c - 4*a*c^2))^(1/3)*log((1/2)^(1/3)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*x*(-((b^2*c - 4*a*c^2)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) - 1)/(b^2*c - 4*a*c^2))^(1/3) + b*x^2 + (1/2)^(2/3)*(b^3 - 4*a*b*c)*(-((b^2*c - 4*a*c^2)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) - 1)/(b^2*c - 4*a*c^2))^(2/3)) + 1/3*(1/2)^(1/3)*(((b^2*c - 4*a*c^2)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) + 1)/(b^2*c - 4*a*c^2))^(1/3)*log((1/2)^(1/3)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*(((b^2*c - 4*a*c^2)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) + 1)/(b^2*c - 4*a*c^2))^(1/3) + b*x) + 1/3*(1/2)^(1/3)*(-((b^2*c - 4*a*c^2)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) - 1)/(b^2*c - 4*a*c^2))^(1/3)*log(-(1/2)^(1/3)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*(-((b^2*c - 4*a*c^2)*sqrt(b^2/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) - 1)/(b^2*c - 4*a*c^2))^(1/3) + b*x)","B",0
147,1,2875,0,1.700741," ","integrate(x/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","-\frac{2}{3} \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} + 1}{a b^{2} - 4 \, a^{2} c}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} x \left(-\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} + 1}{a b^{2} - 4 \, a^{2} c}\right)^{\frac{1}{3}} - 2 \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{5}{6}} {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} \left(-\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} + 1}{a b^{2} - 4 \, a^{2} c}\right)^{\frac{1}{3}} \sqrt{\frac{2 \, b c x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} x - {\left(b^{4} - 4 \, a b^{2} c\right)} x\right)} \left(-\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} + 1}{a b^{2} - 4 \, a^{2} c}\right)^{\frac{2}{3}} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - 4 \, a b c - {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}\right)} \left(-\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} + 1}{a b^{2} - 4 \, a^{2} c}\right)^{\frac{1}{3}}}{b c}} + \sqrt{3} b}{3 \, b}\right) + \frac{2}{3} \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} - 1}{a b^{2} - 4 \, a^{2} c}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} x \left(\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} - 1}{a b^{2} - 4 \, a^{2} c}\right)^{\frac{1}{3}} - 2 \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{5}{6}} {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} \left(\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} - 1}{a b^{2} - 4 \, a^{2} c}\right)^{\frac{1}{3}} \sqrt{\frac{2 \, b c x^{2} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} x + {\left(b^{4} - 4 \, a b^{2} c\right)} x\right)} \left(\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} - 1}{a b^{2} - 4 \, a^{2} c}\right)^{\frac{2}{3}} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - 4 \, a b c + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}\right)} \left(\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} - 1}{a b^{2} - 4 \, a^{2} c}\right)^{\frac{1}{3}}}{b c}} - \sqrt{3} b}{3 \, b}\right) - \frac{1}{6} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} + 1}{a b^{2} - 4 \, a^{2} c}\right)^{\frac{1}{3}} \log\left(2 \, b c x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} x - {\left(b^{4} - 4 \, a b^{2} c\right)} x\right)} \left(-\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} + 1}{a b^{2} - 4 \, a^{2} c}\right)^{\frac{2}{3}} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - 4 \, a b c - {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}\right)} \left(-\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} + 1}{a b^{2} - 4 \, a^{2} c}\right)^{\frac{1}{3}}\right) - \frac{1}{6} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} - 1}{a b^{2} - 4 \, a^{2} c}\right)^{\frac{1}{3}} \log\left(2 \, b c x^{2} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} x + {\left(b^{4} - 4 \, a b^{2} c\right)} x\right)} \left(\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} - 1}{a b^{2} - 4 \, a^{2} c}\right)^{\frac{2}{3}} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - 4 \, a b c + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}\right)} \left(\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} - 1}{a b^{2} - 4 \, a^{2} c}\right)^{\frac{1}{3}}\right) + \frac{1}{3} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} + 1}{a b^{2} - 4 \, a^{2} c}\right)^{\frac{1}{3}} \log\left(2 \, b c x + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{4} - 4 \, a b^{2} c - {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}\right)} \left(-\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} + 1}{a b^{2} - 4 \, a^{2} c}\right)^{\frac{2}{3}}\right) + \frac{1}{3} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} - 1}{a b^{2} - 4 \, a^{2} c}\right)^{\frac{1}{3}} \log\left(2 \, b c x + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{4} - 4 \, a b^{2} c + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}\right)} \left(\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{\frac{b^{2}}{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} - 1}{a b^{2} - 4 \, a^{2} c}\right)^{\frac{2}{3}}\right)"," ",0,"-2/3*sqrt(3)*(1/2)^(1/3)*(-((a*b^2 - 4*a^2*c)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) + 1)/(a*b^2 - 4*a^2*c))^(1/3)*arctan(-1/3*(2*sqrt(3)*(1/2)^(1/3)*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))*x*(-((a*b^2 - 4*a^2*c)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) + 1)/(a*b^2 - 4*a^2*c))^(1/3) - 2*sqrt(3)*(1/2)^(5/6)*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))*(-((a*b^2 - 4*a^2*c)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) + 1)/(a*b^2 - 4*a^2*c))^(1/3)*sqrt((2*b*c*x^2 + (1/2)^(2/3)*((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))*x - (b^4 - 4*a*b^2*c)*x)*(-((a*b^2 - 4*a^2*c)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) + 1)/(a*b^2 - 4*a^2*c))^(2/3) + (1/2)^(1/3)*(b^3 - 4*a*b*c - (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)))*(-((a*b^2 - 4*a^2*c)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) + 1)/(a*b^2 - 4*a^2*c))^(1/3))/(b*c)) + sqrt(3)*b)/b) + 2/3*sqrt(3)*(1/2)^(1/3)*(((a*b^2 - 4*a^2*c)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) - 1)/(a*b^2 - 4*a^2*c))^(1/3)*arctan(-1/3*(2*sqrt(3)*(1/2)^(1/3)*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))*x*(((a*b^2 - 4*a^2*c)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) - 1)/(a*b^2 - 4*a^2*c))^(1/3) - 2*sqrt(3)*(1/2)^(5/6)*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))*(((a*b^2 - 4*a^2*c)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) - 1)/(a*b^2 - 4*a^2*c))^(1/3)*sqrt((2*b*c*x^2 - (1/2)^(2/3)*((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))*x + (b^4 - 4*a*b^2*c)*x)*(((a*b^2 - 4*a^2*c)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) - 1)/(a*b^2 - 4*a^2*c))^(2/3) + (1/2)^(1/3)*(b^3 - 4*a*b*c + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)))*(((a*b^2 - 4*a^2*c)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) - 1)/(a*b^2 - 4*a^2*c))^(1/3))/(b*c)) - sqrt(3)*b)/b) - 1/6*(1/2)^(1/3)*(-((a*b^2 - 4*a^2*c)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) + 1)/(a*b^2 - 4*a^2*c))^(1/3)*log(2*b*c*x^2 + (1/2)^(2/3)*((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))*x - (b^4 - 4*a*b^2*c)*x)*(-((a*b^2 - 4*a^2*c)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) + 1)/(a*b^2 - 4*a^2*c))^(2/3) + (1/2)^(1/3)*(b^3 - 4*a*b*c - (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)))*(-((a*b^2 - 4*a^2*c)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) + 1)/(a*b^2 - 4*a^2*c))^(1/3)) - 1/6*(1/2)^(1/3)*(((a*b^2 - 4*a^2*c)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) - 1)/(a*b^2 - 4*a^2*c))^(1/3)*log(2*b*c*x^2 - (1/2)^(2/3)*((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))*x + (b^4 - 4*a*b^2*c)*x)*(((a*b^2 - 4*a^2*c)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) - 1)/(a*b^2 - 4*a^2*c))^(2/3) + (1/2)^(1/3)*(b^3 - 4*a*b*c + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)))*(((a*b^2 - 4*a^2*c)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) - 1)/(a*b^2 - 4*a^2*c))^(1/3)) + 1/3*(1/2)^(1/3)*(-((a*b^2 - 4*a^2*c)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) + 1)/(a*b^2 - 4*a^2*c))^(1/3)*log(2*b*c*x + (1/2)^(2/3)*(b^4 - 4*a*b^2*c - (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)))*(-((a*b^2 - 4*a^2*c)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) + 1)/(a*b^2 - 4*a^2*c))^(2/3)) + 1/3*(1/2)^(1/3)*(((a*b^2 - 4*a^2*c)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) - 1)/(a*b^2 - 4*a^2*c))^(1/3)*log(2*b*c*x + (1/2)^(2/3)*(b^4 - 4*a*b^2*c + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)))*(((a*b^2 - 4*a^2*c)*sqrt(b^2/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) - 1)/(a*b^2 - 4*a^2*c))^(2/3))","B",0
148,1,3978,0,2.024206," ","integrate(1/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\frac{2}{3} \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} + b}{a^{2} b^{2} - 4 \, a^{3} c}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} x \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} - \sqrt{3} {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} x\right)} \left(\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} + b}{a^{2} b^{2} - 4 \, a^{3} c}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{6}} {\left(\sqrt{3} {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} - \sqrt{3} {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)}\right)} \sqrt{\frac{2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{6} - 8 \, a b^{4} c + 20 \, a^{2} b^{2} c^{2} - 16 \, a^{3} c^{3} - {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}}\right)} \left(\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} + b}{a^{2} b^{2} - 4 \, a^{3} c}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} - {\left(b^{4} c - 6 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} x\right)} \left(\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} + b}{a^{2} b^{2} - 4 \, a^{3} c}\right)^{\frac{1}{3}}}{b^{2} c^{2} - 2 \, a c^{3}}} \left(\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} + b}{a^{2} b^{2} - 4 \, a^{3} c}\right)^{\frac{2}{3}} + 2 \, \sqrt{3} {\left(b^{2} c - 2 \, a c^{2}\right)}}{6 \, {\left(b^{2} c - 2 \, a c^{2}\right)}}\right) - \frac{2}{3} \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} - b}{a^{2} b^{2} - 4 \, a^{3} c}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} x \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} + \sqrt{3} {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} x\right)} \left(-\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} - b}{a^{2} b^{2} - 4 \, a^{3} c}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{6}} {\left(\sqrt{3} {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} + \sqrt{3} {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)}\right)} \sqrt{\frac{2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{6} - 8 \, a b^{4} c + 20 \, a^{2} b^{2} c^{2} - 16 \, a^{3} c^{3} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}}\right)} \left(-\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} - b}{a^{2} b^{2} - 4 \, a^{3} c}\right)^{\frac{2}{3}} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} + {\left(b^{4} c - 6 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} x\right)} \left(-\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} - b}{a^{2} b^{2} - 4 \, a^{3} c}\right)^{\frac{1}{3}}}{b^{2} c^{2} - 2 \, a c^{3}}} \left(-\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} - b}{a^{2} b^{2} - 4 \, a^{3} c}\right)^{\frac{2}{3}} - 2 \, \sqrt{3} {\left(b^{2} c - 2 \, a c^{2}\right)}}{6 \, {\left(b^{2} c - 2 \, a c^{2}\right)}}\right) - \frac{1}{6} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} + b}{a^{2} b^{2} - 4 \, a^{3} c}\right)^{\frac{1}{3}} \log\left(-2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} x^{2} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{6} - 8 \, a b^{4} c + 20 \, a^{2} b^{2} c^{2} - 16 \, a^{3} c^{3} - {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}}\right)} \left(\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} + b}{a^{2} b^{2} - 4 \, a^{3} c}\right)^{\frac{2}{3}} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} - {\left(b^{4} c - 6 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} x\right)} \left(\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} + b}{a^{2} b^{2} - 4 \, a^{3} c}\right)^{\frac{1}{3}}\right) - \frac{1}{6} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} - b}{a^{2} b^{2} - 4 \, a^{3} c}\right)^{\frac{1}{3}} \log\left(-2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} x^{2} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{6} - 8 \, a b^{4} c + 20 \, a^{2} b^{2} c^{2} - 16 \, a^{3} c^{3} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}}\right)} \left(-\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} - b}{a^{2} b^{2} - 4 \, a^{3} c}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} x \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} + {\left(b^{4} c - 6 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} x\right)} \left(-\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} - b}{a^{2} b^{2} - 4 \, a^{3} c}\right)^{\frac{1}{3}}\right) + \frac{1}{3} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} + b}{a^{2} b^{2} - 4 \, a^{3} c}\right)^{\frac{1}{3}} \log\left(-2 \, {\left(b^{2} c - 2 \, a c^{2}\right)} x + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2} - {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}}\right)} \left(\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} + b}{a^{2} b^{2} - 4 \, a^{3} c}\right)^{\frac{1}{3}}\right) + \frac{1}{3} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} - b}{a^{2} b^{2} - 4 \, a^{3} c}\right)^{\frac{1}{3}} \log\left(-2 \, {\left(b^{2} c - 2 \, a c^{2}\right)} x + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}}\right)} \left(-\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}}} - b}{a^{2} b^{2} - 4 \, a^{3} c}\right)^{\frac{1}{3}}\right)"," ",0,"2/3*sqrt(3)*(1/2)^(1/3)*(((a^2*b^2 - 4*a^3*c)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) + b)/(a^2*b^2 - 4*a^3*c))^(1/3)*arctan(-1/6*(2*(1/2)^(2/3)*(sqrt(3)*(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*x*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) - sqrt(3)*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*x)*(((a^2*b^2 - 4*a^3*c)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) + b)/(a^2*b^2 - 4*a^3*c))^(2/3) - (1/2)^(1/6)*(sqrt(3)*(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) - sqrt(3)*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2))*sqrt((2*(b^2*c^2 - 2*a*c^3)*x^2 + (1/2)^(2/3)*(b^6 - 8*a*b^4*c + 20*a^2*b^2*c^2 - 16*a^3*c^3 - (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)))*(((a^2*b^2 - 4*a^3*c)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) + b)/(a^2*b^2 - 4*a^3*c))^(2/3) - (1/2)^(1/3)*((a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) - (b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*x)*(((a^2*b^2 - 4*a^3*c)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) + b)/(a^2*b^2 - 4*a^3*c))^(1/3))/(b^2*c^2 - 2*a*c^3))*(((a^2*b^2 - 4*a^3*c)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) + b)/(a^2*b^2 - 4*a^3*c))^(2/3) + 2*sqrt(3)*(b^2*c - 2*a*c^2))/(b^2*c - 2*a*c^2)) - 2/3*sqrt(3)*(1/2)^(1/3)*(-((a^2*b^2 - 4*a^3*c)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) - b)/(a^2*b^2 - 4*a^3*c))^(1/3)*arctan(-1/6*(2*(1/2)^(2/3)*(sqrt(3)*(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*x*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) + sqrt(3)*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*x)*(-((a^2*b^2 - 4*a^3*c)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) - b)/(a^2*b^2 - 4*a^3*c))^(2/3) - (1/2)^(1/6)*(sqrt(3)*(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) + sqrt(3)*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2))*sqrt((2*(b^2*c^2 - 2*a*c^3)*x^2 + (1/2)^(2/3)*(b^6 - 8*a*b^4*c + 20*a^2*b^2*c^2 - 16*a^3*c^3 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)))*(-((a^2*b^2 - 4*a^3*c)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) - b)/(a^2*b^2 - 4*a^3*c))^(2/3) + (1/2)^(1/3)*((a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) + (b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*x)*(-((a^2*b^2 - 4*a^3*c)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) - b)/(a^2*b^2 - 4*a^3*c))^(1/3))/(b^2*c^2 - 2*a*c^3))*(-((a^2*b^2 - 4*a^3*c)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) - b)/(a^2*b^2 - 4*a^3*c))^(2/3) - 2*sqrt(3)*(b^2*c - 2*a*c^2))/(b^2*c - 2*a*c^2)) - 1/6*(1/2)^(1/3)*(((a^2*b^2 - 4*a^3*c)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) + b)/(a^2*b^2 - 4*a^3*c))^(1/3)*log(-2*(b^2*c^2 - 2*a*c^3)*x^2 - (1/2)^(2/3)*(b^6 - 8*a*b^4*c + 20*a^2*b^2*c^2 - 16*a^3*c^3 - (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)))*(((a^2*b^2 - 4*a^3*c)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) + b)/(a^2*b^2 - 4*a^3*c))^(2/3) + (1/2)^(1/3)*((a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) - (b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*x)*(((a^2*b^2 - 4*a^3*c)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) + b)/(a^2*b^2 - 4*a^3*c))^(1/3)) - 1/6*(1/2)^(1/3)*(-((a^2*b^2 - 4*a^3*c)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) - b)/(a^2*b^2 - 4*a^3*c))^(1/3)*log(-2*(b^2*c^2 - 2*a*c^3)*x^2 - (1/2)^(2/3)*(b^6 - 8*a*b^4*c + 20*a^2*b^2*c^2 - 16*a^3*c^3 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)))*(-((a^2*b^2 - 4*a^3*c)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) - b)/(a^2*b^2 - 4*a^3*c))^(2/3) - (1/2)^(1/3)*((a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*x*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) + (b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*x)*(-((a^2*b^2 - 4*a^3*c)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) - b)/(a^2*b^2 - 4*a^3*c))^(1/3)) + 1/3*(1/2)^(1/3)*(((a^2*b^2 - 4*a^3*c)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) + b)/(a^2*b^2 - 4*a^3*c))^(1/3)*log(-2*(b^2*c - 2*a*c^2)*x + (1/2)^(1/3)*(b^4 - 6*a*b^2*c + 8*a^2*c^2 - (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)))*(((a^2*b^2 - 4*a^3*c)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) + b)/(a^2*b^2 - 4*a^3*c))^(1/3)) + 1/3*(1/2)^(1/3)*(-((a^2*b^2 - 4*a^3*c)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) - b)/(a^2*b^2 - 4*a^3*c))^(1/3)*log(-2*(b^2*c - 2*a*c^2)*x + (1/2)^(1/3)*(b^4 - 6*a*b^2*c + 8*a^2*c^2 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)))*(-((a^2*b^2 - 4*a^3*c)*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)) - b)/(a^2*b^2 - 4*a^3*c))^(1/3))","B",0
149,1,5266,0,3.992071," ","integrate(1/x^2/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} a x \left(\frac{b^{3} - 2 \, a b c + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}}{a^{4} b^{2} - 4 \, a^{5} c}\right)^{\frac{1}{3}} \arctan\left(\frac{\left(\frac{1}{2}\right)^{\frac{5}{6}} {\left(\sqrt{3} {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}} - \sqrt{3} {\left(b^{6} - 8 \, a b^{4} c + 18 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)}\right)} \left(\frac{b^{3} - 2 \, a b c + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}}{a^{4} b^{2} - 4 \, a^{5} c}\right)^{\frac{1}{3}} \sqrt{\frac{2 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4} + 2 \, a^{2} c^{5}\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(a^{4} b^{8} - 13 \, a^{5} b^{6} c + 60 \, a^{6} b^{4} c^{2} - 112 \, a^{7} b^{2} c^{3} + 64 \, a^{8} c^{4}\right)} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}} - {\left(b^{9} - 11 \, a b^{7} c + 42 \, a^{2} b^{5} c^{2} - 62 \, a^{3} b^{3} c^{3} + 24 \, a^{4} b c^{4}\right)} x\right)} \left(\frac{b^{3} - 2 \, a b c + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}}{a^{4} b^{2} - 4 \, a^{5} c}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{7} c - 8 \, a b^{5} c^{2} + 18 \, a^{2} b^{3} c^{3} - 8 \, a^{3} b c^{4} - {\left(a^{4} b^{6} c - 10 \, a^{5} b^{4} c^{2} + 32 \, a^{6} b^{2} c^{3} - 32 \, a^{7} c^{4}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}\right)} \left(\frac{b^{3} - 2 \, a b c + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}}{a^{4} b^{2} - 4 \, a^{5} c}\right)^{\frac{1}{3}}}{b^{4} c^{3} - 4 \, a b^{2} c^{4} + 2 \, a^{2} c^{5}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\sqrt{3} {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}} - \sqrt{3} {\left(b^{6} - 8 \, a b^{4} c + 18 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} x\right)} \left(\frac{b^{3} - 2 \, a b c + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}}{a^{4} b^{2} - 4 \, a^{5} c}\right)^{\frac{1}{3}} + \sqrt{3} {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)}}{3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)}}\right) - 4 \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} a x \left(\frac{b^{3} - 2 \, a b c - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}}{a^{4} b^{2} - 4 \, a^{5} c}\right)^{\frac{1}{3}} \arctan\left(\frac{\left(\frac{1}{2}\right)^{\frac{5}{6}} {\left(\sqrt{3} {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}} + \sqrt{3} {\left(b^{6} - 8 \, a b^{4} c + 18 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)}\right)} \left(\frac{b^{3} - 2 \, a b c - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}}{a^{4} b^{2} - 4 \, a^{5} c}\right)^{\frac{1}{3}} \sqrt{\frac{2 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4} + 2 \, a^{2} c^{5}\right)} x^{2} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(a^{4} b^{8} - 13 \, a^{5} b^{6} c + 60 \, a^{6} b^{4} c^{2} - 112 \, a^{7} b^{2} c^{3} + 64 \, a^{8} c^{4}\right)} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}} + {\left(b^{9} - 11 \, a b^{7} c + 42 \, a^{2} b^{5} c^{2} - 62 \, a^{3} b^{3} c^{3} + 24 \, a^{4} b c^{4}\right)} x\right)} \left(\frac{b^{3} - 2 \, a b c - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}}{a^{4} b^{2} - 4 \, a^{5} c}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{7} c - 8 \, a b^{5} c^{2} + 18 \, a^{2} b^{3} c^{3} - 8 \, a^{3} b c^{4} + {\left(a^{4} b^{6} c - 10 \, a^{5} b^{4} c^{2} + 32 \, a^{6} b^{2} c^{3} - 32 \, a^{7} c^{4}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}\right)} \left(\frac{b^{3} - 2 \, a b c - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}}{a^{4} b^{2} - 4 \, a^{5} c}\right)^{\frac{1}{3}}}{b^{4} c^{3} - 4 \, a b^{2} c^{4} + 2 \, a^{2} c^{5}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\sqrt{3} {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}} + \sqrt{3} {\left(b^{6} - 8 \, a b^{4} c + 18 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} x\right)} \left(\frac{b^{3} - 2 \, a b c - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}}{a^{4} b^{2} - 4 \, a^{5} c}\right)^{\frac{1}{3}} - \sqrt{3} {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)}}{3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)}}\right) - \left(\frac{1}{2}\right)^{\frac{1}{3}} a x \left(\frac{b^{3} - 2 \, a b c + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}}{a^{4} b^{2} - 4 \, a^{5} c}\right)^{\frac{1}{3}} \log\left(2 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4} + 2 \, a^{2} c^{5}\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(a^{4} b^{8} - 13 \, a^{5} b^{6} c + 60 \, a^{6} b^{4} c^{2} - 112 \, a^{7} b^{2} c^{3} + 64 \, a^{8} c^{4}\right)} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}} - {\left(b^{9} - 11 \, a b^{7} c + 42 \, a^{2} b^{5} c^{2} - 62 \, a^{3} b^{3} c^{3} + 24 \, a^{4} b c^{4}\right)} x\right)} \left(\frac{b^{3} - 2 \, a b c + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}}{a^{4} b^{2} - 4 \, a^{5} c}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{7} c - 8 \, a b^{5} c^{2} + 18 \, a^{2} b^{3} c^{3} - 8 \, a^{3} b c^{4} - {\left(a^{4} b^{6} c - 10 \, a^{5} b^{4} c^{2} + 32 \, a^{6} b^{2} c^{3} - 32 \, a^{7} c^{4}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}\right)} \left(\frac{b^{3} - 2 \, a b c + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}}{a^{4} b^{2} - 4 \, a^{5} c}\right)^{\frac{1}{3}}\right) - \left(\frac{1}{2}\right)^{\frac{1}{3}} a x \left(\frac{b^{3} - 2 \, a b c - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}}{a^{4} b^{2} - 4 \, a^{5} c}\right)^{\frac{1}{3}} \log\left(2 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4} + 2 \, a^{2} c^{5}\right)} x^{2} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(a^{4} b^{8} - 13 \, a^{5} b^{6} c + 60 \, a^{6} b^{4} c^{2} - 112 \, a^{7} b^{2} c^{3} + 64 \, a^{8} c^{4}\right)} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}} + {\left(b^{9} - 11 \, a b^{7} c + 42 \, a^{2} b^{5} c^{2} - 62 \, a^{3} b^{3} c^{3} + 24 \, a^{4} b c^{4}\right)} x\right)} \left(\frac{b^{3} - 2 \, a b c - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}}{a^{4} b^{2} - 4 \, a^{5} c}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{7} c - 8 \, a b^{5} c^{2} + 18 \, a^{2} b^{3} c^{3} - 8 \, a^{3} b c^{4} + {\left(a^{4} b^{6} c - 10 \, a^{5} b^{4} c^{2} + 32 \, a^{6} b^{2} c^{3} - 32 \, a^{7} c^{4}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}\right)} \left(\frac{b^{3} - 2 \, a b c - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}}{a^{4} b^{2} - 4 \, a^{5} c}\right)^{\frac{1}{3}}\right) + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} a x \left(\frac{b^{3} - 2 \, a b c + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}}{a^{4} b^{2} - 4 \, a^{5} c}\right)^{\frac{1}{3}} \log\left(\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{9} - 11 \, a b^{7} c + 42 \, a^{2} b^{5} c^{2} - 62 \, a^{3} b^{3} c^{3} + 24 \, a^{4} b c^{4} - {\left(a^{4} b^{8} - 13 \, a^{5} b^{6} c + 60 \, a^{6} b^{4} c^{2} - 112 \, a^{7} b^{2} c^{3} + 64 \, a^{8} c^{4}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}\right)} \left(\frac{b^{3} - 2 \, a b c + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}}{a^{4} b^{2} - 4 \, a^{5} c}\right)^{\frac{2}{3}} + 2 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4} + 2 \, a^{2} c^{5}\right)} x\right) + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} a x \left(\frac{b^{3} - 2 \, a b c - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}}{a^{4} b^{2} - 4 \, a^{5} c}\right)^{\frac{1}{3}} \log\left(\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{9} - 11 \, a b^{7} c + 42 \, a^{2} b^{5} c^{2} - 62 \, a^{3} b^{3} c^{3} + 24 \, a^{4} b c^{4} + {\left(a^{4} b^{8} - 13 \, a^{5} b^{6} c + 60 \, a^{6} b^{4} c^{2} - 112 \, a^{7} b^{2} c^{3} + 64 \, a^{8} c^{4}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}\right)} \left(\frac{b^{3} - 2 \, a b c - {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}}}}{a^{4} b^{2} - 4 \, a^{5} c}\right)^{\frac{2}{3}} + 2 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4} + 2 \, a^{2} c^{5}\right)} x\right) - 6}{6 \, a x}"," ",0,"1/6*(4*sqrt(3)*(1/2)^(1/3)*a*x*((b^3 - 2*a*b*c + (a^4*b^2 - 4*a^5*c)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))/(a^4*b^2 - 4*a^5*c))^(1/3)*arctan(1/3*((1/2)^(5/6)*(sqrt(3)*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)) - sqrt(3)*(b^6 - 8*a*b^4*c + 18*a^2*b^2*c^2 - 8*a^3*c^3))*((b^3 - 2*a*b*c + (a^4*b^2 - 4*a^5*c)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))/(a^4*b^2 - 4*a^5*c))^(1/3)*sqrt((2*(b^4*c^3 - 4*a*b^2*c^4 + 2*a^2*c^5)*x^2 + (1/2)^(2/3)*((a^4*b^8 - 13*a^5*b^6*c + 60*a^6*b^4*c^2 - 112*a^7*b^2*c^3 + 64*a^8*c^4)*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)) - (b^9 - 11*a*b^7*c + 42*a^2*b^5*c^2 - 62*a^3*b^3*c^3 + 24*a^4*b*c^4)*x)*((b^3 - 2*a*b*c + (a^4*b^2 - 4*a^5*c)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))/(a^4*b^2 - 4*a^5*c))^(2/3) - (1/2)^(1/3)*(b^7*c - 8*a*b^5*c^2 + 18*a^2*b^3*c^3 - 8*a^3*b*c^4 - (a^4*b^6*c - 10*a^5*b^4*c^2 + 32*a^6*b^2*c^3 - 32*a^7*c^4)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))*((b^3 - 2*a*b*c + (a^4*b^2 - 4*a^5*c)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))/(a^4*b^2 - 4*a^5*c))^(1/3))/(b^4*c^3 - 4*a*b^2*c^4 + 2*a^2*c^5)) - (1/2)^(1/3)*(sqrt(3)*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)) - sqrt(3)*(b^6 - 8*a*b^4*c + 18*a^2*b^2*c^2 - 8*a^3*c^3)*x)*((b^3 - 2*a*b*c + (a^4*b^2 - 4*a^5*c)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))/(a^4*b^2 - 4*a^5*c))^(1/3) + sqrt(3)*(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3))/(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)) - 4*sqrt(3)*(1/2)^(1/3)*a*x*((b^3 - 2*a*b*c - (a^4*b^2 - 4*a^5*c)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))/(a^4*b^2 - 4*a^5*c))^(1/3)*arctan(1/3*((1/2)^(5/6)*(sqrt(3)*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)) + sqrt(3)*(b^6 - 8*a*b^4*c + 18*a^2*b^2*c^2 - 8*a^3*c^3))*((b^3 - 2*a*b*c - (a^4*b^2 - 4*a^5*c)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))/(a^4*b^2 - 4*a^5*c))^(1/3)*sqrt((2*(b^4*c^3 - 4*a*b^2*c^4 + 2*a^2*c^5)*x^2 - (1/2)^(2/3)*((a^4*b^8 - 13*a^5*b^6*c + 60*a^6*b^4*c^2 - 112*a^7*b^2*c^3 + 64*a^8*c^4)*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)) + (b^9 - 11*a*b^7*c + 42*a^2*b^5*c^2 - 62*a^3*b^3*c^3 + 24*a^4*b*c^4)*x)*((b^3 - 2*a*b*c - (a^4*b^2 - 4*a^5*c)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))/(a^4*b^2 - 4*a^5*c))^(2/3) - (1/2)^(1/3)*(b^7*c - 8*a*b^5*c^2 + 18*a^2*b^3*c^3 - 8*a^3*b*c^4 + (a^4*b^6*c - 10*a^5*b^4*c^2 + 32*a^6*b^2*c^3 - 32*a^7*c^4)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))*((b^3 - 2*a*b*c - (a^4*b^2 - 4*a^5*c)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))/(a^4*b^2 - 4*a^5*c))^(1/3))/(b^4*c^3 - 4*a*b^2*c^4 + 2*a^2*c^5)) - (1/2)^(1/3)*(sqrt(3)*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)) + sqrt(3)*(b^6 - 8*a*b^4*c + 18*a^2*b^2*c^2 - 8*a^3*c^3)*x)*((b^3 - 2*a*b*c - (a^4*b^2 - 4*a^5*c)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))/(a^4*b^2 - 4*a^5*c))^(1/3) - sqrt(3)*(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3))/(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)) - (1/2)^(1/3)*a*x*((b^3 - 2*a*b*c + (a^4*b^2 - 4*a^5*c)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))/(a^4*b^2 - 4*a^5*c))^(1/3)*log(2*(b^4*c^3 - 4*a*b^2*c^4 + 2*a^2*c^5)*x^2 + (1/2)^(2/3)*((a^4*b^8 - 13*a^5*b^6*c + 60*a^6*b^4*c^2 - 112*a^7*b^2*c^3 + 64*a^8*c^4)*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)) - (b^9 - 11*a*b^7*c + 42*a^2*b^5*c^2 - 62*a^3*b^3*c^3 + 24*a^4*b*c^4)*x)*((b^3 - 2*a*b*c + (a^4*b^2 - 4*a^5*c)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))/(a^4*b^2 - 4*a^5*c))^(2/3) - (1/2)^(1/3)*(b^7*c - 8*a*b^5*c^2 + 18*a^2*b^3*c^3 - 8*a^3*b*c^4 - (a^4*b^6*c - 10*a^5*b^4*c^2 + 32*a^6*b^2*c^3 - 32*a^7*c^4)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))*((b^3 - 2*a*b*c + (a^4*b^2 - 4*a^5*c)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))/(a^4*b^2 - 4*a^5*c))^(1/3)) - (1/2)^(1/3)*a*x*((b^3 - 2*a*b*c - (a^4*b^2 - 4*a^5*c)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))/(a^4*b^2 - 4*a^5*c))^(1/3)*log(2*(b^4*c^3 - 4*a*b^2*c^4 + 2*a^2*c^5)*x^2 - (1/2)^(2/3)*((a^4*b^8 - 13*a^5*b^6*c + 60*a^6*b^4*c^2 - 112*a^7*b^2*c^3 + 64*a^8*c^4)*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)) + (b^9 - 11*a*b^7*c + 42*a^2*b^5*c^2 - 62*a^3*b^3*c^3 + 24*a^4*b*c^4)*x)*((b^3 - 2*a*b*c - (a^4*b^2 - 4*a^5*c)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))/(a^4*b^2 - 4*a^5*c))^(2/3) - (1/2)^(1/3)*(b^7*c - 8*a*b^5*c^2 + 18*a^2*b^3*c^3 - 8*a^3*b*c^4 + (a^4*b^6*c - 10*a^5*b^4*c^2 + 32*a^6*b^2*c^3 - 32*a^7*c^4)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))*((b^3 - 2*a*b*c - (a^4*b^2 - 4*a^5*c)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))/(a^4*b^2 - 4*a^5*c))^(1/3)) + 2*(1/2)^(1/3)*a*x*((b^3 - 2*a*b*c + (a^4*b^2 - 4*a^5*c)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))/(a^4*b^2 - 4*a^5*c))^(1/3)*log((1/2)^(2/3)*(b^9 - 11*a*b^7*c + 42*a^2*b^5*c^2 - 62*a^3*b^3*c^3 + 24*a^4*b*c^4 - (a^4*b^8 - 13*a^5*b^6*c + 60*a^6*b^4*c^2 - 112*a^7*b^2*c^3 + 64*a^8*c^4)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))*((b^3 - 2*a*b*c + (a^4*b^2 - 4*a^5*c)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))/(a^4*b^2 - 4*a^5*c))^(2/3) + 2*(b^4*c^3 - 4*a*b^2*c^4 + 2*a^2*c^5)*x) + 2*(1/2)^(1/3)*a*x*((b^3 - 2*a*b*c - (a^4*b^2 - 4*a^5*c)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))/(a^4*b^2 - 4*a^5*c))^(1/3)*log((1/2)^(2/3)*(b^9 - 11*a*b^7*c + 42*a^2*b^5*c^2 - 62*a^3*b^3*c^3 + 24*a^4*b*c^4 + (a^4*b^8 - 13*a^5*b^6*c + 60*a^6*b^4*c^2 - 112*a^7*b^2*c^3 + 64*a^8*c^4)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))*((b^3 - 2*a*b*c - (a^4*b^2 - 4*a^5*c)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)))/(a^4*b^2 - 4*a^5*c))^(2/3) + 2*(b^4*c^3 - 4*a*b^2*c^4 + 2*a^2*c^5)*x) - 6)/(a*x)","B",0
150,1,5771,0,3.764347," ","integrate(1/x^3/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} a x^{2} \left(-\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{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^{2} - 4 \, a^{6} c}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left(a^{5} b^{8} - 13 \, a^{6} b^{6} c + 60 \, a^{7} b^{4} c^{2} - 112 \, a^{8} b^{2} c^{3} + 64 \, a^{9} c^{4}\right)} x \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}} - \sqrt{3} {\left(b^{10} - 12 \, a b^{8} c + 52 \, a^{2} b^{6} c^{2} - 95 \, a^{3} b^{4} c^{3} + 60 \, a^{4} b^{2} c^{4}\right)} x\right)} \left(-\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{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^{2} - 4 \, a^{6} c}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{6}} {\left(\sqrt{3} {\left(a^{5} b^{8} - 13 \, a^{6} b^{6} c + 60 \, a^{7} b^{4} c^{2} - 112 \, a^{8} b^{2} c^{3} + 64 \, a^{9} c^{4}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}} - \sqrt{3} {\left(b^{10} - 12 \, a b^{8} c + 52 \, a^{2} b^{6} c^{2} - 95 \, a^{3} b^{4} c^{3} + 60 \, a^{4} b^{2} c^{4}\right)}\right)} \left(-\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{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^{2} - 4 \, a^{6} c}\right)^{\frac{2}{3}} \sqrt{\frac{2 \, {\left(b^{5} c^{4} - 5 \, a b^{3} c^{5} + 5 \, a^{2} b c^{6}\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 130 \, a^{4} b^{3} c^{4} - 40 \, a^{5} b c^{5} - {\left(a^{5} b^{9} - 14 \, a^{6} b^{7} c + 72 \, a^{7} b^{5} c^{2} - 160 \, a^{8} b^{3} c^{3} + 128 \, a^{9} b c^{4}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \left(-\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{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^{2} - 4 \, a^{6} c}\right)^{\frac{2}{3}} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a^{5} b^{6} c^{2} - 10 \, a^{6} b^{4} c^{3} + 32 \, a^{7} b^{2} c^{4} - 32 \, a^{8} c^{5}\right)} x \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}} - {\left(b^{8} c^{2} - 9 \, a b^{6} c^{3} + 25 \, a^{2} b^{4} c^{4} - 20 \, a^{3} b^{2} c^{5}\right)} x\right)} \left(-\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{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^{2} - 4 \, a^{6} c}\right)^{\frac{1}{3}}}{b^{5} c^{4} - 5 \, a b^{3} c^{5} + 5 \, a^{2} b c^{6}}} + 2 \, \sqrt{3} {\left(b^{5} c^{3} - 5 \, a b^{3} c^{4} + 5 \, a^{2} b c^{5}\right)}}{6 \, {\left(b^{5} c^{3} - 5 \, a b^{3} c^{4} + 5 \, a^{2} b c^{5}\right)}}\right) - 4 \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} a x^{2} \left(-\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{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^{2} - 4 \, a^{6} c}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left(a^{5} b^{8} - 13 \, a^{6} b^{6} c + 60 \, a^{7} b^{4} c^{2} - 112 \, a^{8} b^{2} c^{3} + 64 \, a^{9} c^{4}\right)} x \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}} + \sqrt{3} {\left(b^{10} - 12 \, a b^{8} c + 52 \, a^{2} b^{6} c^{2} - 95 \, a^{3} b^{4} c^{3} + 60 \, a^{4} b^{2} c^{4}\right)} x\right)} \left(-\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{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^{2} - 4 \, a^{6} c}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{6}} {\left(\sqrt{3} {\left(a^{5} b^{8} - 13 \, a^{6} b^{6} c + 60 \, a^{7} b^{4} c^{2} - 112 \, a^{8} b^{2} c^{3} + 64 \, a^{9} c^{4}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}} + \sqrt{3} {\left(b^{10} - 12 \, a b^{8} c + 52 \, a^{2} b^{6} c^{2} - 95 \, a^{3} b^{4} c^{3} + 60 \, a^{4} b^{2} c^{4}\right)}\right)} \left(-\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{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^{2} - 4 \, a^{6} c}\right)^{\frac{2}{3}} \sqrt{\frac{2 \, {\left(b^{5} c^{4} - 5 \, a b^{3} c^{5} + 5 \, a^{2} b c^{6}\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 130 \, a^{4} b^{3} c^{4} - 40 \, a^{5} b c^{5} + {\left(a^{5} b^{9} - 14 \, a^{6} b^{7} c + 72 \, a^{7} b^{5} c^{2} - 160 \, a^{8} b^{3} c^{3} + 128 \, a^{9} b c^{4}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \left(-\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{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^{2} - 4 \, a^{6} c}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a^{5} b^{6} c^{2} - 10 \, a^{6} b^{4} c^{3} + 32 \, a^{7} b^{2} c^{4} - 32 \, a^{8} c^{5}\right)} x \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}} + {\left(b^{8} c^{2} - 9 \, a b^{6} c^{3} + 25 \, a^{2} b^{4} c^{4} - 20 \, a^{3} b^{2} c^{5}\right)} x\right)} \left(-\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{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^{2} - 4 \, a^{6} c}\right)^{\frac{1}{3}}}{b^{5} c^{4} - 5 \, a b^{3} c^{5} + 5 \, a^{2} b c^{6}}} - 2 \, \sqrt{3} {\left(b^{5} c^{3} - 5 \, a b^{3} c^{4} + 5 \, a^{2} b c^{5}\right)}}{6 \, {\left(b^{5} c^{3} - 5 \, a b^{3} c^{4} + 5 \, a^{2} b c^{5}\right)}}\right) - \left(\frac{1}{2}\right)^{\frac{1}{3}} a x^{2} \left(-\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{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^{2} - 4 \, a^{6} c}\right)^{\frac{1}{3}} \log\left(2 \, {\left(b^{5} c^{4} - 5 \, a b^{3} c^{5} + 5 \, a^{2} b c^{6}\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 130 \, a^{4} b^{3} c^{4} - 40 \, a^{5} b c^{5} - {\left(a^{5} b^{9} - 14 \, a^{6} b^{7} c + 72 \, a^{7} b^{5} c^{2} - 160 \, a^{8} b^{3} c^{3} + 128 \, a^{9} b c^{4}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \left(-\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{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^{2} - 4 \, a^{6} c}\right)^{\frac{2}{3}} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a^{5} b^{6} c^{2} - 10 \, a^{6} b^{4} c^{3} + 32 \, a^{7} b^{2} c^{4} - 32 \, a^{8} c^{5}\right)} x \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}} - {\left(b^{8} c^{2} - 9 \, a b^{6} c^{3} + 25 \, a^{2} b^{4} c^{4} - 20 \, a^{3} b^{2} c^{5}\right)} x\right)} \left(-\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{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^{2} - 4 \, a^{6} c}\right)^{\frac{1}{3}}\right) - \left(\frac{1}{2}\right)^{\frac{1}{3}} a x^{2} \left(-\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{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^{2} - 4 \, a^{6} c}\right)^{\frac{1}{3}} \log\left(2 \, {\left(b^{5} c^{4} - 5 \, a b^{3} c^{5} + 5 \, a^{2} b c^{6}\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 130 \, a^{4} b^{3} c^{4} - 40 \, a^{5} b c^{5} + {\left(a^{5} b^{9} - 14 \, a^{6} b^{7} c + 72 \, a^{7} b^{5} c^{2} - 160 \, a^{8} b^{3} c^{3} + 128 \, a^{9} b c^{4}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \left(-\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{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^{2} - 4 \, a^{6} c}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a^{5} b^{6} c^{2} - 10 \, a^{6} b^{4} c^{3} + 32 \, a^{7} b^{2} c^{4} - 32 \, a^{8} c^{5}\right)} x \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}} + {\left(b^{8} c^{2} - 9 \, a b^{6} c^{3} + 25 \, a^{2} b^{4} c^{4} - 20 \, a^{3} b^{2} c^{5}\right)} x\right)} \left(-\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{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^{2} - 4 \, a^{6} c}\right)^{\frac{1}{3}}\right) + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} a x^{2} \left(-\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{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^{2} - 4 \, a^{6} c}\right)^{\frac{1}{3}} \log\left(2 \, {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 5 \, a^{2} b c^{4}\right)} x + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{8} - 9 \, a b^{6} c + 25 \, a^{2} b^{4} c^{2} - 20 \, a^{3} b^{2} c^{3} - {\left(a^{5} b^{6} - 10 \, a^{6} b^{4} c + 32 \, a^{7} b^{2} c^{2} - 32 \, a^{8} c^{3}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \left(-\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{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^{2} - 4 \, a^{6} c}\right)^{\frac{1}{3}}\right) + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} a x^{2} \left(-\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{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^{2} - 4 \, a^{6} c}\right)^{\frac{1}{3}} \log\left(2 \, {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 5 \, a^{2} b c^{4}\right)} x + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{8} - 9 \, a b^{6} c + 25 \, a^{2} b^{4} c^{2} - 20 \, a^{3} b^{2} c^{3} + {\left(a^{5} b^{6} - 10 \, a^{6} b^{4} c + 32 \, a^{7} b^{2} c^{2} - 32 \, a^{8} c^{3}\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \left(-\frac{b^{4} - 3 \, a b^{2} c + a^{2} c^{2} - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{\frac{b^{10} - 10 \, a b^{8} c + 35 \, a^{2} b^{6} c^{2} - 50 \, a^{3} b^{4} c^{3} + 25 \, a^{4} b^{2} c^{4}}{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^{2} - 4 \, a^{6} c}\right)^{\frac{1}{3}}\right) - 3}{6 \, a x^{2}}"," ",0,"1/6*(4*sqrt(3)*(1/2)^(1/3)*a*x^2*(-(b^4 - 3*a*b^2*c + a^2*c^2 + (a^5*b^2 - 4*a^6*c)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(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^2 - 4*a^6*c))^(1/3)*arctan(-1/6*(2*(1/2)^(2/3)*(sqrt(3)*(a^5*b^8 - 13*a^6*b^6*c + 60*a^7*b^4*c^2 - 112*a^8*b^2*c^3 + 64*a^9*c^4)*x*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)) - sqrt(3)*(b^10 - 12*a*b^8*c + 52*a^2*b^6*c^2 - 95*a^3*b^4*c^3 + 60*a^4*b^2*c^4)*x)*(-(b^4 - 3*a*b^2*c + a^2*c^2 + (a^5*b^2 - 4*a^6*c)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(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^2 - 4*a^6*c))^(2/3) - (1/2)^(1/6)*(sqrt(3)*(a^5*b^8 - 13*a^6*b^6*c + 60*a^7*b^4*c^2 - 112*a^8*b^2*c^3 + 64*a^9*c^4)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)) - sqrt(3)*(b^10 - 12*a*b^8*c + 52*a^2*b^6*c^2 - 95*a^3*b^4*c^3 + 60*a^4*b^2*c^4))*(-(b^4 - 3*a*b^2*c + a^2*c^2 + (a^5*b^2 - 4*a^6*c)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(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^2 - 4*a^6*c))^(2/3)*sqrt((2*(b^5*c^4 - 5*a*b^3*c^5 + 5*a^2*b*c^6)*x^2 + (1/2)^(2/3)*(b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 130*a^4*b^3*c^4 - 40*a^5*b*c^5 - (a^5*b^9 - 14*a^6*b^7*c + 72*a^7*b^5*c^2 - 160*a^8*b^3*c^3 + 128*a^9*b*c^4)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*(-(b^4 - 3*a*b^2*c + a^2*c^2 + (a^5*b^2 - 4*a^6*c)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(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^2 - 4*a^6*c))^(2/3) + (1/2)^(1/3)*((a^5*b^6*c^2 - 10*a^6*b^4*c^3 + 32*a^7*b^2*c^4 - 32*a^8*c^5)*x*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)) - (b^8*c^2 - 9*a*b^6*c^3 + 25*a^2*b^4*c^4 - 20*a^3*b^2*c^5)*x)*(-(b^4 - 3*a*b^2*c + a^2*c^2 + (a^5*b^2 - 4*a^6*c)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(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^2 - 4*a^6*c))^(1/3))/(b^5*c^4 - 5*a*b^3*c^5 + 5*a^2*b*c^6)) + 2*sqrt(3)*(b^5*c^3 - 5*a*b^3*c^4 + 5*a^2*b*c^5))/(b^5*c^3 - 5*a*b^3*c^4 + 5*a^2*b*c^5)) - 4*sqrt(3)*(1/2)^(1/3)*a*x^2*(-(b^4 - 3*a*b^2*c + a^2*c^2 - (a^5*b^2 - 4*a^6*c)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(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^2 - 4*a^6*c))^(1/3)*arctan(-1/6*(2*(1/2)^(2/3)*(sqrt(3)*(a^5*b^8 - 13*a^6*b^6*c + 60*a^7*b^4*c^2 - 112*a^8*b^2*c^3 + 64*a^9*c^4)*x*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)) + sqrt(3)*(b^10 - 12*a*b^8*c + 52*a^2*b^6*c^2 - 95*a^3*b^4*c^3 + 60*a^4*b^2*c^4)*x)*(-(b^4 - 3*a*b^2*c + a^2*c^2 - (a^5*b^2 - 4*a^6*c)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(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^2 - 4*a^6*c))^(2/3) - (1/2)^(1/6)*(sqrt(3)*(a^5*b^8 - 13*a^6*b^6*c + 60*a^7*b^4*c^2 - 112*a^8*b^2*c^3 + 64*a^9*c^4)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)) + sqrt(3)*(b^10 - 12*a*b^8*c + 52*a^2*b^6*c^2 - 95*a^3*b^4*c^3 + 60*a^4*b^2*c^4))*(-(b^4 - 3*a*b^2*c + a^2*c^2 - (a^5*b^2 - 4*a^6*c)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(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^2 - 4*a^6*c))^(2/3)*sqrt((2*(b^5*c^4 - 5*a*b^3*c^5 + 5*a^2*b*c^6)*x^2 + (1/2)^(2/3)*(b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 130*a^4*b^3*c^4 - 40*a^5*b*c^5 + (a^5*b^9 - 14*a^6*b^7*c + 72*a^7*b^5*c^2 - 160*a^8*b^3*c^3 + 128*a^9*b*c^4)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*(-(b^4 - 3*a*b^2*c + a^2*c^2 - (a^5*b^2 - 4*a^6*c)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(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^2 - 4*a^6*c))^(2/3) - (1/2)^(1/3)*((a^5*b^6*c^2 - 10*a^6*b^4*c^3 + 32*a^7*b^2*c^4 - 32*a^8*c^5)*x*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)) + (b^8*c^2 - 9*a*b^6*c^3 + 25*a^2*b^4*c^4 - 20*a^3*b^2*c^5)*x)*(-(b^4 - 3*a*b^2*c + a^2*c^2 - (a^5*b^2 - 4*a^6*c)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(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^2 - 4*a^6*c))^(1/3))/(b^5*c^4 - 5*a*b^3*c^5 + 5*a^2*b*c^6)) - 2*sqrt(3)*(b^5*c^3 - 5*a*b^3*c^4 + 5*a^2*b*c^5))/(b^5*c^3 - 5*a*b^3*c^4 + 5*a^2*b*c^5)) - (1/2)^(1/3)*a*x^2*(-(b^4 - 3*a*b^2*c + a^2*c^2 + (a^5*b^2 - 4*a^6*c)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(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^2 - 4*a^6*c))^(1/3)*log(2*(b^5*c^4 - 5*a*b^3*c^5 + 5*a^2*b*c^6)*x^2 + (1/2)^(2/3)*(b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 130*a^4*b^3*c^4 - 40*a^5*b*c^5 - (a^5*b^9 - 14*a^6*b^7*c + 72*a^7*b^5*c^2 - 160*a^8*b^3*c^3 + 128*a^9*b*c^4)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*(-(b^4 - 3*a*b^2*c + a^2*c^2 + (a^5*b^2 - 4*a^6*c)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(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^2 - 4*a^6*c))^(2/3) + (1/2)^(1/3)*((a^5*b^6*c^2 - 10*a^6*b^4*c^3 + 32*a^7*b^2*c^4 - 32*a^8*c^5)*x*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)) - (b^8*c^2 - 9*a*b^6*c^3 + 25*a^2*b^4*c^4 - 20*a^3*b^2*c^5)*x)*(-(b^4 - 3*a*b^2*c + a^2*c^2 + (a^5*b^2 - 4*a^6*c)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(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^2 - 4*a^6*c))^(1/3)) - (1/2)^(1/3)*a*x^2*(-(b^4 - 3*a*b^2*c + a^2*c^2 - (a^5*b^2 - 4*a^6*c)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(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^2 - 4*a^6*c))^(1/3)*log(2*(b^5*c^4 - 5*a*b^3*c^5 + 5*a^2*b*c^6)*x^2 + (1/2)^(2/3)*(b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 130*a^4*b^3*c^4 - 40*a^5*b*c^5 + (a^5*b^9 - 14*a^6*b^7*c + 72*a^7*b^5*c^2 - 160*a^8*b^3*c^3 + 128*a^9*b*c^4)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*(-(b^4 - 3*a*b^2*c + a^2*c^2 - (a^5*b^2 - 4*a^6*c)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(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^2 - 4*a^6*c))^(2/3) - (1/2)^(1/3)*((a^5*b^6*c^2 - 10*a^6*b^4*c^3 + 32*a^7*b^2*c^4 - 32*a^8*c^5)*x*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)) + (b^8*c^2 - 9*a*b^6*c^3 + 25*a^2*b^4*c^4 - 20*a^3*b^2*c^5)*x)*(-(b^4 - 3*a*b^2*c + a^2*c^2 - (a^5*b^2 - 4*a^6*c)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(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^2 - 4*a^6*c))^(1/3)) + 2*(1/2)^(1/3)*a*x^2*(-(b^4 - 3*a*b^2*c + a^2*c^2 + (a^5*b^2 - 4*a^6*c)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(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^2 - 4*a^6*c))^(1/3)*log(2*(b^5*c^2 - 5*a*b^3*c^3 + 5*a^2*b*c^4)*x + (1/2)^(1/3)*(b^8 - 9*a*b^6*c + 25*a^2*b^4*c^2 - 20*a^3*b^2*c^3 - (a^5*b^6 - 10*a^6*b^4*c + 32*a^7*b^2*c^2 - 32*a^8*c^3)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*(-(b^4 - 3*a*b^2*c + a^2*c^2 + (a^5*b^2 - 4*a^6*c)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(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^2 - 4*a^6*c))^(1/3)) + 2*(1/2)^(1/3)*a*x^2*(-(b^4 - 3*a*b^2*c + a^2*c^2 - (a^5*b^2 - 4*a^6*c)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(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^2 - 4*a^6*c))^(1/3)*log(2*(b^5*c^2 - 5*a*b^3*c^3 + 5*a^2*b*c^4)*x + (1/2)^(1/3)*(b^8 - 9*a*b^6*c + 25*a^2*b^4*c^2 - 20*a^3*b^2*c^3 + (a^5*b^6 - 10*a^6*b^4*c + 32*a^7*b^2*c^2 - 32*a^8*c^3)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*(-(b^4 - 3*a*b^2*c + a^2*c^2 - (a^5*b^2 - 4*a^6*c)*sqrt((b^10 - 10*a*b^8*c + 35*a^2*b^6*c^2 - 50*a^3*b^4*c^3 + 25*a^4*b^2*c^4)/(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^2 - 4*a^6*c))^(1/3)) - 3)/(a*x^2)","B",0
151,1,27,0,1.288076," ","integrate(x^11/(x^6+4*x^3+3),x, algorithm=""fricas"")","\frac{1}{6} \, x^{6} - \frac{4}{3} \, x^{3} + \frac{9}{2} \, \log\left(x^{3} + 3\right) - \frac{1}{6} \, \log\left(x^{3} + 1\right)"," ",0,"1/6*x^6 - 4/3*x^3 + 9/2*log(x^3 + 3) - 1/6*log(x^3 + 1)","A",0
152,1,22,0,1.126431," ","integrate(x^8/(x^6+4*x^3+3),x, algorithm=""fricas"")","\frac{1}{3} \, x^{3} - \frac{3}{2} \, \log\left(x^{3} + 3\right) + \frac{1}{6} \, \log\left(x^{3} + 1\right)"," ",0,"1/3*x^3 - 3/2*log(x^3 + 3) + 1/6*log(x^3 + 1)","A",0
153,1,17,0,1.205223," ","integrate(x^5/(x^6+4*x^3+3),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(x^{3} + 3\right) - \frac{1}{6} \, \log\left(x^{3} + 1\right)"," ",0,"1/2*log(x^3 + 3) - 1/6*log(x^3 + 1)","A",0
154,1,17,0,1.210954," ","integrate(x^2/(x^6+4*x^3+3),x, algorithm=""fricas"")","-\frac{1}{6} \, \log\left(x^{3} + 3\right) + \frac{1}{6} \, \log\left(x^{3} + 1\right)"," ",0,"-1/6*log(x^3 + 3) + 1/6*log(x^3 + 1)","B",0
155,1,21,0,1.253097," ","integrate(1/x/(x^6+4*x^3+3),x, algorithm=""fricas"")","\frac{1}{18} \, \log\left(x^{3} + 3\right) - \frac{1}{6} \, \log\left(x^{3} + 1\right) + \frac{1}{3} \, \log\left(x\right)"," ",0,"1/18*log(x^3 + 3) - 1/6*log(x^3 + 1) + 1/3*log(x)","A",0
156,1,35,0,1.271474," ","integrate(1/x^4/(x^6+4*x^3+3),x, algorithm=""fricas"")","-\frac{x^{3} \log\left(x^{3} + 3\right) - 9 \, x^{3} \log\left(x^{3} + 1\right) + 24 \, x^{3} \log\left(x\right) + 6}{54 \, x^{3}}"," ",0,"-1/54*(x^3*log(x^3 + 3) - 9*x^3*log(x^3 + 1) + 24*x^3*log(x) + 6)/x^3","A",0
157,1,40,0,1.208856," ","integrate(1/x^7/(x^6+4*x^3+3),x, algorithm=""fricas"")","\frac{x^{6} \log\left(x^{3} + 3\right) - 27 \, x^{6} \log\left(x^{3} + 1\right) + 78 \, x^{6} \log\left(x\right) + 24 \, x^{3} - 9}{162 \, x^{6}}"," ",0,"1/162*(x^6*log(x^3 + 3) - 27*x^6*log(x^3 + 1) + 78*x^6*log(x) + 24*x^3 - 9)/x^6","A",0
158,1,102,0,1.298880," ","integrate(x^10/(x^6+4*x^3+3),x, algorithm=""fricas"")","\frac{1}{5} \, x^{5} - 2 \, x^{2} + \frac{3}{2} \, \sqrt{3} \left(-9\right)^{\frac{1}{3}} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(2 \, \left(-9\right)^{\frac{1}{3}} x + 3\right)}\right) - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{3}{4} \, \left(-9\right)^{\frac{1}{3}} \log\left(3 \, x^{2} - \left(-9\right)^{\frac{2}{3}} x - 3 \, \left(-9\right)^{\frac{1}{3}}\right) + \frac{3}{2} \, \left(-9\right)^{\frac{1}{3}} \log\left(3 \, x + \left(-9\right)^{\frac{2}{3}}\right) - \frac{1}{12} \, \log\left(x^{2} - x + 1\right) + \frac{1}{6} \, \log\left(x + 1\right)"," ",0,"1/5*x^5 - 2*x^2 + 3/2*sqrt(3)*(-9)^(1/3)*arctan(1/9*sqrt(3)*(2*(-9)^(1/3)*x + 3)) - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 3/4*(-9)^(1/3)*log(3*x^2 - (-9)^(2/3)*x - 3*(-9)^(1/3)) + 3/2*(-9)^(1/3)*log(3*x + (-9)^(2/3)) - 1/12*log(x^2 - x + 1) + 1/6*log(x + 1)","A",0
159,1,90,0,1.116779," ","integrate(x^9/(x^6+4*x^3+3),x, algorithm=""fricas"")","\frac{1}{4} \, x^{4} + \frac{3}{2} \cdot 3^{\frac{5}{6}} \arctan\left(\frac{2}{3} \cdot 3^{\frac{1}{6}} x - \frac{1}{3} \, \sqrt{3}\right) - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{3}{4} \cdot 3^{\frac{1}{3}} \log\left(x^{2} - 3^{\frac{1}{3}} x + 3^{\frac{2}{3}}\right) + \frac{3}{2} \cdot 3^{\frac{1}{3}} \log\left(x + 3^{\frac{1}{3}}\right) - 4 \, x + \frac{1}{12} \, \log\left(x^{2} - x + 1\right) - \frac{1}{6} \, \log\left(x + 1\right)"," ",0,"1/4*x^4 + 3/2*3^(5/6)*arctan(2/3*3^(1/6)*x - 1/3*sqrt(3)) - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 3/4*3^(1/3)*log(x^2 - 3^(1/3)*x + 3^(2/3)) + 3/2*3^(1/3)*log(x + 3^(1/3)) - 4*x + 1/12*log(x^2 - x + 1) - 1/6*log(x + 1)","A",0
160,1,99,0,1.179558," ","integrate(x^7/(x^6+4*x^3+3),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} - \frac{1}{2} \cdot 9^{\frac{1}{3}} \sqrt{3} \arctan\left(\frac{2}{9} \cdot 9^{\frac{1}{3}} \sqrt{3} x - \frac{1}{3} \, \sqrt{3}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{1}{4} \cdot 9^{\frac{1}{3}} \log\left(3 \, x^{2} - 9^{\frac{2}{3}} x + 3 \cdot 9^{\frac{1}{3}}\right) + \frac{1}{2} \cdot 9^{\frac{1}{3}} \log\left(3 \, x + 9^{\frac{2}{3}}\right) + \frac{1}{12} \, \log\left(x^{2} - x + 1\right) - \frac{1}{6} \, \log\left(x + 1\right)"," ",0,"1/2*x^2 - 1/2*9^(1/3)*sqrt(3)*arctan(2/9*9^(1/3)*sqrt(3)*x - 1/3*sqrt(3)) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/4*9^(1/3)*log(3*x^2 - 9^(2/3)*x + 3*9^(1/3)) + 1/2*9^(1/3)*log(3*x + 9^(2/3)) + 1/12*log(x^2 - x + 1) - 1/6*log(x + 1)","A",0
161,1,88,0,1.506215," ","integrate(x^6/(x^6+4*x^3+3),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{3} \left(-3\right)^{\frac{1}{3}} \arctan\left(\frac{1}{9} \, \sqrt{3} {\left(2 \, \left(-3\right)^{\frac{2}{3}} x - 3\right)}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{1}{4} \, \left(-3\right)^{\frac{1}{3}} \log\left(x^{2} + \left(-3\right)^{\frac{1}{3}} x + \left(-3\right)^{\frac{2}{3}}\right) + \frac{1}{2} \, \left(-3\right)^{\frac{1}{3}} \log\left(x - \left(-3\right)^{\frac{1}{3}}\right) + x - \frac{1}{12} \, \log\left(x^{2} - x + 1\right) + \frac{1}{6} \, \log\left(x + 1\right)"," ",0,"1/2*sqrt(3)*(-3)^(1/3)*arctan(1/9*sqrt(3)*(2*(-3)^(2/3)*x - 3)) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/4*(-3)^(1/3)*log(x^2 + (-3)^(1/3)*x + (-3)^(2/3)) + 1/2*(-3)^(1/3)*log(x - (-3)^(1/3)) + x - 1/12*log(x^2 - x + 1) + 1/6*log(x + 1)","A",0
162,1,106,0,1.468391," ","integrate(x^4/(x^6+4*x^3+3),x, algorithm=""fricas"")","-\frac{1}{12} \cdot 3^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(-3^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} x + x^{2} - 3^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}}\right) + \frac{1}{6} \cdot 3^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(3^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} + x\right) - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{2} \cdot 3^{\frac{1}{6}} \left(-1\right)^{\frac{1}{3}} \arctan\left(\frac{1}{3} \cdot 3^{\frac{1}{6}} {\left(2 \, \left(-1\right)^{\frac{1}{3}} x + 3^{\frac{1}{3}}\right)}\right) - \frac{1}{12} \, \log\left(x^{2} - x + 1\right) + \frac{1}{6} \, \log\left(x + 1\right)"," ",0,"-1/12*3^(2/3)*(-1)^(1/3)*log(-3^(1/3)*(-1)^(2/3)*x + x^2 - 3^(2/3)*(-1)^(1/3)) + 1/6*3^(2/3)*(-1)^(1/3)*log(3^(1/3)*(-1)^(2/3) + x) - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/2*3^(1/6)*(-1)^(1/3)*arctan(1/3*3^(1/6)*(2*(-1)^(1/3)*x + 3^(1/3))) - 1/12*log(x^2 - x + 1) + 1/6*log(x + 1)","A",0
163,1,102,0,1.306321," ","integrate(x^3/(x^6+4*x^3+3),x, algorithm=""fricas"")","\frac{1}{6} \cdot 9^{\frac{1}{6}} \sqrt{3} \arctan\left(\frac{1}{27} \cdot 9^{\frac{1}{6}} {\left(2 \cdot 9^{\frac{2}{3}} \sqrt{3} x - 3 \cdot 9^{\frac{1}{3}} \sqrt{3}\right)}\right) - \frac{1}{36} \cdot 9^{\frac{2}{3}} \log\left(3 \, x^{2} - 9^{\frac{2}{3}} x + 3 \cdot 9^{\frac{1}{3}}\right) + \frac{1}{18} \cdot 9^{\frac{2}{3}} \log\left(3 \, x + 9^{\frac{2}{3}}\right) - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{12} \, \log\left(x^{2} - x + 1\right) - \frac{1}{6} \, \log\left(x + 1\right)"," ",0,"1/6*9^(1/6)*sqrt(3)*arctan(1/27*9^(1/6)*(2*9^(2/3)*sqrt(3)*x - 3*9^(1/3)*sqrt(3))) - 1/36*9^(2/3)*log(3*x^2 - 9^(2/3)*x + 3*9^(1/3)) + 1/18*9^(2/3)*log(3*x + 9^(2/3)) - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/12*log(x^2 - x + 1) - 1/6*log(x + 1)","A",0
164,1,84,0,1.018315," ","integrate(x/(x^6+4*x^3+3),x, algorithm=""fricas"")","-\frac{1}{36} \cdot 3^{\frac{2}{3}} \log\left(x^{2} - 3^{\frac{1}{3}} x + 3^{\frac{2}{3}}\right) + \frac{1}{18} \cdot 3^{\frac{2}{3}} \log\left(x + 3^{\frac{1}{3}}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{6} \cdot 3^{\frac{1}{6}} \arctan\left(-\frac{1}{3} \cdot 3^{\frac{1}{6}} {\left(2 \, x - 3^{\frac{1}{3}}\right)}\right) + \frac{1}{12} \, \log\left(x^{2} - x + 1\right) - \frac{1}{6} \, \log\left(x + 1\right)"," ",0,"-1/36*3^(2/3)*log(x^2 - 3^(1/3)*x + 3^(2/3)) + 1/18*3^(2/3)*log(x + 3^(1/3)) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/6*3^(1/6)*arctan(-1/3*3^(1/6)*(2*x - 3^(1/3))) + 1/12*log(x^2 - x + 1) - 1/6*log(x + 1)","A",0
165,1,124,0,1.418504," ","integrate(1/(x^6+4*x^3+3),x, algorithm=""fricas"")","\frac{1}{18} \cdot 9^{\frac{1}{6}} \sqrt{3} \left(-1\right)^{\frac{1}{3}} \arctan\left(\frac{1}{27} \cdot 9^{\frac{1}{6}} {\left(2 \cdot 9^{\frac{2}{3}} \sqrt{3} \left(-1\right)^{\frac{2}{3}} x - 3 \cdot 9^{\frac{1}{3}} \sqrt{3}\right)}\right) - \frac{1}{108} \cdot 9^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(9^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} x + 3 \, x^{2} + 3 \cdot 9^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}}\right) + \frac{1}{54} \cdot 9^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(-9^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} + 3 \, x\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{1}{12} \, \log\left(x^{2} - x + 1\right) + \frac{1}{6} \, \log\left(x + 1\right)"," ",0,"1/18*9^(1/6)*sqrt(3)*(-1)^(1/3)*arctan(1/27*9^(1/6)*(2*9^(2/3)*sqrt(3)*(-1)^(2/3)*x - 3*9^(1/3)*sqrt(3))) - 1/108*9^(2/3)*(-1)^(1/3)*log(9^(2/3)*(-1)^(1/3)*x + 3*x^2 + 3*9^(1/3)*(-1)^(2/3)) + 1/54*9^(2/3)*(-1)^(1/3)*log(-9^(2/3)*(-1)^(1/3) + 3*x) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/12*log(x^2 - x + 1) + 1/6*log(x + 1)","A",0
166,1,117,0,1.182276," ","integrate(1/x^2/(x^6+4*x^3+3),x, algorithm=""fricas"")","-\frac{3^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} x \log\left(-3^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} x + x^{2} - 3^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}}\right) - 2 \cdot 3^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} x \log\left(3^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} + x\right) + 18 \, \sqrt{3} x \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - 6 \cdot 3^{\frac{1}{6}} \left(-1\right)^{\frac{1}{3}} x \arctan\left(\frac{1}{3} \cdot 3^{\frac{1}{6}} {\left(2 \, \left(-1\right)^{\frac{1}{3}} x + 3^{\frac{1}{3}}\right)}\right) + 9 \, x \log\left(x^{2} - x + 1\right) - 18 \, x \log\left(x + 1\right) + 36}{108 \, x}"," ",0,"-1/108*(3^(2/3)*(-1)^(1/3)*x*log(-3^(1/3)*(-1)^(2/3)*x + x^2 - 3^(2/3)*(-1)^(1/3)) - 2*3^(2/3)*(-1)^(1/3)*x*log(3^(1/3)*(-1)^(2/3) + x) + 18*sqrt(3)*x*arctan(1/3*sqrt(3)*(2*x - 1)) - 6*3^(1/6)*(-1)^(1/3)*x*arctan(1/3*3^(1/6)*(2*(-1)^(1/3)*x + 3^(1/3))) + 9*x*log(x^2 - x + 1) - 18*x*log(x + 1) + 36)/x","A",0
167,1,126,0,1.161083," ","integrate(1/x^3/(x^6+4*x^3+3),x, algorithm=""fricas"")","\frac{6 \cdot 9^{\frac{1}{6}} \sqrt{3} x^{2} \arctan\left(\frac{1}{27} \cdot 9^{\frac{1}{6}} {\left(2 \cdot 9^{\frac{2}{3}} \sqrt{3} x - 3 \cdot 9^{\frac{1}{3}} \sqrt{3}\right)}\right) - 9^{\frac{2}{3}} x^{2} \log\left(3 \, x^{2} - 9^{\frac{2}{3}} x + 3 \cdot 9^{\frac{1}{3}}\right) + 2 \cdot 9^{\frac{2}{3}} x^{2} \log\left(3 \, x + 9^{\frac{2}{3}}\right) - 54 \, \sqrt{3} x^{2} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + 27 \, x^{2} \log\left(x^{2} - x + 1\right) - 54 \, x^{2} \log\left(x + 1\right) - 54}{324 \, x^{2}}"," ",0,"1/324*(6*9^(1/6)*sqrt(3)*x^2*arctan(1/27*9^(1/6)*(2*9^(2/3)*sqrt(3)*x - 3*9^(1/3)*sqrt(3))) - 9^(2/3)*x^2*log(3*x^2 - 9^(2/3)*x + 3*9^(1/3)) + 2*9^(2/3)*x^2*log(3*x + 9^(2/3)) - 54*sqrt(3)*x^2*arctan(1/3*sqrt(3)*(2*x - 1)) + 27*x^2*log(x^2 - x + 1) - 54*x^2*log(x + 1) - 54)/x^2","A",0
168,1,112,0,1.159675," ","integrate(1/x^5/(x^6+4*x^3+3),x, algorithm=""fricas"")","-\frac{3^{\frac{2}{3}} x^{4} \log\left(x^{2} - 3^{\frac{1}{3}} x + 3^{\frac{2}{3}}\right) - 2 \cdot 3^{\frac{2}{3}} x^{4} \log\left(x + 3^{\frac{1}{3}}\right) - 54 \, \sqrt{3} x^{4} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - 6 \cdot 3^{\frac{1}{6}} x^{4} \arctan\left(-\frac{1}{3} \cdot 3^{\frac{1}{6}} {\left(2 \, x - 3^{\frac{1}{3}}\right)}\right) - 27 \, x^{4} \log\left(x^{2} - x + 1\right) + 54 \, x^{4} \log\left(x + 1\right) - 144 \, x^{3} + 27}{324 \, x^{4}}"," ",0,"-1/324*(3^(2/3)*x^4*log(x^2 - 3^(1/3)*x + 3^(2/3)) - 2*3^(2/3)*x^4*log(x + 3^(1/3)) - 54*sqrt(3)*x^4*arctan(1/3*sqrt(3)*(2*x - 1)) - 6*3^(1/6)*x^4*arctan(-1/3*3^(1/6)*(2*x - 3^(1/3))) - 27*x^4*log(x^2 - x + 1) + 54*x^4*log(x + 1) - 144*x^3 + 27)/x^4","A",0
169,1,153,0,1.154543," ","integrate(1/x^6/(x^6+4*x^3+3),x, algorithm=""fricas"")","\frac{30 \cdot 9^{\frac{1}{6}} \sqrt{3} \left(-1\right)^{\frac{1}{3}} x^{5} \arctan\left(\frac{1}{27} \cdot 9^{\frac{1}{6}} {\left(2 \cdot 9^{\frac{2}{3}} \sqrt{3} \left(-1\right)^{\frac{2}{3}} x - 3 \cdot 9^{\frac{1}{3}} \sqrt{3}\right)}\right) - 5 \cdot 9^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} x^{5} \log\left(9^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} x + 3 \, x^{2} + 3 \cdot 9^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}}\right) + 10 \cdot 9^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} x^{5} \log\left(-9^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} + 3 \, x\right) + 810 \, \sqrt{3} x^{5} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - 405 \, x^{5} \log\left(x^{2} - x + 1\right) + 810 \, x^{5} \log\left(x + 1\right) + 1080 \, x^{3} - 324}{4860 \, x^{5}}"," ",0,"1/4860*(30*9^(1/6)*sqrt(3)*(-1)^(1/3)*x^5*arctan(1/27*9^(1/6)*(2*9^(2/3)*sqrt(3)*(-1)^(2/3)*x - 3*9^(1/3)*sqrt(3))) - 5*9^(2/3)*(-1)^(1/3)*x^5*log(9^(2/3)*(-1)^(1/3)*x + 3*x^2 + 3*9^(1/3)*(-1)^(2/3)) + 10*9^(2/3)*(-1)^(1/3)*x^5*log(-9^(2/3)*(-1)^(1/3) + 3*x) + 810*sqrt(3)*x^5*arctan(1/3*sqrt(3)*(2*x - 1)) - 405*x^5*log(x^2 - x + 1) + 810*x^5*log(x + 1) + 1080*x^3 - 324)/x^5","A",0
170,1,1028,0,1.381625," ","integrate(x^6/(x^6-x^3+1),x, algorithm=""fricas"")","\frac{1}{54} \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \log\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}\right) + \frac{2}{27} \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \arctan\left(-\frac{6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 18 \, {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} x - 24 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}} {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)}}{108 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2}\right)}}\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \frac{1}{27} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \arctan\left(\frac{6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} x + 24 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}} {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)}}{108 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2}\right)}}\right) + \frac{1}{27} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \arctan\left(\frac{18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \sqrt{-2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}} - 6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x + 216 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)}{216 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)}\right) - \frac{1}{108} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \log\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}\right) + \frac{1}{108} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \log\left(-2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}\right) + x"," ",0,"1/54*18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) - 2))*log(18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) - 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2) + 2/27*18^(2/3)*12^(1/6)*arctan(-1/108*(6*18^(1/3)*12^(5/6)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2)) - 108*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 108*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^2 - 18*(18^(1/3)*12^(5/6)*x - 24*cos(2/3*arctan(sqrt(3) - 2)))*sin(2/3*arctan(sqrt(3) - 2)) - sqrt(18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) - 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2)*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*cos(2/3*arctan(sqrt(3) - 2)) - 3*18^(1/3)*12^(5/6)*sqrt(2)*sin(2/3*arctan(sqrt(3) - 2))))/(cos(2/3*arctan(sqrt(3) - 2))^2 - 3*sin(2/3*arctan(sqrt(3) - 2))^2))*sin(2/3*arctan(sqrt(3) - 2)) - 1/27*(18^(2/3)*12^(1/6)*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2)) - 18^(2/3)*12^(1/6)*sin(2/3*arctan(sqrt(3) - 2)))*arctan(1/108*(6*18^(1/3)*12^(5/6)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2)) + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*(18^(1/3)*12^(5/6)*x + 24*cos(2/3*arctan(sqrt(3) - 2)))*sin(2/3*arctan(sqrt(3) - 2)) - sqrt(18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) + 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2)*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*cos(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(5/6)*sqrt(2)*sin(2/3*arctan(sqrt(3) - 2))))/(cos(2/3*arctan(sqrt(3) - 2))^2 - 3*sin(2/3*arctan(sqrt(3) - 2))^2)) + 1/27*(18^(2/3)*12^(1/6)*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2)) + 18^(2/3)*12^(1/6)*sin(2/3*arctan(sqrt(3) - 2)))*arctan(1/216*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*sqrt(-2*18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2) - 6*18^(1/3)*12^(5/6)*sqrt(3)*x + 216*sin(2/3*arctan(sqrt(3) - 2)))/cos(2/3*arctan(sqrt(3) - 2))) - 1/108*(18^(2/3)*12^(1/6)*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2)) + 18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) - 2)))*log(18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) + 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2) + 1/108*(18^(2/3)*12^(1/6)*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2)) - 18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) - 2)))*log(-2*18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2) + x","B",0
171,1,32,0,1.179782," ","integrate(x^5/(x^6-x^3+1),x, algorithm=""fricas"")","\frac{1}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{3} - 1\right)}\right) + \frac{1}{6} \, \log\left(x^{6} - x^{3} + 1\right)"," ",0,"1/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^3 - 1)) + 1/6*log(x^6 - x^3 + 1)","A",0
172,1,1583,0,1.730056," ","integrate(x^4/(x^6-x^3+1),x, algorithm=""fricas"")","\frac{1}{54} \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 36 \, x^{2}\right) + \frac{2}{27} \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \arctan\left(\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 864 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{3} - 6 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x - 36 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 12 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 72 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{3}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 36 \, x^{2}} {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 2 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)}}{108 \, {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 10 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4}\right)}}\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - \frac{1}{27} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \arctan\left(\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 864 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{3} - 6 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x - 36 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 12 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 72 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{3}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 36 \, x^{2}} {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)}}{108 \, {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 10 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4}\right)}}\right) - \frac{1}{27} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \arctan\left(-\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} x - 216 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 216 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 36 \, x^{2}}}{432 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)}\right) - \frac{1}{108} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 36 \, x^{2}\right) + \frac{1}{108} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 36 \, x^{2}\right)"," ",0,"1/54*18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) + 2))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) + 2))^4 - 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) + 2))^2 + 36*x^2) + 2/27*18^(2/3)*12^(1/6)*arctan(1/108*(6*18^(2/3)*12^(2/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2))^4 + 864*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2))^3 - 6*(18^(2/3)*12^(2/3)*sqrt(3)*x - 36*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^2)*sin(2/3*arctan(sqrt(3) + 2))^2 - 12*(18^(2/3)*12^(2/3)*x*cos(2/3*arctan(sqrt(3) + 2)) + 72*cos(2/3*arctan(sqrt(3) + 2))^3)*sin(2/3*arctan(sqrt(3) + 2)) - sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) + 2))^4 - 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) + 2))^2 + 36*x^2)*(18^(2/3)*12^(2/3)*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 18^(2/3)*12^(2/3)*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2))^2 - 2*18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2))))/(3*cos(2/3*arctan(sqrt(3) + 2))^4 - 10*cos(2/3*arctan(sqrt(3) + 2))^2*sin(2/3*arctan(sqrt(3) + 2))^2 + 3*sin(2/3*arctan(sqrt(3) + 2))^4))*sin(2/3*arctan(sqrt(3) + 2)) - 1/27*(18^(2/3)*12^(1/6)*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2)) - 18^(2/3)*12^(1/6)*sin(2/3*arctan(sqrt(3) + 2)))*arctan(1/108*(6*18^(2/3)*12^(2/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2))^4 - 864*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2))^3 - 6*(18^(2/3)*12^(2/3)*sqrt(3)*x - 36*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^2)*sin(2/3*arctan(sqrt(3) + 2))^2 + 12*(18^(2/3)*12^(2/3)*x*cos(2/3*arctan(sqrt(3) + 2)) + 72*cos(2/3*arctan(sqrt(3) + 2))^3)*sin(2/3*arctan(sqrt(3) + 2)) - sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) + 2))^4 + 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) + 2))^2 + 36*x^2)*(18^(2/3)*12^(2/3)*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 18^(2/3)*12^(2/3)*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 2*18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2))))/(3*cos(2/3*arctan(sqrt(3) + 2))^4 - 10*cos(2/3*arctan(sqrt(3) + 2))^2*sin(2/3*arctan(sqrt(3) + 2))^2 + 3*sin(2/3*arctan(sqrt(3) + 2))^4)) - 1/27*(18^(2/3)*12^(1/6)*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2)) + 18^(2/3)*12^(1/6)*sin(2/3*arctan(sqrt(3) + 2)))*arctan(-1/432*(6*18^(2/3)*12^(2/3)*x - 216*cos(2/3*arctan(sqrt(3) + 2))^2 + 216*sin(2/3*arctan(sqrt(3) + 2))^2 - 18^(2/3)*12^(2/3)*sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) + 2))^4 - 12*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 6*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) + 2))^2 + 36*x^2))/(cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2)))) - 1/108*(18^(2/3)*12^(1/6)*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2)) + 18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) + 2)))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) + 2))^4 + 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) + 2))^2 + 36*x^2) + 1/108*(18^(2/3)*12^(1/6)*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2)) - 18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) + 2)))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) + 2))^4 - 12*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 6*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) + 2))^2 + 36*x^2)","B",0
173,1,1031,0,1.425431," ","integrate(x^3/(x^6-x^3+1),x, algorithm=""fricas"")","\frac{1}{54} \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \log\left(2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}\right) + \frac{2}{27} \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \arctan\left(\frac{18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \sqrt{2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}} - 6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x - 216 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)}{216 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)}\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - \frac{1}{27} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \arctan\left(-\frac{6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 18 \, {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} x + 24 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - \sqrt{-18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}} {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)}}{108 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2}\right)}}\right) - \frac{1}{27} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \arctan\left(\frac{6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} x - 24 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - \sqrt{-18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}} {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)}}{108 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2}\right)}}\right) - \frac{1}{108} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \log\left(-18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}\right) + \frac{1}{108} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \log\left(-18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}\right)"," ",0,"1/54*18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) + 2))*log(2*18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2) + 2/27*18^(2/3)*12^(1/6)*arctan(1/216*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*sqrt(2*18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2) - 6*18^(1/3)*12^(5/6)*sqrt(3)*x - 216*sin(2/3*arctan(sqrt(3) + 2)))/cos(2/3*arctan(sqrt(3) + 2)))*sin(2/3*arctan(sqrt(3) + 2)) - 1/27*(18^(2/3)*12^(1/6)*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2)) - 18^(2/3)*12^(1/6)*sin(2/3*arctan(sqrt(3) + 2)))*arctan(-1/108*(6*18^(1/3)*12^(5/6)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2)) + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2))^2 - 18*(18^(1/3)*12^(5/6)*x + 24*cos(2/3*arctan(sqrt(3) + 2)))*sin(2/3*arctan(sqrt(3) + 2)) - sqrt(-18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) + 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2)*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*cos(2/3*arctan(sqrt(3) + 2)) - 3*18^(1/3)*12^(5/6)*sqrt(2)*sin(2/3*arctan(sqrt(3) + 2))))/(cos(2/3*arctan(sqrt(3) + 2))^2 - 3*sin(2/3*arctan(sqrt(3) + 2))^2)) - 1/27*(18^(2/3)*12^(1/6)*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2)) + 18^(2/3)*12^(1/6)*sin(2/3*arctan(sqrt(3) + 2)))*arctan(1/108*(6*18^(1/3)*12^(5/6)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2)) - 108*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 108*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*(18^(1/3)*12^(5/6)*x - 24*cos(2/3*arctan(sqrt(3) + 2)))*sin(2/3*arctan(sqrt(3) + 2)) - sqrt(-18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) - 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2)*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*cos(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(5/6)*sqrt(2)*sin(2/3*arctan(sqrt(3) + 2))))/(cos(2/3*arctan(sqrt(3) + 2))^2 - 3*sin(2/3*arctan(sqrt(3) + 2))^2)) - 1/108*(18^(2/3)*12^(1/6)*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2)) + 18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) + 2)))*log(-18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) + 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2) + 1/108*(18^(2/3)*12^(1/6)*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2)) - 18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) + 2)))*log(-18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) - 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2)","B",0
174,1,18,0,1.127716," ","integrate(x^2/(x^6-x^3+1),x, algorithm=""fricas"")","\frac{2}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{3} - 1\right)}\right)"," ",0,"2/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^3 - 1))","A",0
175,1,1583,0,1.498046," ","integrate(x/(x^6-x^3+1),x, algorithm=""fricas"")","\frac{1}{54} \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}\right) - \frac{2}{27} \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \arctan\left(\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 864 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{3} - 6 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x - 36 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 12 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 72 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{3}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}} {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)}}{108 \, {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 10 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4}\right)}}\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \frac{1}{27} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \arctan\left(\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 864 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{3} - 6 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x - 36 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 12 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 72 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{3}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}} {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 2 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)}}{108 \, {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 10 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4}\right)}}\right) + \frac{1}{27} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \arctan\left(-\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} x - 216 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 216 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}}}{432 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)}\right) + \frac{1}{108} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}\right) - \frac{1}{108} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}\right)"," ",0,"1/54*18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) - 2))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 + 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2) - 2/27*18^(2/3)*12^(1/6)*arctan(1/108*(6*18^(2/3)*12^(2/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^4 - 864*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2))^3 - 6*(18^(2/3)*12^(2/3)*sqrt(3)*x - 36*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2)*sin(2/3*arctan(sqrt(3) - 2))^2 + 12*(18^(2/3)*12^(2/3)*x*cos(2/3*arctan(sqrt(3) - 2)) + 72*cos(2/3*arctan(sqrt(3) - 2))^3)*sin(2/3*arctan(sqrt(3) - 2)) - sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 + 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2)*(18^(2/3)*12^(2/3)*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 18^(2/3)*12^(2/3)*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 2*18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2))))/(3*cos(2/3*arctan(sqrt(3) - 2))^4 - 10*cos(2/3*arctan(sqrt(3) - 2))^2*sin(2/3*arctan(sqrt(3) - 2))^2 + 3*sin(2/3*arctan(sqrt(3) - 2))^4))*sin(2/3*arctan(sqrt(3) - 2)) - 1/27*(18^(2/3)*12^(1/6)*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2)) + 18^(2/3)*12^(1/6)*sin(2/3*arctan(sqrt(3) - 2)))*arctan(1/108*(6*18^(2/3)*12^(2/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^4 + 864*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2))^3 - 6*(18^(2/3)*12^(2/3)*sqrt(3)*x - 36*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2)*sin(2/3*arctan(sqrt(3) - 2))^2 - 12*(18^(2/3)*12^(2/3)*x*cos(2/3*arctan(sqrt(3) - 2)) + 72*cos(2/3*arctan(sqrt(3) - 2))^3)*sin(2/3*arctan(sqrt(3) - 2)) - sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 - 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2)*(18^(2/3)*12^(2/3)*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 18^(2/3)*12^(2/3)*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^2 - 2*18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2))))/(3*cos(2/3*arctan(sqrt(3) - 2))^4 - 10*cos(2/3*arctan(sqrt(3) - 2))^2*sin(2/3*arctan(sqrt(3) - 2))^2 + 3*sin(2/3*arctan(sqrt(3) - 2))^4)) + 1/27*(18^(2/3)*12^(1/6)*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2)) - 18^(2/3)*12^(1/6)*sin(2/3*arctan(sqrt(3) - 2)))*arctan(-1/432*(6*18^(2/3)*12^(2/3)*x - 216*cos(2/3*arctan(sqrt(3) - 2))^2 + 216*sin(2/3*arctan(sqrt(3) - 2))^2 - 18^(2/3)*12^(2/3)*sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 - 12*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 6*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2))/(cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2)))) + 1/108*(18^(2/3)*12^(1/6)*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2)) - 18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) - 2)))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 - 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2) - 1/108*(18^(2/3)*12^(1/6)*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2)) + 18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) - 2)))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 - 12*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 6*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2)","B",0
176,1,1027,0,1.292187," ","integrate(1/(x^6-x^3+1),x, algorithm=""fricas"")","\frac{1}{54} \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \log\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}\right) - \frac{2}{27} \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \arctan\left(\frac{6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} x + 24 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}} {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)}}{108 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2}\right)}}\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \frac{1}{27} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \arctan\left(-\frac{6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 18 \, {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} x - 24 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}} {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)}}{108 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2}\right)}}\right) - \frac{1}{27} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \arctan\left(\frac{18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \sqrt{-2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}} - 6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x + 216 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)}{216 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)}\right) + \frac{1}{108} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \log\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}\right) - \frac{1}{108} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \log\left(-2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}\right)"," ",0,"1/54*18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) - 2))*log(18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) + 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2) - 2/27*18^(2/3)*12^(1/6)*arctan(1/108*(6*18^(1/3)*12^(5/6)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2)) + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*(18^(1/3)*12^(5/6)*x + 24*cos(2/3*arctan(sqrt(3) - 2)))*sin(2/3*arctan(sqrt(3) - 2)) - sqrt(18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) + 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2)*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*cos(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(5/6)*sqrt(2)*sin(2/3*arctan(sqrt(3) - 2))))/(cos(2/3*arctan(sqrt(3) - 2))^2 - 3*sin(2/3*arctan(sqrt(3) - 2))^2))*sin(2/3*arctan(sqrt(3) - 2)) - 1/27*(18^(2/3)*12^(1/6)*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2)) + 18^(2/3)*12^(1/6)*sin(2/3*arctan(sqrt(3) - 2)))*arctan(-1/108*(6*18^(1/3)*12^(5/6)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2)) - 108*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 108*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^2 - 18*(18^(1/3)*12^(5/6)*x - 24*cos(2/3*arctan(sqrt(3) - 2)))*sin(2/3*arctan(sqrt(3) - 2)) - sqrt(18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) - 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2)*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*cos(2/3*arctan(sqrt(3) - 2)) - 3*18^(1/3)*12^(5/6)*sqrt(2)*sin(2/3*arctan(sqrt(3) - 2))))/(cos(2/3*arctan(sqrt(3) - 2))^2 - 3*sin(2/3*arctan(sqrt(3) - 2))^2)) - 1/27*(18^(2/3)*12^(1/6)*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2)) - 18^(2/3)*12^(1/6)*sin(2/3*arctan(sqrt(3) - 2)))*arctan(1/216*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*sqrt(-2*18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2) - 6*18^(1/3)*12^(5/6)*sqrt(3)*x + 216*sin(2/3*arctan(sqrt(3) - 2)))/cos(2/3*arctan(sqrt(3) - 2))) + 1/108*(18^(2/3)*12^(1/6)*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2)) - 18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) - 2)))*log(18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) - 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2) - 1/108*(18^(2/3)*12^(1/6)*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2)) + 18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) - 2)))*log(-2*18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2)","B",0
177,1,34,0,1.230010," ","integrate(1/x/(x^6-x^3+1),x, algorithm=""fricas"")","\frac{1}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{3} - 1\right)}\right) - \frac{1}{6} \, \log\left(x^{6} - x^{3} + 1\right) + \log\left(x\right)"," ",0,"1/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^3 - 1)) - 1/6*log(x^6 - x^3 + 1) + log(x)","A",0
178,1,1598,0,1.650116," ","integrate(1/x^2/(x^6-x^3+1),x, algorithm=""fricas"")","\frac{2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 36 \, x^{2}\right) + 8 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \arctan\left(-\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} x - 216 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 216 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 36 \, x^{2}}}{432 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)}\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 4 \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \arctan\left(\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 864 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{3} - 6 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x - 36 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 12 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 72 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{3}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 36 \, x^{2}} {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 2 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)}}{108 \, {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 10 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4}\right)}}\right) + 4 \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \arctan\left(\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 864 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{3} - 6 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x - 36 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 12 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 72 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{3}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 36 \, x^{2}} {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)}}{108 \, {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 10 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4}\right)}}\right) + {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 36 \, x^{2}\right) - {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 36 \, x^{2}\right) - 108}{108 \, x}"," ",0,"1/108*(2*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) + 2))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) + 2))^4 - 12*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 6*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) + 2))^2 + 36*x^2) + 8*18^(2/3)*12^(1/6)*x*arctan(-1/432*(6*18^(2/3)*12^(2/3)*x - 216*cos(2/3*arctan(sqrt(3) + 2))^2 + 216*sin(2/3*arctan(sqrt(3) + 2))^2 - 18^(2/3)*12^(2/3)*sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) + 2))^4 - 12*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 6*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) + 2))^2 + 36*x^2))/(cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2))))*sin(2/3*arctan(sqrt(3) + 2)) + 4*(18^(2/3)*12^(1/6)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2)) - 18^(2/3)*12^(1/6)*x*sin(2/3*arctan(sqrt(3) + 2)))*arctan(1/108*(6*18^(2/3)*12^(2/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2))^4 + 864*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2))^3 - 6*(18^(2/3)*12^(2/3)*sqrt(3)*x - 36*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^2)*sin(2/3*arctan(sqrt(3) + 2))^2 - 12*(18^(2/3)*12^(2/3)*x*cos(2/3*arctan(sqrt(3) + 2)) + 72*cos(2/3*arctan(sqrt(3) + 2))^3)*sin(2/3*arctan(sqrt(3) + 2)) - sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) + 2))^4 - 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) + 2))^2 + 36*x^2)*(18^(2/3)*12^(2/3)*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 18^(2/3)*12^(2/3)*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2))^2 - 2*18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2))))/(3*cos(2/3*arctan(sqrt(3) + 2))^4 - 10*cos(2/3*arctan(sqrt(3) + 2))^2*sin(2/3*arctan(sqrt(3) + 2))^2 + 3*sin(2/3*arctan(sqrt(3) + 2))^4)) + 4*(18^(2/3)*12^(1/6)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2)) + 18^(2/3)*12^(1/6)*x*sin(2/3*arctan(sqrt(3) + 2)))*arctan(1/108*(6*18^(2/3)*12^(2/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2))^4 - 864*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2))^3 - 6*(18^(2/3)*12^(2/3)*sqrt(3)*x - 36*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^2)*sin(2/3*arctan(sqrt(3) + 2))^2 + 12*(18^(2/3)*12^(2/3)*x*cos(2/3*arctan(sqrt(3) + 2)) + 72*cos(2/3*arctan(sqrt(3) + 2))^3)*sin(2/3*arctan(sqrt(3) + 2)) - sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) + 2))^4 + 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) + 2))^2 + 36*x^2)*(18^(2/3)*12^(2/3)*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 18^(2/3)*12^(2/3)*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 2*18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2))))/(3*cos(2/3*arctan(sqrt(3) + 2))^4 - 10*cos(2/3*arctan(sqrt(3) + 2))^2*sin(2/3*arctan(sqrt(3) + 2))^2 + 3*sin(2/3*arctan(sqrt(3) + 2))^4)) + (18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) - 18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) + 2)))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) + 2))^4 + 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) + 2))^2 + 36*x^2) - (18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) + 18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) + 2)))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) + 2))^4 - 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) + 2))^2 + 36*x^2) - 108)/x","B",0
179,1,1066,0,1.446119," ","integrate(1/x^3/(x^6-x^3+1),x, algorithm=""fricas"")","\frac{2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \log\left(-18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}\right) - 8 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x^{2} \arctan\left(-\frac{6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 18 \, {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} x + 24 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - \sqrt{-18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}} {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)}}{108 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2}\right)}}\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 4 \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} x^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \arctan\left(\frac{6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} x - 24 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - \sqrt{-18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}} {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)}}{108 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2}\right)}}\right) - 4 \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} x^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \arctan\left(\frac{18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \sqrt{2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}} - 6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x - 216 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)}{216 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)}\right) + {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} x^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \log\left(2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}\right) - {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} x^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \log\left(-18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}\right) - 54}{108 \, x^{2}}"," ",0,"1/108*(2*18^(2/3)*12^(1/6)*x^2*cos(2/3*arctan(sqrt(3) + 2))*log(-18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) + 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2) - 8*18^(2/3)*12^(1/6)*x^2*arctan(-1/108*(6*18^(1/3)*12^(5/6)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2)) + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2))^2 - 18*(18^(1/3)*12^(5/6)*x + 24*cos(2/3*arctan(sqrt(3) + 2)))*sin(2/3*arctan(sqrt(3) + 2)) - sqrt(-18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) + 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2)*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*cos(2/3*arctan(sqrt(3) + 2)) - 3*18^(1/3)*12^(5/6)*sqrt(2)*sin(2/3*arctan(sqrt(3) + 2))))/(cos(2/3*arctan(sqrt(3) + 2))^2 - 3*sin(2/3*arctan(sqrt(3) + 2))^2))*sin(2/3*arctan(sqrt(3) + 2)) + 4*(18^(2/3)*12^(1/6)*sqrt(3)*x^2*cos(2/3*arctan(sqrt(3) + 2)) - 18^(2/3)*12^(1/6)*x^2*sin(2/3*arctan(sqrt(3) + 2)))*arctan(1/108*(6*18^(1/3)*12^(5/6)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2)) - 108*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 108*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*(18^(1/3)*12^(5/6)*x - 24*cos(2/3*arctan(sqrt(3) + 2)))*sin(2/3*arctan(sqrt(3) + 2)) - sqrt(-18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) - 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2)*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*cos(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(5/6)*sqrt(2)*sin(2/3*arctan(sqrt(3) + 2))))/(cos(2/3*arctan(sqrt(3) + 2))^2 - 3*sin(2/3*arctan(sqrt(3) + 2))^2)) - 4*(18^(2/3)*12^(1/6)*sqrt(3)*x^2*cos(2/3*arctan(sqrt(3) + 2)) + 18^(2/3)*12^(1/6)*x^2*sin(2/3*arctan(sqrt(3) + 2)))*arctan(1/216*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*sqrt(2*18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2) - 6*18^(1/3)*12^(5/6)*sqrt(3)*x - 216*sin(2/3*arctan(sqrt(3) + 2)))/cos(2/3*arctan(sqrt(3) + 2))) + (18^(2/3)*12^(1/6)*sqrt(3)*x^2*sin(2/3*arctan(sqrt(3) + 2)) - 18^(2/3)*12^(1/6)*x^2*cos(2/3*arctan(sqrt(3) + 2)))*log(2*18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2) - (18^(2/3)*12^(1/6)*sqrt(3)*x^2*sin(2/3*arctan(sqrt(3) + 2)) + 18^(2/3)*12^(1/6)*x^2*cos(2/3*arctan(sqrt(3) + 2)))*log(-18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) - 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2) - 54)/x^2","B",0
180,1,51,0,1.173249," ","integrate(1/x^4/(x^6-x^3+1),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} x^{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{3} - 1\right)}\right) + 3 \, x^{3} \log\left(x^{6} - x^{3} + 1\right) - 18 \, x^{3} \log\left(x\right) + 6}{18 \, x^{3}}"," ",0,"-1/18*(2*sqrt(3)*x^3*arctan(1/3*sqrt(3)*(2*x^3 - 1)) + 3*x^3*log(x^6 - x^3 + 1) - 18*x^3*log(x) + 6)/x^3","A",0
181,1,1623,0,1.620242," ","integrate(1/x^5/(x^6-x^3+1),x, algorithm=""fricas"")","\frac{2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x^{4} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}\right) + 8 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x^{4} \arctan\left(\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 864 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{3} - 6 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x - 36 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 12 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 72 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{3}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}} {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 2 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)}}{108 \, {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 10 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4}\right)}}\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 108 \, x^{3} - 4 \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x^{4} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} x^{4} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \arctan\left(\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 864 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{3} - 6 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x - 36 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 12 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 72 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{3}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}} {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)}}{108 \, {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 10 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4}\right)}}\right) - 4 \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x^{4} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} x^{4} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \arctan\left(-\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} x - 216 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 216 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}}}{432 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)}\right) - {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x^{4} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} x^{4} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}\right) + {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x^{4} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} x^{4} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}\right) - 27}{108 \, x^{4}}"," ",0,"1/108*(2*18^(2/3)*12^(1/6)*x^4*cos(2/3*arctan(sqrt(3) - 2))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 - 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2) + 8*18^(2/3)*12^(1/6)*x^4*arctan(1/108*(6*18^(2/3)*12^(2/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^4 + 864*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2))^3 - 6*(18^(2/3)*12^(2/3)*sqrt(3)*x - 36*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2)*sin(2/3*arctan(sqrt(3) - 2))^2 - 12*(18^(2/3)*12^(2/3)*x*cos(2/3*arctan(sqrt(3) - 2)) + 72*cos(2/3*arctan(sqrt(3) - 2))^3)*sin(2/3*arctan(sqrt(3) - 2)) - sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 - 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2)*(18^(2/3)*12^(2/3)*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 18^(2/3)*12^(2/3)*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^2 - 2*18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2))))/(3*cos(2/3*arctan(sqrt(3) - 2))^4 - 10*cos(2/3*arctan(sqrt(3) - 2))^2*sin(2/3*arctan(sqrt(3) - 2))^2 + 3*sin(2/3*arctan(sqrt(3) - 2))^4))*sin(2/3*arctan(sqrt(3) - 2)) - 108*x^3 - 4*(18^(2/3)*12^(1/6)*sqrt(3)*x^4*cos(2/3*arctan(sqrt(3) - 2)) - 18^(2/3)*12^(1/6)*x^4*sin(2/3*arctan(sqrt(3) - 2)))*arctan(1/108*(6*18^(2/3)*12^(2/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^4 - 864*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2))^3 - 6*(18^(2/3)*12^(2/3)*sqrt(3)*x - 36*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2)*sin(2/3*arctan(sqrt(3) - 2))^2 + 12*(18^(2/3)*12^(2/3)*x*cos(2/3*arctan(sqrt(3) - 2)) + 72*cos(2/3*arctan(sqrt(3) - 2))^3)*sin(2/3*arctan(sqrt(3) - 2)) - sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 + 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2)*(18^(2/3)*12^(2/3)*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 18^(2/3)*12^(2/3)*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 2*18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2))))/(3*cos(2/3*arctan(sqrt(3) - 2))^4 - 10*cos(2/3*arctan(sqrt(3) - 2))^2*sin(2/3*arctan(sqrt(3) - 2))^2 + 3*sin(2/3*arctan(sqrt(3) - 2))^4)) - 4*(18^(2/3)*12^(1/6)*sqrt(3)*x^4*cos(2/3*arctan(sqrt(3) - 2)) + 18^(2/3)*12^(1/6)*x^4*sin(2/3*arctan(sqrt(3) - 2)))*arctan(-1/432*(6*18^(2/3)*12^(2/3)*x - 216*cos(2/3*arctan(sqrt(3) - 2))^2 + 216*sin(2/3*arctan(sqrt(3) - 2))^2 - 18^(2/3)*12^(2/3)*sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 - 12*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 6*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2))/(cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2)))) - (18^(2/3)*12^(1/6)*sqrt(3)*x^4*sin(2/3*arctan(sqrt(3) - 2)) + 18^(2/3)*12^(1/6)*x^4*cos(2/3*arctan(sqrt(3) - 2)))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 + 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2) + (18^(2/3)*12^(1/6)*sqrt(3)*x^4*sin(2/3*arctan(sqrt(3) - 2)) - 18^(2/3)*12^(1/6)*x^4*cos(2/3*arctan(sqrt(3) - 2)))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 - 12*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 6*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2) - 27)/x^4","B",0
182,1,1996,0,3.213365," ","integrate(1/(x^6+x^3+2),x, algorithm=""fricas"")","\frac{1}{294} \cdot 112^{\frac{1}{6}} 49^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) \log\left(112^{\frac{1}{6}} 49^{\frac{2}{3}} \sqrt{7} x \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) + 7 \cdot 112^{\frac{1}{6}} 49^{\frac{2}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) + 14 \cdot 49^{\frac{1}{3}} 14^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} + 14 \cdot 49^{\frac{1}{3}} 14^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} + 98 \, x^{2}\right) - \frac{2}{147} \cdot 112^{\frac{1}{6}} 49^{\frac{2}{3}} \arctan\left(\frac{14 \cdot 112^{\frac{5}{6}} 49^{\frac{1}{3}} \sqrt{7} x \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) + 2744 \, \sqrt{7} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} + 2744 \, \sqrt{7} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} + 98 \, {\left(112^{\frac{5}{6}} 49^{\frac{1}{3}} x + 224 \, \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) - \sqrt{112^{\frac{1}{6}} 49^{\frac{2}{3}} \sqrt{7} x \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) + 7 \cdot 112^{\frac{1}{6}} 49^{\frac{2}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) + 14 \cdot 49^{\frac{1}{3}} 14^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} + 14 \cdot 49^{\frac{1}{3}} 14^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} + 98 \, x^{2}} {\left(112^{\frac{5}{6}} 49^{\frac{1}{3}} \sqrt{7} \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) + 7 \cdot 112^{\frac{5}{6}} 49^{\frac{1}{3}} \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)\right)}}{2744 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} - 7 \, \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2}\right)}}\right) \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) + \frac{1}{147} \, {\left(112^{\frac{1}{6}} 49^{\frac{2}{3}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) + 112^{\frac{1}{6}} 49^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)\right)} \arctan\left(\frac{70 \cdot 112^{\frac{5}{6}} 49^{\frac{1}{3}} {\left(\sqrt{7} x + 7 \, \sqrt{3} x\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{3} - 27440 \, {\left(\sqrt{7} + 2 \, \sqrt{3}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{4} - 5488 \, {\left(\sqrt{7} - 2 \, \sqrt{3}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{4} - 14 \, {\left(112^{\frac{5}{6}} 49^{\frac{1}{3}} {\left(\sqrt{7} \sqrt{3} x - 7 \, x\right)} - 1568 \, {\left(\sqrt{7} \sqrt{3} - 5\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{3} + 14 \, {\left(112^{\frac{5}{6}} 49^{\frac{1}{3}} {\left(13 \, \sqrt{7} x - 21 \, \sqrt{3} x\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) - 784 \, {\left(3 \, \sqrt{7} + 4 \, \sqrt{3}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} - 14 \, {\left(112^{\frac{5}{6}} 49^{\frac{1}{3}} {\left(9 \, \sqrt{7} \sqrt{3} x + 49 \, x\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} - 1568 \, {\left(\sqrt{7} \sqrt{3} + 11\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{3}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) - {\left(5 \cdot 112^{\frac{5}{6}} 49^{\frac{1}{3}} {\left(\sqrt{7} + 7 \, \sqrt{3}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{3} - 112^{\frac{5}{6}} 49^{\frac{1}{3}} {\left(9 \, \sqrt{7} \sqrt{3} + 49\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) + 112^{\frac{5}{6}} 49^{\frac{1}{3}} {\left(13 \, \sqrt{7} - 21 \, \sqrt{3}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} - 112^{\frac{5}{6}} 49^{\frac{1}{3}} {\left(\sqrt{7} \sqrt{3} - 7\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{3}\right)} \sqrt{-112^{\frac{1}{6}} 49^{\frac{2}{3}} {\left(\sqrt{7} \sqrt{3} x + 7 \, x\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) - 112^{\frac{1}{6}} 49^{\frac{2}{3}} {\left(\sqrt{7} x - 7 \, \sqrt{3} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) + 28 \cdot 49^{\frac{1}{3}} 14^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} + 28 \cdot 49^{\frac{1}{3}} 14^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} + 196 \, x^{2}}}{5488 \, {\left(25 \, \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{4} - 38 \, \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{4}\right)}}\right) + \frac{1}{147} \, {\left(112^{\frac{1}{6}} 49^{\frac{2}{3}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) - 112^{\frac{1}{6}} 49^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)\right)} \arctan\left(-\frac{70 \cdot 112^{\frac{5}{6}} 49^{\frac{1}{3}} {\left(\sqrt{7} x - 7 \, \sqrt{3} x\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{3} - 27440 \, {\left(\sqrt{7} - 2 \, \sqrt{3}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{4} - 5488 \, {\left(\sqrt{7} + 2 \, \sqrt{3}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{4} + 14 \, {\left(112^{\frac{5}{6}} 49^{\frac{1}{3}} {\left(\sqrt{7} \sqrt{3} x + 7 \, x\right)} - 1568 \, {\left(\sqrt{7} \sqrt{3} + 5\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{3} + 14 \, {\left(112^{\frac{5}{6}} 49^{\frac{1}{3}} {\left(13 \, \sqrt{7} x + 21 \, \sqrt{3} x\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) - 784 \, {\left(3 \, \sqrt{7} - 4 \, \sqrt{3}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} + 14 \, {\left(112^{\frac{5}{6}} 49^{\frac{1}{3}} {\left(9 \, \sqrt{7} \sqrt{3} x - 49 \, x\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} - 1568 \, {\left(\sqrt{7} \sqrt{3} - 11\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{3}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) - {\left(5 \cdot 112^{\frac{5}{6}} 49^{\frac{1}{3}} {\left(\sqrt{7} - 7 \, \sqrt{3}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{3} + 112^{\frac{5}{6}} 49^{\frac{1}{3}} {\left(9 \, \sqrt{7} \sqrt{3} - 49\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) + 112^{\frac{5}{6}} 49^{\frac{1}{3}} {\left(13 \, \sqrt{7} + 21 \, \sqrt{3}\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} + 112^{\frac{5}{6}} 49^{\frac{1}{3}} {\left(\sqrt{7} \sqrt{3} + 7\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{3}\right)} \sqrt{112^{\frac{1}{6}} 49^{\frac{2}{3}} {\left(\sqrt{7} \sqrt{3} x - 7 \, x\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) - 112^{\frac{1}{6}} 49^{\frac{2}{3}} {\left(\sqrt{7} x + 7 \, \sqrt{3} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) + 28 \cdot 49^{\frac{1}{3}} 14^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} + 28 \cdot 49^{\frac{1}{3}} 14^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} + 196 \, x^{2}}}{5488 \, {\left(25 \, \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{4} - 38 \, \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{4}\right)}}\right) + \frac{1}{588} \, {\left(112^{\frac{1}{6}} 49^{\frac{2}{3}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) - 112^{\frac{1}{6}} 49^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)\right)} \log\left(-112^{\frac{1}{6}} 49^{\frac{2}{3}} {\left(\sqrt{7} \sqrt{3} x + 7 \, x\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) - 112^{\frac{1}{6}} 49^{\frac{2}{3}} {\left(\sqrt{7} x - 7 \, \sqrt{3} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) + 28 \cdot 49^{\frac{1}{3}} 14^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} + 28 \cdot 49^{\frac{1}{3}} 14^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} + 196 \, x^{2}\right) - \frac{1}{588} \, {\left(112^{\frac{1}{6}} 49^{\frac{2}{3}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) + 112^{\frac{1}{6}} 49^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)\right)} \log\left(112^{\frac{1}{6}} 49^{\frac{2}{3}} {\left(\sqrt{7} \sqrt{3} x - 7 \, x\right)} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) - 112^{\frac{1}{6}} 49^{\frac{2}{3}} {\left(\sqrt{7} x + 7 \, \sqrt{3} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right) + 28 \cdot 49^{\frac{1}{3}} 14^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} + 28 \cdot 49^{\frac{1}{3}} 14^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{1}{3} \, \sqrt{7} + \frac{4}{3}\right)\right)^{2} + 196 \, x^{2}\right)"," ",0,"1/294*112^(1/6)*49^(2/3)*cos(2/3*arctan(1/3*sqrt(7) + 4/3))*log(112^(1/6)*49^(2/3)*sqrt(7)*x*sin(2/3*arctan(1/3*sqrt(7) + 4/3)) + 7*112^(1/6)*49^(2/3)*x*cos(2/3*arctan(1/3*sqrt(7) + 4/3)) + 14*49^(1/3)*14^(1/3)*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^2 + 14*49^(1/3)*14^(1/3)*sin(2/3*arctan(1/3*sqrt(7) + 4/3))^2 + 98*x^2) - 2/147*112^(1/6)*49^(2/3)*arctan(1/2744*(14*112^(5/6)*49^(1/3)*sqrt(7)*x*cos(2/3*arctan(1/3*sqrt(7) + 4/3)) + 2744*sqrt(7)*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^2 + 2744*sqrt(7)*sin(2/3*arctan(1/3*sqrt(7) + 4/3))^2 + 98*(112^(5/6)*49^(1/3)*x + 224*cos(2/3*arctan(1/3*sqrt(7) + 4/3)))*sin(2/3*arctan(1/3*sqrt(7) + 4/3)) - sqrt(112^(1/6)*49^(2/3)*sqrt(7)*x*sin(2/3*arctan(1/3*sqrt(7) + 4/3)) + 7*112^(1/6)*49^(2/3)*x*cos(2/3*arctan(1/3*sqrt(7) + 4/3)) + 14*49^(1/3)*14^(1/3)*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^2 + 14*49^(1/3)*14^(1/3)*sin(2/3*arctan(1/3*sqrt(7) + 4/3))^2 + 98*x^2)*(112^(5/6)*49^(1/3)*sqrt(7)*sqrt(2)*cos(2/3*arctan(1/3*sqrt(7) + 4/3)) + 7*112^(5/6)*49^(1/3)*sqrt(2)*sin(2/3*arctan(1/3*sqrt(7) + 4/3))))/(cos(2/3*arctan(1/3*sqrt(7) + 4/3))^2 - 7*sin(2/3*arctan(1/3*sqrt(7) + 4/3))^2))*sin(2/3*arctan(1/3*sqrt(7) + 4/3)) + 1/147*(112^(1/6)*49^(2/3)*sqrt(3)*cos(2/3*arctan(1/3*sqrt(7) + 4/3)) + 112^(1/6)*49^(2/3)*sin(2/3*arctan(1/3*sqrt(7) + 4/3)))*arctan(1/5488*(70*112^(5/6)*49^(1/3)*(sqrt(7)*x + 7*sqrt(3)*x)*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^3 - 27440*(sqrt(7) + 2*sqrt(3))*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^4 - 5488*(sqrt(7) - 2*sqrt(3))*sin(2/3*arctan(1/3*sqrt(7) + 4/3))^4 - 14*(112^(5/6)*49^(1/3)*(sqrt(7)*sqrt(3)*x - 7*x) - 1568*(sqrt(7)*sqrt(3) - 5)*cos(2/3*arctan(1/3*sqrt(7) + 4/3)))*sin(2/3*arctan(1/3*sqrt(7) + 4/3))^3 + 14*(112^(5/6)*49^(1/3)*(13*sqrt(7)*x - 21*sqrt(3)*x)*cos(2/3*arctan(1/3*sqrt(7) + 4/3)) - 784*(3*sqrt(7) + 4*sqrt(3))*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^2)*sin(2/3*arctan(1/3*sqrt(7) + 4/3))^2 - 14*(112^(5/6)*49^(1/3)*(9*sqrt(7)*sqrt(3)*x + 49*x)*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^2 - 1568*(sqrt(7)*sqrt(3) + 11)*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^3)*sin(2/3*arctan(1/3*sqrt(7) + 4/3)) - (5*112^(5/6)*49^(1/3)*(sqrt(7) + 7*sqrt(3))*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^3 - 112^(5/6)*49^(1/3)*(9*sqrt(7)*sqrt(3) + 49)*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^2*sin(2/3*arctan(1/3*sqrt(7) + 4/3)) + 112^(5/6)*49^(1/3)*(13*sqrt(7) - 21*sqrt(3))*cos(2/3*arctan(1/3*sqrt(7) + 4/3))*sin(2/3*arctan(1/3*sqrt(7) + 4/3))^2 - 112^(5/6)*49^(1/3)*(sqrt(7)*sqrt(3) - 7)*sin(2/3*arctan(1/3*sqrt(7) + 4/3))^3)*sqrt(-112^(1/6)*49^(2/3)*(sqrt(7)*sqrt(3)*x + 7*x)*cos(2/3*arctan(1/3*sqrt(7) + 4/3)) - 112^(1/6)*49^(2/3)*(sqrt(7)*x - 7*sqrt(3)*x)*sin(2/3*arctan(1/3*sqrt(7) + 4/3)) + 28*49^(1/3)*14^(1/3)*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^2 + 28*49^(1/3)*14^(1/3)*sin(2/3*arctan(1/3*sqrt(7) + 4/3))^2 + 196*x^2))/(25*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^4 - 38*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^2*sin(2/3*arctan(1/3*sqrt(7) + 4/3))^2 + sin(2/3*arctan(1/3*sqrt(7) + 4/3))^4)) + 1/147*(112^(1/6)*49^(2/3)*sqrt(3)*cos(2/3*arctan(1/3*sqrt(7) + 4/3)) - 112^(1/6)*49^(2/3)*sin(2/3*arctan(1/3*sqrt(7) + 4/3)))*arctan(-1/5488*(70*112^(5/6)*49^(1/3)*(sqrt(7)*x - 7*sqrt(3)*x)*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^3 - 27440*(sqrt(7) - 2*sqrt(3))*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^4 - 5488*(sqrt(7) + 2*sqrt(3))*sin(2/3*arctan(1/3*sqrt(7) + 4/3))^4 + 14*(112^(5/6)*49^(1/3)*(sqrt(7)*sqrt(3)*x + 7*x) - 1568*(sqrt(7)*sqrt(3) + 5)*cos(2/3*arctan(1/3*sqrt(7) + 4/3)))*sin(2/3*arctan(1/3*sqrt(7) + 4/3))^3 + 14*(112^(5/6)*49^(1/3)*(13*sqrt(7)*x + 21*sqrt(3)*x)*cos(2/3*arctan(1/3*sqrt(7) + 4/3)) - 784*(3*sqrt(7) - 4*sqrt(3))*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^2)*sin(2/3*arctan(1/3*sqrt(7) + 4/3))^2 + 14*(112^(5/6)*49^(1/3)*(9*sqrt(7)*sqrt(3)*x - 49*x)*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^2 - 1568*(sqrt(7)*sqrt(3) - 11)*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^3)*sin(2/3*arctan(1/3*sqrt(7) + 4/3)) - (5*112^(5/6)*49^(1/3)*(sqrt(7) - 7*sqrt(3))*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^3 + 112^(5/6)*49^(1/3)*(9*sqrt(7)*sqrt(3) - 49)*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^2*sin(2/3*arctan(1/3*sqrt(7) + 4/3)) + 112^(5/6)*49^(1/3)*(13*sqrt(7) + 21*sqrt(3))*cos(2/3*arctan(1/3*sqrt(7) + 4/3))*sin(2/3*arctan(1/3*sqrt(7) + 4/3))^2 + 112^(5/6)*49^(1/3)*(sqrt(7)*sqrt(3) + 7)*sin(2/3*arctan(1/3*sqrt(7) + 4/3))^3)*sqrt(112^(1/6)*49^(2/3)*(sqrt(7)*sqrt(3)*x - 7*x)*cos(2/3*arctan(1/3*sqrt(7) + 4/3)) - 112^(1/6)*49^(2/3)*(sqrt(7)*x + 7*sqrt(3)*x)*sin(2/3*arctan(1/3*sqrt(7) + 4/3)) + 28*49^(1/3)*14^(1/3)*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^2 + 28*49^(1/3)*14^(1/3)*sin(2/3*arctan(1/3*sqrt(7) + 4/3))^2 + 196*x^2))/(25*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^4 - 38*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^2*sin(2/3*arctan(1/3*sqrt(7) + 4/3))^2 + sin(2/3*arctan(1/3*sqrt(7) + 4/3))^4)) + 1/588*(112^(1/6)*49^(2/3)*sqrt(3)*sin(2/3*arctan(1/3*sqrt(7) + 4/3)) - 112^(1/6)*49^(2/3)*cos(2/3*arctan(1/3*sqrt(7) + 4/3)))*log(-112^(1/6)*49^(2/3)*(sqrt(7)*sqrt(3)*x + 7*x)*cos(2/3*arctan(1/3*sqrt(7) + 4/3)) - 112^(1/6)*49^(2/3)*(sqrt(7)*x - 7*sqrt(3)*x)*sin(2/3*arctan(1/3*sqrt(7) + 4/3)) + 28*49^(1/3)*14^(1/3)*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^2 + 28*49^(1/3)*14^(1/3)*sin(2/3*arctan(1/3*sqrt(7) + 4/3))^2 + 196*x^2) - 1/588*(112^(1/6)*49^(2/3)*sqrt(3)*sin(2/3*arctan(1/3*sqrt(7) + 4/3)) + 112^(1/6)*49^(2/3)*cos(2/3*arctan(1/3*sqrt(7) + 4/3)))*log(112^(1/6)*49^(2/3)*(sqrt(7)*sqrt(3)*x - 7*x)*cos(2/3*arctan(1/3*sqrt(7) + 4/3)) - 112^(1/6)*49^(2/3)*(sqrt(7)*x + 7*sqrt(3)*x)*sin(2/3*arctan(1/3*sqrt(7) + 4/3)) + 28*49^(1/3)*14^(1/3)*cos(2/3*arctan(1/3*sqrt(7) + 4/3))^2 + 28*49^(1/3)*14^(1/3)*sin(2/3*arctan(1/3*sqrt(7) + 4/3))^2 + 196*x^2)","B",0
183,1,18,0,1.187976," ","integrate(x^2/(x^6+x^3+2),x, algorithm=""fricas"")","\frac{2}{21} \, \sqrt{7} \arctan\left(\frac{1}{7} \, \sqrt{7} {\left(2 \, x^{3} + 1\right)}\right)"," ",0,"2/21*sqrt(7)*arctan(1/7*sqrt(7)*(2*x^3 + 1))","A",0
184,1,1435,0,1.506159," ","integrate(x^3/(x^6+x^3+2),x, algorithm=""fricas"")","\frac{1}{294} \cdot 98^{\frac{2}{3}} 56^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) \log\left(-2 \cdot 98^{\frac{2}{3}} 56^{\frac{1}{6}} \sqrt{7} x \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) + 14 \cdot 98^{\frac{1}{3}} 7^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)^{2} + 14 \cdot 98^{\frac{1}{3}} 7^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)^{2} + 98 \, x^{2}\right) - \frac{2}{147} \cdot 98^{\frac{2}{3}} 56^{\frac{1}{6}} \arctan\left(\frac{98^{\frac{1}{3}} 56^{\frac{5}{6}} \sqrt{7} \sqrt{2} \sqrt{-2 \cdot 98^{\frac{2}{3}} 56^{\frac{1}{6}} \sqrt{7} x \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) + 14 \cdot 98^{\frac{1}{3}} 7^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)^{2} + 14 \cdot 98^{\frac{1}{3}} 7^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)^{2} + 98 \, x^{2}} - 14 \cdot 98^{\frac{1}{3}} 56^{\frac{5}{6}} \sqrt{7} x + 5488 \, \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)}{5488 \, \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)}\right) \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) + \frac{1}{147} \, {\left(98^{\frac{2}{3}} 56^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) + 98^{\frac{2}{3}} 56^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)\right)} \arctan\left(\frac{14 \cdot 98^{\frac{1}{3}} 56^{\frac{5}{6}} \sqrt{7} x \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) + 2744 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)^{2} + 2744 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)^{2} + 14 \, {\left(98^{\frac{1}{3}} 56^{\frac{5}{6}} \sqrt{7} \sqrt{3} x + 784 \, \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) - \sqrt{98^{\frac{2}{3}} 56^{\frac{1}{6}} \sqrt{7} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) + 98^{\frac{2}{3}} 56^{\frac{1}{6}} \sqrt{7} x \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) + 14 \cdot 98^{\frac{1}{3}} 7^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)^{2} + 14 \cdot 98^{\frac{1}{3}} 7^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)^{2} + 98 \, x^{2}} {\left(98^{\frac{1}{3}} 56^{\frac{5}{6}} \sqrt{7} \sqrt{3} \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) + 98^{\frac{1}{3}} 56^{\frac{5}{6}} \sqrt{7} \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)\right)}}{2744 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)^{2} - 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)^{2}\right)}}\right) + \frac{1}{147} \, {\left(98^{\frac{2}{3}} 56^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) - 98^{\frac{2}{3}} 56^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)\right)} \arctan\left(-\frac{14 \cdot 98^{\frac{1}{3}} 56^{\frac{5}{6}} \sqrt{7} x \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) - 2744 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)^{2} - 2744 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)^{2} - 14 \, {\left(98^{\frac{1}{3}} 56^{\frac{5}{6}} \sqrt{7} \sqrt{3} x - 784 \, \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) + \sqrt{-98^{\frac{2}{3}} 56^{\frac{1}{6}} \sqrt{7} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) + 98^{\frac{2}{3}} 56^{\frac{1}{6}} \sqrt{7} x \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) + 14 \cdot 98^{\frac{1}{3}} 7^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)^{2} + 14 \cdot 98^{\frac{1}{3}} 7^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)^{2} + 98 \, x^{2}} {\left(98^{\frac{1}{3}} 56^{\frac{5}{6}} \sqrt{7} \sqrt{3} \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) - 98^{\frac{1}{3}} 56^{\frac{5}{6}} \sqrt{7} \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)\right)}}{2744 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)^{2} - 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)^{2}\right)}}\right) + \frac{1}{588} \, {\left(98^{\frac{2}{3}} 56^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) - 98^{\frac{2}{3}} 56^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)\right)} \log\left(98^{\frac{2}{3}} 56^{\frac{1}{6}} \sqrt{7} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) + 98^{\frac{2}{3}} 56^{\frac{1}{6}} \sqrt{7} x \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) + 14 \cdot 98^{\frac{1}{3}} 7^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)^{2} + 14 \cdot 98^{\frac{1}{3}} 7^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)^{2} + 98 \, x^{2}\right) - \frac{1}{588} \, {\left(98^{\frac{2}{3}} 56^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) + 98^{\frac{2}{3}} 56^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)\right)} \log\left(-98^{\frac{2}{3}} 56^{\frac{1}{6}} \sqrt{7} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) + 98^{\frac{2}{3}} 56^{\frac{1}{6}} \sqrt{7} x \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right) + 14 \cdot 98^{\frac{1}{3}} 7^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)^{2} + 14 \cdot 98^{\frac{1}{3}} 7^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\frac{2}{7} \, \sqrt{14} \sqrt{7} + \sqrt{7}\right)\right)^{2} + 98 \, x^{2}\right)"," ",0,"1/294*98^(2/3)*56^(1/6)*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))*log(-2*98^(2/3)*56^(1/6)*sqrt(7)*x*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) + 14*98^(1/3)*7^(1/3)*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))^2 + 14*98^(1/3)*7^(1/3)*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))^2 + 98*x^2) - 2/147*98^(2/3)*56^(1/6)*arctan(1/5488*(98^(1/3)*56^(5/6)*sqrt(7)*sqrt(2)*sqrt(-2*98^(2/3)*56^(1/6)*sqrt(7)*x*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) + 14*98^(1/3)*7^(1/3)*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))^2 + 14*98^(1/3)*7^(1/3)*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))^2 + 98*x^2) - 14*98^(1/3)*56^(5/6)*sqrt(7)*x + 5488*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))))/cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))))*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) + 1/147*(98^(2/3)*56^(1/6)*sqrt(3)*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) + 98^(2/3)*56^(1/6)*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))))*arctan(1/2744*(14*98^(1/3)*56^(5/6)*sqrt(7)*x*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) + 2744*sqrt(3)*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))^2 + 2744*sqrt(3)*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))^2 + 14*(98^(1/3)*56^(5/6)*sqrt(7)*sqrt(3)*x + 784*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))))*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) - sqrt(98^(2/3)*56^(1/6)*sqrt(7)*sqrt(3)*x*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) + 98^(2/3)*56^(1/6)*sqrt(7)*x*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) + 14*98^(1/3)*7^(1/3)*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))^2 + 14*98^(1/3)*7^(1/3)*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))^2 + 98*x^2)*(98^(1/3)*56^(5/6)*sqrt(7)*sqrt(3)*sqrt(2)*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) + 98^(1/3)*56^(5/6)*sqrt(7)*sqrt(2)*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))))/(cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))^2 - 3*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))^2)) + 1/147*(98^(2/3)*56^(1/6)*sqrt(3)*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) - 98^(2/3)*56^(1/6)*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))))*arctan(-1/2744*(14*98^(1/3)*56^(5/6)*sqrt(7)*x*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) - 2744*sqrt(3)*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))^2 - 2744*sqrt(3)*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))^2 - 14*(98^(1/3)*56^(5/6)*sqrt(7)*sqrt(3)*x - 784*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))))*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) + sqrt(-98^(2/3)*56^(1/6)*sqrt(7)*sqrt(3)*x*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) + 98^(2/3)*56^(1/6)*sqrt(7)*x*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) + 14*98^(1/3)*7^(1/3)*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))^2 + 14*98^(1/3)*7^(1/3)*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))^2 + 98*x^2)*(98^(1/3)*56^(5/6)*sqrt(7)*sqrt(3)*sqrt(2)*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) - 98^(1/3)*56^(5/6)*sqrt(7)*sqrt(2)*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))))/(cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))^2 - 3*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))^2)) + 1/588*(98^(2/3)*56^(1/6)*sqrt(3)*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) - 98^(2/3)*56^(1/6)*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))))*log(98^(2/3)*56^(1/6)*sqrt(7)*sqrt(3)*x*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) + 98^(2/3)*56^(1/6)*sqrt(7)*x*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) + 14*98^(1/3)*7^(1/3)*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))^2 + 14*98^(1/3)*7^(1/3)*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))^2 + 98*x^2) - 1/588*(98^(2/3)*56^(1/6)*sqrt(3)*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) + 98^(2/3)*56^(1/6)*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))))*log(-98^(2/3)*56^(1/6)*sqrt(7)*sqrt(3)*x*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) + 98^(2/3)*56^(1/6)*sqrt(7)*x*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7))) + 14*98^(1/3)*7^(1/3)*cos(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))^2 + 14*98^(1/3)*7^(1/3)*sin(2/3*arctan(2/7*sqrt(14)*sqrt(7) + sqrt(7)))^2 + 98*x^2)","B",0
185,1,451,0,1.352944," ","integrate(x^14*(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(21 \, b^{6} - 140 \, a b^{4} c + 240 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(1280 \, c^{6} x^{15} + 128 \, b c^{5} x^{12} - 16 \, {\left(9 \, b^{2} c^{4} - 20 \, a c^{5}\right)} x^{9} + 8 \, {\left(21 \, b^{3} c^{3} - 68 \, a b c^{4}\right)} x^{6} + 315 \, b^{5} c - 1680 \, a b^{3} c^{2} + 1808 \, a^{2} b c^{3} - 2 \, {\left(105 \, b^{4} c^{2} - 448 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{92160 \, c^{6}}, \frac{15 \, {\left(21 \, b^{6} - 140 \, a b^{4} c + 240 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) + 2 \, {\left(1280 \, c^{6} x^{15} + 128 \, b c^{5} x^{12} - 16 \, {\left(9 \, b^{2} c^{4} - 20 \, a c^{5}\right)} x^{9} + 8 \, {\left(21 \, b^{3} c^{3} - 68 \, a b c^{4}\right)} x^{6} + 315 \, b^{5} c - 1680 \, a b^{3} c^{2} + 1808 \, a^{2} b c^{3} - 2 \, {\left(105 \, b^{4} c^{2} - 448 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{46080 \, c^{6}}\right]"," ",0,"[-1/92160*(15*(21*b^6 - 140*a*b^4*c + 240*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) - 4*(1280*c^6*x^15 + 128*b*c^5*x^12 - 16*(9*b^2*c^4 - 20*a*c^5)*x^9 + 8*(21*b^3*c^3 - 68*a*b*c^4)*x^6 + 315*b^5*c - 1680*a*b^3*c^2 + 1808*a^2*b*c^3 - 2*(105*b^4*c^2 - 448*a*b^2*c^3 + 240*a^2*c^4)*x^3)*sqrt(c*x^6 + b*x^3 + a))/c^6, 1/46080*(15*(21*b^6 - 140*a*b^4*c + 240*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) + 2*(1280*c^6*x^15 + 128*b*c^5*x^12 - 16*(9*b^2*c^4 - 20*a*c^5)*x^9 + 8*(21*b^3*c^3 - 68*a*b*c^4)*x^6 + 315*b^5*c - 1680*a*b^3*c^2 + 1808*a^2*b*c^3 - 2*(105*b^4*c^2 - 448*a*b^2*c^3 + 240*a^2*c^4)*x^3)*sqrt(c*x^6 + b*x^3 + a))/c^6]","A",0
186,1,367,0,1.749656," ","integrate(x^11*(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(384 \, c^{5} x^{12} + 48 \, b c^{4} x^{9} - 8 \, {\left(7 \, b^{2} c^{3} - 16 \, a c^{4}\right)} x^{6} - 105 \, b^{4} c + 460 \, a b^{2} c^{2} - 256 \, a^{2} c^{3} + 2 \, {\left(35 \, b^{3} c^{2} - 116 \, a b c^{3}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{23040 \, c^{5}}, -\frac{15 \, {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) - 2 \, {\left(384 \, c^{5} x^{12} + 48 \, b c^{4} x^{9} - 8 \, {\left(7 \, b^{2} c^{3} - 16 \, a c^{4}\right)} x^{6} - 105 \, b^{4} c + 460 \, a b^{2} c^{2} - 256 \, a^{2} c^{3} + 2 \, {\left(35 \, b^{3} c^{2} - 116 \, a b c^{3}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{11520 \, c^{5}}\right]"," ",0,"[1/23040*(15*(7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) + 4*(384*c^5*x^12 + 48*b*c^4*x^9 - 8*(7*b^2*c^3 - 16*a*c^4)*x^6 - 105*b^4*c + 460*a*b^2*c^2 - 256*a^2*c^3 + 2*(35*b^3*c^2 - 116*a*b*c^3)*x^3)*sqrt(c*x^6 + b*x^3 + a))/c^5, -1/11520*(15*(7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) - 2*(384*c^5*x^12 + 48*b*c^4*x^9 - 8*(7*b^2*c^3 - 16*a*c^4)*x^6 - 105*b^4*c + 460*a*b^2*c^2 - 256*a^2*c^3 + 2*(35*b^3*c^2 - 116*a*b*c^3)*x^3)*sqrt(c*x^6 + b*x^3 + a))/c^5]","A",0
187,1,303,0,1.219942," ","integrate(x^8*(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} + 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(48 \, c^{4} x^{9} + 8 \, b c^{3} x^{6} + 15 \, b^{3} c - 52 \, a b c^{2} - 2 \, {\left(5 \, b^{2} c^{2} - 12 \, a c^{3}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{2304 \, c^{4}}, \frac{3 \, {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) + 2 \, {\left(48 \, c^{4} x^{9} + 8 \, b c^{3} x^{6} + 15 \, b^{3} c - 52 \, a b c^{2} - 2 \, {\left(5 \, b^{2} c^{2} - 12 \, a c^{3}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{1152 \, c^{4}}\right]"," ",0,"[1/2304*(3*(5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 + 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) + 4*(48*c^4*x^9 + 8*b*c^3*x^6 + 15*b^3*c - 52*a*b*c^2 - 2*(5*b^2*c^2 - 12*a*c^3)*x^3)*sqrt(c*x^6 + b*x^3 + a))/c^4, 1/1152*(3*(5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) + 2*(48*c^4*x^9 + 8*b*c^3*x^6 + 15*b^3*c - 52*a*b*c^2 - 2*(5*b^2*c^2 - 12*a*c^3)*x^3)*sqrt(c*x^6 + b*x^3 + a))/c^4]","A",0
188,1,237,0,1.218986," ","integrate(x^5*(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} - 4 \, a b c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} + 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(8 \, c^{3} x^{6} + 2 \, b c^{2} x^{3} - 3 \, b^{2} c + 8 \, a c^{2}\right)} \sqrt{c x^{6} + b x^{3} + a}}{288 \, c^{3}}, -\frac{3 \, {\left(b^{3} - 4 \, a b c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) - 2 \, {\left(8 \, c^{3} x^{6} + 2 \, b c^{2} x^{3} - 3 \, b^{2} c + 8 \, a c^{2}\right)} \sqrt{c x^{6} + b x^{3} + a}}{144 \, c^{3}}\right]"," ",0,"[-1/288*(3*(b^3 - 4*a*b*c)*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 + 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) - 4*(8*c^3*x^6 + 2*b*c^2*x^3 - 3*b^2*c + 8*a*c^2)*sqrt(c*x^6 + b*x^3 + a))/c^3, -1/144*(3*(b^3 - 4*a*b*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) - 2*(8*c^3*x^6 + 2*b*c^2*x^3 - 3*b^2*c + 8*a*c^2)*sqrt(c*x^6 + b*x^3 + a))/c^3]","A",0
189,1,197,0,1.340060," ","integrate(x^2*(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 4 \, a c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c^{2} x^{3} + b c\right)}}{48 \, c^{2}}, \frac{{\left(b^{2} - 4 \, a c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) + 2 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c^{2} x^{3} + b c\right)}}{24 \, c^{2}}\right]"," ",0,"[-1/48*((b^2 - 4*a*c)*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c^2*x^3 + b*c))/c^2, 1/24*((b^2 - 4*a*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) + 2*sqrt(c*x^6 + b*x^3 + a)*(2*c^2*x^3 + b*c))/c^2]","A",0
190,1,566,0,1.367037," ","integrate((c*x^6+b*x^3+a)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{b \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) + 2 \, \sqrt{a} c \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) + 4 \, \sqrt{c x^{6} + b x^{3} + a} c}{12 \, c}, -\frac{b \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) - \sqrt{a} c \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) - 2 \, \sqrt{c x^{6} + b x^{3} + a} c}{6 \, c}, \frac{4 \, \sqrt{-a} c \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + b \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, \sqrt{c x^{6} + b x^{3} + a} c}{12 \, c}, \frac{2 \, \sqrt{-a} c \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) - b \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) + 2 \, \sqrt{c x^{6} + b x^{3} + a} c}{6 \, c}\right]"," ",0,"[1/12*(b*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) + 2*sqrt(a)*c*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) + 4*sqrt(c*x^6 + b*x^3 + a)*c)/c, -1/6*(b*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) - sqrt(a)*c*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) - 2*sqrt(c*x^6 + b*x^3 + a)*c)/c, 1/12*(4*sqrt(-a)*c*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + b*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) + 4*sqrt(c*x^6 + b*x^3 + a)*c)/c, 1/6*(2*sqrt(-a)*c*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) - b*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) + 2*sqrt(c*x^6 + b*x^3 + a)*c)/c]","A",0
191,1,601,0,1.568470," ","integrate((c*x^6+b*x^3+a)^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{2 \, a \sqrt{c} x^{3} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) + \sqrt{a} b x^{3} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) - 4 \, \sqrt{c x^{6} + b x^{3} + a} a}{12 \, a x^{3}}, -\frac{4 \, a \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) - \sqrt{a} b x^{3} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) + 4 \, \sqrt{c x^{6} + b x^{3} + a} a}{12 \, a x^{3}}, \frac{\sqrt{-a} b x^{3} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + a \sqrt{c} x^{3} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) - 2 \, \sqrt{c x^{6} + b x^{3} + a} a}{6 \, a x^{3}}, \frac{\sqrt{-a} b x^{3} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) - 2 \, a \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) - 2 \, \sqrt{c x^{6} + b x^{3} + a} a}{6 \, a x^{3}}\right]"," ",0,"[1/12*(2*a*sqrt(c)*x^3*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) + sqrt(a)*b*x^3*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) - 4*sqrt(c*x^6 + b*x^3 + a)*a)/(a*x^3), -1/12*(4*a*sqrt(-c)*x^3*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) - sqrt(a)*b*x^3*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) + 4*sqrt(c*x^6 + b*x^3 + a)*a)/(a*x^3), 1/6*(sqrt(-a)*b*x^3*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + a*sqrt(c)*x^3*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) - 2*sqrt(c*x^6 + b*x^3 + a)*a)/(a*x^3), 1/6*(sqrt(-a)*b*x^3*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) - 2*a*sqrt(-c)*x^3*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) - 2*sqrt(c*x^6 + b*x^3 + a)*a)/(a*x^3)]","A",0
192,1,215,0,1.365530," ","integrate((c*x^6+b*x^3+a)^(1/2)/x^7,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 4 \, a c\right)} \sqrt{a} x^{6} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) + 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(a b x^{3} + 2 \, a^{2}\right)}}{48 \, a^{2} x^{6}}, -\frac{{\left(b^{2} - 4 \, a c\right)} \sqrt{-a} x^{6} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + 2 \, \sqrt{c x^{6} + b x^{3} + a} {\left(a b x^{3} + 2 \, a^{2}\right)}}{24 \, a^{2} x^{6}}\right]"," ",0,"[-1/48*((b^2 - 4*a*c)*sqrt(a)*x^6*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) + 4*sqrt(c*x^6 + b*x^3 + a)*(a*b*x^3 + 2*a^2))/(a^2*x^6), -1/24*((b^2 - 4*a*c)*sqrt(-a)*x^6*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + 2*sqrt(c*x^6 + b*x^3 + a)*(a*b*x^3 + 2*a^2))/(a^2*x^6)]","A",0
193,1,259,0,1.363108," ","integrate((c*x^6+b*x^3+a)^(1/2)/x^10,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} - 4 \, a b c\right)} \sqrt{a} x^{9} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} + 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) - 4 \, {\left({\left(3 \, a b^{2} - 8 \, a^{2} c\right)} x^{6} - 2 \, a^{2} b x^{3} - 8 \, a^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{288 \, a^{3} x^{9}}, \frac{3 \, {\left(b^{3} - 4 \, a b c\right)} \sqrt{-a} x^{9} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + 2 \, {\left({\left(3 \, a b^{2} - 8 \, a^{2} c\right)} x^{6} - 2 \, a^{2} b x^{3} - 8 \, a^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{144 \, a^{3} x^{9}}\right]"," ",0,"[-1/288*(3*(b^3 - 4*a*b*c)*sqrt(a)*x^9*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 + 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) - 4*((3*a*b^2 - 8*a^2*c)*x^6 - 2*a^2*b*x^3 - 8*a^3)*sqrt(c*x^6 + b*x^3 + a))/(a^3*x^9), 1/144*(3*(b^3 - 4*a*b*c)*sqrt(-a)*x^9*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + 2*((3*a*b^2 - 8*a^2*c)*x^6 - 2*a^2*b*x^3 - 8*a^3)*sqrt(c*x^6 + b*x^3 + a))/(a^3*x^9)]","A",0
194,1,325,0,1.399869," ","integrate((c*x^6+b*x^3+a)^(1/2)/x^13,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{a} x^{12} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} + 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) - 4 \, {\left({\left(15 \, a b^{3} - 52 \, a^{2} b c\right)} x^{9} + 8 \, a^{3} b x^{3} - 2 \, {\left(5 \, a^{2} b^{2} - 12 \, a^{3} c\right)} x^{6} + 48 \, a^{4}\right)} \sqrt{c x^{6} + b x^{3} + a}}{2304 \, a^{4} x^{12}}, -\frac{3 \, {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-a} x^{12} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + 2 \, {\left({\left(15 \, a b^{3} - 52 \, a^{2} b c\right)} x^{9} + 8 \, a^{3} b x^{3} - 2 \, {\left(5 \, a^{2} b^{2} - 12 \, a^{3} c\right)} x^{6} + 48 \, a^{4}\right)} \sqrt{c x^{6} + b x^{3} + a}}{1152 \, a^{4} x^{12}}\right]"," ",0,"[1/2304*(3*(5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*sqrt(a)*x^12*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 + 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) - 4*((15*a*b^3 - 52*a^2*b*c)*x^9 + 8*a^3*b*x^3 - 2*(5*a^2*b^2 - 12*a^3*c)*x^6 + 48*a^4)*sqrt(c*x^6 + b*x^3 + a))/(a^4*x^12), -1/1152*(3*(5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*sqrt(-a)*x^12*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + 2*((15*a*b^3 - 52*a^2*b*c)*x^9 + 8*a^3*b*x^3 - 2*(5*a^2*b^2 - 12*a^3*c)*x^6 + 48*a^4)*sqrt(c*x^6 + b*x^3 + a))/(a^4*x^12)]","A",0
195,1,389,0,1.521804," ","integrate((c*x^6+b*x^3+a)^(1/2)/x^16,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} \sqrt{a} x^{15} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) + 4 \, {\left({\left(105 \, a b^{4} - 460 \, a^{2} b^{2} c + 256 \, a^{3} c^{2}\right)} x^{12} - 2 \, {\left(35 \, a^{2} b^{3} - 116 \, a^{3} b c\right)} x^{9} - 48 \, a^{4} b x^{3} + 8 \, {\left(7 \, a^{3} b^{2} - 16 \, a^{4} c\right)} x^{6} - 384 \, a^{5}\right)} \sqrt{c x^{6} + b x^{3} + a}}{23040 \, a^{5} x^{15}}, \frac{15 \, {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} \sqrt{-a} x^{15} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + 2 \, {\left({\left(105 \, a b^{4} - 460 \, a^{2} b^{2} c + 256 \, a^{3} c^{2}\right)} x^{12} - 2 \, {\left(35 \, a^{2} b^{3} - 116 \, a^{3} b c\right)} x^{9} - 48 \, a^{4} b x^{3} + 8 \, {\left(7 \, a^{3} b^{2} - 16 \, a^{4} c\right)} x^{6} - 384 \, a^{5}\right)} \sqrt{c x^{6} + b x^{3} + a}}{11520 \, a^{5} x^{15}}\right]"," ",0,"[1/23040*(15*(7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*sqrt(a)*x^15*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) + 4*((105*a*b^4 - 460*a^2*b^2*c + 256*a^3*c^2)*x^12 - 2*(35*a^2*b^3 - 116*a^3*b*c)*x^9 - 48*a^4*b*x^3 + 8*(7*a^3*b^2 - 16*a^4*c)*x^6 - 384*a^5)*sqrt(c*x^6 + b*x^3 + a))/(a^5*x^15), 1/11520*(15*(7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*sqrt(-a)*x^15*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + 2*((105*a*b^4 - 460*a^2*b^2*c + 256*a^3*c^2)*x^12 - 2*(35*a^2*b^3 - 116*a^3*b*c)*x^9 - 48*a^4*b*x^3 + 8*(7*a^3*b^2 - 16*a^4*c)*x^6 - 384*a^5)*sqrt(c*x^6 + b*x^3 + a))/(a^5*x^15)]","A",0
196,0,0,0,1.036380," ","integrate(x^3*(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{6} + b x^{3} + a} x^{3}, x\right)"," ",0,"integral(sqrt(c*x^6 + b*x^3 + a)*x^3, x)","F",0
197,0,0,0,1.228930," ","integrate(x*(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{6} + b x^{3} + a} x, x\right)"," ",0,"integral(sqrt(c*x^6 + b*x^3 + a)*x, x)","F",0
198,0,0,0,1.234527," ","integrate((c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{6} + b x^{3} + a}, x\right)"," ",0,"integral(sqrt(c*x^6 + b*x^3 + a), x)","F",0
199,0,0,0,1.448557," ","integrate((c*x^6+b*x^3+a)^(1/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{6} + b x^{3} + a}}{x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^6 + b*x^3 + a)/x^2, x)","F",0
200,0,0,0,1.212618," ","integrate((c*x^6+b*x^3+a)^(1/2)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{6} + b x^{3} + a}}{x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^6 + b*x^3 + a)/x^3, x)","F",0
201,1,641,0,1.555067," ","integrate(x^14*(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(33 \, b^{8} - 336 \, a b^{6} c + 1120 \, a^{2} b^{4} c^{2} - 1280 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(71680 \, c^{8} x^{21} + 87040 \, b c^{7} x^{18} + 1280 \, {\left(b^{2} c^{6} + 84 \, a c^{7}\right)} x^{15} - 128 \, {\left(11 \, b^{3} c^{5} - 52 \, a b c^{6}\right)} x^{12} + 16 \, {\left(99 \, b^{4} c^{4} - 568 \, a b^{2} c^{5} + 560 \, a^{2} c^{6}\right)} x^{9} - 3465 \, b^{7} c + 30660 \, a b^{5} c^{2} - 81648 \, a^{2} b^{3} c^{3} + 58816 \, a^{3} b c^{4} - 8 \, {\left(231 \, b^{5} c^{3} - 1560 \, a b^{3} c^{4} + 2416 \, a^{2} b c^{5}\right)} x^{6} + 2 \, {\left(1155 \, b^{6} c^{2} - 8988 \, a b^{4} c^{3} + 18896 \, a^{2} b^{2} c^{4} - 6720 \, a^{3} c^{5}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{6881280 \, c^{7}}, -\frac{105 \, {\left(33 \, b^{8} - 336 \, a b^{6} c + 1120 \, a^{2} b^{4} c^{2} - 1280 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) - 2 \, {\left(71680 \, c^{8} x^{21} + 87040 \, b c^{7} x^{18} + 1280 \, {\left(b^{2} c^{6} + 84 \, a c^{7}\right)} x^{15} - 128 \, {\left(11 \, b^{3} c^{5} - 52 \, a b c^{6}\right)} x^{12} + 16 \, {\left(99 \, b^{4} c^{4} - 568 \, a b^{2} c^{5} + 560 \, a^{2} c^{6}\right)} x^{9} - 3465 \, b^{7} c + 30660 \, a b^{5} c^{2} - 81648 \, a^{2} b^{3} c^{3} + 58816 \, a^{3} b c^{4} - 8 \, {\left(231 \, b^{5} c^{3} - 1560 \, a b^{3} c^{4} + 2416 \, a^{2} b c^{5}\right)} x^{6} + 2 \, {\left(1155 \, b^{6} c^{2} - 8988 \, a b^{4} c^{3} + 18896 \, a^{2} b^{2} c^{4} - 6720 \, a^{3} c^{5}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{3440640 \, c^{7}}\right]"," ",0,"[1/6881280*(105*(33*b^8 - 336*a*b^6*c + 1120*a^2*b^4*c^2 - 1280*a^3*b^2*c^3 + 256*a^4*c^4)*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) + 4*(71680*c^8*x^21 + 87040*b*c^7*x^18 + 1280*(b^2*c^6 + 84*a*c^7)*x^15 - 128*(11*b^3*c^5 - 52*a*b*c^6)*x^12 + 16*(99*b^4*c^4 - 568*a*b^2*c^5 + 560*a^2*c^6)*x^9 - 3465*b^7*c + 30660*a*b^5*c^2 - 81648*a^2*b^3*c^3 + 58816*a^3*b*c^4 - 8*(231*b^5*c^3 - 1560*a*b^3*c^4 + 2416*a^2*b*c^5)*x^6 + 2*(1155*b^6*c^2 - 8988*a*b^4*c^3 + 18896*a^2*b^2*c^4 - 6720*a^3*c^5)*x^3)*sqrt(c*x^6 + b*x^3 + a))/c^7, -1/3440640*(105*(33*b^8 - 336*a*b^6*c + 1120*a^2*b^4*c^2 - 1280*a^3*b^2*c^3 + 256*a^4*c^4)*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) - 2*(71680*c^8*x^21 + 87040*b*c^7*x^18 + 1280*(b^2*c^6 + 84*a*c^7)*x^15 - 128*(11*b^3*c^5 - 52*a*b*c^6)*x^12 + 16*(99*b^4*c^4 - 568*a*b^2*c^5 + 560*a^2*c^6)*x^9 - 3465*b^7*c + 30660*a*b^5*c^2 - 81648*a^2*b^3*c^3 + 58816*a^3*b*c^4 - 8*(231*b^5*c^3 - 1560*a*b^3*c^4 + 2416*a^2*b*c^5)*x^6 + 2*(1155*b^6*c^2 - 8988*a*b^4*c^3 + 18896*a^2*b^2*c^4 - 6720*a^3*c^5)*x^3)*sqrt(c*x^6 + b*x^3 + a))/c^7]","A",0
202,1,535,0,1.244914," ","integrate(x^11*(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(3 \, b^{7} - 28 \, a b^{5} c + 80 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(5120 \, c^{7} x^{18} + 6400 \, b c^{6} x^{15} + 128 \, {\left(b^{2} c^{5} + 64 \, a c^{6}\right)} x^{12} - 16 \, {\left(9 \, b^{3} c^{4} - 44 \, a b c^{5}\right)} x^{9} + 315 \, b^{6} c - 2520 \, a b^{4} c^{2} + 5488 \, a^{2} b^{2} c^{3} - 2048 \, a^{3} c^{4} + 8 \, {\left(21 \, b^{4} c^{3} - 124 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} x^{6} - 2 \, {\left(105 \, b^{5} c^{2} - 728 \, a b^{3} c^{3} + 1168 \, a^{2} b c^{4}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{430080 \, c^{6}}, \frac{105 \, {\left(3 \, b^{7} - 28 \, a b^{5} c + 80 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) + 2 \, {\left(5120 \, c^{7} x^{18} + 6400 \, b c^{6} x^{15} + 128 \, {\left(b^{2} c^{5} + 64 \, a c^{6}\right)} x^{12} - 16 \, {\left(9 \, b^{3} c^{4} - 44 \, a b c^{5}\right)} x^{9} + 315 \, b^{6} c - 2520 \, a b^{4} c^{2} + 5488 \, a^{2} b^{2} c^{3} - 2048 \, a^{3} c^{4} + 8 \, {\left(21 \, b^{4} c^{3} - 124 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} x^{6} - 2 \, {\left(105 \, b^{5} c^{2} - 728 \, a b^{3} c^{3} + 1168 \, a^{2} b c^{4}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{215040 \, c^{6}}\right]"," ",0,"[-1/430080*(105*(3*b^7 - 28*a*b^5*c + 80*a^2*b^3*c^2 - 64*a^3*b*c^3)*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) - 4*(5120*c^7*x^18 + 6400*b*c^6*x^15 + 128*(b^2*c^5 + 64*a*c^6)*x^12 - 16*(9*b^3*c^4 - 44*a*b*c^5)*x^9 + 315*b^6*c - 2520*a*b^4*c^2 + 5488*a^2*b^2*c^3 - 2048*a^3*c^4 + 8*(21*b^4*c^3 - 124*a*b^2*c^4 + 128*a^2*c^5)*x^6 - 2*(105*b^5*c^2 - 728*a*b^3*c^3 + 1168*a^2*b*c^4)*x^3)*sqrt(c*x^6 + b*x^3 + a))/c^6, 1/215040*(105*(3*b^7 - 28*a*b^5*c + 80*a^2*b^3*c^2 - 64*a^3*b*c^3)*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) + 2*(5120*c^7*x^18 + 6400*b*c^6*x^15 + 128*(b^2*c^5 + 64*a*c^6)*x^12 - 16*(9*b^3*c^4 - 44*a*b*c^5)*x^9 + 315*b^6*c - 2520*a*b^4*c^2 + 5488*a^2*b^2*c^3 - 2048*a^3*c^4 + 8*(21*b^4*c^3 - 124*a*b^2*c^4 + 128*a^2*c^5)*x^6 - 2*(105*b^5*c^2 - 728*a*b^3*c^3 + 1168*a^2*b*c^4)*x^3)*sqrt(c*x^6 + b*x^3 + a))/c^6]","A",0
203,1,451,0,1.296376," ","integrate(x^8*(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} + 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(1280 \, c^{6} x^{15} + 1664 \, b c^{5} x^{12} + 16 \, {\left(3 \, b^{2} c^{4} + 140 \, a c^{5}\right)} x^{9} - 8 \, {\left(7 \, b^{3} c^{3} - 36 \, a b c^{4}\right)} x^{6} - 105 \, b^{5} c + 760 \, a b^{3} c^{2} - 1296 \, a^{2} b c^{3} + 2 \, {\left(35 \, b^{4} c^{2} - 216 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{92160 \, c^{5}}, -\frac{15 \, {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) - 2 \, {\left(1280 \, c^{6} x^{15} + 1664 \, b c^{5} x^{12} + 16 \, {\left(3 \, b^{2} c^{4} + 140 \, a c^{5}\right)} x^{9} - 8 \, {\left(7 \, b^{3} c^{3} - 36 \, a b c^{4}\right)} x^{6} - 105 \, b^{5} c + 760 \, a b^{3} c^{2} - 1296 \, a^{2} b c^{3} + 2 \, {\left(35 \, b^{4} c^{2} - 216 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{46080 \, c^{5}}\right]"," ",0,"[-1/92160*(15*(7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 + 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) - 4*(1280*c^6*x^15 + 1664*b*c^5*x^12 + 16*(3*b^2*c^4 + 140*a*c^5)*x^9 - 8*(7*b^3*c^3 - 36*a*b*c^4)*x^6 - 105*b^5*c + 760*a*b^3*c^2 - 1296*a^2*b*c^3 + 2*(35*b^4*c^2 - 216*a*b^2*c^3 + 240*a^2*c^4)*x^3)*sqrt(c*x^6 + b*x^3 + a))/c^5, -1/46080*(15*(7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) - 2*(1280*c^6*x^15 + 1664*b*c^5*x^12 + 16*(3*b^2*c^4 + 140*a*c^5)*x^9 - 8*(7*b^3*c^3 - 36*a*b*c^4)*x^6 - 105*b^5*c + 760*a*b^3*c^2 - 1296*a^2*b*c^3 + 2*(35*b^4*c^2 - 216*a*b^2*c^3 + 240*a^2*c^4)*x^3)*sqrt(c*x^6 + b*x^3 + a))/c^5]","A",0
204,1,361,0,1.211872," ","integrate(x^5*(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} + 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(128 \, c^{5} x^{12} + 176 \, b c^{4} x^{9} + 8 \, {\left(b^{2} c^{3} + 32 \, a c^{4}\right)} x^{6} + 15 \, b^{4} c - 100 \, a b^{2} c^{2} + 128 \, a^{2} c^{3} - 2 \, {\left(5 \, b^{3} c^{2} - 28 \, a b c^{3}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{7680 \, c^{4}}, \frac{15 \, {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) + 2 \, {\left(128 \, c^{5} x^{12} + 176 \, b c^{4} x^{9} + 8 \, {\left(b^{2} c^{3} + 32 \, a c^{4}\right)} x^{6} + 15 \, b^{4} c - 100 \, a b^{2} c^{2} + 128 \, a^{2} c^{3} - 2 \, {\left(5 \, b^{3} c^{2} - 28 \, a b c^{3}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{3840 \, c^{4}}\right]"," ",0,"[1/7680*(15*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 + 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) + 4*(128*c^5*x^12 + 176*b*c^4*x^9 + 8*(b^2*c^3 + 32*a*c^4)*x^6 + 15*b^4*c - 100*a*b^2*c^2 + 128*a^2*c^3 - 2*(5*b^3*c^2 - 28*a*b*c^3)*x^3)*sqrt(c*x^6 + b*x^3 + a))/c^4, 1/3840*(15*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) + 2*(128*c^5*x^12 + 176*b*c^4*x^9 + 8*(b^2*c^3 + 32*a*c^4)*x^6 + 15*b^4*c - 100*a*b^2*c^2 + 128*a^2*c^3 - 2*(5*b^3*c^2 - 28*a*b*c^3)*x^3)*sqrt(c*x^6 + b*x^3 + a))/c^4]","A",0
205,1,297,0,1.383477," ","integrate(x^2*(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(16 \, c^{4} x^{9} + 24 \, b c^{3} x^{6} - 3 \, b^{3} c + 20 \, a b c^{2} + 2 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{768 \, c^{3}}, -\frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) - 2 \, {\left(16 \, c^{4} x^{9} + 24 \, b c^{3} x^{6} - 3 \, b^{3} c + 20 \, a b c^{2} + 2 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{384 \, c^{3}}\right]"," ",0,"[1/768*(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) + 4*(16*c^4*x^9 + 24*b*c^3*x^6 - 3*b^3*c + 20*a*b*c^2 + 2*(b^2*c^2 + 20*a*c^3)*x^3)*sqrt(c*x^6 + b*x^3 + a))/c^3, -1/384*(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) - 2*(16*c^4*x^9 + 24*b*c^3*x^6 - 3*b^3*c + 20*a*b*c^2 + 2*(b^2*c^2 + 20*a*c^3)*x^3)*sqrt(c*x^6 + b*x^3 + a))/c^3]","A",0
206,1,727,0,1.821160," ","integrate((c*x^6+b*x^3+a)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{48 \, a^{\frac{3}{2}} c^{2} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) - 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(8 \, c^{3} x^{6} + 14 \, b c^{2} x^{3} + 3 \, b^{2} c + 32 \, a c^{2}\right)} \sqrt{c x^{6} + b x^{3} + a}}{288 \, c^{2}}, \frac{24 \, a^{\frac{3}{2}} c^{2} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) + 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) + 2 \, {\left(8 \, c^{3} x^{6} + 14 \, b c^{2} x^{3} + 3 \, b^{2} c + 32 \, a c^{2}\right)} \sqrt{c x^{6} + b x^{3} + a}}{144 \, c^{2}}, \frac{96 \, \sqrt{-a} a c^{2} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) - 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(8 \, c^{3} x^{6} + 14 \, b c^{2} x^{3} + 3 \, b^{2} c + 32 \, a c^{2}\right)} \sqrt{c x^{6} + b x^{3} + a}}{288 \, c^{2}}, \frac{48 \, \sqrt{-a} a c^{2} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) + 2 \, {\left(8 \, c^{3} x^{6} + 14 \, b c^{2} x^{3} + 3 \, b^{2} c + 32 \, a c^{2}\right)} \sqrt{c x^{6} + b x^{3} + a}}{144 \, c^{2}}\right]"," ",0,"[1/288*(48*a^(3/2)*c^2*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) - 3*(b^3 - 12*a*b*c)*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) + 4*(8*c^3*x^6 + 14*b*c^2*x^3 + 3*b^2*c + 32*a*c^2)*sqrt(c*x^6 + b*x^3 + a))/c^2, 1/144*(24*a^(3/2)*c^2*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) + 3*(b^3 - 12*a*b*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) + 2*(8*c^3*x^6 + 14*b*c^2*x^3 + 3*b^2*c + 32*a*c^2)*sqrt(c*x^6 + b*x^3 + a))/c^2, 1/288*(96*sqrt(-a)*a*c^2*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) - 3*(b^3 - 12*a*b*c)*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) + 4*(8*c^3*x^6 + 14*b*c^2*x^3 + 3*b^2*c + 32*a*c^2)*sqrt(c*x^6 + b*x^3 + a))/c^2, 1/144*(48*sqrt(-a)*a*c^2*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + 3*(b^3 - 12*a*b*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) + 2*(8*c^3*x^6 + 14*b*c^2*x^3 + 3*b^2*c + 32*a*c^2)*sqrt(c*x^6 + b*x^3 + a))/c^2]","A",0
207,1,713,0,1.553937," ","integrate((c*x^6+b*x^3+a)^(3/2)/x^4,x, algorithm=""fricas"")","\left[\frac{12 \, \sqrt{a} b c x^{3} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) + 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{c} x^{3} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(2 \, c^{2} x^{6} + 5 \, b c x^{3} - 4 \, a c\right)} \sqrt{c x^{6} + b x^{3} + a}}{48 \, c x^{3}}, \frac{6 \, \sqrt{a} b c x^{3} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) - 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) + 2 \, {\left(2 \, c^{2} x^{6} + 5 \, b c x^{3} - 4 \, a c\right)} \sqrt{c x^{6} + b x^{3} + a}}{24 \, c x^{3}}, \frac{24 \, \sqrt{-a} b c x^{3} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{c} x^{3} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(2 \, c^{2} x^{6} + 5 \, b c x^{3} - 4 \, a c\right)} \sqrt{c x^{6} + b x^{3} + a}}{48 \, c x^{3}}, \frac{12 \, \sqrt{-a} b c x^{3} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) - 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) + 2 \, {\left(2 \, c^{2} x^{6} + 5 \, b c x^{3} - 4 \, a c\right)} \sqrt{c x^{6} + b x^{3} + a}}{24 \, c x^{3}}\right]"," ",0,"[1/48*(12*sqrt(a)*b*c*x^3*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) + 3*(b^2 + 4*a*c)*sqrt(c)*x^3*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) + 4*(2*c^2*x^6 + 5*b*c*x^3 - 4*a*c)*sqrt(c*x^6 + b*x^3 + a))/(c*x^3), 1/24*(6*sqrt(a)*b*c*x^3*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) - 3*(b^2 + 4*a*c)*sqrt(-c)*x^3*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) + 2*(2*c^2*x^6 + 5*b*c*x^3 - 4*a*c)*sqrt(c*x^6 + b*x^3 + a))/(c*x^3), 1/48*(24*sqrt(-a)*b*c*x^3*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + 3*(b^2 + 4*a*c)*sqrt(c)*x^3*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) + 4*(2*c^2*x^6 + 5*b*c*x^3 - 4*a*c)*sqrt(c*x^6 + b*x^3 + a))/(c*x^3), 1/24*(12*sqrt(-a)*b*c*x^3*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) - 3*(b^2 + 4*a*c)*sqrt(-c)*x^3*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) + 2*(2*c^2*x^6 + 5*b*c*x^3 - 4*a*c)*sqrt(c*x^6 + b*x^3 + a))/(c*x^3)]","A",0
208,1,713,0,1.457473," ","integrate((c*x^6+b*x^3+a)^(3/2)/x^7,x, algorithm=""fricas"")","\left[\frac{12 \, a b \sqrt{c} x^{6} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) + 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{a} x^{6} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) + 4 \, {\left(4 \, a c x^{6} - 5 \, a b x^{3} - 2 \, a^{2}\right)} \sqrt{c x^{6} + b x^{3} + a}}{48 \, a x^{6}}, -\frac{24 \, a b \sqrt{-c} x^{6} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) - 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{a} x^{6} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) - 4 \, {\left(4 \, a c x^{6} - 5 \, a b x^{3} - 2 \, a^{2}\right)} \sqrt{c x^{6} + b x^{3} + a}}{48 \, a x^{6}}, \frac{6 \, a b \sqrt{c} x^{6} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) + 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{-a} x^{6} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + 2 \, {\left(4 \, a c x^{6} - 5 \, a b x^{3} - 2 \, a^{2}\right)} \sqrt{c x^{6} + b x^{3} + a}}{24 \, a x^{6}}, -\frac{12 \, a b \sqrt{-c} x^{6} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) - 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{-a} x^{6} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) - 2 \, {\left(4 \, a c x^{6} - 5 \, a b x^{3} - 2 \, a^{2}\right)} \sqrt{c x^{6} + b x^{3} + a}}{24 \, a x^{6}}\right]"," ",0,"[1/48*(12*a*b*sqrt(c)*x^6*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) + 3*(b^2 + 4*a*c)*sqrt(a)*x^6*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) + 4*(4*a*c*x^6 - 5*a*b*x^3 - 2*a^2)*sqrt(c*x^6 + b*x^3 + a))/(a*x^6), -1/48*(24*a*b*sqrt(-c)*x^6*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) - 3*(b^2 + 4*a*c)*sqrt(a)*x^6*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) - 4*(4*a*c*x^6 - 5*a*b*x^3 - 2*a^2)*sqrt(c*x^6 + b*x^3 + a))/(a*x^6), 1/24*(6*a*b*sqrt(c)*x^6*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) + 3*(b^2 + 4*a*c)*sqrt(-a)*x^6*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + 2*(4*a*c*x^6 - 5*a*b*x^3 - 2*a^2)*sqrt(c*x^6 + b*x^3 + a))/(a*x^6), -1/24*(12*a*b*sqrt(-c)*x^6*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) - 3*(b^2 + 4*a*c)*sqrt(-a)*x^6*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) - 2*(4*a*c*x^6 - 5*a*b*x^3 - 2*a^2)*sqrt(c*x^6 + b*x^3 + a))/(a*x^6)]","A",0
209,1,771,0,1.596416," ","integrate((c*x^6+b*x^3+a)^(3/2)/x^10,x, algorithm=""fricas"")","\left[\frac{48 \, a^{2} c^{\frac{3}{2}} x^{9} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) - 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{a} x^{9} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) - 4 \, {\left({\left(3 \, a b^{2} + 32 \, a^{2} c\right)} x^{6} + 14 \, a^{2} b x^{3} + 8 \, a^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{288 \, a^{2} x^{9}}, -\frac{96 \, a^{2} \sqrt{-c} c x^{9} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) + 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{a} x^{9} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) + 4 \, {\left({\left(3 \, a b^{2} + 32 \, a^{2} c\right)} x^{6} + 14 \, a^{2} b x^{3} + 8 \, a^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{288 \, a^{2} x^{9}}, \frac{24 \, a^{2} c^{\frac{3}{2}} x^{9} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) - 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{-a} x^{9} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) - 2 \, {\left({\left(3 \, a b^{2} + 32 \, a^{2} c\right)} x^{6} + 14 \, a^{2} b x^{3} + 8 \, a^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{144 \, a^{2} x^{9}}, -\frac{48 \, a^{2} \sqrt{-c} c x^{9} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) + 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{-a} x^{9} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + 2 \, {\left({\left(3 \, a b^{2} + 32 \, a^{2} c\right)} x^{6} + 14 \, a^{2} b x^{3} + 8 \, a^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{144 \, a^{2} x^{9}}\right]"," ",0,"[1/288*(48*a^2*c^(3/2)*x^9*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) - 3*(b^3 - 12*a*b*c)*sqrt(a)*x^9*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) - 4*((3*a*b^2 + 32*a^2*c)*x^6 + 14*a^2*b*x^3 + 8*a^3)*sqrt(c*x^6 + b*x^3 + a))/(a^2*x^9), -1/288*(96*a^2*sqrt(-c)*c*x^9*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) + 3*(b^3 - 12*a*b*c)*sqrt(a)*x^9*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) + 4*((3*a*b^2 + 32*a^2*c)*x^6 + 14*a^2*b*x^3 + 8*a^3)*sqrt(c*x^6 + b*x^3 + a))/(a^2*x^9), 1/144*(24*a^2*c^(3/2)*x^9*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) - 3*(b^3 - 12*a*b*c)*sqrt(-a)*x^9*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) - 2*((3*a*b^2 + 32*a^2*c)*x^6 + 14*a^2*b*x^3 + 8*a^3)*sqrt(c*x^6 + b*x^3 + a))/(a^2*x^9), -1/144*(48*a^2*sqrt(-c)*c*x^9*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) + 3*(b^3 - 12*a*b*c)*sqrt(-a)*x^9*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + 2*((3*a*b^2 + 32*a^2*c)*x^6 + 14*a^2*b*x^3 + 8*a^3)*sqrt(c*x^6 + b*x^3 + a))/(a^2*x^9)]","A",0
210,1,319,0,1.404305," ","integrate((c*x^6+b*x^3+a)^(3/2)/x^13,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{a} x^{12} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) + 4 \, {\left({\left(3 \, a b^{3} - 20 \, a^{2} b c\right)} x^{9} - 24 \, a^{3} b x^{3} - 2 \, {\left(a^{2} b^{2} + 20 \, a^{3} c\right)} x^{6} - 16 \, a^{4}\right)} \sqrt{c x^{6} + b x^{3} + a}}{768 \, a^{3} x^{12}}, \frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-a} x^{12} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + 2 \, {\left({\left(3 \, a b^{3} - 20 \, a^{2} b c\right)} x^{9} - 24 \, a^{3} b x^{3} - 2 \, {\left(a^{2} b^{2} + 20 \, a^{3} c\right)} x^{6} - 16 \, a^{4}\right)} \sqrt{c x^{6} + b x^{3} + a}}{384 \, a^{3} x^{12}}\right]"," ",0,"[1/768*(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(a)*x^12*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) + 4*((3*a*b^3 - 20*a^2*b*c)*x^9 - 24*a^3*b*x^3 - 2*(a^2*b^2 + 20*a^3*c)*x^6 - 16*a^4)*sqrt(c*x^6 + b*x^3 + a))/(a^3*x^12), 1/384*(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-a)*x^12*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + 2*((3*a*b^3 - 20*a^2*b*c)*x^9 - 24*a^3*b*x^3 - 2*(a^2*b^2 + 20*a^3*c)*x^6 - 16*a^4)*sqrt(c*x^6 + b*x^3 + a))/(a^3*x^12)]","A",0
211,1,383,0,1.672809," ","integrate((c*x^6+b*x^3+a)^(3/2)/x^16,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} \sqrt{a} x^{15} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} + 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) - 4 \, {\left({\left(15 \, a b^{4} - 100 \, a^{2} b^{2} c + 128 \, a^{3} c^{2}\right)} x^{12} - 2 \, {\left(5 \, a^{2} b^{3} - 28 \, a^{3} b c\right)} x^{9} + 176 \, a^{4} b x^{3} + 8 \, {\left(a^{3} b^{2} + 32 \, a^{4} c\right)} x^{6} + 128 \, a^{5}\right)} \sqrt{c x^{6} + b x^{3} + a}}{7680 \, a^{4} x^{15}}, -\frac{15 \, {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} \sqrt{-a} x^{15} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + 2 \, {\left({\left(15 \, a b^{4} - 100 \, a^{2} b^{2} c + 128 \, a^{3} c^{2}\right)} x^{12} - 2 \, {\left(5 \, a^{2} b^{3} - 28 \, a^{3} b c\right)} x^{9} + 176 \, a^{4} b x^{3} + 8 \, {\left(a^{3} b^{2} + 32 \, a^{4} c\right)} x^{6} + 128 \, a^{5}\right)} \sqrt{c x^{6} + b x^{3} + a}}{3840 \, a^{4} x^{15}}\right]"," ",0,"[1/7680*(15*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*sqrt(a)*x^15*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 + 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) - 4*((15*a*b^4 - 100*a^2*b^2*c + 128*a^3*c^2)*x^12 - 2*(5*a^2*b^3 - 28*a^3*b*c)*x^9 + 176*a^4*b*x^3 + 8*(a^3*b^2 + 32*a^4*c)*x^6 + 128*a^5)*sqrt(c*x^6 + b*x^3 + a))/(a^4*x^15), -1/3840*(15*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*sqrt(-a)*x^15*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + 2*((15*a*b^4 - 100*a^2*b^2*c + 128*a^3*c^2)*x^12 - 2*(5*a^2*b^3 - 28*a^3*b*c)*x^9 + 176*a^4*b*x^3 + 8*(a^3*b^2 + 32*a^4*c)*x^6 + 128*a^5)*sqrt(c*x^6 + b*x^3 + a))/(a^4*x^15)]","A",0
212,1,473,0,2.090173," ","integrate((c*x^6+b*x^3+a)^(3/2)/x^19,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{a} x^{18} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} + 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) - 4 \, {\left({\left(105 \, a b^{5} - 760 \, a^{2} b^{3} c + 1296 \, a^{3} b c^{2}\right)} x^{15} - 2 \, {\left(35 \, a^{2} b^{4} - 216 \, a^{3} b^{2} c + 240 \, a^{4} c^{2}\right)} x^{12} + 8 \, {\left(7 \, a^{3} b^{3} - 36 \, a^{4} b c\right)} x^{9} - 1664 \, a^{5} b x^{3} - 16 \, {\left(3 \, a^{4} b^{2} + 140 \, a^{5} c\right)} x^{6} - 1280 \, a^{6}\right)} \sqrt{c x^{6} + b x^{3} + a}}{92160 \, a^{5} x^{18}}, \frac{15 \, {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{-a} x^{18} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + 2 \, {\left({\left(105 \, a b^{5} - 760 \, a^{2} b^{3} c + 1296 \, a^{3} b c^{2}\right)} x^{15} - 2 \, {\left(35 \, a^{2} b^{4} - 216 \, a^{3} b^{2} c + 240 \, a^{4} c^{2}\right)} x^{12} + 8 \, {\left(7 \, a^{3} b^{3} - 36 \, a^{4} b c\right)} x^{9} - 1664 \, a^{5} b x^{3} - 16 \, {\left(3 \, a^{4} b^{2} + 140 \, a^{5} c\right)} x^{6} - 1280 \, a^{6}\right)} \sqrt{c x^{6} + b x^{3} + a}}{46080 \, a^{5} x^{18}}\right]"," ",0,"[-1/92160*(15*(7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(a)*x^18*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 + 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) - 4*((105*a*b^5 - 760*a^2*b^3*c + 1296*a^3*b*c^2)*x^15 - 2*(35*a^2*b^4 - 216*a^3*b^2*c + 240*a^4*c^2)*x^12 + 8*(7*a^3*b^3 - 36*a^4*b*c)*x^9 - 1664*a^5*b*x^3 - 16*(3*a^4*b^2 + 140*a^5*c)*x^6 - 1280*a^6)*sqrt(c*x^6 + b*x^3 + a))/(a^5*x^18), 1/46080*(15*(7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(-a)*x^18*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + 2*((105*a*b^5 - 760*a^2*b^3*c + 1296*a^3*b*c^2)*x^15 - 2*(35*a^2*b^4 - 216*a^3*b^2*c + 240*a^4*c^2)*x^12 + 8*(7*a^3*b^3 - 36*a^4*b*c)*x^9 - 1664*a^5*b*x^3 - 16*(3*a^4*b^2 + 140*a^5*c)*x^6 - 1280*a^6)*sqrt(c*x^6 + b*x^3 + a))/(a^5*x^18)]","A",0
213,1,557,0,2.626035," ","integrate((c*x^6+b*x^3+a)^(3/2)/x^22,x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(3 \, b^{7} - 28 \, a b^{5} c + 80 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} \sqrt{a} x^{21} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) + 4 \, {\left({\left(315 \, a b^{6} - 2520 \, a^{2} b^{4} c + 5488 \, a^{3} b^{2} c^{2} - 2048 \, a^{4} c^{3}\right)} x^{18} - 2 \, {\left(105 \, a^{2} b^{5} - 728 \, a^{3} b^{3} c + 1168 \, a^{4} b c^{2}\right)} x^{15} + 8 \, {\left(21 \, a^{3} b^{4} - 124 \, a^{4} b^{2} c + 128 \, a^{5} c^{2}\right)} x^{12} + 6400 \, a^{6} b x^{3} - 16 \, {\left(9 \, a^{4} b^{3} - 44 \, a^{5} b c\right)} x^{9} + 5120 \, a^{7} + 128 \, {\left(a^{5} b^{2} + 64 \, a^{6} c\right)} x^{6}\right)} \sqrt{c x^{6} + b x^{3} + a}}{430080 \, a^{6} x^{21}}, -\frac{105 \, {\left(3 \, b^{7} - 28 \, a b^{5} c + 80 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} \sqrt{-a} x^{21} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + 2 \, {\left({\left(315 \, a b^{6} - 2520 \, a^{2} b^{4} c + 5488 \, a^{3} b^{2} c^{2} - 2048 \, a^{4} c^{3}\right)} x^{18} - 2 \, {\left(105 \, a^{2} b^{5} - 728 \, a^{3} b^{3} c + 1168 \, a^{4} b c^{2}\right)} x^{15} + 8 \, {\left(21 \, a^{3} b^{4} - 124 \, a^{4} b^{2} c + 128 \, a^{5} c^{2}\right)} x^{12} + 6400 \, a^{6} b x^{3} - 16 \, {\left(9 \, a^{4} b^{3} - 44 \, a^{5} b c\right)} x^{9} + 5120 \, a^{7} + 128 \, {\left(a^{5} b^{2} + 64 \, a^{6} c\right)} x^{6}\right)} \sqrt{c x^{6} + b x^{3} + a}}{215040 \, a^{6} x^{21}}\right]"," ",0,"[-1/430080*(105*(3*b^7 - 28*a*b^5*c + 80*a^2*b^3*c^2 - 64*a^3*b*c^3)*sqrt(a)*x^21*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) + 4*((315*a*b^6 - 2520*a^2*b^4*c + 5488*a^3*b^2*c^2 - 2048*a^4*c^3)*x^18 - 2*(105*a^2*b^5 - 728*a^3*b^3*c + 1168*a^4*b*c^2)*x^15 + 8*(21*a^3*b^4 - 124*a^4*b^2*c + 128*a^5*c^2)*x^12 + 6400*a^6*b*x^3 - 16*(9*a^4*b^3 - 44*a^5*b*c)*x^9 + 5120*a^7 + 128*(a^5*b^2 + 64*a^6*c)*x^6)*sqrt(c*x^6 + b*x^3 + a))/(a^6*x^21), -1/215040*(105*(3*b^7 - 28*a*b^5*c + 80*a^2*b^3*c^2 - 64*a^3*b*c^3)*sqrt(-a)*x^21*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + 2*((315*a*b^6 - 2520*a^2*b^4*c + 5488*a^3*b^2*c^2 - 2048*a^4*c^3)*x^18 - 2*(105*a^2*b^5 - 728*a^3*b^3*c + 1168*a^4*b*c^2)*x^15 + 8*(21*a^3*b^4 - 124*a^4*b^2*c + 128*a^5*c^2)*x^12 + 6400*a^6*b*x^3 - 16*(9*a^4*b^3 - 44*a^5*b*c)*x^9 + 5120*a^7 + 128*(a^5*b^2 + 64*a^6*c)*x^6)*sqrt(c*x^6 + b*x^3 + a))/(a^6*x^21)]","A",0
214,0,0,0,1.137101," ","integrate(x^3*(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{9} + b x^{6} + a x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}, x\right)"," ",0,"integral((c*x^9 + b*x^6 + a*x^3)*sqrt(c*x^6 + b*x^3 + a), x)","F",0
215,0,0,0,1.548006," ","integrate(x*(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{7} + b x^{4} + a x\right)} \sqrt{c x^{6} + b x^{3} + a}, x\right)"," ",0,"integral((c*x^7 + b*x^4 + a*x)*sqrt(c*x^6 + b*x^3 + a), x)","F",0
216,0,0,0,1.193844," ","integrate((c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)^(3/2), x)","F",0
217,0,0,0,1.530210," ","integrate((c*x^6+b*x^3+a)^(3/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}}{x^{2}}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)^(3/2)/x^2, x)","F",0
218,0,0,0,1.554884," ","integrate((c*x^6+b*x^3+a)^(3/2)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}}}{x^{3}}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)^(3/2)/x^3, x)","F",0
219,1,303,0,0.640674," ","integrate(x^14/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, b^{4} - 120 \, a b^{2} c + 48 \, a^{2} c^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(48 \, c^{4} x^{9} - 56 \, b c^{3} x^{6} - 105 \, b^{3} c + 220 \, a b c^{2} + 2 \, {\left(35 \, b^{2} c^{2} - 36 \, a c^{3}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{2304 \, c^{5}}, -\frac{3 \, {\left(35 \, b^{4} - 120 \, a b^{2} c + 48 \, a^{2} c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) - 2 \, {\left(48 \, c^{4} x^{9} - 56 \, b c^{3} x^{6} - 105 \, b^{3} c + 220 \, a b c^{2} + 2 \, {\left(35 \, b^{2} c^{2} - 36 \, a c^{3}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{1152 \, c^{5}}\right]"," ",0,"[1/2304*(3*(35*b^4 - 120*a*b^2*c + 48*a^2*c^2)*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) + 4*(48*c^4*x^9 - 56*b*c^3*x^6 - 105*b^3*c + 220*a*b*c^2 + 2*(35*b^2*c^2 - 36*a*c^3)*x^3)*sqrt(c*x^6 + b*x^3 + a))/c^5, -1/1152*(3*(35*b^4 - 120*a*b^2*c + 48*a^2*c^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) - 2*(48*c^4*x^9 - 56*b*c^3*x^6 - 105*b^3*c + 220*a*b*c^2 + 2*(35*b^2*c^2 - 36*a*c^3)*x^3)*sqrt(c*x^6 + b*x^3 + a))/c^5]","A",0
220,1,241,0,1.357335," ","integrate(x^11/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{3} - 12 \, a b c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(8 \, c^{3} x^{6} - 10 \, b c^{2} x^{3} + 15 \, b^{2} c - 16 \, a c^{2}\right)} \sqrt{c x^{6} + b x^{3} + a}}{288 \, c^{4}}, \frac{3 \, {\left(5 \, b^{3} - 12 \, a b c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) + 2 \, {\left(8 \, c^{3} x^{6} - 10 \, b c^{2} x^{3} + 15 \, b^{2} c - 16 \, a c^{2}\right)} \sqrt{c x^{6} + b x^{3} + a}}{144 \, c^{4}}\right]"," ",0,"[-1/288*(3*(5*b^3 - 12*a*b*c)*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) - 4*(8*c^3*x^6 - 10*b*c^2*x^3 + 15*b^2*c - 16*a*c^2)*sqrt(c*x^6 + b*x^3 + a))/c^4, 1/144*(3*(5*b^3 - 12*a*b*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) + 2*(8*c^3*x^6 - 10*b*c^2*x^3 + 15*b^2*c - 16*a*c^2)*sqrt(c*x^6 + b*x^3 + a))/c^4]","A",0
221,1,203,0,1.455592," ","integrate(x^8/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b^{2} - 4 \, a c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} + 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c^{2} x^{3} - 3 \, b c\right)}}{48 \, c^{3}}, -\frac{{\left(3 \, b^{2} - 4 \, a c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) - 2 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c^{2} x^{3} - 3 \, b c\right)}}{24 \, c^{3}}\right]"," ",0,"[-1/48*((3*b^2 - 4*a*c)*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 + 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c^2*x^3 - 3*b*c))/c^3, -1/24*((3*b^2 - 4*a*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) - 2*sqrt(c*x^6 + b*x^3 + a)*(2*c^2*x^3 - 3*b*c))/c^3]","A",0
222,1,161,0,1.346582," ","integrate(x^5/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{b \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} + 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, \sqrt{c x^{6} + b x^{3} + a} c}{12 \, c^{2}}, \frac{b \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) + 2 \, \sqrt{c x^{6} + b x^{3} + a} c}{6 \, c^{2}}\right]"," ",0,"[1/12*(b*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 + 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) + 4*sqrt(c*x^6 + b*x^3 + a)*c)/c^2, 1/6*(b*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) + 2*sqrt(c*x^6 + b*x^3 + a)*c)/c^2]","A",0
223,1,118,0,1.214460," ","integrate(x^2/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right)}{6 \, \sqrt{c}}, -\frac{\sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right)}{3 \, c}\right]"," ",0,"[1/6*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c)/sqrt(c), -1/3*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c))/c]","A",0
224,1,124,0,1.100758," ","integrate(1/x/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right)}{6 \, \sqrt{a}}, \frac{\sqrt{-a} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right)}{3 \, a}\right]"," ",0,"[1/6*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6)/sqrt(a), 1/3*sqrt(-a)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2))/a]","A",0
225,1,179,0,1.359645," ","integrate(1/x^4/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b x^{3} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} + 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) - 4 \, \sqrt{c x^{6} + b x^{3} + a} a}{12 \, a^{2} x^{3}}, -\frac{\sqrt{-a} b x^{3} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + 2 \, \sqrt{c x^{6} + b x^{3} + a} a}{6 \, a^{2} x^{3}}\right]"," ",0,"[1/12*(sqrt(a)*b*x^3*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 + 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) - 4*sqrt(c*x^6 + b*x^3 + a)*a)/(a^2*x^3), -1/6*(sqrt(-a)*b*x^3*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + 2*sqrt(c*x^6 + b*x^3 + a)*a)/(a^2*x^3)]","A",0
226,1,221,0,1.413517," ","integrate(1/x^7/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b^{2} - 4 \, a c\right)} \sqrt{a} x^{6} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} + 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(3 \, a b x^{3} - 2 \, a^{2}\right)}}{48 \, a^{3} x^{6}}, \frac{{\left(3 \, b^{2} - 4 \, a c\right)} \sqrt{-a} x^{6} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + 2 \, \sqrt{c x^{6} + b x^{3} + a} {\left(3 \, a b x^{3} - 2 \, a^{2}\right)}}{24 \, a^{3} x^{6}}\right]"," ",0,"[-1/48*((3*b^2 - 4*a*c)*sqrt(a)*x^6*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 + 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) - 4*sqrt(c*x^6 + b*x^3 + a)*(3*a*b*x^3 - 2*a^2))/(a^3*x^6), 1/24*((3*b^2 - 4*a*c)*sqrt(-a)*x^6*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + 2*sqrt(c*x^6 + b*x^3 + a)*(3*a*b*x^3 - 2*a^2))/(a^3*x^6)]","A",0
227,1,263,0,1.275073," ","integrate(1/x^10/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{3} - 12 \, a b c\right)} \sqrt{a} x^{9} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) + 4 \, {\left({\left(15 \, a b^{2} - 16 \, a^{2} c\right)} x^{6} - 10 \, a^{2} b x^{3} + 8 \, a^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{288 \, a^{4} x^{9}}, -\frac{3 \, {\left(5 \, b^{3} - 12 \, a b c\right)} \sqrt{-a} x^{9} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + 2 \, {\left({\left(15 \, a b^{2} - 16 \, a^{2} c\right)} x^{6} - 10 \, a^{2} b x^{3} + 8 \, a^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{144 \, a^{4} x^{9}}\right]"," ",0,"[-1/288*(3*(5*b^3 - 12*a*b*c)*sqrt(a)*x^9*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) + 4*((15*a*b^2 - 16*a^2*c)*x^6 - 10*a^2*b*x^3 + 8*a^3)*sqrt(c*x^6 + b*x^3 + a))/(a^4*x^9), -1/144*(3*(5*b^3 - 12*a*b*c)*sqrt(-a)*x^9*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + 2*((15*a*b^2 - 16*a^2*c)*x^6 - 10*a^2*b*x^3 + 8*a^3)*sqrt(c*x^6 + b*x^3 + a))/(a^4*x^9)]","A",0
228,1,327,0,1.775761," ","integrate(1/x^13/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, b^{4} - 120 \, a b^{2} c + 48 \, a^{2} c^{2}\right)} \sqrt{a} x^{12} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) + 4 \, {\left(5 \, {\left(21 \, a b^{3} - 44 \, a^{2} b c\right)} x^{9} + 56 \, a^{3} b x^{3} - 2 \, {\left(35 \, a^{2} b^{2} - 36 \, a^{3} c\right)} x^{6} - 48 \, a^{4}\right)} \sqrt{c x^{6} + b x^{3} + a}}{2304 \, a^{5} x^{12}}, \frac{3 \, {\left(35 \, b^{4} - 120 \, a b^{2} c + 48 \, a^{2} c^{2}\right)} \sqrt{-a} x^{12} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + 2 \, {\left(5 \, {\left(21 \, a b^{3} - 44 \, a^{2} b c\right)} x^{9} + 56 \, a^{3} b x^{3} - 2 \, {\left(35 \, a^{2} b^{2} - 36 \, a^{3} c\right)} x^{6} - 48 \, a^{4}\right)} \sqrt{c x^{6} + b x^{3} + a}}{1152 \, a^{5} x^{12}}\right]"," ",0,"[1/2304*(3*(35*b^4 - 120*a*b^2*c + 48*a^2*c^2)*sqrt(a)*x^12*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) + 4*(5*(21*a*b^3 - 44*a^2*b*c)*x^9 + 56*a^3*b*x^3 - 2*(35*a^2*b^2 - 36*a^3*c)*x^6 - 48*a^4)*sqrt(c*x^6 + b*x^3 + a))/(a^5*x^12), 1/1152*(3*(35*b^4 - 120*a*b^2*c + 48*a^2*c^2)*sqrt(-a)*x^12*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + 2*(5*(21*a*b^3 - 44*a^2*b*c)*x^9 + 56*a^3*b*x^3 - 2*(35*a^2*b^2 - 36*a^3*c)*x^6 - 48*a^4)*sqrt(c*x^6 + b*x^3 + a))/(a^5*x^12)]","A",0
229,0,0,0,1.391338," ","integrate(x^3/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{\sqrt{c x^{6} + b x^{3} + a}}, x\right)"," ",0,"integral(x^3/sqrt(c*x^6 + b*x^3 + a), x)","F",0
230,0,0,0,1.323660," ","integrate(x/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\sqrt{c x^{6} + b x^{3} + a}}, x\right)"," ",0,"integral(x/sqrt(c*x^6 + b*x^3 + a), x)","F",0
231,0,0,0,1.256933," ","integrate(1/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{c x^{6} + b x^{3} + a}}, x\right)"," ",0,"integral(1/sqrt(c*x^6 + b*x^3 + a), x)","F",0
232,0,0,0,1.307784," ","integrate(1/x^2/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{6} + b x^{3} + a}}{c x^{8} + b x^{5} + a x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^6 + b*x^3 + a)/(c*x^8 + b*x^5 + a*x^2), x)","F",0
233,0,0,0,1.011070," ","integrate(1/x^3/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{6} + b x^{3} + a}}{c x^{9} + b x^{6} + a x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^6 + b*x^3 + a)/(c*x^9 + b*x^6 + a*x^3), x)","F",0
234,1,591,0,1.905951," ","integrate(x^14/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{6} + 5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(5 \, b^{5} - 24 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{3}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} + 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{9} - 5 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{6} - 15 \, a b^{3} c + 52 \, a^{2} b c^{2} - {\left(15 \, b^{4} c - 62 \, a b^{2} c^{2} + 24 \, a^{2} c^{3}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{48 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{6} + {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x^{3}\right)}}, -\frac{3 \, {\left({\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{6} + 5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(5 \, b^{5} - 24 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) - 2 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{9} - 5 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{6} - 15 \, a b^{3} c + 52 \, a^{2} b c^{2} - {\left(15 \, b^{4} c - 62 \, a b^{2} c^{2} + 24 \, a^{2} c^{3}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{24 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{6} + {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x^{3}\right)}}\right]"," ",0,"[-1/48*(3*((5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*x^6 + 5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2 + (5*b^5 - 24*a*b^3*c + 16*a^2*b*c^2)*x^3)*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 + 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) - 4*(2*(b^2*c^3 - 4*a*c^4)*x^9 - 5*(b^3*c^2 - 4*a*b*c^3)*x^6 - 15*a*b^3*c + 52*a^2*b*c^2 - (15*b^4*c - 62*a*b^2*c^2 + 24*a^2*c^3)*x^3)*sqrt(c*x^6 + b*x^3 + a))/(a*b^2*c^4 - 4*a^2*c^5 + (b^2*c^5 - 4*a*c^6)*x^6 + (b^3*c^4 - 4*a*b*c^5)*x^3), -1/24*(3*((5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*x^6 + 5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2 + (5*b^5 - 24*a*b^3*c + 16*a^2*b*c^2)*x^3)*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) - 2*(2*(b^2*c^3 - 4*a*c^4)*x^9 - 5*(b^3*c^2 - 4*a*b*c^3)*x^6 - 15*a*b^3*c + 52*a^2*b*c^2 - (15*b^4*c - 62*a*b^2*c^2 + 24*a^2*c^3)*x^3)*sqrt(c*x^6 + b*x^3 + a))/(a*b^2*c^4 - 4*a^2*c^5 + (b^2*c^5 - 4*a*c^6)*x^6 + (b^3*c^4 - 4*a*b*c^5)*x^3)]","A",0
235,1,459,0,1.370798," ","integrate(x^11/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} x^{6} + a b^{3} - 4 \, a^{2} b c + {\left(b^{4} - 4 \, a b^{2} c\right)} x^{3}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} + 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{6} + 3 \, a b^{2} c - 8 \, a^{2} c^{2} + {\left(3 \, b^{3} c - 10 \, a b c^{2}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{12 \, {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{6} + a b^{2} c^{3} - 4 \, a^{2} c^{4} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x^{3}\right)}}, \frac{3 \, {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} x^{6} + a b^{3} - 4 \, a^{2} b c + {\left(b^{4} - 4 \, a b^{2} c\right)} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) + 2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{6} + 3 \, a b^{2} c - 8 \, a^{2} c^{2} + {\left(3 \, b^{3} c - 10 \, a b c^{2}\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{6 \, {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{6} + a b^{2} c^{3} - 4 \, a^{2} c^{4} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x^{3}\right)}}\right]"," ",0,"[1/12*(3*((b^3*c - 4*a*b*c^2)*x^6 + a*b^3 - 4*a^2*b*c + (b^4 - 4*a*b^2*c)*x^3)*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 + 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) + 4*((b^2*c^2 - 4*a*c^3)*x^6 + 3*a*b^2*c - 8*a^2*c^2 + (3*b^3*c - 10*a*b*c^2)*x^3)*sqrt(c*x^6 + b*x^3 + a))/((b^2*c^4 - 4*a*c^5)*x^6 + a*b^2*c^3 - 4*a^2*c^4 + (b^3*c^3 - 4*a*b*c^4)*x^3), 1/6*(3*((b^3*c - 4*a*b*c^2)*x^6 + a*b^3 - 4*a^2*b*c + (b^4 - 4*a*b^2*c)*x^3)*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) + 2*((b^2*c^2 - 4*a*c^3)*x^6 + 3*a*b^2*c - 8*a^2*c^2 + (3*b^3*c - 10*a*b*c^2)*x^3)*sqrt(c*x^6 + b*x^3 + a))/((b^2*c^4 - 4*a*c^5)*x^6 + a*b^2*c^3 - 4*a^2*c^4 + (b^3*c^3 - 4*a*b*c^4)*x^3)]","A",0
236,1,387,0,1.337776," ","integrate(x^8/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{6} + {\left(b^{3} - 4 \, a b c\right)} x^{3} + a b^{2} - 4 \, a^{2} c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{6} - 8 \, b c x^{3} - b^{2} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left({\left(b^{2} c - 2 \, a c^{2}\right)} x^{3} + a b c\right)}}{6 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{6} + a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{3}\right)}}, -\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{6} + {\left(b^{3} - 4 \, a b c\right)} x^{3} + a b^{2} - 4 \, a^{2} c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{6} + b c x^{3} + a c\right)}}\right) + 2 \, \sqrt{c x^{6} + b x^{3} + a} {\left({\left(b^{2} c - 2 \, a c^{2}\right)} x^{3} + a b c\right)}}{3 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{6} + a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{3}\right)}}\right]"," ",0,"[1/6*(((b^2*c - 4*a*c^2)*x^6 + (b^3 - 4*a*b*c)*x^3 + a*b^2 - 4*a^2*c)*sqrt(c)*log(-8*c^2*x^6 - 8*b*c*x^3 - b^2 - 4*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(c) - 4*a*c) - 4*sqrt(c*x^6 + b*x^3 + a)*((b^2*c - 2*a*c^2)*x^3 + a*b*c))/((b^2*c^3 - 4*a*c^4)*x^6 + a*b^2*c^2 - 4*a^2*c^3 + (b^3*c^2 - 4*a*b*c^3)*x^3), -1/3*(((b^2*c - 4*a*c^2)*x^6 + (b^3 - 4*a*b*c)*x^3 + a*b^2 - 4*a^2*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)*sqrt(-c)/(c^2*x^6 + b*c*x^3 + a*c)) + 2*sqrt(c*x^6 + b*x^3 + a)*((b^2*c - 2*a*c^2)*x^3 + a*b*c))/((b^2*c^3 - 4*a*c^4)*x^6 + a*b^2*c^2 - 4*a^2*c^3 + (b^3*c^2 - 4*a*b*c^3)*x^3)]","A",0
237,1,68,0,0.945164," ","integrate(x^5/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)}}{3 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{6} + {\left(b^{3} - 4 \, a b c\right)} x^{3} + a b^{2} - 4 \, a^{2} c\right)}}"," ",0,"2/3*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)/((b^2*c - 4*a*c^2)*x^6 + (b^3 - 4*a*b*c)*x^3 + a*b^2 - 4*a^2*c)","A",0
238,1,67,0,1.198496," ","integrate(x^2/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c x^{6} + b x^{3} + a} {\left(2 \, c x^{3} + b\right)}}{3 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{6} + {\left(b^{3} - 4 \, a b c\right)} x^{3} + a b^{2} - 4 \, a^{2} c\right)}}"," ",0,"-2/3*sqrt(c*x^6 + b*x^3 + a)*(2*c*x^3 + b)/((b^2*c - 4*a*c^2)*x^6 + (b^3 - 4*a*b*c)*x^3 + a*b^2 - 4*a^2*c)","A",0
239,1,389,0,1.665769," ","integrate(1/x/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{6} + {\left(b^{3} - 4 \, a b c\right)} x^{3} + a b^{2} - 4 \, a^{2} c\right)} \sqrt{a} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) + 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(a b c x^{3} + a b^{2} - 2 \, a^{2} c\right)}}{6 \, {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{6} + a^{3} b^{2} - 4 \, a^{4} c + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{3}\right)}}, \frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} x^{6} + {\left(b^{3} - 4 \, a b c\right)} x^{3} + a b^{2} - 4 \, a^{2} c\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + 2 \, \sqrt{c x^{6} + b x^{3} + a} {\left(a b c x^{3} + a b^{2} - 2 \, a^{2} c\right)}}{3 \, {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} x^{6} + a^{3} b^{2} - 4 \, a^{4} c + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{3}\right)}}\right]"," ",0,"[1/6*(((b^2*c - 4*a*c^2)*x^6 + (b^3 - 4*a*b*c)*x^3 + a*b^2 - 4*a^2*c)*sqrt(a)*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) + 4*sqrt(c*x^6 + b*x^3 + a)*(a*b*c*x^3 + a*b^2 - 2*a^2*c))/((a^2*b^2*c - 4*a^3*c^2)*x^6 + a^3*b^2 - 4*a^4*c + (a^2*b^3 - 4*a^3*b*c)*x^3), 1/3*(((b^2*c - 4*a*c^2)*x^6 + (b^3 - 4*a*b*c)*x^3 + a*b^2 - 4*a^2*c)*sqrt(-a)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + 2*sqrt(c*x^6 + b*x^3 + a)*(a*b*c*x^3 + a*b^2 - 2*a^2*c))/((a^2*b^2*c - 4*a^3*c^2)*x^6 + a^3*b^2 - 4*a^4*c + (a^2*b^3 - 4*a^3*b*c)*x^3)]","B",0
240,1,485,0,1.526894," ","integrate(1/x^4/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} x^{9} + {\left(b^{4} - 4 \, a b^{2} c\right)} x^{6} + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{3}\right)} \sqrt{a} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} + 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) - 4 \, {\left({\left(3 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{6} + a^{2} b^{2} - 4 \, a^{3} c + {\left(3 \, a b^{3} - 10 \, a^{2} b c\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{12 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{9} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{6} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}\right)}}, -\frac{3 \, {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} x^{9} + {\left(b^{4} - 4 \, a b^{2} c\right)} x^{6} + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{3}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + 2 \, {\left({\left(3 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{6} + a^{2} b^{2} - 4 \, a^{3} c + {\left(3 \, a b^{3} - 10 \, a^{2} b c\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{6 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{9} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{6} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}\right)}}\right]"," ",0,"[1/12*(3*((b^3*c - 4*a*b*c^2)*x^9 + (b^4 - 4*a*b^2*c)*x^6 + (a*b^3 - 4*a^2*b*c)*x^3)*sqrt(a)*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 + 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) - 4*((3*a*b^2*c - 8*a^2*c^2)*x^6 + a^2*b^2 - 4*a^3*c + (3*a*b^3 - 10*a^2*b*c)*x^3)*sqrt(c*x^6 + b*x^3 + a))/((a^3*b^2*c - 4*a^4*c^2)*x^9 + (a^3*b^3 - 4*a^4*b*c)*x^6 + (a^4*b^2 - 4*a^5*c)*x^3), -1/6*(3*((b^3*c - 4*a*b*c^2)*x^9 + (b^4 - 4*a*b^2*c)*x^6 + (a*b^3 - 4*a^2*b*c)*x^3)*sqrt(-a)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + 2*((3*a*b^2*c - 8*a^2*c^2)*x^6 + a^2*b^2 - 4*a^3*c + (3*a*b^3 - 10*a^2*b*c)*x^3)*sqrt(c*x^6 + b*x^3 + a))/((a^3*b^2*c - 4*a^4*c^2)*x^9 + (a^3*b^3 - 4*a^4*b*c)*x^6 + (a^4*b^2 - 4*a^5*c)*x^3)]","A",0
241,1,615,0,1.845987," ","integrate(1/x^7/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{12} + {\left(5 \, b^{5} - 24 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{9} + {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} x^{6}\right)} \sqrt{a} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} + 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) - 4 \, {\left({\left(15 \, a b^{3} c - 52 \, a^{2} b c^{2}\right)} x^{9} + {\left(15 \, a b^{4} - 62 \, a^{2} b^{2} c + 24 \, a^{3} c^{2}\right)} x^{6} - 2 \, a^{3} b^{2} + 8 \, a^{4} c + 5 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{48 \, {\left({\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} x^{12} + {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} x^{9} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} x^{6}\right)}}, \frac{3 \, {\left({\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{12} + {\left(5 \, b^{5} - 24 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x^{9} + {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} x^{6}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + 2 \, {\left({\left(15 \, a b^{3} c - 52 \, a^{2} b c^{2}\right)} x^{9} + {\left(15 \, a b^{4} - 62 \, a^{2} b^{2} c + 24 \, a^{3} c^{2}\right)} x^{6} - 2 \, a^{3} b^{2} + 8 \, a^{4} c + 5 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{24 \, {\left({\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} x^{12} + {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} x^{9} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} x^{6}\right)}}\right]"," ",0,"[-1/48*(3*((5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*x^12 + (5*b^5 - 24*a*b^3*c + 16*a^2*b*c^2)*x^9 + (5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2)*x^6)*sqrt(a)*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 + 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) - 4*((15*a*b^3*c - 52*a^2*b*c^2)*x^9 + (15*a*b^4 - 62*a^2*b^2*c + 24*a^3*c^2)*x^6 - 2*a^3*b^2 + 8*a^4*c + 5*(a^2*b^3 - 4*a^3*b*c)*x^3)*sqrt(c*x^6 + b*x^3 + a))/((a^4*b^2*c - 4*a^5*c^2)*x^12 + (a^4*b^3 - 4*a^5*b*c)*x^9 + (a^5*b^2 - 4*a^6*c)*x^6), 1/24*(3*((5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*x^12 + (5*b^5 - 24*a*b^3*c + 16*a^2*b*c^2)*x^9 + (5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2)*x^6)*sqrt(-a)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + 2*((15*a*b^3*c - 52*a^2*b*c^2)*x^9 + (15*a*b^4 - 62*a^2*b^2*c + 24*a^3*c^2)*x^6 - 2*a^3*b^2 + 8*a^4*c + 5*(a^2*b^3 - 4*a^3*b*c)*x^3)*sqrt(c*x^6 + b*x^3 + a))/((a^4*b^2*c - 4*a^5*c^2)*x^12 + (a^4*b^3 - 4*a^5*b*c)*x^9 + (a^5*b^2 - 4*a^6*c)*x^6)]","A",0
242,1,705,0,2.102817," ","integrate(1/x^10/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(7 \, b^{5} c - 40 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} x^{15} + {\left(7 \, b^{6} - 40 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2}\right)} x^{12} + {\left(7 \, a b^{5} - 40 \, a^{2} b^{3} c + 48 \, a^{3} b c^{2}\right)} x^{9}\right)} \sqrt{a} \log\left(-\frac{{\left(b^{2} + 4 \, a c\right)} x^{6} + 8 \, a b x^{3} - 4 \, \sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{6}}\right) + 4 \, {\left({\left(105 \, a b^{4} c - 460 \, a^{2} b^{2} c^{2} + 256 \, a^{3} c^{3}\right)} x^{12} + {\left(105 \, a b^{5} - 530 \, a^{2} b^{3} c + 488 \, a^{3} b c^{2}\right)} x^{9} + {\left(35 \, a^{2} b^{4} - 172 \, a^{3} b^{2} c + 128 \, a^{4} c^{2}\right)} x^{6} + 8 \, a^{4} b^{2} - 32 \, a^{5} c - 14 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{288 \, {\left({\left(a^{5} b^{2} c - 4 \, a^{6} c^{2}\right)} x^{15} + {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} x^{12} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} x^{9}\right)}}, -\frac{15 \, {\left({\left(7 \, b^{5} c - 40 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} x^{15} + {\left(7 \, b^{6} - 40 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2}\right)} x^{12} + {\left(7 \, a b^{5} - 40 \, a^{2} b^{3} c + 48 \, a^{3} b c^{2}\right)} x^{9}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{6} + b x^{3} + a} {\left(b x^{3} + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{6} + a b x^{3} + a^{2}\right)}}\right) + 2 \, {\left({\left(105 \, a b^{4} c - 460 \, a^{2} b^{2} c^{2} + 256 \, a^{3} c^{3}\right)} x^{12} + {\left(105 \, a b^{5} - 530 \, a^{2} b^{3} c + 488 \, a^{3} b c^{2}\right)} x^{9} + {\left(35 \, a^{2} b^{4} - 172 \, a^{3} b^{2} c + 128 \, a^{4} c^{2}\right)} x^{6} + 8 \, a^{4} b^{2} - 32 \, a^{5} c - 14 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{3}\right)} \sqrt{c x^{6} + b x^{3} + a}}{144 \, {\left({\left(a^{5} b^{2} c - 4 \, a^{6} c^{2}\right)} x^{15} + {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} x^{12} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} x^{9}\right)}}\right]"," ",0,"[-1/288*(15*((7*b^5*c - 40*a*b^3*c^2 + 48*a^2*b*c^3)*x^15 + (7*b^6 - 40*a*b^4*c + 48*a^2*b^2*c^2)*x^12 + (7*a*b^5 - 40*a^2*b^3*c + 48*a^3*b*c^2)*x^9)*sqrt(a)*log(-((b^2 + 4*a*c)*x^6 + 8*a*b*x^3 - 4*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(a) + 8*a^2)/x^6) + 4*((105*a*b^4*c - 460*a^2*b^2*c^2 + 256*a^3*c^3)*x^12 + (105*a*b^5 - 530*a^2*b^3*c + 488*a^3*b*c^2)*x^9 + (35*a^2*b^4 - 172*a^3*b^2*c + 128*a^4*c^2)*x^6 + 8*a^4*b^2 - 32*a^5*c - 14*(a^3*b^3 - 4*a^4*b*c)*x^3)*sqrt(c*x^6 + b*x^3 + a))/((a^5*b^2*c - 4*a^6*c^2)*x^15 + (a^5*b^3 - 4*a^6*b*c)*x^12 + (a^6*b^2 - 4*a^7*c)*x^9), -1/144*(15*((7*b^5*c - 40*a*b^3*c^2 + 48*a^2*b*c^3)*x^15 + (7*b^6 - 40*a*b^4*c + 48*a^2*b^2*c^2)*x^12 + (7*a*b^5 - 40*a^2*b^3*c + 48*a^3*b*c^2)*x^9)*sqrt(-a)*arctan(1/2*sqrt(c*x^6 + b*x^3 + a)*(b*x^3 + 2*a)*sqrt(-a)/(a*c*x^6 + a*b*x^3 + a^2)) + 2*((105*a*b^4*c - 460*a^2*b^2*c^2 + 256*a^3*c^3)*x^12 + (105*a*b^5 - 530*a^2*b^3*c + 488*a^3*b*c^2)*x^9 + (35*a^2*b^4 - 172*a^3*b^2*c + 128*a^4*c^2)*x^6 + 8*a^4*b^2 - 32*a^5*c - 14*(a^3*b^3 - 4*a^4*b*c)*x^3)*sqrt(c*x^6 + b*x^3 + a))/((a^5*b^2*c - 4*a^6*c^2)*x^15 + (a^5*b^3 - 4*a^6*b*c)*x^12 + (a^6*b^2 - 4*a^7*c)*x^9)]","A",0
243,0,0,0,1.185495," ","integrate(x^3/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{6} + b x^{3} + a} x^{3}}{c^{2} x^{12} + 2 \, b c x^{9} + {\left(b^{2} + 2 \, a c\right)} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^6 + b*x^3 + a)*x^3/(c^2*x^12 + 2*b*c*x^9 + (b^2 + 2*a*c)*x^6 + 2*a*b*x^3 + a^2), x)","F",0
244,0,0,0,0.998561," ","integrate(x/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{6} + b x^{3} + a} x}{c^{2} x^{12} + 2 \, b c x^{9} + {\left(b^{2} + 2 \, a c\right)} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^6 + b*x^3 + a)*x/(c^2*x^12 + 2*b*c*x^9 + (b^2 + 2*a*c)*x^6 + 2*a*b*x^3 + a^2), x)","F",0
245,0,0,0,1.383422," ","integrate(1/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{6} + b x^{3} + a}}{c^{2} x^{12} + 2 \, b c x^{9} + {\left(b^{2} + 2 \, a c\right)} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^6 + b*x^3 + a)/(c^2*x^12 + 2*b*c*x^9 + (b^2 + 2*a*c)*x^6 + 2*a*b*x^3 + a^2), x)","F",0
246,0,0,0,1.519300," ","integrate(1/x^2/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{6} + b x^{3} + a}}{c^{2} x^{14} + 2 \, b c x^{11} + {\left(b^{2} + 2 \, a c\right)} x^{8} + 2 \, a b x^{5} + a^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^6 + b*x^3 + a)/(c^2*x^14 + 2*b*c*x^11 + (b^2 + 2*a*c)*x^8 + 2*a*b*x^5 + a^2*x^2), x)","F",0
247,0,0,0,1.634581," ","integrate(1/x^3/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{6} + b x^{3} + a}}{c^{2} x^{15} + 2 \, b c x^{12} + {\left(b^{2} + 2 \, a c\right)} x^{9} + 2 \, a b x^{6} + a^{2} x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^6 + b*x^3 + a)/(c^2*x^15 + 2*b*c*x^12 + (b^2 + 2*a*c)*x^9 + 2*a*b*x^6 + a^2*x^3), x)","F",0
248,1,241,0,1.078368," ","integrate((d*x)^m*(c*x^6+b*x^3+a)^2,x, algorithm=""fricas"")","\frac{{\left({\left(c^{2} m^{4} + 22 \, c^{2} m^{3} + 159 \, c^{2} m^{2} + 418 \, c^{2} m + 280 \, c^{2}\right)} x^{13} + 2 \, {\left(b c m^{4} + 25 \, b c m^{3} + 195 \, b c m^{2} + 535 \, b c m + 364 \, b c\right)} x^{10} + {\left({\left(b^{2} + 2 \, a c\right)} m^{4} + 28 \, {\left(b^{2} + 2 \, a c\right)} m^{3} + 249 \, {\left(b^{2} + 2 \, a c\right)} m^{2} + 520 \, b^{2} + 1040 \, a c + 742 \, {\left(b^{2} + 2 \, a c\right)} m\right)} x^{7} + 2 \, {\left(a b m^{4} + 31 \, a b m^{3} + 321 \, a b m^{2} + 1201 \, a b m + 910 \, a b\right)} x^{4} + {\left(a^{2} m^{4} + 34 \, a^{2} m^{3} + 411 \, a^{2} m^{2} + 2074 \, a^{2} m + 3640 \, a^{2}\right)} x\right)} \left(d x\right)^{m}}{m^{5} + 35 \, m^{4} + 445 \, m^{3} + 2485 \, m^{2} + 5714 \, m + 3640}"," ",0,"((c^2*m^4 + 22*c^2*m^3 + 159*c^2*m^2 + 418*c^2*m + 280*c^2)*x^13 + 2*(b*c*m^4 + 25*b*c*m^3 + 195*b*c*m^2 + 535*b*c*m + 364*b*c)*x^10 + ((b^2 + 2*a*c)*m^4 + 28*(b^2 + 2*a*c)*m^3 + 249*(b^2 + 2*a*c)*m^2 + 520*b^2 + 1040*a*c + 742*(b^2 + 2*a*c)*m)*x^7 + 2*(a*b*m^4 + 31*a*b*m^3 + 321*a*b*m^2 + 1201*a*b*m + 910*a*b)*x^4 + (a^2*m^4 + 34*a^2*m^3 + 411*a^2*m^2 + 2074*a^2*m + 3640*a^2)*x)*(d*x)^m/(m^5 + 35*m^4 + 445*m^3 + 2485*m^2 + 5714*m + 3640)","B",0
249,1,71,0,1.307928," ","integrate((d*x)^m*(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\frac{{\left({\left(c m^{2} + 5 \, c m + 4 \, c\right)} x^{7} + {\left(b m^{2} + 8 \, b m + 7 \, b\right)} x^{4} + {\left(a m^{2} + 11 \, a m + 28 \, a\right)} x\right)} \left(d x\right)^{m}}{m^{3} + 12 \, m^{2} + 39 \, m + 28}"," ",0,"((c*m^2 + 5*c*m + 4*c)*x^7 + (b*m^2 + 8*b*m + 7*b)*x^4 + (a*m^2 + 11*a*m + 28*a)*x)*(d*x)^m/(m^3 + 12*m^2 + 39*m + 28)","A",0
250,0,0,0,1.288584," ","integrate((d*x)^m/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{c x^{6} + b x^{3} + a}, x\right)"," ",0,"integral((d*x)^m/(c*x^6 + b*x^3 + a), x)","F",0
251,0,0,0,1.403954," ","integrate((d*x)^m/(c*x^6+b*x^3+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{c^{2} x^{12} + 2 \, b c x^{9} + {\left(b^{2} + 2 \, a c\right)} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral((d*x)^m/(c^2*x^12 + 2*b*c*x^9 + (b^2 + 2*a*c)*x^6 + 2*a*b*x^3 + a^2), x)","F",0
252,0,0,0,1.229671," ","integrate((d*x)^m*(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{6} + b x^{3} + a\right)}^{\frac{3}{2}} \left(d x\right)^{m}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)^(3/2)*(d*x)^m, x)","F",0
253,0,0,0,1.462893," ","integrate((d*x)^m*(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{6} + b x^{3} + a} \left(d x\right)^{m}, x\right)"," ",0,"integral(sqrt(c*x^6 + b*x^3 + a)*(d*x)^m, x)","F",0
254,0,0,0,0.808128," ","integrate((d*x)^m/(c*x^6+b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{\sqrt{c x^{6} + b x^{3} + a}}, x\right)"," ",0,"integral((d*x)^m/sqrt(c*x^6 + b*x^3 + a), x)","F",0
255,0,0,0,1.176966," ","integrate((d*x)^m/(c*x^6+b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{6} + b x^{3} + a} \left(d x\right)^{m}}{c^{2} x^{12} + 2 \, b c x^{9} + {\left(b^{2} + 2 \, a c\right)} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^6 + b*x^3 + a)*(d*x)^m/(c^2*x^12 + 2*b*c*x^9 + (b^2 + 2*a*c)*x^6 + 2*a*b*x^3 + a^2), x)","F",0
256,0,0,0,0.892409," ","integrate((d*x)^m*(c*x^6+b*x^3+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{6} + b x^{3} + a\right)}^{p} \left(d x\right)^{m}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)^p*(d*x)^m, x)","F",0
257,0,0,0,1.162464," ","integrate(x^8*(c*x^6+b*x^3+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{6} + b x^{3} + a\right)}^{p} x^{8}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)^p*x^8, x)","F",0
258,0,0,0,0.756490," ","integrate(x^5*(c*x^6+b*x^3+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{6} + b x^{3} + a\right)}^{p} x^{5}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)^p*x^5, x)","F",0
259,0,0,0,1.160032," ","integrate(x^2*(c*x^6+b*x^3+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{6} + b x^{3} + a\right)}^{p} x^{2}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)^p*x^2, x)","F",0
260,0,0,0,0.983856," ","integrate(x^4*(c*x^6+b*x^3+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{6} + b x^{3} + a\right)}^{p} x^{4}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)^p*x^4, x)","F",0
261,0,0,0,0.825800," ","integrate(x^3*(c*x^6+b*x^3+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{6} + b x^{3} + a\right)}^{p} x^{3}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)^p*x^3, x)","F",0
262,0,0,0,0.848486," ","integrate(x*(c*x^6+b*x^3+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{6} + b x^{3} + a\right)}^{p} x, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)^p*x, x)","F",0
263,0,0,0,1.059976," ","integrate((c*x^6+b*x^3+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{6} + b x^{3} + a\right)}^{p}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)^p, x)","F",0
264,0,0,0,0.854881," ","integrate((c*x^6+b*x^3+a)^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{6} + b x^{3} + a\right)}^{p}}{x}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)^p/x, x)","F",0
265,0,0,0,1.000244," ","integrate((c*x^6+b*x^3+a)^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{6} + b x^{3} + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)^p/x^2, x)","F",0
266,0,0,0,0.962889," ","integrate((c*x^6+b*x^3+a)^p/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{6} + b x^{3} + a\right)}^{p}}{x^{3}}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)^p/x^3, x)","F",0
267,0,0,0,1.072868," ","integrate((c*x^6+b*x^3+a)^p/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{6} + b x^{3} + a\right)}^{p}}{x^{4}}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)^p/x^4, x)","F",0
268,0,0,0,0.784990," ","integrate((c*x^6+b*x^3+a)^p/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{6} + b x^{3} + a\right)}^{p}}{x^{5}}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)^p/x^5, x)","F",0
269,0,0,0,1.019154," ","integrate((c*x^6+b*x^3+a)^p/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{6} + b x^{3} + a\right)}^{p}}{x^{6}}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)^p/x^6, x)","F",0
270,0,0,0,0.795265," ","integrate((c*x^6+b*x^3+a)^p/x^7,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{6} + b x^{3} + a\right)}^{p}}{x^{7}}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)^p/x^7, x)","F",0
271,0,0,0,1.190303," ","integrate(x^m/(x^8+2*x^4+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{x^{8} + 2 \, x^{4} + 1}, x\right)"," ",0,"integral(x^m/(x^8 + 2*x^4 + 1), x)","F",0
272,1,31,0,0.930869," ","integrate(x^9/(x^8+2*x^4+1),x, algorithm=""fricas"")","\frac{2 \, x^{6} + 3 \, x^{2} - 3 \, {\left(x^{4} + 1\right)} \arctan\left(x^{2}\right)}{4 \, {\left(x^{4} + 1\right)}}"," ",0,"1/4*(2*x^6 + 3*x^2 - 3*(x^4 + 1)*arctan(x^2))/(x^4 + 1)","A",0
273,1,23,0,0.938212," ","integrate(x^7/(x^8+2*x^4+1),x, algorithm=""fricas"")","\frac{{\left(x^{4} + 1\right)} \log\left(x^{4} + 1\right) + 1}{4 \, {\left(x^{4} + 1\right)}}"," ",0,"1/4*((x^4 + 1)*log(x^4 + 1) + 1)/(x^4 + 1)","A",0
274,1,24,0,0.941523," ","integrate(x^5/(x^8+2*x^4+1),x, algorithm=""fricas"")","-\frac{x^{2} - {\left(x^{4} + 1\right)} \arctan\left(x^{2}\right)}{4 \, {\left(x^{4} + 1\right)}}"," ",0,"-1/4*(x^2 - (x^4 + 1)*arctan(x^2))/(x^4 + 1)","A",0
275,1,9,0,0.857862," ","integrate(x^3/(x^8+2*x^4+1),x, algorithm=""fricas"")","-\frac{1}{4 \, {\left(x^{4} + 1\right)}}"," ",0,"-1/4/(x^4 + 1)","A",0
276,1,23,0,1.118573," ","integrate(x/(x^8+2*x^4+1),x, algorithm=""fricas"")","\frac{x^{2} + {\left(x^{4} + 1\right)} \arctan\left(x^{2}\right)}{4 \, {\left(x^{4} + 1\right)}}"," ",0,"1/4*(x^2 + (x^4 + 1)*arctan(x^2))/(x^4 + 1)","A",0
277,1,32,0,0.782247," ","integrate(1/x/(x^8+2*x^4+1),x, algorithm=""fricas"")","-\frac{{\left(x^{4} + 1\right)} \log\left(x^{4} + 1\right) - 4 \, {\left(x^{4} + 1\right)} \log\left(x\right) - 1}{4 \, {\left(x^{4} + 1\right)}}"," ",0,"-1/4*((x^4 + 1)*log(x^4 + 1) - 4*(x^4 + 1)*log(x) - 1)/(x^4 + 1)","A",0
278,1,31,0,1.020815," ","integrate(1/x^3/(x^8+2*x^4+1),x, algorithm=""fricas"")","-\frac{3 \, x^{4} + 3 \, {\left(x^{6} + x^{2}\right)} \arctan\left(x^{2}\right) + 2}{4 \, {\left(x^{6} + x^{2}\right)}}"," ",0,"-1/4*(3*x^4 + 3*(x^6 + x^2)*arctan(x^2) + 2)/(x^6 + x^2)","A",0
279,1,44,0,1.129475," ","integrate(1/x^5/(x^8+2*x^4+1),x, algorithm=""fricas"")","-\frac{2 \, x^{4} - 2 \, {\left(x^{8} + x^{4}\right)} \log\left(x^{4} + 1\right) + 8 \, {\left(x^{8} + x^{4}\right)} \log\left(x\right) + 1}{4 \, {\left(x^{8} + x^{4}\right)}}"," ",0,"-1/4*(2*x^4 - 2*(x^8 + x^4)*log(x^4 + 1) + 8*(x^8 + x^4)*log(x) + 1)/(x^8 + x^4)","A",0
280,1,36,0,1.097452," ","integrate(1/x^7/(x^8+2*x^4+1),x, algorithm=""fricas"")","\frac{15 \, x^{8} + 10 \, x^{4} + 15 \, {\left(x^{10} + x^{6}\right)} \arctan\left(x^{2}\right) - 2}{12 \, {\left(x^{10} + x^{6}\right)}}"," ",0,"1/12*(15*x^8 + 10*x^4 + 15*(x^10 + x^6)*arctan(x^2) - 2)/(x^10 + x^6)","A",0
281,1,132,0,1.018218," ","integrate(x^8/(x^8+2*x^4+1),x, algorithm=""fricas"")","\frac{32 \, x^{5} + 20 \, \sqrt{2} {\left(x^{4} + 1\right)} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + \sqrt{2} x + 1} - 1\right) + 20 \, \sqrt{2} {\left(x^{4} + 1\right)} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} - \sqrt{2} x + 1} + 1\right) - 5 \, \sqrt{2} {\left(x^{4} + 1\right)} \log\left(x^{2} + \sqrt{2} x + 1\right) + 5 \, \sqrt{2} {\left(x^{4} + 1\right)} \log\left(x^{2} - \sqrt{2} x + 1\right) + 40 \, x}{32 \, {\left(x^{4} + 1\right)}}"," ",0,"1/32*(32*x^5 + 20*sqrt(2)*(x^4 + 1)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 + sqrt(2)*x + 1) - 1) + 20*sqrt(2)*(x^4 + 1)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 - sqrt(2)*x + 1) + 1) - 5*sqrt(2)*(x^4 + 1)*log(x^2 + sqrt(2)*x + 1) + 5*sqrt(2)*(x^4 + 1)*log(x^2 - sqrt(2)*x + 1) + 40*x)/(x^4 + 1)","A",0
282,1,129,0,1.365946," ","integrate(x^6/(x^8+2*x^4+1),x, algorithm=""fricas"")","-\frac{8 \, x^{3} + 12 \, \sqrt{2} {\left(x^{4} + 1\right)} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + \sqrt{2} x + 1} - 1\right) + 12 \, \sqrt{2} {\left(x^{4} + 1\right)} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} - \sqrt{2} x + 1} + 1\right) + 3 \, \sqrt{2} {\left(x^{4} + 1\right)} \log\left(x^{2} + \sqrt{2} x + 1\right) - 3 \, \sqrt{2} {\left(x^{4} + 1\right)} \log\left(x^{2} - \sqrt{2} x + 1\right)}{32 \, {\left(x^{4} + 1\right)}}"," ",0,"-1/32*(8*x^3 + 12*sqrt(2)*(x^4 + 1)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 + sqrt(2)*x + 1) - 1) + 12*sqrt(2)*(x^4 + 1)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 - sqrt(2)*x + 1) + 1) + 3*sqrt(2)*(x^4 + 1)*log(x^2 + sqrt(2)*x + 1) - 3*sqrt(2)*(x^4 + 1)*log(x^2 - sqrt(2)*x + 1))/(x^4 + 1)","A",0
283,1,126,0,1.298388," ","integrate(x^4/(x^8+2*x^4+1),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} {\left(x^{4} + 1\right)} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + \sqrt{2} x + 1} - 1\right) + 4 \, \sqrt{2} {\left(x^{4} + 1\right)} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} - \sqrt{2} x + 1} + 1\right) - \sqrt{2} {\left(x^{4} + 1\right)} \log\left(x^{2} + \sqrt{2} x + 1\right) + \sqrt{2} {\left(x^{4} + 1\right)} \log\left(x^{2} - \sqrt{2} x + 1\right) + 8 \, x}{32 \, {\left(x^{4} + 1\right)}}"," ",0,"-1/32*(4*sqrt(2)*(x^4 + 1)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 + sqrt(2)*x + 1) - 1) + 4*sqrt(2)*(x^4 + 1)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 - sqrt(2)*x + 1) + 1) - sqrt(2)*(x^4 + 1)*log(x^2 + sqrt(2)*x + 1) + sqrt(2)*(x^4 + 1)*log(x^2 - sqrt(2)*x + 1) + 8*x)/(x^4 + 1)","A",0
284,1,128,0,1.107952," ","integrate(x^2/(x^8+2*x^4+1),x, algorithm=""fricas"")","\frac{8 \, x^{3} - 4 \, \sqrt{2} {\left(x^{4} + 1\right)} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + \sqrt{2} x + 1} - 1\right) - 4 \, \sqrt{2} {\left(x^{4} + 1\right)} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} - \sqrt{2} x + 1} + 1\right) - \sqrt{2} {\left(x^{4} + 1\right)} \log\left(x^{2} + \sqrt{2} x + 1\right) + \sqrt{2} {\left(x^{4} + 1\right)} \log\left(x^{2} - \sqrt{2} x + 1\right)}{32 \, {\left(x^{4} + 1\right)}}"," ",0,"1/32*(8*x^3 - 4*sqrt(2)*(x^4 + 1)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 + sqrt(2)*x + 1) - 1) - 4*sqrt(2)*(x^4 + 1)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 - sqrt(2)*x + 1) + 1) - sqrt(2)*(x^4 + 1)*log(x^2 + sqrt(2)*x + 1) + sqrt(2)*(x^4 + 1)*log(x^2 - sqrt(2)*x + 1))/(x^4 + 1)","A",0
285,1,127,0,1.131615," ","integrate(1/(x^8+2*x^4+1),x, algorithm=""fricas"")","-\frac{12 \, \sqrt{2} {\left(x^{4} + 1\right)} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + \sqrt{2} x + 1} - 1\right) + 12 \, \sqrt{2} {\left(x^{4} + 1\right)} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} - \sqrt{2} x + 1} + 1\right) - 3 \, \sqrt{2} {\left(x^{4} + 1\right)} \log\left(x^{2} + \sqrt{2} x + 1\right) + 3 \, \sqrt{2} {\left(x^{4} + 1\right)} \log\left(x^{2} - \sqrt{2} x + 1\right) - 8 \, x}{32 \, {\left(x^{4} + 1\right)}}"," ",0,"-1/32*(12*sqrt(2)*(x^4 + 1)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 + sqrt(2)*x + 1) - 1) + 12*sqrt(2)*(x^4 + 1)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 - sqrt(2)*x + 1) + 1) - 3*sqrt(2)*(x^4 + 1)*log(x^2 + sqrt(2)*x + 1) + 3*sqrt(2)*(x^4 + 1)*log(x^2 - sqrt(2)*x + 1) - 8*x)/(x^4 + 1)","A",0
286,1,130,0,1.275124," ","integrate(1/x^2/(x^8+2*x^4+1),x, algorithm=""fricas"")","-\frac{40 \, x^{4} - 20 \, \sqrt{2} {\left(x^{5} + x\right)} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + \sqrt{2} x + 1} - 1\right) - 20 \, \sqrt{2} {\left(x^{5} + x\right)} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} - \sqrt{2} x + 1} + 1\right) - 5 \, \sqrt{2} {\left(x^{5} + x\right)} \log\left(x^{2} + \sqrt{2} x + 1\right) + 5 \, \sqrt{2} {\left(x^{5} + x\right)} \log\left(x^{2} - \sqrt{2} x + 1\right) + 32}{32 \, {\left(x^{5} + x\right)}}"," ",0,"-1/32*(40*x^4 - 20*sqrt(2)*(x^5 + x)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 + sqrt(2)*x + 1) - 1) - 20*sqrt(2)*(x^5 + x)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 - sqrt(2)*x + 1) + 1) - 5*sqrt(2)*(x^5 + x)*log(x^2 + sqrt(2)*x + 1) + 5*sqrt(2)*(x^5 + x)*log(x^2 - sqrt(2)*x + 1) + 32)/(x^5 + x)","A",0
287,1,140,0,1.305344," ","integrate(1/x^4/(x^8+2*x^4+1),x, algorithm=""fricas"")","-\frac{56 \, x^{4} - 84 \, \sqrt{2} {\left(x^{7} + x^{3}\right)} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + \sqrt{2} x + 1} - 1\right) - 84 \, \sqrt{2} {\left(x^{7} + x^{3}\right)} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} - \sqrt{2} x + 1} + 1\right) + 21 \, \sqrt{2} {\left(x^{7} + x^{3}\right)} \log\left(x^{2} + \sqrt{2} x + 1\right) - 21 \, \sqrt{2} {\left(x^{7} + x^{3}\right)} \log\left(x^{2} - \sqrt{2} x + 1\right) + 32}{96 \, {\left(x^{7} + x^{3}\right)}}"," ",0,"-1/96*(56*x^4 - 84*sqrt(2)*(x^7 + x^3)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 + sqrt(2)*x + 1) - 1) - 84*sqrt(2)*(x^7 + x^3)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 - sqrt(2)*x + 1) + 1) + 21*sqrt(2)*(x^7 + x^3)*log(x^2 + sqrt(2)*x + 1) - 21*sqrt(2)*(x^7 + x^3)*log(x^2 - sqrt(2)*x + 1) + 32)/(x^7 + x^3)","A",0
288,1,145,0,1.279160," ","integrate(1/x^6/(x^8+2*x^4+1),x, algorithm=""fricas"")","\frac{360 \, x^{8} + 288 \, x^{4} - 180 \, \sqrt{2} {\left(x^{9} + x^{5}\right)} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + \sqrt{2} x + 1} - 1\right) - 180 \, \sqrt{2} {\left(x^{9} + x^{5}\right)} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} - \sqrt{2} x + 1} + 1\right) - 45 \, \sqrt{2} {\left(x^{9} + x^{5}\right)} \log\left(x^{2} + \sqrt{2} x + 1\right) + 45 \, \sqrt{2} {\left(x^{9} + x^{5}\right)} \log\left(x^{2} - \sqrt{2} x + 1\right) - 32}{160 \, {\left(x^{9} + x^{5}\right)}}"," ",0,"1/160*(360*x^8 + 288*x^4 - 180*sqrt(2)*(x^9 + x^5)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 + sqrt(2)*x + 1) - 1) - 180*sqrt(2)*(x^9 + x^5)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 - sqrt(2)*x + 1) + 1) - 45*sqrt(2)*(x^9 + x^5)*log(x^2 + sqrt(2)*x + 1) + 45*sqrt(2)*(x^9 + x^5)*log(x^2 - sqrt(2)*x + 1) - 32)/(x^9 + x^5)","A",0
289,1,145,0,1.234565," ","integrate(1/x^8/(x^8+2*x^4+1),x, algorithm=""fricas"")","\frac{616 \, x^{8} + 352 \, x^{4} - 924 \, \sqrt{2} {\left(x^{11} + x^{7}\right)} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + \sqrt{2} x + 1} - 1\right) - 924 \, \sqrt{2} {\left(x^{11} + x^{7}\right)} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} - \sqrt{2} x + 1} + 1\right) + 231 \, \sqrt{2} {\left(x^{11} + x^{7}\right)} \log\left(x^{2} + \sqrt{2} x + 1\right) - 231 \, \sqrt{2} {\left(x^{11} + x^{7}\right)} \log\left(x^{2} - \sqrt{2} x + 1\right) - 96}{672 \, {\left(x^{11} + x^{7}\right)}}"," ",0,"1/672*(616*x^8 + 352*x^4 - 924*sqrt(2)*(x^11 + x^7)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 + sqrt(2)*x + 1) - 1) - 924*sqrt(2)*(x^11 + x^7)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 - sqrt(2)*x + 1) + 1) + 231*sqrt(2)*(x^11 + x^7)*log(x^2 + sqrt(2)*x + 1) - 231*sqrt(2)*(x^11 + x^7)*log(x^2 - sqrt(2)*x + 1) - 96)/(x^11 + x^7)","A",0
290,0,0,0,1.133489," ","integrate(x^m/(x^8-2*x^4+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{x^{8} - 2 \, x^{4} + 1}, x\right)"," ",0,"integral(x^m/(x^8 - 2*x^4 + 1), x)","F",0
291,1,46,0,1.141366," ","integrate(x^9/(x^8-2*x^4+1),x, algorithm=""fricas"")","\frac{4 \, x^{6} - 6 \, x^{2} - 3 \, {\left(x^{4} - 1\right)} \log\left(x^{2} + 1\right) + 3 \, {\left(x^{4} - 1\right)} \log\left(x^{2} - 1\right)}{8 \, {\left(x^{4} - 1\right)}}"," ",0,"1/8*(4*x^6 - 6*x^2 - 3*(x^4 - 1)*log(x^2 + 1) + 3*(x^4 - 1)*log(x^2 - 1))/(x^4 - 1)","A",0
292,1,23,0,1.268286," ","integrate(x^7/(x^8-2*x^4+1),x, algorithm=""fricas"")","\frac{{\left(x^{4} - 1\right)} \log\left(x^{4} - 1\right) - 1}{4 \, {\left(x^{4} - 1\right)}}"," ",0,"1/4*((x^4 - 1)*log(x^4 - 1) - 1)/(x^4 - 1)","A",0
293,1,40,0,1.168332," ","integrate(x^5/(x^8-2*x^4+1),x, algorithm=""fricas"")","-\frac{2 \, x^{2} + {\left(x^{4} - 1\right)} \log\left(x^{2} + 1\right) - {\left(x^{4} - 1\right)} \log\left(x^{2} - 1\right)}{8 \, {\left(x^{4} - 1\right)}}"," ",0,"-1/8*(2*x^2 + (x^4 - 1)*log(x^2 + 1) - (x^4 - 1)*log(x^2 - 1))/(x^4 - 1)","B",0
294,1,9,0,1.145720," ","integrate(x^3/(x^8-2*x^4+1),x, algorithm=""fricas"")","-\frac{1}{4 \, {\left(x^{4} - 1\right)}}"," ",0,"-1/4/(x^4 - 1)","A",0
295,1,40,0,1.260293," ","integrate(x/(x^8-2*x^4+1),x, algorithm=""fricas"")","-\frac{2 \, x^{2} - {\left(x^{4} - 1\right)} \log\left(x^{2} + 1\right) + {\left(x^{4} - 1\right)} \log\left(x^{2} - 1\right)}{8 \, {\left(x^{4} - 1\right)}}"," ",0,"-1/8*(2*x^2 - (x^4 - 1)*log(x^2 + 1) + (x^4 - 1)*log(x^2 - 1))/(x^4 - 1)","B",0
296,1,32,0,0.980877," ","integrate(1/x/(x^8-2*x^4+1),x, algorithm=""fricas"")","-\frac{{\left(x^{4} - 1\right)} \log\left(x^{4} - 1\right) - 4 \, {\left(x^{4} - 1\right)} \log\left(x\right) + 1}{4 \, {\left(x^{4} - 1\right)}}"," ",0,"-1/4*((x^4 - 1)*log(x^4 - 1) - 4*(x^4 - 1)*log(x) + 1)/(x^4 - 1)","A",0
297,1,54,0,1.162438," ","integrate(1/x^3/(x^8-2*x^4+1),x, algorithm=""fricas"")","-\frac{6 \, x^{4} - 3 \, {\left(x^{6} - x^{2}\right)} \log\left(x^{2} + 1\right) + 3 \, {\left(x^{6} - x^{2}\right)} \log\left(x^{2} - 1\right) - 4}{8 \, {\left(x^{6} - x^{2}\right)}}"," ",0,"-1/8*(6*x^4 - 3*(x^6 - x^2)*log(x^2 + 1) + 3*(x^6 - x^2)*log(x^2 - 1) - 4)/(x^6 - x^2)","B",0
298,1,50,0,0.862832," ","integrate(1/x^5/(x^8-2*x^4+1),x, algorithm=""fricas"")","-\frac{2 \, x^{4} + 2 \, {\left(x^{8} - x^{4}\right)} \log\left(x^{4} - 1\right) - 8 \, {\left(x^{8} - x^{4}\right)} \log\left(x\right) - 1}{4 \, {\left(x^{8} - x^{4}\right)}}"," ",0,"-1/4*(2*x^4 + 2*(x^8 - x^4)*log(x^4 - 1) - 8*(x^8 - x^4)*log(x) - 1)/(x^8 - x^4)","A",0
299,1,59,0,1.226548," ","integrate(1/x^7/(x^8-2*x^4+1),x, algorithm=""fricas"")","-\frac{30 \, x^{8} - 20 \, x^{4} - 15 \, {\left(x^{10} - x^{6}\right)} \log\left(x^{2} + 1\right) + 15 \, {\left(x^{10} - x^{6}\right)} \log\left(x^{2} - 1\right) - 4}{24 \, {\left(x^{10} - x^{6}\right)}}"," ",0,"-1/24*(30*x^8 - 20*x^4 - 15*(x^10 - x^6)*log(x^2 + 1) + 15*(x^10 - x^6)*log(x^2 - 1) - 4)/(x^10 - x^6)","B",0
300,1,49,0,1.190217," ","integrate(x^8/(x^8-2*x^4+1),x, algorithm=""fricas"")","\frac{16 \, x^{5} - 10 \, {\left(x^{4} - 1\right)} \arctan\left(x\right) - 5 \, {\left(x^{4} - 1\right)} \log\left(x + 1\right) + 5 \, {\left(x^{4} - 1\right)} \log\left(x - 1\right) - 20 \, x}{16 \, {\left(x^{4} - 1\right)}}"," ",0,"1/16*(16*x^5 - 10*(x^4 - 1)*arctan(x) - 5*(x^4 - 1)*log(x + 1) + 5*(x^4 - 1)*log(x - 1) - 20*x)/(x^4 - 1)","B",0
301,1,46,0,1.232466," ","integrate(x^6/(x^8-2*x^4+1),x, algorithm=""fricas"")","-\frac{4 \, x^{3} - 6 \, {\left(x^{4} - 1\right)} \arctan\left(x\right) + 3 \, {\left(x^{4} - 1\right)} \log\left(x + 1\right) - 3 \, {\left(x^{4} - 1\right)} \log\left(x - 1\right)}{16 \, {\left(x^{4} - 1\right)}}"," ",0,"-1/16*(4*x^3 - 6*(x^4 - 1)*arctan(x) + 3*(x^4 - 1)*log(x + 1) - 3*(x^4 - 1)*log(x - 1))/(x^4 - 1)","B",0
302,1,43,0,1.267893," ","integrate(x^4/(x^8-2*x^4+1),x, algorithm=""fricas"")","-\frac{2 \, {\left(x^{4} - 1\right)} \arctan\left(x\right) + {\left(x^{4} - 1\right)} \log\left(x + 1\right) - {\left(x^{4} - 1\right)} \log\left(x - 1\right) + 4 \, x}{16 \, {\left(x^{4} - 1\right)}}"," ",0,"-1/16*(2*(x^4 - 1)*arctan(x) + (x^4 - 1)*log(x + 1) - (x^4 - 1)*log(x - 1) + 4*x)/(x^4 - 1)","B",0
303,1,45,0,1.216643," ","integrate(x^2/(x^8-2*x^4+1),x, algorithm=""fricas"")","-\frac{4 \, x^{3} + 2 \, {\left(x^{4} - 1\right)} \arctan\left(x\right) - {\left(x^{4} - 1\right)} \log\left(x + 1\right) + {\left(x^{4} - 1\right)} \log\left(x - 1\right)}{16 \, {\left(x^{4} - 1\right)}}"," ",0,"-1/16*(4*x^3 + 2*(x^4 - 1)*arctan(x) - (x^4 - 1)*log(x + 1) + (x^4 - 1)*log(x - 1))/(x^4 - 1)","B",0
304,1,44,0,1.298986," ","integrate(1/(x^8-2*x^4+1),x, algorithm=""fricas"")","\frac{6 \, {\left(x^{4} - 1\right)} \arctan\left(x\right) + 3 \, {\left(x^{4} - 1\right)} \log\left(x + 1\right) - 3 \, {\left(x^{4} - 1\right)} \log\left(x - 1\right) - 4 \, x}{16 \, {\left(x^{4} - 1\right)}}"," ",0,"1/16*(6*(x^4 - 1)*arctan(x) + 3*(x^4 - 1)*log(x + 1) - 3*(x^4 - 1)*log(x - 1) - 4*x)/(x^4 - 1)","B",0
305,1,55,0,1.255248," ","integrate(1/x^2/(x^8-2*x^4+1),x, algorithm=""fricas"")","-\frac{20 \, x^{4} + 10 \, {\left(x^{5} - x\right)} \arctan\left(x\right) - 5 \, {\left(x^{5} - x\right)} \log\left(x + 1\right) + 5 \, {\left(x^{5} - x\right)} \log\left(x - 1\right) - 16}{16 \, {\left(x^{5} - x\right)}}"," ",0,"-1/16*(20*x^4 + 10*(x^5 - x)*arctan(x) - 5*(x^5 - x)*log(x + 1) + 5*(x^5 - x)*log(x - 1) - 16)/(x^5 - x)","B",0
306,1,63,0,1.220987," ","integrate(1/x^4/(x^8-2*x^4+1),x, algorithm=""fricas"")","-\frac{28 \, x^{4} - 42 \, {\left(x^{7} - x^{3}\right)} \arctan\left(x\right) - 21 \, {\left(x^{7} - x^{3}\right)} \log\left(x + 1\right) + 21 \, {\left(x^{7} - x^{3}\right)} \log\left(x - 1\right) - 16}{48 \, {\left(x^{7} - x^{3}\right)}}"," ",0,"-1/48*(28*x^4 - 42*(x^7 - x^3)*arctan(x) - 21*(x^7 - x^3)*log(x + 1) + 21*(x^7 - x^3)*log(x - 1) - 16)/(x^7 - x^3)","B",0
307,1,68,0,1.358205," ","integrate(1/x^6/(x^8-2*x^4+1),x, algorithm=""fricas"")","-\frac{180 \, x^{8} - 144 \, x^{4} + 90 \, {\left(x^{9} - x^{5}\right)} \arctan\left(x\right) - 45 \, {\left(x^{9} - x^{5}\right)} \log\left(x + 1\right) + 45 \, {\left(x^{9} - x^{5}\right)} \log\left(x - 1\right) - 16}{80 \, {\left(x^{9} - x^{5}\right)}}"," ",0,"-1/80*(180*x^8 - 144*x^4 + 90*(x^9 - x^5)*arctan(x) - 45*(x^9 - x^5)*log(x + 1) + 45*(x^9 - x^5)*log(x - 1) - 16)/(x^9 - x^5)","B",0
308,1,68,0,1.177531," ","integrate(1/x^8/(x^8-2*x^4+1),x, algorithm=""fricas"")","-\frac{308 \, x^{8} - 176 \, x^{4} - 462 \, {\left(x^{11} - x^{7}\right)} \arctan\left(x\right) - 231 \, {\left(x^{11} - x^{7}\right)} \log\left(x + 1\right) + 231 \, {\left(x^{11} - x^{7}\right)} \log\left(x - 1\right) - 48}{336 \, {\left(x^{11} - x^{7}\right)}}"," ",0,"-1/336*(308*x^8 - 176*x^4 - 462*(x^11 - x^7)*arctan(x) - 231*(x^11 - x^7)*log(x + 1) + 231*(x^11 - x^7)*log(x - 1) - 48)/(x^11 - x^7)","B",0
309,0,0,0,1.218007," ","integrate(x^m/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{c x^{8} + b x^{4} + a}, x\right)"," ",0,"integral(x^m/(c*x^8 + b*x^4 + a), x)","F",0
310,1,254,0,1.365036," ","integrate(x^11/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} - {\left(b^{2} - 2 \, a c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{8} + 2 \, b c x^{4} + b^{2} - 2 \, a c + {\left(2 \, c x^{4} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{8} + b x^{4} + a}\right) - {\left(b^{3} - 4 \, a b c\right)} \log\left(c x^{8} + b x^{4} + a\right)}{8 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}, \frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x^{4} - 2 \, {\left(b^{2} - 2 \, a c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{4} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left(b^{3} - 4 \, a b c\right)} \log\left(c x^{8} + b x^{4} + a\right)}{8 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}\right]"," ",0,"[1/8*(2*(b^2*c - 4*a*c^2)*x^4 - (b^2 - 2*a*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^8 + 2*b*c*x^4 + b^2 - 2*a*c + (2*c*x^4 + b)*sqrt(b^2 - 4*a*c))/(c*x^8 + b*x^4 + a)) - (b^3 - 4*a*b*c)*log(c*x^8 + b*x^4 + a))/(b^2*c^2 - 4*a*c^3), 1/8*(2*(b^2*c - 4*a*c^2)*x^4 - 2*(b^2 - 2*a*c)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^4 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - (b^3 - 4*a*b*c)*log(c*x^8 + b*x^4 + a))/(b^2*c^2 - 4*a*c^3)]","A",0
311,1,1071,0,1.439204," ","integrate(x^9/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} c \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-{\left(a b^{2} - a^{2} c\right)} x^{2} + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{3} - 3 \, a b c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-{\left(a b^{2} - a^{2} c\right)} x^{2} - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{3} - 3 \, a b c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-{\left(a b^{2} - a^{2} c\right)} x^{2} + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{3} - 3 \, a b c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-{\left(a b^{2} - a^{2} c\right)} x^{2} - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}}\right) - 2 \, x^{2}}{4 \, c}"," ",0,"-1/4*(sqrt(1/2)*c*sqrt(-(b^3 - 3*a*b*c + (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-(a*b^2 - a^2*c)*x^2 + 1/2*sqrt(1/2)*(b^4 - 5*a*b^2*c + 4*a^2*c^2 - (b^3*c^3 - 4*a*b*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(b^3 - 3*a*b*c + (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))) - sqrt(1/2)*c*sqrt(-(b^3 - 3*a*b*c + (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-(a*b^2 - a^2*c)*x^2 - 1/2*sqrt(1/2)*(b^4 - 5*a*b^2*c + 4*a^2*c^2 - (b^3*c^3 - 4*a*b*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(b^3 - 3*a*b*c + (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))) + sqrt(1/2)*c*sqrt(-(b^3 - 3*a*b*c - (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-(a*b^2 - a^2*c)*x^2 + 1/2*sqrt(1/2)*(b^4 - 5*a*b^2*c + 4*a^2*c^2 + (b^3*c^3 - 4*a*b*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(b^3 - 3*a*b*c - (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))) - sqrt(1/2)*c*sqrt(-(b^3 - 3*a*b*c - (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-(a*b^2 - a^2*c)*x^2 - 1/2*sqrt(1/2)*(b^4 - 5*a*b^2*c + 4*a^2*c^2 + (b^3*c^3 - 4*a*b*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(b^3 - 3*a*b*c - (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))) - 2*x^2)/c","B",0
312,1,197,0,1.422057," ","integrate(x^7/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} - 4 \, a c} b \log\left(\frac{2 \, c^{2} x^{8} + 2 \, b c x^{4} + b^{2} - 2 \, a c + {\left(2 \, c x^{4} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{8} + b x^{4} + a}\right) + {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{8} + b x^{4} + a\right)}{8 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}, \frac{2 \, \sqrt{-b^{2} + 4 \, a c} b \arctan\left(-\frac{{\left(2 \, c x^{4} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) + {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{8} + b x^{4} + a\right)}{8 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\right]"," ",0,"[1/8*(sqrt(b^2 - 4*a*c)*b*log((2*c^2*x^8 + 2*b*c*x^4 + b^2 - 2*a*c + (2*c*x^4 + b)*sqrt(b^2 - 4*a*c))/(c*x^8 + b*x^4 + a)) + (b^2 - 4*a*c)*log(c*x^8 + b*x^4 + a))/(b^2*c - 4*a*c^2), 1/8*(2*sqrt(-b^2 + 4*a*c)*b*arctan(-(2*c*x^4 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) + (b^2 - 4*a*c)*log(c*x^8 + b*x^4 + a))/(b^2*c - 4*a*c^2)]","A",0
313,1,567,0,1.249041," ","integrate(x^5/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b + \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(x^{2} + \frac{\sqrt{\frac{1}{2}} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{-\frac{b + \frac{b^{2} c - 4 \, a c^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}\right) - \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b + \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(x^{2} - \frac{\sqrt{\frac{1}{2}} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{-\frac{b + \frac{b^{2} c - 4 \, a c^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}\right) - \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b - \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(x^{2} + \frac{\sqrt{\frac{1}{2}} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{-\frac{b - \frac{b^{2} c - 4 \, a c^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}\right) + \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b - \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(x^{2} - \frac{\sqrt{\frac{1}{2}} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{-\frac{b - \frac{b^{2} c - 4 \, a c^{2}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}}}{\sqrt{b^{2} c^{2} - 4 \, a c^{3}}}\right)"," ",0,"1/4*sqrt(1/2)*sqrt(-(b + (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2))*log(x^2 + sqrt(1/2)*(b^2*c - 4*a*c^2)*sqrt(-(b + (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2))/sqrt(b^2*c^2 - 4*a*c^3)) - 1/4*sqrt(1/2)*sqrt(-(b + (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2))*log(x^2 - sqrt(1/2)*(b^2*c - 4*a*c^2)*sqrt(-(b + (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2))/sqrt(b^2*c^2 - 4*a*c^3)) - 1/4*sqrt(1/2)*sqrt(-(b - (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2))*log(x^2 + sqrt(1/2)*(b^2*c - 4*a*c^2)*sqrt(-(b - (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2))/sqrt(b^2*c^2 - 4*a*c^3)) + 1/4*sqrt(1/2)*sqrt(-(b - (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2))*log(x^2 - sqrt(1/2)*(b^2*c - 4*a*c^2)*sqrt(-(b - (b^2*c - 4*a*c^2)/sqrt(b^2*c^2 - 4*a*c^3))/(b^2*c - 4*a*c^2))/sqrt(b^2*c^2 - 4*a*c^3))","B",0
314,1,129,0,1.294621," ","integrate(x^3/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{2 \, c^{2} x^{8} + 2 \, b c x^{4} + b^{2} - 2 \, a c - {\left(2 \, c x^{4} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{8} + b x^{4} + a}\right)}{4 \, \sqrt{b^{2} - 4 \, a c}}, -\frac{\sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{4} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right)}{2 \, {\left(b^{2} - 4 \, a c\right)}}\right]"," ",0,"[1/4*log((2*c^2*x^8 + 2*b*c*x^4 + b^2 - 2*a*c - (2*c*x^4 + b)*sqrt(b^2 - 4*a*c))/(c*x^8 + b*x^4 + a))/sqrt(b^2 - 4*a*c), -1/2*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^4 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c))/(b^2 - 4*a*c)]","A",0
315,1,619,0,1.254284," ","integrate(x/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{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(c x^{2} + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{2} - 4 \, a c - \frac{a b^{3} - 4 \, a^{2} b c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}\right)} \sqrt{-\frac{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}}\right) + \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{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(c x^{2} - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{2} - 4 \, a c - \frac{a b^{3} - 4 \, a^{2} b c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}\right)} \sqrt{-\frac{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}}\right) - \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{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(c x^{2} + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{2} - 4 \, a c + \frac{a b^{3} - 4 \, a^{2} b c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}\right)} \sqrt{-\frac{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}}\right) + \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{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(c x^{2} - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{2} - 4 \, a c + \frac{a b^{3} - 4 \, a^{2} b c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}\right)} \sqrt{-\frac{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}}\right)"," ",0,"-1/4*sqrt(1/2)*sqrt(-(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(c*x^2 + 1/2*sqrt(1/2)*(b^2 - 4*a*c - (a*b^3 - 4*a^2*b*c)/sqrt(a^2*b^2 - 4*a^3*c))*sqrt(-(b + (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))) + 1/4*sqrt(1/2)*sqrt(-(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(c*x^2 - 1/2*sqrt(1/2)*(b^2 - 4*a*c - (a*b^3 - 4*a^2*b*c)/sqrt(a^2*b^2 - 4*a^3*c))*sqrt(-(b + (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))) - 1/4*sqrt(1/2)*sqrt(-(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(c*x^2 + 1/2*sqrt(1/2)*(b^2 - 4*a*c + (a*b^3 - 4*a^2*b*c)/sqrt(a^2*b^2 - 4*a^3*c))*sqrt(-(b - (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))) + 1/4*sqrt(1/2)*sqrt(-(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(c*x^2 - 1/2*sqrt(1/2)*(b^2 - 4*a*c + (a*b^3 - 4*a^2*b*c)/sqrt(a^2*b^2 - 4*a^3*c))*sqrt(-(b - (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c)))","B",0
316,1,223,0,1.240033," ","integrate(1/x/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} - 4 \, a c} b \log\left(\frac{2 \, c^{2} x^{8} + 2 \, b c x^{4} + b^{2} - 2 \, a c + {\left(2 \, c x^{4} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{8} + b x^{4} + a}\right) - {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{8} + b x^{4} + a\right) + 8 \, {\left(b^{2} - 4 \, a c\right)} \log\left(x\right)}{8 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}, \frac{2 \, \sqrt{-b^{2} + 4 \, a c} b \arctan\left(-\frac{{\left(2 \, c x^{4} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{8} + b x^{4} + a\right) + 8 \, {\left(b^{2} - 4 \, a c\right)} \log\left(x\right)}{8 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}\right]"," ",0,"[1/8*(sqrt(b^2 - 4*a*c)*b*log((2*c^2*x^8 + 2*b*c*x^4 + b^2 - 2*a*c + (2*c*x^4 + b)*sqrt(b^2 - 4*a*c))/(c*x^8 + b*x^4 + a)) - (b^2 - 4*a*c)*log(c*x^8 + b*x^4 + a) + 8*(b^2 - 4*a*c)*log(x))/(a*b^2 - 4*a^2*c), 1/8*(2*sqrt(-b^2 + 4*a*c)*b*arctan(-(2*c*x^4 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - (b^2 - 4*a*c)*log(c*x^8 + b*x^4 + a) + 8*(b^2 - 4*a*c)*log(x))/(a*b^2 - 4*a^2*c)]","A",0
317,1,1134,0,1.403566," ","integrate(1/x^3/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} a x^{2} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(-{\left(b^{2} c^{2} - a c^{3}\right)} x^{2} + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2} - {\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}\right) - \sqrt{\frac{1}{2}} a x^{2} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(-{\left(b^{2} c^{2} - a c^{3}\right)} x^{2} - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2} - {\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}\right) + \sqrt{\frac{1}{2}} a x^{2} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(-{\left(b^{2} c^{2} - a c^{3}\right)} x^{2} + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2} + {\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}\right) - \sqrt{\frac{1}{2}} a x^{2} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left(-{\left(b^{2} c^{2} - a c^{3}\right)} x^{2} - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2} + {\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}\right) + 2}{4 \, a x^{2}}"," ",0,"-1/4*(sqrt(1/2)*a*x^2*sqrt(-(b^3 - 3*a*b*c + (a^3*b^2 - 4*a^4*c)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log(-(b^2*c^2 - a*c^3)*x^2 + 1/2*sqrt(1/2)*(b^5 - 5*a*b^3*c + 4*a^2*b*c^2 - (a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(b^3 - 3*a*b*c + (a^3*b^2 - 4*a^4*c)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))) - sqrt(1/2)*a*x^2*sqrt(-(b^3 - 3*a*b*c + (a^3*b^2 - 4*a^4*c)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log(-(b^2*c^2 - a*c^3)*x^2 - 1/2*sqrt(1/2)*(b^5 - 5*a*b^3*c + 4*a^2*b*c^2 - (a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(b^3 - 3*a*b*c + (a^3*b^2 - 4*a^4*c)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))) + sqrt(1/2)*a*x^2*sqrt(-(b^3 - 3*a*b*c - (a^3*b^2 - 4*a^4*c)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log(-(b^2*c^2 - a*c^3)*x^2 + 1/2*sqrt(1/2)*(b^5 - 5*a*b^3*c + 4*a^2*b*c^2 + (a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(b^3 - 3*a*b*c - (a^3*b^2 - 4*a^4*c)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))) - sqrt(1/2)*a*x^2*sqrt(-(b^3 - 3*a*b*c - (a^3*b^2 - 4*a^4*c)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log(-(b^2*c^2 - a*c^3)*x^2 - 1/2*sqrt(1/2)*(b^5 - 5*a*b^3*c + 4*a^2*b*c^2 + (a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(b^3 - 3*a*b*c - (a^3*b^2 - 4*a^4*c)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))) + 2)/(a*x^2)","B",0
318,1,293,0,1.879393," ","integrate(1/x^5/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 2 \, a c\right)} \sqrt{b^{2} - 4 \, a c} x^{4} \log\left(\frac{2 \, c^{2} x^{8} + 2 \, b c x^{4} + b^{2} - 2 \, a c + {\left(2 \, c x^{4} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{8} + b x^{4} + a}\right) - {\left(b^{3} - 4 \, a b c\right)} x^{4} \log\left(c x^{8} + b x^{4} + a\right) + 8 \, {\left(b^{3} - 4 \, a b c\right)} x^{4} \log\left(x\right) + 2 \, a b^{2} - 8 \, a^{2} c}{8 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x^{4}}, -\frac{2 \, {\left(b^{2} - 2 \, a c\right)} \sqrt{-b^{2} + 4 \, a c} x^{4} \arctan\left(-\frac{{\left(2 \, c x^{4} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left(b^{3} - 4 \, a b c\right)} x^{4} \log\left(c x^{8} + b x^{4} + a\right) + 8 \, {\left(b^{3} - 4 \, a b c\right)} x^{4} \log\left(x\right) + 2 \, a b^{2} - 8 \, a^{2} c}{8 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x^{4}}\right]"," ",0,"[-1/8*((b^2 - 2*a*c)*sqrt(b^2 - 4*a*c)*x^4*log((2*c^2*x^8 + 2*b*c*x^4 + b^2 - 2*a*c + (2*c*x^4 + b)*sqrt(b^2 - 4*a*c))/(c*x^8 + b*x^4 + a)) - (b^3 - 4*a*b*c)*x^4*log(c*x^8 + b*x^4 + a) + 8*(b^3 - 4*a*b*c)*x^4*log(x) + 2*a*b^2 - 8*a^2*c)/((a^2*b^2 - 4*a^3*c)*x^4), -1/8*(2*(b^2 - 2*a*c)*sqrt(-b^2 + 4*a*c)*x^4*arctan(-(2*c*x^4 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - (b^3 - 4*a*b*c)*x^4*log(c*x^8 + b*x^4 + a) + 8*(b^3 - 4*a*b*c)*x^4*log(x) + 2*a*b^2 - 8*a^2*c)/((a^2*b^2 - 4*a^3*c)*x^4)]","A",0
319,1,6296,0,5.663265," ","integrate(x^10/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","\frac{4 \, x^{3} + 12 \, c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \arctan\left(-\frac{{\left({\left(b^{6} c^{7} - 10 \, a b^{4} c^{8} + 32 \, a^{2} b^{2} c^{9} - 32 \, a^{3} c^{10}\right)} x \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}} - {\left(b^{9} - 9 \, a b^{7} c + 26 \, a^{2} b^{5} c^{2} - 25 \, a^{3} b^{3} c^{3} + 4 \, a^{4} b c^{4}\right)} x + \sqrt{\frac{1}{2}} {\left(b^{9} - 9 \, a b^{7} c + 26 \, a^{2} b^{5} c^{2} - 25 \, a^{3} b^{3} c^{3} + 4 \, a^{4} b c^{4} - {\left(b^{6} c^{7} - 10 \, a b^{4} c^{8} + 32 \, a^{2} b^{2} c^{9} - 32 \, a^{3} c^{10}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}\right)} \sqrt{\frac{2 \, {\left(a^{3} b^{6} - 5 \, a^{4} b^{4} c + 6 \, a^{5} b^{2} c^{2} - a^{6} c^{3}\right)} x^{2} - \sqrt{\frac{1}{2}} {\left(b^{11} - 12 \, a b^{9} c + 53 \, a^{2} b^{7} c^{2} - 103 \, a^{3} b^{5} c^{3} + 79 \, a^{4} b^{3} c^{4} - 12 \, a^{5} b c^{5} - {\left(b^{8} c^{7} - 13 \, a b^{6} c^{8} + 60 \, a^{2} b^{4} c^{9} - 112 \, a^{3} b^{2} c^{10} + 64 \, a^{4} c^{11}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}\right)} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}}{a^{3} b^{6} - 5 \, a^{4} b^{4} c + 6 \, a^{5} b^{2} c^{2} - a^{6} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}}}{2 \, {\left(a^{2} b^{6} - 5 \, a^{3} b^{4} c + 6 \, a^{4} b^{2} c^{2} - a^{5} c^{3}\right)}}\right) - 12 \, c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \arctan\left(\frac{\sqrt{\frac{1}{2}} {\left(b^{9} - 9 \, a b^{7} c + 26 \, a^{2} b^{5} c^{2} - 25 \, a^{3} b^{3} c^{3} + 4 \, a^{4} b c^{4} + {\left(b^{6} c^{7} - 10 \, a b^{4} c^{8} + 32 \, a^{2} b^{2} c^{9} - 32 \, a^{3} c^{10}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \sqrt{\frac{2 \, {\left(a^{3} b^{6} - 5 \, a^{4} b^{4} c + 6 \, a^{5} b^{2} c^{2} - a^{6} c^{3}\right)} x^{2} - \sqrt{\frac{1}{2}} {\left(b^{11} - 12 \, a b^{9} c + 53 \, a^{2} b^{7} c^{2} - 103 \, a^{3} b^{5} c^{3} + 79 \, a^{4} b^{3} c^{4} - 12 \, a^{5} b c^{5} + {\left(b^{8} c^{7} - 13 \, a b^{6} c^{8} + 60 \, a^{2} b^{4} c^{9} - 112 \, a^{3} b^{2} c^{10} + 64 \, a^{4} c^{11}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}\right)} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}}{a^{3} b^{6} - 5 \, a^{4} b^{4} c + 6 \, a^{5} b^{2} c^{2} - a^{6} c^{3}}} - {\left({\left(b^{6} c^{7} - 10 \, a b^{4} c^{8} + 32 \, a^{2} b^{2} c^{9} - 32 \, a^{3} c^{10}\right)} x \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}} + {\left(b^{9} - 9 \, a b^{7} c + 26 \, a^{2} b^{5} c^{2} - 25 \, a^{3} b^{3} c^{3} + 4 \, a^{4} b c^{4}\right)} x\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}}}{2 \, {\left(a^{2} b^{6} - 5 \, a^{3} b^{4} c + 6 \, a^{4} b^{2} c^{2} - a^{5} c^{3}\right)}}\right) - 3 \, c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{14} - 16 \, a b^{12} c + 102 \, a^{2} b^{10} c^{2} - 328 \, a^{3} b^{8} c^{3} + 553 \, a^{4} b^{6} c^{4} - 457 \, a^{5} b^{4} c^{5} + 152 \, a^{6} b^{2} c^{6} - 16 \, a^{7} c^{7} - {\left(b^{11} c^{7} - 17 \, a b^{9} c^{8} + 113 \, a^{2} b^{7} c^{9} - 364 \, a^{3} b^{5} c^{10} + 560 \, a^{4} b^{3} c^{11} - 320 \, a^{5} b c^{12}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}} - {\left(a^{5} b^{6} - 5 \, a^{6} b^{4} c + 6 \, a^{7} b^{2} c^{2} - a^{8} c^{3}\right)} x\right) + 3 \, c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{14} - 16 \, a b^{12} c + 102 \, a^{2} b^{10} c^{2} - 328 \, a^{3} b^{8} c^{3} + 553 \, a^{4} b^{6} c^{4} - 457 \, a^{5} b^{4} c^{5} + 152 \, a^{6} b^{2} c^{6} - 16 \, a^{7} c^{7} - {\left(b^{11} c^{7} - 17 \, a b^{9} c^{8} + 113 \, a^{2} b^{7} c^{9} - 364 \, a^{3} b^{5} c^{10} + 560 \, a^{4} b^{3} c^{11} - 320 \, a^{5} b c^{12}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}} - {\left(a^{5} b^{6} - 5 \, a^{6} b^{4} c + 6 \, a^{7} b^{2} c^{2} - a^{8} c^{3}\right)} x\right) - 3 \, c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{14} - 16 \, a b^{12} c + 102 \, a^{2} b^{10} c^{2} - 328 \, a^{3} b^{8} c^{3} + 553 \, a^{4} b^{6} c^{4} - 457 \, a^{5} b^{4} c^{5} + 152 \, a^{6} b^{2} c^{6} - 16 \, a^{7} c^{7} + {\left(b^{11} c^{7} - 17 \, a b^{9} c^{8} + 113 \, a^{2} b^{7} c^{9} - 364 \, a^{3} b^{5} c^{10} + 560 \, a^{4} b^{3} c^{11} - 320 \, a^{5} b c^{12}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}} - {\left(a^{5} b^{6} - 5 \, a^{6} b^{4} c + 6 \, a^{7} b^{2} c^{2} - a^{8} c^{3}\right)} x\right) + 3 \, c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{14} - 16 \, a b^{12} c + 102 \, a^{2} b^{10} c^{2} - 328 \, a^{3} b^{8} c^{3} + 553 \, a^{4} b^{6} c^{4} - 457 \, a^{5} b^{4} c^{5} + 152 \, a^{6} b^{2} c^{6} - 16 \, a^{7} c^{7} + {\left(b^{11} c^{7} - 17 \, a b^{9} c^{8} + 113 \, a^{2} b^{7} c^{9} - 364 \, a^{3} b^{5} c^{10} + 560 \, a^{4} b^{3} c^{11} - 320 \, a^{5} b c^{12}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} \sqrt{\frac{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}}{b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}}}}{b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}}} - {\left(a^{5} b^{6} - 5 \, a^{6} b^{4} c + 6 \, a^{7} b^{2} c^{2} - a^{8} c^{3}\right)} x\right)}{12 \, c}"," ",0,"1/12*(4*x^3 + 12*c*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*arctan(-1/2*((b^6*c^7 - 10*a*b^4*c^8 + 32*a^2*b^2*c^9 - 32*a^3*c^10)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)) - (b^9 - 9*a*b^7*c + 26*a^2*b^5*c^2 - 25*a^3*b^3*c^3 + 4*a^4*b*c^4)*x + sqrt(1/2)*(b^9 - 9*a*b^7*c + 26*a^2*b^5*c^2 - 25*a^3*b^3*c^3 + 4*a^4*b*c^4 - (b^6*c^7 - 10*a*b^4*c^8 + 32*a^2*b^2*c^9 - 32*a^3*c^10)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))*sqrt((2*(a^3*b^6 - 5*a^4*b^4*c + 6*a^5*b^2*c^2 - a^6*c^3)*x^2 - sqrt(1/2)*(b^11 - 12*a*b^9*c + 53*a^2*b^7*c^2 - 103*a^3*b^5*c^3 + 79*a^4*b^3*c^4 - 12*a^5*b*c^5 - (b^8*c^7 - 13*a*b^6*c^8 + 60*a^2*b^4*c^9 - 112*a^3*b^2*c^10 + 64*a^4*c^11)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))/(a^3*b^6 - 5*a^4*b^4*c + 6*a^5*b^2*c^2 - a^6*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))/(a^2*b^6 - 5*a^3*b^4*c + 6*a^4*b^2*c^2 - a^5*c^3)) - 12*c*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*arctan(1/2*(sqrt(1/2)*(b^9 - 9*a*b^7*c + 26*a^2*b^5*c^2 - 25*a^3*b^3*c^3 + 4*a^4*b*c^4 + (b^6*c^7 - 10*a*b^4*c^8 + 32*a^2*b^2*c^9 - 32*a^3*c^10)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*sqrt((2*(a^3*b^6 - 5*a^4*b^4*c + 6*a^5*b^2*c^2 - a^6*c^3)*x^2 - sqrt(1/2)*(b^11 - 12*a*b^9*c + 53*a^2*b^7*c^2 - 103*a^3*b^5*c^3 + 79*a^4*b^3*c^4 - 12*a^5*b*c^5 + (b^8*c^7 - 13*a*b^6*c^8 + 60*a^2*b^4*c^9 - 112*a^3*b^2*c^10 + 64*a^4*c^11)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))/(a^3*b^6 - 5*a^4*b^4*c + 6*a^5*b^2*c^2 - a^6*c^3)) - ((b^6*c^7 - 10*a*b^4*c^8 + 32*a^2*b^2*c^9 - 32*a^3*c^10)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)) + (b^9 - 9*a*b^7*c + 26*a^2*b^5*c^2 - 25*a^3*b^3*c^3 + 4*a^4*b*c^4)*x)*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9))))/(a^2*b^6 - 5*a^3*b^4*c + 6*a^4*b^2*c^2 - a^5*c^3)) - 3*c*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*log(1/2*sqrt(1/2)*(b^14 - 16*a*b^12*c + 102*a^2*b^10*c^2 - 328*a^3*b^8*c^3 + 553*a^4*b^6*c^4 - 457*a^5*b^4*c^5 + 152*a^6*b^2*c^6 - 16*a^7*c^7 - (b^11*c^7 - 17*a*b^9*c^8 + 113*a^2*b^7*c^9 - 364*a^3*b^5*c^10 + 560*a^4*b^3*c^11 - 320*a^5*b*c^12)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)) - (a^5*b^6 - 5*a^6*b^4*c + 6*a^7*b^2*c^2 - a^8*c^3)*x) + 3*c*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*log(-1/2*sqrt(1/2)*(b^14 - 16*a*b^12*c + 102*a^2*b^10*c^2 - 328*a^3*b^8*c^3 + 553*a^4*b^6*c^4 - 457*a^5*b^4*c^5 + 152*a^6*b^2*c^6 - 16*a^7*c^7 - (b^11*c^7 - 17*a*b^9*c^8 + 113*a^2*b^7*c^9 - 364*a^3*b^5*c^10 + 560*a^4*b^3*c^11 - 320*a^5*b*c^12)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)) - (a^5*b^6 - 5*a^6*b^4*c + 6*a^7*b^2*c^2 - a^8*c^3)*x) - 3*c*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*log(1/2*sqrt(1/2)*(b^14 - 16*a*b^12*c + 102*a^2*b^10*c^2 - 328*a^3*b^8*c^3 + 553*a^4*b^6*c^4 - 457*a^5*b^4*c^5 + 152*a^6*b^2*c^6 - 16*a^7*c^7 + (b^11*c^7 - 17*a*b^9*c^8 + 113*a^2*b^7*c^9 - 364*a^3*b^5*c^10 + 560*a^4*b^3*c^11 - 320*a^5*b*c^12)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)) - (a^5*b^6 - 5*a^6*b^4*c + 6*a^7*b^2*c^2 - a^8*c^3)*x) + 3*c*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*log(-1/2*sqrt(1/2)*(b^14 - 16*a*b^12*c + 102*a^2*b^10*c^2 - 328*a^3*b^8*c^3 + 553*a^4*b^6*c^4 - 457*a^5*b^4*c^5 + 152*a^6*b^2*c^6 - 16*a^7*c^7 + (b^11*c^7 - 17*a*b^9*c^8 + 113*a^2*b^7*c^9 - 364*a^3*b^5*c^10 + 560*a^4*b^3*c^11 - 320*a^5*b*c^12)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)))*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*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)/(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)))/(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)) - (a^5*b^6 - 5*a^6*b^4*c + 6*a^7*b^2*c^2 - a^8*c^3)*x))/c","B",0
320,1,5082,0,2.612257," ","integrate(x^8/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","-\frac{4 \, c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \arctan\left(\frac{{\left(2 \, \sqrt{\frac{1}{2}} {\left({\left(b^{10} c^{5} - 16 \, a b^{8} c^{6} + 98 \, a^{2} b^{6} c^{7} - 280 \, a^{3} b^{4} c^{8} + 352 \, a^{4} b^{2} c^{9} - 128 \, a^{5} c^{10}\right)} x \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}} + {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 128 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5}\right)} x\right)} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}} - {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 128 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5} + {\left(b^{10} c^{5} - 16 \, a b^{8} c^{6} + 98 \, a^{2} b^{6} c^{7} - 280 \, a^{3} b^{4} c^{8} + 352 \, a^{4} b^{2} c^{9} - 128 \, a^{5} c^{10}\right)} \sqrt{\frac{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}}{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{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}} \sqrt{\frac{2 \, {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}\right)} x^{2} + \sqrt{\frac{1}{2}} {\left(b^{8} - 9 \, a b^{6} c + 27 \, a^{2} b^{4} c^{2} - 30 \, a^{3} b^{2} c^{3} + 8 \, a^{4} c^{4} + {\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)} \sqrt{\frac{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}}{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{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}}{a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}}}{4 \, {\left(a^{4} b^{4} - 3 \, a^{5} b^{2} c + a^{6} c^{2}\right)}}\right) - 4 \, c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} {\left({\left(b^{10} c^{5} - 16 \, a b^{8} c^{6} + 98 \, a^{2} b^{6} c^{7} - 280 \, a^{3} b^{4} c^{8} + 352 \, a^{4} b^{2} c^{9} - 128 \, a^{5} c^{10}\right)} x \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}} - {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 128 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5}\right)} x\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}} + {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 128 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5} - {\left(b^{10} c^{5} - 16 \, a b^{8} c^{6} + 98 \, a^{2} b^{6} c^{7} - 280 \, a^{3} b^{4} c^{8} + 352 \, a^{4} b^{2} c^{9} - 128 \, a^{5} c^{10}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}} \sqrt{\frac{2 \, {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}\right)} x^{2} + \sqrt{\frac{1}{2}} {\left(b^{8} - 9 \, a b^{6} c + 27 \, a^{2} b^{4} c^{2} - 30 \, a^{3} b^{2} c^{3} + 8 \, a^{4} c^{4} - {\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)} \sqrt{\frac{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}}{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{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}}{a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}}}}{4 \, {\left(a^{4} b^{4} - 3 \, a^{5} b^{2} c + a^{6} c^{2}\right)}}\right) - c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \log\left({\left(a b^{4} - 3 \, a^{2} b^{2} c + a^{3} c^{2}\right)} x + \frac{1}{2} \, {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} - {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}}\right) + c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \log\left({\left(a b^{4} - 3 \, a^{2} b^{2} c + a^{3} c^{2}\right)} x - \frac{1}{2} \, {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} - {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}}\right) - c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \log\left({\left(a b^{4} - 3 \, a^{2} b^{2} c + a^{3} c^{2}\right)} x + \frac{1}{2} \, {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} + {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}}\right) + c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \log\left({\left(a b^{4} - 3 \, a^{2} b^{2} c + a^{3} c^{2}\right)} x - \frac{1}{2} \, {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} + {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}}\right) - 4 \, x}{4 \, c}"," ",0,"-1/4*(4*c*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*arctan(1/4*(2*sqrt(1/2)*((b^10*c^5 - 16*a*b^8*c^6 + 98*a^2*b^6*c^7 - 280*a^3*b^4*c^8 + 352*a^4*b^2*c^9 - 128*a^5*c^10)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)) + (b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 128*a^4*b^3*c^4 - 32*a^5*b*c^5)*x)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)) - (b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 128*a^4*b^3*c^4 - 32*a^5*b*c^5 + (b^10*c^5 - 16*a*b^8*c^6 + 98*a^2*b^6*c^7 - 280*a^3*b^4*c^8 + 352*a^4*b^2*c^9 - 128*a^5*c^10)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7))*sqrt((2*(a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)*x^2 + sqrt(1/2)*(b^8 - 9*a*b^6*c + 27*a^2*b^4*c^2 - 30*a^3*b^2*c^3 + 8*a^4*c^4 + (b^7*c^5 - 12*a*b^5*c^6 + 48*a^2*b^3*c^7 - 64*a^3*b*c^8)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))/(a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))/(a^4*b^4 - 3*a^5*b^2*c + a^6*c^2)) - 4*c*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*arctan(1/4*(2*sqrt(1/2)*((b^10*c^5 - 16*a*b^8*c^6 + 98*a^2*b^6*c^7 - 280*a^3*b^4*c^8 + 352*a^4*b^2*c^9 - 128*a^5*c^10)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)) - (b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 128*a^4*b^3*c^4 - 32*a^5*b*c^5)*x)*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)) + (b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 128*a^4*b^3*c^4 - 32*a^5*b*c^5 - (b^10*c^5 - 16*a*b^8*c^6 + 98*a^2*b^6*c^7 - 280*a^3*b^4*c^8 + 352*a^4*b^2*c^9 - 128*a^5*c^10)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7))*sqrt((2*(a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)*x^2 + sqrt(1/2)*(b^8 - 9*a*b^6*c + 27*a^2*b^4*c^2 - 30*a^3*b^2*c^3 + 8*a^4*c^4 - (b^7*c^5 - 12*a*b^5*c^6 + 48*a^2*b^3*c^7 - 64*a^3*b*c^8)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))/(a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)))/(a^4*b^4 - 3*a^5*b^2*c + a^6*c^2)) - c*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*log((a*b^4 - 3*a^2*b^2*c + a^3*c^2)*x + 1/2*(b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3 - (b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))) + c*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*log((a*b^4 - 3*a^2*b^2*c + a^3*c^2)*x - 1/2*(b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3 - (b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))) - c*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*log((a*b^4 - 3*a^2*b^2*c + a^3*c^2)*x + 1/2*(b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3 + (b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))) + c*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*log((a*b^4 - 3*a^2*b^2*c + a^3*c^2)*x - 1/2*(b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3 + (b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))) - 4*x)/c","B",0
321,1,3912,0,1.934855," ","integrate(x^6/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","-\sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \arctan\left(\frac{{\left({\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} x - \sqrt{\frac{1}{2}} {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} + {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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{2 \, {\left(a b^{2} - a^{2} c\right)} x^{2} - \sqrt{\frac{1}{2}} {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2} + {\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} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{3} - 3 \, a b c - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}}{a b^{2} - a^{2} c}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}}}{2 \, {\left(a b^{2} - a^{2} c\right)}}\right) + \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \arctan\left(\frac{\sqrt{\frac{1}{2}} {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} - {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \sqrt{\frac{2 \, {\left(a b^{2} - a^{2} c\right)} x^{2} - \sqrt{\frac{1}{2}} {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2} - {\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} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{3} - 3 \, a b c + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}}{a b^{2} - a^{2} c}} + {\left({\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}} - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} x\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}}}{2 \, {\left(a b^{2} - a^{2} c\right)}}\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{7} - 9 \, a b^{5} c + 24 \, a^{2} b^{3} c^{2} - 16 \, a^{3} b c^{3} - {\left(b^{8} c^{3} - 14 \, a b^{6} c^{4} + 72 \, a^{2} b^{4} c^{5} - 160 \, a^{3} b^{2} c^{6} + 128 \, a^{4} c^{7}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}} - {\left(a^{2} b^{2} - a^{3} c\right)} x\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{7} - 9 \, a b^{5} c + 24 \, a^{2} b^{3} c^{2} - 16 \, a^{3} b c^{3} - {\left(b^{8} c^{3} - 14 \, a b^{6} c^{4} + 72 \, a^{2} b^{4} c^{5} - 160 \, a^{3} b^{2} c^{6} + 128 \, a^{4} c^{7}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}} - {\left(a^{2} b^{2} - a^{3} c\right)} x\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{7} - 9 \, a b^{5} c + 24 \, a^{2} b^{3} c^{2} - 16 \, a^{3} b c^{3} + {\left(b^{8} c^{3} - 14 \, a b^{6} c^{4} + 72 \, a^{2} b^{4} c^{5} - 160 \, a^{3} b^{2} c^{6} + 128 \, a^{4} c^{7}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}} - {\left(a^{2} b^{2} - a^{3} c\right)} x\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{7} - 9 \, a b^{5} c + 24 \, a^{2} b^{3} c^{2} - 16 \, a^{3} b c^{3} + {\left(b^{8} c^{3} - 14 \, a b^{6} c^{4} + 72 \, a^{2} b^{4} c^{5} - 160 \, a^{3} b^{2} c^{6} + 128 \, a^{4} c^{7}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}} - {\left(a^{2} b^{2} - a^{3} c\right)} x\right)"," ",0,"-sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*arctan(1/2*((b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)) + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*x - sqrt(1/2)*(b^4 - 5*a*b^2*c + 4*a^2*c^2 + (b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt((2*(a*b^2 - a^2*c)*x^2 - sqrt(1/2)*(b^5 - 5*a*b^3*c + 4*a^2*b*c^2 + (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 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt(-(b^3 - 3*a*b*c - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))/(a*b^2 - a^2*c)))*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))/(a*b^2 - a^2*c)) + sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*arctan(1/2*(sqrt(1/2)*(b^4 - 5*a*b^2*c + 4*a^2*c^2 - (b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*sqrt((2*(a*b^2 - a^2*c)*x^2 - sqrt(1/2)*(b^5 - 5*a*b^3*c + 4*a^2*b*c^2 - (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 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt(-(b^3 - 3*a*b*c + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))/(a*b^2 - a^2*c)) + ((b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)) - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*x)*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))))/(a*b^2 - a^2*c)) + 1/4*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*log(1/2*sqrt(1/2)*(b^7 - 9*a*b^5*c + 24*a^2*b^3*c^2 - 16*a^3*b*c^3 - (b^8*c^3 - 14*a*b^6*c^4 + 72*a^2*b^4*c^5 - 160*a^3*b^2*c^6 + 128*a^4*c^7)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*sqrt(-(b^3 - 3*a*b*c + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)) - (a^2*b^2 - a^3*c)*x) - 1/4*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*log(-1/2*sqrt(1/2)*(b^7 - 9*a*b^5*c + 24*a^2*b^3*c^2 - 16*a^3*b*c^3 - (b^8*c^3 - 14*a*b^6*c^4 + 72*a^2*b^4*c^5 - 160*a^3*b^2*c^6 + 128*a^4*c^7)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*sqrt(-(b^3 - 3*a*b*c + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)) - (a^2*b^2 - a^3*c)*x) + 1/4*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*log(1/2*sqrt(1/2)*(b^7 - 9*a*b^5*c + 24*a^2*b^3*c^2 - 16*a^3*b*c^3 + (b^8*c^3 - 14*a*b^6*c^4 + 72*a^2*b^4*c^5 - 160*a^3*b^2*c^6 + 128*a^4*c^7)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*sqrt(-(b^3 - 3*a*b*c - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)) - (a^2*b^2 - a^3*c)*x) - 1/4*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*log(-1/2*sqrt(1/2)*(b^7 - 9*a*b^5*c + 24*a^2*b^3*c^2 - 16*a^3*b*c^3 + (b^8*c^3 - 14*a*b^6*c^4 + 72*a^2*b^4*c^5 - 160*a^3*b^2*c^6 + 128*a^4*c^7)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))*sqrt(-(b^3 - 3*a*b*c - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)) - (a^2*b^2 - a^3*c)*x)","B",0
322,1,2479,0,1.530806," ","integrate(x^4/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","-\sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}} \arctan\left(\frac{{\left(\sqrt{\frac{1}{2}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2} - \frac{b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}\right)} \sqrt{x^{2} + \sqrt{\frac{1}{2}} {\left(b^{2} - 4 \, a c\right)} \sqrt{-\frac{b + \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}} \sqrt{-\frac{b + \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}} - \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} x - \frac{{\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}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}\right)} \sqrt{-\frac{b + \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}}{2 \, a}\right) + \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}} \arctan\left(-\frac{{\left(\sqrt{\frac{1}{2}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2} + \frac{b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}\right)} \sqrt{x^{2} + \sqrt{\frac{1}{2}} {\left(b^{2} - 4 \, a c\right)} \sqrt{-\frac{b - \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}} \sqrt{-\frac{b - \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}} - \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} x + \frac{{\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}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}\right)} \sqrt{-\frac{b - \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}}{2 \, a}\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}} \log\left(x + \frac{{\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}} \log\left(x - \frac{{\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}} \log\left(x + \frac{{\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}} \log\left(x - \frac{{\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}}{\sqrt{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}\right)"," ",0,"-sqrt(sqrt(1/2)*sqrt(-(b + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))*arctan(1/2*(sqrt(1/2)*(b^4 - 8*a*b^2*c + 16*a^2*c^2 - (b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*sqrt(x^2 + sqrt(1/2)*(b^2 - 4*a*c)*sqrt(-(b + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))*sqrt(-(b + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)) - sqrt(1/2)*((b^4 - 8*a*b^2*c + 16*a^2*c^2)*x - (b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*sqrt(-(b + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/a) + sqrt(sqrt(1/2)*sqrt(-(b - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))*arctan(-1/2*(sqrt(1/2)*(b^4 - 8*a*b^2*c + 16*a^2*c^2 + (b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*sqrt(x^2 + sqrt(1/2)*(b^2 - 4*a*c)*sqrt(-(b - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))*sqrt(-(b - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)) - sqrt(1/2)*((b^4 - 8*a*b^2*c + 16*a^2*c^2)*x + (b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*sqrt(-(b - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/a) + 1/4*sqrt(sqrt(1/2)*sqrt(-(b + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))*log(x + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*sqrt(sqrt(1/2)*sqrt(-(b + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) - 1/4*sqrt(sqrt(1/2)*sqrt(-(b + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))*log(x - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*sqrt(sqrt(1/2)*sqrt(-(b + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) - 1/4*sqrt(sqrt(1/2)*sqrt(-(b - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))*log(x + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*sqrt(sqrt(1/2)*sqrt(-(b - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)) + 1/4*sqrt(sqrt(1/2)*sqrt(-(b - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))*log(x - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*sqrt(sqrt(1/2)*sqrt(-(b - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/sqrt(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))","B",0
323,1,2746,0,1.660455," ","integrate(x^2/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","\sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \arctan\left(-\frac{{\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} x \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} + \frac{\sqrt{\frac{1}{2}} {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \sqrt{\frac{2 \, c x^{2} - \sqrt{\frac{1}{2}} {\left(b^{3} - 4 \, a b c + \frac{a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}\right)} \sqrt{-\frac{b - \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}}{c}}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}\right) - \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \arctan\left(-{\left(\frac{{\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} x}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}} - \frac{\sqrt{\frac{1}{2}} {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} \sqrt{\frac{2 \, c x^{2} - \sqrt{\frac{1}{2}} {\left(b^{3} - 4 \, a b c - \frac{a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}\right)} \sqrt{-\frac{b + \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}}{c}}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}}\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2} - \frac{a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \sqrt{-\frac{b + \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}} + c x\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2} - \frac{a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \sqrt{-\frac{b + \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}} + c x\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2} + \frac{a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \sqrt{-\frac{b - \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}} + c x\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2} + \frac{a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}}} \sqrt{-\frac{b - \frac{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}{\sqrt{a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}}}}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}}} + c x\right)"," ",0,"sqrt(sqrt(1/2)*sqrt(-(b - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*arctan(-(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*x*sqrt(sqrt(1/2)*sqrt(-(b - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)))/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3) + sqrt(1/2)*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*sqrt(sqrt(1/2)*sqrt(-(b - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*sqrt((2*c*x^2 - sqrt(1/2)*(b^3 - 4*a*b*c + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))*sqrt(-(b - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)))/c)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)) - sqrt(sqrt(1/2)*sqrt(-(b + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*arctan(-((a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*x/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3) - sqrt(1/2)*(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*sqrt((2*c*x^2 - sqrt(1/2)*(b^3 - 4*a*b*c - (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))*sqrt(-(b + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)))/c)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))*sqrt(sqrt(1/2)*sqrt(-(b + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)))) - 1/4*sqrt(sqrt(1/2)*sqrt(-(b + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*log(1/2*sqrt(1/2)*(b^4 - 8*a*b^2*c + 16*a^2*c^2 - (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))*sqrt(sqrt(1/2)*sqrt(-(b + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*sqrt(-(b + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)) + c*x) + 1/4*sqrt(sqrt(1/2)*sqrt(-(b + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*log(-1/2*sqrt(1/2)*(b^4 - 8*a*b^2*c + 16*a^2*c^2 - (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))*sqrt(sqrt(1/2)*sqrt(-(b + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*sqrt(-(b + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)) + c*x) - 1/4*sqrt(sqrt(1/2)*sqrt(-(b - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*log(1/2*sqrt(1/2)*(b^4 - 8*a*b^2*c + 16*a^2*c^2 + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))*sqrt(sqrt(1/2)*sqrt(-(b - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*sqrt(-(b - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)) + c*x) + 1/4*sqrt(sqrt(1/2)*sqrt(-(b - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*log(-1/2*sqrt(1/2)*(b^4 - 8*a*b^2*c + 16*a^2*c^2 + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))*sqrt(sqrt(1/2)*sqrt(-(b - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)))*sqrt(-(b - (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)/sqrt(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3))/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)) + c*x)","B",0
324,1,3929,0,1.867796," ","integrate(1/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","-\sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}} \arctan\left(\frac{{\left(2 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{8} - 14 \, a^{4} b^{6} c + 72 \, a^{5} b^{4} c^{2} - 160 \, a^{6} b^{2} c^{3} + 128 \, a^{7} c^{4}\right)} x \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}} - {\left(b^{7} - 9 \, a b^{5} c + 24 \, a^{2} b^{3} c^{2} - 16 \, a^{3} b c^{3}\right)} x\right)} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}} + {\left(b^{7} - 9 \, a b^{5} c + 24 \, a^{2} b^{3} c^{2} - 16 \, a^{3} b c^{3} - {\left(a^{3} b^{8} - 14 \, a^{4} b^{6} c + 72 \, a^{5} b^{4} c^{2} - 160 \, a^{6} b^{2} c^{3} + 128 \, a^{7} c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{3} - 3 \, a b c + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}} \sqrt{\frac{2 \, {\left(b^{2} c^{2} - a c^{3}\right)} x^{2} + \sqrt{\frac{1}{2}} {\left(b^{6} - 7 \, a b^{4} c + 14 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3} - {\left(a^{3} b^{7} - 12 \, a^{4} b^{5} c + 48 \, a^{5} b^{3} c^{2} - 64 \, a^{6} b c^{3}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{3} - 3 \, a b c + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}}{b^{2} c^{2} - a c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}}}{4 \, {\left(b^{2} c^{2} - a c^{3}\right)}}\right) + \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{8} - 14 \, a^{4} b^{6} c + 72 \, a^{5} b^{4} c^{2} - 160 \, a^{6} b^{2} c^{3} + 128 \, a^{7} c^{4}\right)} x \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}} + {\left(b^{7} - 9 \, a b^{5} c + 24 \, a^{2} b^{3} c^{2} - 16 \, a^{3} b c^{3}\right)} x\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}} - {\left(b^{7} - 9 \, a b^{5} c + 24 \, a^{2} b^{3} c^{2} - 16 \, a^{3} b c^{3} + {\left(a^{3} b^{8} - 14 \, a^{4} b^{6} c + 72 \, a^{5} b^{4} c^{2} - 160 \, a^{6} b^{2} c^{3} + 128 \, a^{7} c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}} \sqrt{\frac{2 \, {\left(b^{2} c^{2} - a c^{3}\right)} x^{2} + \sqrt{\frac{1}{2}} {\left(b^{6} - 7 \, a b^{4} c + 14 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3} + {\left(a^{3} b^{7} - 12 \, a^{4} b^{5} c + 48 \, a^{5} b^{3} c^{2} - 64 \, a^{6} b c^{3}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{3} - 3 \, a b c - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}}{b^{2} c^{2} - a c^{3}}}}{4 \, {\left(b^{2} c^{2} - a c^{3}\right)}}\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}} \log\left(-{\left(b^{2} c - a c^{2}\right)} x + \frac{1}{2} \, {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} - {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}}\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}} \log\left(-{\left(b^{2} c - a c^{2}\right)} x - \frac{1}{2} \, {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} - {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}}\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}} \log\left(-{\left(b^{2} c - a c^{2}\right)} x + \frac{1}{2} \, {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}}\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}} \log\left(-{\left(b^{2} c - a c^{2}\right)} x - \frac{1}{2} \, {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}}}}\right)"," ",0,"-sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))*arctan(1/4*(2*sqrt(1/2)*((a^3*b^8 - 14*a^4*b^6*c + 72*a^5*b^4*c^2 - 160*a^6*b^2*c^3 + 128*a^7*c^4)*x*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)) - (b^7 - 9*a*b^5*c + 24*a^2*b^3*c^2 - 16*a^3*b*c^3)*x)*sqrt(-(b^3 - 3*a*b*c + (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(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^4 - 8*a^4*b^2*c + 16*a^5*c^2)) + (b^7 - 9*a*b^5*c + 24*a^2*b^3*c^2 - 16*a^3*b*c^3 - (a^3*b^8 - 14*a^4*b^6*c + 72*a^5*b^4*c^2 - 160*a^6*b^2*c^3 + 128*a^7*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-(b^3 - 3*a*b*c + (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(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^4 - 8*a^4*b^2*c + 16*a^5*c^2))*sqrt((2*(b^2*c^2 - a*c^3)*x^2 + sqrt(1/2)*(b^6 - 7*a*b^4*c + 14*a^2*b^2*c^2 - 8*a^3*c^3 - (a^3*b^7 - 12*a^4*b^5*c + 48*a^5*b^3*c^2 - 64*a^6*b*c^3)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-(b^3 - 3*a*b*c + (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))/(b^2*c^2 - a*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))/(b^2*c^2 - a*c^3)) + sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))*arctan(1/4*(2*sqrt(1/2)*((a^3*b^8 - 14*a^4*b^6*c + 72*a^5*b^4*c^2 - 160*a^6*b^2*c^3 + 128*a^7*c^4)*x*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)) + (b^7 - 9*a*b^5*c + 24*a^2*b^3*c^2 - 16*a^3*b*c^3)*x)*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))*sqrt(-(b^3 - 3*a*b*c - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(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^4 - 8*a^4*b^2*c + 16*a^5*c^2)) - (b^7 - 9*a*b^5*c + 24*a^2*b^3*c^2 - 16*a^3*b*c^3 + (a^3*b^8 - 14*a^4*b^6*c + 72*a^5*b^4*c^2 - 160*a^6*b^2*c^3 + 128*a^7*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))*sqrt(-(b^3 - 3*a*b*c - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(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^4 - 8*a^4*b^2*c + 16*a^5*c^2))*sqrt((2*(b^2*c^2 - a*c^3)*x^2 + sqrt(1/2)*(b^6 - 7*a*b^4*c + 14*a^2*b^2*c^2 - 8*a^3*c^3 + (a^3*b^7 - 12*a^4*b^5*c + 48*a^5*b^3*c^2 - 64*a^6*b*c^3)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-(b^3 - 3*a*b*c - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))/(b^2*c^2 - a*c^3)))/(b^2*c^2 - a*c^3)) + 1/4*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))*log(-(b^2*c - a*c^2)*x + 1/2*(b^4 - 5*a*b^2*c + 4*a^2*c^2 - (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))) - 1/4*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))*log(-(b^2*c - a*c^2)*x - 1/2*(b^4 - 5*a*b^2*c + 4*a^2*c^2 - (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c + (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))) + 1/4*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))*log(-(b^2*c - a*c^2)*x + 1/2*(b^4 - 5*a*b^2*c + 4*a^2*c^2 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))) - 1/4*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(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^4 - 8*a^4*b^2*c + 16*a^5*c^2)))*log(-(b^2*c - a*c^2)*x - 1/2*(b^4 - 5*a*b^2*c + 4*a^2*c^2 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^3 - 3*a*b*c - (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(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^4 - 8*a^4*b^2*c + 16*a^5*c^2))))","B",0
325,1,5125,0,3.474231," ","integrate(1/x^2/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","-\frac{4 \, a x \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \arctan\left(-\frac{{\left({\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} x \sqrt{\frac{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}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}} + {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} x - \sqrt{\frac{1}{2}} {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} + {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} \sqrt{\frac{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}}{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{2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} x^{2} - \sqrt{\frac{1}{2}} {\left(b^{9} - 10 \, a b^{7} c + 34 \, a^{2} b^{5} c^{2} - 43 \, a^{3} b^{3} c^{3} + 12 \, a^{4} b c^{4} + {\left(a^{5} b^{8} - 13 \, a^{6} b^{6} c + 60 \, a^{7} b^{4} c^{2} - 112 \, a^{8} b^{2} c^{3} + 64 \, a^{9} c^{4}\right)} \sqrt{\frac{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}}{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^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}}{b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}}}{2 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} + a^{2} c^{3}\right)}}\right) - 4 \, a x \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \arctan\left(-\frac{\sqrt{\frac{1}{2}} {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} - {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} \sqrt{\frac{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}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \sqrt{\frac{2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} x^{2} - \sqrt{\frac{1}{2}} {\left(b^{9} - 10 \, a b^{7} c + 34 \, a^{2} b^{5} c^{2} - 43 \, a^{3} b^{3} c^{3} + 12 \, a^{4} b c^{4} - {\left(a^{5} b^{8} - 13 \, a^{6} b^{6} c + 60 \, a^{7} b^{4} c^{2} - 112 \, a^{8} b^{2} c^{3} + 64 \, a^{9} c^{4}\right)} \sqrt{\frac{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}}{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^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}}{b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}}} + {\left({\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} x \sqrt{\frac{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}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}} - {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} x\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}}}{2 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} + a^{2} c^{3}\right)}}\right) - a x \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 128 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5} - {\left(a^{5} b^{10} - 16 \, a^{6} b^{8} c + 98 \, a^{7} b^{6} c^{2} - 280 \, a^{8} b^{4} c^{3} + 352 \, a^{9} b^{2} c^{4} - 128 \, a^{10} c^{5}\right)} \sqrt{\frac{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}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}} + {\left(b^{4} c^{4} - 3 \, a b^{2} c^{5} + a^{2} c^{6}\right)} x\right) + a x \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 128 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5} - {\left(a^{5} b^{10} - 16 \, a^{6} b^{8} c + 98 \, a^{7} b^{6} c^{2} - 280 \, a^{8} b^{4} c^{3} + 352 \, a^{9} b^{2} c^{4} - 128 \, a^{10} c^{5}\right)} \sqrt{\frac{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}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}} + {\left(b^{4} c^{4} - 3 \, a b^{2} c^{5} + a^{2} c^{6}\right)} x\right) - a x \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 128 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5} + {\left(a^{5} b^{10} - 16 \, a^{6} b^{8} c + 98 \, a^{7} b^{6} c^{2} - 280 \, a^{8} b^{4} c^{3} + 352 \, a^{9} b^{2} c^{4} - 128 \, a^{10} c^{5}\right)} \sqrt{\frac{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}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}} + {\left(b^{4} c^{4} - 3 \, a b^{2} c^{5} + a^{2} c^{6}\right)} x\right) + a x \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 128 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5} + {\left(a^{5} b^{10} - 16 \, a^{6} b^{8} c + 98 \, a^{7} b^{6} c^{2} - 280 \, a^{8} b^{4} c^{3} + 352 \, a^{9} b^{2} c^{4} - 128 \, a^{10} c^{5}\right)} \sqrt{\frac{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}}{a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}}} + {\left(b^{4} c^{4} - 3 \, a b^{2} c^{5} + a^{2} c^{6}\right)} x\right) + 4}{4 \, a x}"," ",0,"-1/4*(4*a*x*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*arctan(-1/2*((a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*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)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)) + (b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3)*x - sqrt(1/2)*(b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3 + (a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^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)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt((2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*x^2 - sqrt(1/2)*(b^9 - 10*a*b^7*c + 34*a^2*b^5*c^2 - 43*a^3*b^3*c^3 + 12*a^4*b*c^4 + (a^5*b^8 - 13*a^6*b^6*c + 60*a^7*b^4*c^2 - 112*a^8*b^2*c^3 + 64*a^9*c^4)*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)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))/(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))/(b^4*c - 3*a*b^2*c^2 + a^2*c^3)) - 4*a*x*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*arctan(-1/2*(sqrt(1/2)*(b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3 - (a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^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)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*sqrt((2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*x^2 - sqrt(1/2)*(b^9 - 10*a*b^7*c + 34*a^2*b^5*c^2 - 43*a^3*b^3*c^3 + 12*a^4*b*c^4 - (a^5*b^8 - 13*a^6*b^6*c + 60*a^7*b^4*c^2 - 112*a^8*b^2*c^3 + 64*a^9*c^4)*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)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))/(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)) + ((a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*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)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)) - (b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3)*x)*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2))))/(b^4*c - 3*a*b^2*c^2 + a^2*c^3)) - a*x*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*log(1/2*sqrt(1/2)*(b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 128*a^4*b^3*c^4 - 32*a^5*b*c^5 - (a^5*b^10 - 16*a^6*b^8*c + 98*a^7*b^6*c^2 - 280*a^8*b^4*c^3 + 352*a^9*b^2*c^4 - 128*a^10*c^5)*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)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)) + (b^4*c^4 - 3*a*b^2*c^5 + a^2*c^6)*x) + a*x*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*log(-1/2*sqrt(1/2)*(b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 128*a^4*b^3*c^4 - 32*a^5*b*c^5 - (a^5*b^10 - 16*a^6*b^8*c + 98*a^7*b^6*c^2 - 280*a^8*b^4*c^3 + 352*a^9*b^2*c^4 - 128*a^10*c^5)*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)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)) + (b^4*c^4 - 3*a*b^2*c^5 + a^2*c^6)*x) - a*x*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*log(1/2*sqrt(1/2)*(b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 128*a^4*b^3*c^4 - 32*a^5*b*c^5 + (a^5*b^10 - 16*a^6*b^8*c + 98*a^7*b^6*c^2 - 280*a^8*b^4*c^3 + 352*a^9*b^2*c^4 - 128*a^10*c^5)*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)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)) + (b^4*c^4 - 3*a*b^2*c^5 + a^2*c^6)*x) + a*x*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*log(-1/2*sqrt(1/2)*(b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 128*a^4*b^3*c^4 - 32*a^5*b*c^5 + (a^5*b^10 - 16*a^6*b^8*c + 98*a^7*b^6*c^2 - 280*a^8*b^4*c^3 + 352*a^9*b^2*c^4 - 128*a^10*c^5)*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)/(a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^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)/(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^4 - 8*a^6*b^2*c + 16*a^7*c^2)) + (b^4*c^4 - 3*a*b^2*c^5 + a^2*c^6)*x) + 4)/(a*x)","B",0
326,1,6324,0,4.075022," ","integrate(1/x^4/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","\frac{12 \, a x^{3} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}} \arctan\left(-\frac{{\left(2 \, \sqrt{\frac{1}{2}} {\left({\left(a^{7} b^{11} - 17 \, a^{8} b^{9} c + 113 \, a^{9} b^{7} c^{2} - 364 \, a^{10} b^{5} c^{3} + 560 \, a^{11} b^{3} c^{4} - 320 \, a^{12} b c^{5}\right)} x \sqrt{\frac{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}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}} + {\left(b^{14} - 16 \, a b^{12} c + 102 \, a^{2} b^{10} c^{2} - 328 \, a^{3} b^{8} c^{3} + 553 \, a^{4} b^{6} c^{4} - 457 \, a^{5} b^{4} c^{5} + 152 \, a^{6} b^{2} c^{6} - 16 \, a^{7} c^{7}\right)} x\right)} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}} - {\left(b^{14} - 16 \, a b^{12} c + 102 \, a^{2} b^{10} c^{2} - 328 \, a^{3} b^{8} c^{3} + 553 \, a^{4} b^{6} c^{4} - 457 \, a^{5} b^{4} c^{5} + 152 \, a^{6} b^{2} c^{6} - 16 \, a^{7} c^{7} + {\left(a^{7} b^{11} - 17 \, a^{8} b^{9} c + 113 \, a^{9} b^{7} c^{2} - 364 \, a^{10} b^{5} c^{3} + 560 \, a^{11} b^{3} c^{4} - 320 \, a^{12} b c^{5}\right)} \sqrt{\frac{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}}{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{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}} \sqrt{\frac{2 \, {\left(b^{6} c^{4} - 5 \, a b^{4} c^{5} + 6 \, a^{2} b^{2} c^{6} - a^{3} c^{7}\right)} x^{2} + \sqrt{\frac{1}{2}} {\left(b^{12} - 13 \, a b^{10} c + 64 \, a^{2} b^{8} c^{2} - 147 \, a^{3} b^{6} c^{3} + 156 \, a^{4} b^{4} c^{4} - 66 \, a^{5} b^{2} c^{5} + 8 \, a^{6} c^{6} + {\left(a^{7} b^{9} - 14 \, a^{8} b^{7} c + 72 \, a^{9} b^{5} c^{2} - 160 \, a^{10} b^{3} c^{3} + 128 \, a^{11} b c^{4}\right)} \sqrt{\frac{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}}{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{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}}{b^{6} c^{4} - 5 \, a b^{4} c^{5} + 6 \, a^{2} b^{2} c^{6} - a^{3} c^{7}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}}}{4 \, {\left(b^{6} c^{5} - 5 \, a b^{4} c^{6} + 6 \, a^{2} b^{2} c^{7} - a^{3} c^{8}\right)}}\right) - 12 \, a x^{3} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}} \arctan\left(-\frac{2 \, \sqrt{\frac{1}{2}} {\left({\left(a^{7} b^{11} - 17 \, a^{8} b^{9} c + 113 \, a^{9} b^{7} c^{2} - 364 \, a^{10} b^{5} c^{3} + 560 \, a^{11} b^{3} c^{4} - 320 \, a^{12} b c^{5}\right)} x \sqrt{\frac{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}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}} - {\left(b^{14} - 16 \, a b^{12} c + 102 \, a^{2} b^{10} c^{2} - 328 \, a^{3} b^{8} c^{3} + 553 \, a^{4} b^{6} c^{4} - 457 \, a^{5} b^{4} c^{5} + 152 \, a^{6} b^{2} c^{6} - 16 \, a^{7} c^{7}\right)} x\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}} + {\left(b^{14} - 16 \, a b^{12} c + 102 \, a^{2} b^{10} c^{2} - 328 \, a^{3} b^{8} c^{3} + 553 \, a^{4} b^{6} c^{4} - 457 \, a^{5} b^{4} c^{5} + 152 \, a^{6} b^{2} c^{6} - 16 \, a^{7} c^{7} - {\left(a^{7} b^{11} - 17 \, a^{8} b^{9} c + 113 \, a^{9} b^{7} c^{2} - 364 \, a^{10} b^{5} c^{3} + 560 \, a^{11} b^{3} c^{4} - 320 \, a^{12} b c^{5}\right)} \sqrt{\frac{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}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}} \sqrt{\frac{2 \, {\left(b^{6} c^{4} - 5 \, a b^{4} c^{5} + 6 \, a^{2} b^{2} c^{6} - a^{3} c^{7}\right)} x^{2} + \sqrt{\frac{1}{2}} {\left(b^{12} - 13 \, a b^{10} c + 64 \, a^{2} b^{8} c^{2} - 147 \, a^{3} b^{6} c^{3} + 156 \, a^{4} b^{4} c^{4} - 66 \, a^{5} b^{2} c^{5} + 8 \, a^{6} c^{6} - {\left(a^{7} b^{9} - 14 \, a^{8} b^{7} c + 72 \, a^{9} b^{5} c^{2} - 160 \, a^{10} b^{3} c^{3} + 128 \, a^{11} b c^{4}\right)} \sqrt{\frac{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}}{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{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}}{b^{6} c^{4} - 5 \, a b^{4} c^{5} + 6 \, a^{2} b^{2} c^{6} - a^{3} c^{7}}}}{4 \, {\left(b^{6} c^{5} - 5 \, a b^{4} c^{6} + 6 \, a^{2} b^{2} c^{7} - a^{3} c^{8}\right)}}\right) - 3 \, a x^{3} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}} \log\left(-{\left(b^{6} c^{2} - 5 \, a b^{4} c^{3} + 6 \, a^{2} b^{2} c^{4} - a^{3} c^{5}\right)} x + \frac{1}{2} \, {\left(b^{9} - 9 \, a b^{7} c + 26 \, a^{2} b^{5} c^{2} - 25 \, a^{3} b^{3} c^{3} + 4 \, a^{4} b c^{4} - {\left(a^{7} b^{6} - 10 \, a^{8} b^{4} c + 32 \, a^{9} b^{2} c^{2} - 32 \, a^{10} c^{3}\right)} \sqrt{\frac{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}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}}\right) + 3 \, a x^{3} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}} \log\left(-{\left(b^{6} c^{2} - 5 \, a b^{4} c^{3} + 6 \, a^{2} b^{2} c^{4} - a^{3} c^{5}\right)} x - \frac{1}{2} \, {\left(b^{9} - 9 \, a b^{7} c + 26 \, a^{2} b^{5} c^{2} - 25 \, a^{3} b^{3} c^{3} + 4 \, a^{4} b c^{4} - {\left(a^{7} b^{6} - 10 \, a^{8} b^{4} c + 32 \, a^{9} b^{2} c^{2} - 32 \, a^{10} c^{3}\right)} \sqrt{\frac{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}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}}\right) - 3 \, a x^{3} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}} \log\left(-{\left(b^{6} c^{2} - 5 \, a b^{4} c^{3} + 6 \, a^{2} b^{2} c^{4} - a^{3} c^{5}\right)} x + \frac{1}{2} \, {\left(b^{9} - 9 \, a b^{7} c + 26 \, a^{2} b^{5} c^{2} - 25 \, a^{3} b^{3} c^{3} + 4 \, a^{4} b c^{4} + {\left(a^{7} b^{6} - 10 \, a^{8} b^{4} c + 32 \, a^{9} b^{2} c^{2} - 32 \, a^{10} c^{3}\right)} \sqrt{\frac{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}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}}\right) + 3 \, a x^{3} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}} \log\left(-{\left(b^{6} c^{2} - 5 \, a b^{4} c^{3} + 6 \, a^{2} b^{2} c^{4} - a^{3} c^{5}\right)} x - \frac{1}{2} \, {\left(b^{9} - 9 \, a b^{7} c + 26 \, a^{2} b^{5} c^{2} - 25 \, a^{3} b^{3} c^{3} + 4 \, a^{4} b c^{4} + {\left(a^{7} b^{6} - 10 \, a^{8} b^{4} c + 32 \, a^{9} b^{2} c^{2} - 32 \, a^{10} c^{3}\right)} \sqrt{\frac{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}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{7} - 7 \, a b^{5} c + 14 \, a^{2} b^{3} c^{2} - 7 \, a^{3} b c^{3} - {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} \sqrt{\frac{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}}{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^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}}}}\right) - 4}{12 \, a x^{3}}"," ",0,"1/12*(12*a*x^3*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^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)/(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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))*arctan(-1/4*(2*sqrt(1/2)*((a^7*b^11 - 17*a^8*b^9*c + 113*a^9*b^7*c^2 - 364*a^10*b^5*c^3 + 560*a^11*b^3*c^4 - 320*a^12*b*c^5)*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)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)) + (b^14 - 16*a*b^12*c + 102*a^2*b^10*c^2 - 328*a^3*b^8*c^3 + 553*a^4*b^6*c^4 - 457*a^5*b^4*c^5 + 152*a^6*b^2*c^6 - 16*a^7*c^7)*x)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^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)/(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^4 - 8*a^8*b^2*c + 16*a^9*c^2)) - (b^14 - 16*a*b^12*c + 102*a^2*b^10*c^2 - 328*a^3*b^8*c^3 + 553*a^4*b^6*c^4 - 457*a^5*b^4*c^5 + 152*a^6*b^2*c^6 - 16*a^7*c^7 + (a^7*b^11 - 17*a^8*b^9*c + 113*a^9*b^7*c^2 - 364*a^10*b^5*c^3 + 560*a^11*b^3*c^4 - 320*a^12*b*c^5)*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)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^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)/(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^4 - 8*a^8*b^2*c + 16*a^9*c^2))*sqrt((2*(b^6*c^4 - 5*a*b^4*c^5 + 6*a^2*b^2*c^6 - a^3*c^7)*x^2 + sqrt(1/2)*(b^12 - 13*a*b^10*c + 64*a^2*b^8*c^2 - 147*a^3*b^6*c^3 + 156*a^4*b^4*c^4 - 66*a^5*b^2*c^5 + 8*a^6*c^6 + (a^7*b^9 - 14*a^8*b^7*c + 72*a^9*b^5*c^2 - 160*a^10*b^3*c^3 + 128*a^11*b*c^4)*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)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^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)/(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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))/(b^6*c^4 - 5*a*b^4*c^5 + 6*a^2*b^2*c^6 - a^3*c^7)))*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^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)/(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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))/(b^6*c^5 - 5*a*b^4*c^6 + 6*a^2*b^2*c^7 - a^3*c^8)) - 12*a*x^3*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^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)/(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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))*arctan(-1/4*(2*sqrt(1/2)*((a^7*b^11 - 17*a^8*b^9*c + 113*a^9*b^7*c^2 - 364*a^10*b^5*c^3 + 560*a^11*b^3*c^4 - 320*a^12*b*c^5)*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)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)) - (b^14 - 16*a*b^12*c + 102*a^2*b^10*c^2 - 328*a^3*b^8*c^3 + 553*a^4*b^6*c^4 - 457*a^5*b^4*c^5 + 152*a^6*b^2*c^6 - 16*a^7*c^7)*x)*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^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)/(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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^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)/(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^4 - 8*a^8*b^2*c + 16*a^9*c^2)) + (b^14 - 16*a*b^12*c + 102*a^2*b^10*c^2 - 328*a^3*b^8*c^3 + 553*a^4*b^6*c^4 - 457*a^5*b^4*c^5 + 152*a^6*b^2*c^6 - 16*a^7*c^7 - (a^7*b^11 - 17*a^8*b^9*c + 113*a^9*b^7*c^2 - 364*a^10*b^5*c^3 + 560*a^11*b^3*c^4 - 320*a^12*b*c^5)*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)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^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)/(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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^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)/(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^4 - 8*a^8*b^2*c + 16*a^9*c^2))*sqrt((2*(b^6*c^4 - 5*a*b^4*c^5 + 6*a^2*b^2*c^6 - a^3*c^7)*x^2 + sqrt(1/2)*(b^12 - 13*a*b^10*c + 64*a^2*b^8*c^2 - 147*a^3*b^6*c^3 + 156*a^4*b^4*c^4 - 66*a^5*b^2*c^5 + 8*a^6*c^6 - (a^7*b^9 - 14*a^8*b^7*c + 72*a^9*b^5*c^2 - 160*a^10*b^3*c^3 + 128*a^11*b*c^4)*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)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^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)/(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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))/(b^6*c^4 - 5*a*b^4*c^5 + 6*a^2*b^2*c^6 - a^3*c^7)))/(b^6*c^5 - 5*a*b^4*c^6 + 6*a^2*b^2*c^7 - a^3*c^8)) - 3*a*x^3*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^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)/(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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))*log(-(b^6*c^2 - 5*a*b^4*c^3 + 6*a^2*b^2*c^4 - a^3*c^5)*x + 1/2*(b^9 - 9*a*b^7*c + 26*a^2*b^5*c^2 - 25*a^3*b^3*c^3 + 4*a^4*b*c^4 - (a^7*b^6 - 10*a^8*b^4*c + 32*a^9*b^2*c^2 - 32*a^10*c^3)*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)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^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)/(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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))) + 3*a*x^3*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^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)/(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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))*log(-(b^6*c^2 - 5*a*b^4*c^3 + 6*a^2*b^2*c^4 - a^3*c^5)*x - 1/2*(b^9 - 9*a*b^7*c + 26*a^2*b^5*c^2 - 25*a^3*b^3*c^3 + 4*a^4*b*c^4 - (a^7*b^6 - 10*a^8*b^4*c + 32*a^9*b^2*c^2 - 32*a^10*c^3)*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)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^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)/(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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))) - 3*a*x^3*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^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)/(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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))*log(-(b^6*c^2 - 5*a*b^4*c^3 + 6*a^2*b^2*c^4 - a^3*c^5)*x + 1/2*(b^9 - 9*a*b^7*c + 26*a^2*b^5*c^2 - 25*a^3*b^3*c^3 + 4*a^4*b*c^4 + (a^7*b^6 - 10*a^8*b^4*c + 32*a^9*b^2*c^2 - 32*a^10*c^3)*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)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^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)/(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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))) + 3*a*x^3*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^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)/(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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))*log(-(b^6*c^2 - 5*a*b^4*c^3 + 6*a^2*b^2*c^4 - a^3*c^5)*x - 1/2*(b^9 - 9*a*b^7*c + 26*a^2*b^5*c^2 - 25*a^3*b^3*c^3 + 4*a^4*b*c^4 + (a^7*b^6 - 10*a^8*b^4*c + 32*a^9*b^2*c^2 - 32*a^10*c^3)*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)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(sqrt(1/2)*sqrt(-(b^7 - 7*a*b^5*c + 14*a^2*b^3*c^2 - 7*a^3*b*c^3 - (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^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)/(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^4 - 8*a^8*b^2*c + 16*a^9*c^2)))) - 4)/(a*x^3)","B",0
327,0,0,0,1.267792," ","integrate(x^m/(x^8+x^4+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{x^{8} + x^{4} + 1}, x\right)"," ",0,"integral(x^m/(x^8 + x^4 + 1), x)","F",0
328,1,35,0,1.416935," ","integrate(x^11/(x^8+x^4+1),x, algorithm=""fricas"")","\frac{1}{4} \, x^{4} - \frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{4} + 1\right)}\right) - \frac{1}{8} \, \log\left(x^{8} + x^{4} + 1\right)"," ",0,"1/4*x^4 - 1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^4 + 1)) - 1/8*log(x^8 + x^4 + 1)","A",0
329,1,40,0,1.225953," ","integrate(x^9/(x^8+x^4+1),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} x^{2}\right) - \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(x^{6} + 2 \, x^{2}\right)}\right)"," ",0,"1/2*x^2 - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*x^2) - 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(x^6 + 2*x^2))","A",0
330,1,30,0,1.212273," ","integrate(x^7/(x^8+x^4+1),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{4} + 1\right)}\right) + \frac{1}{8} \, \log\left(x^{8} + x^{4} + 1\right)"," ",0,"-1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^4 + 1)) + 1/8*log(x^8 + x^4 + 1)","A",0
331,1,61,0,0.972558," ","integrate(x^5/(x^8+x^4+1),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + 1\right)}\right) + \frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) - \frac{1}{8} \, \log\left(x^{4} + x^{2} + 1\right) + \frac{1}{8} \, \log\left(x^{4} - x^{2} + 1\right)"," ",0,"1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 + 1)) + 1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)) - 1/8*log(x^4 + x^2 + 1) + 1/8*log(x^4 - x^2 + 1)","A",0
332,1,18,0,1.139843," ","integrate(x^3/(x^8+x^4+1),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{4} + 1\right)}\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^4 + 1))","A",0
333,1,61,0,1.500819," ","integrate(x/(x^8+x^4+1),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + 1\right)}\right) + \frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) + \frac{1}{8} \, \log\left(x^{4} + x^{2} + 1\right) - \frac{1}{8} \, \log\left(x^{4} - x^{2} + 1\right)"," ",0,"1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 + 1)) + 1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 - 1)) + 1/8*log(x^4 + x^2 + 1) - 1/8*log(x^4 - x^2 + 1)","A",0
334,1,32,0,1.260834," ","integrate(1/x/(x^8+x^4+1),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{4} + 1\right)}\right) - \frac{1}{8} \, \log\left(x^{8} + x^{4} + 1\right) + \log\left(x\right)"," ",0,"-1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^4 + 1)) - 1/8*log(x^8 + x^4 + 1) + log(x)","A",0
335,1,45,0,1.084201," ","integrate(1/x^3/(x^8+x^4+1),x, algorithm=""fricas"")","-\frac{\sqrt{3} x^{2} \arctan\left(\frac{1}{3} \, \sqrt{3} x^{2}\right) + \sqrt{3} x^{2} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(x^{6} + 2 \, x^{2}\right)}\right) + 3}{6 \, x^{2}}"," ",0,"-1/6*(sqrt(3)*x^2*arctan(1/3*sqrt(3)*x^2) + sqrt(3)*x^2*arctan(1/3*sqrt(3)*(x^6 + 2*x^2)) + 3)/x^2","A",0
336,1,49,0,1.084541," ","integrate(1/x^5/(x^8+x^4+1),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} x^{4} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{4} + 1\right)}\right) - 3 \, x^{4} \log\left(x^{8} + x^{4} + 1\right) + 24 \, x^{4} \log\left(x\right) + 6}{24 \, x^{4}}"," ",0,"-1/24*(2*sqrt(3)*x^4*arctan(1/3*sqrt(3)*(2*x^4 + 1)) - 3*x^4*log(x^8 + x^4 + 1) + 24*x^4*log(x) + 6)/x^4","A",0
337,1,84,0,1.458104," ","integrate(1/x^7/(x^8+x^4+1),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} x^{6} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + 1\right)}\right) + 2 \, \sqrt{3} x^{6} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} - 1\right)}\right) - 3 \, x^{6} \log\left(x^{4} + x^{2} + 1\right) + 3 \, x^{6} \log\left(x^{4} - x^{2} + 1\right) + 12 \, x^{4} - 4}{24 \, x^{6}}"," ",0,"1/24*(2*sqrt(3)*x^6*arctan(1/3*sqrt(3)*(2*x^2 + 1)) + 2*sqrt(3)*x^6*arctan(1/3*sqrt(3)*(2*x^2 - 1)) - 3*x^6*log(x^4 + x^2 + 1) + 3*x^6*log(x^4 - x^2 + 1) + 12*x^4 - 4)/x^6","A",0
338,1,212,0,0.946810," ","integrate(x^8/(x^8+x^4+1),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{6} \sqrt{3} \sqrt{2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2} - \sqrt{3}\right) + \frac{1}{12} \, \sqrt{6} \sqrt{3} \sqrt{2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{-\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2} + \sqrt{3}\right) - \frac{1}{48} \, \sqrt{6} \sqrt{2} \log\left(\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2\right) + \frac{1}{48} \, \sqrt{6} \sqrt{2} \log\left(-\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2\right) - \frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + x - \frac{1}{8} \, \log\left(x^{2} + x + 1\right) + \frac{1}{8} \, \log\left(x^{2} - x + 1\right)"," ",0,"1/12*sqrt(6)*sqrt(3)*sqrt(2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x + 1/3*sqrt(6)*sqrt(3)*sqrt(sqrt(6)*sqrt(2)*x + 2*x^2 + 2) - sqrt(3)) + 1/12*sqrt(6)*sqrt(3)*sqrt(2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x + 1/3*sqrt(6)*sqrt(3)*sqrt(-sqrt(6)*sqrt(2)*x + 2*x^2 + 2) + sqrt(3)) - 1/48*sqrt(6)*sqrt(2)*log(sqrt(6)*sqrt(2)*x + 2*x^2 + 2) + 1/48*sqrt(6)*sqrt(2)*log(-sqrt(6)*sqrt(2)*x + 2*x^2 + 2) - 1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + x - 1/8*log(x^2 + x + 1) + 1/8*log(x^2 - x + 1)","A",0
339,1,70,0,1.210710," ","integrate(x^6/(x^8+x^4+1),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(x^{3} + 2 \, x\right)}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} x\right) + \frac{1}{12} \, \sqrt{3} \log\left(\frac{x^{4} + 5 \, x^{2} - 2 \, \sqrt{3} {\left(x^{3} + x\right)} + 1}{x^{4} - x^{2} + 1}\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(x^3 + 2*x)) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*x) + 1/12*sqrt(3)*log((x^4 + 5*x^2 - 2*sqrt(3)*(x^3 + x) + 1)/(x^4 - x^2 + 1))","A",0
340,1,211,0,1.525475," ","integrate(x^4/(x^8+x^4+1),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{6} \sqrt{3} \sqrt{2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2} - \sqrt{3}\right) - \frac{1}{12} \, \sqrt{6} \sqrt{3} \sqrt{2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{-\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2} + \sqrt{3}\right) - \frac{1}{48} \, \sqrt{6} \sqrt{2} \log\left(\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2\right) + \frac{1}{48} \, \sqrt{6} \sqrt{2} \log\left(-\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2\right) - \frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{8} \, \log\left(x^{2} + x + 1\right) - \frac{1}{8} \, \log\left(x^{2} - x + 1\right)"," ",0,"-1/12*sqrt(6)*sqrt(3)*sqrt(2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x + 1/3*sqrt(6)*sqrt(3)*sqrt(sqrt(6)*sqrt(2)*x + 2*x^2 + 2) - sqrt(3)) - 1/12*sqrt(6)*sqrt(3)*sqrt(2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x + 1/3*sqrt(6)*sqrt(3)*sqrt(-sqrt(6)*sqrt(2)*x + 2*x^2 + 2) + sqrt(3)) - 1/48*sqrt(6)*sqrt(2)*log(sqrt(6)*sqrt(2)*x + 2*x^2 + 2) + 1/48*sqrt(6)*sqrt(2)*log(-sqrt(6)*sqrt(2)*x + 2*x^2 + 2) - 1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/8*log(x^2 + x + 1) - 1/8*log(x^2 - x + 1)","A",0
341,1,211,0,1.446788," ","integrate(x^2/(x^8+x^4+1),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{6} \sqrt{3} \sqrt{2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2} - \sqrt{3}\right) - \frac{1}{12} \, \sqrt{6} \sqrt{3} \sqrt{2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{-\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2} + \sqrt{3}\right) + \frac{1}{48} \, \sqrt{6} \sqrt{2} \log\left(\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2\right) - \frac{1}{48} \, \sqrt{6} \sqrt{2} \log\left(-\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2\right) - \frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{1}{8} \, \log\left(x^{2} + x + 1\right) + \frac{1}{8} \, \log\left(x^{2} - x + 1\right)"," ",0,"-1/12*sqrt(6)*sqrt(3)*sqrt(2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x + 1/3*sqrt(6)*sqrt(3)*sqrt(sqrt(6)*sqrt(2)*x + 2*x^2 + 2) - sqrt(3)) - 1/12*sqrt(6)*sqrt(3)*sqrt(2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x + 1/3*sqrt(6)*sqrt(3)*sqrt(-sqrt(6)*sqrt(2)*x + 2*x^2 + 2) + sqrt(3)) + 1/48*sqrt(6)*sqrt(2)*log(sqrt(6)*sqrt(2)*x + 2*x^2 + 2) - 1/48*sqrt(6)*sqrt(2)*log(-sqrt(6)*sqrt(2)*x + 2*x^2 + 2) - 1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/8*log(x^2 + x + 1) + 1/8*log(x^2 - x + 1)","A",0
342,1,70,0,1.123820," ","integrate(1/(x^8+x^4+1),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(x^{3} + 2 \, x\right)}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} x\right) + \frac{1}{12} \, \sqrt{3} \log\left(\frac{x^{4} + 5 \, x^{2} + 2 \, \sqrt{3} {\left(x^{3} + x\right)} + 1}{x^{4} - x^{2} + 1}\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(x^3 + 2*x)) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*x) + 1/12*sqrt(3)*log((x^4 + 5*x^2 + 2*sqrt(3)*(x^3 + x) + 1)/(x^4 - x^2 + 1))","A",0
343,1,224,0,1.317693," ","integrate(1/x^2/(x^8+x^4+1),x, algorithm=""fricas"")","\frac{4 \, \sqrt{6} \sqrt{3} \sqrt{2} x \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2} - \sqrt{3}\right) + 4 \, \sqrt{6} \sqrt{3} \sqrt{2} x \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{-\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2} + \sqrt{3}\right) + \sqrt{6} \sqrt{2} x \log\left(\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2\right) - \sqrt{6} \sqrt{2} x \log\left(-\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2\right) - 4 \, \sqrt{3} x \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - 4 \, \sqrt{3} x \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + 6 \, x \log\left(x^{2} + x + 1\right) - 6 \, x \log\left(x^{2} - x + 1\right) - 48}{48 \, x}"," ",0,"1/48*(4*sqrt(6)*sqrt(3)*sqrt(2)*x*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x + 1/3*sqrt(6)*sqrt(3)*sqrt(sqrt(6)*sqrt(2)*x + 2*x^2 + 2) - sqrt(3)) + 4*sqrt(6)*sqrt(3)*sqrt(2)*x*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x + 1/3*sqrt(6)*sqrt(3)*sqrt(-sqrt(6)*sqrt(2)*x + 2*x^2 + 2) + sqrt(3)) + sqrt(6)*sqrt(2)*x*log(sqrt(6)*sqrt(2)*x + 2*x^2 + 2) - sqrt(6)*sqrt(2)*x*log(-sqrt(6)*sqrt(2)*x + 2*x^2 + 2) - 4*sqrt(3)*x*arctan(1/3*sqrt(3)*(2*x + 1)) - 4*sqrt(3)*x*arctan(1/3*sqrt(3)*(2*x - 1)) + 6*x*log(x^2 + x + 1) - 6*x*log(x^2 - x + 1) - 48)/x","A",0
344,1,240,0,1.230649," ","integrate(1/x^4/(x^8+x^4+1),x, algorithm=""fricas"")","\frac{4 \, \sqrt{6} \sqrt{3} \sqrt{2} x^{3} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2} - \sqrt{3}\right) + 4 \, \sqrt{6} \sqrt{3} \sqrt{2} x^{3} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{-\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2} + \sqrt{3}\right) - \sqrt{6} \sqrt{2} x^{3} \log\left(\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2\right) + \sqrt{6} \sqrt{2} x^{3} \log\left(-\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2\right) - 4 \, \sqrt{3} x^{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - 4 \, \sqrt{3} x^{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - 6 \, x^{3} \log\left(x^{2} + x + 1\right) + 6 \, x^{3} \log\left(x^{2} - x + 1\right) - 16}{48 \, x^{3}}"," ",0,"1/48*(4*sqrt(6)*sqrt(3)*sqrt(2)*x^3*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x + 1/3*sqrt(6)*sqrt(3)*sqrt(sqrt(6)*sqrt(2)*x + 2*x^2 + 2) - sqrt(3)) + 4*sqrt(6)*sqrt(3)*sqrt(2)*x^3*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x + 1/3*sqrt(6)*sqrt(3)*sqrt(-sqrt(6)*sqrt(2)*x + 2*x^2 + 2) + sqrt(3)) - sqrt(6)*sqrt(2)*x^3*log(sqrt(6)*sqrt(2)*x + 2*x^2 + 2) + sqrt(6)*sqrt(2)*x^3*log(-sqrt(6)*sqrt(2)*x + 2*x^2 + 2) - 4*sqrt(3)*x^3*arctan(1/3*sqrt(3)*(2*x + 1)) - 4*sqrt(3)*x^3*arctan(1/3*sqrt(3)*(2*x - 1)) - 6*x^3*log(x^2 + x + 1) + 6*x^3*log(x^2 - x + 1) - 16)/x^3","B",0
345,1,90,0,1.195717," ","integrate(1/x^6/(x^8+x^4+1),x, algorithm=""fricas"")","\frac{10 \, \sqrt{3} x^{5} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(x^{3} + 2 \, x\right)}\right) + 10 \, \sqrt{3} x^{5} \arctan\left(\frac{1}{3} \, \sqrt{3} x\right) + 5 \, \sqrt{3} x^{5} \log\left(\frac{x^{4} + 5 \, x^{2} - 2 \, \sqrt{3} {\left(x^{3} + x\right)} + 1}{x^{4} - x^{2} + 1}\right) + 60 \, x^{4} - 12}{60 \, x^{5}}"," ",0,"1/60*(10*sqrt(3)*x^5*arctan(1/3*sqrt(3)*(x^3 + 2*x)) + 10*sqrt(3)*x^5*arctan(1/3*sqrt(3)*x) + 5*sqrt(3)*x^5*log((x^4 + 5*x^2 - 2*sqrt(3)*(x^3 + x) + 1)/(x^4 - x^2 + 1)) + 60*x^4 - 12)/x^5","A",0
346,1,246,0,1.200504," ","integrate(1/x^8/(x^8+x^4+1),x, algorithm=""fricas"")","-\frac{28 \, \sqrt{6} \sqrt{3} \sqrt{2} x^{7} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2} - \sqrt{3}\right) + 28 \, \sqrt{6} \sqrt{3} \sqrt{2} x^{7} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{-\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2} + \sqrt{3}\right) + 7 \, \sqrt{6} \sqrt{2} x^{7} \log\left(\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2\right) - 7 \, \sqrt{6} \sqrt{2} x^{7} \log\left(-\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2\right) + 28 \, \sqrt{3} x^{7} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + 28 \, \sqrt{3} x^{7} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - 42 \, x^{7} \log\left(x^{2} + x + 1\right) + 42 \, x^{7} \log\left(x^{2} - x + 1\right) - 112 \, x^{4} + 48}{336 \, x^{7}}"," ",0,"-1/336*(28*sqrt(6)*sqrt(3)*sqrt(2)*x^7*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x + 1/3*sqrt(6)*sqrt(3)*sqrt(sqrt(6)*sqrt(2)*x + 2*x^2 + 2) - sqrt(3)) + 28*sqrt(6)*sqrt(3)*sqrt(2)*x^7*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x + 1/3*sqrt(6)*sqrt(3)*sqrt(-sqrt(6)*sqrt(2)*x + 2*x^2 + 2) + sqrt(3)) + 7*sqrt(6)*sqrt(2)*x^7*log(sqrt(6)*sqrt(2)*x + 2*x^2 + 2) - 7*sqrt(6)*sqrt(2)*x^7*log(-sqrt(6)*sqrt(2)*x + 2*x^2 + 2) + 28*sqrt(3)*x^7*arctan(1/3*sqrt(3)*(2*x + 1)) + 28*sqrt(3)*x^7*arctan(1/3*sqrt(3)*(2*x - 1)) - 42*x^7*log(x^2 + x + 1) + 42*x^7*log(x^2 - x + 1) - 112*x^4 + 48)/x^7","B",0
347,0,0,0,1.244477," ","integrate(x^m/(x^8-x^4+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{x^{8} - x^{4} + 1}, x\right)"," ",0,"integral(x^m/(x^8 - x^4 + 1), x)","F",0
348,1,37,0,1.135481," ","integrate(x^11/(x^8-x^4+1),x, algorithm=""fricas"")","\frac{1}{4} \, x^{4} - \frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{4} - 1\right)}\right) + \frac{1}{8} \, \log\left(x^{8} - x^{4} + 1\right)"," ",0,"1/4*x^4 - 1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^4 - 1)) + 1/8*log(x^8 - x^4 + 1)","A",0
349,1,47,0,1.172759," ","integrate(x^9/(x^8-x^4+1),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} + \frac{1}{12} \, \sqrt{3} \log\left(\frac{x^{8} + 5 \, x^{4} - 2 \, \sqrt{3} {\left(x^{6} + x^{2}\right)} + 1}{x^{8} - x^{4} + 1}\right)"," ",0,"1/2*x^2 + 1/12*sqrt(3)*log((x^8 + 5*x^4 - 2*sqrt(3)*(x^6 + x^2) + 1)/(x^8 - x^4 + 1))","A",0
350,1,32,0,1.163024," ","integrate(x^7/(x^8-x^4+1),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{4} - 1\right)}\right) + \frac{1}{8} \, \log\left(x^{8} - x^{4} + 1\right)"," ",0,"1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^4 - 1)) + 1/8*log(x^8 - x^4 + 1)","A",0
351,1,171,0,1.165251," ","integrate(x^5/(x^8-x^4+1),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{6} \sqrt{3} \sqrt{2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x^{2} + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2 \, x^{4} + \sqrt{6} \sqrt{2} x^{2} + 2} - \sqrt{3}\right) - \frac{1}{12} \, \sqrt{6} \sqrt{3} \sqrt{2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x^{2} + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2 \, x^{4} - \sqrt{6} \sqrt{2} x^{2} + 2} + \sqrt{3}\right) - \frac{1}{48} \, \sqrt{6} \sqrt{2} \log\left(2 \, x^{4} + \sqrt{6} \sqrt{2} x^{2} + 2\right) + \frac{1}{48} \, \sqrt{6} \sqrt{2} \log\left(2 \, x^{4} - \sqrt{6} \sqrt{2} x^{2} + 2\right)"," ",0,"-1/12*sqrt(6)*sqrt(3)*sqrt(2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x^2 + 1/3*sqrt(6)*sqrt(3)*sqrt(2*x^4 + sqrt(6)*sqrt(2)*x^2 + 2) - sqrt(3)) - 1/12*sqrt(6)*sqrt(3)*sqrt(2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x^2 + 1/3*sqrt(6)*sqrt(3)*sqrt(2*x^4 - sqrt(6)*sqrt(2)*x^2 + 2) + sqrt(3)) - 1/48*sqrt(6)*sqrt(2)*log(2*x^4 + sqrt(6)*sqrt(2)*x^2 + 2) + 1/48*sqrt(6)*sqrt(2)*log(2*x^4 - sqrt(6)*sqrt(2)*x^2 + 2)","B",0
352,1,18,0,1.702358," ","integrate(x^3/(x^8-x^4+1),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{4} - 1\right)}\right)"," ",0,"1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^4 - 1))","A",0
353,1,171,0,1.168826," ","integrate(x/(x^8-x^4+1),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{6} \sqrt{3} \sqrt{2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x^{2} + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2 \, x^{4} + \sqrt{6} \sqrt{2} x^{2} + 2} - \sqrt{3}\right) - \frac{1}{12} \, \sqrt{6} \sqrt{3} \sqrt{2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x^{2} + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2 \, x^{4} - \sqrt{6} \sqrt{2} x^{2} + 2} + \sqrt{3}\right) + \frac{1}{48} \, \sqrt{6} \sqrt{2} \log\left(2 \, x^{4} + \sqrt{6} \sqrt{2} x^{2} + 2\right) - \frac{1}{48} \, \sqrt{6} \sqrt{2} \log\left(2 \, x^{4} - \sqrt{6} \sqrt{2} x^{2} + 2\right)"," ",0,"-1/12*sqrt(6)*sqrt(3)*sqrt(2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x^2 + 1/3*sqrt(6)*sqrt(3)*sqrt(2*x^4 + sqrt(6)*sqrt(2)*x^2 + 2) - sqrt(3)) - 1/12*sqrt(6)*sqrt(3)*sqrt(2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x^2 + 1/3*sqrt(6)*sqrt(3)*sqrt(2*x^4 - sqrt(6)*sqrt(2)*x^2 + 2) + sqrt(3)) + 1/48*sqrt(6)*sqrt(2)*log(2*x^4 + sqrt(6)*sqrt(2)*x^2 + 2) - 1/48*sqrt(6)*sqrt(2)*log(2*x^4 - sqrt(6)*sqrt(2)*x^2 + 2)","B",0
354,1,34,0,1.115136," ","integrate(1/x/(x^8-x^4+1),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{4} - 1\right)}\right) - \frac{1}{8} \, \log\left(x^{8} - x^{4} + 1\right) + \log\left(x\right)"," ",0,"1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^4 - 1)) - 1/8*log(x^8 - x^4 + 1) + log(x)","A",0
355,1,50,0,1.241905," ","integrate(1/x^3/(x^8-x^4+1),x, algorithm=""fricas"")","\frac{\sqrt{3} x^{2} \log\left(\frac{x^{8} + 5 \, x^{4} + 2 \, \sqrt{3} {\left(x^{6} + x^{2}\right)} + 1}{x^{8} - x^{4} + 1}\right) - 6}{12 \, x^{2}}"," ",0,"1/12*(sqrt(3)*x^2*log((x^8 + 5*x^4 + 2*sqrt(3)*(x^6 + x^2) + 1)/(x^8 - x^4 + 1)) - 6)/x^2","A",0
356,1,51,0,1.224100," ","integrate(1/x^5/(x^8-x^4+1),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} x^{4} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{4} - 1\right)}\right) + 3 \, x^{4} \log\left(x^{8} - x^{4} + 1\right) - 24 \, x^{4} \log\left(x\right) + 6}{24 \, x^{4}}"," ",0,"-1/24*(2*sqrt(3)*x^4*arctan(1/3*sqrt(3)*(2*x^4 - 1)) + 3*x^4*log(x^8 - x^4 + 1) - 24*x^4*log(x) + 6)/x^4","A",0
357,1,193,0,1.325756," ","integrate(1/x^7/(x^8-x^4+1),x, algorithm=""fricas"")","\frac{4 \, \sqrt{6} \sqrt{3} \sqrt{2} x^{6} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x^{2} + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2 \, x^{4} + \sqrt{6} \sqrt{2} x^{2} + 2} - \sqrt{3}\right) + 4 \, \sqrt{6} \sqrt{3} \sqrt{2} x^{6} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x^{2} + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2 \, x^{4} - \sqrt{6} \sqrt{2} x^{2} + 2} + \sqrt{3}\right) + \sqrt{6} \sqrt{2} x^{6} \log\left(2 \, x^{4} + \sqrt{6} \sqrt{2} x^{2} + 2\right) - \sqrt{6} \sqrt{2} x^{6} \log\left(2 \, x^{4} - \sqrt{6} \sqrt{2} x^{2} + 2\right) - 24 \, x^{4} - 8}{48 \, x^{6}}"," ",0,"1/48*(4*sqrt(6)*sqrt(3)*sqrt(2)*x^6*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x^2 + 1/3*sqrt(6)*sqrt(3)*sqrt(2*x^4 + sqrt(6)*sqrt(2)*x^2 + 2) - sqrt(3)) + 4*sqrt(6)*sqrt(3)*sqrt(2)*x^6*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x^2 + 1/3*sqrt(6)*sqrt(3)*sqrt(2*x^4 - sqrt(6)*sqrt(2)*x^2 + 2) + sqrt(3)) + sqrt(6)*sqrt(2)*x^6*log(2*x^4 + sqrt(6)*sqrt(2)*x^2 + 2) - sqrt(6)*sqrt(2)*x^6*log(2*x^4 - sqrt(6)*sqrt(2)*x^2 + 2) - 24*x^4 - 8)/x^6","B",0
358,1,716,0,1.429789," ","integrate(x^8/(x^8-x^4+1),x, algorithm=""fricas"")","-\frac{1}{48} \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} - 2 \, \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} \log\left(12 \, x^{2} + 2 \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + 12\right) + \frac{1}{48} \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} - 2 \, \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} \log\left(12 \, x^{2} - 2 \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + 12\right) - \frac{1}{96} \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(12 \, x^{2} + \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + 12\right) + \frac{1}{96} \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(12 \, x^{2} - \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + 12\right) - \frac{1}{12} \, \sqrt{6} \sqrt{2} \sqrt{\sqrt{3} + 2} \arctan\left(\frac{1}{6} \, \sqrt{6} \sqrt{12 \, x^{2} + 2 \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + 12} {\left(\sqrt{3} \sqrt{2} - 2 \, \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} + \frac{1}{3} \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} - \sqrt{3} + 2\right) - \frac{1}{12} \, \sqrt{6} \sqrt{2} \sqrt{\sqrt{3} + 2} \arctan\left(\frac{1}{6} \, \sqrt{6} \sqrt{12 \, x^{2} - 2 \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + 12} {\left(\sqrt{3} \sqrt{2} - 2 \, \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} + \frac{1}{3} \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + \sqrt{3} - 2\right) - \frac{1}{24} \, \sqrt{6} \sqrt{2} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(\frac{1}{12} \, \sqrt{6} \sqrt{12 \, x^{2} + \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + 12} {\left(\sqrt{3} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{3} + 8} - \frac{1}{6} \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} - \sqrt{3} - 2\right) - \frac{1}{24} \, \sqrt{6} \sqrt{2} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(\frac{1}{12} \, \sqrt{6} \sqrt{12 \, x^{2} - \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + 12} {\left(\sqrt{3} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{3} + 8} - \frac{1}{6} \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + \sqrt{3} + 2\right) + x"," ",0,"-1/48*sqrt(6)*(sqrt(3)*sqrt(2) - 2*sqrt(2))*sqrt(sqrt(3) + 2)*log(12*x^2 + 2*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + 12) + 1/48*sqrt(6)*(sqrt(3)*sqrt(2) - 2*sqrt(2))*sqrt(sqrt(3) + 2)*log(12*x^2 - 2*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + 12) - 1/96*sqrt(6)*(sqrt(3)*sqrt(2) + 2*sqrt(2))*sqrt(-4*sqrt(3) + 8)*log(12*x^2 + sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + 12) + 1/96*sqrt(6)*(sqrt(3)*sqrt(2) + 2*sqrt(2))*sqrt(-4*sqrt(3) + 8)*log(12*x^2 - sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + 12) - 1/12*sqrt(6)*sqrt(2)*sqrt(sqrt(3) + 2)*arctan(1/6*sqrt(6)*sqrt(12*x^2 + 2*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + 12)*(sqrt(3)*sqrt(2) - 2*sqrt(2))*sqrt(sqrt(3) + 2) + 1/3*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) - sqrt(3) + 2) - 1/12*sqrt(6)*sqrt(2)*sqrt(sqrt(3) + 2)*arctan(1/6*sqrt(6)*sqrt(12*x^2 - 2*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + 12)*(sqrt(3)*sqrt(2) - 2*sqrt(2))*sqrt(sqrt(3) + 2) + 1/3*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + sqrt(3) - 2) - 1/24*sqrt(6)*sqrt(2)*sqrt(-4*sqrt(3) + 8)*arctan(1/12*sqrt(6)*sqrt(12*x^2 + sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + 12)*(sqrt(3)*sqrt(2) + 2*sqrt(2))*sqrt(-4*sqrt(3) + 8) - 1/6*sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) - sqrt(3) - 2) - 1/24*sqrt(6)*sqrt(2)*sqrt(-4*sqrt(3) + 8)*arctan(1/12*sqrt(6)*sqrt(12*x^2 - sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + 12)*(sqrt(3)*sqrt(2) + 2*sqrt(2))*sqrt(-4*sqrt(3) + 8) - 1/6*sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + sqrt(3) + 2) + x","B",0
359,1,215,0,1.267393," ","integrate(x^6/(x^8-x^4+1),x, algorithm=""fricas"")","-\frac{1}{6} \, \sqrt{3} \sqrt{2} \arctan\left(-\frac{\sqrt{3} \sqrt{2} {\left(x^{3} - x\right)} + x^{2} - \sqrt{x^{4} + \sqrt{3} \sqrt{2} {\left(x^{3} + x\right)} + 3 \, x^{2} + 1} {\left(\sqrt{3} \sqrt{2} x - 2\right)}}{3 \, x^{2} - 2}\right) - \frac{1}{6} \, \sqrt{3} \sqrt{2} \arctan\left(-\frac{\sqrt{3} \sqrt{2} {\left(x^{3} - x\right)} - x^{2} - \sqrt{x^{4} - \sqrt{3} \sqrt{2} {\left(x^{3} + x\right)} + 3 \, x^{2} + 1} {\left(\sqrt{3} \sqrt{2} x + 2\right)}}{3 \, x^{2} - 2}\right) - \frac{1}{24} \, \sqrt{3} \sqrt{2} \log\left(x^{4} + \sqrt{3} \sqrt{2} {\left(x^{3} + x\right)} + 3 \, x^{2} + 1\right) + \frac{1}{24} \, \sqrt{3} \sqrt{2} \log\left(x^{4} - \sqrt{3} \sqrt{2} {\left(x^{3} + x\right)} + 3 \, x^{2} + 1\right)"," ",0,"-1/6*sqrt(3)*sqrt(2)*arctan(-(sqrt(3)*sqrt(2)*(x^3 - x) + x^2 - sqrt(x^4 + sqrt(3)*sqrt(2)*(x^3 + x) + 3*x^2 + 1)*(sqrt(3)*sqrt(2)*x - 2))/(3*x^2 - 2)) - 1/6*sqrt(3)*sqrt(2)*arctan(-(sqrt(3)*sqrt(2)*(x^3 - x) - x^2 - sqrt(x^4 - sqrt(3)*sqrt(2)*(x^3 + x) + 3*x^2 + 1)*(sqrt(3)*sqrt(2)*x + 2))/(3*x^2 - 2)) - 1/24*sqrt(3)*sqrt(2)*log(x^4 + sqrt(3)*sqrt(2)*(x^3 + x) + 3*x^2 + 1) + 1/24*sqrt(3)*sqrt(2)*log(x^4 - sqrt(3)*sqrt(2)*(x^3 + x) + 3*x^2 + 1)","A",0
360,1,567,0,1.323728," ","integrate(x^4/(x^8-x^4+1),x, algorithm=""fricas"")","\frac{1}{48} \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} - 2 \, \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} \log\left(2 \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + 12 \, x^{2} + 12\right) - \frac{1}{48} \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} - 2 \, \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} \log\left(-2 \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + 12 \, x^{2} + 12\right) + \frac{1}{96} \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(\sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + 12 \, x^{2} + 12\right) - \frac{1}{96} \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(-\sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + 12 \, x^{2} + 12\right) - \frac{1}{12} \, \sqrt{6} \sqrt{2} \sqrt{\sqrt{3} + 2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + \frac{1}{6} \, \sqrt{6} \sqrt{2} \sqrt{2 \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + 12 \, x^{2} + 12} \sqrt{\sqrt{3} + 2} - \sqrt{3} - 2\right) - \frac{1}{12} \, \sqrt{6} \sqrt{2} \sqrt{\sqrt{3} + 2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + \frac{1}{6} \, \sqrt{6} \sqrt{2} \sqrt{-2 \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + 12 \, x^{2} + 12} \sqrt{\sqrt{3} + 2} + \sqrt{3} + 2\right) + \frac{1}{24} \, \sqrt{6} \sqrt{2} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(-\frac{1}{6} \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + \frac{1}{12} \, \sqrt{6} \sqrt{2} \sqrt{\sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + 12 \, x^{2} + 12} \sqrt{-4 \, \sqrt{3} + 8} + \sqrt{3} - 2\right) + \frac{1}{24} \, \sqrt{6} \sqrt{2} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(-\frac{1}{6} \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + \frac{1}{12} \, \sqrt{6} \sqrt{2} \sqrt{-\sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + 12 \, x^{2} + 12} \sqrt{-4 \, \sqrt{3} + 8} - \sqrt{3} + 2\right)"," ",0,"1/48*sqrt(6)*(sqrt(3)*sqrt(2) - 2*sqrt(2))*sqrt(sqrt(3) + 2)*log(2*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 12*x^2 + 12) - 1/48*sqrt(6)*(sqrt(3)*sqrt(2) - 2*sqrt(2))*sqrt(sqrt(3) + 2)*log(-2*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 12*x^2 + 12) + 1/96*sqrt(6)*(sqrt(3)*sqrt(2) + 2*sqrt(2))*sqrt(-4*sqrt(3) + 8)*log(sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 12*x^2 + 12) - 1/96*sqrt(6)*(sqrt(3)*sqrt(2) + 2*sqrt(2))*sqrt(-4*sqrt(3) + 8)*log(-sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 12*x^2 + 12) - 1/12*sqrt(6)*sqrt(2)*sqrt(sqrt(3) + 2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 1/6*sqrt(6)*sqrt(2)*sqrt(2*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 12*x^2 + 12)*sqrt(sqrt(3) + 2) - sqrt(3) - 2) - 1/12*sqrt(6)*sqrt(2)*sqrt(sqrt(3) + 2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 1/6*sqrt(6)*sqrt(2)*sqrt(-2*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 12*x^2 + 12)*sqrt(sqrt(3) + 2) + sqrt(3) + 2) + 1/24*sqrt(6)*sqrt(2)*sqrt(-4*sqrt(3) + 8)*arctan(-1/6*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 1/12*sqrt(6)*sqrt(2)*sqrt(sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 12*x^2 + 12)*sqrt(-4*sqrt(3) + 8) + sqrt(3) - 2) + 1/24*sqrt(6)*sqrt(2)*sqrt(-4*sqrt(3) + 8)*arctan(-1/6*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 1/12*sqrt(6)*sqrt(2)*sqrt(-sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 12*x^2 + 12)*sqrt(-4*sqrt(3) + 8) - sqrt(3) + 2)","B",0
361,1,567,0,1.301846," ","integrate(x^2/(x^8-x^4+1),x, algorithm=""fricas"")","-\frac{1}{48} \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} - 2 \, \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} \log\left(2 \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + 12 \, x^{2} + 12\right) + \frac{1}{48} \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} - 2 \, \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} \log\left(-2 \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + 12 \, x^{2} + 12\right) - \frac{1}{96} \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(\sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + 12 \, x^{2} + 12\right) + \frac{1}{96} \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(-\sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + 12 \, x^{2} + 12\right) - \frac{1}{12} \, \sqrt{6} \sqrt{2} \sqrt{\sqrt{3} + 2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + \frac{1}{6} \, \sqrt{6} \sqrt{2} \sqrt{2 \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + 12 \, x^{2} + 12} \sqrt{\sqrt{3} + 2} - \sqrt{3} - 2\right) - \frac{1}{12} \, \sqrt{6} \sqrt{2} \sqrt{\sqrt{3} + 2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + \frac{1}{6} \, \sqrt{6} \sqrt{2} \sqrt{-2 \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + 12 \, x^{2} + 12} \sqrt{\sqrt{3} + 2} + \sqrt{3} + 2\right) + \frac{1}{24} \, \sqrt{6} \sqrt{2} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(-\frac{1}{6} \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + \frac{1}{12} \, \sqrt{6} \sqrt{2} \sqrt{\sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + 12 \, x^{2} + 12} \sqrt{-4 \, \sqrt{3} + 8} + \sqrt{3} - 2\right) + \frac{1}{24} \, \sqrt{6} \sqrt{2} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(-\frac{1}{6} \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + \frac{1}{12} \, \sqrt{6} \sqrt{2} \sqrt{-\sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + 12 \, x^{2} + 12} \sqrt{-4 \, \sqrt{3} + 8} - \sqrt{3} + 2\right)"," ",0,"-1/48*sqrt(6)*(sqrt(3)*sqrt(2) - 2*sqrt(2))*sqrt(sqrt(3) + 2)*log(2*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 12*x^2 + 12) + 1/48*sqrt(6)*(sqrt(3)*sqrt(2) - 2*sqrt(2))*sqrt(sqrt(3) + 2)*log(-2*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 12*x^2 + 12) - 1/96*sqrt(6)*(sqrt(3)*sqrt(2) + 2*sqrt(2))*sqrt(-4*sqrt(3) + 8)*log(sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 12*x^2 + 12) + 1/96*sqrt(6)*(sqrt(3)*sqrt(2) + 2*sqrt(2))*sqrt(-4*sqrt(3) + 8)*log(-sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 12*x^2 + 12) - 1/12*sqrt(6)*sqrt(2)*sqrt(sqrt(3) + 2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 1/6*sqrt(6)*sqrt(2)*sqrt(2*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 12*x^2 + 12)*sqrt(sqrt(3) + 2) - sqrt(3) - 2) - 1/12*sqrt(6)*sqrt(2)*sqrt(sqrt(3) + 2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 1/6*sqrt(6)*sqrt(2)*sqrt(-2*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 12*x^2 + 12)*sqrt(sqrt(3) + 2) + sqrt(3) + 2) + 1/24*sqrt(6)*sqrt(2)*sqrt(-4*sqrt(3) + 8)*arctan(-1/6*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 1/12*sqrt(6)*sqrt(2)*sqrt(sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 12*x^2 + 12)*sqrt(-4*sqrt(3) + 8) + sqrt(3) - 2) + 1/24*sqrt(6)*sqrt(2)*sqrt(-4*sqrt(3) + 8)*arctan(-1/6*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 1/12*sqrt(6)*sqrt(2)*sqrt(-sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 12*x^2 + 12)*sqrt(-4*sqrt(3) + 8) - sqrt(3) + 2)","B",0
362,1,215,0,1.460597," ","integrate(1/(x^8-x^4+1),x, algorithm=""fricas"")","-\frac{1}{6} \, \sqrt{3} \sqrt{2} \arctan\left(-\frac{\sqrt{3} \sqrt{2} {\left(x^{3} - x\right)} + x^{2} - \sqrt{x^{4} + \sqrt{3} \sqrt{2} {\left(x^{3} + x\right)} + 3 \, x^{2} + 1} {\left(\sqrt{3} \sqrt{2} x - 2\right)}}{3 \, x^{2} - 2}\right) - \frac{1}{6} \, \sqrt{3} \sqrt{2} \arctan\left(-\frac{\sqrt{3} \sqrt{2} {\left(x^{3} - x\right)} - x^{2} - \sqrt{x^{4} - \sqrt{3} \sqrt{2} {\left(x^{3} + x\right)} + 3 \, x^{2} + 1} {\left(\sqrt{3} \sqrt{2} x + 2\right)}}{3 \, x^{2} - 2}\right) + \frac{1}{24} \, \sqrt{3} \sqrt{2} \log\left(x^{4} + \sqrt{3} \sqrt{2} {\left(x^{3} + x\right)} + 3 \, x^{2} + 1\right) - \frac{1}{24} \, \sqrt{3} \sqrt{2} \log\left(x^{4} - \sqrt{3} \sqrt{2} {\left(x^{3} + x\right)} + 3 \, x^{2} + 1\right)"," ",0,"-1/6*sqrt(3)*sqrt(2)*arctan(-(sqrt(3)*sqrt(2)*(x^3 - x) + x^2 - sqrt(x^4 + sqrt(3)*sqrt(2)*(x^3 + x) + 3*x^2 + 1)*(sqrt(3)*sqrt(2)*x - 2))/(3*x^2 - 2)) - 1/6*sqrt(3)*sqrt(2)*arctan(-(sqrt(3)*sqrt(2)*(x^3 - x) - x^2 - sqrt(x^4 - sqrt(3)*sqrt(2)*(x^3 + x) + 3*x^2 + 1)*(sqrt(3)*sqrt(2)*x + 2))/(3*x^2 - 2)) + 1/24*sqrt(3)*sqrt(2)*log(x^4 + sqrt(3)*sqrt(2)*(x^3 + x) + 3*x^2 + 1) - 1/24*sqrt(3)*sqrt(2)*log(x^4 - sqrt(3)*sqrt(2)*(x^3 + x) + 3*x^2 + 1)","A",0
363,1,732,0,1.557381," ","integrate(1/x^2/(x^8-x^4+1),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{6} \sqrt{2} x \sqrt{\sqrt{3} + 2} \arctan\left(\frac{1}{6} \, \sqrt{6} \sqrt{12 \, x^{2} + 2 \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + 12} {\left(\sqrt{3} \sqrt{2} - 2 \, \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} + \frac{1}{3} \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} - \sqrt{3} + 2\right) + 8 \, \sqrt{6} \sqrt{2} x \sqrt{\sqrt{3} + 2} \arctan\left(\frac{1}{6} \, \sqrt{6} \sqrt{12 \, x^{2} - 2 \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + 12} {\left(\sqrt{3} \sqrt{2} - 2 \, \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} + \frac{1}{3} \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + \sqrt{3} - 2\right) + 4 \, \sqrt{6} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(\frac{1}{12} \, \sqrt{6} \sqrt{12 \, x^{2} + \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + 12} {\left(\sqrt{3} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{3} + 8} - \frac{1}{6} \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} - \sqrt{3} - 2\right) + 4 \, \sqrt{6} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(\frac{1}{12} \, \sqrt{6} \sqrt{12 \, x^{2} - \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + 12} {\left(\sqrt{3} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{3} + 8} - \frac{1}{6} \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + \sqrt{3} + 2\right) - 2 \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} x - 2 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} \log\left(12 \, x^{2} + 2 \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + 12\right) + 2 \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} x - 2 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} \log\left(12 \, x^{2} - 2 \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + 12\right) - \sqrt{6} {\left(\sqrt{3} \sqrt{2} x + 2 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(12 \, x^{2} + \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + 12\right) + \sqrt{6} {\left(\sqrt{3} \sqrt{2} x + 2 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(12 \, x^{2} - \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + 12\right) + 96}{96 \, x}"," ",0,"-1/96*(8*sqrt(6)*sqrt(2)*x*sqrt(sqrt(3) + 2)*arctan(1/6*sqrt(6)*sqrt(12*x^2 + 2*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + 12)*(sqrt(3)*sqrt(2) - 2*sqrt(2))*sqrt(sqrt(3) + 2) + 1/3*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) - sqrt(3) + 2) + 8*sqrt(6)*sqrt(2)*x*sqrt(sqrt(3) + 2)*arctan(1/6*sqrt(6)*sqrt(12*x^2 - 2*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + 12)*(sqrt(3)*sqrt(2) - 2*sqrt(2))*sqrt(sqrt(3) + 2) + 1/3*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + sqrt(3) - 2) + 4*sqrt(6)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8)*arctan(1/12*sqrt(6)*sqrt(12*x^2 + sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + 12)*(sqrt(3)*sqrt(2) + 2*sqrt(2))*sqrt(-4*sqrt(3) + 8) - 1/6*sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) - sqrt(3) - 2) + 4*sqrt(6)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8)*arctan(1/12*sqrt(6)*sqrt(12*x^2 - sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + 12)*(sqrt(3)*sqrt(2) + 2*sqrt(2))*sqrt(-4*sqrt(3) + 8) - 1/6*sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + sqrt(3) + 2) - 2*sqrt(6)*(sqrt(3)*sqrt(2)*x - 2*sqrt(2)*x)*sqrt(sqrt(3) + 2)*log(12*x^2 + 2*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + 12) + 2*sqrt(6)*(sqrt(3)*sqrt(2)*x - 2*sqrt(2)*x)*sqrt(sqrt(3) + 2)*log(12*x^2 - 2*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + 12) - sqrt(6)*(sqrt(3)*sqrt(2)*x + 2*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8)*log(12*x^2 + sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + 12) + sqrt(6)*(sqrt(3)*sqrt(2)*x + 2*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8)*log(12*x^2 - sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + 12) + 96)/x","B",0
364,1,756,0,0.964148," ","integrate(1/x^4/(x^8-x^4+1),x, algorithm=""fricas"")","\frac{8 \, \sqrt{6} \sqrt{2} x^{3} \sqrt{\sqrt{3} + 2} \arctan\left(\frac{1}{6} \, \sqrt{6} \sqrt{12 \, x^{2} + 2 \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + 12} {\left(\sqrt{3} \sqrt{2} - 2 \, \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} + \frac{1}{3} \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} - \sqrt{3} + 2\right) + 8 \, \sqrt{6} \sqrt{2} x^{3} \sqrt{\sqrt{3} + 2} \arctan\left(\frac{1}{6} \, \sqrt{6} \sqrt{12 \, x^{2} - 2 \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + 12} {\left(\sqrt{3} \sqrt{2} - 2 \, \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} + \frac{1}{3} \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + \sqrt{3} - 2\right) + 4 \, \sqrt{6} \sqrt{2} x^{3} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(\frac{1}{12} \, \sqrt{6} \sqrt{12 \, x^{2} + \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + 12} {\left(\sqrt{3} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{3} + 8} - \frac{1}{6} \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} - \sqrt{3} - 2\right) + 4 \, \sqrt{6} \sqrt{2} x^{3} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(\frac{1}{12} \, \sqrt{6} \sqrt{12 \, x^{2} - \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + 12} {\left(\sqrt{3} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{3} + 8} - \frac{1}{6} \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + \sqrt{3} + 2\right) + 2 \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} x^{3} - 2 \, \sqrt{2} x^{3}\right)} \sqrt{\sqrt{3} + 2} \log\left(12 \, x^{2} + 2 \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + 12\right) - 2 \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} x^{3} - 2 \, \sqrt{2} x^{3}\right)} \sqrt{\sqrt{3} + 2} \log\left(12 \, x^{2} - 2 \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + 12\right) + \sqrt{6} {\left(\sqrt{3} \sqrt{2} x^{3} + 2 \, \sqrt{2} x^{3}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(12 \, x^{2} + \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + 12\right) - \sqrt{6} {\left(\sqrt{3} \sqrt{2} x^{3} + 2 \, \sqrt{2} x^{3}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(12 \, x^{2} - \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + 12\right) - 32}{96 \, x^{3}}"," ",0,"1/96*(8*sqrt(6)*sqrt(2)*x^3*sqrt(sqrt(3) + 2)*arctan(1/6*sqrt(6)*sqrt(12*x^2 + 2*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + 12)*(sqrt(3)*sqrt(2) - 2*sqrt(2))*sqrt(sqrt(3) + 2) + 1/3*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) - sqrt(3) + 2) + 8*sqrt(6)*sqrt(2)*x^3*sqrt(sqrt(3) + 2)*arctan(1/6*sqrt(6)*sqrt(12*x^2 - 2*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + 12)*(sqrt(3)*sqrt(2) - 2*sqrt(2))*sqrt(sqrt(3) + 2) + 1/3*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + sqrt(3) - 2) + 4*sqrt(6)*sqrt(2)*x^3*sqrt(-4*sqrt(3) + 8)*arctan(1/12*sqrt(6)*sqrt(12*x^2 + sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + 12)*(sqrt(3)*sqrt(2) + 2*sqrt(2))*sqrt(-4*sqrt(3) + 8) - 1/6*sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) - sqrt(3) - 2) + 4*sqrt(6)*sqrt(2)*x^3*sqrt(-4*sqrt(3) + 8)*arctan(1/12*sqrt(6)*sqrt(12*x^2 - sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + 12)*(sqrt(3)*sqrt(2) + 2*sqrt(2))*sqrt(-4*sqrt(3) + 8) - 1/6*sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + sqrt(3) + 2) + 2*sqrt(6)*(sqrt(3)*sqrt(2)*x^3 - 2*sqrt(2)*x^3)*sqrt(sqrt(3) + 2)*log(12*x^2 + 2*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + 12) - 2*sqrt(6)*(sqrt(3)*sqrt(2)*x^3 - 2*sqrt(2)*x^3)*sqrt(sqrt(3) + 2)*log(12*x^2 - 2*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + 12) + sqrt(6)*(sqrt(3)*sqrt(2)*x^3 + 2*sqrt(2)*x^3)*sqrt(-4*sqrt(3) + 8)*log(12*x^2 + sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + 12) - sqrt(6)*(sqrt(3)*sqrt(2)*x^3 + 2*sqrt(2)*x^3)*sqrt(-4*sqrt(3) + 8)*log(12*x^2 - sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + 12) - 32)/x^3","B",0
365,1,238,0,2.126318," ","integrate(1/x^6/(x^8-x^4+1),x, algorithm=""fricas"")","\frac{20 \, \sqrt{3} \sqrt{2} x^{5} \arctan\left(-\frac{\sqrt{3} \sqrt{2} {\left(x^{3} - x\right)} + x^{2} - \sqrt{x^{4} + \sqrt{3} \sqrt{2} {\left(x^{3} + x\right)} + 3 \, x^{2} + 1} {\left(\sqrt{3} \sqrt{2} x - 2\right)}}{3 \, x^{2} - 2}\right) + 20 \, \sqrt{3} \sqrt{2} x^{5} \arctan\left(-\frac{\sqrt{3} \sqrt{2} {\left(x^{3} - x\right)} - x^{2} - \sqrt{x^{4} - \sqrt{3} \sqrt{2} {\left(x^{3} + x\right)} + 3 \, x^{2} + 1} {\left(\sqrt{3} \sqrt{2} x + 2\right)}}{3 \, x^{2} - 2}\right) + 5 \, \sqrt{3} \sqrt{2} x^{5} \log\left(x^{4} + \sqrt{3} \sqrt{2} {\left(x^{3} + x\right)} + 3 \, x^{2} + 1\right) - 5 \, \sqrt{3} \sqrt{2} x^{5} \log\left(x^{4} - \sqrt{3} \sqrt{2} {\left(x^{3} + x\right)} + 3 \, x^{2} + 1\right) - 120 \, x^{4} - 24}{120 \, x^{5}}"," ",0,"1/120*(20*sqrt(3)*sqrt(2)*x^5*arctan(-(sqrt(3)*sqrt(2)*(x^3 - x) + x^2 - sqrt(x^4 + sqrt(3)*sqrt(2)*(x^3 + x) + 3*x^2 + 1)*(sqrt(3)*sqrt(2)*x - 2))/(3*x^2 - 2)) + 20*sqrt(3)*sqrt(2)*x^5*arctan(-(sqrt(3)*sqrt(2)*(x^3 - x) - x^2 - sqrt(x^4 - sqrt(3)*sqrt(2)*(x^3 + x) + 3*x^2 + 1)*(sqrt(3)*sqrt(2)*x + 2))/(3*x^2 - 2)) + 5*sqrt(3)*sqrt(2)*x^5*log(x^4 + sqrt(3)*sqrt(2)*(x^3 + x) + 3*x^2 + 1) - 5*sqrt(3)*sqrt(2)*x^5*log(x^4 - sqrt(3)*sqrt(2)*(x^3 + x) + 3*x^2 + 1) - 120*x^4 - 24)/x^5","A",0
366,1,614,0,1.730757," ","integrate(1/x^8/(x^8-x^4+1),x, algorithm=""fricas"")","\frac{56 \, \sqrt{6} \sqrt{2} x^{7} \sqrt{\sqrt{3} + 2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + \frac{1}{6} \, \sqrt{6} \sqrt{2} \sqrt{2 \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + 12 \, x^{2} + 12} \sqrt{\sqrt{3} + 2} - \sqrt{3} - 2\right) + 56 \, \sqrt{6} \sqrt{2} x^{7} \sqrt{\sqrt{3} + 2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + \frac{1}{6} \, \sqrt{6} \sqrt{2} \sqrt{-2 \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + 12 \, x^{2} + 12} \sqrt{\sqrt{3} + 2} + \sqrt{3} + 2\right) - 28 \, \sqrt{6} \sqrt{2} x^{7} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(-\frac{1}{6} \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + \frac{1}{12} \, \sqrt{6} \sqrt{2} \sqrt{\sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + 12 \, x^{2} + 12} \sqrt{-4 \, \sqrt{3} + 8} + \sqrt{3} - 2\right) - 28 \, \sqrt{6} \sqrt{2} x^{7} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(-\frac{1}{6} \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + \frac{1}{12} \, \sqrt{6} \sqrt{2} \sqrt{-\sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + 12 \, x^{2} + 12} \sqrt{-4 \, \sqrt{3} + 8} - \sqrt{3} + 2\right) - 224 \, x^{4} - 14 \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} x^{7} - 2 \, \sqrt{2} x^{7}\right)} \sqrt{\sqrt{3} + 2} \log\left(2 \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + 12 \, x^{2} + 12\right) + 14 \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} x^{7} - 2 \, \sqrt{2} x^{7}\right)} \sqrt{\sqrt{3} + 2} \log\left(-2 \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + 12 \, x^{2} + 12\right) - 7 \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} x^{7} + 2 \, \sqrt{2} x^{7}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(\sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + 12 \, x^{2} + 12\right) + 7 \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} x^{7} + 2 \, \sqrt{2} x^{7}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(-\sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + 12 \, x^{2} + 12\right) - 96}{672 \, x^{7}}"," ",0,"1/672*(56*sqrt(6)*sqrt(2)*x^7*sqrt(sqrt(3) + 2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 1/6*sqrt(6)*sqrt(2)*sqrt(2*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 12*x^2 + 12)*sqrt(sqrt(3) + 2) - sqrt(3) - 2) + 56*sqrt(6)*sqrt(2)*x^7*sqrt(sqrt(3) + 2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 1/6*sqrt(6)*sqrt(2)*sqrt(-2*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 12*x^2 + 12)*sqrt(sqrt(3) + 2) + sqrt(3) + 2) - 28*sqrt(6)*sqrt(2)*x^7*sqrt(-4*sqrt(3) + 8)*arctan(-1/6*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 1/12*sqrt(6)*sqrt(2)*sqrt(sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 12*x^2 + 12)*sqrt(-4*sqrt(3) + 8) + sqrt(3) - 2) - 28*sqrt(6)*sqrt(2)*x^7*sqrt(-4*sqrt(3) + 8)*arctan(-1/6*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 1/12*sqrt(6)*sqrt(2)*sqrt(-sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 12*x^2 + 12)*sqrt(-4*sqrt(3) + 8) - sqrt(3) + 2) - 224*x^4 - 14*sqrt(6)*(sqrt(3)*sqrt(2)*x^7 - 2*sqrt(2)*x^7)*sqrt(sqrt(3) + 2)*log(2*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 12*x^2 + 12) + 14*sqrt(6)*(sqrt(3)*sqrt(2)*x^7 - 2*sqrt(2)*x^7)*sqrt(sqrt(3) + 2)*log(-2*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 12*x^2 + 12) - 7*sqrt(6)*(sqrt(3)*sqrt(2)*x^7 + 2*sqrt(2)*x^7)*sqrt(-4*sqrt(3) + 8)*log(sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 12*x^2 + 12) + 7*sqrt(6)*(sqrt(3)*sqrt(2)*x^7 + 2*sqrt(2)*x^7)*sqrt(-4*sqrt(3) + 8)*log(-sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 12*x^2 + 12) - 96)/x^7","B",0
367,0,0,0,1.092073," ","integrate(x^m/(x^8+3*x^4+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{x^{8} + 3 \, x^{4} + 1}, x\right)"," ",0,"integral(x^m/(x^8 + 3*x^4 + 1), x)","F",0
368,1,62,0,1.476494," ","integrate(x^11/(x^8+3*x^4+1),x, algorithm=""fricas"")","\frac{1}{4} \, x^{4} + \frac{7}{40} \, \sqrt{5} \log\left(\frac{2 \, x^{8} + 6 \, x^{4} - \sqrt{5} {\left(2 \, x^{4} + 3\right)} + 7}{x^{8} + 3 \, x^{4} + 1}\right) - \frac{3}{8} \, \log\left(x^{8} + 3 \, x^{4} + 1\right)"," ",0,"1/4*x^4 + 7/40*sqrt(5)*log((2*x^8 + 6*x^4 - sqrt(5)*(2*x^4 + 3) + 7)/(x^8 + 3*x^4 + 1)) - 3/8*log(x^8 + 3*x^4 + 1)","A",0
369,1,154,0,1.289945," ","integrate(x^9/(x^8+3*x^4+1),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} - \frac{1}{5} \, \sqrt{5} \sqrt{-4 \, \sqrt{5} + 9} \arctan\left(\frac{1}{4} \, \sqrt{2 \, x^{4} - \sqrt{5} + 3} {\left(3 \, \sqrt{5} \sqrt{2} + 7 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{5} + 9} - \frac{1}{2} \, {\left(3 \, \sqrt{5} x^{2} + 7 \, x^{2}\right)} \sqrt{-4 \, \sqrt{5} + 9}\right) - \frac{1}{5} \, \sqrt{5} \sqrt{4 \, \sqrt{5} + 9} \arctan\left(-\frac{1}{4} \, {\left(6 \, \sqrt{5} x^{2} - 14 \, x^{2} - \sqrt{2 \, x^{4} + \sqrt{5} + 3} {\left(3 \, \sqrt{5} \sqrt{2} - 7 \, \sqrt{2}\right)}\right)} \sqrt{4 \, \sqrt{5} + 9}\right)"," ",0,"1/2*x^2 - 1/5*sqrt(5)*sqrt(-4*sqrt(5) + 9)*arctan(1/4*sqrt(2*x^4 - sqrt(5) + 3)*(3*sqrt(5)*sqrt(2) + 7*sqrt(2))*sqrt(-4*sqrt(5) + 9) - 1/2*(3*sqrt(5)*x^2 + 7*x^2)*sqrt(-4*sqrt(5) + 9)) - 1/5*sqrt(5)*sqrt(4*sqrt(5) + 9)*arctan(-1/4*(6*sqrt(5)*x^2 - 14*x^2 - sqrt(2*x^4 + sqrt(5) + 3)*(3*sqrt(5)*sqrt(2) - 7*sqrt(2)))*sqrt(4*sqrt(5) + 9))","B",0
370,1,56,0,1.397507," ","integrate(x^7/(x^8+3*x^4+1),x, algorithm=""fricas"")","\frac{3}{40} \, \sqrt{5} \log\left(\frac{2 \, x^{8} + 6 \, x^{4} + \sqrt{5} {\left(2 \, x^{4} + 3\right)} + 7}{x^{8} + 3 \, x^{4} + 1}\right) + \frac{1}{8} \, \log\left(x^{8} + 3 \, x^{4} + 1\right)"," ",0,"3/40*sqrt(5)*log((2*x^8 + 6*x^4 + sqrt(5)*(2*x^4 + 3) + 7)/(x^8 + 3*x^4 + 1)) + 1/8*log(x^8 + 3*x^4 + 1)","A",0
371,1,165,0,1.447215," ","integrate(x^5/(x^8+3*x^4+1),x, algorithm=""fricas"")","-\frac{1}{10} \, \sqrt{10} \sqrt{\sqrt{5} + 3} \arctan\left(\frac{1}{40} \, \sqrt{10} \sqrt{2 \, x^{4} + \sqrt{5} + 3} {\left(3 \, \sqrt{5} \sqrt{2} - 5 \, \sqrt{2}\right)} \sqrt{\sqrt{5} + 3} - \frac{1}{20} \, \sqrt{10} {\left(3 \, \sqrt{5} x^{2} - 5 \, x^{2}\right)} \sqrt{\sqrt{5} + 3}\right) + \frac{1}{10} \, \sqrt{10} \sqrt{-\sqrt{5} + 3} \arctan\left(\frac{1}{40} \, \sqrt{10} \sqrt{2 \, x^{4} - \sqrt{5} + 3} {\left(3 \, \sqrt{5} \sqrt{2} + 5 \, \sqrt{2}\right)} \sqrt{-\sqrt{5} + 3} - \frac{1}{20} \, \sqrt{10} {\left(3 \, \sqrt{5} x^{2} + 5 \, x^{2}\right)} \sqrt{-\sqrt{5} + 3}\right)"," ",0,"-1/10*sqrt(10)*sqrt(sqrt(5) + 3)*arctan(1/40*sqrt(10)*sqrt(2*x^4 + sqrt(5) + 3)*(3*sqrt(5)*sqrt(2) - 5*sqrt(2))*sqrt(sqrt(5) + 3) - 1/20*sqrt(10)*(3*sqrt(5)*x^2 - 5*x^2)*sqrt(sqrt(5) + 3)) + 1/10*sqrt(10)*sqrt(-sqrt(5) + 3)*arctan(1/40*sqrt(10)*sqrt(2*x^4 - sqrt(5) + 3)*(3*sqrt(5)*sqrt(2) + 5*sqrt(2))*sqrt(-sqrt(5) + 3) - 1/20*sqrt(10)*(3*sqrt(5)*x^2 + 5*x^2)*sqrt(-sqrt(5) + 3))","B",0
372,1,43,0,1.589876," ","integrate(x^3/(x^8+3*x^4+1),x, algorithm=""fricas"")","\frac{1}{20} \, \sqrt{5} \log\left(\frac{2 \, x^{8} + 6 \, x^{4} - \sqrt{5} {\left(2 \, x^{4} + 3\right)} + 7}{x^{8} + 3 \, x^{4} + 1}\right)"," ",0,"1/20*sqrt(5)*log((2*x^8 + 6*x^4 - sqrt(5)*(2*x^4 + 3) + 7)/(x^8 + 3*x^4 + 1))","B",0
373,1,128,0,1.363748," ","integrate(x/(x^8+3*x^4+1),x, algorithm=""fricas"")","\frac{1}{10} \, \sqrt{10} \sqrt{-\sqrt{5} + 3} \arctan\left(-\frac{1}{10} \, \sqrt{10} \sqrt{5} x^{2} \sqrt{-\sqrt{5} + 3} + \frac{1}{20} \, \sqrt{10} \sqrt{5} \sqrt{2} \sqrt{2 \, x^{4} + \sqrt{5} + 3} \sqrt{-\sqrt{5} + 3}\right) - \frac{1}{10} \, \sqrt{10} \sqrt{\sqrt{5} + 3} \arctan\left(-\frac{1}{20} \, {\left(2 \, \sqrt{10} \sqrt{5} x^{2} - \sqrt{10} \sqrt{5} \sqrt{2} \sqrt{2 \, x^{4} - \sqrt{5} + 3}\right)} \sqrt{\sqrt{5} + 3}\right)"," ",0,"1/10*sqrt(10)*sqrt(-sqrt(5) + 3)*arctan(-1/10*sqrt(10)*sqrt(5)*x^2*sqrt(-sqrt(5) + 3) + 1/20*sqrt(10)*sqrt(5)*sqrt(2)*sqrt(2*x^4 + sqrt(5) + 3)*sqrt(-sqrt(5) + 3)) - 1/10*sqrt(10)*sqrt(sqrt(5) + 3)*arctan(-1/20*(2*sqrt(10)*sqrt(5)*x^2 - sqrt(10)*sqrt(5)*sqrt(2)*sqrt(2*x^4 - sqrt(5) + 3))*sqrt(sqrt(5) + 3))","B",0
374,1,58,0,1.449790," ","integrate(1/x/(x^8+3*x^4+1),x, algorithm=""fricas"")","\frac{3}{40} \, \sqrt{5} \log\left(\frac{2 \, x^{8} + 6 \, x^{4} + \sqrt{5} {\left(2 \, x^{4} + 3\right)} + 7}{x^{8} + 3 \, x^{4} + 1}\right) - \frac{1}{8} \, \log\left(x^{8} + 3 \, x^{4} + 1\right) + \log\left(x\right)"," ",0,"3/40*sqrt(5)*log((2*x^8 + 6*x^4 + sqrt(5)*(2*x^4 + 3) + 7)/(x^8 + 3*x^4 + 1)) - 1/8*log(x^8 + 3*x^4 + 1) + log(x)","A",0
375,1,158,0,0.955050," ","integrate(1/x^3/(x^8+3*x^4+1),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{5} x^{2} \sqrt{-4 \, \sqrt{5} + 9} \arctan\left(\frac{1}{4} \, \sqrt{2 \, x^{4} + \sqrt{5} + 3} {\left(\sqrt{5} \sqrt{2} + 3 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{5} + 9} - \frac{1}{2} \, {\left(\sqrt{5} x^{2} + 3 \, x^{2}\right)} \sqrt{-4 \, \sqrt{5} + 9}\right) + 2 \, \sqrt{5} x^{2} \sqrt{4 \, \sqrt{5} + 9} \arctan\left(-\frac{1}{4} \, {\left(2 \, \sqrt{5} x^{2} - 6 \, x^{2} - \sqrt{2 \, x^{4} - \sqrt{5} + 3} {\left(\sqrt{5} \sqrt{2} - 3 \, \sqrt{2}\right)}\right)} \sqrt{4 \, \sqrt{5} + 9}\right) + 5}{10 \, x^{2}}"," ",0,"-1/10*(2*sqrt(5)*x^2*sqrt(-4*sqrt(5) + 9)*arctan(1/4*sqrt(2*x^4 + sqrt(5) + 3)*(sqrt(5)*sqrt(2) + 3*sqrt(2))*sqrt(-4*sqrt(5) + 9) - 1/2*(sqrt(5)*x^2 + 3*x^2)*sqrt(-4*sqrt(5) + 9)) + 2*sqrt(5)*x^2*sqrt(4*sqrt(5) + 9)*arctan(-1/4*(2*sqrt(5)*x^2 - 6*x^2 - sqrt(2*x^4 - sqrt(5) + 3)*(sqrt(5)*sqrt(2) - 3*sqrt(2)))*sqrt(4*sqrt(5) + 9)) + 5)/x^2","B",0
376,1,76,0,1.184259," ","integrate(1/x^5/(x^8+3*x^4+1),x, algorithm=""fricas"")","\frac{7 \, \sqrt{5} x^{4} \log\left(\frac{2 \, x^{8} + 6 \, x^{4} - \sqrt{5} {\left(2 \, x^{4} + 3\right)} + 7}{x^{8} + 3 \, x^{4} + 1}\right) + 15 \, x^{4} \log\left(x^{8} + 3 \, x^{4} + 1\right) - 120 \, x^{4} \log\left(x\right) - 10}{40 \, x^{4}}"," ",0,"1/40*(7*sqrt(5)*x^4*log((2*x^8 + 6*x^4 - sqrt(5)*(2*x^4 + 3) + 7)/(x^8 + 3*x^4 + 1)) + 15*x^4*log(x^8 + 3*x^4 + 1) - 120*x^4*log(x) - 10)/x^4","A",0
377,1,180,0,0.785957," ","integrate(1/x^7/(x^8+3*x^4+1),x, algorithm=""fricas"")","\frac{3 \, \sqrt{10} x^{6} \sqrt{-55 \, \sqrt{5} + 123} \arctan\left(\frac{1}{40} \, \sqrt{10} \sqrt{2 \, x^{4} + \sqrt{5} + 3} {\left(7 \, \sqrt{5} \sqrt{2} + 15 \, \sqrt{2}\right)} \sqrt{-55 \, \sqrt{5} + 123} - \frac{1}{20} \, \sqrt{10} {\left(7 \, \sqrt{5} x^{2} + 15 \, x^{2}\right)} \sqrt{-55 \, \sqrt{5} + 123}\right) - 3 \, \sqrt{10} x^{6} \sqrt{55 \, \sqrt{5} + 123} \arctan\left(\frac{1}{40} \, {\left(\sqrt{10} \sqrt{2 \, x^{4} - \sqrt{5} + 3} {\left(7 \, \sqrt{5} \sqrt{2} - 15 \, \sqrt{2}\right)} - 2 \, \sqrt{10} {\left(7 \, \sqrt{5} x^{2} - 15 \, x^{2}\right)}\right)} \sqrt{55 \, \sqrt{5} + 123}\right) + 45 \, x^{4} - 5}{30 \, x^{6}}"," ",0,"1/30*(3*sqrt(10)*x^6*sqrt(-55*sqrt(5) + 123)*arctan(1/40*sqrt(10)*sqrt(2*x^4 + sqrt(5) + 3)*(7*sqrt(5)*sqrt(2) + 15*sqrt(2))*sqrt(-55*sqrt(5) + 123) - 1/20*sqrt(10)*(7*sqrt(5)*x^2 + 15*x^2)*sqrt(-55*sqrt(5) + 123)) - 3*sqrt(10)*x^6*sqrt(55*sqrt(5) + 123)*arctan(1/40*(sqrt(10)*sqrt(2*x^4 - sqrt(5) + 3)*(7*sqrt(5)*sqrt(2) - 15*sqrt(2)) - 2*sqrt(10)*(7*sqrt(5)*x^2 - 15*x^2))*sqrt(55*sqrt(5) + 123)) + 45*x^4 - 5)/x^6","B",0
378,1,1012,0,1.677953," ","integrate(x^8/(x^8+3*x^4+1),x, algorithm=""fricas"")","\frac{1}{80} \, \sqrt{10} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} \sqrt{55 \, \sqrt{5} + 123} {\left(55 \, \sqrt{5} - 123\right)} \arctan\left(\frac{1}{80} \, \sqrt{10} \sqrt{20 \, x^{2} + \sqrt{10} {\left(3 \, \sqrt{5} \sqrt{2} x - 5 \, \sqrt{2} x\right)} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{1}{4}} - 5 \, \sqrt{110 \, \sqrt{5} + 246} {\left(3 \, \sqrt{5} - 7\right)}} {\left(1292 \, \sqrt{5} - 2889\right)} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{5}{4}} \sqrt{55 \, \sqrt{5} + 123} + \frac{1}{40} \, \sqrt{10} {\left(2889 \, \sqrt{5} x - 6460 \, x\right)} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{5}{4}} \sqrt{55 \, \sqrt{5} + 123} - \frac{1}{8} \, {\left(55 \, \sqrt{5} \sqrt{2} - 123 \, \sqrt{2}\right)} \sqrt{110 \, \sqrt{5} + 246} \sqrt{55 \, \sqrt{5} + 123}\right) + \frac{1}{80} \, \sqrt{10} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} \sqrt{55 \, \sqrt{5} + 123} {\left(55 \, \sqrt{5} - 123\right)} \arctan\left(\frac{1}{80} \, \sqrt{10} \sqrt{20 \, x^{2} - \sqrt{10} {\left(3 \, \sqrt{5} \sqrt{2} x - 5 \, \sqrt{2} x\right)} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{1}{4}} - 5 \, \sqrt{110 \, \sqrt{5} + 246} {\left(3 \, \sqrt{5} - 7\right)}} {\left(1292 \, \sqrt{5} - 2889\right)} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{5}{4}} \sqrt{55 \, \sqrt{5} + 123} + \frac{1}{40} \, \sqrt{10} {\left(2889 \, \sqrt{5} x - 6460 \, x\right)} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{5}{4}} \sqrt{55 \, \sqrt{5} + 123} + \frac{1}{8} \, {\left(55 \, \sqrt{5} \sqrt{2} - 123 \, \sqrt{2}\right)} \sqrt{110 \, \sqrt{5} + 246} \sqrt{55 \, \sqrt{5} + 123}\right) - \frac{1}{80} \, \sqrt{10} {\left(55 \, \sqrt{5} + 123\right)} \sqrt{-55 \, \sqrt{5} + 123} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} \arctan\left(\frac{1}{80} \, \sqrt{10} \sqrt{20 \, x^{2} + \sqrt{10} {\left(3 \, \sqrt{5} \sqrt{2} x + 5 \, \sqrt{2} x\right)} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{1}{4}} + 5 \, {\left(3 \, \sqrt{5} + 7\right)} \sqrt{-110 \, \sqrt{5} + 246}} {\left(1292 \, \sqrt{5} + 2889\right)} \sqrt{-55 \, \sqrt{5} + 123} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{5}{4}} - \frac{1}{40} \, {\left(\sqrt{10} {\left(2889 \, \sqrt{5} x + 6460 \, x\right)} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{5}{4}} + 5 \, {\left(55 \, \sqrt{5} \sqrt{2} + 123 \, \sqrt{2}\right)} \sqrt{-110 \, \sqrt{5} + 246}\right)} \sqrt{-55 \, \sqrt{5} + 123}\right) - \frac{1}{80} \, \sqrt{10} {\left(55 \, \sqrt{5} + 123\right)} \sqrt{-55 \, \sqrt{5} + 123} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} \arctan\left(\frac{1}{80} \, \sqrt{10} \sqrt{20 \, x^{2} - \sqrt{10} {\left(3 \, \sqrt{5} \sqrt{2} x + 5 \, \sqrt{2} x\right)} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{1}{4}} + 5 \, {\left(3 \, \sqrt{5} + 7\right)} \sqrt{-110 \, \sqrt{5} + 246}} {\left(1292 \, \sqrt{5} + 2889\right)} \sqrt{-55 \, \sqrt{5} + 123} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{5}{4}} - \frac{1}{40} \, {\left(\sqrt{10} {\left(2889 \, \sqrt{5} x + 6460 \, x\right)} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{5}{4}} - 5 \, {\left(55 \, \sqrt{5} \sqrt{2} + 123 \, \sqrt{2}\right)} \sqrt{-110 \, \sqrt{5} + 246}\right)} \sqrt{-55 \, \sqrt{5} + 123}\right) - \frac{1}{80} \, \sqrt{10} \sqrt{2} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{1}{4}} \log\left(20 \, x^{2} + \sqrt{10} {\left(3 \, \sqrt{5} \sqrt{2} x - 5 \, \sqrt{2} x\right)} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{1}{4}} - 5 \, \sqrt{110 \, \sqrt{5} + 246} {\left(3 \, \sqrt{5} - 7\right)}\right) + \frac{1}{80} \, \sqrt{10} \sqrt{2} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{1}{4}} \log\left(20 \, x^{2} - \sqrt{10} {\left(3 \, \sqrt{5} \sqrt{2} x - 5 \, \sqrt{2} x\right)} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{1}{4}} - 5 \, \sqrt{110 \, \sqrt{5} + 246} {\left(3 \, \sqrt{5} - 7\right)}\right) + \frac{1}{80} \, \sqrt{10} \sqrt{2} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{1}{4}} \log\left(20 \, x^{2} + \sqrt{10} {\left(3 \, \sqrt{5} \sqrt{2} x + 5 \, \sqrt{2} x\right)} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{1}{4}} + 5 \, {\left(3 \, \sqrt{5} + 7\right)} \sqrt{-110 \, \sqrt{5} + 246}\right) - \frac{1}{80} \, \sqrt{10} \sqrt{2} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{1}{4}} \log\left(20 \, x^{2} - \sqrt{10} {\left(3 \, \sqrt{5} \sqrt{2} x + 5 \, \sqrt{2} x\right)} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{1}{4}} + 5 \, {\left(3 \, \sqrt{5} + 7\right)} \sqrt{-110 \, \sqrt{5} + 246}\right) + x"," ",0,"1/80*sqrt(10)*(110*sqrt(5) + 246)^(3/4)*sqrt(55*sqrt(5) + 123)*(55*sqrt(5) - 123)*arctan(1/80*sqrt(10)*sqrt(20*x^2 + sqrt(10)*(3*sqrt(5)*sqrt(2)*x - 5*sqrt(2)*x)*(110*sqrt(5) + 246)^(1/4) - 5*sqrt(110*sqrt(5) + 246)*(3*sqrt(5) - 7))*(1292*sqrt(5) - 2889)*(110*sqrt(5) + 246)^(5/4)*sqrt(55*sqrt(5) + 123) + 1/40*sqrt(10)*(2889*sqrt(5)*x - 6460*x)*(110*sqrt(5) + 246)^(5/4)*sqrt(55*sqrt(5) + 123) - 1/8*(55*sqrt(5)*sqrt(2) - 123*sqrt(2))*sqrt(110*sqrt(5) + 246)*sqrt(55*sqrt(5) + 123)) + 1/80*sqrt(10)*(110*sqrt(5) + 246)^(3/4)*sqrt(55*sqrt(5) + 123)*(55*sqrt(5) - 123)*arctan(1/80*sqrt(10)*sqrt(20*x^2 - sqrt(10)*(3*sqrt(5)*sqrt(2)*x - 5*sqrt(2)*x)*(110*sqrt(5) + 246)^(1/4) - 5*sqrt(110*sqrt(5) + 246)*(3*sqrt(5) - 7))*(1292*sqrt(5) - 2889)*(110*sqrt(5) + 246)^(5/4)*sqrt(55*sqrt(5) + 123) + 1/40*sqrt(10)*(2889*sqrt(5)*x - 6460*x)*(110*sqrt(5) + 246)^(5/4)*sqrt(55*sqrt(5) + 123) + 1/8*(55*sqrt(5)*sqrt(2) - 123*sqrt(2))*sqrt(110*sqrt(5) + 246)*sqrt(55*sqrt(5) + 123)) - 1/80*sqrt(10)*(55*sqrt(5) + 123)*sqrt(-55*sqrt(5) + 123)*(-110*sqrt(5) + 246)^(3/4)*arctan(1/80*sqrt(10)*sqrt(20*x^2 + sqrt(10)*(3*sqrt(5)*sqrt(2)*x + 5*sqrt(2)*x)*(-110*sqrt(5) + 246)^(1/4) + 5*(3*sqrt(5) + 7)*sqrt(-110*sqrt(5) + 246))*(1292*sqrt(5) + 2889)*sqrt(-55*sqrt(5) + 123)*(-110*sqrt(5) + 246)^(5/4) - 1/40*(sqrt(10)*(2889*sqrt(5)*x + 6460*x)*(-110*sqrt(5) + 246)^(5/4) + 5*(55*sqrt(5)*sqrt(2) + 123*sqrt(2))*sqrt(-110*sqrt(5) + 246))*sqrt(-55*sqrt(5) + 123)) - 1/80*sqrt(10)*(55*sqrt(5) + 123)*sqrt(-55*sqrt(5) + 123)*(-110*sqrt(5) + 246)^(3/4)*arctan(1/80*sqrt(10)*sqrt(20*x^2 - sqrt(10)*(3*sqrt(5)*sqrt(2)*x + 5*sqrt(2)*x)*(-110*sqrt(5) + 246)^(1/4) + 5*(3*sqrt(5) + 7)*sqrt(-110*sqrt(5) + 246))*(1292*sqrt(5) + 2889)*sqrt(-55*sqrt(5) + 123)*(-110*sqrt(5) + 246)^(5/4) - 1/40*(sqrt(10)*(2889*sqrt(5)*x + 6460*x)*(-110*sqrt(5) + 246)^(5/4) - 5*(55*sqrt(5)*sqrt(2) + 123*sqrt(2))*sqrt(-110*sqrt(5) + 246))*sqrt(-55*sqrt(5) + 123)) - 1/80*sqrt(10)*sqrt(2)*(110*sqrt(5) + 246)^(1/4)*log(20*x^2 + sqrt(10)*(3*sqrt(5)*sqrt(2)*x - 5*sqrt(2)*x)*(110*sqrt(5) + 246)^(1/4) - 5*sqrt(110*sqrt(5) + 246)*(3*sqrt(5) - 7)) + 1/80*sqrt(10)*sqrt(2)*(110*sqrt(5) + 246)^(1/4)*log(20*x^2 - sqrt(10)*(3*sqrt(5)*sqrt(2)*x - 5*sqrt(2)*x)*(110*sqrt(5) + 246)^(1/4) - 5*sqrt(110*sqrt(5) + 246)*(3*sqrt(5) - 7)) + 1/80*sqrt(10)*sqrt(2)*(-110*sqrt(5) + 246)^(1/4)*log(20*x^2 + sqrt(10)*(3*sqrt(5)*sqrt(2)*x + 5*sqrt(2)*x)*(-110*sqrt(5) + 246)^(1/4) + 5*(3*sqrt(5) + 7)*sqrt(-110*sqrt(5) + 246)) - 1/80*sqrt(10)*sqrt(2)*(-110*sqrt(5) + 246)^(1/4)*log(20*x^2 - sqrt(10)*(3*sqrt(5)*sqrt(2)*x + 5*sqrt(2)*x)*(-110*sqrt(5) + 246)^(1/4) + 5*(3*sqrt(5) + 7)*sqrt(-110*sqrt(5) + 246)) + x","B",0
379,1,725,0,1.576526," ","integrate(x^6/(x^8+3*x^4+1),x, algorithm=""fricas"")","\frac{1}{10} \, \sqrt{5} \sqrt{2} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \, \sqrt{2 \, x^{2} + {\left(3 \, \sqrt{5} \sqrt{2} x - 7 \, \sqrt{2} x\right)} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{3}{4}} - \sqrt{4 \, \sqrt{5} + 9} {\left(\sqrt{5} - 3\right)}} {\left(21 \, \sqrt{5} - 47\right)} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{5}{4}} - \frac{1}{2} \, {\left(21 \, \sqrt{5} \sqrt{2} x - 47 \, \sqrt{2} x\right)} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{5}{4}} - 1\right) + \frac{1}{10} \, \sqrt{5} \sqrt{2} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \, \sqrt{2 \, x^{2} - {\left(3 \, \sqrt{5} \sqrt{2} x - 7 \, \sqrt{2} x\right)} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{3}{4}} - \sqrt{4 \, \sqrt{5} + 9} {\left(\sqrt{5} - 3\right)}} {\left(21 \, \sqrt{5} - 47\right)} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{5}{4}} - \frac{1}{2} \, {\left(21 \, \sqrt{5} \sqrt{2} x - 47 \, \sqrt{2} x\right)} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{5}{4}} + 1\right) + \frac{1}{10} \, \sqrt{5} \sqrt{2} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \, \sqrt{2 \, x^{2} + {\left(3 \, \sqrt{5} \sqrt{2} x + 7 \, \sqrt{2} x\right)} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{3}{4}} + {\left(\sqrt{5} + 3\right)} \sqrt{-4 \, \sqrt{5} + 9}} {\left(21 \, \sqrt{5} + 47\right)} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{5}{4}} - \frac{1}{2} \, {\left(21 \, \sqrt{5} \sqrt{2} x + 47 \, \sqrt{2} x\right)} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{5}{4}} - 1\right) + \frac{1}{10} \, \sqrt{5} \sqrt{2} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \, \sqrt{2 \, x^{2} - {\left(3 \, \sqrt{5} \sqrt{2} x + 7 \, \sqrt{2} x\right)} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{3}{4}} + {\left(\sqrt{5} + 3\right)} \sqrt{-4 \, \sqrt{5} + 9}} {\left(21 \, \sqrt{5} + 47\right)} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{5}{4}} - \frac{1}{2} \, {\left(21 \, \sqrt{5} \sqrt{2} x + 47 \, \sqrt{2} x\right)} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{5}{4}} + 1\right) + \frac{1}{40} \, \sqrt{5} \sqrt{2} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}} \log\left(2 \, x^{2} + {\left(3 \, \sqrt{5} \sqrt{2} x - 7 \, \sqrt{2} x\right)} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{3}{4}} - \sqrt{4 \, \sqrt{5} + 9} {\left(\sqrt{5} - 3\right)}\right) - \frac{1}{40} \, \sqrt{5} \sqrt{2} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}} \log\left(2 \, x^{2} - {\left(3 \, \sqrt{5} \sqrt{2} x - 7 \, \sqrt{2} x\right)} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{3}{4}} - \sqrt{4 \, \sqrt{5} + 9} {\left(\sqrt{5} - 3\right)}\right) + \frac{1}{40} \, \sqrt{5} \sqrt{2} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}} \log\left(2 \, x^{2} + {\left(3 \, \sqrt{5} \sqrt{2} x + 7 \, \sqrt{2} x\right)} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{3}{4}} + {\left(\sqrt{5} + 3\right)} \sqrt{-4 \, \sqrt{5} + 9}\right) - \frac{1}{40} \, \sqrt{5} \sqrt{2} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}} \log\left(2 \, x^{2} - {\left(3 \, \sqrt{5} \sqrt{2} x + 7 \, \sqrt{2} x\right)} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{3}{4}} + {\left(\sqrt{5} + 3\right)} \sqrt{-4 \, \sqrt{5} + 9}\right)"," ",0,"1/10*sqrt(5)*sqrt(2)*(4*sqrt(5) + 9)^(1/4)*arctan(1/2*sqrt(2*x^2 + (3*sqrt(5)*sqrt(2)*x - 7*sqrt(2)*x)*(4*sqrt(5) + 9)^(3/4) - sqrt(4*sqrt(5) + 9)*(sqrt(5) - 3))*(21*sqrt(5) - 47)*(4*sqrt(5) + 9)^(5/4) - 1/2*(21*sqrt(5)*sqrt(2)*x - 47*sqrt(2)*x)*(4*sqrt(5) + 9)^(5/4) - 1) + 1/10*sqrt(5)*sqrt(2)*(4*sqrt(5) + 9)^(1/4)*arctan(1/2*sqrt(2*x^2 - (3*sqrt(5)*sqrt(2)*x - 7*sqrt(2)*x)*(4*sqrt(5) + 9)^(3/4) - sqrt(4*sqrt(5) + 9)*(sqrt(5) - 3))*(21*sqrt(5) - 47)*(4*sqrt(5) + 9)^(5/4) - 1/2*(21*sqrt(5)*sqrt(2)*x - 47*sqrt(2)*x)*(4*sqrt(5) + 9)^(5/4) + 1) + 1/10*sqrt(5)*sqrt(2)*(-4*sqrt(5) + 9)^(1/4)*arctan(1/2*sqrt(2*x^2 + (3*sqrt(5)*sqrt(2)*x + 7*sqrt(2)*x)*(-4*sqrt(5) + 9)^(3/4) + (sqrt(5) + 3)*sqrt(-4*sqrt(5) + 9))*(21*sqrt(5) + 47)*(-4*sqrt(5) + 9)^(5/4) - 1/2*(21*sqrt(5)*sqrt(2)*x + 47*sqrt(2)*x)*(-4*sqrt(5) + 9)^(5/4) - 1) + 1/10*sqrt(5)*sqrt(2)*(-4*sqrt(5) + 9)^(1/4)*arctan(1/2*sqrt(2*x^2 - (3*sqrt(5)*sqrt(2)*x + 7*sqrt(2)*x)*(-4*sqrt(5) + 9)^(3/4) + (sqrt(5) + 3)*sqrt(-4*sqrt(5) + 9))*(21*sqrt(5) + 47)*(-4*sqrt(5) + 9)^(5/4) - 1/2*(21*sqrt(5)*sqrt(2)*x + 47*sqrt(2)*x)*(-4*sqrt(5) + 9)^(5/4) + 1) + 1/40*sqrt(5)*sqrt(2)*(4*sqrt(5) + 9)^(1/4)*log(2*x^2 + (3*sqrt(5)*sqrt(2)*x - 7*sqrt(2)*x)*(4*sqrt(5) + 9)^(3/4) - sqrt(4*sqrt(5) + 9)*(sqrt(5) - 3)) - 1/40*sqrt(5)*sqrt(2)*(4*sqrt(5) + 9)^(1/4)*log(2*x^2 - (3*sqrt(5)*sqrt(2)*x - 7*sqrt(2)*x)*(4*sqrt(5) + 9)^(3/4) - sqrt(4*sqrt(5) + 9)*(sqrt(5) - 3)) + 1/40*sqrt(5)*sqrt(2)*(-4*sqrt(5) + 9)^(1/4)*log(2*x^2 + (3*sqrt(5)*sqrt(2)*x + 7*sqrt(2)*x)*(-4*sqrt(5) + 9)^(3/4) + (sqrt(5) + 3)*sqrt(-4*sqrt(5) + 9)) - 1/40*sqrt(5)*sqrt(2)*(-4*sqrt(5) + 9)^(1/4)*log(2*x^2 - (3*sqrt(5)*sqrt(2)*x + 7*sqrt(2)*x)*(-4*sqrt(5) + 9)^(3/4) + (sqrt(5) + 3)*sqrt(-4*sqrt(5) + 9))","B",0
380,1,843,0,1.103679," ","integrate(x^4/(x^8+3*x^4+1),x, algorithm=""fricas"")","\frac{1}{80} \, \sqrt{10} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} \sqrt{\sqrt{5} + 3} {\left(\sqrt{5} - 3\right)} \arctan\left(-\frac{1}{80} \, \sqrt{10} {\left(7 \, \sqrt{5} x - 15 \, x\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} \sqrt{\sqrt{5} + 3} + \frac{1}{80} \, \sqrt{\sqrt{10} \sqrt{5} \sqrt{2} x {\left(2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} + 10 \, x^{2} + 5 \, \sqrt{2 \, \sqrt{5} + 6}} {\left(7 \, \sqrt{5} - 15\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} \sqrt{\sqrt{5} + 3} + \frac{1}{8} \, {\left(\sqrt{5} \sqrt{2} - 3 \, \sqrt{2}\right)} \sqrt{2 \, \sqrt{5} + 6} \sqrt{\sqrt{5} + 3}\right) + \frac{1}{80} \, \sqrt{10} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} \sqrt{\sqrt{5} + 3} {\left(\sqrt{5} - 3\right)} \arctan\left(-\frac{1}{80} \, \sqrt{10} {\left(7 \, \sqrt{5} x - 15 \, x\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} \sqrt{\sqrt{5} + 3} + \frac{1}{80} \, \sqrt{-\sqrt{10} \sqrt{5} \sqrt{2} x {\left(2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} + 10 \, x^{2} + 5 \, \sqrt{2 \, \sqrt{5} + 6}} {\left(7 \, \sqrt{5} - 15\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} \sqrt{\sqrt{5} + 3} - \frac{1}{8} \, {\left(\sqrt{5} \sqrt{2} - 3 \, \sqrt{2}\right)} \sqrt{2 \, \sqrt{5} + 6} \sqrt{\sqrt{5} + 3}\right) + \frac{1}{80} \, \sqrt{10} {\left(\sqrt{5} + 3\right)} \sqrt{-\sqrt{5} + 3} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} \arctan\left(\frac{1}{80} \, \sqrt{\sqrt{10} \sqrt{5} \sqrt{2} x {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} + 10 \, x^{2} + 5 \, \sqrt{-2 \, \sqrt{5} + 6}} {\left(7 \, \sqrt{5} + 15\right)} \sqrt{-\sqrt{5} + 3} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} - \frac{1}{80} \, {\left(\sqrt{10} {\left(7 \, \sqrt{5} x + 15 \, x\right)} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} + 10 \, {\left(\sqrt{5} \sqrt{2} + 3 \, \sqrt{2}\right)} \sqrt{-2 \, \sqrt{5} + 6}\right)} \sqrt{-\sqrt{5} + 3}\right) + \frac{1}{80} \, \sqrt{10} {\left(\sqrt{5} + 3\right)} \sqrt{-\sqrt{5} + 3} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} \arctan\left(\frac{1}{80} \, \sqrt{-\sqrt{10} \sqrt{5} \sqrt{2} x {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} + 10 \, x^{2} + 5 \, \sqrt{-2 \, \sqrt{5} + 6}} {\left(7 \, \sqrt{5} + 15\right)} \sqrt{-\sqrt{5} + 3} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} - \frac{1}{80} \, {\left(\sqrt{10} {\left(7 \, \sqrt{5} x + 15 \, x\right)} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} - 10 \, {\left(\sqrt{5} \sqrt{2} + 3 \, \sqrt{2}\right)} \sqrt{-2 \, \sqrt{5} + 6}\right)} \sqrt{-\sqrt{5} + 3}\right) + \frac{1}{80} \, \sqrt{10} \sqrt{2} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} \log\left(\sqrt{10} \sqrt{5} \sqrt{2} x {\left(2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} + 10 \, x^{2} + 5 \, \sqrt{2 \, \sqrt{5} + 6}\right) - \frac{1}{80} \, \sqrt{10} \sqrt{2} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} \log\left(-\sqrt{10} \sqrt{5} \sqrt{2} x {\left(2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} + 10 \, x^{2} + 5 \, \sqrt{2 \, \sqrt{5} + 6}\right) - \frac{1}{80} \, \sqrt{10} \sqrt{2} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} \log\left(\sqrt{10} \sqrt{5} \sqrt{2} x {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} + 10 \, x^{2} + 5 \, \sqrt{-2 \, \sqrt{5} + 6}\right) + \frac{1}{80} \, \sqrt{10} \sqrt{2} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} \log\left(-\sqrt{10} \sqrt{5} \sqrt{2} x {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} + 10 \, x^{2} + 5 \, \sqrt{-2 \, \sqrt{5} + 6}\right)"," ",0,"1/80*sqrt(10)*(2*sqrt(5) + 6)^(3/4)*sqrt(sqrt(5) + 3)*(sqrt(5) - 3)*arctan(-1/80*sqrt(10)*(7*sqrt(5)*x - 15*x)*(2*sqrt(5) + 6)^(5/4)*sqrt(sqrt(5) + 3) + 1/80*sqrt(sqrt(10)*sqrt(5)*sqrt(2)*x*(2*sqrt(5) + 6)^(1/4) + 10*x^2 + 5*sqrt(2*sqrt(5) + 6))*(7*sqrt(5) - 15)*(2*sqrt(5) + 6)^(5/4)*sqrt(sqrt(5) + 3) + 1/8*(sqrt(5)*sqrt(2) - 3*sqrt(2))*sqrt(2*sqrt(5) + 6)*sqrt(sqrt(5) + 3)) + 1/80*sqrt(10)*(2*sqrt(5) + 6)^(3/4)*sqrt(sqrt(5) + 3)*(sqrt(5) - 3)*arctan(-1/80*sqrt(10)*(7*sqrt(5)*x - 15*x)*(2*sqrt(5) + 6)^(5/4)*sqrt(sqrt(5) + 3) + 1/80*sqrt(-sqrt(10)*sqrt(5)*sqrt(2)*x*(2*sqrt(5) + 6)^(1/4) + 10*x^2 + 5*sqrt(2*sqrt(5) + 6))*(7*sqrt(5) - 15)*(2*sqrt(5) + 6)^(5/4)*sqrt(sqrt(5) + 3) - 1/8*(sqrt(5)*sqrt(2) - 3*sqrt(2))*sqrt(2*sqrt(5) + 6)*sqrt(sqrt(5) + 3)) + 1/80*sqrt(10)*(sqrt(5) + 3)*sqrt(-sqrt(5) + 3)*(-2*sqrt(5) + 6)^(3/4)*arctan(1/80*sqrt(sqrt(10)*sqrt(5)*sqrt(2)*x*(-2*sqrt(5) + 6)^(1/4) + 10*x^2 + 5*sqrt(-2*sqrt(5) + 6))*(7*sqrt(5) + 15)*sqrt(-sqrt(5) + 3)*(-2*sqrt(5) + 6)^(5/4) - 1/80*(sqrt(10)*(7*sqrt(5)*x + 15*x)*(-2*sqrt(5) + 6)^(5/4) + 10*(sqrt(5)*sqrt(2) + 3*sqrt(2))*sqrt(-2*sqrt(5) + 6))*sqrt(-sqrt(5) + 3)) + 1/80*sqrt(10)*(sqrt(5) + 3)*sqrt(-sqrt(5) + 3)*(-2*sqrt(5) + 6)^(3/4)*arctan(1/80*sqrt(-sqrt(10)*sqrt(5)*sqrt(2)*x*(-2*sqrt(5) + 6)^(1/4) + 10*x^2 + 5*sqrt(-2*sqrt(5) + 6))*(7*sqrt(5) + 15)*sqrt(-sqrt(5) + 3)*(-2*sqrt(5) + 6)^(5/4) - 1/80*(sqrt(10)*(7*sqrt(5)*x + 15*x)*(-2*sqrt(5) + 6)^(5/4) - 10*(sqrt(5)*sqrt(2) + 3*sqrt(2))*sqrt(-2*sqrt(5) + 6))*sqrt(-sqrt(5) + 3)) + 1/80*sqrt(10)*sqrt(2)*(2*sqrt(5) + 6)^(1/4)*log(sqrt(10)*sqrt(5)*sqrt(2)*x*(2*sqrt(5) + 6)^(1/4) + 10*x^2 + 5*sqrt(2*sqrt(5) + 6)) - 1/80*sqrt(10)*sqrt(2)*(2*sqrt(5) + 6)^(1/4)*log(-sqrt(10)*sqrt(5)*sqrt(2)*x*(2*sqrt(5) + 6)^(1/4) + 10*x^2 + 5*sqrt(2*sqrt(5) + 6)) - 1/80*sqrt(10)*sqrt(2)*(-2*sqrt(5) + 6)^(1/4)*log(sqrt(10)*sqrt(5)*sqrt(2)*x*(-2*sqrt(5) + 6)^(1/4) + 10*x^2 + 5*sqrt(-2*sqrt(5) + 6)) + 1/80*sqrt(10)*sqrt(2)*(-2*sqrt(5) + 6)^(1/4)*log(-sqrt(10)*sqrt(5)*sqrt(2)*x*(-2*sqrt(5) + 6)^(1/4) + 10*x^2 + 5*sqrt(-2*sqrt(5) + 6))","B",0
381,1,955,0,1.861662," ","integrate(x^2/(x^8+3*x^4+1),x, algorithm=""fricas"")","\frac{1}{80} \, \sqrt{10} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} \sqrt{\sqrt{5} + 3} {\left(\sqrt{5} - 3\right)} \arctan\left(-\frac{1}{40} \, \sqrt{10} {\left(3 \, \sqrt{5} x - 5 \, x\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} \sqrt{\sqrt{5} + 3} + \frac{1}{80} \, \sqrt{\sqrt{10} {\left(3 \, \sqrt{5} \sqrt{2} x - 5 \, \sqrt{2} x\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} + 40 \, x^{2} - 10 \, \sqrt{2 \, \sqrt{5} + 6} {\left(\sqrt{5} - 3\right)}} {\left(3 \, \sqrt{5} - 5\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} \sqrt{\sqrt{5} + 3} + \frac{1}{8} \, {\left(\sqrt{5} \sqrt{2} - 3 \, \sqrt{2}\right)} \sqrt{2 \, \sqrt{5} + 6} \sqrt{\sqrt{5} + 3}\right) + \frac{1}{80} \, \sqrt{10} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} \sqrt{\sqrt{5} + 3} {\left(\sqrt{5} - 3\right)} \arctan\left(-\frac{1}{40} \, \sqrt{10} {\left(3 \, \sqrt{5} x - 5 \, x\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} \sqrt{\sqrt{5} + 3} + \frac{1}{80} \, \sqrt{-\sqrt{10} {\left(3 \, \sqrt{5} \sqrt{2} x - 5 \, \sqrt{2} x\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} + 40 \, x^{2} - 10 \, \sqrt{2 \, \sqrt{5} + 6} {\left(\sqrt{5} - 3\right)}} {\left(3 \, \sqrt{5} - 5\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} \sqrt{\sqrt{5} + 3} - \frac{1}{8} \, {\left(\sqrt{5} \sqrt{2} - 3 \, \sqrt{2}\right)} \sqrt{2 \, \sqrt{5} + 6} \sqrt{\sqrt{5} + 3}\right) + \frac{1}{80} \, \sqrt{10} {\left(\sqrt{5} + 3\right)} \sqrt{-\sqrt{5} + 3} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} \arctan\left(\frac{1}{80} \, \sqrt{\sqrt{10} {\left(3 \, \sqrt{5} \sqrt{2} x + 5 \, \sqrt{2} x\right)} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} + 40 \, x^{2} + 10 \, {\left(\sqrt{5} + 3\right)} \sqrt{-2 \, \sqrt{5} + 6}} {\left(3 \, \sqrt{5} + 5\right)} \sqrt{-\sqrt{5} + 3} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} - \frac{1}{40} \, {\left(\sqrt{10} {\left(3 \, \sqrt{5} x + 5 \, x\right)} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} + 5 \, {\left(\sqrt{5} \sqrt{2} + 3 \, \sqrt{2}\right)} \sqrt{-2 \, \sqrt{5} + 6}\right)} \sqrt{-\sqrt{5} + 3}\right) + \frac{1}{80} \, \sqrt{10} {\left(\sqrt{5} + 3\right)} \sqrt{-\sqrt{5} + 3} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} \arctan\left(\frac{1}{80} \, \sqrt{-\sqrt{10} {\left(3 \, \sqrt{5} \sqrt{2} x + 5 \, \sqrt{2} x\right)} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} + 40 \, x^{2} + 10 \, {\left(\sqrt{5} + 3\right)} \sqrt{-2 \, \sqrt{5} + 6}} {\left(3 \, \sqrt{5} + 5\right)} \sqrt{-\sqrt{5} + 3} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} - \frac{1}{40} \, {\left(\sqrt{10} {\left(3 \, \sqrt{5} x + 5 \, x\right)} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} - 5 \, {\left(\sqrt{5} \sqrt{2} + 3 \, \sqrt{2}\right)} \sqrt{-2 \, \sqrt{5} + 6}\right)} \sqrt{-\sqrt{5} + 3}\right) - \frac{1}{80} \, \sqrt{10} \sqrt{2} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} \log\left(\sqrt{10} {\left(3 \, \sqrt{5} \sqrt{2} x - 5 \, \sqrt{2} x\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} + 40 \, x^{2} - 10 \, \sqrt{2 \, \sqrt{5} + 6} {\left(\sqrt{5} - 3\right)}\right) + \frac{1}{80} \, \sqrt{10} \sqrt{2} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} \log\left(-\sqrt{10} {\left(3 \, \sqrt{5} \sqrt{2} x - 5 \, \sqrt{2} x\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} + 40 \, x^{2} - 10 \, \sqrt{2 \, \sqrt{5} + 6} {\left(\sqrt{5} - 3\right)}\right) + \frac{1}{80} \, \sqrt{10} \sqrt{2} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} \log\left(\sqrt{10} {\left(3 \, \sqrt{5} \sqrt{2} x + 5 \, \sqrt{2} x\right)} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} + 40 \, x^{2} + 10 \, {\left(\sqrt{5} + 3\right)} \sqrt{-2 \, \sqrt{5} + 6}\right) - \frac{1}{80} \, \sqrt{10} \sqrt{2} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} \log\left(-\sqrt{10} {\left(3 \, \sqrt{5} \sqrt{2} x + 5 \, \sqrt{2} x\right)} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} + 40 \, x^{2} + 10 \, {\left(\sqrt{5} + 3\right)} \sqrt{-2 \, \sqrt{5} + 6}\right)"," ",0,"1/80*sqrt(10)*(2*sqrt(5) + 6)^(3/4)*sqrt(sqrt(5) + 3)*(sqrt(5) - 3)*arctan(-1/40*sqrt(10)*(3*sqrt(5)*x - 5*x)*(2*sqrt(5) + 6)^(3/4)*sqrt(sqrt(5) + 3) + 1/80*sqrt(sqrt(10)*(3*sqrt(5)*sqrt(2)*x - 5*sqrt(2)*x)*(2*sqrt(5) + 6)^(3/4) + 40*x^2 - 10*sqrt(2*sqrt(5) + 6)*(sqrt(5) - 3))*(3*sqrt(5) - 5)*(2*sqrt(5) + 6)^(3/4)*sqrt(sqrt(5) + 3) + 1/8*(sqrt(5)*sqrt(2) - 3*sqrt(2))*sqrt(2*sqrt(5) + 6)*sqrt(sqrt(5) + 3)) + 1/80*sqrt(10)*(2*sqrt(5) + 6)^(3/4)*sqrt(sqrt(5) + 3)*(sqrt(5) - 3)*arctan(-1/40*sqrt(10)*(3*sqrt(5)*x - 5*x)*(2*sqrt(5) + 6)^(3/4)*sqrt(sqrt(5) + 3) + 1/80*sqrt(-sqrt(10)*(3*sqrt(5)*sqrt(2)*x - 5*sqrt(2)*x)*(2*sqrt(5) + 6)^(3/4) + 40*x^2 - 10*sqrt(2*sqrt(5) + 6)*(sqrt(5) - 3))*(3*sqrt(5) - 5)*(2*sqrt(5) + 6)^(3/4)*sqrt(sqrt(5) + 3) - 1/8*(sqrt(5)*sqrt(2) - 3*sqrt(2))*sqrt(2*sqrt(5) + 6)*sqrt(sqrt(5) + 3)) + 1/80*sqrt(10)*(sqrt(5) + 3)*sqrt(-sqrt(5) + 3)*(-2*sqrt(5) + 6)^(3/4)*arctan(1/80*sqrt(sqrt(10)*(3*sqrt(5)*sqrt(2)*x + 5*sqrt(2)*x)*(-2*sqrt(5) + 6)^(3/4) + 40*x^2 + 10*(sqrt(5) + 3)*sqrt(-2*sqrt(5) + 6))*(3*sqrt(5) + 5)*sqrt(-sqrt(5) + 3)*(-2*sqrt(5) + 6)^(3/4) - 1/40*(sqrt(10)*(3*sqrt(5)*x + 5*x)*(-2*sqrt(5) + 6)^(3/4) + 5*(sqrt(5)*sqrt(2) + 3*sqrt(2))*sqrt(-2*sqrt(5) + 6))*sqrt(-sqrt(5) + 3)) + 1/80*sqrt(10)*(sqrt(5) + 3)*sqrt(-sqrt(5) + 3)*(-2*sqrt(5) + 6)^(3/4)*arctan(1/80*sqrt(-sqrt(10)*(3*sqrt(5)*sqrt(2)*x + 5*sqrt(2)*x)*(-2*sqrt(5) + 6)^(3/4) + 40*x^2 + 10*(sqrt(5) + 3)*sqrt(-2*sqrt(5) + 6))*(3*sqrt(5) + 5)*sqrt(-sqrt(5) + 3)*(-2*sqrt(5) + 6)^(3/4) - 1/40*(sqrt(10)*(3*sqrt(5)*x + 5*x)*(-2*sqrt(5) + 6)^(3/4) - 5*(sqrt(5)*sqrt(2) + 3*sqrt(2))*sqrt(-2*sqrt(5) + 6))*sqrt(-sqrt(5) + 3)) - 1/80*sqrt(10)*sqrt(2)*(2*sqrt(5) + 6)^(1/4)*log(sqrt(10)*(3*sqrt(5)*sqrt(2)*x - 5*sqrt(2)*x)*(2*sqrt(5) + 6)^(3/4) + 40*x^2 - 10*sqrt(2*sqrt(5) + 6)*(sqrt(5) - 3)) + 1/80*sqrt(10)*sqrt(2)*(2*sqrt(5) + 6)^(1/4)*log(-sqrt(10)*(3*sqrt(5)*sqrt(2)*x - 5*sqrt(2)*x)*(2*sqrt(5) + 6)^(3/4) + 40*x^2 - 10*sqrt(2*sqrt(5) + 6)*(sqrt(5) - 3)) + 1/80*sqrt(10)*sqrt(2)*(-2*sqrt(5) + 6)^(1/4)*log(sqrt(10)*(3*sqrt(5)*sqrt(2)*x + 5*sqrt(2)*x)*(-2*sqrt(5) + 6)^(3/4) + 40*x^2 + 10*(sqrt(5) + 3)*sqrt(-2*sqrt(5) + 6)) - 1/80*sqrt(10)*sqrt(2)*(-2*sqrt(5) + 6)^(1/4)*log(-sqrt(10)*(3*sqrt(5)*sqrt(2)*x + 5*sqrt(2)*x)*(-2*sqrt(5) + 6)^(3/4) + 40*x^2 + 10*(sqrt(5) + 3)*sqrt(-2*sqrt(5) + 6))","B",0
382,1,733,0,1.762553," ","integrate(1/(x^8+3*x^4+1),x, algorithm=""fricas"")","\frac{1}{10} \, \sqrt{5} \sqrt{2} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \, \sqrt{2 \, x^{2} - \sqrt{4 \, \sqrt{5} + 9} {\left(3 \, \sqrt{5} - 7\right)} + {\left(\sqrt{5} \sqrt{2} x - 3 \, \sqrt{2} x\right)} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}}} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{3}{4}} {\left(3 \, \sqrt{5} - 7\right)} - \frac{1}{2} \, {\left(3 \, \sqrt{5} \sqrt{2} x - 7 \, \sqrt{2} x\right)} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{3}{4}} - 1\right) + \frac{1}{10} \, \sqrt{5} \sqrt{2} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \, \sqrt{2 \, x^{2} - \sqrt{4 \, \sqrt{5} + 9} {\left(3 \, \sqrt{5} - 7\right)} - {\left(\sqrt{5} \sqrt{2} x - 3 \, \sqrt{2} x\right)} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}}} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{3}{4}} {\left(3 \, \sqrt{5} - 7\right)} - \frac{1}{2} \, {\left(3 \, \sqrt{5} \sqrt{2} x - 7 \, \sqrt{2} x\right)} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{3}{4}} + 1\right) + \frac{1}{10} \, \sqrt{5} \sqrt{2} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \, \sqrt{2 \, x^{2} + {\left(3 \, \sqrt{5} + 7\right)} \sqrt{-4 \, \sqrt{5} + 9} + {\left(\sqrt{5} \sqrt{2} x + 3 \, \sqrt{2} x\right)} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}}} {\left(3 \, \sqrt{5} + 7\right)} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{3}{4}} - \frac{1}{2} \, {\left(3 \, \sqrt{5} \sqrt{2} x + 7 \, \sqrt{2} x\right)} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{3}{4}} - 1\right) + \frac{1}{10} \, \sqrt{5} \sqrt{2} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \, \sqrt{2 \, x^{2} + {\left(3 \, \sqrt{5} + 7\right)} \sqrt{-4 \, \sqrt{5} + 9} - {\left(\sqrt{5} \sqrt{2} x + 3 \, \sqrt{2} x\right)} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}}} {\left(3 \, \sqrt{5} + 7\right)} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{3}{4}} - \frac{1}{2} \, {\left(3 \, \sqrt{5} \sqrt{2} x + 7 \, \sqrt{2} x\right)} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{3}{4}} + 1\right) - \frac{1}{40} \, \sqrt{5} \sqrt{2} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}} \log\left(2 \, x^{2} - \sqrt{4 \, \sqrt{5} + 9} {\left(3 \, \sqrt{5} - 7\right)} + {\left(\sqrt{5} \sqrt{2} x - 3 \, \sqrt{2} x\right)} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}}\right) + \frac{1}{40} \, \sqrt{5} \sqrt{2} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}} \log\left(2 \, x^{2} - \sqrt{4 \, \sqrt{5} + 9} {\left(3 \, \sqrt{5} - 7\right)} - {\left(\sqrt{5} \sqrt{2} x - 3 \, \sqrt{2} x\right)} {\left(4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}}\right) - \frac{1}{40} \, \sqrt{5} \sqrt{2} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}} \log\left(2 \, x^{2} + {\left(3 \, \sqrt{5} + 7\right)} \sqrt{-4 \, \sqrt{5} + 9} + {\left(\sqrt{5} \sqrt{2} x + 3 \, \sqrt{2} x\right)} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}}\right) + \frac{1}{40} \, \sqrt{5} \sqrt{2} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}} \log\left(2 \, x^{2} + {\left(3 \, \sqrt{5} + 7\right)} \sqrt{-4 \, \sqrt{5} + 9} - {\left(\sqrt{5} \sqrt{2} x + 3 \, \sqrt{2} x\right)} {\left(-4 \, \sqrt{5} + 9\right)}^{\frac{1}{4}}\right)"," ",0,"1/10*sqrt(5)*sqrt(2)*(4*sqrt(5) + 9)^(1/4)*arctan(1/2*sqrt(2*x^2 - sqrt(4*sqrt(5) + 9)*(3*sqrt(5) - 7) + (sqrt(5)*sqrt(2)*x - 3*sqrt(2)*x)*(4*sqrt(5) + 9)^(1/4))*(4*sqrt(5) + 9)^(3/4)*(3*sqrt(5) - 7) - 1/2*(3*sqrt(5)*sqrt(2)*x - 7*sqrt(2)*x)*(4*sqrt(5) + 9)^(3/4) - 1) + 1/10*sqrt(5)*sqrt(2)*(4*sqrt(5) + 9)^(1/4)*arctan(1/2*sqrt(2*x^2 - sqrt(4*sqrt(5) + 9)*(3*sqrt(5) - 7) - (sqrt(5)*sqrt(2)*x - 3*sqrt(2)*x)*(4*sqrt(5) + 9)^(1/4))*(4*sqrt(5) + 9)^(3/4)*(3*sqrt(5) - 7) - 1/2*(3*sqrt(5)*sqrt(2)*x - 7*sqrt(2)*x)*(4*sqrt(5) + 9)^(3/4) + 1) + 1/10*sqrt(5)*sqrt(2)*(-4*sqrt(5) + 9)^(1/4)*arctan(1/2*sqrt(2*x^2 + (3*sqrt(5) + 7)*sqrt(-4*sqrt(5) + 9) + (sqrt(5)*sqrt(2)*x + 3*sqrt(2)*x)*(-4*sqrt(5) + 9)^(1/4))*(3*sqrt(5) + 7)*(-4*sqrt(5) + 9)^(3/4) - 1/2*(3*sqrt(5)*sqrt(2)*x + 7*sqrt(2)*x)*(-4*sqrt(5) + 9)^(3/4) - 1) + 1/10*sqrt(5)*sqrt(2)*(-4*sqrt(5) + 9)^(1/4)*arctan(1/2*sqrt(2*x^2 + (3*sqrt(5) + 7)*sqrt(-4*sqrt(5) + 9) - (sqrt(5)*sqrt(2)*x + 3*sqrt(2)*x)*(-4*sqrt(5) + 9)^(1/4))*(3*sqrt(5) + 7)*(-4*sqrt(5) + 9)^(3/4) - 1/2*(3*sqrt(5)*sqrt(2)*x + 7*sqrt(2)*x)*(-4*sqrt(5) + 9)^(3/4) + 1) - 1/40*sqrt(5)*sqrt(2)*(4*sqrt(5) + 9)^(1/4)*log(2*x^2 - sqrt(4*sqrt(5) + 9)*(3*sqrt(5) - 7) + (sqrt(5)*sqrt(2)*x - 3*sqrt(2)*x)*(4*sqrt(5) + 9)^(1/4)) + 1/40*sqrt(5)*sqrt(2)*(4*sqrt(5) + 9)^(1/4)*log(2*x^2 - sqrt(4*sqrt(5) + 9)*(3*sqrt(5) - 7) - (sqrt(5)*sqrt(2)*x - 3*sqrt(2)*x)*(4*sqrt(5) + 9)^(1/4)) - 1/40*sqrt(5)*sqrt(2)*(-4*sqrt(5) + 9)^(1/4)*log(2*x^2 + (3*sqrt(5) + 7)*sqrt(-4*sqrt(5) + 9) + (sqrt(5)*sqrt(2)*x + 3*sqrt(2)*x)*(-4*sqrt(5) + 9)^(1/4)) + 1/40*sqrt(5)*sqrt(2)*(-4*sqrt(5) + 9)^(1/4)*log(2*x^2 + (3*sqrt(5) + 7)*sqrt(-4*sqrt(5) + 9) - (sqrt(5)*sqrt(2)*x + 3*sqrt(2)*x)*(-4*sqrt(5) + 9)^(1/4))","B",0
383,1,1017,0,1.500032," ","integrate(1/x^2/(x^8+3*x^4+1),x, algorithm=""fricas"")","-\frac{\sqrt{10} {\left(55 \, \sqrt{5} x - 123 \, x\right)} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} \sqrt{55 \, \sqrt{5} + 123} \arctan\left(-\frac{1}{20} \, \sqrt{10} {\left(161 \, \sqrt{5} x - 360 \, x\right)} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} \sqrt{55 \, \sqrt{5} + 123} + \frac{1}{40} \, \sqrt{\sqrt{10} {\left(47 \, \sqrt{5} \sqrt{2} x - 105 \, \sqrt{2} x\right)} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} + 40 \, x^{2} - 20 \, \sqrt{110 \, \sqrt{5} + 246} {\left(4 \, \sqrt{5} - 9\right)}} {\left(161 \, \sqrt{5} - 360\right)} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} \sqrt{55 \, \sqrt{5} + 123} + \frac{1}{8} \, {\left(55 \, \sqrt{5} \sqrt{2} - 123 \, \sqrt{2}\right)} \sqrt{110 \, \sqrt{5} + 246} \sqrt{55 \, \sqrt{5} + 123}\right) + \sqrt{10} {\left(55 \, \sqrt{5} x - 123 \, x\right)} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} \sqrt{55 \, \sqrt{5} + 123} \arctan\left(-\frac{1}{20} \, \sqrt{10} {\left(161 \, \sqrt{5} x - 360 \, x\right)} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} \sqrt{55 \, \sqrt{5} + 123} + \frac{1}{40} \, \sqrt{-\sqrt{10} {\left(47 \, \sqrt{5} \sqrt{2} x - 105 \, \sqrt{2} x\right)} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} + 40 \, x^{2} - 20 \, \sqrt{110 \, \sqrt{5} + 246} {\left(4 \, \sqrt{5} - 9\right)}} {\left(161 \, \sqrt{5} - 360\right)} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} \sqrt{55 \, \sqrt{5} + 123} - \frac{1}{8} \, {\left(55 \, \sqrt{5} \sqrt{2} - 123 \, \sqrt{2}\right)} \sqrt{110 \, \sqrt{5} + 246} \sqrt{55 \, \sqrt{5} + 123}\right) + \sqrt{10} {\left(55 \, \sqrt{5} x + 123 \, x\right)} \sqrt{-55 \, \sqrt{5} + 123} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} \arctan\left(\frac{1}{40} \, \sqrt{\sqrt{10} {\left(47 \, \sqrt{5} \sqrt{2} x + 105 \, \sqrt{2} x\right)} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} + 40 \, x^{2} + 20 \, {\left(4 \, \sqrt{5} + 9\right)} \sqrt{-110 \, \sqrt{5} + 246}} {\left(161 \, \sqrt{5} + 360\right)} \sqrt{-55 \, \sqrt{5} + 123} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} - \frac{1}{40} \, {\left(2 \, \sqrt{10} {\left(161 \, \sqrt{5} x + 360 \, x\right)} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} + 5 \, {\left(55 \, \sqrt{5} \sqrt{2} + 123 \, \sqrt{2}\right)} \sqrt{-110 \, \sqrt{5} + 246}\right)} \sqrt{-55 \, \sqrt{5} + 123}\right) + \sqrt{10} {\left(55 \, \sqrt{5} x + 123 \, x\right)} \sqrt{-55 \, \sqrt{5} + 123} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} \arctan\left(\frac{1}{40} \, \sqrt{-\sqrt{10} {\left(47 \, \sqrt{5} \sqrt{2} x + 105 \, \sqrt{2} x\right)} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} + 40 \, x^{2} + 20 \, {\left(4 \, \sqrt{5} + 9\right)} \sqrt{-110 \, \sqrt{5} + 246}} {\left(161 \, \sqrt{5} + 360\right)} \sqrt{-55 \, \sqrt{5} + 123} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} - \frac{1}{40} \, {\left(2 \, \sqrt{10} {\left(161 \, \sqrt{5} x + 360 \, x\right)} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} - 5 \, {\left(55 \, \sqrt{5} \sqrt{2} + 123 \, \sqrt{2}\right)} \sqrt{-110 \, \sqrt{5} + 246}\right)} \sqrt{-55 \, \sqrt{5} + 123}\right) - \sqrt{10} \sqrt{2} x {\left(110 \, \sqrt{5} + 246\right)}^{\frac{1}{4}} \log\left(\sqrt{10} {\left(47 \, \sqrt{5} \sqrt{2} x - 105 \, \sqrt{2} x\right)} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} + 40 \, x^{2} - 20 \, \sqrt{110 \, \sqrt{5} + 246} {\left(4 \, \sqrt{5} - 9\right)}\right) + \sqrt{10} \sqrt{2} x {\left(110 \, \sqrt{5} + 246\right)}^{\frac{1}{4}} \log\left(-\sqrt{10} {\left(47 \, \sqrt{5} \sqrt{2} x - 105 \, \sqrt{2} x\right)} {\left(110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} + 40 \, x^{2} - 20 \, \sqrt{110 \, \sqrt{5} + 246} {\left(4 \, \sqrt{5} - 9\right)}\right) + \sqrt{10} \sqrt{2} x {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{1}{4}} \log\left(\sqrt{10} {\left(47 \, \sqrt{5} \sqrt{2} x + 105 \, \sqrt{2} x\right)} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} + 40 \, x^{2} + 20 \, {\left(4 \, \sqrt{5} + 9\right)} \sqrt{-110 \, \sqrt{5} + 246}\right) - \sqrt{10} \sqrt{2} x {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{1}{4}} \log\left(-\sqrt{10} {\left(47 \, \sqrt{5} \sqrt{2} x + 105 \, \sqrt{2} x\right)} {\left(-110 \, \sqrt{5} + 246\right)}^{\frac{3}{4}} + 40 \, x^{2} + 20 \, {\left(4 \, \sqrt{5} + 9\right)} \sqrt{-110 \, \sqrt{5} + 246}\right) + 80}{80 \, x}"," ",0,"-1/80*(sqrt(10)*(55*sqrt(5)*x - 123*x)*(110*sqrt(5) + 246)^(3/4)*sqrt(55*sqrt(5) + 123)*arctan(-1/20*sqrt(10)*(161*sqrt(5)*x - 360*x)*(110*sqrt(5) + 246)^(3/4)*sqrt(55*sqrt(5) + 123) + 1/40*sqrt(sqrt(10)*(47*sqrt(5)*sqrt(2)*x - 105*sqrt(2)*x)*(110*sqrt(5) + 246)^(3/4) + 40*x^2 - 20*sqrt(110*sqrt(5) + 246)*(4*sqrt(5) - 9))*(161*sqrt(5) - 360)*(110*sqrt(5) + 246)^(3/4)*sqrt(55*sqrt(5) + 123) + 1/8*(55*sqrt(5)*sqrt(2) - 123*sqrt(2))*sqrt(110*sqrt(5) + 246)*sqrt(55*sqrt(5) + 123)) + sqrt(10)*(55*sqrt(5)*x - 123*x)*(110*sqrt(5) + 246)^(3/4)*sqrt(55*sqrt(5) + 123)*arctan(-1/20*sqrt(10)*(161*sqrt(5)*x - 360*x)*(110*sqrt(5) + 246)^(3/4)*sqrt(55*sqrt(5) + 123) + 1/40*sqrt(-sqrt(10)*(47*sqrt(5)*sqrt(2)*x - 105*sqrt(2)*x)*(110*sqrt(5) + 246)^(3/4) + 40*x^2 - 20*sqrt(110*sqrt(5) + 246)*(4*sqrt(5) - 9))*(161*sqrt(5) - 360)*(110*sqrt(5) + 246)^(3/4)*sqrt(55*sqrt(5) + 123) - 1/8*(55*sqrt(5)*sqrt(2) - 123*sqrt(2))*sqrt(110*sqrt(5) + 246)*sqrt(55*sqrt(5) + 123)) + sqrt(10)*(55*sqrt(5)*x + 123*x)*sqrt(-55*sqrt(5) + 123)*(-110*sqrt(5) + 246)^(3/4)*arctan(1/40*sqrt(sqrt(10)*(47*sqrt(5)*sqrt(2)*x + 105*sqrt(2)*x)*(-110*sqrt(5) + 246)^(3/4) + 40*x^2 + 20*(4*sqrt(5) + 9)*sqrt(-110*sqrt(5) + 246))*(161*sqrt(5) + 360)*sqrt(-55*sqrt(5) + 123)*(-110*sqrt(5) + 246)^(3/4) - 1/40*(2*sqrt(10)*(161*sqrt(5)*x + 360*x)*(-110*sqrt(5) + 246)^(3/4) + 5*(55*sqrt(5)*sqrt(2) + 123*sqrt(2))*sqrt(-110*sqrt(5) + 246))*sqrt(-55*sqrt(5) + 123)) + sqrt(10)*(55*sqrt(5)*x + 123*x)*sqrt(-55*sqrt(5) + 123)*(-110*sqrt(5) + 246)^(3/4)*arctan(1/40*sqrt(-sqrt(10)*(47*sqrt(5)*sqrt(2)*x + 105*sqrt(2)*x)*(-110*sqrt(5) + 246)^(3/4) + 40*x^2 + 20*(4*sqrt(5) + 9)*sqrt(-110*sqrt(5) + 246))*(161*sqrt(5) + 360)*sqrt(-55*sqrt(5) + 123)*(-110*sqrt(5) + 246)^(3/4) - 1/40*(2*sqrt(10)*(161*sqrt(5)*x + 360*x)*(-110*sqrt(5) + 246)^(3/4) - 5*(55*sqrt(5)*sqrt(2) + 123*sqrt(2))*sqrt(-110*sqrt(5) + 246))*sqrt(-55*sqrt(5) + 123)) - sqrt(10)*sqrt(2)*x*(110*sqrt(5) + 246)^(1/4)*log(sqrt(10)*(47*sqrt(5)*sqrt(2)*x - 105*sqrt(2)*x)*(110*sqrt(5) + 246)^(3/4) + 40*x^2 - 20*sqrt(110*sqrt(5) + 246)*(4*sqrt(5) - 9)) + sqrt(10)*sqrt(2)*x*(110*sqrt(5) + 246)^(1/4)*log(-sqrt(10)*(47*sqrt(5)*sqrt(2)*x - 105*sqrt(2)*x)*(110*sqrt(5) + 246)^(3/4) + 40*x^2 - 20*sqrt(110*sqrt(5) + 246)*(4*sqrt(5) - 9)) + sqrt(10)*sqrt(2)*x*(-110*sqrt(5) + 246)^(1/4)*log(sqrt(10)*(47*sqrt(5)*sqrt(2)*x + 105*sqrt(2)*x)*(-110*sqrt(5) + 246)^(3/4) + 40*x^2 + 20*(4*sqrt(5) + 9)*sqrt(-110*sqrt(5) + 246)) - sqrt(10)*sqrt(2)*x*(-110*sqrt(5) + 246)^(1/4)*log(-sqrt(10)*(47*sqrt(5)*sqrt(2)*x + 105*sqrt(2)*x)*(-110*sqrt(5) + 246)^(3/4) + 40*x^2 + 20*(4*sqrt(5) + 9)*sqrt(-110*sqrt(5) + 246)) + 80)/x","B",0
384,1,1057,0,1.794560," ","integrate(1/x^4/(x^8+3*x^4+1),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{10} \sqrt{2} x^{3} {\left(754 \, \sqrt{5} + 1686\right)}^{\frac{1}{4}} \log\left(20 \, x^{2} + \sqrt{10} {\left(7 \, \sqrt{5} \sqrt{2} x - 15 \, \sqrt{2} x\right)} {\left(754 \, \sqrt{5} + 1686\right)}^{\frac{1}{4}} - 5 \, \sqrt{754 \, \sqrt{5} + 1686} {\left(21 \, \sqrt{5} - 47\right)}\right) - 3 \, \sqrt{10} \sqrt{2} x^{3} {\left(754 \, \sqrt{5} + 1686\right)}^{\frac{1}{4}} \log\left(20 \, x^{2} - \sqrt{10} {\left(7 \, \sqrt{5} \sqrt{2} x - 15 \, \sqrt{2} x\right)} {\left(754 \, \sqrt{5} + 1686\right)}^{\frac{1}{4}} - 5 \, \sqrt{754 \, \sqrt{5} + 1686} {\left(21 \, \sqrt{5} - 47\right)}\right) - 3 \, \sqrt{10} \sqrt{2} x^{3} {\left(-754 \, \sqrt{5} + 1686\right)}^{\frac{1}{4}} \log\left(20 \, x^{2} + \sqrt{10} {\left(7 \, \sqrt{5} \sqrt{2} x + 15 \, \sqrt{2} x\right)} {\left(-754 \, \sqrt{5} + 1686\right)}^{\frac{1}{4}} + 5 \, {\left(21 \, \sqrt{5} + 47\right)} \sqrt{-754 \, \sqrt{5} + 1686}\right) + 3 \, \sqrt{10} \sqrt{2} x^{3} {\left(-754 \, \sqrt{5} + 1686\right)}^{\frac{1}{4}} \log\left(20 \, x^{2} - \sqrt{10} {\left(7 \, \sqrt{5} \sqrt{2} x + 15 \, \sqrt{2} x\right)} {\left(-754 \, \sqrt{5} + 1686\right)}^{\frac{1}{4}} + 5 \, {\left(21 \, \sqrt{5} + 47\right)} \sqrt{-754 \, \sqrt{5} + 1686}\right) - 3 \, \sqrt{10} {\left(377 \, \sqrt{5} x^{3} - 843 \, x^{3}\right)} {\left(754 \, \sqrt{5} + 1686\right)}^{\frac{3}{4}} \sqrt{377 \, \sqrt{5} + 843} \arctan\left(\frac{1}{80} \, \sqrt{10} \sqrt{20 \, x^{2} + \sqrt{10} {\left(7 \, \sqrt{5} \sqrt{2} x - 15 \, \sqrt{2} x\right)} {\left(754 \, \sqrt{5} + 1686\right)}^{\frac{1}{4}} - 5 \, \sqrt{754 \, \sqrt{5} + 1686} {\left(21 \, \sqrt{5} - 47\right)}} {\left(23184 \, \sqrt{5} - 51841\right)} {\left(754 \, \sqrt{5} + 1686\right)}^{\frac{5}{4}} \sqrt{377 \, \sqrt{5} + 843} + \frac{1}{40} \, \sqrt{10} {\left(51841 \, \sqrt{5} x - 115920 \, x\right)} {\left(754 \, \sqrt{5} + 1686\right)}^{\frac{5}{4}} \sqrt{377 \, \sqrt{5} + 843} - \frac{1}{8} \, {\left(377 \, \sqrt{5} \sqrt{2} - 843 \, \sqrt{2}\right)} \sqrt{754 \, \sqrt{5} + 1686} \sqrt{377 \, \sqrt{5} + 843}\right) - 3 \, \sqrt{10} {\left(377 \, \sqrt{5} x^{3} - 843 \, x^{3}\right)} {\left(754 \, \sqrt{5} + 1686\right)}^{\frac{3}{4}} \sqrt{377 \, \sqrt{5} + 843} \arctan\left(\frac{1}{80} \, \sqrt{10} \sqrt{20 \, x^{2} - \sqrt{10} {\left(7 \, \sqrt{5} \sqrt{2} x - 15 \, \sqrt{2} x\right)} {\left(754 \, \sqrt{5} + 1686\right)}^{\frac{1}{4}} - 5 \, \sqrt{754 \, \sqrt{5} + 1686} {\left(21 \, \sqrt{5} - 47\right)}} {\left(23184 \, \sqrt{5} - 51841\right)} {\left(754 \, \sqrt{5} + 1686\right)}^{\frac{5}{4}} \sqrt{377 \, \sqrt{5} + 843} + \frac{1}{40} \, \sqrt{10} {\left(51841 \, \sqrt{5} x - 115920 \, x\right)} {\left(754 \, \sqrt{5} + 1686\right)}^{\frac{5}{4}} \sqrt{377 \, \sqrt{5} + 843} + \frac{1}{8} \, {\left(377 \, \sqrt{5} \sqrt{2} - 843 \, \sqrt{2}\right)} \sqrt{754 \, \sqrt{5} + 1686} \sqrt{377 \, \sqrt{5} + 843}\right) + 3 \, \sqrt{10} {\left(377 \, \sqrt{5} x^{3} + 843 \, x^{3}\right)} \sqrt{-377 \, \sqrt{5} + 843} {\left(-754 \, \sqrt{5} + 1686\right)}^{\frac{3}{4}} \arctan\left(\frac{1}{80} \, \sqrt{10} \sqrt{20 \, x^{2} + \sqrt{10} {\left(7 \, \sqrt{5} \sqrt{2} x + 15 \, \sqrt{2} x\right)} {\left(-754 \, \sqrt{5} + 1686\right)}^{\frac{1}{4}} + 5 \, {\left(21 \, \sqrt{5} + 47\right)} \sqrt{-754 \, \sqrt{5} + 1686}} {\left(23184 \, \sqrt{5} + 51841\right)} \sqrt{-377 \, \sqrt{5} + 843} {\left(-754 \, \sqrt{5} + 1686\right)}^{\frac{5}{4}} - \frac{1}{40} \, {\left(\sqrt{10} {\left(51841 \, \sqrt{5} x + 115920 \, x\right)} {\left(-754 \, \sqrt{5} + 1686\right)}^{\frac{5}{4}} + 5 \, {\left(377 \, \sqrt{5} \sqrt{2} + 843 \, \sqrt{2}\right)} \sqrt{-754 \, \sqrt{5} + 1686}\right)} \sqrt{-377 \, \sqrt{5} + 843}\right) + 3 \, \sqrt{10} {\left(377 \, \sqrt{5} x^{3} + 843 \, x^{3}\right)} \sqrt{-377 \, \sqrt{5} + 843} {\left(-754 \, \sqrt{5} + 1686\right)}^{\frac{3}{4}} \arctan\left(\frac{1}{80} \, \sqrt{10} \sqrt{20 \, x^{2} - \sqrt{10} {\left(7 \, \sqrt{5} \sqrt{2} x + 15 \, \sqrt{2} x\right)} {\left(-754 \, \sqrt{5} + 1686\right)}^{\frac{1}{4}} + 5 \, {\left(21 \, \sqrt{5} + 47\right)} \sqrt{-754 \, \sqrt{5} + 1686}} {\left(23184 \, \sqrt{5} + 51841\right)} \sqrt{-377 \, \sqrt{5} + 843} {\left(-754 \, \sqrt{5} + 1686\right)}^{\frac{5}{4}} - \frac{1}{40} \, {\left(\sqrt{10} {\left(51841 \, \sqrt{5} x + 115920 \, x\right)} {\left(-754 \, \sqrt{5} + 1686\right)}^{\frac{5}{4}} - 5 \, {\left(377 \, \sqrt{5} \sqrt{2} + 843 \, \sqrt{2}\right)} \sqrt{-754 \, \sqrt{5} + 1686}\right)} \sqrt{-377 \, \sqrt{5} + 843}\right) + 80}{240 \, x^{3}}"," ",0,"-1/240*(3*sqrt(10)*sqrt(2)*x^3*(754*sqrt(5) + 1686)^(1/4)*log(20*x^2 + sqrt(10)*(7*sqrt(5)*sqrt(2)*x - 15*sqrt(2)*x)*(754*sqrt(5) + 1686)^(1/4) - 5*sqrt(754*sqrt(5) + 1686)*(21*sqrt(5) - 47)) - 3*sqrt(10)*sqrt(2)*x^3*(754*sqrt(5) + 1686)^(1/4)*log(20*x^2 - sqrt(10)*(7*sqrt(5)*sqrt(2)*x - 15*sqrt(2)*x)*(754*sqrt(5) + 1686)^(1/4) - 5*sqrt(754*sqrt(5) + 1686)*(21*sqrt(5) - 47)) - 3*sqrt(10)*sqrt(2)*x^3*(-754*sqrt(5) + 1686)^(1/4)*log(20*x^2 + sqrt(10)*(7*sqrt(5)*sqrt(2)*x + 15*sqrt(2)*x)*(-754*sqrt(5) + 1686)^(1/4) + 5*(21*sqrt(5) + 47)*sqrt(-754*sqrt(5) + 1686)) + 3*sqrt(10)*sqrt(2)*x^3*(-754*sqrt(5) + 1686)^(1/4)*log(20*x^2 - sqrt(10)*(7*sqrt(5)*sqrt(2)*x + 15*sqrt(2)*x)*(-754*sqrt(5) + 1686)^(1/4) + 5*(21*sqrt(5) + 47)*sqrt(-754*sqrt(5) + 1686)) - 3*sqrt(10)*(377*sqrt(5)*x^3 - 843*x^3)*(754*sqrt(5) + 1686)^(3/4)*sqrt(377*sqrt(5) + 843)*arctan(1/80*sqrt(10)*sqrt(20*x^2 + sqrt(10)*(7*sqrt(5)*sqrt(2)*x - 15*sqrt(2)*x)*(754*sqrt(5) + 1686)^(1/4) - 5*sqrt(754*sqrt(5) + 1686)*(21*sqrt(5) - 47))*(23184*sqrt(5) - 51841)*(754*sqrt(5) + 1686)^(5/4)*sqrt(377*sqrt(5) + 843) + 1/40*sqrt(10)*(51841*sqrt(5)*x - 115920*x)*(754*sqrt(5) + 1686)^(5/4)*sqrt(377*sqrt(5) + 843) - 1/8*(377*sqrt(5)*sqrt(2) - 843*sqrt(2))*sqrt(754*sqrt(5) + 1686)*sqrt(377*sqrt(5) + 843)) - 3*sqrt(10)*(377*sqrt(5)*x^3 - 843*x^3)*(754*sqrt(5) + 1686)^(3/4)*sqrt(377*sqrt(5) + 843)*arctan(1/80*sqrt(10)*sqrt(20*x^2 - sqrt(10)*(7*sqrt(5)*sqrt(2)*x - 15*sqrt(2)*x)*(754*sqrt(5) + 1686)^(1/4) - 5*sqrt(754*sqrt(5) + 1686)*(21*sqrt(5) - 47))*(23184*sqrt(5) - 51841)*(754*sqrt(5) + 1686)^(5/4)*sqrt(377*sqrt(5) + 843) + 1/40*sqrt(10)*(51841*sqrt(5)*x - 115920*x)*(754*sqrt(5) + 1686)^(5/4)*sqrt(377*sqrt(5) + 843) + 1/8*(377*sqrt(5)*sqrt(2) - 843*sqrt(2))*sqrt(754*sqrt(5) + 1686)*sqrt(377*sqrt(5) + 843)) + 3*sqrt(10)*(377*sqrt(5)*x^3 + 843*x^3)*sqrt(-377*sqrt(5) + 843)*(-754*sqrt(5) + 1686)^(3/4)*arctan(1/80*sqrt(10)*sqrt(20*x^2 + sqrt(10)*(7*sqrt(5)*sqrt(2)*x + 15*sqrt(2)*x)*(-754*sqrt(5) + 1686)^(1/4) + 5*(21*sqrt(5) + 47)*sqrt(-754*sqrt(5) + 1686))*(23184*sqrt(5) + 51841)*sqrt(-377*sqrt(5) + 843)*(-754*sqrt(5) + 1686)^(5/4) - 1/40*(sqrt(10)*(51841*sqrt(5)*x + 115920*x)*(-754*sqrt(5) + 1686)^(5/4) + 5*(377*sqrt(5)*sqrt(2) + 843*sqrt(2))*sqrt(-754*sqrt(5) + 1686))*sqrt(-377*sqrt(5) + 843)) + 3*sqrt(10)*(377*sqrt(5)*x^3 + 843*x^3)*sqrt(-377*sqrt(5) + 843)*(-754*sqrt(5) + 1686)^(3/4)*arctan(1/80*sqrt(10)*sqrt(20*x^2 - sqrt(10)*(7*sqrt(5)*sqrt(2)*x + 15*sqrt(2)*x)*(-754*sqrt(5) + 1686)^(1/4) + 5*(21*sqrt(5) + 47)*sqrt(-754*sqrt(5) + 1686))*(23184*sqrt(5) + 51841)*sqrt(-377*sqrt(5) + 843)*(-754*sqrt(5) + 1686)^(5/4) - 1/40*(sqrt(10)*(51841*sqrt(5)*x + 115920*x)*(-754*sqrt(5) + 1686)^(5/4) - 5*(377*sqrt(5)*sqrt(2) + 843*sqrt(2))*sqrt(-754*sqrt(5) + 1686))*sqrt(-377*sqrt(5) + 843)) + 80)/x^3","B",0
385,0,0,0,1.371826," ","integrate(x^m/(x^8-3*x^4+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{x^{8} - 3 \, x^{4} + 1}, x\right)"," ",0,"integral(x^m/(x^8 - 3*x^4 + 1), x)","F",0
386,1,62,0,0.681358," ","integrate(x^11/(x^8-3*x^4+1),x, algorithm=""fricas"")","\frac{1}{4} \, x^{4} + \frac{7}{40} \, \sqrt{5} \log\left(\frac{2 \, x^{8} - 6 \, x^{4} - \sqrt{5} {\left(2 \, x^{4} - 3\right)} + 7}{x^{8} - 3 \, x^{4} + 1}\right) + \frac{3}{8} \, \log\left(x^{8} - 3 \, x^{4} + 1\right)"," ",0,"1/4*x^4 + 7/40*sqrt(5)*log((2*x^8 - 6*x^4 - sqrt(5)*(2*x^4 - 3) + 7)/(x^8 - 3*x^4 + 1)) + 3/8*log(x^8 - 3*x^4 + 1)","A",0
387,1,114,0,1.162191," ","integrate(x^9/(x^8-3*x^4+1),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} + \frac{1}{10} \, \sqrt{5} \log\left(\frac{2 \, x^{4} + 2 \, x^{2} - \sqrt{5} {\left(2 \, x^{2} + 1\right)} + 3}{x^{4} + x^{2} - 1}\right) + \frac{1}{10} \, \sqrt{5} \log\left(\frac{2 \, x^{4} - 2 \, x^{2} - \sqrt{5} {\left(2 \, x^{2} - 1\right)} + 3}{x^{4} - x^{2} - 1}\right) - \frac{1}{4} \, \log\left(x^{4} + x^{2} - 1\right) + \frac{1}{4} \, \log\left(x^{4} - x^{2} - 1\right)"," ",0,"1/2*x^2 + 1/10*sqrt(5)*log((2*x^4 + 2*x^2 - sqrt(5)*(2*x^2 + 1) + 3)/(x^4 + x^2 - 1)) + 1/10*sqrt(5)*log((2*x^4 - 2*x^2 - sqrt(5)*(2*x^2 - 1) + 3)/(x^4 - x^2 - 1)) - 1/4*log(x^4 + x^2 - 1) + 1/4*log(x^4 - x^2 - 1)","B",0
388,1,57,0,1.039711," ","integrate(x^7/(x^8-3*x^4+1),x, algorithm=""fricas"")","\frac{3}{40} \, \sqrt{5} \log\left(\frac{2 \, x^{8} - 6 \, x^{4} - \sqrt{5} {\left(2 \, x^{4} - 3\right)} + 7}{x^{8} - 3 \, x^{4} + 1}\right) + \frac{1}{8} \, \log\left(x^{8} - 3 \, x^{4} + 1\right)"," ",0,"3/40*sqrt(5)*log((2*x^8 - 6*x^4 - sqrt(5)*(2*x^4 - 3) + 7)/(x^8 - 3*x^4 + 1)) + 1/8*log(x^8 - 3*x^4 + 1)","A",0
389,1,109,0,1.167524," ","integrate(x^5/(x^8-3*x^4+1),x, algorithm=""fricas"")","\frac{1}{40} \, \sqrt{5} \log\left(\frac{2 \, x^{4} + 2 \, x^{2} - \sqrt{5} {\left(2 \, x^{2} + 1\right)} + 3}{x^{4} + x^{2} - 1}\right) + \frac{1}{40} \, \sqrt{5} \log\left(\frac{2 \, x^{4} - 2 \, x^{2} - \sqrt{5} {\left(2 \, x^{2} - 1\right)} + 3}{x^{4} - x^{2} - 1}\right) - \frac{1}{8} \, \log\left(x^{4} + x^{2} - 1\right) + \frac{1}{8} \, \log\left(x^{4} - x^{2} - 1\right)"," ",0,"1/40*sqrt(5)*log((2*x^4 + 2*x^2 - sqrt(5)*(2*x^2 + 1) + 3)/(x^4 + x^2 - 1)) + 1/40*sqrt(5)*log((2*x^4 - 2*x^2 - sqrt(5)*(2*x^2 - 1) + 3)/(x^4 - x^2 - 1)) - 1/8*log(x^4 + x^2 - 1) + 1/8*log(x^4 - x^2 - 1)","B",0
390,1,43,0,1.276610," ","integrate(x^3/(x^8-3*x^4+1),x, algorithm=""fricas"")","\frac{1}{20} \, \sqrt{5} \log\left(\frac{2 \, x^{8} - 6 \, x^{4} - \sqrt{5} {\left(2 \, x^{4} - 3\right)} + 7}{x^{8} - 3 \, x^{4} + 1}\right)"," ",0,"1/20*sqrt(5)*log((2*x^8 - 6*x^4 - sqrt(5)*(2*x^4 - 3) + 7)/(x^8 - 3*x^4 + 1))","B",0
391,1,107,0,1.227705," ","integrate(x/(x^8-3*x^4+1),x, algorithm=""fricas"")","\frac{1}{40} \, \sqrt{5} \log\left(\frac{2 \, x^{4} + 2 \, x^{2} + \sqrt{5} {\left(2 \, x^{2} + 1\right)} + 3}{x^{4} + x^{2} - 1}\right) + \frac{1}{40} \, \sqrt{5} \log\left(\frac{2 \, x^{4} - 2 \, x^{2} + \sqrt{5} {\left(2 \, x^{2} - 1\right)} + 3}{x^{4} - x^{2} - 1}\right) - \frac{1}{8} \, \log\left(x^{4} + x^{2} - 1\right) + \frac{1}{8} \, \log\left(x^{4} - x^{2} - 1\right)"," ",0,"1/40*sqrt(5)*log((2*x^4 + 2*x^2 + sqrt(5)*(2*x^2 + 1) + 3)/(x^4 + x^2 - 1)) + 1/40*sqrt(5)*log((2*x^4 - 2*x^2 + sqrt(5)*(2*x^2 - 1) + 3)/(x^4 - x^2 - 1)) - 1/8*log(x^4 + x^2 - 1) + 1/8*log(x^4 - x^2 - 1)","B",0
392,1,59,0,1.278249," ","integrate(1/x/(x^8-3*x^4+1),x, algorithm=""fricas"")","\frac{3}{40} \, \sqrt{5} \log\left(\frac{2 \, x^{8} - 6 \, x^{4} - \sqrt{5} {\left(2 \, x^{4} - 3\right)} + 7}{x^{8} - 3 \, x^{4} + 1}\right) - \frac{1}{8} \, \log\left(x^{8} - 3 \, x^{4} + 1\right) + \log\left(x\right)"," ",0,"3/40*sqrt(5)*log((2*x^8 - 6*x^4 - sqrt(5)*(2*x^4 - 3) + 7)/(x^8 - 3*x^4 + 1)) - 1/8*log(x^8 - 3*x^4 + 1) + log(x)","A",0
393,1,125,0,1.109289," ","integrate(1/x^3/(x^8-3*x^4+1),x, algorithm=""fricas"")","\frac{2 \, \sqrt{5} x^{2} \log\left(\frac{2 \, x^{4} + 2 \, x^{2} + \sqrt{5} {\left(2 \, x^{2} + 1\right)} + 3}{x^{4} + x^{2} - 1}\right) + 2 \, \sqrt{5} x^{2} \log\left(\frac{2 \, x^{4} - 2 \, x^{2} + \sqrt{5} {\left(2 \, x^{2} - 1\right)} + 3}{x^{4} - x^{2} - 1}\right) - 5 \, x^{2} \log\left(x^{4} + x^{2} - 1\right) + 5 \, x^{2} \log\left(x^{4} - x^{2} - 1\right) - 10}{20 \, x^{2}}"," ",0,"1/20*(2*sqrt(5)*x^2*log((2*x^4 + 2*x^2 + sqrt(5)*(2*x^2 + 1) + 3)/(x^4 + x^2 - 1)) + 2*sqrt(5)*x^2*log((2*x^4 - 2*x^2 + sqrt(5)*(2*x^2 - 1) + 3)/(x^4 - x^2 - 1)) - 5*x^2*log(x^4 + x^2 - 1) + 5*x^2*log(x^4 - x^2 - 1) - 10)/x^2","B",0
394,1,76,0,1.279047," ","integrate(1/x^5/(x^8-3*x^4+1),x, algorithm=""fricas"")","\frac{7 \, \sqrt{5} x^{4} \log\left(\frac{2 \, x^{8} - 6 \, x^{4} - \sqrt{5} {\left(2 \, x^{4} - 3\right)} + 7}{x^{8} - 3 \, x^{4} + 1}\right) - 15 \, x^{4} \log\left(x^{8} - 3 \, x^{4} + 1\right) + 120 \, x^{4} \log\left(x\right) - 10}{40 \, x^{4}}"," ",0,"1/40*(7*sqrt(5)*x^4*log((2*x^8 - 6*x^4 - sqrt(5)*(2*x^4 - 3) + 7)/(x^8 - 3*x^4 + 1)) - 15*x^4*log(x^8 - 3*x^4 + 1) + 120*x^4*log(x) - 10)/x^4","A",0
395,1,130,0,1.199833," ","integrate(1/x^7/(x^8-3*x^4+1),x, algorithm=""fricas"")","\frac{33 \, \sqrt{5} x^{6} \log\left(\frac{2 \, x^{4} + 2 \, x^{2} + \sqrt{5} {\left(2 \, x^{2} + 1\right)} + 3}{x^{4} + x^{2} - 1}\right) + 33 \, \sqrt{5} x^{6} \log\left(\frac{2 \, x^{4} - 2 \, x^{2} + \sqrt{5} {\left(2 \, x^{2} - 1\right)} + 3}{x^{4} - x^{2} - 1}\right) - 75 \, x^{6} \log\left(x^{4} + x^{2} - 1\right) + 75 \, x^{6} \log\left(x^{4} - x^{2} - 1\right) - 180 \, x^{4} - 20}{120 \, x^{6}}"," ",0,"1/120*(33*sqrt(5)*x^6*log((2*x^4 + 2*x^2 + sqrt(5)*(2*x^2 + 1) + 3)/(x^4 + x^2 - 1)) + 33*sqrt(5)*x^6*log((2*x^4 - 2*x^2 + sqrt(5)*(2*x^2 - 1) + 3)/(x^4 - x^2 - 1)) - 75*x^6*log(x^4 + x^2 - 1) + 75*x^6*log(x^4 - x^2 - 1) - 180*x^4 - 20)/x^6","B",0
396,1,304,0,1.311665," ","integrate(x^8/(x^8-3*x^4+1),x, algorithm=""fricas"")","-\frac{1}{10} \, \sqrt{10} \sqrt{5 \, \sqrt{5} + 11} \arctan\left(\frac{1}{20} \, {\left(\sqrt{10} \sqrt{2 \, x^{2} + \sqrt{5} + 1} {\left(2 \, \sqrt{5} \sqrt{2} - 5 \, \sqrt{2}\right)} - 2 \, \sqrt{10} {\left(2 \, \sqrt{5} x - 5 \, x\right)}\right)} \sqrt{5 \, \sqrt{5} + 11}\right) - \frac{1}{10} \, \sqrt{10} \sqrt{5 \, \sqrt{5} - 11} \arctan\left(\frac{1}{20} \, {\left(\sqrt{10} \sqrt{2 \, x^{2} + \sqrt{5} - 1} {\left(2 \, \sqrt{5} \sqrt{2} + 5 \, \sqrt{2}\right)} - 2 \, \sqrt{10} {\left(2 \, \sqrt{5} x + 5 \, x\right)}\right)} \sqrt{5 \, \sqrt{5} - 11}\right) + \frac{1}{40} \, \sqrt{10} \sqrt{5 \, \sqrt{5} - 11} \log\left(\sqrt{10} \sqrt{5 \, \sqrt{5} - 11} {\left(3 \, \sqrt{5} + 5\right)} + 20 \, x\right) - \frac{1}{40} \, \sqrt{10} \sqrt{5 \, \sqrt{5} - 11} \log\left(-\sqrt{10} \sqrt{5 \, \sqrt{5} - 11} {\left(3 \, \sqrt{5} + 5\right)} + 20 \, x\right) - \frac{1}{40} \, \sqrt{10} \sqrt{5 \, \sqrt{5} + 11} \log\left(\sqrt{10} \sqrt{5 \, \sqrt{5} + 11} {\left(3 \, \sqrt{5} - 5\right)} + 20 \, x\right) + \frac{1}{40} \, \sqrt{10} \sqrt{5 \, \sqrt{5} + 11} \log\left(-\sqrt{10} \sqrt{5 \, \sqrt{5} + 11} {\left(3 \, \sqrt{5} - 5\right)} + 20 \, x\right) + x"," ",0,"-1/10*sqrt(10)*sqrt(5*sqrt(5) + 11)*arctan(1/20*(sqrt(10)*sqrt(2*x^2 + sqrt(5) + 1)*(2*sqrt(5)*sqrt(2) - 5*sqrt(2)) - 2*sqrt(10)*(2*sqrt(5)*x - 5*x))*sqrt(5*sqrt(5) + 11)) - 1/10*sqrt(10)*sqrt(5*sqrt(5) - 11)*arctan(1/20*(sqrt(10)*sqrt(2*x^2 + sqrt(5) - 1)*(2*sqrt(5)*sqrt(2) + 5*sqrt(2)) - 2*sqrt(10)*(2*sqrt(5)*x + 5*x))*sqrt(5*sqrt(5) - 11)) + 1/40*sqrt(10)*sqrt(5*sqrt(5) - 11)*log(sqrt(10)*sqrt(5*sqrt(5) - 11)*(3*sqrt(5) + 5) + 20*x) - 1/40*sqrt(10)*sqrt(5*sqrt(5) - 11)*log(-sqrt(10)*sqrt(5*sqrt(5) - 11)*(3*sqrt(5) + 5) + 20*x) - 1/40*sqrt(10)*sqrt(5*sqrt(5) + 11)*log(sqrt(10)*sqrt(5*sqrt(5) + 11)*(3*sqrt(5) - 5) + 20*x) + 1/40*sqrt(10)*sqrt(5*sqrt(5) + 11)*log(-sqrt(10)*sqrt(5*sqrt(5) + 11)*(3*sqrt(5) - 5) + 20*x) + x","B",0
397,1,255,0,1.268084," ","integrate(x^6/(x^8-3*x^4+1),x, algorithm=""fricas"")","\frac{1}{5} \, \sqrt{5} \sqrt{\sqrt{5} + 2} \arctan\left(\frac{1}{4} \, \sqrt{2 \, x^{2} + \sqrt{5} + 1} {\left(\sqrt{5} \sqrt{2} - 3 \, \sqrt{2}\right)} \sqrt{\sqrt{5} + 2} - \frac{1}{2} \, {\left(\sqrt{5} x - 3 \, x\right)} \sqrt{\sqrt{5} + 2}\right) + \frac{1}{5} \, \sqrt{5} \sqrt{\sqrt{5} - 2} \arctan\left(\frac{1}{4} \, \sqrt{2 \, x^{2} + \sqrt{5} - 1} {\left(\sqrt{5} \sqrt{2} + 3 \, \sqrt{2}\right)} \sqrt{\sqrt{5} - 2} - \frac{1}{2} \, {\left(\sqrt{5} x + 3 \, x\right)} \sqrt{\sqrt{5} - 2}\right) - \frac{1}{20} \, \sqrt{5} \sqrt{\sqrt{5} + 2} \log\left(\sqrt{\sqrt{5} + 2} {\left(\sqrt{5} - 1\right)} + 2 \, x\right) + \frac{1}{20} \, \sqrt{5} \sqrt{\sqrt{5} + 2} \log\left(-\sqrt{\sqrt{5} + 2} {\left(\sqrt{5} - 1\right)} + 2 \, x\right) + \frac{1}{20} \, \sqrt{5} \sqrt{\sqrt{5} - 2} \log\left({\left(\sqrt{5} + 1\right)} \sqrt{\sqrt{5} - 2} + 2 \, x\right) - \frac{1}{20} \, \sqrt{5} \sqrt{\sqrt{5} - 2} \log\left(-{\left(\sqrt{5} + 1\right)} \sqrt{\sqrt{5} - 2} + 2 \, x\right)"," ",0,"1/5*sqrt(5)*sqrt(sqrt(5) + 2)*arctan(1/4*sqrt(2*x^2 + sqrt(5) + 1)*(sqrt(5)*sqrt(2) - 3*sqrt(2))*sqrt(sqrt(5) + 2) - 1/2*(sqrt(5)*x - 3*x)*sqrt(sqrt(5) + 2)) + 1/5*sqrt(5)*sqrt(sqrt(5) - 2)*arctan(1/4*sqrt(2*x^2 + sqrt(5) - 1)*(sqrt(5)*sqrt(2) + 3*sqrt(2))*sqrt(sqrt(5) - 2) - 1/2*(sqrt(5)*x + 3*x)*sqrt(sqrt(5) - 2)) - 1/20*sqrt(5)*sqrt(sqrt(5) + 2)*log(sqrt(sqrt(5) + 2)*(sqrt(5) - 1) + 2*x) + 1/20*sqrt(5)*sqrt(sqrt(5) + 2)*log(-sqrt(sqrt(5) + 2)*(sqrt(5) - 1) + 2*x) + 1/20*sqrt(5)*sqrt(sqrt(5) - 2)*log((sqrt(5) + 1)*sqrt(sqrt(5) - 2) + 2*x) - 1/20*sqrt(5)*sqrt(sqrt(5) - 2)*log(-(sqrt(5) + 1)*sqrt(sqrt(5) - 2) + 2*x)","B",0
398,1,271,0,1.423660," ","integrate(x^4/(x^8-3*x^4+1),x, algorithm=""fricas"")","-\frac{1}{10} \, \sqrt{10} \sqrt{\sqrt{5} + 1} \arctan\left(\frac{1}{40} \, \sqrt{10} \sqrt{2 \, x^{2} + \sqrt{5} + 1} {\left(\sqrt{5} \sqrt{2} - 5 \, \sqrt{2}\right)} \sqrt{\sqrt{5} + 1} - \frac{1}{20} \, \sqrt{10} {\left(\sqrt{5} x - 5 \, x\right)} \sqrt{\sqrt{5} + 1}\right) - \frac{1}{10} \, \sqrt{10} \sqrt{\sqrt{5} - 1} \arctan\left(\frac{1}{40} \, \sqrt{10} \sqrt{2 \, x^{2} + \sqrt{5} - 1} {\left(\sqrt{5} \sqrt{2} + 5 \, \sqrt{2}\right)} \sqrt{\sqrt{5} - 1} - \frac{1}{20} \, \sqrt{10} {\left(\sqrt{5} x + 5 \, x\right)} \sqrt{\sqrt{5} - 1}\right) - \frac{1}{40} \, \sqrt{10} \sqrt{\sqrt{5} + 1} \log\left(\sqrt{10} \sqrt{5} \sqrt{\sqrt{5} + 1} + 10 \, x\right) + \frac{1}{40} \, \sqrt{10} \sqrt{\sqrt{5} + 1} \log\left(-\sqrt{10} \sqrt{5} \sqrt{\sqrt{5} + 1} + 10 \, x\right) + \frac{1}{40} \, \sqrt{10} \sqrt{\sqrt{5} - 1} \log\left(\sqrt{10} \sqrt{5} \sqrt{\sqrt{5} - 1} + 10 \, x\right) - \frac{1}{40} \, \sqrt{10} \sqrt{\sqrt{5} - 1} \log\left(-\sqrt{10} \sqrt{5} \sqrt{\sqrt{5} - 1} + 10 \, x\right)"," ",0,"-1/10*sqrt(10)*sqrt(sqrt(5) + 1)*arctan(1/40*sqrt(10)*sqrt(2*x^2 + sqrt(5) + 1)*(sqrt(5)*sqrt(2) - 5*sqrt(2))*sqrt(sqrt(5) + 1) - 1/20*sqrt(10)*(sqrt(5)*x - 5*x)*sqrt(sqrt(5) + 1)) - 1/10*sqrt(10)*sqrt(sqrt(5) - 1)*arctan(1/40*sqrt(10)*sqrt(2*x^2 + sqrt(5) - 1)*(sqrt(5)*sqrt(2) + 5*sqrt(2))*sqrt(sqrt(5) - 1) - 1/20*sqrt(10)*(sqrt(5)*x + 5*x)*sqrt(sqrt(5) - 1)) - 1/40*sqrt(10)*sqrt(sqrt(5) + 1)*log(sqrt(10)*sqrt(5)*sqrt(sqrt(5) + 1) + 10*x) + 1/40*sqrt(10)*sqrt(sqrt(5) + 1)*log(-sqrt(10)*sqrt(5)*sqrt(sqrt(5) + 1) + 10*x) + 1/40*sqrt(10)*sqrt(sqrt(5) - 1)*log(sqrt(10)*sqrt(5)*sqrt(sqrt(5) - 1) + 10*x) - 1/40*sqrt(10)*sqrt(sqrt(5) - 1)*log(-sqrt(10)*sqrt(5)*sqrt(sqrt(5) - 1) + 10*x)","B",0
399,1,255,0,1.079974," ","integrate(x^2/(x^8-3*x^4+1),x, algorithm=""fricas"")","\frac{1}{10} \, \sqrt{10} \sqrt{\sqrt{5} + 1} \arctan\left(\frac{1}{20} \, \sqrt{10} \sqrt{5} \sqrt{2} \sqrt{2 \, x^{2} + \sqrt{5} - 1} \sqrt{\sqrt{5} + 1} - \frac{1}{10} \, \sqrt{10} \sqrt{5} x \sqrt{\sqrt{5} + 1}\right) - \frac{1}{10} \, \sqrt{10} \sqrt{\sqrt{5} - 1} \arctan\left(\frac{1}{20} \, \sqrt{10} \sqrt{5} \sqrt{2} \sqrt{2 \, x^{2} + \sqrt{5} + 1} \sqrt{\sqrt{5} - 1} - \frac{1}{10} \, \sqrt{10} \sqrt{5} x \sqrt{\sqrt{5} - 1}\right) - \frac{1}{40} \, \sqrt{10} \sqrt{\sqrt{5} - 1} \log\left(\sqrt{10} {\left(\sqrt{5} + 5\right)} \sqrt{\sqrt{5} - 1} + 20 \, x\right) + \frac{1}{40} \, \sqrt{10} \sqrt{\sqrt{5} - 1} \log\left(-\sqrt{10} {\left(\sqrt{5} + 5\right)} \sqrt{\sqrt{5} - 1} + 20 \, x\right) - \frac{1}{40} \, \sqrt{10} \sqrt{\sqrt{5} + 1} \log\left(\sqrt{10} \sqrt{\sqrt{5} + 1} {\left(\sqrt{5} - 5\right)} + 20 \, x\right) + \frac{1}{40} \, \sqrt{10} \sqrt{\sqrt{5} + 1} \log\left(-\sqrt{10} \sqrt{\sqrt{5} + 1} {\left(\sqrt{5} - 5\right)} + 20 \, x\right)"," ",0,"1/10*sqrt(10)*sqrt(sqrt(5) + 1)*arctan(1/20*sqrt(10)*sqrt(5)*sqrt(2)*sqrt(2*x^2 + sqrt(5) - 1)*sqrt(sqrt(5) + 1) - 1/10*sqrt(10)*sqrt(5)*x*sqrt(sqrt(5) + 1)) - 1/10*sqrt(10)*sqrt(sqrt(5) - 1)*arctan(1/20*sqrt(10)*sqrt(5)*sqrt(2)*sqrt(2*x^2 + sqrt(5) + 1)*sqrt(sqrt(5) - 1) - 1/10*sqrt(10)*sqrt(5)*x*sqrt(sqrt(5) - 1)) - 1/40*sqrt(10)*sqrt(sqrt(5) - 1)*log(sqrt(10)*(sqrt(5) + 5)*sqrt(sqrt(5) - 1) + 20*x) + 1/40*sqrt(10)*sqrt(sqrt(5) - 1)*log(-sqrt(10)*(sqrt(5) + 5)*sqrt(sqrt(5) - 1) + 20*x) - 1/40*sqrt(10)*sqrt(sqrt(5) + 1)*log(sqrt(10)*sqrt(sqrt(5) + 1)*(sqrt(5) - 5) + 20*x) + 1/40*sqrt(10)*sqrt(sqrt(5) + 1)*log(-sqrt(10)*sqrt(sqrt(5) + 1)*(sqrt(5) - 5) + 20*x)","B",0
400,1,251,0,1.489996," ","integrate(1/(x^8-3*x^4+1),x, algorithm=""fricas"")","-\frac{1}{5} \, \sqrt{5} \sqrt{\sqrt{5} + 2} \arctan\left(\frac{1}{4} \, \sqrt{2 \, x^{2} + \sqrt{5} - 1} {\left(\sqrt{5} \sqrt{2} - \sqrt{2}\right)} \sqrt{\sqrt{5} + 2} - \frac{1}{2} \, {\left(\sqrt{5} x - x\right)} \sqrt{\sqrt{5} + 2}\right) + \frac{1}{5} \, \sqrt{5} \sqrt{\sqrt{5} - 2} \arctan\left(\frac{1}{4} \, \sqrt{2 \, x^{2} + \sqrt{5} + 1} {\left(\sqrt{5} \sqrt{2} + \sqrt{2}\right)} \sqrt{\sqrt{5} - 2} - \frac{1}{2} \, {\left(\sqrt{5} x + x\right)} \sqrt{\sqrt{5} - 2}\right) - \frac{1}{20} \, \sqrt{5} \sqrt{\sqrt{5} - 2} \log\left({\left(\sqrt{5} + 3\right)} \sqrt{\sqrt{5} - 2} + 2 \, x\right) + \frac{1}{20} \, \sqrt{5} \sqrt{\sqrt{5} - 2} \log\left(-{\left(\sqrt{5} + 3\right)} \sqrt{\sqrt{5} - 2} + 2 \, x\right) - \frac{1}{20} \, \sqrt{5} \sqrt{\sqrt{5} + 2} \log\left(\sqrt{\sqrt{5} + 2} {\left(\sqrt{5} - 3\right)} + 2 \, x\right) + \frac{1}{20} \, \sqrt{5} \sqrt{\sqrt{5} + 2} \log\left(-\sqrt{\sqrt{5} + 2} {\left(\sqrt{5} - 3\right)} + 2 \, x\right)"," ",0,"-1/5*sqrt(5)*sqrt(sqrt(5) + 2)*arctan(1/4*sqrt(2*x^2 + sqrt(5) - 1)*(sqrt(5)*sqrt(2) - sqrt(2))*sqrt(sqrt(5) + 2) - 1/2*(sqrt(5)*x - x)*sqrt(sqrt(5) + 2)) + 1/5*sqrt(5)*sqrt(sqrt(5) - 2)*arctan(1/4*sqrt(2*x^2 + sqrt(5) + 1)*(sqrt(5)*sqrt(2) + sqrt(2))*sqrt(sqrt(5) - 2) - 1/2*(sqrt(5)*x + x)*sqrt(sqrt(5) - 2)) - 1/20*sqrt(5)*sqrt(sqrt(5) - 2)*log((sqrt(5) + 3)*sqrt(sqrt(5) - 2) + 2*x) + 1/20*sqrt(5)*sqrt(sqrt(5) - 2)*log(-(sqrt(5) + 3)*sqrt(sqrt(5) - 2) + 2*x) - 1/20*sqrt(5)*sqrt(sqrt(5) + 2)*log(sqrt(sqrt(5) + 2)*(sqrt(5) - 3) + 2*x) + 1/20*sqrt(5)*sqrt(sqrt(5) + 2)*log(-sqrt(sqrt(5) + 2)*(sqrt(5) - 3) + 2*x)","B",0
401,1,313,0,1.312455," ","integrate(1/x^2/(x^8-3*x^4+1),x, algorithm=""fricas"")","\frac{4 \, \sqrt{10} x \sqrt{5 \, \sqrt{5} + 11} \arctan\left(\frac{1}{40} \, {\left(\sqrt{10} \sqrt{2 \, x^{2} + \sqrt{5} - 1} {\left(3 \, \sqrt{5} \sqrt{2} - 5 \, \sqrt{2}\right)} - 2 \, \sqrt{10} {\left(3 \, \sqrt{5} x - 5 \, x\right)}\right)} \sqrt{5 \, \sqrt{5} + 11}\right) - 4 \, \sqrt{10} x \sqrt{5 \, \sqrt{5} - 11} \arctan\left(\frac{1}{40} \, {\left(\sqrt{10} \sqrt{2 \, x^{2} + \sqrt{5} + 1} {\left(3 \, \sqrt{5} \sqrt{2} + 5 \, \sqrt{2}\right)} - 2 \, \sqrt{10} {\left(3 \, \sqrt{5} x + 5 \, x\right)}\right)} \sqrt{5 \, \sqrt{5} - 11}\right) - \sqrt{10} x \sqrt{5 \, \sqrt{5} - 11} \log\left(\sqrt{10} \sqrt{5 \, \sqrt{5} - 11} {\left(2 \, \sqrt{5} + 5\right)} + 10 \, x\right) + \sqrt{10} x \sqrt{5 \, \sqrt{5} - 11} \log\left(-\sqrt{10} \sqrt{5 \, \sqrt{5} - 11} {\left(2 \, \sqrt{5} + 5\right)} + 10 \, x\right) - \sqrt{10} x \sqrt{5 \, \sqrt{5} + 11} \log\left(\sqrt{10} \sqrt{5 \, \sqrt{5} + 11} {\left(2 \, \sqrt{5} - 5\right)} + 10 \, x\right) + \sqrt{10} x \sqrt{5 \, \sqrt{5} + 11} \log\left(-\sqrt{10} \sqrt{5 \, \sqrt{5} + 11} {\left(2 \, \sqrt{5} - 5\right)} + 10 \, x\right) - 40}{40 \, x}"," ",0,"1/40*(4*sqrt(10)*x*sqrt(5*sqrt(5) + 11)*arctan(1/40*(sqrt(10)*sqrt(2*x^2 + sqrt(5) - 1)*(3*sqrt(5)*sqrt(2) - 5*sqrt(2)) - 2*sqrt(10)*(3*sqrt(5)*x - 5*x))*sqrt(5*sqrt(5) + 11)) - 4*sqrt(10)*x*sqrt(5*sqrt(5) - 11)*arctan(1/40*(sqrt(10)*sqrt(2*x^2 + sqrt(5) + 1)*(3*sqrt(5)*sqrt(2) + 5*sqrt(2)) - 2*sqrt(10)*(3*sqrt(5)*x + 5*x))*sqrt(5*sqrt(5) - 11)) - sqrt(10)*x*sqrt(5*sqrt(5) - 11)*log(sqrt(10)*sqrt(5*sqrt(5) - 11)*(2*sqrt(5) + 5) + 10*x) + sqrt(10)*x*sqrt(5*sqrt(5) - 11)*log(-sqrt(10)*sqrt(5*sqrt(5) - 11)*(2*sqrt(5) + 5) + 10*x) - sqrt(10)*x*sqrt(5*sqrt(5) + 11)*log(sqrt(10)*sqrt(5*sqrt(5) + 11)*(2*sqrt(5) - 5) + 10*x) + sqrt(10)*x*sqrt(5*sqrt(5) + 11)*log(-sqrt(10)*sqrt(5*sqrt(5) + 11)*(2*sqrt(5) - 5) + 10*x) - 40)/x","B",0
402,1,327,0,1.400761," ","integrate(1/x^4/(x^8-3*x^4+1),x, algorithm=""fricas"")","\frac{12 \, \sqrt{10} x^{3} \sqrt{13 \, \sqrt{5} + 29} \arctan\left(\frac{1}{20} \, {\left(\sqrt{10} \sqrt{2 \, x^{2} + \sqrt{5} - 1} {\left(2 \, \sqrt{5} \sqrt{2} - 5 \, \sqrt{2}\right)} - 2 \, \sqrt{10} {\left(2 \, \sqrt{5} x - 5 \, x\right)}\right)} \sqrt{13 \, \sqrt{5} + 29}\right) + 12 \, \sqrt{10} x^{3} \sqrt{13 \, \sqrt{5} - 29} \arctan\left(\frac{1}{20} \, {\left(\sqrt{10} \sqrt{2 \, x^{2} + \sqrt{5} + 1} {\left(2 \, \sqrt{5} \sqrt{2} + 5 \, \sqrt{2}\right)} - 2 \, \sqrt{10} {\left(2 \, \sqrt{5} x + 5 \, x\right)}\right)} \sqrt{13 \, \sqrt{5} - 29}\right) - 3 \, \sqrt{10} x^{3} \sqrt{13 \, \sqrt{5} - 29} \log\left(\sqrt{10} \sqrt{13 \, \sqrt{5} - 29} {\left(7 \, \sqrt{5} + 15\right)} + 20 \, x\right) + 3 \, \sqrt{10} x^{3} \sqrt{13 \, \sqrt{5} - 29} \log\left(-\sqrt{10} \sqrt{13 \, \sqrt{5} - 29} {\left(7 \, \sqrt{5} + 15\right)} + 20 \, x\right) + 3 \, \sqrt{10} x^{3} \sqrt{13 \, \sqrt{5} + 29} \log\left(\sqrt{10} \sqrt{13 \, \sqrt{5} + 29} {\left(7 \, \sqrt{5} - 15\right)} + 20 \, x\right) - 3 \, \sqrt{10} x^{3} \sqrt{13 \, \sqrt{5} + 29} \log\left(-\sqrt{10} \sqrt{13 \, \sqrt{5} + 29} {\left(7 \, \sqrt{5} - 15\right)} + 20 \, x\right) - 40}{120 \, x^{3}}"," ",0,"1/120*(12*sqrt(10)*x^3*sqrt(13*sqrt(5) + 29)*arctan(1/20*(sqrt(10)*sqrt(2*x^2 + sqrt(5) - 1)*(2*sqrt(5)*sqrt(2) - 5*sqrt(2)) - 2*sqrt(10)*(2*sqrt(5)*x - 5*x))*sqrt(13*sqrt(5) + 29)) + 12*sqrt(10)*x^3*sqrt(13*sqrt(5) - 29)*arctan(1/20*(sqrt(10)*sqrt(2*x^2 + sqrt(5) + 1)*(2*sqrt(5)*sqrt(2) + 5*sqrt(2)) - 2*sqrt(10)*(2*sqrt(5)*x + 5*x))*sqrt(13*sqrt(5) - 29)) - 3*sqrt(10)*x^3*sqrt(13*sqrt(5) - 29)*log(sqrt(10)*sqrt(13*sqrt(5) - 29)*(7*sqrt(5) + 15) + 20*x) + 3*sqrt(10)*x^3*sqrt(13*sqrt(5) - 29)*log(-sqrt(10)*sqrt(13*sqrt(5) - 29)*(7*sqrt(5) + 15) + 20*x) + 3*sqrt(10)*x^3*sqrt(13*sqrt(5) + 29)*log(sqrt(10)*sqrt(13*sqrt(5) + 29)*(7*sqrt(5) - 15) + 20*x) - 3*sqrt(10)*x^3*sqrt(13*sqrt(5) + 29)*log(-sqrt(10)*sqrt(13*sqrt(5) + 29)*(7*sqrt(5) - 15) + 20*x) - 40)/x^3","B",0
403,1,300,0,1.193071," ","integrate(1/x^6/(x^8-3*x^4+1),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{5} x^{5} \sqrt{17 \, \sqrt{5} + 38} \arctan\left(\frac{1}{4} \, {\left(\sqrt{2 \, x^{2} + \sqrt{5} - 1} {\left(3 \, \sqrt{5} \sqrt{2} - 7 \, \sqrt{2}\right)} - 6 \, \sqrt{5} x + 14 \, x\right)} \sqrt{17 \, \sqrt{5} + 38}\right) + 4 \, \sqrt{5} x^{5} \sqrt{17 \, \sqrt{5} - 38} \arctan\left(\frac{1}{4} \, {\left(\sqrt{2 \, x^{2} + \sqrt{5} + 1} {\left(3 \, \sqrt{5} \sqrt{2} + 7 \, \sqrt{2}\right)} - 6 \, \sqrt{5} x - 14 \, x\right)} \sqrt{17 \, \sqrt{5} - 38}\right) + \sqrt{5} x^{5} \sqrt{17 \, \sqrt{5} - 38} \log\left(\sqrt{17 \, \sqrt{5} - 38} {\left(5 \, \sqrt{5} + 11\right)} + 2 \, x\right) - \sqrt{5} x^{5} \sqrt{17 \, \sqrt{5} - 38} \log\left(-\sqrt{17 \, \sqrt{5} - 38} {\left(5 \, \sqrt{5} + 11\right)} + 2 \, x\right) - \sqrt{5} x^{5} \sqrt{17 \, \sqrt{5} + 38} \log\left(\sqrt{17 \, \sqrt{5} + 38} {\left(5 \, \sqrt{5} - 11\right)} + 2 \, x\right) + \sqrt{5} x^{5} \sqrt{17 \, \sqrt{5} + 38} \log\left(-\sqrt{17 \, \sqrt{5} + 38} {\left(5 \, \sqrt{5} - 11\right)} + 2 \, x\right) + 60 \, x^{4} + 4}{20 \, x^{5}}"," ",0,"-1/20*(4*sqrt(5)*x^5*sqrt(17*sqrt(5) + 38)*arctan(1/4*(sqrt(2*x^2 + sqrt(5) - 1)*(3*sqrt(5)*sqrt(2) - 7*sqrt(2)) - 6*sqrt(5)*x + 14*x)*sqrt(17*sqrt(5) + 38)) + 4*sqrt(5)*x^5*sqrt(17*sqrt(5) - 38)*arctan(1/4*(sqrt(2*x^2 + sqrt(5) + 1)*(3*sqrt(5)*sqrt(2) + 7*sqrt(2)) - 6*sqrt(5)*x - 14*x)*sqrt(17*sqrt(5) - 38)) + sqrt(5)*x^5*sqrt(17*sqrt(5) - 38)*log(sqrt(17*sqrt(5) - 38)*(5*sqrt(5) + 11) + 2*x) - sqrt(5)*x^5*sqrt(17*sqrt(5) - 38)*log(-sqrt(17*sqrt(5) - 38)*(5*sqrt(5) + 11) + 2*x) - sqrt(5)*x^5*sqrt(17*sqrt(5) + 38)*log(sqrt(17*sqrt(5) + 38)*(5*sqrt(5) - 11) + 2*x) + sqrt(5)*x^5*sqrt(17*sqrt(5) + 38)*log(-sqrt(17*sqrt(5) + 38)*(5*sqrt(5) - 11) + 2*x) + 60*x^4 + 4)/x^5","B",0
404,1,332,0,1.205004," ","integrate(1/x^8/(x^8-3*x^4+1),x, algorithm=""fricas"")","\frac{28 \, \sqrt{10} x^{7} \sqrt{89 \, \sqrt{5} + 199} \arctan\left(\frac{1}{40} \, {\left(\sqrt{10} \sqrt{2 \, x^{2} + \sqrt{5} - 1} {\left(11 \, \sqrt{5} \sqrt{2} - 25 \, \sqrt{2}\right)} - 2 \, \sqrt{10} {\left(11 \, \sqrt{5} x - 25 \, x\right)}\right)} \sqrt{89 \, \sqrt{5} + 199}\right) + 28 \, \sqrt{10} x^{7} \sqrt{89 \, \sqrt{5} - 199} \arctan\left(\frac{1}{40} \, {\left(\sqrt{10} \sqrt{2 \, x^{2} + \sqrt{5} + 1} {\left(11 \, \sqrt{5} \sqrt{2} + 25 \, \sqrt{2}\right)} - 2 \, \sqrt{10} {\left(11 \, \sqrt{5} x + 25 \, x\right)}\right)} \sqrt{89 \, \sqrt{5} - 199}\right) - 7 \, \sqrt{10} x^{7} \sqrt{89 \, \sqrt{5} - 199} \log\left(\sqrt{10} \sqrt{89 \, \sqrt{5} - 199} {\left(9 \, \sqrt{5} + 20\right)} + 10 \, x\right) + 7 \, \sqrt{10} x^{7} \sqrt{89 \, \sqrt{5} - 199} \log\left(-\sqrt{10} \sqrt{89 \, \sqrt{5} - 199} {\left(9 \, \sqrt{5} + 20\right)} + 10 \, x\right) + 7 \, \sqrt{10} x^{7} \sqrt{89 \, \sqrt{5} + 199} \log\left(\sqrt{10} \sqrt{89 \, \sqrt{5} + 199} {\left(9 \, \sqrt{5} - 20\right)} + 10 \, x\right) - 7 \, \sqrt{10} x^{7} \sqrt{89 \, \sqrt{5} + 199} \log\left(-\sqrt{10} \sqrt{89 \, \sqrt{5} + 199} {\left(9 \, \sqrt{5} - 20\right)} + 10 \, x\right) - 280 \, x^{4} - 40}{280 \, x^{7}}"," ",0,"1/280*(28*sqrt(10)*x^7*sqrt(89*sqrt(5) + 199)*arctan(1/40*(sqrt(10)*sqrt(2*x^2 + sqrt(5) - 1)*(11*sqrt(5)*sqrt(2) - 25*sqrt(2)) - 2*sqrt(10)*(11*sqrt(5)*x - 25*x))*sqrt(89*sqrt(5) + 199)) + 28*sqrt(10)*x^7*sqrt(89*sqrt(5) - 199)*arctan(1/40*(sqrt(10)*sqrt(2*x^2 + sqrt(5) + 1)*(11*sqrt(5)*sqrt(2) + 25*sqrt(2)) - 2*sqrt(10)*(11*sqrt(5)*x + 25*x))*sqrt(89*sqrt(5) - 199)) - 7*sqrt(10)*x^7*sqrt(89*sqrt(5) - 199)*log(sqrt(10)*sqrt(89*sqrt(5) - 199)*(9*sqrt(5) + 20) + 10*x) + 7*sqrt(10)*x^7*sqrt(89*sqrt(5) - 199)*log(-sqrt(10)*sqrt(89*sqrt(5) - 199)*(9*sqrt(5) + 20) + 10*x) + 7*sqrt(10)*x^7*sqrt(89*sqrt(5) + 199)*log(sqrt(10)*sqrt(89*sqrt(5) + 199)*(9*sqrt(5) - 20) + 10*x) - 7*sqrt(10)*x^7*sqrt(89*sqrt(5) + 199)*log(-sqrt(10)*sqrt(89*sqrt(5) + 199)*(9*sqrt(5) - 20) + 10*x) - 280*x^4 - 40)/x^7","B",0
405,1,17,0,1.275898," ","integrate(x^3/(x^8+3*x^4+2),x, algorithm=""fricas"")","-\frac{1}{4} \, \log\left(x^{4} + 2\right) + \frac{1}{4} \, \log\left(x^{4} + 1\right)"," ",0,"-1/4*log(x^4 + 2) + 1/4*log(x^4 + 1)","A",0
406,1,22,0,1.204242," ","integrate(x^11/(x^8+3*x^4+2),x, algorithm=""fricas"")","\frac{1}{4} \, x^{4} - \log\left(x^{4} + 2\right) + \frac{1}{4} \, \log\left(x^{4} + 1\right)"," ",0,"1/4*x^4 - log(x^4 + 2) + 1/4*log(x^4 + 1)","A",0
407,1,30,0,1.198735," ","integrate(x^9/(x^10+x^5+2),x, algorithm=""fricas"")","-\frac{1}{35} \, \sqrt{7} \arctan\left(\frac{1}{7} \, \sqrt{7} {\left(2 \, x^{5} + 1\right)}\right) + \frac{1}{10} \, \log\left(x^{10} + x^{5} + 2\right)"," ",0,"-1/35*sqrt(7)*arctan(1/7*sqrt(7)*(2*x^5 + 1)) + 1/10*log(x^10 + x^5 + 2)","A",0
408,1,18,0,1.217249," ","integrate(x^4/(x^10+x^5+2),x, algorithm=""fricas"")","\frac{2}{35} \, \sqrt{7} \arctan\left(\frac{1}{7} \, \sqrt{7} {\left(2 \, x^{5} + 1\right)}\right)"," ",0,"2/35*sqrt(7)*arctan(1/7*sqrt(7)*(2*x^5 + 1))","A",0
409,1,32,0,1.163874," ","integrate(1/x/(x^10+x^5+1),x, algorithm=""fricas"")","-\frac{1}{15} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{5} + 1\right)}\right) - \frac{1}{10} \, \log\left(x^{10} + x^{5} + 1\right) + \log\left(x\right)"," ",0,"-1/15*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^5 + 1)) - 1/10*log(x^10 + x^5 + 1) + log(x)","A",0
410,1,49,0,1.272523," ","integrate(1/x^6/(x^10+x^5+1),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} x^{5} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{5} + 1\right)}\right) - 3 \, x^{5} \log\left(x^{10} + x^{5} + 1\right) + 30 \, x^{5} \log\left(x\right) + 6}{30 \, x^{5}}"," ",0,"-1/30*(2*sqrt(3)*x^5*arctan(1/3*sqrt(3)*(2*x^5 + 1)) - 3*x^5*log(x^10 + x^5 + 1) + 30*x^5*log(x) + 6)/x^5","A",0
411,1,32,0,1.061354," ","integrate(1/(x^11+x^6+x),x, algorithm=""fricas"")","-\frac{1}{15} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{5} + 1\right)}\right) - \frac{1}{10} \, \log\left(x^{10} + x^{5} + 1\right) + \log\left(x\right)"," ",0,"-1/15*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^5 + 1)) - 1/10*log(x^10 + x^5 + 1) + log(x)","A",0
412,1,466,0,1.303305," ","integrate(x^3/(c+a/x^2+b/x),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{4} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} x^{2} + 6 \, {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 12 \, {\left(b^{5} c - 6 \, a b^{3} c^{2} + 8 \, a^{2} b c^{3}\right)} x + 6 \, {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} \log\left(c x^{2} + b x + a\right)}{12 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)}}, \frac{3 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{4} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} x^{2} + 12 \, {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 12 \, {\left(b^{5} c - 6 \, a b^{3} c^{2} + 8 \, a^{2} b c^{3}\right)} x + 6 \, {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} \log\left(c x^{2} + b x + a\right)}{12 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)}}\right]"," ",0,"[1/12*(3*(b^2*c^4 - 4*a*c^5)*x^4 - 4*(b^3*c^3 - 4*a*b*c^4)*x^3 + 6*(b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*x^2 + 6*(b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 12*(b^5*c - 6*a*b^3*c^2 + 8*a^2*b*c^3)*x + 6*(b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3)*log(c*x^2 + b*x + a))/(b^2*c^5 - 4*a*c^6), 1/12*(3*(b^2*c^4 - 4*a*c^5)*x^4 - 4*(b^3*c^3 - 4*a*b*c^4)*x^3 + 6*(b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*x^2 + 12*(b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 12*(b^5*c - 6*a*b^3*c^2 + 8*a^2*b*c^3)*x + 6*(b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3)*log(c*x^2 + b*x + a))/(b^2*c^5 - 4*a*c^6)]","A",0
413,1,383,0,1.337228," ","integrate(x^2/(c+a/x^2+b/x),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2} + 3 \, {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 6 \, {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} x - 3 \, {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} \log\left(c x^{2} + b x + a\right)}{6 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)}}, \frac{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2} - 6 \, {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 6 \, {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} x - 3 \, {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} \log\left(c x^{2} + b x + a\right)}{6 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)}}\right]"," ",0,"[1/6*(2*(b^2*c^3 - 4*a*c^4)*x^3 - 3*(b^3*c^2 - 4*a*b*c^3)*x^2 + 3*(b^4 - 4*a*b^2*c + 2*a^2*c^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 6*(b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*x - 3*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*log(c*x^2 + b*x + a))/(b^2*c^4 - 4*a*c^5), 1/6*(2*(b^2*c^3 - 4*a*c^4)*x^3 - 3*(b^3*c^2 - 4*a*b*c^3)*x^2 - 6*(b^4 - 4*a*b^2*c + 2*a^2*c^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 6*(b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*x - 3*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*log(c*x^2 + b*x + a))/(b^2*c^4 - 4*a*c^5)]","A",0
414,1,297,0,1.413495," ","integrate(x/(c+a/x^2+b/x),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} - {\left(b^{3} - 3 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}, \frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + 2 \, {\left(b^{3} - 3 \, a b c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}\right]"," ",0,"[1/2*((b^2*c^2 - 4*a*c^3)*x^2 - (b^3 - 3*a*b*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*(b^3*c - 4*a*b*c^2)*x + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*log(c*x^2 + b*x + a))/(b^2*c^3 - 4*a*c^4), 1/2*((b^2*c^2 - 4*a*c^3)*x^2 + 2*(b^3 - 3*a*b*c)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 2*(b^3*c - 4*a*b*c^2)*x + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*log(c*x^2 + b*x + a))/(b^2*c^3 - 4*a*c^4)]","A",0
415,1,235,0,1.433922," ","integrate(1/(c+a/x^2+b/x),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 2 \, a c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x + {\left(b^{3} - 4 \, a b c\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}, -\frac{2 \, {\left(b^{2} - 2 \, a c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x + {\left(b^{3} - 4 \, a b c\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}\right]"," ",0,"[-1/2*((b^2 - 2*a*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*(b^2*c - 4*a*c^2)*x + (b^3 - 4*a*b*c)*log(c*x^2 + b*x + a))/(b^2*c^2 - 4*a*c^3), -1/2*(2*(b^2 - 2*a*c)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 2*(b^2*c - 4*a*c^2)*x + (b^3 - 4*a*b*c)*log(c*x^2 + b*x + a))/(b^2*c^2 - 4*a*c^3)]","A",0
416,1,185,0,1.348880," ","integrate(1/(c+a/x^2+b/x)/x,x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} - 4 \, a c} b \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}, \frac{2 \, \sqrt{-b^{2} + 4 \, a c} b \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\right]"," ",0,"[1/2*(sqrt(b^2 - 4*a*c)*b*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (b^2 - 4*a*c)*log(c*x^2 + b*x + a))/(b^2*c - 4*a*c^2), 1/2*(2*sqrt(-b^2 + 4*a*c)*b*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (b^2 - 4*a*c)*log(c*x^2 + b*x + a))/(b^2*c - 4*a*c^2)]","A",0
417,1,120,0,1.242601," ","integrate(1/(c+a/x^2+b/x)/x^2,x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right)}{\sqrt{b^{2} - 4 \, a c}}, -\frac{2 \, \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right)}{b^{2} - 4 \, a c}\right]"," ",0,"[log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a))/sqrt(b^2 - 4*a*c), -2*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c))/(b^2 - 4*a*c)]","A",0
418,1,211,0,1.405576," ","integrate(1/(c+a/x^2+b/x)/x^3,x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} - 4 \, a c} b \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left(b^{2} - 4 \, a c\right)} \log\left(x\right)}{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}, \frac{2 \, \sqrt{-b^{2} + 4 \, a c} b \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left(b^{2} - 4 \, a c\right)} \log\left(x\right)}{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}\right]"," ",0,"[1/2*(sqrt(b^2 - 4*a*c)*b*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - (b^2 - 4*a*c)*log(c*x^2 + b*x + a) + 2*(b^2 - 4*a*c)*log(x))/(a*b^2 - 4*a^2*c), 1/2*(2*sqrt(-b^2 + 4*a*c)*b*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - (b^2 - 4*a*c)*log(c*x^2 + b*x + a) + 2*(b^2 - 4*a*c)*log(x))/(a*b^2 - 4*a^2*c)]","A",0
419,1,269,0,0.888808," ","integrate(1/(c+a/x^2+b/x)/x^4,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 2 \, a c\right)} \sqrt{b^{2} - 4 \, a c} x \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, a b^{2} - 8 \, a^{2} c - {\left(b^{3} - 4 \, a b c\right)} x \log\left(c x^{2} + b x + a\right) + 2 \, {\left(b^{3} - 4 \, a b c\right)} x \log\left(x\right)}{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x}, -\frac{2 \, {\left(b^{2} - 2 \, a c\right)} \sqrt{-b^{2} + 4 \, a c} x \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, a b^{2} - 8 \, a^{2} c - {\left(b^{3} - 4 \, a b c\right)} x \log\left(c x^{2} + b x + a\right) + 2 \, {\left(b^{3} - 4 \, a b c\right)} x \log\left(x\right)}{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x}\right]"," ",0,"[-1/2*((b^2 - 2*a*c)*sqrt(b^2 - 4*a*c)*x*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*a*b^2 - 8*a^2*c - (b^3 - 4*a*b*c)*x*log(c*x^2 + b*x + a) + 2*(b^3 - 4*a*b*c)*x*log(x))/((a^2*b^2 - 4*a^3*c)*x), -1/2*(2*(b^2 - 2*a*c)*sqrt(-b^2 + 4*a*c)*x*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*a*b^2 - 8*a^2*c - (b^3 - 4*a*b*c)*x*log(c*x^2 + b*x + a) + 2*(b^3 - 4*a*b*c)*x*log(x))/((a^2*b^2 - 4*a^3*c)*x)]","A",0
420,1,358,0,1.361260," ","integrate(1/(c+a/x^2+b/x)/x^5,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{3} - 3 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} x^{2} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + a^{2} b^{2} - 4 \, a^{3} c + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} x^{2} \log\left(c x^{2} + b x + a\right) - 2 \, {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} x^{2} \log\left(x\right) - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x}{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x^{2}}, \frac{2 \, {\left(b^{3} - 3 \, a b c\right)} \sqrt{-b^{2} + 4 \, a c} x^{2} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - a^{2} b^{2} + 4 \, a^{3} c - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} x^{2} \log\left(c x^{2} + b x + a\right) + 2 \, {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} x^{2} \log\left(x\right) + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x}{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} x^{2}}\right]"," ",0,"[-1/2*((b^3 - 3*a*b*c)*sqrt(b^2 - 4*a*c)*x^2*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + a^2*b^2 - 4*a^3*c + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*x^2*log(c*x^2 + b*x + a) - 2*(b^4 - 5*a*b^2*c + 4*a^2*c^2)*x^2*log(x) - 2*(a*b^3 - 4*a^2*b*c)*x)/((a^3*b^2 - 4*a^4*c)*x^2), 1/2*(2*(b^3 - 3*a*b*c)*sqrt(-b^2 + 4*a*c)*x^2*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - a^2*b^2 + 4*a^3*c - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*x^2*log(c*x^2 + b*x + a) + 2*(b^4 - 5*a*b^2*c + 4*a^2*c^2)*x^2*log(x) + 2*(a*b^3 - 4*a^2*b*c)*x)/((a^3*b^2 - 4*a^4*c)*x^2)]","A",0
421,1,445,0,1.471425," ","integrate(1/(c+a/x^2+b/x)/x^6,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} x^{3} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, a^{3} b^{2} + 8 \, a^{4} c + 3 \, {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} x^{3} \log\left(c x^{2} + b x + a\right) - 6 \, {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} x^{3} \log\left(x\right) - 6 \, {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} x^{2} + 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x}{6 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}}, -\frac{6 \, {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c} x^{3} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, a^{3} b^{2} - 8 \, a^{4} c - 3 \, {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} x^{3} \log\left(c x^{2} + b x + a\right) + 6 \, {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} x^{3} \log\left(x\right) + 6 \, {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} x^{2} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x}{6 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{3}}\right]"," ",0,"[1/6*(3*(b^4 - 4*a*b^2*c + 2*a^2*c^2)*sqrt(b^2 - 4*a*c)*x^3*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*a^3*b^2 + 8*a^4*c + 3*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*x^3*log(c*x^2 + b*x + a) - 6*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*x^3*log(x) - 6*(a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*x^2 + 3*(a^2*b^3 - 4*a^3*b*c)*x)/((a^4*b^2 - 4*a^5*c)*x^3), -1/6*(6*(b^4 - 4*a*b^2*c + 2*a^2*c^2)*sqrt(-b^2 + 4*a*c)*x^3*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*a^3*b^2 - 8*a^4*c - 3*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*x^3*log(c*x^2 + b*x + a) + 6*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*x^3*log(x) + 6*(a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*x^2 - 3*(a^2*b^3 - 4*a^3*b*c)*x)/((a^4*b^2 - 4*a^5*c)*x^3)]","A",0
422,1,1029,0,1.332271," ","integrate(x/(c+a/x^2+b/x)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a b^{6} - 16 \, a^{2} b^{4} c + 36 \, a^{3} b^{2} c^{2} - 16 \, a^{4} c^{3} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{4} - 3 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{3} - {\left(4 \, b^{6} c - 33 \, a b^{4} c^{2} + 72 \, a^{2} b^{2} c^{3} - 16 \, a^{3} c^{4}\right)} x^{2} - {\left(3 \, a b^{5} - 20 \, a^{2} b^{3} c + 30 \, a^{3} b c^{2} + {\left(3 \, b^{5} c - 20 \, a b^{3} c^{2} + 30 \, a^{2} b c^{3}\right)} x^{2} + {\left(3 \, b^{6} - 20 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(b^{7} - 11 \, a b^{5} c + 41 \, a^{2} b^{3} c^{2} - 52 \, a^{3} b c^{3}\right)} x + {\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3} + {\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} x^{2} + {\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} x^{2} + {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} x\right)}}, \frac{2 \, a b^{6} - 16 \, a^{2} b^{4} c + 36 \, a^{3} b^{2} c^{2} - 16 \, a^{4} c^{3} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{4} - 3 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{3} - {\left(4 \, b^{6} c - 33 \, a b^{4} c^{2} + 72 \, a^{2} b^{2} c^{3} - 16 \, a^{3} c^{4}\right)} x^{2} + 2 \, {\left(3 \, a b^{5} - 20 \, a^{2} b^{3} c + 30 \, a^{3} b c^{2} + {\left(3 \, b^{5} c - 20 \, a b^{3} c^{2} + 30 \, a^{2} b c^{3}\right)} x^{2} + {\left(3 \, b^{6} - 20 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(b^{7} - 11 \, a b^{5} c + 41 \, a^{2} b^{3} c^{2} - 52 \, a^{3} b c^{3}\right)} x + {\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3} + {\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} x^{2} + {\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} x^{2} + {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} x\right)}}\right]"," ",0,"[1/2*(2*a*b^6 - 16*a^2*b^4*c + 36*a^3*b^2*c^2 - 16*a^4*c^3 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^4 - 3*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^3 - (4*b^6*c - 33*a*b^4*c^2 + 72*a^2*b^2*c^3 - 16*a^3*c^4)*x^2 - (3*a*b^5 - 20*a^2*b^3*c + 30*a^3*b*c^2 + (3*b^5*c - 20*a*b^3*c^2 + 30*a^2*b*c^3)*x^2 + (3*b^6 - 20*a*b^4*c + 30*a^2*b^2*c^2)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(b^7 - 11*a*b^5*c + 41*a^2*b^3*c^2 - 52*a^3*b*c^3)*x + (3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3 + (3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*x^2 + (3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*x)*log(c*x^2 + b*x + a))/(a*b^4*c^4 - 8*a^2*b^2*c^5 + 16*a^3*c^6 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*x^2 + (b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*x), 1/2*(2*a*b^6 - 16*a^2*b^4*c + 36*a^3*b^2*c^2 - 16*a^4*c^3 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^4 - 3*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^3 - (4*b^6*c - 33*a*b^4*c^2 + 72*a^2*b^2*c^3 - 16*a^3*c^4)*x^2 + 2*(3*a*b^5 - 20*a^2*b^3*c + 30*a^3*b*c^2 + (3*b^5*c - 20*a*b^3*c^2 + 30*a^2*b*c^3)*x^2 + (3*b^6 - 20*a*b^4*c + 30*a^2*b^2*c^2)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(b^7 - 11*a*b^5*c + 41*a^2*b^3*c^2 - 52*a^3*b*c^3)*x + (3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3 + (3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*x^2 + (3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*x)*log(c*x^2 + b*x + a))/(a*b^4*c^4 - 8*a^2*b^2*c^5 + 16*a^3*c^6 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*x^2 + (b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*x)]","B",0
423,1,837,0,1.619945," ","integrate(1/(c+a/x^2+b/x)^2,x, algorithm=""fricas"")","\left[-\frac{a b^{5} - 7 \, a^{2} b^{3} c + 12 \, a^{3} b c^{2} - {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{3} - {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{2} + {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2} + {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} x^{2} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(b^{6} - 9 \, a b^{4} c + 26 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} x + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{2} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{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^{2} + {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x}, -\frac{a b^{5} - 7 \, a^{2} b^{3} c + 12 \, a^{3} b c^{2} - {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{3} - {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{2} + 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2} + {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} x^{2} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(b^{6} - 9 \, a b^{4} c + 26 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} x + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{2} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{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^{2} + {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x}\right]"," ",0,"[-(a*b^5 - 7*a^2*b^3*c + 12*a^3*b*c^2 - (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^3 - (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^2 + (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2 + (b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*x^2 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (b^6 - 9*a*b^4*c + 26*a^2*b^2*c^2 - 24*a^3*c^3)*x + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^2 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*x)*log(c*x^2 + b*x + 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^2 + (b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x), -(a*b^5 - 7*a^2*b^3*c + 12*a^3*b*c^2 - (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^3 - (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^2 + 2*(a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2 + (b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*x^2 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (b^6 - 9*a*b^4*c + 26*a^2*b^2*c^2 - 24*a^3*c^3)*x + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^2 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*x)*log(c*x^2 + b*x + 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^2 + (b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x)]","B",0
424,1,635,0,1.284280," ","integrate(1/(c+a/x^2+b/x)^2/x,x, algorithm=""fricas"")","\left[\frac{2 \, a b^{4} - 12 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(a b^{3} - 6 \, a^{2} b c + {\left(b^{3} c - 6 \, a b c^{2}\right)} x^{2} + {\left(b^{4} - 6 \, a b^{2} c\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(b^{5} - 7 \, a b^{3} c + 12 \, a^{2} b c^{2}\right)} x + {\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^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\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^{2} + {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x\right)}}, \frac{2 \, a b^{4} - 12 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + 2 \, {\left(a b^{3} - 6 \, a^{2} b c + {\left(b^{3} c - 6 \, a b c^{2}\right)} x^{2} + {\left(b^{4} - 6 \, a b^{2} c\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(b^{5} - 7 \, a b^{3} c + 12 \, a^{2} b c^{2}\right)} x + {\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^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\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^{2} + {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x\right)}}\right]"," ",0,"[1/2*(2*a*b^4 - 12*a^2*b^2*c + 16*a^3*c^2 + (a*b^3 - 6*a^2*b*c + (b^3*c - 6*a*b*c^2)*x^2 + (b^4 - 6*a*b^2*c)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(b^5 - 7*a*b^3*c + 12*a^2*b*c^2)*x + (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^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x)*log(c*x^2 + b*x + 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^2 + (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x), 1/2*(2*a*b^4 - 12*a^2*b^2*c + 16*a^3*c^2 + 2*(a*b^3 - 6*a^2*b*c + (b^3*c - 6*a*b*c^2)*x^2 + (b^4 - 6*a*b^2*c)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(b^5 - 7*a*b^3*c + 12*a^2*b*c^2)*x + (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^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x)*log(c*x^2 + b*x + 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^2 + (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x)]","B",0
425,1,387,0,1.199573," ","integrate(1/(c+a/x^2+b/x)^2/x^2,x, algorithm=""fricas"")","\left[-\frac{a b^{3} - 4 \, a^{2} b c + 2 \, {\left(a c^{2} x^{2} + a b c x + a^{2} c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} x}{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^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x}, -\frac{a b^{3} - 4 \, a^{2} b c - 4 \, {\left(a c^{2} x^{2} + a b c x + a^{2} c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} x}{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^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x}\right]"," ",0,"[-(a*b^3 - 4*a^2*b*c + 2*(a*c^2*x^2 + a*b*c*x + a^2*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*x)/(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^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x), -(a*b^3 - 4*a^2*b*c - 4*(a*c^2*x^2 + a*b*c*x + a^2*c)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*x)/(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^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x)]","B",0
426,1,338,0,1.170514," ","integrate(1/(c+a/x^2+b/x)^2/x^3,x, algorithm=""fricas"")","\left[\frac{2 \, a b^{2} - 8 \, a^{2} c - {\left(b c x^{2} + b^{2} x + a b\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(b^{3} - 4 \, a b c\right)} x}{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^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x}, \frac{2 \, a b^{2} - 8 \, a^{2} c - 2 \, {\left(b c x^{2} + b^{2} x + a b\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(b^{3} - 4 \, a b c\right)} x}{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^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x}\right]"," ",0,"[(2*a*b^2 - 8*a^2*c - (b*c*x^2 + b^2*x + a*b)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (b^3 - 4*a*b*c)*x)/(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^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x), (2*a*b^2 - 8*a^2*c - 2*(b*c*x^2 + b^2*x + a*b)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (b^3 - 4*a*b*c)*x)/(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^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x)]","B",0
427,1,341,0,1.263906," ","integrate(1/(c+a/x^2+b/x)^2/x^4,x, algorithm=""fricas"")","\left[-\frac{b^{3} - 4 \, a b c + 2 \, {\left(c^{2} x^{2} + b c x + a c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x}{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^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x}, -\frac{b^{3} - 4 \, a b c - 4 \, {\left(c^{2} x^{2} + b c x + a c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x}{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^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x}\right]"," ",0,"[-(b^3 - 4*a*b*c + 2*(c^2*x^2 + b*c*x + a*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(b^2*c - 4*a*c^2)*x)/(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^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x), -(b^3 - 4*a*b*c - 4*(c^2*x^2 + b*c*x + a*c)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(b^2*c - 4*a*c^2)*x)/(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^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x)]","B",0
428,1,781,0,1.487977," ","integrate(1/(c+a/x^2+b/x)^2/x^5,x, algorithm=""fricas"")","\left[\frac{2 \, a b^{4} - 12 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(a b^{3} - 6 \, a^{2} b c + {\left(b^{3} c - 6 \, a b c^{2}\right)} x^{2} + {\left(b^{4} - 6 \, a b^{2} c\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} x - {\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^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 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^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x\right)} \log\left(x\right)}{2 \, {\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^{2} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x\right)}}, \frac{2 \, a b^{4} - 12 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + 2 \, {\left(a b^{3} - 6 \, a^{2} b c + {\left(b^{3} c - 6 \, a b c^{2}\right)} x^{2} + {\left(b^{4} - 6 \, a b^{2} c\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} x - {\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^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 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^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x\right)} \log\left(x\right)}{2 \, {\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^{2} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x\right)}}\right]"," ",0,"[1/2*(2*a*b^4 - 12*a^2*b^2*c + 16*a^3*c^2 + (a*b^3 - 6*a^2*b*c + (b^3*c - 6*a*b*c^2)*x^2 + (b^4 - 6*a*b^2*c)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(a*b^3*c - 4*a^2*b*c^2)*x - (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^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x)*log(c*x^2 + b*x + a) + 2*(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^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x)*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^2 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x), 1/2*(2*a*b^4 - 12*a^2*b^2*c + 16*a^3*c^2 + 2*(a*b^3 - 6*a^2*b*c + (b^3*c - 6*a*b*c^2)*x^2 + (b^4 - 6*a*b^2*c)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(a*b^3*c - 4*a^2*b*c^2)*x - (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^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x)*log(c*x^2 + b*x + a) + 2*(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^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x)*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^2 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x)]","B",0
429,1,975,0,1.787299," ","integrate(1/(c+a/x^2+b/x)^2/x^6,x, algorithm=""fricas"")","\left[-\frac{a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + 2 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} x^{2} + {\left({\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} x^{3} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} x^{2} + {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2}\right)} x - {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} x^{2} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} x^{2} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \log\left(x\right)}{{\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} x^{3} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} x}, -\frac{a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + 2 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left({\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} x^{3} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} x^{2} + {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2}\right)} x - {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} x^{2} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} x^{2} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \log\left(x\right)}{{\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} x^{3} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} x^{2} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} x}\right]"," ",0,"[-(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + 2*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*x^2 + ((b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*x^3 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*x^2 + (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2)*x - ((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*x^2 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*log(c*x^2 + b*x + a) + 2*((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*x^2 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*log(x))/((a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*x^3 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*x), -(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + 2*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*x^2 + 2*((b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*x^3 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*x^2 + (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2)*x - ((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*x^2 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*log(c*x^2 + b*x + a) + 2*((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*x^2 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*log(x))/((a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*x^3 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*x^2 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*x)]","B",0
430,1,1226,0,2.004343," ","integrate(1/(c+a/x^2+b/x)^2/x^7,x, algorithm=""fricas"")","\left[-\frac{a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} - 2 \, {\left(3 \, a b^{5} c - 23 \, a^{2} b^{3} c^{2} + 44 \, a^{3} b c^{3}\right)} x^{3} - {\left(6 \, a b^{6} - 49 \, a^{2} b^{4} c + 108 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} x^{2} + {\left({\left(3 \, b^{5} c - 20 \, a b^{3} c^{2} + 30 \, a^{2} b c^{3}\right)} x^{4} + {\left(3 \, b^{6} - 20 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2}\right)} x^{3} + {\left(3 \, a b^{5} - 20 \, a^{2} b^{3} c + 30 \, a^{3} b c^{2}\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 3 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x + {\left({\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} x^{4} + {\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} x^{3} + {\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} x^{2}\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left({\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} x^{4} + {\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} x^{3} + {\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left({\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} x^{4} + {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x^{3} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} x^{2}\right)}}, -\frac{a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} - 2 \, {\left(3 \, a b^{5} c - 23 \, a^{2} b^{3} c^{2} + 44 \, a^{3} b c^{3}\right)} x^{3} - {\left(6 \, a b^{6} - 49 \, a^{2} b^{4} c + 108 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} x^{2} - 2 \, {\left({\left(3 \, b^{5} c - 20 \, a b^{3} c^{2} + 30 \, a^{2} b c^{3}\right)} x^{4} + {\left(3 \, b^{6} - 20 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2}\right)} x^{3} + {\left(3 \, a b^{5} - 20 \, a^{2} b^{3} c + 30 \, a^{3} b c^{2}\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 3 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x + {\left({\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} x^{4} + {\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} x^{3} + {\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} x^{2}\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left({\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} x^{4} + {\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} x^{3} + {\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left({\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} x^{4} + {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x^{3} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} x^{2}\right)}}\right]"," ",0,"[-1/2*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 - 2*(3*a*b^5*c - 23*a^2*b^3*c^2 + 44*a^3*b*c^3)*x^3 - (6*a*b^6 - 49*a^2*b^4*c + 108*a^3*b^2*c^2 - 32*a^4*c^3)*x^2 + ((3*b^5*c - 20*a*b^3*c^2 + 30*a^2*b*c^3)*x^4 + (3*b^6 - 20*a*b^4*c + 30*a^2*b^2*c^2)*x^3 + (3*a*b^5 - 20*a^2*b^3*c + 30*a^3*b*c^2)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 3*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x + ((3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*x^4 + (3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*x^3 + (3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3)*x^2)*log(c*x^2 + b*x + a) - 2*((3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*x^4 + (3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*x^3 + (3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3)*x^2)*log(x))/((a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*x^4 + (a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*x^2), -1/2*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2 - 2*(3*a*b^5*c - 23*a^2*b^3*c^2 + 44*a^3*b*c^3)*x^3 - (6*a*b^6 - 49*a^2*b^4*c + 108*a^3*b^2*c^2 - 32*a^4*c^3)*x^2 - 2*((3*b^5*c - 20*a*b^3*c^2 + 30*a^2*b*c^3)*x^4 + (3*b^6 - 20*a*b^4*c + 30*a^2*b^2*c^2)*x^3 + (3*a*b^5 - 20*a^2*b^3*c + 30*a^3*b*c^2)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 3*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x + ((3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*x^4 + (3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*x^3 + (3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3)*x^2)*log(c*x^2 + b*x + a) - 2*((3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*x^4 + (3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*x^3 + (3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3)*x^2)*log(x))/((a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*x^4 + (a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*x^2)]","B",0
431,1,1926,0,1.006142," ","integrate(1/(c+a/x^2+b/x)^3,x, algorithm=""fricas"")","\left[-\frac{5 \, a^{2} b^{7} - 56 \, a^{3} b^{5} c + 202 \, a^{4} b^{3} c^{2} - 232 \, a^{5} b c^{3} - 2 \, {\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^{5} - 4 \, {\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^{4} + 2 \, {\left(2 \, b^{8} c - 26 \, a b^{6} c^{2} + 123 \, a^{2} b^{4} c^{3} - 254 \, a^{3} b^{2} c^{4} + 200 \, a^{4} c^{5}\right)} x^{3} + {\left(5 \, b^{9} - 58 \, a b^{7} c + 225 \, a^{2} b^{5} c^{2} - 314 \, a^{3} b^{3} c^{3} + 88 \, a^{4} b c^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3} + {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} x^{3} + {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} x^{2} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(5 \, a b^{8} - 59 \, a^{2} b^{6} c + 235 \, a^{3} b^{4} c^{2} - 346 \, a^{4} b^{2} c^{3} + 120 \, a^{5} c^{4}\right)} x + 3 \, {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3} + {\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^{4} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} x^{3} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} x^{2} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\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^{4} + 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^{3} + {\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^{2} + 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\right)}}, -\frac{5 \, a^{2} b^{7} - 56 \, a^{3} b^{5} c + 202 \, a^{4} b^{3} c^{2} - 232 \, a^{5} b c^{3} - 2 \, {\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^{5} - 4 \, {\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^{4} + 2 \, {\left(2 \, b^{8} c - 26 \, a b^{6} c^{2} + 123 \, a^{2} b^{4} c^{3} - 254 \, a^{3} b^{2} c^{4} + 200 \, a^{4} c^{5}\right)} x^{3} + {\left(5 \, b^{9} - 58 \, a b^{7} c + 225 \, a^{2} b^{5} c^{2} - 314 \, a^{3} b^{3} c^{3} + 88 \, a^{4} b c^{4}\right)} x^{2} + 6 \, {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3} + {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} x^{3} + {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} x^{2} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(5 \, a b^{8} - 59 \, a^{2} b^{6} c + 235 \, a^{3} b^{4} c^{2} - 346 \, a^{4} b^{2} c^{3} + 120 \, a^{5} c^{4}\right)} x + 3 \, {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3} + {\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^{4} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} x^{3} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} x^{2} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\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^{4} + 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^{3} + {\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^{2} + 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\right)}}\right]"," ",0,"[-1/2*(5*a^2*b^7 - 56*a^3*b^5*c + 202*a^4*b^3*c^2 - 232*a^5*b*c^3 - 2*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*x^5 - 4*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^4 + 2*(2*b^8*c - 26*a*b^6*c^2 + 123*a^2*b^4*c^3 - 254*a^3*b^2*c^4 + 200*a^4*c^5)*x^3 + (5*b^9 - 58*a*b^7*c + 225*a^2*b^5*c^2 - 314*a^3*b^3*c^3 + 88*a^4*b*c^4)*x^2 + 3*(a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3 + (b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*x^4 + 2*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*x^3 + (b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*x^2 + 2*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(5*a*b^8 - 59*a^2*b^6*c + 235*a^3*b^4*c^2 - 346*a^4*b^2*c^3 + 120*a^5*c^4)*x + 3*(a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3 + (b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^4 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*x^3 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*x^2 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*x)*log(c*x^2 + b*x + 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^4 + 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^3 + (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^2 + 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), -1/2*(5*a^2*b^7 - 56*a^3*b^5*c + 202*a^4*b^3*c^2 - 232*a^5*b*c^3 - 2*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*x^5 - 4*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^4 + 2*(2*b^8*c - 26*a*b^6*c^2 + 123*a^2*b^4*c^3 - 254*a^3*b^2*c^4 + 200*a^4*c^5)*x^3 + (5*b^9 - 58*a*b^7*c + 225*a^2*b^5*c^2 - 314*a^3*b^3*c^3 + 88*a^4*b*c^4)*x^2 + 6*(a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3 + (b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*x^4 + 2*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*x^3 + (b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*x^2 + 2*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(5*a*b^8 - 59*a^2*b^6*c + 235*a^3*b^4*c^2 - 346*a^4*b^2*c^3 + 120*a^5*c^4)*x + 3*(a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3 + (b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^4 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*x^3 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*x^2 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*x)*log(c*x^2 + b*x + 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^4 + 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^3 + (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^2 + 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)]","B",0
432,1,1603,0,1.679336," ","integrate(1/(c+a/x^2+b/x)^3/x,x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} b^{6} - 33 \, a^{3} b^{4} c + 108 \, a^{4} b^{2} c^{2} - 96 \, a^{5} c^{3} + 2 \, {\left(2 \, b^{7} c - 23 \, a b^{5} c^{2} + 85 \, a^{2} b^{3} c^{3} - 100 \, a^{3} b c^{4}\right)} x^{3} + {\left(3 \, b^{8} - 31 \, a b^{6} c + 87 \, a^{2} b^{4} c^{2} - 12 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{2} + {\left(a^{2} b^{5} - 10 \, a^{3} b^{3} c + 30 \, a^{4} b c^{2} + {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} x^{4} + 2 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} x^{3} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} x^{2} + 2 \, {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(3 \, a b^{7} - 34 \, a^{2} b^{5} c + 119 \, a^{3} b^{3} c^{2} - 124 \, a^{4} b c^{3}\right)} x + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\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^{4} + 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^{3} + {\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^{2} + 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\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\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^{4} + 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^{3} + {\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^{2} + 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\right)}}, \frac{3 \, a^{2} b^{6} - 33 \, a^{3} b^{4} c + 108 \, a^{4} b^{2} c^{2} - 96 \, a^{5} c^{3} + 2 \, {\left(2 \, b^{7} c - 23 \, a b^{5} c^{2} + 85 \, a^{2} b^{3} c^{3} - 100 \, a^{3} b c^{4}\right)} x^{3} + {\left(3 \, b^{8} - 31 \, a b^{6} c + 87 \, a^{2} b^{4} c^{2} - 12 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{2} + 2 \, {\left(a^{2} b^{5} - 10 \, a^{3} b^{3} c + 30 \, a^{4} b c^{2} + {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} x^{4} + 2 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} x^{3} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} x^{2} + 2 \, {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(3 \, a b^{7} - 34 \, a^{2} b^{5} c + 119 \, a^{3} b^{3} c^{2} - 124 \, a^{4} b c^{3}\right)} x + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\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^{4} + 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^{3} + {\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^{2} + 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\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\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^{4} + 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^{3} + {\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^{2} + 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\right)}}\right]"," ",0,"[1/2*(3*a^2*b^6 - 33*a^3*b^4*c + 108*a^4*b^2*c^2 - 96*a^5*c^3 + 2*(2*b^7*c - 23*a*b^5*c^2 + 85*a^2*b^3*c^3 - 100*a^3*b*c^4)*x^3 + (3*b^8 - 31*a*b^6*c + 87*a^2*b^4*c^2 - 12*a^3*b^2*c^3 - 128*a^4*c^4)*x^2 + (a^2*b^5 - 10*a^3*b^3*c + 30*a^4*b*c^2 + (b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*x^4 + 2*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*x^3 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*x^2 + 2*(a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(3*a*b^7 - 34*a^2*b^5*c + 119*a^3*b^3*c^2 - 124*a^4*b*c^3)*x + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (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^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x)*log(c*x^2 + b*x + 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^4 + 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^3 + (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^2 + 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), 1/2*(3*a^2*b^6 - 33*a^3*b^4*c + 108*a^4*b^2*c^2 - 96*a^5*c^3 + 2*(2*b^7*c - 23*a*b^5*c^2 + 85*a^2*b^3*c^3 - 100*a^3*b*c^4)*x^3 + (3*b^8 - 31*a*b^6*c + 87*a^2*b^4*c^2 - 12*a^3*b^2*c^3 - 128*a^4*c^4)*x^2 + 2*(a^2*b^5 - 10*a^3*b^3*c + 30*a^4*b*c^2 + (b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*x^4 + 2*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*x^3 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*x^2 + 2*(a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(3*a*b^7 - 34*a^2*b^5*c + 119*a^3*b^3*c^2 - 124*a^4*b*c^3)*x + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (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^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x)*log(c*x^2 + b*x + 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^4 + 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^3 + (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^2 + 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)]","B",0
433,1,953,0,0.755063," ","integrate(1/(c+a/x^2+b/x)^3/x^2,x, algorithm=""fricas"")","\left[-\frac{a^{2} b^{5} - 14 \, a^{3} b^{3} c + 40 \, a^{4} b c^{2} + 2 \, {\left(b^{6} c - 12 \, a b^{4} c^{2} + 42 \, a^{2} b^{2} c^{3} - 40 \, a^{3} c^{4}\right)} x^{3} + {\left(b^{7} - 12 \, a b^{5} c + 30 \, a^{2} b^{3} c^{2} + 8 \, a^{3} b c^{3}\right)} x^{2} - 12 \, {\left(a^{2} c^{4} x^{4} + 2 \, a^{2} b c^{3} x^{3} + 2 \, a^{3} b c^{2} x + a^{4} c^{2} + {\left(a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(a b^{6} - 14 \, a^{2} b^{4} c + 46 \, a^{3} b^{2} c^{2} - 24 \, a^{4} c^{3}\right)} x}{2 \, {\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^{4} + 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^{3} + {\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^{2} + 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\right)}}, -\frac{a^{2} b^{5} - 14 \, a^{3} b^{3} c + 40 \, a^{4} b c^{2} + 2 \, {\left(b^{6} c - 12 \, a b^{4} c^{2} + 42 \, a^{2} b^{2} c^{3} - 40 \, a^{3} c^{4}\right)} x^{3} + {\left(b^{7} - 12 \, a b^{5} c + 30 \, a^{2} b^{3} c^{2} + 8 \, a^{3} b c^{3}\right)} x^{2} + 24 \, {\left(a^{2} c^{4} x^{4} + 2 \, a^{2} b c^{3} x^{3} + 2 \, a^{3} b c^{2} x + a^{4} c^{2} + {\left(a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(a b^{6} - 14 \, a^{2} b^{4} c + 46 \, a^{3} b^{2} c^{2} - 24 \, a^{4} c^{3}\right)} x}{2 \, {\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^{4} + 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^{3} + {\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^{2} + 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\right)}}\right]"," ",0,"[-1/2*(a^2*b^5 - 14*a^3*b^3*c + 40*a^4*b*c^2 + 2*(b^6*c - 12*a*b^4*c^2 + 42*a^2*b^2*c^3 - 40*a^3*c^4)*x^3 + (b^7 - 12*a*b^5*c + 30*a^2*b^3*c^2 + 8*a^3*b*c^3)*x^2 - 12*(a^2*c^4*x^4 + 2*a^2*b*c^3*x^3 + 2*a^3*b*c^2*x + a^4*c^2 + (a^2*b^2*c^2 + 2*a^3*c^3)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(a*b^6 - 14*a^2*b^4*c + 46*a^3*b^2*c^2 - 24*a^4*c^3)*x)/(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^4 + 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^3 + (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^2 + 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), -1/2*(a^2*b^5 - 14*a^3*b^3*c + 40*a^4*b*c^2 + 2*(b^6*c - 12*a*b^4*c^2 + 42*a^2*b^2*c^3 - 40*a^3*c^4)*x^3 + (b^7 - 12*a*b^5*c + 30*a^2*b^3*c^2 + 8*a^3*b*c^3)*x^2 + 24*(a^2*c^4*x^4 + 2*a^2*b*c^3*x^3 + 2*a^3*b*c^2*x + a^4*c^2 + (a^2*b^2*c^2 + 2*a^3*c^3)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(a*b^6 - 14*a^2*b^4*c + 46*a^3*b^2*c^2 - 24*a^4*c^3)*x)/(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^4 + 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^3 + (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^2 + 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)]","B",0
434,1,872,0,1.110477," ","integrate(1/(c+a/x^2+b/x)^3/x^3,x, algorithm=""fricas"")","\left[-\frac{a^{2} b^{4} + 4 \, a^{3} b^{2} c - 32 \, a^{4} c^{2} + 6 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 3 \, a b^{4} c + 12 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} x^{2} - 6 \, {\left(a b c^{3} x^{4} + 2 \, a b^{2} c^{2} x^{3} + 2 \, a^{2} b^{2} c x + a^{3} b c + {\left(a b^{3} c + 2 \, a^{2} b c^{2}\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(a b^{5} + a^{2} b^{3} c - 20 \, a^{3} b c^{2}\right)} x}{2 \, {\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^{4} + 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^{3} + {\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^{2} + 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\right)}}, -\frac{a^{2} b^{4} + 4 \, a^{3} b^{2} c - 32 \, a^{4} c^{2} + 6 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 3 \, a b^{4} c + 12 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} x^{2} - 12 \, {\left(a b c^{3} x^{4} + 2 \, a b^{2} c^{2} x^{3} + 2 \, a^{2} b^{2} c x + a^{3} b c + {\left(a b^{3} c + 2 \, a^{2} b c^{2}\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(a b^{5} + a^{2} b^{3} c - 20 \, a^{3} b c^{2}\right)} x}{2 \, {\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^{4} + 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^{3} + {\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^{2} + 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\right)}}\right]"," ",0,"[-1/2*(a^2*b^4 + 4*a^3*b^2*c - 32*a^4*c^2 + 6*(a*b^3*c^2 - 4*a^2*b*c^3)*x^3 + (b^6 - 3*a*b^4*c + 12*a^2*b^2*c^2 - 64*a^3*c^3)*x^2 - 6*(a*b*c^3*x^4 + 2*a*b^2*c^2*x^3 + 2*a^2*b^2*c*x + a^3*b*c + (a*b^3*c + 2*a^2*b*c^2)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(a*b^5 + a^2*b^3*c - 20*a^3*b*c^2)*x)/(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^4 + 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^3 + (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^2 + 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), -1/2*(a^2*b^4 + 4*a^3*b^2*c - 32*a^4*c^2 + 6*(a*b^3*c^2 - 4*a^2*b*c^3)*x^3 + (b^6 - 3*a*b^4*c + 12*a^2*b^2*c^2 - 64*a^3*c^3)*x^2 - 12*(a*b*c^3*x^4 + 2*a*b^2*c^2*x^3 + 2*a^2*b^2*c*x + a^3*b*c + (a*b^3*c + 2*a^2*b*c^2)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(a*b^5 + a^2*b^3*c - 20*a^3*b*c^2)*x)/(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^4 + 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^3 + (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^2 + 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)]","B",0
435,1,887,0,1.102958," ","integrate(1/(c+a/x^2+b/x)^3/x^4,x, algorithm=""fricas"")","\left[\frac{6 \, a^{2} b^{3} - 24 \, a^{3} b c + 2 \, {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} x^{3} + 3 \, {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} x^{2} + 2 \, {\left({\left(b^{2} c^{2} + 2 \, a c^{3}\right)} x^{4} + a^{2} b^{2} + 2 \, a^{3} c + 2 \, {\left(b^{3} c + 2 \, a b c^{2}\right)} x^{3} + {\left(b^{4} + 4 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} + 2 \, a^{2} b c\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(5 \, a b^{4} - 22 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} x}{2 \, {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\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^{4} + 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^{3} + {\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^{2} + 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\right)}}, \frac{6 \, a^{2} b^{3} - 24 \, a^{3} b c + 2 \, {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} x^{3} + 3 \, {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} x^{2} - 4 \, {\left({\left(b^{2} c^{2} + 2 \, a c^{3}\right)} x^{4} + a^{2} b^{2} + 2 \, a^{3} c + 2 \, {\left(b^{3} c + 2 \, a b c^{2}\right)} x^{3} + {\left(b^{4} + 4 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} + 2 \, a^{2} b c\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(5 \, a b^{4} - 22 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} x}{2 \, {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\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^{4} + 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^{3} + {\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^{2} + 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\right)}}\right]"," ",0,"[1/2*(6*a^2*b^3 - 24*a^3*b*c + 2*(b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*x^3 + 3*(b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*x^2 + 2*((b^2*c^2 + 2*a*c^3)*x^4 + a^2*b^2 + 2*a^3*c + 2*(b^3*c + 2*a*b*c^2)*x^3 + (b^4 + 4*a*b^2*c + 4*a^2*c^2)*x^2 + 2*(a*b^3 + 2*a^2*b*c)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(5*a*b^4 - 22*a^2*b^2*c + 8*a^3*c^2)*x)/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (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^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x), 1/2*(6*a^2*b^3 - 24*a^3*b*c + 2*(b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*x^3 + 3*(b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*x^2 - 4*((b^2*c^2 + 2*a*c^3)*x^4 + a^2*b^2 + 2*a^3*c + 2*(b^3*c + 2*a*b*c^2)*x^3 + (b^4 + 4*a*b^2*c + 4*a^2*c^2)*x^2 + 2*(a*b^3 + 2*a^2*b*c)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(5*a*b^4 - 22*a^2*b^2*c + 8*a^3*c^2)*x)/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (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^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x)]","B",0
436,1,788,0,1.186021," ","integrate(1/(c+a/x^2+b/x)^3/x^5,x, algorithm=""fricas"")","\left[-\frac{a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2} + 6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{3} + 9 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} x^{2} - 6 \, {\left(b c^{3} x^{4} + 2 \, b^{2} c^{2} x^{3} + 2 \, a b^{2} c x + a^{2} b c + {\left(b^{3} c + 2 \, a b c^{2}\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} x}{2 \, {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\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^{4} + 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^{3} + {\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^{2} + 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\right)}}, -\frac{a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2} + 6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{3} + 9 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} x^{2} - 12 \, {\left(b c^{3} x^{4} + 2 \, b^{2} c^{2} x^{3} + 2 \, a b^{2} c x + a^{2} b c + {\left(b^{3} c + 2 \, a b c^{2}\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} x}{2 \, {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\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^{4} + 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^{3} + {\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^{2} + 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\right)}}\right]"," ",0,"[-1/2*(a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2 + 6*(b^3*c^2 - 4*a*b*c^3)*x^3 + 9*(b^4*c - 4*a*b^2*c^2)*x^2 - 6*(b*c^3*x^4 + 2*b^2*c^2*x^3 + 2*a*b^2*c*x + a^2*b*c + (b^3*c + 2*a*b*c^2)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(b^5 + a*b^3*c - 20*a^2*b*c^2)*x)/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (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^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x), -1/2*(a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2 + 6*(b^3*c^2 - 4*a*b*c^3)*x^3 + 9*(b^4*c - 4*a*b^2*c^2)*x^2 - 12*(b*c^3*x^4 + 2*b^2*c^2*x^3 + 2*a*b^2*c*x + a^2*b*c + (b^3*c + 2*a*b*c^2)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(b^5 + a*b^3*c - 20*a^2*b*c^2)*x)/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (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^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x)]","B",0
437,1,785,0,1.695866," ","integrate(1/(c+a/x^2+b/x)^3/x^6,x, algorithm=""fricas"")","\left[-\frac{b^{5} - 14 \, a b^{3} c + 40 \, a^{2} b c^{2} - 12 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{3} - 18 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2} - 12 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{3} + 2 \, a b c^{2} x + a^{2} c^{2} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 4 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} x}{2 \, {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\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^{4} + 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^{3} + {\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^{2} + 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\right)}}, -\frac{b^{5} - 14 \, a b^{3} c + 40 \, a^{2} b c^{2} - 12 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{3} - 18 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2} + 24 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{3} + 2 \, a b c^{2} x + a^{2} c^{2} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 4 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} x}{2 \, {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\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^{4} + 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^{3} + {\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^{2} + 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\right)}}\right]"," ",0,"[-1/2*(b^5 - 14*a*b^3*c + 40*a^2*b*c^2 - 12*(b^2*c^3 - 4*a*c^4)*x^3 - 18*(b^3*c^2 - 4*a*b*c^3)*x^2 - 12*(c^4*x^4 + 2*b*c^3*x^3 + 2*a*b*c^2*x + a^2*c^2 + (b^2*c^2 + 2*a*c^3)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 4*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*x)/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (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^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x), -1/2*(b^5 - 14*a*b^3*c + 40*a^2*b*c^2 - 12*(b^2*c^3 - 4*a*c^4)*x^3 - 18*(b^3*c^2 - 4*a*b*c^3)*x^2 + 24*(c^4*x^4 + 2*b*c^3*x^3 + 2*a*b*c^2*x + a^2*c^2 + (b^2*c^2 + 2*a*c^3)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 4*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*x)/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (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^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x)]","B",0
438,1,1985,0,3.243331," ","integrate(1/(c+a/x^2+b/x)^3/x^7,x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} b^{6} - 33 \, a^{3} b^{4} c + 108 \, a^{4} b^{2} c^{2} - 96 \, a^{5} c^{3} + 2 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} x^{3} + {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} x^{2} + {\left(a^{2} b^{5} - 10 \, a^{3} b^{3} c + 30 \, a^{4} b c^{2} + {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} x^{4} + 2 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} x^{3} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} x^{2} + 2 \, {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 23 \, a^{3} b^{3} c^{2} + 4 \, a^{4} b c^{3}\right)} x - {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\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^{4} + 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^{3} + {\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^{2} + 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\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\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^{4} + 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^{3} + {\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^{2} + 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\right)} \log\left(x\right)}{2 \, {\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^{4} + 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^{3} + {\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^{2} + 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\right)}}, \frac{3 \, a^{2} b^{6} - 33 \, a^{3} b^{4} c + 108 \, a^{4} b^{2} c^{2} - 96 \, a^{5} c^{3} + 2 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} x^{3} + {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} x^{2} + 2 \, {\left(a^{2} b^{5} - 10 \, a^{3} b^{3} c + 30 \, a^{4} b c^{2} + {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} x^{4} + 2 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} x^{3} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} x^{2} + 2 \, {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 23 \, a^{3} b^{3} c^{2} + 4 \, a^{4} b c^{3}\right)} x - {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\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^{4} + 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^{3} + {\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^{2} + 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\right)} \log\left(c x^{2} + b x + a\right) + 2 \, {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\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^{4} + 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^{3} + {\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^{2} + 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\right)} \log\left(x\right)}{2 \, {\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^{4} + 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^{3} + {\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^{2} + 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\right)}}\right]"," ",0,"[1/2*(3*a^2*b^6 - 33*a^3*b^4*c + 108*a^4*b^2*c^2 - 96*a^5*c^3 + 2*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*x^3 + (4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4)*x^2 + (a^2*b^5 - 10*a^3*b^3*c + 30*a^4*b*c^2 + (b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*x^4 + 2*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*x^3 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*x^2 + 2*(a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(a*b^7 - 10*a^2*b^5*c + 23*a^3*b^3*c^2 + 4*a^4*b*c^3)*x - (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (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^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x)*log(c*x^2 + b*x + a) + 2*(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (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^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x)*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^4 + 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^3 + (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^2 + 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), 1/2*(3*a^2*b^6 - 33*a^3*b^4*c + 108*a^4*b^2*c^2 - 96*a^5*c^3 + 2*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*x^3 + (4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4)*x^2 + 2*(a^2*b^5 - 10*a^3*b^3*c + 30*a^4*b*c^2 + (b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*x^4 + 2*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*x^3 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*x^2 + 2*(a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(a*b^7 - 10*a^2*b^5*c + 23*a^3*b^3*c^2 + 4*a^4*b*c^3)*x - (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (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^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x)*log(c*x^2 + b*x + a) + 2*(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (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^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x)*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^4 + 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^3 + (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^2 + 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)]","B",0
439,1,2280,0,3.188384," ","integrate(1/(c+a/x^2+b/x)^3/x^8,x, algorithm=""fricas"")","\left[-\frac{2 \, a^{3} b^{6} - 24 \, a^{4} b^{4} c + 96 \, a^{5} b^{2} c^{2} - 128 \, a^{6} c^{3} + 6 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} x^{4} + 3 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} x^{3} + 2 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} x^{2} + 3 \, {\left({\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} x^{5} + 2 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} x^{4} + {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} x^{3} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} x^{2} + {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(9 \, a^{2} b^{7} - 104 \, a^{3} b^{5} c + 394 \, a^{4} b^{3} c^{2} - 488 \, a^{5} b c^{3}\right)} x - 3 \, {\left({\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^{5} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} x^{4} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} x^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} x^{2} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 6 \, {\left({\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^{5} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} x^{4} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} x^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} x^{2} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} x\right)} \log\left(x\right)}{2 \, {\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^{5} + 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^{4} + {\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^{3} + 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^{2} + {\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\right)}}, -\frac{2 \, a^{3} b^{6} - 24 \, a^{4} b^{4} c + 96 \, a^{5} b^{2} c^{2} - 128 \, a^{6} c^{3} + 6 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} x^{4} + 3 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} x^{3} + 2 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} x^{2} + 6 \, {\left({\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} x^{5} + 2 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} x^{4} + {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} x^{3} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} x^{2} + {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(9 \, a^{2} b^{7} - 104 \, a^{3} b^{5} c + 394 \, a^{4} b^{3} c^{2} - 488 \, a^{5} b c^{3}\right)} x - 3 \, {\left({\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^{5} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} x^{4} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} x^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} x^{2} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 6 \, {\left({\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^{5} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} x^{4} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} x^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} x^{2} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} x\right)} \log\left(x\right)}{2 \, {\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^{5} + 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^{4} + {\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^{3} + 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^{2} + {\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\right)}}\right]"," ",0,"[-1/2*(2*a^3*b^6 - 24*a^4*b^4*c + 96*a^5*b^2*c^2 - 128*a^6*c^3 + 6*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*x^4 + 3*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*x^3 + 2*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*x^2 + 3*((b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*x^5 + 2*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*x^4 + (b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*x^3 + 2*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*x^2 + (a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (9*a^2*b^7 - 104*a^3*b^5*c + 394*a^4*b^3*c^2 - 488*a^5*b*c^3)*x - 3*((b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^5 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*x^4 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*x^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*x^2 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*x)*log(c*x^2 + b*x + a) + 6*((b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^5 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*x^4 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*x^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*x^2 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*x)*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^5 + 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^4 + (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^3 + 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^2 + (a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*x), -1/2*(2*a^3*b^6 - 24*a^4*b^4*c + 96*a^5*b^2*c^2 - 128*a^6*c^3 + 6*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*x^4 + 3*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*x^3 + 2*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*x^2 + 6*((b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*x^5 + 2*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*x^4 + (b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*x^3 + 2*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*x^2 + (a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (9*a^2*b^7 - 104*a^3*b^5*c + 394*a^4*b^3*c^2 - 488*a^5*b*c^3)*x - 3*((b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^5 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*x^4 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*x^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*x^2 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*x)*log(c*x^2 + b*x + a) + 6*((b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^5 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*x^4 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*x^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*x^2 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*x)*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^5 + 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^4 + (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^3 + 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^2 + (a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*x)]","B",0
440,1,30,0,1.723030," ","integrate(x^2/(15+2/x^2+13/x),x, algorithm=""fricas"")","\frac{1}{45} \, x^{3} - \frac{13}{450} \, x^{2} + \frac{139}{3375} \, x + \frac{1}{4375} \, \log\left(5 \, x + 1\right) - \frac{16}{567} \, \log\left(3 \, x + 2\right)"," ",0,"1/45*x^3 - 13/450*x^2 + 139/3375*x + 1/4375*log(5*x + 1) - 16/567*log(3*x + 2)","A",0
441,1,25,0,0.759096," ","integrate(x/(15+2/x^2+13/x),x, algorithm=""fricas"")","\frac{1}{30} \, x^{2} - \frac{13}{225} \, x - \frac{1}{875} \, \log\left(5 \, x + 1\right) + \frac{8}{189} \, \log\left(3 \, x + 2\right)"," ",0,"1/30*x^2 - 13/225*x - 1/875*log(5*x + 1) + 8/189*log(3*x + 2)","A",0
442,1,20,0,1.220701," ","integrate(1/(15+2/x^2+13/x),x, algorithm=""fricas"")","\frac{1}{15} \, x + \frac{1}{175} \, \log\left(5 \, x + 1\right) - \frac{4}{63} \, \log\left(3 \, x + 2\right)"," ",0,"1/15*x + 1/175*log(5*x + 1) - 4/63*log(3*x + 2)","A",0
443,1,17,0,1.403117," ","integrate(1/(15+2/x^2+13/x)/x,x, algorithm=""fricas"")","-\frac{1}{35} \, \log\left(5 \, x + 1\right) + \frac{2}{21} \, \log\left(3 \, x + 2\right)"," ",0,"-1/35*log(5*x + 1) + 2/21*log(3*x + 2)","A",0
444,1,17,0,1.043885," ","integrate(1/(15+2/x^2+13/x)/x^2,x, algorithm=""fricas"")","\frac{1}{7} \, \log\left(5 \, x + 1\right) - \frac{1}{7} \, \log\left(3 \, x + 2\right)"," ",0,"1/7*log(5*x + 1) - 1/7*log(3*x + 2)","A",0
445,1,21,0,1.302380," ","integrate(1/(15+2/x^2+13/x)/x^3,x, algorithm=""fricas"")","-\frac{5}{7} \, \log\left(5 \, x + 1\right) + \frac{3}{14} \, \log\left(3 \, x + 2\right) + \frac{1}{2} \, \log\left(x\right)"," ",0,"-5/7*log(5*x + 1) + 3/14*log(3*x + 2) + 1/2*log(x)","A",0
446,1,30,0,1.296301," ","integrate(1/(15+2/x^2+13/x)/x^4,x, algorithm=""fricas"")","\frac{100 \, x \log\left(5 \, x + 1\right) - 9 \, x \log\left(3 \, x + 2\right) - 91 \, x \log\left(x\right) - 14}{28 \, x}"," ",0,"1/28*(100*x*log(5*x + 1) - 9*x*log(3*x + 2) - 91*x*log(x) - 14)/x","A",0
447,1,39,0,1.300765," ","integrate(1/(15+2/x^2+13/x)/x^5,x, algorithm=""fricas"")","-\frac{1000 \, x^{2} \log\left(5 \, x + 1\right) - 27 \, x^{2} \log\left(3 \, x + 2\right) - 973 \, x^{2} \log\left(x\right) - 182 \, x + 14}{56 \, x^{2}}"," ",0,"-1/56*(1000*x^2*log(5*x + 1) - 27*x^2*log(3*x + 2) - 973*x^2*log(x) - 182*x + 14)/x^2","A",0
448,1,44,0,1.143065," ","integrate(1/(15+2/x^2+13/x)/x^6,x, algorithm=""fricas"")","\frac{30000 \, x^{3} \log\left(5 \, x + 1\right) - 243 \, x^{3} \log\left(3 \, x + 2\right) - 29757 \, x^{3} \log\left(x\right) - 5838 \, x^{2} + 546 \, x - 56}{336 \, x^{3}}"," ",0,"1/336*(30000*x^3*log(5*x + 1) - 243*x^3*log(3*x + 2) - 29757*x^3*log(x) - 5838*x^2 + 546*x - 56)/x^3","A",0
449,1,959,0,1.591976," ","integrate((a+c/x^2+b/x)^(5/2),x, algorithm=""fricas"")","\left[\frac{960 \, a^{\frac{3}{2}} b c^{2} x^{3} \log\left(-8 \, a^{2} x^{2} - 8 \, a b x - b^{2} - 4 \, a c - 4 \, {\left(2 \, a x^{2} + b x\right)} \sqrt{a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}\right) - 15 \, {\left(b^{4} - 24 \, a b^{2} c - 48 \, a^{2} c^{2}\right)} \sqrt{c} x^{3} \log\left(-\frac{8 \, b c x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 8 \, c^{2} - 4 \, {\left(b x^{2} + 2 \, c x\right)} \sqrt{c} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{x^{2}}\right) + 4 \, {\left(192 \, a^{2} c^{2} x^{4} - 136 \, b c^{3} x - 48 \, c^{4} - {\left(15 \, b^{3} c + 556 \, a b c^{2}\right)} x^{3} - 2 \, {\left(59 \, b^{2} c^{2} + 108 \, a c^{3}\right)} x^{2}\right)} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{768 \, c^{2} x^{3}}, -\frac{1920 \, \sqrt{-a} a b c^{2} x^{3} \arctan\left(\frac{{\left(2 \, a x^{2} + b x\right)} \sqrt{-a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a^{2} x^{2} + a b x + a c\right)}}\right) + 15 \, {\left(b^{4} - 24 \, a b^{2} c - 48 \, a^{2} c^{2}\right)} \sqrt{c} x^{3} \log\left(-\frac{8 \, b c x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 8 \, c^{2} - 4 \, {\left(b x^{2} + 2 \, c x\right)} \sqrt{c} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{x^{2}}\right) - 4 \, {\left(192 \, a^{2} c^{2} x^{4} - 136 \, b c^{3} x - 48 \, c^{4} - {\left(15 \, b^{3} c + 556 \, a b c^{2}\right)} x^{3} - 2 \, {\left(59 \, b^{2} c^{2} + 108 \, a c^{3}\right)} x^{2}\right)} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{768 \, c^{2} x^{3}}, \frac{480 \, a^{\frac{3}{2}} b c^{2} x^{3} \log\left(-8 \, a^{2} x^{2} - 8 \, a b x - b^{2} - 4 \, a c - 4 \, {\left(2 \, a x^{2} + b x\right)} \sqrt{a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}\right) - 15 \, {\left(b^{4} - 24 \, a b^{2} c - 48 \, a^{2} c^{2}\right)} \sqrt{-c} x^{3} \arctan\left(\frac{{\left(b x^{2} + 2 \, c x\right)} \sqrt{-c} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a c x^{2} + b c x + c^{2}\right)}}\right) + 2 \, {\left(192 \, a^{2} c^{2} x^{4} - 136 \, b c^{3} x - 48 \, c^{4} - {\left(15 \, b^{3} c + 556 \, a b c^{2}\right)} x^{3} - 2 \, {\left(59 \, b^{2} c^{2} + 108 \, a c^{3}\right)} x^{2}\right)} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{384 \, c^{2} x^{3}}, -\frac{960 \, \sqrt{-a} a b c^{2} x^{3} \arctan\left(\frac{{\left(2 \, a x^{2} + b x\right)} \sqrt{-a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a^{2} x^{2} + a b x + a c\right)}}\right) + 15 \, {\left(b^{4} - 24 \, a b^{2} c - 48 \, a^{2} c^{2}\right)} \sqrt{-c} x^{3} \arctan\left(\frac{{\left(b x^{2} + 2 \, c x\right)} \sqrt{-c} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a c x^{2} + b c x + c^{2}\right)}}\right) - 2 \, {\left(192 \, a^{2} c^{2} x^{4} - 136 \, b c^{3} x - 48 \, c^{4} - {\left(15 \, b^{3} c + 556 \, a b c^{2}\right)} x^{3} - 2 \, {\left(59 \, b^{2} c^{2} + 108 \, a c^{3}\right)} x^{2}\right)} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{384 \, c^{2} x^{3}}\right]"," ",0,"[1/768*(960*a^(3/2)*b*c^2*x^3*log(-8*a^2*x^2 - 8*a*b*x - b^2 - 4*a*c - 4*(2*a*x^2 + b*x)*sqrt(a)*sqrt((a*x^2 + b*x + c)/x^2)) - 15*(b^4 - 24*a*b^2*c - 48*a^2*c^2)*sqrt(c)*x^3*log(-(8*b*c*x + (b^2 + 4*a*c)*x^2 + 8*c^2 - 4*(b*x^2 + 2*c*x)*sqrt(c)*sqrt((a*x^2 + b*x + c)/x^2))/x^2) + 4*(192*a^2*c^2*x^4 - 136*b*c^3*x - 48*c^4 - (15*b^3*c + 556*a*b*c^2)*x^3 - 2*(59*b^2*c^2 + 108*a*c^3)*x^2)*sqrt((a*x^2 + b*x + c)/x^2))/(c^2*x^3), -1/768*(1920*sqrt(-a)*a*b*c^2*x^3*arctan(1/2*(2*a*x^2 + b*x)*sqrt(-a)*sqrt((a*x^2 + b*x + c)/x^2)/(a^2*x^2 + a*b*x + a*c)) + 15*(b^4 - 24*a*b^2*c - 48*a^2*c^2)*sqrt(c)*x^3*log(-(8*b*c*x + (b^2 + 4*a*c)*x^2 + 8*c^2 - 4*(b*x^2 + 2*c*x)*sqrt(c)*sqrt((a*x^2 + b*x + c)/x^2))/x^2) - 4*(192*a^2*c^2*x^4 - 136*b*c^3*x - 48*c^4 - (15*b^3*c + 556*a*b*c^2)*x^3 - 2*(59*b^2*c^2 + 108*a*c^3)*x^2)*sqrt((a*x^2 + b*x + c)/x^2))/(c^2*x^3), 1/384*(480*a^(3/2)*b*c^2*x^3*log(-8*a^2*x^2 - 8*a*b*x - b^2 - 4*a*c - 4*(2*a*x^2 + b*x)*sqrt(a)*sqrt((a*x^2 + b*x + c)/x^2)) - 15*(b^4 - 24*a*b^2*c - 48*a^2*c^2)*sqrt(-c)*x^3*arctan(1/2*(b*x^2 + 2*c*x)*sqrt(-c)*sqrt((a*x^2 + b*x + c)/x^2)/(a*c*x^2 + b*c*x + c^2)) + 2*(192*a^2*c^2*x^4 - 136*b*c^3*x - 48*c^4 - (15*b^3*c + 556*a*b*c^2)*x^3 - 2*(59*b^2*c^2 + 108*a*c^3)*x^2)*sqrt((a*x^2 + b*x + c)/x^2))/(c^2*x^3), -1/384*(960*sqrt(-a)*a*b*c^2*x^3*arctan(1/2*(2*a*x^2 + b*x)*sqrt(-a)*sqrt((a*x^2 + b*x + c)/x^2)/(a^2*x^2 + a*b*x + a*c)) + 15*(b^4 - 24*a*b^2*c - 48*a^2*c^2)*sqrt(-c)*x^3*arctan(1/2*(b*x^2 + 2*c*x)*sqrt(-c)*sqrt((a*x^2 + b*x + c)/x^2)/(a*c*x^2 + b*c*x + c^2)) - 2*(192*a^2*c^2*x^4 - 136*b*c^3*x - 48*c^4 - (15*b^3*c + 556*a*b*c^2)*x^3 - 2*(59*b^2*c^2 + 108*a*c^3)*x^2)*sqrt((a*x^2 + b*x + c)/x^2))/(c^2*x^3)]","A",0
450,1,709,0,1.362353," ","integrate((a+c/x^2+b/x)^(3/2),x, algorithm=""fricas"")","\left[\frac{12 \, \sqrt{a} b c x \log\left(-8 \, a^{2} x^{2} - 8 \, a b x - b^{2} - 4 \, a c - 4 \, {\left(2 \, a x^{2} + b x\right)} \sqrt{a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}\right) + 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{c} x \log\left(-\frac{8 \, b c x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 8 \, c^{2} - 4 \, {\left(b x^{2} + 2 \, c x\right)} \sqrt{c} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{x^{2}}\right) + 4 \, {\left(4 \, a c x^{2} - 5 \, b c x - 2 \, c^{2}\right)} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{16 \, c x}, -\frac{24 \, \sqrt{-a} b c x \arctan\left(\frac{{\left(2 \, a x^{2} + b x\right)} \sqrt{-a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a^{2} x^{2} + a b x + a c\right)}}\right) - 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{c} x \log\left(-\frac{8 \, b c x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 8 \, c^{2} - 4 \, {\left(b x^{2} + 2 \, c x\right)} \sqrt{c} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{x^{2}}\right) - 4 \, {\left(4 \, a c x^{2} - 5 \, b c x - 2 \, c^{2}\right)} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{16 \, c x}, \frac{6 \, \sqrt{a} b c x \log\left(-8 \, a^{2} x^{2} - 8 \, a b x - b^{2} - 4 \, a c - 4 \, {\left(2 \, a x^{2} + b x\right)} \sqrt{a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}\right) + 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{-c} x \arctan\left(\frac{{\left(b x^{2} + 2 \, c x\right)} \sqrt{-c} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a c x^{2} + b c x + c^{2}\right)}}\right) + 2 \, {\left(4 \, a c x^{2} - 5 \, b c x - 2 \, c^{2}\right)} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{8 \, c x}, -\frac{12 \, \sqrt{-a} b c x \arctan\left(\frac{{\left(2 \, a x^{2} + b x\right)} \sqrt{-a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a^{2} x^{2} + a b x + a c\right)}}\right) - 3 \, {\left(b^{2} + 4 \, a c\right)} \sqrt{-c} x \arctan\left(\frac{{\left(b x^{2} + 2 \, c x\right)} \sqrt{-c} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a c x^{2} + b c x + c^{2}\right)}}\right) - 2 \, {\left(4 \, a c x^{2} - 5 \, b c x - 2 \, c^{2}\right)} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{8 \, c x}\right]"," ",0,"[1/16*(12*sqrt(a)*b*c*x*log(-8*a^2*x^2 - 8*a*b*x - b^2 - 4*a*c - 4*(2*a*x^2 + b*x)*sqrt(a)*sqrt((a*x^2 + b*x + c)/x^2)) + 3*(b^2 + 4*a*c)*sqrt(c)*x*log(-(8*b*c*x + (b^2 + 4*a*c)*x^2 + 8*c^2 - 4*(b*x^2 + 2*c*x)*sqrt(c)*sqrt((a*x^2 + b*x + c)/x^2))/x^2) + 4*(4*a*c*x^2 - 5*b*c*x - 2*c^2)*sqrt((a*x^2 + b*x + c)/x^2))/(c*x), -1/16*(24*sqrt(-a)*b*c*x*arctan(1/2*(2*a*x^2 + b*x)*sqrt(-a)*sqrt((a*x^2 + b*x + c)/x^2)/(a^2*x^2 + a*b*x + a*c)) - 3*(b^2 + 4*a*c)*sqrt(c)*x*log(-(8*b*c*x + (b^2 + 4*a*c)*x^2 + 8*c^2 - 4*(b*x^2 + 2*c*x)*sqrt(c)*sqrt((a*x^2 + b*x + c)/x^2))/x^2) - 4*(4*a*c*x^2 - 5*b*c*x - 2*c^2)*sqrt((a*x^2 + b*x + c)/x^2))/(c*x), 1/8*(6*sqrt(a)*b*c*x*log(-8*a^2*x^2 - 8*a*b*x - b^2 - 4*a*c - 4*(2*a*x^2 + b*x)*sqrt(a)*sqrt((a*x^2 + b*x + c)/x^2)) + 3*(b^2 + 4*a*c)*sqrt(-c)*x*arctan(1/2*(b*x^2 + 2*c*x)*sqrt(-c)*sqrt((a*x^2 + b*x + c)/x^2)/(a*c*x^2 + b*c*x + c^2)) + 2*(4*a*c*x^2 - 5*b*c*x - 2*c^2)*sqrt((a*x^2 + b*x + c)/x^2))/(c*x), -1/8*(12*sqrt(-a)*b*c*x*arctan(1/2*(2*a*x^2 + b*x)*sqrt(-a)*sqrt((a*x^2 + b*x + c)/x^2)/(a^2*x^2 + a*b*x + a*c)) - 3*(b^2 + 4*a*c)*sqrt(-c)*x*arctan(1/2*(b*x^2 + 2*c*x)*sqrt(-c)*sqrt((a*x^2 + b*x + c)/x^2)/(a*c*x^2 + b*c*x + c^2)) - 2*(4*a*c*x^2 - 5*b*c*x - 2*c^2)*sqrt((a*x^2 + b*x + c)/x^2))/(c*x)]","A",0
451,1,590,0,1.252616," ","integrate((a+c/x^2+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, a x \sqrt{\frac{a x^{2} + b x + c}{x^{2}}} + \sqrt{a} b \log\left(-8 \, a^{2} x^{2} - 8 \, a b x - b^{2} - 4 \, a c - 4 \, {\left(2 \, a x^{2} + b x\right)} \sqrt{a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}\right) + 2 \, a \sqrt{c} \log\left(-\frac{8 \, b c x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 8 \, c^{2} - 4 \, {\left(b x^{2} + 2 \, c x\right)} \sqrt{c} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{x^{2}}\right)}{4 \, a}, \frac{2 \, a x \sqrt{\frac{a x^{2} + b x + c}{x^{2}}} - \sqrt{-a} b \arctan\left(\frac{{\left(2 \, a x^{2} + b x\right)} \sqrt{-a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a^{2} x^{2} + a b x + a c\right)}}\right) + a \sqrt{c} \log\left(-\frac{8 \, b c x + {\left(b^{2} + 4 \, a c\right)} x^{2} + 8 \, c^{2} - 4 \, {\left(b x^{2} + 2 \, c x\right)} \sqrt{c} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{x^{2}}\right)}{2 \, a}, \frac{4 \, a x \sqrt{\frac{a x^{2} + b x + c}{x^{2}}} + 4 \, a \sqrt{-c} \arctan\left(\frac{{\left(b x^{2} + 2 \, c x\right)} \sqrt{-c} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a c x^{2} + b c x + c^{2}\right)}}\right) + \sqrt{a} b \log\left(-8 \, a^{2} x^{2} - 8 \, a b x - b^{2} - 4 \, a c - 4 \, {\left(2 \, a x^{2} + b x\right)} \sqrt{a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}\right)}{4 \, a}, \frac{2 \, a x \sqrt{\frac{a x^{2} + b x + c}{x^{2}}} - \sqrt{-a} b \arctan\left(\frac{{\left(2 \, a x^{2} + b x\right)} \sqrt{-a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a^{2} x^{2} + a b x + a c\right)}}\right) + 2 \, a \sqrt{-c} \arctan\left(\frac{{\left(b x^{2} + 2 \, c x\right)} \sqrt{-c} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a c x^{2} + b c x + c^{2}\right)}}\right)}{2 \, a}\right]"," ",0,"[1/4*(4*a*x*sqrt((a*x^2 + b*x + c)/x^2) + sqrt(a)*b*log(-8*a^2*x^2 - 8*a*b*x - b^2 - 4*a*c - 4*(2*a*x^2 + b*x)*sqrt(a)*sqrt((a*x^2 + b*x + c)/x^2)) + 2*a*sqrt(c)*log(-(8*b*c*x + (b^2 + 4*a*c)*x^2 + 8*c^2 - 4*(b*x^2 + 2*c*x)*sqrt(c)*sqrt((a*x^2 + b*x + c)/x^2))/x^2))/a, 1/2*(2*a*x*sqrt((a*x^2 + b*x + c)/x^2) - sqrt(-a)*b*arctan(1/2*(2*a*x^2 + b*x)*sqrt(-a)*sqrt((a*x^2 + b*x + c)/x^2)/(a^2*x^2 + a*b*x + a*c)) + a*sqrt(c)*log(-(8*b*c*x + (b^2 + 4*a*c)*x^2 + 8*c^2 - 4*(b*x^2 + 2*c*x)*sqrt(c)*sqrt((a*x^2 + b*x + c)/x^2))/x^2))/a, 1/4*(4*a*x*sqrt((a*x^2 + b*x + c)/x^2) + 4*a*sqrt(-c)*arctan(1/2*(b*x^2 + 2*c*x)*sqrt(-c)*sqrt((a*x^2 + b*x + c)/x^2)/(a*c*x^2 + b*c*x + c^2)) + sqrt(a)*b*log(-8*a^2*x^2 - 8*a*b*x - b^2 - 4*a*c - 4*(2*a*x^2 + b*x)*sqrt(a)*sqrt((a*x^2 + b*x + c)/x^2)))/a, 1/2*(2*a*x*sqrt((a*x^2 + b*x + c)/x^2) - sqrt(-a)*b*arctan(1/2*(2*a*x^2 + b*x)*sqrt(-a)*sqrt((a*x^2 + b*x + c)/x^2)/(a^2*x^2 + a*b*x + a*c)) + 2*a*sqrt(-c)*arctan(1/2*(b*x^2 + 2*c*x)*sqrt(-c)*sqrt((a*x^2 + b*x + c)/x^2)/(a*c*x^2 + b*c*x + c^2)))/a]","A",0
452,1,171,0,1.294567," ","integrate(1/(a+c/x^2+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, a x \sqrt{\frac{a x^{2} + b x + c}{x^{2}}} + \sqrt{a} b \log\left(-8 \, a^{2} x^{2} - 8 \, a b x - b^{2} - 4 \, a c + 4 \, {\left(2 \, a x^{2} + b x\right)} \sqrt{a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}\right)}{4 \, a^{2}}, \frac{2 \, a x \sqrt{\frac{a x^{2} + b x + c}{x^{2}}} + \sqrt{-a} b \arctan\left(\frac{{\left(2 \, a x^{2} + b x\right)} \sqrt{-a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a^{2} x^{2} + a b x + a c\right)}}\right)}{2 \, a^{2}}\right]"," ",0,"[1/4*(4*a*x*sqrt((a*x^2 + b*x + c)/x^2) + sqrt(a)*b*log(-8*a^2*x^2 - 8*a*b*x - b^2 - 4*a*c + 4*(2*a*x^2 + b*x)*sqrt(a)*sqrt((a*x^2 + b*x + c)/x^2)))/a^2, 1/2*(2*a*x*sqrt((a*x^2 + b*x + c)/x^2) + sqrt(-a)*b*arctan(1/2*(2*a*x^2 + b*x)*sqrt(-a)*sqrt((a*x^2 + b*x + c)/x^2)/(a^2*x^2 + a*b*x + a*c)))/a^2]","A",0
453,1,465,0,1.346983," ","integrate(1/(a+c/x^2+b/x)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{3} c - 4 \, a b c^{2} + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2} + {\left(b^{4} - 4 \, a b^{2} c\right)} x\right)} \sqrt{a} \log\left(-8 \, a^{2} x^{2} - 8 \, a b x - b^{2} - 4 \, a c + 4 \, {\left(2 \, a x^{2} + b x\right)} \sqrt{a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}\right) + 4 \, {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x^{3} + {\left(3 \, a b^{3} - 10 \, a^{2} b c\right)} x^{2} + {\left(3 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x\right)} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{4 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{2} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x\right)}}, \frac{3 \, {\left(b^{3} c - 4 \, a b c^{2} + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2} + {\left(b^{4} - 4 \, a b^{2} c\right)} x\right)} \sqrt{-a} \arctan\left(\frac{{\left(2 \, a x^{2} + b x\right)} \sqrt{-a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a^{2} x^{2} + a b x + a c\right)}}\right) + 2 \, {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x^{3} + {\left(3 \, a b^{3} - 10 \, a^{2} b c\right)} x^{2} + {\left(3 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x\right)} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{2} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x\right)}}\right]"," ",0,"[1/4*(3*(b^3*c - 4*a*b*c^2 + (a*b^3 - 4*a^2*b*c)*x^2 + (b^4 - 4*a*b^2*c)*x)*sqrt(a)*log(-8*a^2*x^2 - 8*a*b*x - b^2 - 4*a*c + 4*(2*a*x^2 + b*x)*sqrt(a)*sqrt((a*x^2 + b*x + c)/x^2)) + 4*((a^2*b^2 - 4*a^3*c)*x^3 + (3*a*b^3 - 10*a^2*b*c)*x^2 + (3*a*b^2*c - 8*a^2*c^2)*x)*sqrt((a*x^2 + b*x + c)/x^2))/(a^3*b^2*c - 4*a^4*c^2 + (a^4*b^2 - 4*a^5*c)*x^2 + (a^3*b^3 - 4*a^4*b*c)*x), 1/2*(3*(b^3*c - 4*a*b*c^2 + (a*b^3 - 4*a^2*b*c)*x^2 + (b^4 - 4*a*b^2*c)*x)*sqrt(-a)*arctan(1/2*(2*a*x^2 + b*x)*sqrt(-a)*sqrt((a*x^2 + b*x + c)/x^2)/(a^2*x^2 + a*b*x + a*c)) + 2*((a^2*b^2 - 4*a^3*c)*x^3 + (3*a*b^3 - 10*a^2*b*c)*x^2 + (3*a*b^2*c - 8*a^2*c^2)*x)*sqrt((a*x^2 + b*x + c)/x^2))/(a^3*b^2*c - 4*a^4*c^2 + (a^4*b^2 - 4*a^5*c)*x^2 + (a^3*b^3 - 4*a^4*b*c)*x)]","A",0
454,1,1081,0,1.863394," ","integrate(1/(a+c/x^2+b/x)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{4} + 2 \, {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} x^{3} + {\left(b^{7} - 6 \, a b^{5} c + 32 \, a^{3} b c^{3}\right)} x^{2} + 2 \, {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} x\right)} \sqrt{a} \log\left(-8 \, a^{2} x^{2} - 8 \, a b x - b^{2} - 4 \, a c + 4 \, {\left(2 \, a x^{2} + b x\right)} \sqrt{a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}\right) + 4 \, {\left(3 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} x^{5} + 4 \, {\left(5 \, a^{2} b^{5} - 37 \, a^{3} b^{3} c + 64 \, a^{4} b c^{2}\right)} x^{4} + 3 \, {\left(5 \, a b^{6} - 30 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2} + 64 \, a^{4} c^{3}\right)} x^{3} + 6 \, {\left(5 \, a b^{5} c - 35 \, a^{2} b^{3} c^{2} + 52 \, a^{3} b c^{3}\right)} x^{2} + {\left(15 \, a b^{4} c^{2} - 100 \, a^{2} b^{2} c^{3} + 128 \, a^{3} c^{4}\right)} x\right)} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{12 \, {\left(a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4} + {\left(a^{6} b^{4} - 8 \, a^{7} b^{2} c + 16 \, a^{8} c^{2}\right)} x^{4} + 2 \, {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} x^{3} + {\left(a^{4} b^{6} - 6 \, a^{5} b^{4} c + 32 \, a^{7} c^{3}\right)} x^{2} + 2 \, {\left(a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3}\right)} x\right)}}, \frac{15 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} x^{4} + 2 \, {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} x^{3} + {\left(b^{7} - 6 \, a b^{5} c + 32 \, a^{3} b c^{3}\right)} x^{2} + 2 \, {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} x\right)} \sqrt{-a} \arctan\left(\frac{{\left(2 \, a x^{2} + b x\right)} \sqrt{-a} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{2 \, {\left(a^{2} x^{2} + a b x + a c\right)}}\right) + 2 \, {\left(3 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} x^{5} + 4 \, {\left(5 \, a^{2} b^{5} - 37 \, a^{3} b^{3} c + 64 \, a^{4} b c^{2}\right)} x^{4} + 3 \, {\left(5 \, a b^{6} - 30 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2} + 64 \, a^{4} c^{3}\right)} x^{3} + 6 \, {\left(5 \, a b^{5} c - 35 \, a^{2} b^{3} c^{2} + 52 \, a^{3} b c^{3}\right)} x^{2} + {\left(15 \, a b^{4} c^{2} - 100 \, a^{2} b^{2} c^{3} + 128 \, a^{3} c^{4}\right)} x\right)} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}}{6 \, {\left(a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4} + {\left(a^{6} b^{4} - 8 \, a^{7} b^{2} c + 16 \, a^{8} c^{2}\right)} x^{4} + 2 \, {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} x^{3} + {\left(a^{4} b^{6} - 6 \, a^{5} b^{4} c + 32 \, a^{7} c^{3}\right)} x^{2} + 2 \, {\left(a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3}\right)} x\right)}}\right]"," ",0,"[1/12*(15*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^4 + 2*(a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*x^3 + (b^7 - 6*a*b^5*c + 32*a^3*b*c^3)*x^2 + 2*(b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*x)*sqrt(a)*log(-8*a^2*x^2 - 8*a*b*x - b^2 - 4*a*c + 4*(2*a*x^2 + b*x)*sqrt(a)*sqrt((a*x^2 + b*x + c)/x^2)) + 4*(3*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*x^5 + 4*(5*a^2*b^5 - 37*a^3*b^3*c + 64*a^4*b*c^2)*x^4 + 3*(5*a*b^6 - 30*a^2*b^4*c + 16*a^3*b^2*c^2 + 64*a^4*c^3)*x^3 + 6*(5*a*b^5*c - 35*a^2*b^3*c^2 + 52*a^3*b*c^3)*x^2 + (15*a*b^4*c^2 - 100*a^2*b^2*c^3 + 128*a^3*c^4)*x)*sqrt((a*x^2 + b*x + c)/x^2))/(a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4 + (a^6*b^4 - 8*a^7*b^2*c + 16*a^8*c^2)*x^4 + 2*(a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*x^3 + (a^4*b^6 - 6*a^5*b^4*c + 32*a^7*c^3)*x^2 + 2*(a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3)*x), 1/6*(15*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*x^4 + 2*(a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*x^3 + (b^7 - 6*a*b^5*c + 32*a^3*b*c^3)*x^2 + 2*(b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*x)*sqrt(-a)*arctan(1/2*(2*a*x^2 + b*x)*sqrt(-a)*sqrt((a*x^2 + b*x + c)/x^2)/(a^2*x^2 + a*b*x + a*c)) + 2*(3*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*x^5 + 4*(5*a^2*b^5 - 37*a^3*b^3*c + 64*a^4*b*c^2)*x^4 + 3*(5*a*b^6 - 30*a^2*b^4*c + 16*a^3*b^2*c^2 + 64*a^4*c^3)*x^3 + 6*(5*a*b^5*c - 35*a^2*b^3*c^2 + 52*a^3*b*c^3)*x^2 + (15*a*b^4*c^2 - 100*a^2*b^2*c^3 + 128*a^3*c^4)*x)*sqrt((a*x^2 + b*x + c)/x^2))/(a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4 + (a^6*b^4 - 8*a^7*b^2*c + 16*a^8*c^2)*x^4 + 2*(a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*x^3 + (a^4*b^6 - 6*a^5*b^4*c + 32*a^7*c^3)*x^2 + 2*(a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3)*x)]","B",0
455,1,8,0,1.598956," ","integrate((a^2+b^2/x^2+2*a*b/x)^(1/2),x, algorithm=""fricas"")","a x + b \log\left(x\right)"," ",0,"a*x + b*log(x)","A",0
456,1,1059,0,0.956051," ","integrate(1/(c+a/x^4+b/x^2),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} c \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-2 \, {\left(a b^{2} - a^{2} c\right)} x + \sqrt{\frac{1}{2}} {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{3} - 3 \, a b c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-2 \, {\left(a b^{2} - a^{2} c\right)} x - \sqrt{\frac{1}{2}} {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{b^{3} - 3 \, a b c + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{3} - 3 \, a b c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-2 \, {\left(a b^{2} - a^{2} c\right)} x + \sqrt{\frac{1}{2}} {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{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^{3} - 3 \, a b c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-2 \, {\left(a b^{2} - a^{2} c\right)} x - \sqrt{\frac{1}{2}} {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{b^{3} - 3 \, a b c - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}}\right) - 2 \, x}{2 \, c}"," ",0,"-1/2*(sqrt(1/2)*c*sqrt(-(b^3 - 3*a*b*c + (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-2*(a*b^2 - a^2*c)*x + sqrt(1/2)*(b^4 - 5*a*b^2*c + 4*a^2*c^2 - (b^3*c^3 - 4*a*b*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(b^3 - 3*a*b*c + (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))) - sqrt(1/2)*c*sqrt(-(b^3 - 3*a*b*c + (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-2*(a*b^2 - a^2*c)*x - sqrt(1/2)*(b^4 - 5*a*b^2*c + 4*a^2*c^2 - (b^3*c^3 - 4*a*b*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(b^3 - 3*a*b*c + (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))) + sqrt(1/2)*c*sqrt(-(b^3 - 3*a*b*c - (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-2*(a*b^2 - a^2*c)*x + sqrt(1/2)*(b^4 - 5*a*b^2*c + 4*a^2*c^2 + (b^3*c^3 - 4*a*b*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(b^3 - 3*a*b*c - (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))) - sqrt(1/2)*c*sqrt(-(b^3 - 3*a*b*c - (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-2*(a*b^2 - a^2*c)*x - sqrt(1/2)*(b^4 - 5*a*b^2*c + 4*a^2*c^2 + (b^3*c^3 - 4*a*b*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(b^3 - 3*a*b*c - (b^2*c^3 - 4*a*c^4)*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))) - 2*x)/c","B",0
457,1,5260,0,3.178677," ","integrate(1/(c+a/x^6+b/x^3),x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} c \left(-\frac{b^{3} - 2 \, a b c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left(b^{8} c^{4} - 13 \, a b^{6} c^{5} + 60 \, a^{2} b^{4} c^{6} - 112 \, a^{3} b^{2} c^{7} + 64 \, a^{4} c^{8}\right)} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}} - \sqrt{3} {\left(b^{9} - 11 \, a b^{7} c + 42 \, a^{2} b^{5} c^{2} - 62 \, a^{3} b^{3} c^{3} + 24 \, a^{4} b c^{4}\right)} x\right)} \left(-\frac{b^{3} - 2 \, a b c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{6}} {\left(\sqrt{3} {\left(b^{8} c^{4} - 13 \, a b^{6} c^{5} + 60 \, a^{2} b^{4} c^{6} - 112 \, a^{3} b^{2} c^{7} + 64 \, a^{4} c^{8}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}} - \sqrt{3} {\left(b^{9} - 11 \, a b^{7} c + 42 \, a^{2} b^{5} c^{2} - 62 \, a^{3} b^{3} c^{3} + 24 \, a^{4} b c^{4}\right)}\right)} \left(-\frac{b^{3} - 2 \, a b c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{2}{3}} \sqrt{\frac{2 \, {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 2 \, a^{4} c^{2}\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{8} - 10 \, a b^{6} c + 34 \, a^{2} b^{4} c^{2} - 44 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} - {\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)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}\right)} \left(-\frac{b^{3} - 2 \, a b c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{2}{3}} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 16 \, a^{3} b c^{6}\right)} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}} - {\left(a b^{6} - 8 \, a^{2} b^{4} c + 18 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} x\right)} \left(-\frac{b^{3} - 2 \, a b c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}}}{a^{2} b^{4} - 4 \, a^{3} b^{2} c + 2 \, a^{4} c^{2}}} + 2 \, \sqrt{3} {\left(a^{3} b^{4} - 4 \, a^{4} b^{2} c + 2 \, a^{5} c^{2}\right)}}{6 \, {\left(a^{3} b^{4} - 4 \, a^{4} b^{2} c + 2 \, a^{5} c^{2}\right)}}\right) - 4 \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} c \left(-\frac{b^{3} - 2 \, a b c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left(b^{8} c^{4} - 13 \, a b^{6} c^{5} + 60 \, a^{2} b^{4} c^{6} - 112 \, a^{3} b^{2} c^{7} + 64 \, a^{4} c^{8}\right)} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}} + \sqrt{3} {\left(b^{9} - 11 \, a b^{7} c + 42 \, a^{2} b^{5} c^{2} - 62 \, a^{3} b^{3} c^{3} + 24 \, a^{4} b c^{4}\right)} x\right)} \left(-\frac{b^{3} - 2 \, a b c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{6}} {\left(\sqrt{3} {\left(b^{8} c^{4} - 13 \, a b^{6} c^{5} + 60 \, a^{2} b^{4} c^{6} - 112 \, a^{3} b^{2} c^{7} + 64 \, a^{4} c^{8}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}} + \sqrt{3} {\left(b^{9} - 11 \, a b^{7} c + 42 \, a^{2} b^{5} c^{2} - 62 \, a^{3} b^{3} c^{3} + 24 \, a^{4} b c^{4}\right)}\right)} \left(-\frac{b^{3} - 2 \, a b c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{2}{3}} \sqrt{\frac{2 \, {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 2 \, a^{4} c^{2}\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{8} - 10 \, a b^{6} c + 34 \, a^{2} b^{4} c^{2} - 44 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + {\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)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}\right)} \left(-\frac{b^{3} - 2 \, a b c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 16 \, a^{3} b c^{6}\right)} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}} + {\left(a b^{6} - 8 \, a^{2} b^{4} c + 18 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} x\right)} \left(-\frac{b^{3} - 2 \, a b c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}}}{a^{2} b^{4} - 4 \, a^{3} b^{2} c + 2 \, a^{4} c^{2}}} - 2 \, \sqrt{3} {\left(a^{3} b^{4} - 4 \, a^{4} b^{2} c + 2 \, a^{5} c^{2}\right)}}{6 \, {\left(a^{3} b^{4} - 4 \, a^{4} b^{2} c + 2 \, a^{5} c^{2}\right)}}\right) - \left(\frac{1}{2}\right)^{\frac{1}{3}} c \left(-\frac{b^{3} - 2 \, a b c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}} \log\left(2 \, {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 2 \, a^{4} c^{2}\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{8} - 10 \, a b^{6} c + 34 \, a^{2} b^{4} c^{2} - 44 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} - {\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)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}\right)} \left(-\frac{b^{3} - 2 \, a b c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{2}{3}} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 16 \, a^{3} b c^{6}\right)} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}} - {\left(a b^{6} - 8 \, a^{2} b^{4} c + 18 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} x\right)} \left(-\frac{b^{3} - 2 \, a b c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}}\right) - \left(\frac{1}{2}\right)^{\frac{1}{3}} c \left(-\frac{b^{3} - 2 \, a b c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}} \log\left(2 \, {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 2 \, a^{4} c^{2}\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(b^{8} - 10 \, a b^{6} c + 34 \, a^{2} b^{4} c^{2} - 44 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + {\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)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}\right)} \left(-\frac{b^{3} - 2 \, a b c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 16 \, a^{3} b c^{6}\right)} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}} + {\left(a b^{6} - 8 \, a^{2} b^{4} c + 18 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} x\right)} \left(-\frac{b^{3} - 2 \, a b c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}}\right) + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} c \left(-\frac{b^{3} - 2 \, a b c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}} \log\left(2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} x + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{6} - 8 \, a b^{4} c + 18 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3} - {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}\right)} \left(-\frac{b^{3} - 2 \, a b c + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}}\right) + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} c \left(-\frac{b^{3} - 2 \, a b c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}} \log\left(2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} x + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{6} - 8 \, a b^{4} c + 18 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3} + {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}\right)} \left(-\frac{b^{3} - 2 \, a b c - {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}}}}{b^{2} c^{4} - 4 \, a c^{5}}\right)^{\frac{1}{3}}\right) + 6 \, x}{6 \, c}"," ",0,"1/6*(4*sqrt(3)*(1/2)^(1/3)*c*(-(b^3 - 2*a*b*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3)*arctan(-1/6*(2*(1/2)^(2/3)*(sqrt(3)*(b^8*c^4 - 13*a*b^6*c^5 + 60*a^2*b^4*c^6 - 112*a^3*b^2*c^7 + 64*a^4*c^8)*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)) - sqrt(3)*(b^9 - 11*a*b^7*c + 42*a^2*b^5*c^2 - 62*a^3*b^3*c^3 + 24*a^4*b*c^4)*x)*(-(b^3 - 2*a*b*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(2/3) - (1/2)^(1/6)*(sqrt(3)*(b^8*c^4 - 13*a*b^6*c^5 + 60*a^2*b^4*c^6 - 112*a^3*b^2*c^7 + 64*a^4*c^8)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)) - sqrt(3)*(b^9 - 11*a*b^7*c + 42*a^2*b^5*c^2 - 62*a^3*b^3*c^3 + 24*a^4*b*c^4))*(-(b^3 - 2*a*b*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(2/3)*sqrt((2*(a^2*b^4 - 4*a^3*b^2*c + 2*a^4*c^2)*x^2 + (1/2)^(2/3)*(b^8 - 10*a*b^6*c + 34*a^2*b^4*c^2 - 44*a^3*b^2*c^3 + 16*a^4*c^4 - (b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))*(-(b^3 - 2*a*b*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(2/3) + (1/2)^(1/3)*((a*b^5*c^4 - 8*a^2*b^3*c^5 + 16*a^3*b*c^6)*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)) - (a*b^6 - 8*a^2*b^4*c + 18*a^3*b^2*c^2 - 8*a^4*c^3)*x)*(-(b^3 - 2*a*b*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3))/(a^2*b^4 - 4*a^3*b^2*c + 2*a^4*c^2)) + 2*sqrt(3)*(a^3*b^4 - 4*a^4*b^2*c + 2*a^5*c^2))/(a^3*b^4 - 4*a^4*b^2*c + 2*a^5*c^2)) - 4*sqrt(3)*(1/2)^(1/3)*c*(-(b^3 - 2*a*b*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3)*arctan(-1/6*(2*(1/2)^(2/3)*(sqrt(3)*(b^8*c^4 - 13*a*b^6*c^5 + 60*a^2*b^4*c^6 - 112*a^3*b^2*c^7 + 64*a^4*c^8)*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)) + sqrt(3)*(b^9 - 11*a*b^7*c + 42*a^2*b^5*c^2 - 62*a^3*b^3*c^3 + 24*a^4*b*c^4)*x)*(-(b^3 - 2*a*b*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(2/3) - (1/2)^(1/6)*(sqrt(3)*(b^8*c^4 - 13*a*b^6*c^5 + 60*a^2*b^4*c^6 - 112*a^3*b^2*c^7 + 64*a^4*c^8)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)) + sqrt(3)*(b^9 - 11*a*b^7*c + 42*a^2*b^5*c^2 - 62*a^3*b^3*c^3 + 24*a^4*b*c^4))*(-(b^3 - 2*a*b*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(2/3)*sqrt((2*(a^2*b^4 - 4*a^3*b^2*c + 2*a^4*c^2)*x^2 + (1/2)^(2/3)*(b^8 - 10*a*b^6*c + 34*a^2*b^4*c^2 - 44*a^3*b^2*c^3 + 16*a^4*c^4 + (b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))*(-(b^3 - 2*a*b*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(2/3) - (1/2)^(1/3)*((a*b^5*c^4 - 8*a^2*b^3*c^5 + 16*a^3*b*c^6)*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)) + (a*b^6 - 8*a^2*b^4*c + 18*a^3*b^2*c^2 - 8*a^4*c^3)*x)*(-(b^3 - 2*a*b*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3))/(a^2*b^4 - 4*a^3*b^2*c + 2*a^4*c^2)) - 2*sqrt(3)*(a^3*b^4 - 4*a^4*b^2*c + 2*a^5*c^2))/(a^3*b^4 - 4*a^4*b^2*c + 2*a^5*c^2)) - (1/2)^(1/3)*c*(-(b^3 - 2*a*b*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3)*log(2*(a^2*b^4 - 4*a^3*b^2*c + 2*a^4*c^2)*x^2 + (1/2)^(2/3)*(b^8 - 10*a*b^6*c + 34*a^2*b^4*c^2 - 44*a^3*b^2*c^3 + 16*a^4*c^4 - (b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))*(-(b^3 - 2*a*b*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(2/3) + (1/2)^(1/3)*((a*b^5*c^4 - 8*a^2*b^3*c^5 + 16*a^3*b*c^6)*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)) - (a*b^6 - 8*a^2*b^4*c + 18*a^3*b^2*c^2 - 8*a^4*c^3)*x)*(-(b^3 - 2*a*b*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3)) - (1/2)^(1/3)*c*(-(b^3 - 2*a*b*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3)*log(2*(a^2*b^4 - 4*a^3*b^2*c + 2*a^4*c^2)*x^2 + (1/2)^(2/3)*(b^8 - 10*a*b^6*c + 34*a^2*b^4*c^2 - 44*a^3*b^2*c^3 + 16*a^4*c^4 + (b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))*(-(b^3 - 2*a*b*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(2/3) - (1/2)^(1/3)*((a*b^5*c^4 - 8*a^2*b^3*c^5 + 16*a^3*b*c^6)*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)) + (a*b^6 - 8*a^2*b^4*c + 18*a^3*b^2*c^2 - 8*a^4*c^3)*x)*(-(b^3 - 2*a*b*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3)) + 2*(1/2)^(1/3)*c*(-(b^3 - 2*a*b*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3)*log(2*(a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2)*x + (1/2)^(1/3)*(b^6 - 8*a*b^4*c + 18*a^2*b^2*c^2 - 8*a^3*c^3 - (b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))*(-(b^3 - 2*a*b*c + (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3)) + 2*(1/2)^(1/3)*c*(-(b^3 - 2*a*b*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3)*log(2*(a*b^4 - 4*a^2*b^2*c + 2*a^3*c^2)*x + (1/2)^(1/3)*(b^6 - 8*a*b^4*c + 18*a^2*b^2*c^2 - 8*a^3*c^3 + (b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))*(-(b^3 - 2*a*b*c - (b^2*c^4 - 4*a*c^5)*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)))/(b^2*c^4 - 4*a*c^5))^(1/3)) + 6*x)/c","B",0
458,1,5082,0,2.634263," ","integrate(1/(c+a/x^8+b/x^4),x, algorithm=""fricas"")","-\frac{4 \, c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \arctan\left(\frac{{\left(2 \, \sqrt{\frac{1}{2}} {\left({\left(b^{10} c^{5} - 16 \, a b^{8} c^{6} + 98 \, a^{2} b^{6} c^{7} - 280 \, a^{3} b^{4} c^{8} + 352 \, a^{4} b^{2} c^{9} - 128 \, a^{5} c^{10}\right)} x \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}} + {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 128 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5}\right)} x\right)} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}} - {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 128 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5} + {\left(b^{10} c^{5} - 16 \, a b^{8} c^{6} + 98 \, a^{2} b^{6} c^{7} - 280 \, a^{3} b^{4} c^{8} + 352 \, a^{4} b^{2} c^{9} - 128 \, a^{5} c^{10}\right)} \sqrt{\frac{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}}{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{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}} \sqrt{\frac{2 \, {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}\right)} x^{2} + \sqrt{\frac{1}{2}} {\left(b^{8} - 9 \, a b^{6} c + 27 \, a^{2} b^{4} c^{2} - 30 \, a^{3} b^{2} c^{3} + 8 \, a^{4} c^{4} + {\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)} \sqrt{\frac{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}}{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{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}}{a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}}}{4 \, {\left(a^{4} b^{4} - 3 \, a^{5} b^{2} c + a^{6} c^{2}\right)}}\right) - 4 \, c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} {\left({\left(b^{10} c^{5} - 16 \, a b^{8} c^{6} + 98 \, a^{2} b^{6} c^{7} - 280 \, a^{3} b^{4} c^{8} + 352 \, a^{4} b^{2} c^{9} - 128 \, a^{5} c^{10}\right)} x \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}} - {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 128 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5}\right)} x\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}} + {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 128 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5} - {\left(b^{10} c^{5} - 16 \, a b^{8} c^{6} + 98 \, a^{2} b^{6} c^{7} - 280 \, a^{3} b^{4} c^{8} + 352 \, a^{4} b^{2} c^{9} - 128 \, a^{5} c^{10}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}} \sqrt{\frac{2 \, {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}\right)} x^{2} + \sqrt{\frac{1}{2}} {\left(b^{8} - 9 \, a b^{6} c + 27 \, a^{2} b^{4} c^{2} - 30 \, a^{3} b^{2} c^{3} + 8 \, a^{4} c^{4} - {\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)} \sqrt{\frac{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}}{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{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}}{a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}}}}{4 \, {\left(a^{4} b^{4} - 3 \, a^{5} b^{2} c + a^{6} c^{2}\right)}}\right) - c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \log\left({\left(a b^{4} - 3 \, a^{2} b^{2} c + a^{3} c^{2}\right)} x + \frac{1}{2} \, {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} - {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}}\right) + c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \log\left({\left(a b^{4} - 3 \, a^{2} b^{2} c + a^{3} c^{2}\right)} x - \frac{1}{2} \, {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} - {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}}\right) - c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \log\left({\left(a b^{4} - 3 \, a^{2} b^{2} c + a^{3} c^{2}\right)} x + \frac{1}{2} \, {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} + {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}}\right) + c \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}} \log\left({\left(a b^{4} - 3 \, a^{2} b^{2} c + a^{3} c^{2}\right)} x - \frac{1}{2} \, {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} + {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{\frac{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}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}}}}\right) - 4 \, x}{4 \, c}"," ",0,"-1/4*(4*c*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*arctan(1/4*(2*sqrt(1/2)*((b^10*c^5 - 16*a*b^8*c^6 + 98*a^2*b^6*c^7 - 280*a^3*b^4*c^8 + 352*a^4*b^2*c^9 - 128*a^5*c^10)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)) + (b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 128*a^4*b^3*c^4 - 32*a^5*b*c^5)*x)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)) - (b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 128*a^4*b^3*c^4 - 32*a^5*b*c^5 + (b^10*c^5 - 16*a*b^8*c^6 + 98*a^2*b^6*c^7 - 280*a^3*b^4*c^8 + 352*a^4*b^2*c^9 - 128*a^5*c^10)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7))*sqrt((2*(a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)*x^2 + sqrt(1/2)*(b^8 - 9*a*b^6*c + 27*a^2*b^4*c^2 - 30*a^3*b^2*c^3 + 8*a^4*c^4 + (b^7*c^5 - 12*a*b^5*c^6 + 48*a^2*b^3*c^7 - 64*a^3*b*c^8)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))/(a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))/(a^4*b^4 - 3*a^5*b^2*c + a^6*c^2)) - 4*c*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*arctan(1/4*(2*sqrt(1/2)*((b^10*c^5 - 16*a*b^8*c^6 + 98*a^2*b^6*c^7 - 280*a^3*b^4*c^8 + 352*a^4*b^2*c^9 - 128*a^5*c^10)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)) - (b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 128*a^4*b^3*c^4 - 32*a^5*b*c^5)*x)*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)) + (b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 128*a^4*b^3*c^4 - 32*a^5*b*c^5 - (b^10*c^5 - 16*a*b^8*c^6 + 98*a^2*b^6*c^7 - 280*a^3*b^4*c^8 + 352*a^4*b^2*c^9 - 128*a^5*c^10)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7))*sqrt((2*(a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)*x^2 + sqrt(1/2)*(b^8 - 9*a*b^6*c + 27*a^2*b^4*c^2 - 30*a^3*b^2*c^3 + 8*a^4*c^4 - (b^7*c^5 - 12*a*b^5*c^6 + 48*a^2*b^3*c^7 - 64*a^3*b*c^8)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))/(a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)))/(a^4*b^4 - 3*a^5*b^2*c + a^6*c^2)) - c*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*log((a*b^4 - 3*a^2*b^2*c + a^3*c^2)*x + 1/2*(b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3 - (b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))) + c*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*log((a*b^4 - 3*a^2*b^2*c + a^3*c^2)*x - 1/2*(b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3 - (b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))) - c*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*log((a*b^4 - 3*a^2*b^2*c + a^3*c^2)*x + 1/2*(b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3 + (b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))) + c*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))*log((a*b^4 - 3*a^2*b^2*c + a^3*c^2)*x - 1/2*(b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3 + (b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt(sqrt(1/2)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*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)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)))) - 4*x)/c","B",0
459,-1,0,0,0.000000," ","integrate((a+c*x+b*x^(1/2))^(1/2)/x,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
460,1,53,0,1.068209," ","integrate((1/4/c*b^2+c*x+b*x^(1/2))^2,x, algorithm=""fricas"")","\frac{80 \, c^{4} x^{3} + 180 \, b^{2} c^{2} x^{2} + 15 \, b^{4} x + 16 \, {\left(12 \, b c^{3} x^{2} + 5 \, b^{3} c x\right)} \sqrt{x}}{240 \, c^{2}}"," ",0,"1/240*(80*c^4*x^3 + 180*b^2*c^2*x^2 + 15*b^4*x + 16*(12*b*c^3*x^2 + 5*b^3*c*x)*sqrt(x))/c^2","A",0
461,-1,0,0,0.000000," ","integrate(1/(a^2+b^2*x+2*a*b*x^(1/2))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
462,1,84,0,1.467345," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(7/2),x, algorithm=""fricas"")","\frac{7}{3} \, a b^{6} x^{3} + \frac{35}{2} \, a^{4} b^{3} x^{2} + a^{7} x + \frac{63}{40} \, {\left(5 \, a^{2} b^{5} x^{2} + 8 \, a^{5} b^{2} x\right)} x^{\frac{2}{3}} + \frac{3}{20} \, {\left(2 \, b^{7} x^{3} + 100 \, a^{3} b^{4} x^{2} + 35 \, a^{6} b x\right)} x^{\frac{1}{3}}"," ",0,"7/3*a*b^6*x^3 + 35/2*a^4*b^3*x^2 + a^7*x + 63/40*(5*a^2*b^5*x^2 + 8*a^5*b^2*x)*x^(2/3) + 3/20*(2*b^7*x^3 + 100*a^3*b^4*x^2 + 35*a^6*b*x)*x^(1/3)","A",0
463,1,61,0,1.116537," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(5/2),x, algorithm=""fricas"")","5 \, a^{2} b^{3} x^{2} + a^{5} x + \frac{3}{8} \, {\left(b^{5} x^{2} + 16 \, a^{3} b^{2} x\right)} x^{\frac{2}{3}} + \frac{15}{28} \, {\left(4 \, a b^{4} x^{2} + 7 \, a^{4} b x\right)} x^{\frac{1}{3}}"," ",0,"5*a^2*b^3*x^2 + a^5*x + 3/8*(b^5*x^2 + 16*a^3*b^2*x)*x^(2/3) + 15/28*(4*a*b^4*x^2 + 7*a^4*b*x)*x^(1/3)","A",0
464,1,32,0,1.395172," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(3/2),x, algorithm=""fricas"")","\frac{1}{2} \, b^{3} x^{2} + \frac{9}{5} \, a b^{2} x^{\frac{5}{3}} + \frac{9}{4} \, a^{2} b x^{\frac{4}{3}} + a^{3} x"," ",0,"1/2*b^3*x^2 + 9/5*a*b^2*x^(5/3) + 9/4*a^2*b*x^(4/3) + a^3*x","A",0
465,1,10,0,0.949875," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(1/2),x, algorithm=""fricas"")","\frac{3}{4} \, b x^{\frac{4}{3}} + a x"," ",0,"3/4*b*x^(4/3) + a*x","A",0
466,1,33,0,1.370761," ","integrate(1/(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(1/2),x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, a^{2} \log\left(b x^{\frac{1}{3}} + a\right) + b^{2} x^{\frac{2}{3}} - 2 \, a b x^{\frac{1}{3}}\right)}}{2 \, b^{3}}"," ",0,"3/2*(2*a^2*log(b*x^(1/3) + a) + b^2*x^(2/3) - 2*a*b*x^(1/3))/b^3","A",0
467,1,113,0,1.231481," ","integrate(1/(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(3/2),x, algorithm=""fricas"")","\frac{3 \, {\left(6 \, a^{3} b^{3} x + 3 \, a^{6} + 2 \, {\left(b^{6} x^{2} + 2 \, a^{3} b^{3} x + a^{6}\right)} \log\left(b x^{\frac{1}{3}} + a\right) + {\left(4 \, a b^{5} x + a^{4} b^{2}\right)} x^{\frac{2}{3}} - {\left(5 \, a^{2} b^{4} x + 2 \, a^{5} b\right)} x^{\frac{1}{3}}\right)}}{2 \, {\left(b^{9} x^{2} + 2 \, a^{3} b^{6} x + a^{6} b^{3}\right)}}"," ",0,"3/2*(6*a^3*b^3*x + 3*a^6 + 2*(b^6*x^2 + 2*a^3*b^3*x + a^6)*log(b*x^(1/3) + a) + (4*a*b^5*x + a^4*b^2)*x^(2/3) - (5*a^2*b^4*x + 2*a^5*b)*x^(1/3))/(b^9*x^2 + 2*a^3*b^6*x + a^6*b^3)","A",0
468,1,136,0,1.136593," ","integrate(1/(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(5/2),x, algorithm=""fricas"")","\frac{20 \, a b^{9} x^{3} - 60 \, a^{4} b^{6} x^{2} - a^{10} - 9 \, {\left(5 \, a^{2} b^{8} x^{2} - 4 \, a^{5} b^{5} x\right)} x^{\frac{2}{3}} - 3 \, {\left(2 \, b^{10} x^{3} - 20 \, a^{3} b^{7} x^{2} + 5 \, a^{6} b^{4} x\right)} x^{\frac{1}{3}}}{4 \, {\left(b^{15} x^{4} + 4 \, a^{3} b^{12} x^{3} + 6 \, a^{6} b^{9} x^{2} + 4 \, a^{9} b^{6} x + a^{12} b^{3}\right)}}"," ",0,"1/4*(20*a*b^9*x^3 - 60*a^4*b^6*x^2 - a^10 - 9*(5*a^2*b^8*x^2 - 4*a^5*b^5*x)*x^(2/3) - 3*(2*b^10*x^3 - 20*a^3*b^7*x^2 + 5*a^6*b^4*x)*x^(1/3))/(b^15*x^4 + 4*a^3*b^12*x^3 + 6*a^6*b^9*x^2 + 4*a^9*b^6*x + a^12*b^3)","A",0
469,1,209,0,1.308953," ","integrate(1/(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(7/2),x, algorithm=""fricas"")","-\frac{280 \, a^{2} b^{12} x^{4} - 1400 \, a^{5} b^{9} x^{3} + 735 \, a^{8} b^{6} x^{2} - 14 \, a^{11} b^{3} x + a^{14} + 3 \, {\left(5 \, b^{14} x^{4} - 210 \, a^{3} b^{11} x^{3} + 483 \, a^{6} b^{8} x^{2} - 112 \, a^{9} b^{5} x\right)} x^{\frac{2}{3}} - 3 \, {\left(28 \, a b^{13} x^{4} - 357 \, a^{4} b^{10} x^{3} + 390 \, a^{7} b^{7} x^{2} - 35 \, a^{10} b^{4} x\right)} x^{\frac{1}{3}}}{20 \, {\left(b^{21} x^{6} + 6 \, a^{3} b^{18} x^{5} + 15 \, a^{6} b^{15} x^{4} + 20 \, a^{9} b^{12} x^{3} + 15 \, a^{12} b^{9} x^{2} + 6 \, a^{15} b^{6} x + a^{18} b^{3}\right)}}"," ",0,"-1/20*(280*a^2*b^12*x^4 - 1400*a^5*b^9*x^3 + 735*a^8*b^6*x^2 - 14*a^11*b^3*x + a^14 + 3*(5*b^14*x^4 - 210*a^3*b^11*x^3 + 483*a^6*b^8*x^2 - 112*a^9*b^5*x)*x^(2/3) - 3*(28*a*b^13*x^4 - 357*a^4*b^10*x^3 + 390*a^7*b^7*x^2 - 35*a^10*b^4*x)*x^(1/3))/(b^21*x^6 + 6*a^3*b^18*x^5 + 15*a^6*b^15*x^4 + 20*a^9*b^12*x^3 + 15*a^12*b^9*x^2 + 6*a^15*b^6*x + a^18*b^3)","A",0
470,1,275,0,1.573911," ","integrate(1/(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(9/2),x, algorithm=""fricas"")","-\frac{28 \, b^{18} x^{6} - 2856 \, a^{3} b^{15} x^{5} + 18186 \, a^{6} b^{12} x^{4} - 20608 \, a^{9} b^{9} x^{3} + 4200 \, a^{12} b^{6} x^{2} - 48 \, a^{15} b^{3} x + a^{18} - 27 \, {\left(8 \, a b^{17} x^{5} - 244 \, a^{4} b^{14} x^{4} + 840 \, a^{7} b^{11} x^{3} - 553 \, a^{10} b^{8} x^{2} + 56 \, a^{13} b^{5} x\right)} x^{\frac{2}{3}} + 27 \, {\left(35 \, a^{2} b^{16} x^{5} - 448 \, a^{5} b^{13} x^{4} + 876 \, a^{8} b^{10} x^{3} - 328 \, a^{11} b^{7} x^{2} + 14 \, a^{14} b^{4} x\right)} x^{\frac{1}{3}}}{56 \, {\left(b^{27} x^{8} + 8 \, a^{3} b^{24} x^{7} + 28 \, a^{6} b^{21} x^{6} + 56 \, a^{9} b^{18} x^{5} + 70 \, a^{12} b^{15} x^{4} + 56 \, a^{15} b^{12} x^{3} + 28 \, a^{18} b^{9} x^{2} + 8 \, a^{21} b^{6} x + a^{24} b^{3}\right)}}"," ",0,"-1/56*(28*b^18*x^6 - 2856*a^3*b^15*x^5 + 18186*a^6*b^12*x^4 - 20608*a^9*b^9*x^3 + 4200*a^12*b^6*x^2 - 48*a^15*b^3*x + a^18 - 27*(8*a*b^17*x^5 - 244*a^4*b^14*x^4 + 840*a^7*b^11*x^3 - 553*a^10*b^8*x^2 + 56*a^13*b^5*x)*x^(2/3) + 27*(35*a^2*b^16*x^5 - 448*a^5*b^13*x^4 + 876*a^8*b^10*x^3 - 328*a^11*b^7*x^2 + 14*a^14*b^4*x)*x^(1/3))/(b^27*x^8 + 8*a^3*b^24*x^7 + 28*a^6*b^21*x^6 + 56*a^9*b^18*x^5 + 70*a^12*b^15*x^4 + 56*a^15*b^12*x^3 + 28*a^18*b^9*x^2 + 8*a^21*b^6*x + a^24*b^3)","B",0
471,1,343,0,1.412003," ","integrate(1/(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(11/2),x, algorithm=""fricas"")","\frac{440 \, a b^{21} x^{7} - 25630 \, a^{4} b^{18} x^{6} + 186252 \, a^{7} b^{15} x^{5} - 326150 \, a^{10} b^{12} x^{4} + 154000 \, a^{13} b^{9} x^{3} - 16005 \, a^{16} b^{6} x^{2} + 110 \, a^{19} b^{3} x - a^{22} - 27 \, {\left(88 \, a^{2} b^{20} x^{6} - 2200 \, a^{5} b^{17} x^{5} + 9625 \, a^{8} b^{14} x^{4} - 10910 \, a^{11} b^{11} x^{3} + 3245 \, a^{14} b^{8} x^{2} - 176 \, a^{17} b^{5} x\right)} x^{\frac{2}{3}} - 9 \, {\left(5 \, b^{22} x^{7} - 990 \, a^{3} b^{19} x^{6} + 12705 \, a^{6} b^{16} x^{5} - 34760 \, a^{9} b^{13} x^{4} + 25542 \, a^{12} b^{10} x^{3} - 4620 \, a^{15} b^{7} x^{2} + 110 \, a^{18} b^{4} x\right)} x^{\frac{1}{3}}}{120 \, {\left(b^{33} x^{10} + 10 \, a^{3} b^{30} x^{9} + 45 \, a^{6} b^{27} x^{8} + 120 \, a^{9} b^{24} x^{7} + 210 \, a^{12} b^{21} x^{6} + 252 \, a^{15} b^{18} x^{5} + 210 \, a^{18} b^{15} x^{4} + 120 \, a^{21} b^{12} x^{3} + 45 \, a^{24} b^{9} x^{2} + 10 \, a^{27} b^{6} x + a^{30} b^{3}\right)}}"," ",0,"1/120*(440*a*b^21*x^7 - 25630*a^4*b^18*x^6 + 186252*a^7*b^15*x^5 - 326150*a^10*b^12*x^4 + 154000*a^13*b^9*x^3 - 16005*a^16*b^6*x^2 + 110*a^19*b^3*x - a^22 - 27*(88*a^2*b^20*x^6 - 2200*a^5*b^17*x^5 + 9625*a^8*b^14*x^4 - 10910*a^11*b^11*x^3 + 3245*a^14*b^8*x^2 - 176*a^17*b^5*x)*x^(2/3) - 9*(5*b^22*x^7 - 990*a^3*b^19*x^6 + 12705*a^6*b^16*x^5 - 34760*a^9*b^13*x^4 + 25542*a^12*b^10*x^3 - 4620*a^15*b^7*x^2 + 110*a^18*b^4*x)*x^(1/3))/(b^33*x^10 + 10*a^3*b^30*x^9 + 45*a^6*b^27*x^8 + 120*a^9*b^24*x^7 + 210*a^12*b^21*x^6 + 252*a^15*b^18*x^5 + 210*a^18*b^15*x^4 + 120*a^21*b^12*x^3 + 45*a^24*b^9*x^2 + 10*a^27*b^6*x + a^30*b^3)","B",0
472,-2,0,0,0.000000," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^p*(d*x)^m,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented","F(-2)",0
473,1,579,0,1.657485," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^p*x^2,x, algorithm=""fricas"")","\frac{3 \, {\left(2520 \, a^{9} + {\left(16 \, b^{9} p^{8} + 288 \, b^{9} p^{7} + 2184 \, b^{9} p^{6} + 9072 \, b^{9} p^{5} + 22449 \, b^{9} p^{4} + 33642 \, b^{9} p^{3} + 29531 \, b^{9} p^{2} + 13698 \, b^{9} p + 2520 \, b^{9}\right)} x^{3} + 28 \, {\left(8 \, a^{3} b^{6} p^{6} + 60 \, a^{3} b^{6} p^{5} + 170 \, a^{3} b^{6} p^{4} + 225 \, a^{3} b^{6} p^{3} + 137 \, a^{3} b^{6} p^{2} + 30 \, a^{3} b^{6} p\right)} x^{2} - 1680 \, {\left(2 \, a^{6} b^{3} p^{3} + 3 \, a^{6} b^{3} p^{2} + a^{6} b^{3} p\right)} x + {\left(5040 \, a^{7} b^{2} p^{2} + 2520 \, a^{7} b^{2} p + {\left(16 \, a b^{8} p^{8} + 224 \, a b^{8} p^{7} + 1288 \, a b^{8} p^{6} + 3920 \, a b^{8} p^{5} + 6769 \, a b^{8} p^{4} + 6566 \, a b^{8} p^{3} + 3267 \, a b^{8} p^{2} + 630 \, a b^{8} p\right)} x^{2} - 168 \, {\left(4 \, a^{4} b^{5} p^{5} + 20 \, a^{4} b^{5} p^{4} + 35 \, a^{4} b^{5} p^{3} + 25 \, a^{4} b^{5} p^{2} + 6 \, a^{4} b^{5} p\right)} x\right)} x^{\frac{2}{3}} - 4 \, {\left(1260 \, a^{8} b p + 2 \, {\left(8 \, a^{2} b^{7} p^{7} + 84 \, a^{2} b^{7} p^{6} + 350 \, a^{2} b^{7} p^{5} + 735 \, a^{2} b^{7} p^{4} + 812 \, a^{2} b^{7} p^{3} + 441 \, a^{2} b^{7} p^{2} + 90 \, a^{2} b^{7} p\right)} x^{2} - 105 \, {\left(4 \, a^{5} b^{4} p^{4} + 12 \, a^{5} b^{4} p^{3} + 11 \, a^{5} b^{4} p^{2} + 3 \, a^{5} b^{4} p\right)} x\right)} x^{\frac{1}{3}}\right)} {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p}}{32 \, b^{9} p^{9} + 720 \, b^{9} p^{8} + 6960 \, b^{9} p^{7} + 37800 \, b^{9} p^{6} + 126546 \, b^{9} p^{5} + 269325 \, b^{9} p^{4} + 361840 \, b^{9} p^{3} + 293175 \, b^{9} p^{2} + 128322 \, b^{9} p + 22680 \, b^{9}}"," ",0,"3*(2520*a^9 + (16*b^9*p^8 + 288*b^9*p^7 + 2184*b^9*p^6 + 9072*b^9*p^5 + 22449*b^9*p^4 + 33642*b^9*p^3 + 29531*b^9*p^2 + 13698*b^9*p + 2520*b^9)*x^3 + 28*(8*a^3*b^6*p^6 + 60*a^3*b^6*p^5 + 170*a^3*b^6*p^4 + 225*a^3*b^6*p^3 + 137*a^3*b^6*p^2 + 30*a^3*b^6*p)*x^2 - 1680*(2*a^6*b^3*p^3 + 3*a^6*b^3*p^2 + a^6*b^3*p)*x + (5040*a^7*b^2*p^2 + 2520*a^7*b^2*p + (16*a*b^8*p^8 + 224*a*b^8*p^7 + 1288*a*b^8*p^6 + 3920*a*b^8*p^5 + 6769*a*b^8*p^4 + 6566*a*b^8*p^3 + 3267*a*b^8*p^2 + 630*a*b^8*p)*x^2 - 168*(4*a^4*b^5*p^5 + 20*a^4*b^5*p^4 + 35*a^4*b^5*p^3 + 25*a^4*b^5*p^2 + 6*a^4*b^5*p)*x)*x^(2/3) - 4*(1260*a^8*b*p + 2*(8*a^2*b^7*p^7 + 84*a^2*b^7*p^6 + 350*a^2*b^7*p^5 + 735*a^2*b^7*p^4 + 812*a^2*b^7*p^3 + 441*a^2*b^7*p^2 + 90*a^2*b^7*p)*x^2 - 105*(4*a^5*b^4*p^4 + 12*a^5*b^4*p^3 + 11*a^5*b^4*p^2 + 3*a^5*b^4*p)*x)*x^(1/3))*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p/(32*b^9*p^9 + 720*b^9*p^8 + 6960*b^9*p^7 + 37800*b^9*p^6 + 126546*b^9*p^5 + 269325*b^9*p^4 + 361840*b^9*p^3 + 293175*b^9*p^2 + 128322*b^9*p + 22680*b^9)","A",0
474,1,297,0,1.314824," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^p*x,x, algorithm=""fricas"")","-\frac{3 \, {\left(30 \, a^{6} - {\left(8 \, b^{6} p^{5} + 60 \, b^{6} p^{4} + 170 \, b^{6} p^{3} + 225 \, b^{6} p^{2} + 137 \, b^{6} p + 30 \, b^{6}\right)} x^{2} - 20 \, {\left(2 \, a^{3} b^{3} p^{3} + 3 \, a^{3} b^{3} p^{2} + a^{3} b^{3} p\right)} x + 2 \, {\left(30 \, a^{4} b^{2} p^{2} + 15 \, a^{4} b^{2} p - {\left(4 \, a b^{5} p^{5} + 20 \, a b^{5} p^{4} + 35 \, a b^{5} p^{3} + 25 \, a b^{5} p^{2} + 6 \, a b^{5} p\right)} x\right)} x^{\frac{2}{3}} - 5 \, {\left(12 \, a^{5} b p - {\left(4 \, a^{2} b^{4} p^{4} + 12 \, a^{2} b^{4} p^{3} + 11 \, a^{2} b^{4} p^{2} + 3 \, a^{2} b^{4} p\right)} x\right)} x^{\frac{1}{3}}\right)} {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p}}{2 \, {\left(8 \, b^{6} p^{6} + 84 \, b^{6} p^{5} + 350 \, b^{6} p^{4} + 735 \, b^{6} p^{3} + 812 \, b^{6} p^{2} + 441 \, b^{6} p + 90 \, b^{6}\right)}}"," ",0,"-3/2*(30*a^6 - (8*b^6*p^5 + 60*b^6*p^4 + 170*b^6*p^3 + 225*b^6*p^2 + 137*b^6*p + 30*b^6)*x^2 - 20*(2*a^3*b^3*p^3 + 3*a^3*b^3*p^2 + a^3*b^3*p)*x + 2*(30*a^4*b^2*p^2 + 15*a^4*b^2*p - (4*a*b^5*p^5 + 20*a*b^5*p^4 + 35*a*b^5*p^3 + 25*a*b^5*p^2 + 6*a*b^5*p)*x)*x^(2/3) - 5*(12*a^5*b*p - (4*a^2*b^4*p^4 + 12*a^2*b^4*p^3 + 11*a^2*b^4*p^2 + 3*a^2*b^4*p)*x)*x^(1/3))*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p/(8*b^6*p^6 + 84*b^6*p^5 + 350*b^6*p^4 + 735*b^6*p^3 + 812*b^6*p^2 + 441*b^6*p + 90*b^6)","A",0
475,1,110,0,1.498418," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^p,x, algorithm=""fricas"")","-\frac{3 \, {\left(2 \, a^{2} b p x^{\frac{1}{3}} - a^{3} - {\left(2 \, b^{3} p^{2} + 3 \, b^{3} p + b^{3}\right)} x - {\left(2 \, a b^{2} p^{2} + a b^{2} p\right)} x^{\frac{2}{3}}\right)} {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p}}{4 \, b^{3} p^{3} + 12 \, b^{3} p^{2} + 11 \, b^{3} p + 3 \, b^{3}}"," ",0,"-3*(2*a^2*b*p*x^(1/3) - a^3 - (2*b^3*p^2 + 3*b^3*p + b^3)*x - (2*a*b^2*p^2 + a*b^2*p)*x^(2/3))*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p/(4*b^3*p^3 + 12*b^3*p^2 + 11*b^3*p + 3*b^3)","A",0
476,0,0,0,1.297446," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p}}{x}, x\right)"," ",0,"integral((b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p/x, x)","F",0
477,0,0,0,1.578758," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p/x^2, x)","F",0
478,1,82,0,1.666868," ","integrate((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^p/x^2-2/3*b^3*(1-2*p)*(1-p)*p*(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^p/a^3/x,x, algorithm=""fricas"")","-\frac{{\left(a^{2} b p x^{\frac{1}{3}} + a^{3} + {\left(2 \, b^{3} p^{2} - 3 \, b^{3} p + b^{3}\right)} x + 2 \, {\left(a b^{2} p^{2} - a b^{2} p\right)} x^{\frac{2}{3}}\right)} {\left(b^{2} x^{\frac{2}{3}} + 2 \, a b x^{\frac{1}{3}} + a^{2}\right)}^{p}}{a^{3} x}"," ",0,"-(a^2*b*p*x^(1/3) + a^3 + (2*b^3*p^2 - 3*b^3*p + b^3)*x + 2*(a*b^2*p^2 - a*b^2*p)*x^(2/3))*(b^2*x^(2/3) + 2*a*b*x^(1/3) + a^2)^p/(a^3*x)","A",0
479,1,147,0,11.031113," ","integrate(1/(a^2+2*a*b*x^(1/4)+b^2*x^(1/2))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(9 \, a^{5} b^{4} x - 5 \, a^{9} - 6 \, {\left(a b^{8} x^{2} - 2 \, a^{5} b^{4} x + a^{9}\right)} \log\left(b x^{\frac{1}{4}} + a\right) - 2 \, {\left(3 \, a^{2} b^{7} x - a^{6} b^{3}\right)} x^{\frac{3}{4}} + {\left(7 \, a^{3} b^{6} x - 3 \, a^{7} b^{2}\right)} \sqrt{x} + 2 \, {\left(b^{9} x^{2} - 6 \, a^{4} b^{5} x + 3 \, a^{8} b\right)} x^{\frac{1}{4}}\right)}}{b^{12} x^{2} - 2 \, a^{4} b^{8} x + a^{8} b^{4}}"," ",0,"2*(9*a^5*b^4*x - 5*a^9 - 6*(a*b^8*x^2 - 2*a^5*b^4*x + a^9)*log(b*x^(1/4) + a) - 2*(3*a^2*b^7*x - a^6*b^3)*x^(3/4) + (7*a^3*b^6*x - 3*a^7*b^2)*sqrt(x) + 2*(b^9*x^2 - 6*a^4*b^5*x + 3*a^8*b)*x^(1/4))/(b^12*x^2 - 2*a^4*b^8*x + a^8*b^4)","A",0
480,-1,0,0,0.000000," ","integrate(1/(a^2+2*a*b*x^(1/6)+b^2*x^(1/3))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
481,-1,0,0,0.000000," ","integrate((a^2+b^2/x+2*a*b/x^(1/2))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
482,-1,0,0,0.000000," ","integrate((a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
483,-1,0,0,0.000000," ","integrate((a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
484,-1,0,0,0.000000," ","integrate((a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
485,-1,0,0,0.000000," ","integrate((a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
486,-1,0,0,0.000000," ","integrate(1/(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
487,-1,0,0,0.000000," ","integrate(1/(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
488,-1,0,0,0.000000," ","integrate(1/(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
489,-1,0,0,0.000000," ","integrate((a^2+2*a*b/x^(1/4)+b^2/x^(1/2))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
490,-1,0,0,0.000000," ","integrate((a^2+b^2/x^(2/5)+2*a*b/x^(1/5))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
491,1,302,0,0.906030," ","integrate(1/(a^2+2*a*b*x^(1/5)+b^2*x^(2/5))^(5/2),x, algorithm=""fricas"")","\frac{5 \, {\left(300 \, a^{5} b^{15} x^{3} + 100 \, a^{15} b^{5} x + 25 \, a^{20} + 12 \, {\left(b^{20} x^{4} + 4 \, a^{5} b^{15} x^{3} + 6 \, a^{10} b^{10} x^{2} + 4 \, a^{15} b^{5} x + a^{20}\right)} \log\left(b x^{\frac{1}{5}} + a\right) + {\left(48 \, a b^{19} x^{3} - 226 \, a^{6} b^{14} x^{2} + 104 \, a^{11} b^{9} x + 3 \, a^{16} b^{4}\right)} x^{\frac{4}{5}} - {\left(84 \, a^{2} b^{18} x^{3} - 228 \, a^{7} b^{13} x^{2} + 67 \, a^{12} b^{8} x + 4 \, a^{17} b^{3}\right)} x^{\frac{3}{5}} + {\left(136 \, a^{3} b^{17} x^{3} - 197 \, a^{8} b^{12} x^{2} + 48 \, a^{13} b^{7} x + 6 \, a^{18} b^{2}\right)} x^{\frac{2}{5}} - {\left(207 \, a^{4} b^{16} x^{3} - 124 \, a^{9} b^{11} x^{2} + 56 \, a^{14} b^{6} x + 12 \, a^{19} b\right)} x^{\frac{1}{5}}\right)}}{12 \, {\left(b^{25} x^{4} + 4 \, a^{5} b^{20} x^{3} + 6 \, a^{10} b^{15} x^{2} + 4 \, a^{15} b^{10} x + a^{20} b^{5}\right)}}"," ",0,"5/12*(300*a^5*b^15*x^3 + 100*a^15*b^5*x + 25*a^20 + 12*(b^20*x^4 + 4*a^5*b^15*x^3 + 6*a^10*b^10*x^2 + 4*a^15*b^5*x + a^20)*log(b*x^(1/5) + a) + (48*a*b^19*x^3 - 226*a^6*b^14*x^2 + 104*a^11*b^9*x + 3*a^16*b^4)*x^(4/5) - (84*a^2*b^18*x^3 - 228*a^7*b^13*x^2 + 67*a^12*b^8*x + 4*a^17*b^3)*x^(3/5) + (136*a^3*b^17*x^3 - 197*a^8*b^12*x^2 + 48*a^13*b^7*x + 6*a^18*b^2)*x^(2/5) - (207*a^4*b^16*x^3 - 124*a^9*b^11*x^2 + 56*a^14*b^6*x + 12*a^19*b)*x^(1/5))/(b^25*x^4 + 4*a^5*b^20*x^3 + 6*a^10*b^15*x^2 + 4*a^15*b^10*x + a^20*b^5)","A",0
492,-1,0,0,0.000000," ","integrate((a^2+b^2/x^(1/3)+2*a*b/x^(1/6))^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
493,1,38,0,1.644836," ","integrate(x^(-1+4*n)/(b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\frac{c^{2} x^{2 \, n} - 2 \, b c x^{n} + 2 \, b^{2} \log\left(c x^{n} + b\right)}{2 \, c^{3} n}"," ",0,"1/2*(c^2*x^(2*n) - 2*b*c*x^n + 2*b^2*log(c*x^n + b))/(c^3*n)","A",0
494,1,24,0,2.058777," ","integrate(x^(-1+3*n)/(b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\frac{c x^{n} - b \log\left(c x^{n} + b\right)}{c^{2} n}"," ",0,"(c*x^n - b*log(c*x^n + b))/(c^2*n)","A",0
495,1,15,0,1.125527," ","integrate(x^(-1+2*n)/(b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\frac{\log\left(c x^{n} + b\right)}{c n}"," ",0,"log(c*x^n + b)/(c*n)","A",0
496,1,22,0,1.463142," ","integrate(x^(-1+n)/(b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\frac{n \log\left(x\right) - \log\left(c x^{n} + b\right)}{b n}"," ",0,"(n*log(x) - log(c*x^n + b))/(b*n)","A",0
497,1,59,0,1.386376," ","integrate(x^(-1-n)/(b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\frac{2 \, c^{2} n x^{2 \, n} \log\left(x\right) - 2 \, c^{2} x^{2 \, n} \log\left(c x^{n} + b\right) + 2 \, b c x^{n} - b^{2}}{2 \, b^{3} n x^{2 \, n}}"," ",0,"1/2*(2*c^2*n*x^(2*n)*log(x) - 2*c^2*x^(2*n)*log(c*x^n + b) + 2*b*c*x^n - b^2)/(b^3*n*x^(2*n))","A",0
498,1,72,0,1.472718," ","integrate(x^(-1-2*n)/(b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","-\frac{6 \, c^{3} n x^{3 \, n} \log\left(x\right) - 6 \, c^{3} x^{3 \, n} \log\left(c x^{n} + b\right) + 6 \, b c^{2} x^{2 \, n} - 3 \, b^{2} c x^{n} + 2 \, b^{3}}{6 \, b^{4} n x^{3 \, n}}"," ",0,"-1/6*(6*c^3*n*x^(3*n)*log(x) - 6*c^3*x^(3*n)*log(c*x^n + b) + 6*b*c^2*x^(2*n) - 3*b^2*c*x^n + 2*b^3)/(b^4*n*x^(3*n))","A",0
499,1,85,0,1.223693," ","integrate(x^(-1-3*n)/(b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\frac{12 \, c^{4} n x^{4 \, n} \log\left(x\right) - 12 \, c^{4} x^{4 \, n} \log\left(c x^{n} + b\right) + 12 \, b c^{3} x^{3 \, n} - 6 \, b^{2} c^{2} x^{2 \, n} + 4 \, b^{3} c x^{n} - 3 \, b^{4}}{12 \, b^{5} n x^{4 \, n}}"," ",0,"1/12*(12*c^4*n*x^(4*n)*log(x) - 12*c^4*x^(4*n)*log(c*x^n + b) + 12*b*c^3*x^(3*n) - 6*b^2*c^2*x^(2*n) + 4*b^3*c*x^n - 3*b^4)/(b^5*n*x^(4*n))","A",0
500,1,272,0,0.919693," ","integrate(x^(-1+1/4*n)/(b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","-\frac{12 \, b n x^{3} x^{\frac{3}{4} \, n - 3} \left(-\frac{c^{3}}{b^{7} n^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{b^{5} c n^{3} x x^{\frac{1}{4} \, n - 1} \left(-\frac{c^{3}}{b^{7} n^{4}}\right)^{\frac{3}{4}} - b^{5} n^{3} x \sqrt{\frac{b^{4} n^{2} \sqrt{-\frac{c^{3}}{b^{7} n^{4}}} + c^{2} x^{2} x^{\frac{1}{2} \, n - 2}}{x^{2}}} \left(-\frac{c^{3}}{b^{7} n^{4}}\right)^{\frac{3}{4}}}{c^{3}}\right) + 3 \, b n x^{3} x^{\frac{3}{4} \, n - 3} \left(-\frac{c^{3}}{b^{7} n^{4}}\right)^{\frac{1}{4}} \log\left(\frac{b^{2} n \left(-\frac{c^{3}}{b^{7} n^{4}}\right)^{\frac{1}{4}} + c x x^{\frac{1}{4} \, n - 1}}{x}\right) - 3 \, b n x^{3} x^{\frac{3}{4} \, n - 3} \left(-\frac{c^{3}}{b^{7} n^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{b^{2} n \left(-\frac{c^{3}}{b^{7} n^{4}}\right)^{\frac{1}{4}} - c x x^{\frac{1}{4} \, n - 1}}{x}\right) + 4}{3 \, b n x^{3} x^{\frac{3}{4} \, n - 3}}"," ",0,"-1/3*(12*b*n*x^3*x^(3/4*n - 3)*(-c^3/(b^7*n^4))^(1/4)*arctan(-(b^5*c*n^3*x*x^(1/4*n - 1)*(-c^3/(b^7*n^4))^(3/4) - b^5*n^3*x*sqrt((b^4*n^2*sqrt(-c^3/(b^7*n^4)) + c^2*x^2*x^(1/2*n - 2))/x^2)*(-c^3/(b^7*n^4))^(3/4))/c^3) + 3*b*n*x^3*x^(3/4*n - 3)*(-c^3/(b^7*n^4))^(1/4)*log((b^2*n*(-c^3/(b^7*n^4))^(1/4) + c*x*x^(1/4*n - 1))/x) - 3*b*n*x^3*x^(3/4*n - 3)*(-c^3/(b^7*n^4))^(1/4)*log(-(b^2*n*(-c^3/(b^7*n^4))^(1/4) - c*x*x^(1/4*n - 1))/x) + 4)/(b*n*x^3*x^(3/4*n - 3))","A",0
501,1,212,0,1.331115," ","integrate(x^(-1+1/3*n)/(b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} x^{2} x^{\frac{2}{3} \, n - 2} \left(-\frac{c^{2}}{b^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x x^{\frac{1}{3} \, n - 1} \left(-\frac{c^{2}}{b^{2}}\right)^{\frac{2}{3}} - \sqrt{3} c}{3 \, c}\right) + 2 \, x^{2} x^{\frac{2}{3} \, n - 2} \left(-\frac{c^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(\frac{c x x^{\frac{1}{3} \, n - 1} - b \left(-\frac{c^{2}}{b^{2}}\right)^{\frac{1}{3}}}{x}\right) - x^{2} x^{\frac{2}{3} \, n - 2} \left(-\frac{c^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(\frac{c^{2} x^{2} x^{\frac{2}{3} \, n - 2} + b c x x^{\frac{1}{3} \, n - 1} \left(-\frac{c^{2}}{b^{2}}\right)^{\frac{1}{3}} + b^{2} \left(-\frac{c^{2}}{b^{2}}\right)^{\frac{2}{3}}}{x^{2}}\right) - 3}{2 \, b n x^{2} x^{\frac{2}{3} \, n - 2}}"," ",0,"1/2*(2*sqrt(3)*x^2*x^(2/3*n - 2)*(-c^2/b^2)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*x^(1/3*n - 1)*(-c^2/b^2)^(2/3) - sqrt(3)*c)/c) + 2*x^2*x^(2/3*n - 2)*(-c^2/b^2)^(1/3)*log((c*x*x^(1/3*n - 1) - b*(-c^2/b^2)^(1/3))/x) - x^2*x^(2/3*n - 2)*(-c^2/b^2)^(1/3)*log((c^2*x^2*x^(2/3*n - 2) + b*c*x*x^(1/3*n - 1)*(-c^2/b^2)^(1/3) + b^2*(-c^2/b^2)^(2/3))/x^2) - 3)/(b*n*x^2*x^(2/3*n - 2))","A",0
502,1,151,0,1.283088," ","integrate(x^(-1+1/2*n)/(b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\left[\frac{x x^{\frac{1}{2} \, n - 1} \sqrt{-\frac{c}{b}} \log\left(\frac{c x^{2} x^{n - 2} - 2 \, b x x^{\frac{1}{2} \, n - 1} \sqrt{-\frac{c}{b}} - b}{c x^{2} x^{n - 2} + b}\right) - 2}{b n x x^{\frac{1}{2} \, n - 1}}, \frac{2 \, {\left(x x^{\frac{1}{2} \, n - 1} \sqrt{\frac{c}{b}} \arctan\left(\frac{b \sqrt{\frac{c}{b}}}{c x x^{\frac{1}{2} \, n - 1}}\right) - 1\right)}}{b n x x^{\frac{1}{2} \, n - 1}}\right]"," ",0,"[(x*x^(1/2*n - 1)*sqrt(-c/b)*log((c*x^2*x^(n - 2) - 2*b*x*x^(1/2*n - 1)*sqrt(-c/b) - b)/(c*x^2*x^(n - 2) + b)) - 2)/(b*n*x*x^(1/2*n - 1)), 2*(x*x^(1/2*n - 1)*sqrt(c/b)*arctan(b*sqrt(c/b)/(c*x*x^(1/2*n - 1))) - 1)/(b*n*x*x^(1/2*n - 1))]","A",0
503,1,161,0,1.394499," ","integrate(x^(-1-1/2*n)/(b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\left[-\frac{2 \, b x^{3} x^{-\frac{3}{2} \, n - 3} - 6 \, c x x^{-\frac{1}{2} \, n - 1} - 3 \, c \sqrt{-\frac{c}{b}} \log\left(\frac{b x^{2} x^{-n - 2} - 2 \, b x x^{-\frac{1}{2} \, n - 1} \sqrt{-\frac{c}{b}} - c}{b x^{2} x^{-n - 2} + c}\right)}{3 \, b^{2} n}, -\frac{2 \, {\left(b x^{3} x^{-\frac{3}{2} \, n - 3} - 3 \, c x x^{-\frac{1}{2} \, n - 1} - 3 \, c \sqrt{\frac{c}{b}} \arctan\left(\frac{\sqrt{\frac{c}{b}}}{x x^{-\frac{1}{2} \, n - 1}}\right)\right)}}{3 \, b^{2} n}\right]"," ",0,"[-1/3*(2*b*x^3*x^(-3/2*n - 3) - 6*c*x*x^(-1/2*n - 1) - 3*c*sqrt(-c/b)*log((b*x^2*x^(-n - 2) - 2*b*x*x^(-1/2*n - 1)*sqrt(-c/b) - c)/(b*x^2*x^(-n - 2) + c)))/(b^2*n), -2/3*(b*x^3*x^(-3/2*n - 3) - 3*c*x*x^(-1/2*n - 1) - 3*c*sqrt(c/b)*arctan(sqrt(c/b)/(x*x^(-1/2*n - 1))))/(b^2*n)]","A",0
504,1,171,0,1.424882," ","integrate(x^(-1-1/3*n)/(b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","-\frac{3 \, b x^{4} x^{-\frac{4}{3} \, n - 4} - 12 \, c x x^{-\frac{1}{3} \, n - 1} - 4 \, \sqrt{3} c \left(-\frac{c}{b}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x x^{-\frac{1}{3} \, n - 1} \left(-\frac{c}{b}\right)^{\frac{2}{3}} - \sqrt{3} c}{3 \, c}\right) - 4 \, c \left(-\frac{c}{b}\right)^{\frac{1}{3}} \log\left(\frac{x x^{-\frac{1}{3} \, n - 1} - \left(-\frac{c}{b}\right)^{\frac{1}{3}}}{x}\right) + 2 \, c \left(-\frac{c}{b}\right)^{\frac{1}{3}} \log\left(\frac{x^{2} x^{-\frac{2}{3} \, n - 2} + x x^{-\frac{1}{3} \, n - 1} \left(-\frac{c}{b}\right)^{\frac{1}{3}} + \left(-\frac{c}{b}\right)^{\frac{2}{3}}}{x^{2}}\right)}{4 \, b^{2} n}"," ",0,"-1/4*(3*b*x^4*x^(-4/3*n - 4) - 12*c*x*x^(-1/3*n - 1) - 4*sqrt(3)*c*(-c/b)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*x^(-1/3*n - 1)*(-c/b)^(2/3) - sqrt(3)*c)/c) - 4*c*(-c/b)^(1/3)*log((x*x^(-1/3*n - 1) - (-c/b)^(1/3))/x) + 2*c*(-c/b)^(1/3)*log((x^2*x^(-2/3*n - 2) + x*x^(-1/3*n - 1)*(-c/b)^(1/3) + (-c/b)^(2/3))/x^2))/(b^2*n)","A",0
505,1,259,0,1.384658," ","integrate(x^(-1-1/4*n)/(b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","-\frac{4 \, b x^{5} x^{-\frac{5}{4} \, n - 5} + 20 \, b^{2} n \left(-\frac{c^{5}}{b^{9} n^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{b^{7} c n^{3} x x^{-\frac{1}{4} \, n - 1} \left(-\frac{c^{5}}{b^{9} n^{4}}\right)^{\frac{3}{4}} - b^{7} n^{3} x \sqrt{\frac{b^{4} n^{2} \sqrt{-\frac{c^{5}}{b^{9} n^{4}}} + c^{2} x^{2} x^{-\frac{1}{2} \, n - 2}}{x^{2}}} \left(-\frac{c^{5}}{b^{9} n^{4}}\right)^{\frac{3}{4}}}{c^{5}}\right) + 5 \, b^{2} n \left(-\frac{c^{5}}{b^{9} n^{4}}\right)^{\frac{1}{4}} \log\left(\frac{b^{2} n \left(-\frac{c^{5}}{b^{9} n^{4}}\right)^{\frac{1}{4}} + c x x^{-\frac{1}{4} \, n - 1}}{x}\right) - 5 \, b^{2} n \left(-\frac{c^{5}}{b^{9} n^{4}}\right)^{\frac{1}{4}} \log\left(-\frac{b^{2} n \left(-\frac{c^{5}}{b^{9} n^{4}}\right)^{\frac{1}{4}} - c x x^{-\frac{1}{4} \, n - 1}}{x}\right) - 20 \, c x x^{-\frac{1}{4} \, n - 1}}{5 \, b^{2} n}"," ",0,"-1/5*(4*b*x^5*x^(-5/4*n - 5) + 20*b^2*n*(-c^5/(b^9*n^4))^(1/4)*arctan(-(b^7*c*n^3*x*x^(-1/4*n - 1)*(-c^5/(b^9*n^4))^(3/4) - b^7*n^3*x*sqrt((b^4*n^2*sqrt(-c^5/(b^9*n^4)) + c^2*x^2*x^(-1/2*n - 2))/x^2)*(-c^5/(b^9*n^4))^(3/4))/c^5) + 5*b^2*n*(-c^5/(b^9*n^4))^(1/4)*log((b^2*n*(-c^5/(b^9*n^4))^(1/4) + c*x*x^(-1/4*n - 1))/x) - 5*b^2*n*(-c^5/(b^9*n^4))^(1/4)*log(-(b^2*n*(-c^5/(b^9*n^4))^(1/4) - c*x*x^(-1/4*n - 1))/x) - 20*c*x*x^(-1/4*n - 1))/(b^2*n)","A",0
506,1,59,0,1.340174," ","integrate(x^(-1-n*(-1+p))*(b*x^n+c*x^(2*n))^p,x, algorithm=""fricas"")","\frac{{\left(c x x^{-n p + n - 1} x^{n} + b x x^{-n p + n - 1}\right)} {\left(c x^{2 \, n} + b x^{n}\right)}^{p}}{{\left(c n p + c n\right)} x^{n}}"," ",0,"(c*x*x^(-n*p + n - 1)*x^n + b*x*x^(-n*p + n - 1))*(c*x^(2*n) + b*x^n)^p/((c*n*p + c*n)*x^n)","A",0
507,1,59,0,1.150306," ","integrate(x^(-1-n*(1+2*p))*(b*x^n+c*x^(2*n))^p,x, algorithm=""fricas"")","-\frac{{\left(c x x^{-2 \, n p - n - 1} x^{n} + b x x^{-2 \, n p - n - 1}\right)} {\left(c x^{2 \, n} + b x^{n}\right)}^{p}}{b n p + b n}"," ",0,"-(c*x*x^(-2*n*p - n - 1)*x^n + b*x*x^(-2*n*p - n - 1))*(c*x^(2*n) + b*x^n)^p/(b*n*p + b*n)","A",0
508,1,74,0,1.303107," ","integrate(x^(-1+2*n)*(a^2+2*a*b*x^n+b^2*x^(2*n))^(5/2),x, algorithm=""fricas"")","\frac{6 \, b^{5} x^{7 \, n} + 35 \, a b^{4} x^{6 \, n} + 84 \, a^{2} b^{3} x^{5 \, n} + 105 \, a^{3} b^{2} x^{4 \, n} + 70 \, a^{4} b x^{3 \, n} + 21 \, a^{5} x^{2 \, n}}{42 \, n}"," ",0,"1/42*(6*b^5*x^(7*n) + 35*a*b^4*x^(6*n) + 84*a^2*b^3*x^(5*n) + 105*a^3*b^2*x^(4*n) + 70*a^4*b*x^(3*n) + 21*a^5*x^(2*n))/n","A",0
509,1,48,0,1.328801," ","integrate(x^(-1+2*n)*(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""fricas"")","\frac{4 \, b^{3} x^{5 \, n} + 15 \, a b^{2} x^{4 \, n} + 20 \, a^{2} b x^{3 \, n} + 10 \, a^{3} x^{2 \, n}}{20 \, n}"," ",0,"1/20*(4*b^3*x^(5*n) + 15*a*b^2*x^(4*n) + 20*a^2*b*x^(3*n) + 10*a^3*x^(2*n))/n","A",0
510,1,22,0,1.250360," ","integrate(x^(-1+2*n)*(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""fricas"")","\frac{2 \, b x^{3 \, n} + 3 \, a x^{2 \, n}}{6 \, n}"," ",0,"1/6*(2*b*x^(3*n) + 3*a*x^(2*n))/n","A",0
511,1,24,0,1.313268," ","integrate(x^(-1+2*n)/(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""fricas"")","\frac{b x^{n} - a \log\left(b x^{n} + a\right)}{b^{2} n}"," ",0,"(b*x^n - a*log(b*x^n + a))/(b^2*n)","A",0
512,1,41,0,1.303707," ","integrate(x^(-1+2*n)/(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, b x^{n} + a}{2 \, {\left(b^{4} n x^{2 \, n} + 2 \, a b^{3} n x^{n} + a^{2} b^{2} n\right)}}"," ",0,"-1/2*(2*b*x^n + a)/(b^4*n*x^(2*n) + 2*a*b^3*n*x^n + a^2*b^2*n)","A",0
513,1,69,0,1.183404," ","integrate(x^(-1+2*n)/(a^2+2*a*b*x^n+b^2*x^(2*n))^(5/2),x, algorithm=""fricas"")","-\frac{4 \, b x^{n} + a}{12 \, {\left(b^{6} n x^{4 \, n} + 4 \, a b^{5} n x^{3 \, n} + 6 \, a^{2} b^{4} n x^{2 \, n} + 4 \, a^{3} b^{3} n x^{n} + a^{4} b^{2} n\right)}}"," ",0,"-1/12*(4*b*x^n + a)/(b^6*n*x^(4*n) + 4*a*b^5*n*x^(3*n) + 6*a^2*b^4*n*x^(2*n) + 4*a^3*b^3*n*x^n + a^4*b^2*n)","A",0
514,1,97,0,1.210258," ","integrate(x^(-1+2*n)/(a^2+2*a*b*x^n+b^2*x^(2*n))^(7/2),x, algorithm=""fricas"")","-\frac{6 \, b x^{n} + a}{30 \, {\left(b^{8} n x^{6 \, n} + 6 \, a b^{7} n x^{5 \, n} + 15 \, a^{2} b^{6} n x^{4 \, n} + 20 \, a^{3} b^{5} n x^{3 \, n} + 15 \, a^{4} b^{4} n x^{2 \, n} + 6 \, a^{5} b^{3} n x^{n} + a^{6} b^{2} n\right)}}"," ",0,"-1/30*(6*b*x^n + a)/(b^8*n*x^(6*n) + 6*a*b^7*n*x^(5*n) + 15*a^2*b^6*n*x^(4*n) + 20*a^3*b^5*n*x^(3*n) + 15*a^4*b^4*n*x^(2*n) + 6*a^5*b^3*n*x^n + a^6*b^2*n)","A",0
515,1,57,0,1.448419," ","integrate((d*x)^m*(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""fricas"")","\frac{{\left(b m + b\right)} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + {\left(a m + a n + a\right)} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)}}{m^{2} + {\left(m + 1\right)} n + 2 \, m + 1}"," ",0,"((b*m + b)*x*x^n*e^(m*log(d) + m*log(x)) + (a*m + a*n + a)*x*e^(m*log(d) + m*log(x)))/(m^2 + (m + 1)*n + 2*m + 1)","A",0
516,1,28,0,1.105082," ","integrate(x^2*(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""fricas"")","\frac{3 \, b x^{3} x^{n} + {\left(a n + 3 \, a\right)} x^{3}}{3 \, {\left(n + 3\right)}}"," ",0,"1/3*(3*b*x^3*x^n + (a*n + 3*a)*x^3)/(n + 3)","A",0
517,1,28,0,1.154437," ","integrate(x*(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""fricas"")","\frac{2 \, b x^{2} x^{n} + {\left(a n + 2 \, a\right)} x^{2}}{2 \, {\left(n + 2\right)}}"," ",0,"1/2*(2*b*x^2*x^n + (a*n + 2*a)*x^2)/(n + 2)","A",0
518,1,20,0,1.323379," ","integrate((a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""fricas"")","\frac{b x x^{n} + {\left(a n + a\right)} x}{n + 1}"," ",0,"(b*x*x^n + (a*n + a)*x)/(n + 1)","A",0
519,1,15,0,1.359565," ","integrate((a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2)/x,x, algorithm=""fricas"")","\frac{a n \log\left(x\right) + b x^{n}}{n}"," ",0,"(a*n*log(x) + b*x^n)/n","A",0
520,1,23,0,1.285115," ","integrate((a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2)/x^2,x, algorithm=""fricas"")","-\frac{a n - b x^{n} - a}{{\left(n - 1\right)} x}"," ",0,"-(a*n - b*x^n - a)/((n - 1)*x)","A",0
521,1,23,0,1.332670," ","integrate((a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2)/x^3,x, algorithm=""fricas"")","-\frac{a n - 2 \, b x^{n} - 2 \, a}{2 \, {\left(n - 2\right)} x^{2}}"," ",0,"-1/2*(a*n - 2*b*x^n - 2*a)/((n - 2)*x^2)","A",0
522,1,390,0,1.013112," ","integrate((d*x)^m*(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""fricas"")","\frac{{\left(b^{3} m^{3} + 3 \, b^{3} m^{2} + 3 \, b^{3} m + b^{3} + 2 \, {\left(b^{3} m + b^{3}\right)} n^{2} + 3 \, {\left(b^{3} m^{2} + 2 \, b^{3} m + b^{3}\right)} n\right)} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 3 \, {\left(a b^{2} m^{3} + 3 \, a b^{2} m^{2} + 3 \, a b^{2} m + a b^{2} + 3 \, {\left(a b^{2} m + a b^{2}\right)} n^{2} + 4 \, {\left(a b^{2} m^{2} + 2 \, a b^{2} m + a b^{2}\right)} n\right)} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 3 \, {\left(a^{2} b m^{3} + 3 \, a^{2} b m^{2} + 3 \, a^{2} b m + a^{2} b + 6 \, {\left(a^{2} b m + a^{2} b\right)} n^{2} + 5 \, {\left(a^{2} b m^{2} + 2 \, a^{2} b m + a^{2} b\right)} n\right)} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + {\left(a^{3} m^{3} + 6 \, a^{3} n^{3} + 3 \, a^{3} m^{2} + 3 \, a^{3} m + a^{3} + 11 \, {\left(a^{3} m + a^{3}\right)} n^{2} + 6 \, {\left(a^{3} m^{2} + 2 \, a^{3} m + a^{3}\right)} n\right)} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)}}{m^{4} + 6 \, {\left(m + 1\right)} n^{3} + 4 \, m^{3} + 11 \, {\left(m^{2} + 2 \, m + 1\right)} n^{2} + 6 \, m^{2} + 6 \, {\left(m^{3} + 3 \, m^{2} + 3 \, m + 1\right)} n + 4 \, m + 1}"," ",0,"((b^3*m^3 + 3*b^3*m^2 + 3*b^3*m + b^3 + 2*(b^3*m + b^3)*n^2 + 3*(b^3*m^2 + 2*b^3*m + b^3)*n)*x*x^(3*n)*e^(m*log(d) + m*log(x)) + 3*(a*b^2*m^3 + 3*a*b^2*m^2 + 3*a*b^2*m + a*b^2 + 3*(a*b^2*m + a*b^2)*n^2 + 4*(a*b^2*m^2 + 2*a*b^2*m + a*b^2)*n)*x*x^(2*n)*e^(m*log(d) + m*log(x)) + 3*(a^2*b*m^3 + 3*a^2*b*m^2 + 3*a^2*b*m + a^2*b + 6*(a^2*b*m + a^2*b)*n^2 + 5*(a^2*b*m^2 + 2*a^2*b*m + a^2*b)*n)*x*x^n*e^(m*log(d) + m*log(x)) + (a^3*m^3 + 6*a^3*n^3 + 3*a^3*m^2 + 3*a^3*m + a^3 + 11*(a^3*m + a^3)*n^2 + 6*(a^3*m^2 + 2*a^3*m + a^3)*n)*x*e^(m*log(d) + m*log(x)))/(m^4 + 6*(m + 1)*n^3 + 4*m^3 + 11*(m^2 + 2*m + 1)*n^2 + 6*m^2 + 6*(m^3 + 3*m^2 + 3*m + 1)*n + 4*m + 1)","A",0
523,1,144,0,1.100850," ","integrate(x^2*(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""fricas"")","\frac{{\left(2 \, b^{3} n^{2} + 9 \, b^{3} n + 9 \, b^{3}\right)} x^{3} x^{3 \, n} + 9 \, {\left(a b^{2} n^{2} + 4 \, a b^{2} n + 3 \, a b^{2}\right)} x^{3} x^{2 \, n} + 9 \, {\left(2 \, a^{2} b n^{2} + 5 \, a^{2} b n + 3 \, a^{2} b\right)} x^{3} x^{n} + {\left(2 \, a^{3} n^{3} + 11 \, a^{3} n^{2} + 18 \, a^{3} n + 9 \, a^{3}\right)} x^{3}}{3 \, {\left(2 \, n^{3} + 11 \, n^{2} + 18 \, n + 9\right)}}"," ",0,"1/3*((2*b^3*n^2 + 9*b^3*n + 9*b^3)*x^3*x^(3*n) + 9*(a*b^2*n^2 + 4*a*b^2*n + 3*a*b^2)*x^3*x^(2*n) + 9*(2*a^2*b*n^2 + 5*a^2*b*n + 3*a^2*b)*x^3*x^n + (2*a^3*n^3 + 11*a^3*n^2 + 18*a^3*n + 9*a^3)*x^3)/(2*n^3 + 11*n^2 + 18*n + 9)","A",0
524,1,145,0,1.323048," ","integrate(x*(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{3} n^{2} + 3 \, b^{3} n + 2 \, b^{3}\right)} x^{2} x^{3 \, n} + 3 \, {\left(3 \, a b^{2} n^{2} + 8 \, a b^{2} n + 4 \, a b^{2}\right)} x^{2} x^{2 \, n} + 6 \, {\left(3 \, a^{2} b n^{2} + 5 \, a^{2} b n + 2 \, a^{2} b\right)} x^{2} x^{n} + {\left(3 \, a^{3} n^{3} + 11 \, a^{3} n^{2} + 12 \, a^{3} n + 4 \, a^{3}\right)} x^{2}}{2 \, {\left(3 \, n^{3} + 11 \, n^{2} + 12 \, n + 4\right)}}"," ",0,"1/2*(2*(b^3*n^2 + 3*b^3*n + 2*b^3)*x^2*x^(3*n) + 3*(3*a*b^2*n^2 + 8*a*b^2*n + 4*a*b^2)*x^2*x^(2*n) + 6*(3*a^2*b*n^2 + 5*a^2*b*n + 2*a^2*b)*x^2*x^n + (3*a^3*n^3 + 11*a^3*n^2 + 12*a^3*n + 4*a^3)*x^2)/(3*n^3 + 11*n^2 + 12*n + 4)","A",0
525,1,130,0,1.360696," ","integrate((a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""fricas"")","\frac{{\left(2 \, b^{3} n^{2} + 3 \, b^{3} n + b^{3}\right)} x x^{3 \, n} + 3 \, {\left(3 \, a b^{2} n^{2} + 4 \, a b^{2} n + a b^{2}\right)} x x^{2 \, n} + 3 \, {\left(6 \, a^{2} b n^{2} + 5 \, a^{2} b n + a^{2} b\right)} x x^{n} + {\left(6 \, a^{3} n^{3} + 11 \, a^{3} n^{2} + 6 \, a^{3} n + a^{3}\right)} x}{6 \, n^{3} + 11 \, n^{2} + 6 \, n + 1}"," ",0,"((2*b^3*n^2 + 3*b^3*n + b^3)*x*x^(3*n) + 3*(3*a*b^2*n^2 + 4*a*b^2*n + a*b^2)*x*x^(2*n) + 3*(6*a^2*b*n^2 + 5*a^2*b*n + a^2*b)*x*x^n + (6*a^3*n^3 + 11*a^3*n^2 + 6*a^3*n + a^3)*x)/(6*n^3 + 11*n^2 + 6*n + 1)","A",0
526,1,44,0,0.803455," ","integrate((a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2)/x,x, algorithm=""fricas"")","\frac{6 \, a^{3} n \log\left(x\right) + 2 \, b^{3} x^{3 \, n} + 9 \, a b^{2} x^{2 \, n} + 18 \, a^{2} b x^{n}}{6 \, n}"," ",0,"1/6*(6*a^3*n*log(x) + 2*b^3*x^(3*n) + 9*a*b^2*x^(2*n) + 18*a^2*b*x^n)/n","A",0
527,1,131,0,1.343126," ","integrate((a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2)/x^2,x, algorithm=""fricas"")","-\frac{6 \, a^{3} n^{3} - 11 \, a^{3} n^{2} + 6 \, a^{3} n - a^{3} - {\left(2 \, b^{3} n^{2} - 3 \, b^{3} n + b^{3}\right)} x^{3 \, n} - 3 \, {\left(3 \, a b^{2} n^{2} - 4 \, a b^{2} n + a b^{2}\right)} x^{2 \, n} - 3 \, {\left(6 \, a^{2} b n^{2} - 5 \, a^{2} b n + a^{2} b\right)} x^{n}}{{\left(6 \, n^{3} - 11 \, n^{2} + 6 \, n - 1\right)} x}"," ",0,"-(6*a^3*n^3 - 11*a^3*n^2 + 6*a^3*n - a^3 - (2*b^3*n^2 - 3*b^3*n + b^3)*x^(3*n) - 3*(3*a*b^2*n^2 - 4*a*b^2*n + a*b^2)*x^(2*n) - 3*(6*a^2*b*n^2 - 5*a^2*b*n + a^2*b)*x^n)/((6*n^3 - 11*n^2 + 6*n - 1)*x)","A",0
528,1,134,0,1.330265," ","integrate((a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2)/x^3,x, algorithm=""fricas"")","-\frac{3 \, a^{3} n^{3} - 11 \, a^{3} n^{2} + 12 \, a^{3} n - 4 \, a^{3} - 2 \, {\left(b^{3} n^{2} - 3 \, b^{3} n + 2 \, b^{3}\right)} x^{3 \, n} - 3 \, {\left(3 \, a b^{2} n^{2} - 8 \, a b^{2} n + 4 \, a b^{2}\right)} x^{2 \, n} - 6 \, {\left(3 \, a^{2} b n^{2} - 5 \, a^{2} b n + 2 \, a^{2} b\right)} x^{n}}{2 \, {\left(3 \, n^{3} - 11 \, n^{2} + 12 \, n - 4\right)} x^{2}}"," ",0,"-1/2*(3*a^3*n^3 - 11*a^3*n^2 + 12*a^3*n - 4*a^3 - 2*(b^3*n^2 - 3*b^3*n + 2*b^3)*x^(3*n) - 3*(3*a*b^2*n^2 - 8*a*b^2*n + 4*a*b^2)*x^(2*n) - 6*(3*a^2*b*n^2 - 5*a^2*b*n + 2*a^2*b)*x^n)/((3*n^3 - 11*n^2 + 12*n - 4)*x^2)","A",0
529,0,0,0,1.226925," ","integrate((d*x)^m/(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}}, x\right)"," ",0,"integral((d*x)^m/sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2), x)","F",0
530,0,0,0,1.135151," ","integrate(x^2/(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}}, x\right)"," ",0,"integral(x^2/sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2), x)","F",0
531,0,0,0,1.149826," ","integrate(x/(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}}, x\right)"," ",0,"integral(x/sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2), x)","F",0
532,0,0,0,1.400191," ","integrate(1/(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}}, x\right)"," ",0,"integral(1/sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2), x)","F",0
533,1,22,0,1.217007," ","integrate(1/x/(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""fricas"")","\frac{n \log\left(x\right) - \log\left(b x^{n} + a\right)}{a n}"," ",0,"(n*log(x) - log(b*x^n + a))/(a*n)","A",0
534,0,0,0,1.249821," ","integrate(1/x^2/(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}}{b^{2} x^{2} x^{2 \, n} + 2 \, a b x^{2} x^{n} + a^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2)/(b^2*x^2*x^(2*n) + 2*a*b*x^2*x^n + a^2*x^2), x)","F",0
535,0,0,0,1.389222," ","integrate(1/x^3/(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}}{b^{2} x^{3} x^{2 \, n} + 2 \, a b x^{3} x^{n} + a^{2} x^{3}}, x\right)"," ",0,"integral(sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2)/(b^2*x^3*x^(2*n) + 2*a*b*x^3*x^n + a^2*x^3), x)","F",0
536,0,0,0,1.326867," ","integrate((d*x)^m/(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}} \left(d x\right)^{m}}{b^{4} x^{4 \, n} + 4 \, a^{2} b^{2} x^{2 \, n} + 4 \, a^{3} b x^{n} + a^{4} + 2 \, {\left(2 \, a b^{3} x^{n} + a^{2} b^{2}\right)} x^{2 \, n}}, x\right)"," ",0,"integral(sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2)*(d*x)^m/(b^4*x^(4*n) + 4*a^2*b^2*x^(2*n) + 4*a^3*b*x^n + a^4 + 2*(2*a*b^3*x^n + a^2*b^2)*x^(2*n)), x)","F",0
537,0,0,0,1.400625," ","integrate(x^2/(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}} x^{2}}{b^{4} x^{4 \, n} + 4 \, a^{2} b^{2} x^{2 \, n} + 4 \, a^{3} b x^{n} + a^{4} + 2 \, {\left(2 \, a b^{3} x^{n} + a^{2} b^{2}\right)} x^{2 \, n}}, x\right)"," ",0,"integral(sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2)*x^2/(b^4*x^(4*n) + 4*a^2*b^2*x^(2*n) + 4*a^3*b*x^n + a^4 + 2*(2*a*b^3*x^n + a^2*b^2)*x^(2*n)), x)","F",0
538,0,0,0,1.312113," ","integrate(x/(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}} x}{b^{4} x^{4 \, n} + 4 \, a^{2} b^{2} x^{2 \, n} + 4 \, a^{3} b x^{n} + a^{4} + 2 \, {\left(2 \, a b^{3} x^{n} + a^{2} b^{2}\right)} x^{2 \, n}}, x\right)"," ",0,"integral(sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2)*x/(b^4*x^(4*n) + 4*a^2*b^2*x^(2*n) + 4*a^3*b*x^n + a^4 + 2*(2*a*b^3*x^n + a^2*b^2)*x^(2*n)), x)","F",0
539,0,0,0,1.079477," ","integrate(1/(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}}{b^{4} x^{4 \, n} + 4 \, a^{2} b^{2} x^{2 \, n} + 4 \, a^{3} b x^{n} + a^{4} + 2 \, {\left(2 \, a b^{3} x^{n} + a^{2} b^{2}\right)} x^{2 \, n}}, x\right)"," ",0,"integral(sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2)/(b^4*x^(4*n) + 4*a^2*b^2*x^(2*n) + 4*a^3*b*x^n + a^4 + 2*(2*a*b^3*x^n + a^2*b^2)*x^(2*n)), x)","F",0
540,1,106,0,1.486195," ","integrate(1/x/(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""fricas"")","\frac{2 \, b^{2} n x^{2 \, n} \log\left(x\right) + 2 \, a^{2} n \log\left(x\right) + 3 \, a^{2} + 2 \, {\left(2 \, a b n \log\left(x\right) + a b\right)} x^{n} - 2 \, {\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)} \log\left(b x^{n} + a\right)}{2 \, {\left(a^{3} b^{2} n x^{2 \, n} + 2 \, a^{4} b n x^{n} + a^{5} n\right)}}"," ",0,"1/2*(2*b^2*n*x^(2*n)*log(x) + 2*a^2*n*log(x) + 3*a^2 + 2*(2*a*b*n*log(x) + a*b)*x^n - 2*(b^2*x^(2*n) + 2*a*b*x^n + a^2)*log(b*x^n + a))/(a^3*b^2*n*x^(2*n) + 2*a^4*b*n*x^n + a^5*n)","A",0
541,0,0,0,1.043803," ","integrate(1/x^2/(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}}{b^{4} x^{2} x^{4 \, n} + 4 \, a^{2} b^{2} x^{2} x^{2 \, n} + 4 \, a^{3} b x^{2} x^{n} + a^{4} x^{2} + 2 \, {\left(2 \, a b^{3} x^{2} x^{n} + a^{2} b^{2} x^{2}\right)} x^{2 \, n}}, x\right)"," ",0,"integral(sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2)/(b^4*x^2*x^(4*n) + 4*a^2*b^2*x^2*x^(2*n) + 4*a^3*b*x^2*x^n + a^4*x^2 + 2*(2*a*b^3*x^2*x^n + a^2*b^2*x^2)*x^(2*n)), x)","F",0
542,0,0,0,0.895396," ","integrate(1/x^3/(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}}}{b^{4} x^{3} x^{4 \, n} + 4 \, a^{2} b^{2} x^{3} x^{2 \, n} + 4 \, a^{3} b x^{3} x^{n} + a^{4} x^{3} + 2 \, {\left(2 \, a b^{3} x^{3} x^{n} + a^{2} b^{2} x^{3}\right)} x^{2 \, n}}, x\right)"," ",0,"integral(sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2)/(b^4*x^3*x^(4*n) + 4*a^2*b^2*x^3*x^(2*n) + 4*a^3*b*x^3*x^n + a^4*x^3 + 2*(2*a*b^3*x^3*x^n + a^2*b^2*x^3)*x^(2*n)), x)","F",0
543,1,79,0,1.090204," ","integrate((a^2+b^2/(x^(2/(1+2*p)))+2*a*b/(x^(1/(1+2*p))))^p,x, algorithm=""fricas"")","\frac{{\left(a x x^{\left(\frac{1}{2 \, p + 1}\right)} + b x\right)} \left(\frac{a^{2} x^{\frac{2}{2 \, p + 1}} + 2 \, a b x^{\left(\frac{1}{2 \, p + 1}\right)} + b^{2}}{x^{\frac{2}{2 \, p + 1}}}\right)^{p}}{a x^{\left(\frac{1}{2 \, p + 1}\right)}}"," ",0,"(a*x*x^(1/(2*p + 1)) + b*x)*((a^2*x^(2/(2*p + 1)) + 2*a*b*x^(1/(2*p + 1)) + b^2)/x^(2/(2*p + 1)))^p/(a*x^(1/(2*p + 1)))","A",0
544,1,45,0,1.278655," ","integrate(1/((a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2*(1+n)/n)),x, algorithm=""fricas"")","\frac{b x x^{n} + a x}{{\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{\frac{n + 1}{2 \, n}} a}"," ",0,"(b*x*x^n + a*x)/((b^2*x^(2*n) + 2*a*b*x^n + a^2)^(1/2*(n + 1)/n)*a)","A",0
545,1,103,0,0.928365," ","integrate((a^2+b^2/(x^(1/(1+p)))+2*a*b/(x^(1/2/(1+p))))^p,x, algorithm=""fricas"")","\frac{{\left(2 \, a b p x x^{\frac{1}{2 \, {\left(p + 1\right)}}} - b^{2} x + {\left(2 \, a^{2} p + a^{2}\right)} x x^{\left(\frac{1}{p + 1}\right)}\right)} \left(\frac{2 \, a b x^{\frac{1}{2 \, {\left(p + 1\right)}}} + a^{2} x^{\left(\frac{1}{p + 1}\right)} + b^{2}}{x^{\left(\frac{1}{p + 1}\right)}}\right)^{p}}{{\left(2 \, a^{2} p + a^{2}\right)} x^{\left(\frac{1}{p + 1}\right)}}"," ",0,"(2*a*b*p*x*x^(1/2/(p + 1)) - b^2*x + (2*a^2*p + a^2)*x*x^(1/(p + 1)))*((2*a*b*x^(1/2/(p + 1)) + a^2*x^(1/(p + 1)) + b^2)/x^(1/(p + 1)))^p/((2*a^2*p + a^2)*x^(1/(p + 1)))","A",0
546,1,82,0,1.130545," ","integrate(1/((a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2*(1+2*n)/n)),x, algorithm=""fricas"")","\frac{b^{2} n x x^{2 \, n} + {\left(2 \, a b n + a b\right)} x x^{n} + {\left(a^{2} n + a^{2}\right)} x}{{\left(a^{2} n + a^{2}\right)} {\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{\frac{2 \, n + 1}{2 \, n}}}"," ",0,"(b^2*n*x*x^(2*n) + (2*a*b*n + a*b)*x*x^n + (a^2*n + a^2)*x)/((a^2*n + a^2)*(b^2*x^(2*n) + 2*a*b*x^n + a^2)^(1/2*(2*n + 1)/n))","A",0
547,1,165,0,1.076464," ","integrate((d*x)^(-1-2*n*(1+p))*(a^2+2*a*b*x^n+b^2*x^(2*n))^p,x, algorithm=""fricas"")","-\frac{{\left(2 \, a b p x x^{n} e^{\left(-{\left(2 \, n p + 2 \, n + 1\right)} \log\left(d\right) - {\left(2 \, n p + 2 \, n + 1\right)} \log\left(x\right)\right)} - b^{2} x x^{2 \, n} e^{\left(-{\left(2 \, n p + 2 \, n + 1\right)} \log\left(d\right) - {\left(2 \, n p + 2 \, n + 1\right)} \log\left(x\right)\right)} + {\left(2 \, a^{2} p + a^{2}\right)} x e^{\left(-{\left(2 \, n p + 2 \, n + 1\right)} \log\left(d\right) - {\left(2 \, n p + 2 \, n + 1\right)} \log\left(x\right)\right)}\right)} {\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{p}}{2 \, {\left(2 \, a^{2} n p^{2} + 3 \, a^{2} n p + a^{2} n\right)}}"," ",0,"-1/2*(2*a*b*p*x*x^n*e^(-(2*n*p + 2*n + 1)*log(d) - (2*n*p + 2*n + 1)*log(x)) - b^2*x*x^(2*n)*e^(-(2*n*p + 2*n + 1)*log(d) - (2*n*p + 2*n + 1)*log(x)) + (2*a^2*p + a^2)*x*e^(-(2*n*p + 2*n + 1)*log(d) - (2*n*p + 2*n + 1)*log(x)))*(b^2*x^(2*n) + 2*a*b*x^n + a^2)^p/(2*a^2*n*p^2 + 3*a^2*n*p + a^2*n)","A",0
548,1,78,0,1.078221," ","integrate(x^(-1+2*n)*(a^2+2*a*b*x^n+b^2*x^(2*n))^p,x, algorithm=""fricas"")","\frac{{\left(2 \, a b p x^{n} - a^{2} + {\left(2 \, b^{2} p + b^{2}\right)} x^{2 \, n}\right)} {\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2}\right)}^{p}}{2 \, {\left(2 \, b^{2} n p^{2} + 3 \, b^{2} n p + b^{2} n\right)}}"," ",0,"1/2*(2*a*b*p*x^n - a^2 + (2*b^2*p + b^2)*x^(2*n))*(b^2*x^(2*n) + 2*a*b*x^n + a^2)^p/(2*b^2*n*p^2 + 3*b^2*n*p + b^2*n)","A",0
549,1,353,0,1.182714," ","integrate(x^(-1+4*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{3} - 3 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2 \, n} + b^{2} - 2 \, a c + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} x^{n} - \sqrt{b^{2} - 4 \, a c} b}{c x^{2 \, n} + b x^{n} + a}\right) - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2 \, n} + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{n} - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} \log\left(c x^{2 \, n} + b x^{n} + a\right)}{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} n}, \frac{2 \, {\left(b^{3} - 3 \, a b c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{2 \, \sqrt{-b^{2} + 4 \, a c} c x^{n} + \sqrt{-b^{2} + 4 \, a c} b}{b^{2} - 4 \, a c}\right) + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2 \, n} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{n} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} \log\left(c x^{2 \, n} + b x^{n} + a\right)}{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} n}\right]"," ",0,"[-1/2*((b^3 - 3*a*b*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^(2*n) + b^2 - 2*a*c + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*x^n - sqrt(b^2 - 4*a*c)*b)/(c*x^(2*n) + b*x^n + a)) - (b^2*c^2 - 4*a*c^3)*x^(2*n) + 2*(b^3*c - 4*a*b*c^2)*x^n - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*log(c*x^(2*n) + b*x^n + a))/((b^2*c^3 - 4*a*c^4)*n), 1/2*(2*(b^3 - 3*a*b*c)*sqrt(-b^2 + 4*a*c)*arctan(-(2*sqrt(-b^2 + 4*a*c)*c*x^n + sqrt(-b^2 + 4*a*c)*b)/(b^2 - 4*a*c)) + (b^2*c^2 - 4*a*c^3)*x^(2*n) - 2*(b^3*c - 4*a*b*c^2)*x^n + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*log(c*x^(2*n) + b*x^n + a))/((b^2*c^3 - 4*a*c^4)*n)]","A",0
550,1,285,0,1.076950," ","integrate(x^(-1+3*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 2 \, a c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2 \, n} + b^{2} - 2 \, a c + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} x^{n} + \sqrt{b^{2} - 4 \, a c} b}{c x^{2 \, n} + b x^{n} + a}\right) - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x^{n} + {\left(b^{3} - 4 \, a b c\right)} \log\left(c x^{2 \, n} + b x^{n} + a\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} n}, -\frac{2 \, {\left(b^{2} - 2 \, a c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{2 \, \sqrt{-b^{2} + 4 \, a c} c x^{n} + \sqrt{-b^{2} + 4 \, a c} b}{b^{2} - 4 \, a c}\right) - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x^{n} + {\left(b^{3} - 4 \, a b c\right)} \log\left(c x^{2 \, n} + b x^{n} + a\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} n}\right]"," ",0,"[-1/2*((b^2 - 2*a*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^(2*n) + b^2 - 2*a*c + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*x^n + sqrt(b^2 - 4*a*c)*b)/(c*x^(2*n) + b*x^n + a)) - 2*(b^2*c - 4*a*c^2)*x^n + (b^3 - 4*a*b*c)*log(c*x^(2*n) + b*x^n + a))/((b^2*c^2 - 4*a*c^3)*n), -1/2*(2*(b^2 - 2*a*c)*sqrt(-b^2 + 4*a*c)*arctan(-(2*sqrt(-b^2 + 4*a*c)*c*x^n + sqrt(-b^2 + 4*a*c)*b)/(b^2 - 4*a*c)) - 2*(b^2*c - 4*a*c^2)*x^n + (b^3 - 4*a*b*c)*log(c*x^(2*n) + b*x^n + a))/((b^2*c^2 - 4*a*c^3)*n)]","A",0
551,1,231,0,1.578779," ","integrate(x^(-1+2*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} - 4 \, a c} b \log\left(\frac{2 \, c^{2} x^{2 \, n} + b^{2} - 2 \, a c + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} x^{n} + \sqrt{b^{2} - 4 \, a c} b}{c x^{2 \, n} + b x^{n} + a}\right) + {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{2 \, n} + b x^{n} + a\right)}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} n}, \frac{2 \, \sqrt{-b^{2} + 4 \, a c} b \arctan\left(-\frac{2 \, \sqrt{-b^{2} + 4 \, a c} c x^{n} + \sqrt{-b^{2} + 4 \, a c} b}{b^{2} - 4 \, a c}\right) + {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{2 \, n} + b x^{n} + a\right)}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} n}\right]"," ",0,"[1/2*(sqrt(b^2 - 4*a*c)*b*log((2*c^2*x^(2*n) + b^2 - 2*a*c + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*x^n + sqrt(b^2 - 4*a*c)*b)/(c*x^(2*n) + b*x^n + a)) + (b^2 - 4*a*c)*log(c*x^(2*n) + b*x^n + a))/((b^2*c - 4*a*c^2)*n), 1/2*(2*sqrt(-b^2 + 4*a*c)*b*arctan(-(2*sqrt(-b^2 + 4*a*c)*c*x^n + sqrt(-b^2 + 4*a*c)*b)/(b^2 - 4*a*c)) + (b^2 - 4*a*c)*log(c*x^(2*n) + b*x^n + a))/((b^2*c - 4*a*c^2)*n)]","A",0
552,1,159,0,1.223087," ","integrate(x^(-1+n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{2 \, c^{2} x^{2 \, n} + b^{2} - 2 \, a c + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} x^{n} - \sqrt{b^{2} - 4 \, a c} b}{c x^{2 \, n} + b x^{n} + a}\right)}{\sqrt{b^{2} - 4 \, a c} n}, -\frac{2 \, \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{2 \, \sqrt{-b^{2} + 4 \, a c} c x^{n} + \sqrt{-b^{2} + 4 \, a c} b}{b^{2} - 4 \, a c}\right)}{{\left(b^{2} - 4 \, a c\right)} n}\right]"," ",0,"[log((2*c^2*x^(2*n) + b^2 - 2*a*c + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*x^n - sqrt(b^2 - 4*a*c)*b)/(c*x^(2*n) + b*x^n + a))/(sqrt(b^2 - 4*a*c)*n), -2*sqrt(-b^2 + 4*a*c)*arctan(-(2*sqrt(-b^2 + 4*a*c)*c*x^n + sqrt(-b^2 + 4*a*c)*b)/(b^2 - 4*a*c))/((b^2 - 4*a*c)*n)]","B",0
553,1,333,0,1.407896," ","integrate(x^(-1-n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(b^{3} - 4 \, a b c\right)} n x^{n} \log\left(x\right) + {\left(b^{2} - 2 \, a c\right)} \sqrt{b^{2} - 4 \, a c} x^{n} \log\left(\frac{2 \, c^{2} x^{2 \, n} + b^{2} - 2 \, a c + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} x^{n} + \sqrt{b^{2} - 4 \, a c} b}{c x^{2 \, n} + b x^{n} + a}\right) + 2 \, a b^{2} - 8 \, a^{2} c - {\left(b^{3} - 4 \, a b c\right)} x^{n} \log\left(c x^{2 \, n} + b x^{n} + a\right)}{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n x^{n}}, -\frac{2 \, {\left(b^{3} - 4 \, a b c\right)} n x^{n} \log\left(x\right) + 2 \, {\left(b^{2} - 2 \, a c\right)} \sqrt{-b^{2} + 4 \, a c} x^{n} \arctan\left(-\frac{2 \, \sqrt{-b^{2} + 4 \, a c} c x^{n} + \sqrt{-b^{2} + 4 \, a c} b}{b^{2} - 4 \, a c}\right) + 2 \, a b^{2} - 8 \, a^{2} c - {\left(b^{3} - 4 \, a b c\right)} x^{n} \log\left(c x^{2 \, n} + b x^{n} + a\right)}{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n x^{n}}\right]"," ",0,"[-1/2*(2*(b^3 - 4*a*b*c)*n*x^n*log(x) + (b^2 - 2*a*c)*sqrt(b^2 - 4*a*c)*x^n*log((2*c^2*x^(2*n) + b^2 - 2*a*c + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*x^n + sqrt(b^2 - 4*a*c)*b)/(c*x^(2*n) + b*x^n + a)) + 2*a*b^2 - 8*a^2*c - (b^3 - 4*a*b*c)*x^n*log(c*x^(2*n) + b*x^n + a))/((a^2*b^2 - 4*a^3*c)*n*x^n), -1/2*(2*(b^3 - 4*a*b*c)*n*x^n*log(x) + 2*(b^2 - 2*a*c)*sqrt(-b^2 + 4*a*c)*x^n*arctan(-(2*sqrt(-b^2 + 4*a*c)*c*x^n + sqrt(-b^2 + 4*a*c)*b)/(b^2 - 4*a*c)) + 2*a*b^2 - 8*a^2*c - (b^3 - 4*a*b*c)*x^n*log(c*x^(2*n) + b*x^n + a))/((a^2*b^2 - 4*a^3*c)*n*x^n)]","A",0
554,1,429,0,1.409107," ","integrate(x^(-1-2*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\left[-\frac{a^{2} b^{2} - 4 \, a^{3} c - 2 \, {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} n x^{2 \, n} \log\left(x\right) + {\left(b^{3} - 3 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} x^{2 \, n} \log\left(\frac{2 \, c^{2} x^{2 \, n} + b^{2} - 2 \, a c + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} x^{n} - \sqrt{b^{2} - 4 \, a c} b}{c x^{2 \, n} + b x^{n} + a}\right) + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} x^{2 \, n} \log\left(c x^{2 \, n} + b x^{n} + a\right) - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{n}}{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} n x^{2 \, n}}, -\frac{a^{2} b^{2} - 4 \, a^{3} c - 2 \, {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} n x^{2 \, n} \log\left(x\right) - 2 \, {\left(b^{3} - 3 \, a b c\right)} \sqrt{-b^{2} + 4 \, a c} x^{2 \, n} \arctan\left(-\frac{2 \, \sqrt{-b^{2} + 4 \, a c} c x^{n} + \sqrt{-b^{2} + 4 \, a c} b}{b^{2} - 4 \, a c}\right) + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} x^{2 \, n} \log\left(c x^{2 \, n} + b x^{n} + a\right) - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{n}}{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} n x^{2 \, n}}\right]"," ",0,"[-1/2*(a^2*b^2 - 4*a^3*c - 2*(b^4 - 5*a*b^2*c + 4*a^2*c^2)*n*x^(2*n)*log(x) + (b^3 - 3*a*b*c)*sqrt(b^2 - 4*a*c)*x^(2*n)*log((2*c^2*x^(2*n) + b^2 - 2*a*c + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*x^n - sqrt(b^2 - 4*a*c)*b)/(c*x^(2*n) + b*x^n + a)) + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*x^(2*n)*log(c*x^(2*n) + b*x^n + a) - 2*(a*b^3 - 4*a^2*b*c)*x^n)/((a^3*b^2 - 4*a^4*c)*n*x^(2*n)), -1/2*(a^2*b^2 - 4*a^3*c - 2*(b^4 - 5*a*b^2*c + 4*a^2*c^2)*n*x^(2*n)*log(x) - 2*(b^3 - 3*a*b*c)*sqrt(-b^2 + 4*a*c)*x^(2*n)*arctan(-(2*sqrt(-b^2 + 4*a*c)*c*x^n + sqrt(-b^2 + 4*a*c)*b)/(b^2 - 4*a*c)) + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*x^(2*n)*log(c*x^(2*n) + b*x^n + a) - 2*(a*b^3 - 4*a^2*b*c)*x^n)/((a^3*b^2 - 4*a^4*c)*n*x^(2*n))]","A",0
555,1,522,0,1.359107," ","integrate(x^(-1-3*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\left[-\frac{2 \, a^{3} b^{2} - 8 \, a^{4} c + 6 \, {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} n x^{3 \, n} \log\left(x\right) - 3 \, {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} x^{3 \, n} \log\left(\frac{2 \, c^{2} x^{2 \, n} + b^{2} - 2 \, a c + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} x^{n} - \sqrt{b^{2} - 4 \, a c} b}{c x^{2 \, n} + b x^{n} + a}\right) - 3 \, {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} x^{3 \, n} \log\left(c x^{2 \, n} + b x^{n} + a\right) + 6 \, {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} x^{2 \, n} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{n}}{6 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n x^{3 \, n}}, -\frac{2 \, a^{3} b^{2} - 8 \, a^{4} c + 6 \, {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} n x^{3 \, n} \log\left(x\right) + 6 \, {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c} x^{3 \, n} \arctan\left(-\frac{2 \, \sqrt{-b^{2} + 4 \, a c} c x^{n} + \sqrt{-b^{2} + 4 \, a c} b}{b^{2} - 4 \, a c}\right) - 3 \, {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} x^{3 \, n} \log\left(c x^{2 \, n} + b x^{n} + a\right) + 6 \, {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} x^{2 \, n} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} x^{n}}{6 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n x^{3 \, n}}\right]"," ",0,"[-1/6*(2*a^3*b^2 - 8*a^4*c + 6*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*n*x^(3*n)*log(x) - 3*(b^4 - 4*a*b^2*c + 2*a^2*c^2)*sqrt(b^2 - 4*a*c)*x^(3*n)*log((2*c^2*x^(2*n) + b^2 - 2*a*c + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*x^n - sqrt(b^2 - 4*a*c)*b)/(c*x^(2*n) + b*x^n + a)) - 3*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*x^(3*n)*log(c*x^(2*n) + b*x^n + a) + 6*(a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*x^(2*n) - 3*(a^2*b^3 - 4*a^3*b*c)*x^n)/((a^4*b^2 - 4*a^5*c)*n*x^(3*n)), -1/6*(2*a^3*b^2 - 8*a^4*c + 6*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*n*x^(3*n)*log(x) + 6*(b^4 - 4*a*b^2*c + 2*a^2*c^2)*sqrt(-b^2 + 4*a*c)*x^(3*n)*arctan(-(2*sqrt(-b^2 + 4*a*c)*c*x^n + sqrt(-b^2 + 4*a*c)*b)/(b^2 - 4*a*c)) - 3*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*x^(3*n)*log(c*x^(2*n) + b*x^n + a) + 6*(a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*x^(2*n) - 3*(a^2*b^3 - 4*a^3*b*c)*x^n)/((a^4*b^2 - 4*a^5*c)*n*x^(3*n))]","A",0
556,1,4426,0,2.559760," ","integrate(x^(-1+1/4*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","-2 \, \sqrt{2} \sqrt{\sqrt{2} \sqrt{-\frac{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4}}}} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{2} {\left({\left(a^{3} b^{10} c - 15 \, a^{4} b^{8} c^{2} + 86 \, a^{5} b^{6} c^{3} - 232 \, a^{6} b^{4} c^{4} + 288 \, a^{7} b^{2} c^{5} - 128 \, a^{8} c^{6}\right)} n^{7} x \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} - {\left(b^{9} c - 10 \, a b^{7} c^{2} + 33 \, a^{2} b^{5} c^{3} - 40 \, a^{3} b^{3} c^{4} + 16 \, a^{4} b c^{5}\right)} n^{3} x\right)} x^{\frac{1}{4} \, n - 1} \sqrt{-\frac{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4}}} + \sqrt{2} {\left({\left(a^{3} b^{8} - 14 \, a^{4} b^{6} c + 72 \, a^{5} b^{4} c^{2} - 160 \, a^{6} b^{2} c^{3} + 128 \, a^{7} c^{4}\right)} n^{7} x \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} - {\left(b^{7} - 9 \, a b^{5} c + 24 \, a^{2} b^{3} c^{2} - 16 \, a^{3} b c^{3}\right)} n^{3} x\right)} \sqrt{\frac{4 \, {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} x^{2} x^{\frac{1}{2} \, n - 2} - \sqrt{2} {\left({\left(a^{3} b^{9} - 13 \, a^{4} b^{7} c + 60 \, a^{5} b^{5} c^{2} - 112 \, a^{6} b^{3} c^{3} + 64 \, a^{7} b c^{4}\right)} n^{6} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} - {\left(b^{8} - 8 \, a b^{6} c + 21 \, a^{2} b^{4} c^{2} - 22 \, a^{3} b^{2} c^{3} + 8 \, a^{4} c^{4}\right)} n^{2}\right)} \sqrt{-\frac{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4}}}}{x^{2}}} \sqrt{-\frac{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4}}}\right)} \sqrt{\sqrt{2} \sqrt{-\frac{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4}}}}}{16 \, {\left(b^{4} c^{3} - 2 \, a b^{2} c^{4} + a^{2} c^{5}\right)}}\right) + 2 \, \sqrt{2} \sqrt{\sqrt{2} \sqrt{\frac{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4}}}} \arctan\left(\frac{2 \, {\left({\left(a^{3} b^{10} c - 15 \, a^{4} b^{8} c^{2} + 86 \, a^{5} b^{6} c^{3} - 232 \, a^{6} b^{4} c^{4} + 288 \, a^{7} b^{2} c^{5} - 128 \, a^{8} c^{6}\right)} n^{7} x \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} + {\left(b^{9} c - 10 \, a b^{7} c^{2} + 33 \, a^{2} b^{5} c^{3} - 40 \, a^{3} b^{3} c^{4} + 16 \, a^{4} b c^{5}\right)} n^{3} x\right)} x^{\frac{1}{4} \, n - 1} \sqrt{\sqrt{2} \sqrt{\frac{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4}}}} \sqrt{\frac{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4}}} + {\left({\left(a^{3} b^{8} - 14 \, a^{4} b^{6} c + 72 \, a^{5} b^{4} c^{2} - 160 \, a^{6} b^{2} c^{3} + 128 \, a^{7} c^{4}\right)} n^{7} x \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} + {\left(b^{7} - 9 \, a b^{5} c + 24 \, a^{2} b^{3} c^{2} - 16 \, a^{3} b c^{3}\right)} n^{3} x\right)} \sqrt{\sqrt{2} \sqrt{\frac{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4}}}} \sqrt{\frac{4 \, {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} x^{2} x^{\frac{1}{2} \, n - 2} + \sqrt{2} {\left({\left(a^{3} b^{9} - 13 \, a^{4} b^{7} c + 60 \, a^{5} b^{5} c^{2} - 112 \, a^{6} b^{3} c^{3} + 64 \, a^{7} b c^{4}\right)} n^{6} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} + {\left(b^{8} - 8 \, a b^{6} c + 21 \, a^{2} b^{4} c^{2} - 22 \, a^{3} b^{2} c^{3} + 8 \, a^{4} c^{4}\right)} n^{2}\right)} \sqrt{\frac{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4}}}}{x^{2}}} \sqrt{\frac{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4}}}}{8 \, {\left(b^{4} c^{3} - 2 \, a b^{2} c^{4} + a^{2} c^{5}\right)}}\right) + \frac{1}{2} \, \sqrt{2} \sqrt{\sqrt{2} \sqrt{-\frac{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4}}}} \log\left(-\frac{4 \, {\left(b^{2} c - a c^{2}\right)} x x^{\frac{1}{4} \, n - 1} + \sqrt{2} {\left({\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} n^{5} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} n\right)} \sqrt{\sqrt{2} \sqrt{-\frac{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4}}}}}{x}\right) - \frac{1}{2} \, \sqrt{2} \sqrt{\sqrt{2} \sqrt{-\frac{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4}}}} \log\left(-\frac{4 \, {\left(b^{2} c - a c^{2}\right)} x x^{\frac{1}{4} \, n - 1} - \sqrt{2} {\left({\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} n^{5} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} n\right)} \sqrt{\sqrt{2} \sqrt{-\frac{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4}}}}}{x}\right) - \frac{1}{2} \, \sqrt{2} \sqrt{\sqrt{2} \sqrt{\frac{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4}}}} \log\left(-\frac{4 \, {\left(b^{2} c - a c^{2}\right)} x x^{\frac{1}{4} \, n - 1} + \sqrt{2} {\left({\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} n^{5} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} n\right)} \sqrt{\sqrt{2} \sqrt{\frac{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4}}}}}{x}\right) + \frac{1}{2} \, \sqrt{2} \sqrt{\sqrt{2} \sqrt{\frac{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4}}}} \log\left(-\frac{4 \, {\left(b^{2} c - a c^{2}\right)} x x^{\frac{1}{4} \, n - 1} - \sqrt{2} {\left({\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} n^{5} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} n\right)} \sqrt{\sqrt{2} \sqrt{\frac{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} n^{8}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} n^{4}}}}}{x}\right)"," ",0,"-2*sqrt(2)*sqrt(sqrt(2)*sqrt(-((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) + b^3 - 3*a*b*c)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4)))*arctan(1/16*sqrt(2)*(2*sqrt(2)*((a^3*b^10*c - 15*a^4*b^8*c^2 + 86*a^5*b^6*c^3 - 232*a^6*b^4*c^4 + 288*a^7*b^2*c^5 - 128*a^8*c^6)*n^7*x*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) - (b^9*c - 10*a*b^7*c^2 + 33*a^2*b^5*c^3 - 40*a^3*b^3*c^4 + 16*a^4*b*c^5)*n^3*x)*x^(1/4*n - 1)*sqrt(-((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) + b^3 - 3*a*b*c)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4)) + sqrt(2)*((a^3*b^8 - 14*a^4*b^6*c + 72*a^5*b^4*c^2 - 160*a^6*b^2*c^3 + 128*a^7*c^4)*n^7*x*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) - (b^7 - 9*a*b^5*c + 24*a^2*b^3*c^2 - 16*a^3*b*c^3)*n^3*x)*sqrt((4*(b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*x^2*x^(1/2*n - 2) - sqrt(2)*((a^3*b^9 - 13*a^4*b^7*c + 60*a^5*b^5*c^2 - 112*a^6*b^3*c^3 + 64*a^7*b*c^4)*n^6*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) - (b^8 - 8*a*b^6*c + 21*a^2*b^4*c^2 - 22*a^3*b^2*c^3 + 8*a^4*c^4)*n^2)*sqrt(-((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) + b^3 - 3*a*b*c)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4)))/x^2)*sqrt(-((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) + b^3 - 3*a*b*c)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4)))*sqrt(sqrt(2)*sqrt(-((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) + b^3 - 3*a*b*c)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4)))/(b^4*c^3 - 2*a*b^2*c^4 + a^2*c^5)) + 2*sqrt(2)*sqrt(sqrt(2)*sqrt(((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) - b^3 + 3*a*b*c)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4)))*arctan(1/8*(2*((a^3*b^10*c - 15*a^4*b^8*c^2 + 86*a^5*b^6*c^3 - 232*a^6*b^4*c^4 + 288*a^7*b^2*c^5 - 128*a^8*c^6)*n^7*x*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) + (b^9*c - 10*a*b^7*c^2 + 33*a^2*b^5*c^3 - 40*a^3*b^3*c^4 + 16*a^4*b*c^5)*n^3*x)*x^(1/4*n - 1)*sqrt(sqrt(2)*sqrt(((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) - b^3 + 3*a*b*c)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4)))*sqrt(((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) - b^3 + 3*a*b*c)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4)) + ((a^3*b^8 - 14*a^4*b^6*c + 72*a^5*b^4*c^2 - 160*a^6*b^2*c^3 + 128*a^7*c^4)*n^7*x*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) + (b^7 - 9*a*b^5*c + 24*a^2*b^3*c^2 - 16*a^3*b*c^3)*n^3*x)*sqrt(sqrt(2)*sqrt(((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) - b^3 + 3*a*b*c)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4)))*sqrt((4*(b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*x^2*x^(1/2*n - 2) + sqrt(2)*((a^3*b^9 - 13*a^4*b^7*c + 60*a^5*b^5*c^2 - 112*a^6*b^3*c^3 + 64*a^7*b*c^4)*n^6*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) + (b^8 - 8*a*b^6*c + 21*a^2*b^4*c^2 - 22*a^3*b^2*c^3 + 8*a^4*c^4)*n^2)*sqrt(((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) - b^3 + 3*a*b*c)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4)))/x^2)*sqrt(((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) - b^3 + 3*a*b*c)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4)))/(b^4*c^3 - 2*a*b^2*c^4 + a^2*c^5)) + 1/2*sqrt(2)*sqrt(sqrt(2)*sqrt(-((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) + b^3 - 3*a*b*c)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4)))*log(-(4*(b^2*c - a*c^2)*x*x^(1/4*n - 1) + sqrt(2)*((a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*n^5*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*n)*sqrt(sqrt(2)*sqrt(-((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) + b^3 - 3*a*b*c)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4))))/x) - 1/2*sqrt(2)*sqrt(sqrt(2)*sqrt(-((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) + b^3 - 3*a*b*c)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4)))*log(-(4*(b^2*c - a*c^2)*x*x^(1/4*n - 1) - sqrt(2)*((a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*n^5*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*n)*sqrt(sqrt(2)*sqrt(-((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) + b^3 - 3*a*b*c)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4))))/x) - 1/2*sqrt(2)*sqrt(sqrt(2)*sqrt(((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) - b^3 + 3*a*b*c)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4)))*log(-(4*(b^2*c - a*c^2)*x*x^(1/4*n - 1) + sqrt(2)*((a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*n^5*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*n)*sqrt(sqrt(2)*sqrt(((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) - b^3 + 3*a*b*c)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4))))/x) + 1/2*sqrt(2)*sqrt(sqrt(2)*sqrt(((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) - b^3 + 3*a*b*c)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4)))*log(-(4*(b^2*c - a*c^2)*x*x^(1/4*n - 1) - sqrt(2)*((a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*n^5*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*n)*sqrt(sqrt(2)*sqrt(((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*n^8)) - b^3 + 3*a*b*c)/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*n^4))))/x)","B",0
557,1,4699,0,1.984322," ","integrate(x^(-1+1/3*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","2 \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} + b}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left(a^{2} b^{8} c - 14 \, a^{3} b^{6} c^{2} + 72 \, a^{4} b^{4} c^{3} - 160 \, a^{5} b^{2} c^{4} + 128 \, a^{6} c^{5}\right)} n^{5} x \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} - \sqrt{3} {\left(b^{7} c - 8 \, a b^{5} c^{2} + 20 \, a^{2} b^{3} c^{3} - 16 \, a^{3} b c^{4}\right)} n^{2} x\right)} x^{\frac{1}{3} \, n - 1} \left(\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} + b}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3}}\right)^{\frac{2}{3}} + \sqrt{2} \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} n^{5} x \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} - \sqrt{3} {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} n^{2} x\right)} \sqrt{\frac{2 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} x^{2} x^{\frac{2}{3} \, n - 2} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a^{2} b^{7} c - 10 \, a^{3} b^{5} c^{2} + 32 \, a^{4} b^{3} c^{3} - 32 \, a^{5} b c^{4}\right)} n^{4} x \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} - {\left(b^{6} c - 8 \, a b^{4} c^{2} + 20 \, a^{2} b^{2} c^{3} - 16 \, a^{3} c^{4}\right)} n x\right)} x^{\frac{1}{3} \, n - 1} \left(\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} + b}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3}}\right)^{\frac{1}{3}} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(a^{2} b^{9} - 14 \, a^{3} b^{7} c + 72 \, a^{4} b^{5} c^{2} - 160 \, a^{5} b^{3} c^{3} + 128 \, a^{6} b c^{4}\right)} n^{5} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} - {\left(b^{8} - 10 \, a b^{6} c + 36 \, a^{2} b^{4} c^{2} - 56 \, a^{3} b^{2} c^{3} + 32 \, a^{4} c^{4}\right)} n^{2}\right)} \left(\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} + b}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3}}\right)^{\frac{2}{3}}}{x^{2}}} \left(\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} + b}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3}}\right)^{\frac{2}{3}} + 2 \, \sqrt{3} {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)}}{6 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)}}\right) - 2 \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} - b}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left(a^{2} b^{8} c - 14 \, a^{3} b^{6} c^{2} + 72 \, a^{4} b^{4} c^{3} - 160 \, a^{5} b^{2} c^{4} + 128 \, a^{6} c^{5}\right)} n^{5} x \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} + \sqrt{3} {\left(b^{7} c - 8 \, a b^{5} c^{2} + 20 \, a^{2} b^{3} c^{3} - 16 \, a^{3} b c^{4}\right)} n^{2} x\right)} x^{\frac{1}{3} \, n - 1} \left(-\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} - b}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3}}\right)^{\frac{2}{3}} + \sqrt{2} \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} n^{5} x \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} + \sqrt{3} {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} n^{2} x\right)} \sqrt{\frac{2 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} x^{2} x^{\frac{2}{3} \, n - 2} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a^{2} b^{7} c - 10 \, a^{3} b^{5} c^{2} + 32 \, a^{4} b^{3} c^{3} - 32 \, a^{5} b c^{4}\right)} n^{4} x \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} + {\left(b^{6} c - 8 \, a b^{4} c^{2} + 20 \, a^{2} b^{2} c^{3} - 16 \, a^{3} c^{4}\right)} n x\right)} x^{\frac{1}{3} \, n - 1} \left(-\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} - b}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3}}\right)^{\frac{1}{3}} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(a^{2} b^{9} - 14 \, a^{3} b^{7} c + 72 \, a^{4} b^{5} c^{2} - 160 \, a^{5} b^{3} c^{3} + 128 \, a^{6} b c^{4}\right)} n^{5} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} + {\left(b^{8} - 10 \, a b^{6} c + 36 \, a^{2} b^{4} c^{2} - 56 \, a^{3} b^{2} c^{3} + 32 \, a^{4} c^{4}\right)} n^{2}\right)} \left(-\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} - b}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3}}\right)^{\frac{2}{3}}}{x^{2}}} \left(-\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} - b}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3}}\right)^{\frac{2}{3}} - 2 \, \sqrt{3} {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)}}{6 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)}}\right) + \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} + b}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3}}\right)^{\frac{1}{3}} \log\left(-\frac{2 \, {\left(b^{2} c - 2 \, a c^{2}\right)} x x^{\frac{1}{3} \, n - 1} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} n\right)} \left(\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} + b}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3}}\right)^{\frac{1}{3}}}{x}\right) + \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} - b}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3}}\right)^{\frac{1}{3}} \log\left(-\frac{2 \, {\left(b^{2} c - 2 \, a c^{2}\right)} x x^{\frac{1}{3} \, n - 1} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} n^{4} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} n\right)} \left(-\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} - b}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3}}\right)^{\frac{1}{3}}}{x}\right) - \frac{1}{2} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} + b}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3}}\right)^{\frac{1}{3}} \log\left(\frac{8 \, {\left(2 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} x^{2} x^{\frac{2}{3} \, n - 2} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a^{2} b^{7} c - 10 \, a^{3} b^{5} c^{2} + 32 \, a^{4} b^{3} c^{3} - 32 \, a^{5} b c^{4}\right)} n^{4} x \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} - {\left(b^{6} c - 8 \, a b^{4} c^{2} + 20 \, a^{2} b^{2} c^{3} - 16 \, a^{3} c^{4}\right)} n x\right)} x^{\frac{1}{3} \, n - 1} \left(\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} + b}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3}}\right)^{\frac{1}{3}} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(a^{2} b^{9} - 14 \, a^{3} b^{7} c + 72 \, a^{4} b^{5} c^{2} - 160 \, a^{5} b^{3} c^{3} + 128 \, a^{6} b c^{4}\right)} n^{5} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} - {\left(b^{8} - 10 \, a b^{6} c + 36 \, a^{2} b^{4} c^{2} - 56 \, a^{3} b^{2} c^{3} + 32 \, a^{4} c^{4}\right)} n^{2}\right)} \left(\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} + b}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3}}\right)^{\frac{2}{3}}\right)}}{x^{2}}\right) - \frac{1}{2} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} - b}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3}}\right)^{\frac{1}{3}} \log\left(\frac{8 \, {\left(2 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} x^{2} x^{\frac{2}{3} \, n - 2} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a^{2} b^{7} c - 10 \, a^{3} b^{5} c^{2} + 32 \, a^{4} b^{3} c^{3} - 32 \, a^{5} b c^{4}\right)} n^{4} x \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} + {\left(b^{6} c - 8 \, a b^{4} c^{2} + 20 \, a^{2} b^{2} c^{3} - 16 \, a^{3} c^{4}\right)} n x\right)} x^{\frac{1}{3} \, n - 1} \left(-\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} - b}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3}}\right)^{\frac{1}{3}} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(a^{2} b^{9} - 14 \, a^{3} b^{7} c + 72 \, a^{4} b^{5} c^{2} - 160 \, a^{5} b^{3} c^{3} + 128 \, a^{6} b c^{4}\right)} n^{5} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} + {\left(b^{8} - 10 \, a b^{6} c + 36 \, a^{2} b^{4} c^{2} - 56 \, a^{3} b^{2} c^{3} + 32 \, a^{4} c^{4}\right)} n^{2}\right)} \left(-\frac{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3} \sqrt{\frac{b^{4} - 4 \, a b^{2} c + 4 \, a^{2} c^{2}}{{\left(a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3}\right)} n^{6}}} - b}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{3}}\right)^{\frac{2}{3}}\right)}}{x^{2}}\right)"," ",0,"2*sqrt(3)*(1/2)^(1/3)*(((a^2*b^2 - 4*a^3*c)*n^3*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) + b)/((a^2*b^2 - 4*a^3*c)*n^3))^(1/3)*arctan(-1/6*(2*(1/2)^(2/3)*(sqrt(3)*(a^2*b^8*c - 14*a^3*b^6*c^2 + 72*a^4*b^4*c^3 - 160*a^5*b^2*c^4 + 128*a^6*c^5)*n^5*x*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) - sqrt(3)*(b^7*c - 8*a*b^5*c^2 + 20*a^2*b^3*c^3 - 16*a^3*b*c^4)*n^2*x)*x^(1/3*n - 1)*(((a^2*b^2 - 4*a^3*c)*n^3*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) + b)/((a^2*b^2 - 4*a^3*c)*n^3))^(2/3) + sqrt(2)*(1/2)^(2/3)*(sqrt(3)*(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*n^5*x*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) - sqrt(3)*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*n^2*x)*sqrt((2*(b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*x^2*x^(2/3*n - 2) - (1/2)^(1/3)*((a^2*b^7*c - 10*a^3*b^5*c^2 + 32*a^4*b^3*c^3 - 32*a^5*b*c^4)*n^4*x*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) - (b^6*c - 8*a*b^4*c^2 + 20*a^2*b^2*c^3 - 16*a^3*c^4)*n*x)*x^(1/3*n - 1)*(((a^2*b^2 - 4*a^3*c)*n^3*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) + b)/((a^2*b^2 - 4*a^3*c)*n^3))^(1/3) - (1/2)^(2/3)*((a^2*b^9 - 14*a^3*b^7*c + 72*a^4*b^5*c^2 - 160*a^5*b^3*c^3 + 128*a^6*b*c^4)*n^5*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) - (b^8 - 10*a*b^6*c + 36*a^2*b^4*c^2 - 56*a^3*b^2*c^3 + 32*a^4*c^4)*n^2)*(((a^2*b^2 - 4*a^3*c)*n^3*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) + b)/((a^2*b^2 - 4*a^3*c)*n^3))^(2/3))/x^2)*(((a^2*b^2 - 4*a^3*c)*n^3*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) + b)/((a^2*b^2 - 4*a^3*c)*n^3))^(2/3) + 2*sqrt(3)*(b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4))/(b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)) - 2*sqrt(3)*(1/2)^(1/3)*(-((a^2*b^2 - 4*a^3*c)*n^3*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) - b)/((a^2*b^2 - 4*a^3*c)*n^3))^(1/3)*arctan(-1/6*(2*(1/2)^(2/3)*(sqrt(3)*(a^2*b^8*c - 14*a^3*b^6*c^2 + 72*a^4*b^4*c^3 - 160*a^5*b^2*c^4 + 128*a^6*c^5)*n^5*x*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) + sqrt(3)*(b^7*c - 8*a*b^5*c^2 + 20*a^2*b^3*c^3 - 16*a^3*b*c^4)*n^2*x)*x^(1/3*n - 1)*(-((a^2*b^2 - 4*a^3*c)*n^3*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) - b)/((a^2*b^2 - 4*a^3*c)*n^3))^(2/3) + sqrt(2)*(1/2)^(2/3)*(sqrt(3)*(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*n^5*x*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) + sqrt(3)*(b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*n^2*x)*sqrt((2*(b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*x^2*x^(2/3*n - 2) + (1/2)^(1/3)*((a^2*b^7*c - 10*a^3*b^5*c^2 + 32*a^4*b^3*c^3 - 32*a^5*b*c^4)*n^4*x*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) + (b^6*c - 8*a*b^4*c^2 + 20*a^2*b^2*c^3 - 16*a^3*c^4)*n*x)*x^(1/3*n - 1)*(-((a^2*b^2 - 4*a^3*c)*n^3*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) - b)/((a^2*b^2 - 4*a^3*c)*n^3))^(1/3) + (1/2)^(2/3)*((a^2*b^9 - 14*a^3*b^7*c + 72*a^4*b^5*c^2 - 160*a^5*b^3*c^3 + 128*a^6*b*c^4)*n^5*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) + (b^8 - 10*a*b^6*c + 36*a^2*b^4*c^2 - 56*a^3*b^2*c^3 + 32*a^4*c^4)*n^2)*(-((a^2*b^2 - 4*a^3*c)*n^3*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) - b)/((a^2*b^2 - 4*a^3*c)*n^3))^(2/3))/x^2)*(-((a^2*b^2 - 4*a^3*c)*n^3*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) - b)/((a^2*b^2 - 4*a^3*c)*n^3))^(2/3) - 2*sqrt(3)*(b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4))/(b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)) + (1/2)^(1/3)*(((a^2*b^2 - 4*a^3*c)*n^3*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) + b)/((a^2*b^2 - 4*a^3*c)*n^3))^(1/3)*log(-(2*(b^2*c - 2*a*c^2)*x*x^(1/3*n - 1) + (1/2)^(1/3)*((a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*n^4*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*n)*(((a^2*b^2 - 4*a^3*c)*n^3*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) + b)/((a^2*b^2 - 4*a^3*c)*n^3))^(1/3))/x) + (1/2)^(1/3)*(-((a^2*b^2 - 4*a^3*c)*n^3*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) - b)/((a^2*b^2 - 4*a^3*c)*n^3))^(1/3)*log(-(2*(b^2*c - 2*a*c^2)*x*x^(1/3*n - 1) - (1/2)^(1/3)*((a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*n^4*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*n)*(-((a^2*b^2 - 4*a^3*c)*n^3*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) - b)/((a^2*b^2 - 4*a^3*c)*n^3))^(1/3))/x) - 1/2*(1/2)^(1/3)*(((a^2*b^2 - 4*a^3*c)*n^3*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) + b)/((a^2*b^2 - 4*a^3*c)*n^3))^(1/3)*log(8*(2*(b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*x^2*x^(2/3*n - 2) - (1/2)^(1/3)*((a^2*b^7*c - 10*a^3*b^5*c^2 + 32*a^4*b^3*c^3 - 32*a^5*b*c^4)*n^4*x*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) - (b^6*c - 8*a*b^4*c^2 + 20*a^2*b^2*c^3 - 16*a^3*c^4)*n*x)*x^(1/3*n - 1)*(((a^2*b^2 - 4*a^3*c)*n^3*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) + b)/((a^2*b^2 - 4*a^3*c)*n^3))^(1/3) - (1/2)^(2/3)*((a^2*b^9 - 14*a^3*b^7*c + 72*a^4*b^5*c^2 - 160*a^5*b^3*c^3 + 128*a^6*b*c^4)*n^5*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) - (b^8 - 10*a*b^6*c + 36*a^2*b^4*c^2 - 56*a^3*b^2*c^3 + 32*a^4*c^4)*n^2)*(((a^2*b^2 - 4*a^3*c)*n^3*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) + b)/((a^2*b^2 - 4*a^3*c)*n^3))^(2/3))/x^2) - 1/2*(1/2)^(1/3)*(-((a^2*b^2 - 4*a^3*c)*n^3*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) - b)/((a^2*b^2 - 4*a^3*c)*n^3))^(1/3)*log(8*(2*(b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*x^2*x^(2/3*n - 2) + (1/2)^(1/3)*((a^2*b^7*c - 10*a^3*b^5*c^2 + 32*a^4*b^3*c^3 - 32*a^5*b*c^4)*n^4*x*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) + (b^6*c - 8*a*b^4*c^2 + 20*a^2*b^2*c^3 - 16*a^3*c^4)*n*x)*x^(1/3*n - 1)*(-((a^2*b^2 - 4*a^3*c)*n^3*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) - b)/((a^2*b^2 - 4*a^3*c)*n^3))^(1/3) + (1/2)^(2/3)*((a^2*b^9 - 14*a^3*b^7*c + 72*a^4*b^5*c^2 - 160*a^5*b^3*c^3 + 128*a^6*b*c^4)*n^5*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) + (b^8 - 10*a*b^6*c + 36*a^2*b^4*c^2 - 56*a^3*b^2*c^3 + 32*a^4*c^4)*n^2)*(-((a^2*b^2 - 4*a^3*c)*n^3*sqrt((b^4 - 4*a*b^2*c + 4*a^2*c^2)/((a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3)*n^6)) - b)/((a^2*b^2 - 4*a^3*c)*n^3))^(2/3))/x^2)","B",0
558,1,801,0,1.363484," ","integrate(x^(-1+1/2*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \sqrt{-\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} n^{2} \sqrt{\frac{1}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{4}}} + b}{{\left(a b^{2} - 4 \, a^{2} c\right)} n^{2}}} \log\left(\frac{4 \, c x x^{\frac{1}{2} \, n - 1} + \sqrt{2} {\left({\left(a b^{3} - 4 \, a^{2} b c\right)} n^{3} \sqrt{\frac{1}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{4}}} - {\left(b^{2} - 4 \, a c\right)} n\right)} \sqrt{-\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} n^{2} \sqrt{\frac{1}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{4}}} + b}{{\left(a b^{2} - 4 \, a^{2} c\right)} n^{2}}}}{x}\right) - \frac{1}{2} \, \sqrt{2} \sqrt{-\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} n^{2} \sqrt{\frac{1}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{4}}} + b}{{\left(a b^{2} - 4 \, a^{2} c\right)} n^{2}}} \log\left(\frac{4 \, c x x^{\frac{1}{2} \, n - 1} - \sqrt{2} {\left({\left(a b^{3} - 4 \, a^{2} b c\right)} n^{3} \sqrt{\frac{1}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{4}}} - {\left(b^{2} - 4 \, a c\right)} n\right)} \sqrt{-\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} n^{2} \sqrt{\frac{1}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{4}}} + b}{{\left(a b^{2} - 4 \, a^{2} c\right)} n^{2}}}}{x}\right) - \frac{1}{2} \, \sqrt{2} \sqrt{\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} n^{2} \sqrt{\frac{1}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{4}}} - b}{{\left(a b^{2} - 4 \, a^{2} c\right)} n^{2}}} \log\left(\frac{4 \, c x x^{\frac{1}{2} \, n - 1} + \sqrt{2} {\left({\left(a b^{3} - 4 \, a^{2} b c\right)} n^{3} \sqrt{\frac{1}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{4}}} + {\left(b^{2} - 4 \, a c\right)} n\right)} \sqrt{\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} n^{2} \sqrt{\frac{1}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{4}}} - b}{{\left(a b^{2} - 4 \, a^{2} c\right)} n^{2}}}}{x}\right) + \frac{1}{2} \, \sqrt{2} \sqrt{\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} n^{2} \sqrt{\frac{1}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{4}}} - b}{{\left(a b^{2} - 4 \, a^{2} c\right)} n^{2}}} \log\left(\frac{4 \, c x x^{\frac{1}{2} \, n - 1} - \sqrt{2} {\left({\left(a b^{3} - 4 \, a^{2} b c\right)} n^{3} \sqrt{\frac{1}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{4}}} + {\left(b^{2} - 4 \, a c\right)} n\right)} \sqrt{\frac{{\left(a b^{2} - 4 \, a^{2} c\right)} n^{2} \sqrt{\frac{1}{{\left(a^{2} b^{2} - 4 \, a^{3} c\right)} n^{4}}} - b}{{\left(a b^{2} - 4 \, a^{2} c\right)} n^{2}}}}{x}\right)"," ",0,"1/2*sqrt(2)*sqrt(-((a*b^2 - 4*a^2*c)*n^2*sqrt(1/((a^2*b^2 - 4*a^3*c)*n^4)) + b)/((a*b^2 - 4*a^2*c)*n^2))*log((4*c*x*x^(1/2*n - 1) + sqrt(2)*((a*b^3 - 4*a^2*b*c)*n^3*sqrt(1/((a^2*b^2 - 4*a^3*c)*n^4)) - (b^2 - 4*a*c)*n)*sqrt(-((a*b^2 - 4*a^2*c)*n^2*sqrt(1/((a^2*b^2 - 4*a^3*c)*n^4)) + b)/((a*b^2 - 4*a^2*c)*n^2)))/x) - 1/2*sqrt(2)*sqrt(-((a*b^2 - 4*a^2*c)*n^2*sqrt(1/((a^2*b^2 - 4*a^3*c)*n^4)) + b)/((a*b^2 - 4*a^2*c)*n^2))*log((4*c*x*x^(1/2*n - 1) - sqrt(2)*((a*b^3 - 4*a^2*b*c)*n^3*sqrt(1/((a^2*b^2 - 4*a^3*c)*n^4)) - (b^2 - 4*a*c)*n)*sqrt(-((a*b^2 - 4*a^2*c)*n^2*sqrt(1/((a^2*b^2 - 4*a^3*c)*n^4)) + b)/((a*b^2 - 4*a^2*c)*n^2)))/x) - 1/2*sqrt(2)*sqrt(((a*b^2 - 4*a^2*c)*n^2*sqrt(1/((a^2*b^2 - 4*a^3*c)*n^4)) - b)/((a*b^2 - 4*a^2*c)*n^2))*log((4*c*x*x^(1/2*n - 1) + sqrt(2)*((a*b^3 - 4*a^2*b*c)*n^3*sqrt(1/((a^2*b^2 - 4*a^3*c)*n^4)) + (b^2 - 4*a*c)*n)*sqrt(((a*b^2 - 4*a^2*c)*n^2*sqrt(1/((a^2*b^2 - 4*a^3*c)*n^4)) - b)/((a*b^2 - 4*a^2*c)*n^2)))/x) + 1/2*sqrt(2)*sqrt(((a*b^2 - 4*a^2*c)*n^2*sqrt(1/((a^2*b^2 - 4*a^3*c)*n^4)) - b)/((a*b^2 - 4*a^2*c)*n^2))*log((4*c*x*x^(1/2*n - 1) - sqrt(2)*((a*b^3 - 4*a^2*b*c)*n^3*sqrt(1/((a^2*b^2 - 4*a^3*c)*n^4)) + (b^2 - 4*a*c)*n)*sqrt(((a*b^2 - 4*a^2*c)*n^2*sqrt(1/((a^2*b^2 - 4*a^3*c)*n^4)) - b)/((a*b^2 - 4*a^2*c)*n^2)))/x)","B",0
559,1,1229,0,1.248647," ","integrate(x^(-1-1/2*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\frac{\sqrt{2} a n \sqrt{-\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} n^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} n^{4}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} n^{2}}} \log\left(-\frac{4 \, {\left(b^{2} c - a c^{2}\right)} x x^{-\frac{1}{2} \, n - 1} + \sqrt{2} {\left({\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} n^{3} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} n^{4}}} - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} n\right)} \sqrt{-\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} n^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} n^{4}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} n^{2}}}}{x}\right) - \sqrt{2} a n \sqrt{-\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} n^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} n^{4}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} n^{2}}} \log\left(-\frac{4 \, {\left(b^{2} c - a c^{2}\right)} x x^{-\frac{1}{2} \, n - 1} - \sqrt{2} {\left({\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} n^{3} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} n^{4}}} - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} n\right)} \sqrt{-\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} n^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} n^{4}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} n^{2}}}}{x}\right) - \sqrt{2} a n \sqrt{\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} n^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} n^{4}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} n^{2}}} \log\left(-\frac{4 \, {\left(b^{2} c - a c^{2}\right)} x x^{-\frac{1}{2} \, n - 1} + \sqrt{2} {\left({\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} n^{3} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} n^{4}}} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} n\right)} \sqrt{\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} n^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} n^{4}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} n^{2}}}}{x}\right) + \sqrt{2} a n \sqrt{\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} n^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} n^{4}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} n^{2}}} \log\left(-\frac{4 \, {\left(b^{2} c - a c^{2}\right)} x x^{-\frac{1}{2} \, n - 1} - \sqrt{2} {\left({\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} n^{3} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} n^{4}}} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} n\right)} \sqrt{\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} n^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} n^{4}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} n^{2}}}}{x}\right) - 4 \, x x^{-\frac{1}{2} \, n - 1}}{2 \, a n}"," ",0,"1/2*(sqrt(2)*a*n*sqrt(-((a^3*b^2 - 4*a^4*c)*n^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*n^4)) + b^3 - 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*n^2))*log(-(4*(b^2*c - a*c^2)*x*x^(-1/2*n - 1) + sqrt(2)*((a^3*b^3 - 4*a^4*b*c)*n^3*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*n^4)) - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*n)*sqrt(-((a^3*b^2 - 4*a^4*c)*n^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*n^4)) + b^3 - 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*n^2)))/x) - sqrt(2)*a*n*sqrt(-((a^3*b^2 - 4*a^4*c)*n^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*n^4)) + b^3 - 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*n^2))*log(-(4*(b^2*c - a*c^2)*x*x^(-1/2*n - 1) - sqrt(2)*((a^3*b^3 - 4*a^4*b*c)*n^3*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*n^4)) - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*n)*sqrt(-((a^3*b^2 - 4*a^4*c)*n^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*n^4)) + b^3 - 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*n^2)))/x) - sqrt(2)*a*n*sqrt(((a^3*b^2 - 4*a^4*c)*n^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*n^4)) - b^3 + 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*n^2))*log(-(4*(b^2*c - a*c^2)*x*x^(-1/2*n - 1) + sqrt(2)*((a^3*b^3 - 4*a^4*b*c)*n^3*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*n^4)) + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*n)*sqrt(((a^3*b^2 - 4*a^4*c)*n^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*n^4)) - b^3 + 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*n^2)))/x) + sqrt(2)*a*n*sqrt(((a^3*b^2 - 4*a^4*c)*n^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*n^4)) - b^3 + 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*n^2))*log(-(4*(b^2*c - a*c^2)*x*x^(-1/2*n - 1) - sqrt(2)*((a^3*b^3 - 4*a^4*b*c)*n^3*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*n^4)) + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*n)*sqrt(((a^3*b^2 - 4*a^4*c)*n^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*n^4)) - b^3 + 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*n^2)))/x) - 4*x*x^(-1/2*n - 1))/(a*n)","B",0
560,1,6279,0,7.485255," ","integrate(x^(-1-1/3*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} a n \left(\frac{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} + b^{3} - 2 \, a b c}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left(a^{4} b^{12} c - 17 \, a^{5} b^{10} c^{2} + 114 \, a^{6} b^{8} c^{3} - 378 \, a^{7} b^{6} c^{4} + 632 \, a^{8} b^{4} c^{5} - 480 \, a^{9} b^{2} c^{6} + 128 \, a^{10} c^{7}\right)} n^{5} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} - \sqrt{3} {\left(b^{13} c - 15 \, a b^{11} c^{2} + 88 \, a^{2} b^{9} c^{3} - 252 \, a^{3} b^{7} c^{4} + 356 \, a^{4} b^{5} c^{5} - 220 \, a^{5} b^{3} c^{6} + 48 \, a^{6} b c^{7}\right)} n^{2} x\right)} x^{-\frac{1}{3} \, n - 1} \left(\frac{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} + b^{3} - 2 \, a b c}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3}}\right)^{\frac{2}{3}} - \sqrt{2} \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left(a^{4} b^{8} - 13 \, a^{5} b^{6} c + 60 \, a^{6} b^{4} c^{2} - 112 \, a^{7} b^{2} c^{3} + 64 \, a^{8} c^{4}\right)} n^{5} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} - \sqrt{3} {\left(b^{9} - 11 \, a b^{7} c + 42 \, a^{2} b^{5} c^{2} - 62 \, a^{3} b^{3} c^{3} + 24 \, a^{4} b c^{4}\right)} n^{2} x\right)} \sqrt{\frac{2 \, {\left(b^{8} c^{2} - 8 \, a b^{6} c^{3} + 20 \, a^{2} b^{4} c^{4} - 16 \, a^{3} b^{2} c^{5} + 4 \, a^{4} c^{6}\right)} x^{2} x^{-\frac{2}{3} \, n - 2} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a^{4} b^{9} c - 12 \, a^{5} b^{7} c^{2} + 50 \, a^{6} b^{5} c^{3} - 80 \, a^{7} b^{3} c^{4} + 32 \, a^{8} b c^{5}\right)} n^{4} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} - {\left(b^{10} c - 12 \, a b^{8} c^{2} + 52 \, a^{2} b^{6} c^{3} - 96 \, a^{3} b^{4} c^{4} + 68 \, a^{4} b^{2} c^{5} - 16 \, a^{5} c^{6}\right)} n x\right)} x^{-\frac{1}{3} \, n - 1} \left(\frac{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} + b^{3} - 2 \, a b c}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3}}\right)^{\frac{1}{3}} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(a^{4} b^{11} - 16 \, a^{5} b^{9} c + 98 \, a^{6} b^{7} c^{2} - 280 \, a^{7} b^{5} c^{3} + 352 \, a^{8} b^{3} c^{4} - 128 \, a^{9} b c^{5}\right)} n^{5} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} - {\left(b^{12} - 14 \, a b^{10} c + 76 \, a^{2} b^{8} c^{2} - 200 \, a^{3} b^{6} c^{3} + 260 \, a^{4} b^{4} c^{4} - 152 \, a^{5} b^{2} c^{5} + 32 \, a^{6} c^{6}\right)} n^{2}\right)} \left(\frac{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} + b^{3} - 2 \, a b c}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3}}\right)^{\frac{2}{3}}}{x^{2}}} \left(\frac{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} + b^{3} - 2 \, a b c}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3}}\right)^{\frac{2}{3}} + 2 \, \sqrt{3} {\left(b^{8} c^{4} - 8 \, a b^{6} c^{5} + 20 \, a^{2} b^{4} c^{6} - 16 \, a^{3} b^{2} c^{7} + 4 \, a^{4} c^{8}\right)}}{6 \, {\left(b^{8} c^{4} - 8 \, a b^{6} c^{5} + 20 \, a^{2} b^{4} c^{6} - 16 \, a^{3} b^{2} c^{7} + 4 \, a^{4} c^{8}\right)}}\right) - 4 \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} a n \left(-\frac{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} - b^{3} + 2 \, a b c}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left(a^{4} b^{12} c - 17 \, a^{5} b^{10} c^{2} + 114 \, a^{6} b^{8} c^{3} - 378 \, a^{7} b^{6} c^{4} + 632 \, a^{8} b^{4} c^{5} - 480 \, a^{9} b^{2} c^{6} + 128 \, a^{10} c^{7}\right)} n^{5} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} + \sqrt{3} {\left(b^{13} c - 15 \, a b^{11} c^{2} + 88 \, a^{2} b^{9} c^{3} - 252 \, a^{3} b^{7} c^{4} + 356 \, a^{4} b^{5} c^{5} - 220 \, a^{5} b^{3} c^{6} + 48 \, a^{6} b c^{7}\right)} n^{2} x\right)} x^{-\frac{1}{3} \, n - 1} \left(-\frac{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} - b^{3} + 2 \, a b c}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3}}\right)^{\frac{2}{3}} - \sqrt{2} \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left(a^{4} b^{8} - 13 \, a^{5} b^{6} c + 60 \, a^{6} b^{4} c^{2} - 112 \, a^{7} b^{2} c^{3} + 64 \, a^{8} c^{4}\right)} n^{5} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} + \sqrt{3} {\left(b^{9} - 11 \, a b^{7} c + 42 \, a^{2} b^{5} c^{2} - 62 \, a^{3} b^{3} c^{3} + 24 \, a^{4} b c^{4}\right)} n^{2} x\right)} \sqrt{\frac{2 \, {\left(b^{8} c^{2} - 8 \, a b^{6} c^{3} + 20 \, a^{2} b^{4} c^{4} - 16 \, a^{3} b^{2} c^{5} + 4 \, a^{4} c^{6}\right)} x^{2} x^{-\frac{2}{3} \, n - 2} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a^{4} b^{9} c - 12 \, a^{5} b^{7} c^{2} + 50 \, a^{6} b^{5} c^{3} - 80 \, a^{7} b^{3} c^{4} + 32 \, a^{8} b c^{5}\right)} n^{4} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} + {\left(b^{10} c - 12 \, a b^{8} c^{2} + 52 \, a^{2} b^{6} c^{3} - 96 \, a^{3} b^{4} c^{4} + 68 \, a^{4} b^{2} c^{5} - 16 \, a^{5} c^{6}\right)} n x\right)} x^{-\frac{1}{3} \, n - 1} \left(-\frac{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} - b^{3} + 2 \, a b c}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3}}\right)^{\frac{1}{3}} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(a^{4} b^{11} - 16 \, a^{5} b^{9} c + 98 \, a^{6} b^{7} c^{2} - 280 \, a^{7} b^{5} c^{3} + 352 \, a^{8} b^{3} c^{4} - 128 \, a^{9} b c^{5}\right)} n^{5} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} + {\left(b^{12} - 14 \, a b^{10} c + 76 \, a^{2} b^{8} c^{2} - 200 \, a^{3} b^{6} c^{3} + 260 \, a^{4} b^{4} c^{4} - 152 \, a^{5} b^{2} c^{5} + 32 \, a^{6} c^{6}\right)} n^{2}\right)} \left(-\frac{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} - b^{3} + 2 \, a b c}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3}}\right)^{\frac{2}{3}}}{x^{2}}} \left(-\frac{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} - b^{3} + 2 \, a b c}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3}}\right)^{\frac{2}{3}} - 2 \, \sqrt{3} {\left(b^{8} c^{4} - 8 \, a b^{6} c^{5} + 20 \, a^{2} b^{4} c^{6} - 16 \, a^{3} b^{2} c^{7} + 4 \, a^{4} c^{8}\right)}}{6 \, {\left(b^{8} c^{4} - 8 \, a b^{6} c^{5} + 20 \, a^{2} b^{4} c^{6} - 16 \, a^{3} b^{2} c^{7} + 4 \, a^{4} c^{8}\right)}}\right) + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} a n \left(\frac{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} + b^{3} - 2 \, a b c}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} x x^{-\frac{1}{3} \, n - 1} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} n^{4} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} - {\left(b^{6} - 8 \, a b^{4} c + 18 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} n\right)} \left(\frac{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} + b^{3} - 2 \, a b c}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3}}\right)^{\frac{1}{3}}}{x}\right) + 2 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} a n \left(-\frac{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} - b^{3} + 2 \, a b c}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3}}\right)^{\frac{1}{3}} \log\left(\frac{2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} x x^{-\frac{1}{3} \, n - 1} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} n^{4} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} + {\left(b^{6} - 8 \, a b^{4} c + 18 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} n\right)} \left(-\frac{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} - b^{3} + 2 \, a b c}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3}}\right)^{\frac{1}{3}}}{x}\right) - \left(\frac{1}{2}\right)^{\frac{1}{3}} a n \left(\frac{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} + b^{3} - 2 \, a b c}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3}}\right)^{\frac{1}{3}} \log\left(\frac{8 \, {\left(2 \, {\left(b^{8} c^{2} - 8 \, a b^{6} c^{3} + 20 \, a^{2} b^{4} c^{4} - 16 \, a^{3} b^{2} c^{5} + 4 \, a^{4} c^{6}\right)} x^{2} x^{-\frac{2}{3} \, n - 2} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a^{4} b^{9} c - 12 \, a^{5} b^{7} c^{2} + 50 \, a^{6} b^{5} c^{3} - 80 \, a^{7} b^{3} c^{4} + 32 \, a^{8} b c^{5}\right)} n^{4} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} - {\left(b^{10} c - 12 \, a b^{8} c^{2} + 52 \, a^{2} b^{6} c^{3} - 96 \, a^{3} b^{4} c^{4} + 68 \, a^{4} b^{2} c^{5} - 16 \, a^{5} c^{6}\right)} n x\right)} x^{-\frac{1}{3} \, n - 1} \left(\frac{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} + b^{3} - 2 \, a b c}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3}}\right)^{\frac{1}{3}} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(a^{4} b^{11} - 16 \, a^{5} b^{9} c + 98 \, a^{6} b^{7} c^{2} - 280 \, a^{7} b^{5} c^{3} + 352 \, a^{8} b^{3} c^{4} - 128 \, a^{9} b c^{5}\right)} n^{5} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} - {\left(b^{12} - 14 \, a b^{10} c + 76 \, a^{2} b^{8} c^{2} - 200 \, a^{3} b^{6} c^{3} + 260 \, a^{4} b^{4} c^{4} - 152 \, a^{5} b^{2} c^{5} + 32 \, a^{6} c^{6}\right)} n^{2}\right)} \left(\frac{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} + b^{3} - 2 \, a b c}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3}}\right)^{\frac{2}{3}}\right)}}{x^{2}}\right) - \left(\frac{1}{2}\right)^{\frac{1}{3}} a n \left(-\frac{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} - b^{3} + 2 \, a b c}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3}}\right)^{\frac{1}{3}} \log\left(\frac{8 \, {\left(2 \, {\left(b^{8} c^{2} - 8 \, a b^{6} c^{3} + 20 \, a^{2} b^{4} c^{4} - 16 \, a^{3} b^{2} c^{5} + 4 \, a^{4} c^{6}\right)} x^{2} x^{-\frac{2}{3} \, n - 2} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(a^{4} b^{9} c - 12 \, a^{5} b^{7} c^{2} + 50 \, a^{6} b^{5} c^{3} - 80 \, a^{7} b^{3} c^{4} + 32 \, a^{8} b c^{5}\right)} n^{4} x \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} + {\left(b^{10} c - 12 \, a b^{8} c^{2} + 52 \, a^{2} b^{6} c^{3} - 96 \, a^{3} b^{4} c^{4} + 68 \, a^{4} b^{2} c^{5} - 16 \, a^{5} c^{6}\right)} n x\right)} x^{-\frac{1}{3} \, n - 1} \left(-\frac{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} - b^{3} + 2 \, a b c}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3}}\right)^{\frac{1}{3}} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(a^{4} b^{11} - 16 \, a^{5} b^{9} c + 98 \, a^{6} b^{7} c^{2} - 280 \, a^{7} b^{5} c^{3} + 352 \, a^{8} b^{3} c^{4} - 128 \, a^{9} b c^{5}\right)} n^{5} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} + {\left(b^{12} - 14 \, a b^{10} c + 76 \, a^{2} b^{8} c^{2} - 200 \, a^{3} b^{6} c^{3} + 260 \, a^{4} b^{4} c^{4} - 152 \, a^{5} b^{2} c^{5} + 32 \, a^{6} c^{6}\right)} n^{2}\right)} \left(-\frac{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3} \sqrt{\frac{b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 16 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}}{{\left(a^{8} b^{6} - 12 \, a^{9} b^{4} c + 48 \, a^{10} b^{2} c^{2} - 64 \, a^{11} c^{3}\right)} n^{6}}} - b^{3} + 2 \, a b c}{{\left(a^{4} b^{2} - 4 \, a^{5} c\right)} n^{3}}\right)^{\frac{2}{3}}\right)}}{x^{2}}\right) - 6 \, x x^{-\frac{1}{3} \, n - 1}}{2 \, a n}"," ",0,"1/2*(4*sqrt(3)*(1/2)^(1/3)*a*n*(((a^4*b^2 - 4*a^5*c)*n^3*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) + b^3 - 2*a*b*c)/((a^4*b^2 - 4*a^5*c)*n^3))^(1/3)*arctan(-1/6*(2*(1/2)^(2/3)*(sqrt(3)*(a^4*b^12*c - 17*a^5*b^10*c^2 + 114*a^6*b^8*c^3 - 378*a^7*b^6*c^4 + 632*a^8*b^4*c^5 - 480*a^9*b^2*c^6 + 128*a^10*c^7)*n^5*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) - sqrt(3)*(b^13*c - 15*a*b^11*c^2 + 88*a^2*b^9*c^3 - 252*a^3*b^7*c^4 + 356*a^4*b^5*c^5 - 220*a^5*b^3*c^6 + 48*a^6*b*c^7)*n^2*x)*x^(-1/3*n - 1)*(((a^4*b^2 - 4*a^5*c)*n^3*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) + b^3 - 2*a*b*c)/((a^4*b^2 - 4*a^5*c)*n^3))^(2/3) - sqrt(2)*(1/2)^(2/3)*(sqrt(3)*(a^4*b^8 - 13*a^5*b^6*c + 60*a^6*b^4*c^2 - 112*a^7*b^2*c^3 + 64*a^8*c^4)*n^5*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) - sqrt(3)*(b^9 - 11*a*b^7*c + 42*a^2*b^5*c^2 - 62*a^3*b^3*c^3 + 24*a^4*b*c^4)*n^2*x)*sqrt((2*(b^8*c^2 - 8*a*b^6*c^3 + 20*a^2*b^4*c^4 - 16*a^3*b^2*c^5 + 4*a^4*c^6)*x^2*x^(-2/3*n - 2) - (1/2)^(1/3)*((a^4*b^9*c - 12*a^5*b^7*c^2 + 50*a^6*b^5*c^3 - 80*a^7*b^3*c^4 + 32*a^8*b*c^5)*n^4*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) - (b^10*c - 12*a*b^8*c^2 + 52*a^2*b^6*c^3 - 96*a^3*b^4*c^4 + 68*a^4*b^2*c^5 - 16*a^5*c^6)*n*x)*x^(-1/3*n - 1)*(((a^4*b^2 - 4*a^5*c)*n^3*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) + b^3 - 2*a*b*c)/((a^4*b^2 - 4*a^5*c)*n^3))^(1/3) - (1/2)^(2/3)*((a^4*b^11 - 16*a^5*b^9*c + 98*a^6*b^7*c^2 - 280*a^7*b^5*c^3 + 352*a^8*b^3*c^4 - 128*a^9*b*c^5)*n^5*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) - (b^12 - 14*a*b^10*c + 76*a^2*b^8*c^2 - 200*a^3*b^6*c^3 + 260*a^4*b^4*c^4 - 152*a^5*b^2*c^5 + 32*a^6*c^6)*n^2)*(((a^4*b^2 - 4*a^5*c)*n^3*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) + b^3 - 2*a*b*c)/((a^4*b^2 - 4*a^5*c)*n^3))^(2/3))/x^2)*(((a^4*b^2 - 4*a^5*c)*n^3*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) + b^3 - 2*a*b*c)/((a^4*b^2 - 4*a^5*c)*n^3))^(2/3) + 2*sqrt(3)*(b^8*c^4 - 8*a*b^6*c^5 + 20*a^2*b^4*c^6 - 16*a^3*b^2*c^7 + 4*a^4*c^8))/(b^8*c^4 - 8*a*b^6*c^5 + 20*a^2*b^4*c^6 - 16*a^3*b^2*c^7 + 4*a^4*c^8)) - 4*sqrt(3)*(1/2)^(1/3)*a*n*(-((a^4*b^2 - 4*a^5*c)*n^3*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) - b^3 + 2*a*b*c)/((a^4*b^2 - 4*a^5*c)*n^3))^(1/3)*arctan(-1/6*(2*(1/2)^(2/3)*(sqrt(3)*(a^4*b^12*c - 17*a^5*b^10*c^2 + 114*a^6*b^8*c^3 - 378*a^7*b^6*c^4 + 632*a^8*b^4*c^5 - 480*a^9*b^2*c^6 + 128*a^10*c^7)*n^5*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) + sqrt(3)*(b^13*c - 15*a*b^11*c^2 + 88*a^2*b^9*c^3 - 252*a^3*b^7*c^4 + 356*a^4*b^5*c^5 - 220*a^5*b^3*c^6 + 48*a^6*b*c^7)*n^2*x)*x^(-1/3*n - 1)*(-((a^4*b^2 - 4*a^5*c)*n^3*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) - b^3 + 2*a*b*c)/((a^4*b^2 - 4*a^5*c)*n^3))^(2/3) - sqrt(2)*(1/2)^(2/3)*(sqrt(3)*(a^4*b^8 - 13*a^5*b^6*c + 60*a^6*b^4*c^2 - 112*a^7*b^2*c^3 + 64*a^8*c^4)*n^5*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) + sqrt(3)*(b^9 - 11*a*b^7*c + 42*a^2*b^5*c^2 - 62*a^3*b^3*c^3 + 24*a^4*b*c^4)*n^2*x)*sqrt((2*(b^8*c^2 - 8*a*b^6*c^3 + 20*a^2*b^4*c^4 - 16*a^3*b^2*c^5 + 4*a^4*c^6)*x^2*x^(-2/3*n - 2) + (1/2)^(1/3)*((a^4*b^9*c - 12*a^5*b^7*c^2 + 50*a^6*b^5*c^3 - 80*a^7*b^3*c^4 + 32*a^8*b*c^5)*n^4*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) + (b^10*c - 12*a*b^8*c^2 + 52*a^2*b^6*c^3 - 96*a^3*b^4*c^4 + 68*a^4*b^2*c^5 - 16*a^5*c^6)*n*x)*x^(-1/3*n - 1)*(-((a^4*b^2 - 4*a^5*c)*n^3*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) - b^3 + 2*a*b*c)/((a^4*b^2 - 4*a^5*c)*n^3))^(1/3) + (1/2)^(2/3)*((a^4*b^11 - 16*a^5*b^9*c + 98*a^6*b^7*c^2 - 280*a^7*b^5*c^3 + 352*a^8*b^3*c^4 - 128*a^9*b*c^5)*n^5*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) + (b^12 - 14*a*b^10*c + 76*a^2*b^8*c^2 - 200*a^3*b^6*c^3 + 260*a^4*b^4*c^4 - 152*a^5*b^2*c^5 + 32*a^6*c^6)*n^2)*(-((a^4*b^2 - 4*a^5*c)*n^3*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) - b^3 + 2*a*b*c)/((a^4*b^2 - 4*a^5*c)*n^3))^(2/3))/x^2)*(-((a^4*b^2 - 4*a^5*c)*n^3*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) - b^3 + 2*a*b*c)/((a^4*b^2 - 4*a^5*c)*n^3))^(2/3) - 2*sqrt(3)*(b^8*c^4 - 8*a*b^6*c^5 + 20*a^2*b^4*c^6 - 16*a^3*b^2*c^7 + 4*a^4*c^8))/(b^8*c^4 - 8*a*b^6*c^5 + 20*a^2*b^4*c^6 - 16*a^3*b^2*c^7 + 4*a^4*c^8)) + 2*(1/2)^(1/3)*a*n*(((a^4*b^2 - 4*a^5*c)*n^3*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) + b^3 - 2*a*b*c)/((a^4*b^2 - 4*a^5*c)*n^3))^(1/3)*log((2*(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*x*x^(-1/3*n - 1) + (1/2)^(1/3)*((a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*n^4*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) - (b^6 - 8*a*b^4*c + 18*a^2*b^2*c^2 - 8*a^3*c^3)*n)*(((a^4*b^2 - 4*a^5*c)*n^3*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) + b^3 - 2*a*b*c)/((a^4*b^2 - 4*a^5*c)*n^3))^(1/3))/x) + 2*(1/2)^(1/3)*a*n*(-((a^4*b^2 - 4*a^5*c)*n^3*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) - b^3 + 2*a*b*c)/((a^4*b^2 - 4*a^5*c)*n^3))^(1/3)*log((2*(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*x*x^(-1/3*n - 1) - (1/2)^(1/3)*((a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*n^4*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) + (b^6 - 8*a*b^4*c + 18*a^2*b^2*c^2 - 8*a^3*c^3)*n)*(-((a^4*b^2 - 4*a^5*c)*n^3*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) - b^3 + 2*a*b*c)/((a^4*b^2 - 4*a^5*c)*n^3))^(1/3))/x) - (1/2)^(1/3)*a*n*(((a^4*b^2 - 4*a^5*c)*n^3*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) + b^3 - 2*a*b*c)/((a^4*b^2 - 4*a^5*c)*n^3))^(1/3)*log(8*(2*(b^8*c^2 - 8*a*b^6*c^3 + 20*a^2*b^4*c^4 - 16*a^3*b^2*c^5 + 4*a^4*c^6)*x^2*x^(-2/3*n - 2) - (1/2)^(1/3)*((a^4*b^9*c - 12*a^5*b^7*c^2 + 50*a^6*b^5*c^3 - 80*a^7*b^3*c^4 + 32*a^8*b*c^5)*n^4*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) - (b^10*c - 12*a*b^8*c^2 + 52*a^2*b^6*c^3 - 96*a^3*b^4*c^4 + 68*a^4*b^2*c^5 - 16*a^5*c^6)*n*x)*x^(-1/3*n - 1)*(((a^4*b^2 - 4*a^5*c)*n^3*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) + b^3 - 2*a*b*c)/((a^4*b^2 - 4*a^5*c)*n^3))^(1/3) - (1/2)^(2/3)*((a^4*b^11 - 16*a^5*b^9*c + 98*a^6*b^7*c^2 - 280*a^7*b^5*c^3 + 352*a^8*b^3*c^4 - 128*a^9*b*c^5)*n^5*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) - (b^12 - 14*a*b^10*c + 76*a^2*b^8*c^2 - 200*a^3*b^6*c^3 + 260*a^4*b^4*c^4 - 152*a^5*b^2*c^5 + 32*a^6*c^6)*n^2)*(((a^4*b^2 - 4*a^5*c)*n^3*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) + b^3 - 2*a*b*c)/((a^4*b^2 - 4*a^5*c)*n^3))^(2/3))/x^2) - (1/2)^(1/3)*a*n*(-((a^4*b^2 - 4*a^5*c)*n^3*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) - b^3 + 2*a*b*c)/((a^4*b^2 - 4*a^5*c)*n^3))^(1/3)*log(8*(2*(b^8*c^2 - 8*a*b^6*c^3 + 20*a^2*b^4*c^4 - 16*a^3*b^2*c^5 + 4*a^4*c^6)*x^2*x^(-2/3*n - 2) + (1/2)^(1/3)*((a^4*b^9*c - 12*a^5*b^7*c^2 + 50*a^6*b^5*c^3 - 80*a^7*b^3*c^4 + 32*a^8*b*c^5)*n^4*x*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) + (b^10*c - 12*a*b^8*c^2 + 52*a^2*b^6*c^3 - 96*a^3*b^4*c^4 + 68*a^4*b^2*c^5 - 16*a^5*c^6)*n*x)*x^(-1/3*n - 1)*(-((a^4*b^2 - 4*a^5*c)*n^3*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) - b^3 + 2*a*b*c)/((a^4*b^2 - 4*a^5*c)*n^3))^(1/3) + (1/2)^(2/3)*((a^4*b^11 - 16*a^5*b^9*c + 98*a^6*b^7*c^2 - 280*a^7*b^5*c^3 + 352*a^8*b^3*c^4 - 128*a^9*b*c^5)*n^5*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) + (b^12 - 14*a*b^10*c + 76*a^2*b^8*c^2 - 200*a^3*b^6*c^3 + 260*a^4*b^4*c^4 - 152*a^5*b^2*c^5 + 32*a^6*c^6)*n^2)*(-((a^4*b^2 - 4*a^5*c)*n^3*sqrt((b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 16*a^3*b^2*c^3 + 4*a^4*c^4)/((a^8*b^6 - 12*a^9*b^4*c + 48*a^10*b^2*c^2 - 64*a^11*c^3)*n^6)) - b^3 + 2*a*b*c)/((a^4*b^2 - 4*a^5*c)*n^3))^(2/3))/x^2) - 6*x*x^(-1/3*n - 1))/(a*n)","B",0
561,1,5712,0,4.181597," ","integrate(x^(-1-1/4*n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} a n \sqrt{\sqrt{2} \sqrt{\frac{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} - b^{5} + 5 \, a b^{3} c - 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4}}}} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{2} {\left({\left(a^{5} b^{14} c - 19 \, a^{6} b^{12} c^{2} + 147 \, a^{7} b^{10} c^{3} - 590 \, a^{8} b^{8} c^{4} + 1290 \, a^{9} b^{6} c^{5} - 1464 \, a^{10} b^{4} c^{6} + 736 \, a^{11} b^{2} c^{7} - 128 \, a^{12} c^{8}\right)} n^{7} x \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} + {\left(b^{15} c - 16 \, a b^{13} c^{2} + 103 \, a^{2} b^{11} c^{3} - 340 \, a^{3} b^{9} c^{4} + 605 \, a^{4} b^{7} c^{5} - 554 \, a^{5} b^{5} c^{6} + 224 \, a^{6} b^{3} c^{7} - 32 \, a^{7} b c^{8}\right)} n^{3} x\right)} x^{-\frac{1}{4} \, n - 1} \sqrt{\frac{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} - b^{5} + 5 \, a b^{3} c - 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4}}} - \sqrt{2} {\left({\left(a^{5} b^{10} - 16 \, a^{6} b^{8} c + 98 \, a^{7} b^{6} c^{2} - 280 \, a^{8} b^{4} c^{3} + 352 \, a^{9} b^{2} c^{4} - 128 \, a^{10} c^{5}\right)} n^{7} x \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} + {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 128 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5}\right)} n^{3} x\right)} \sqrt{\frac{4 \, {\left(b^{8} c^{2} - 6 \, a b^{6} c^{3} + 11 \, a^{2} b^{4} c^{4} - 6 \, a^{3} b^{2} c^{5} + a^{4} c^{6}\right)} x^{2} x^{-\frac{1}{2} \, n - 2} + \sqrt{2} {\left({\left(a^{5} b^{11} - 15 \, a^{6} b^{9} c + 85 \, a^{7} b^{7} c^{2} - 220 \, a^{8} b^{5} c^{3} + 240 \, a^{9} b^{3} c^{4} - 64 \, a^{10} b c^{5}\right)} n^{6} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} + {\left(b^{12} - 12 \, a b^{10} c + 55 \, a^{2} b^{8} c^{2} - 120 \, a^{3} b^{6} c^{3} + 125 \, a^{4} b^{4} c^{4} - 54 \, a^{5} b^{2} c^{5} + 8 \, a^{6} c^{6}\right)} n^{2}\right)} \sqrt{\frac{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} - b^{5} + 5 \, a b^{3} c - 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4}}}}{x^{2}}} \sqrt{\frac{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} - b^{5} + 5 \, a b^{3} c - 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4}}}\right)} \sqrt{\sqrt{2} \sqrt{\frac{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} - b^{5} + 5 \, a b^{3} c - 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4}}}}}{16 \, {\left(b^{8} c^{5} - 6 \, a b^{6} c^{6} + 11 \, a^{2} b^{4} c^{7} - 6 \, a^{3} b^{2} c^{8} + a^{4} c^{9}\right)}}\right) - 4 \, \sqrt{2} a n \sqrt{\sqrt{2} \sqrt{-\frac{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} + b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4}}}} \arctan\left(\frac{2 \, {\left({\left(a^{5} b^{14} c - 19 \, a^{6} b^{12} c^{2} + 147 \, a^{7} b^{10} c^{3} - 590 \, a^{8} b^{8} c^{4} + 1290 \, a^{9} b^{6} c^{5} - 1464 \, a^{10} b^{4} c^{6} + 736 \, a^{11} b^{2} c^{7} - 128 \, a^{12} c^{8}\right)} n^{7} x \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} - {\left(b^{15} c - 16 \, a b^{13} c^{2} + 103 \, a^{2} b^{11} c^{3} - 340 \, a^{3} b^{9} c^{4} + 605 \, a^{4} b^{7} c^{5} - 554 \, a^{5} b^{5} c^{6} + 224 \, a^{6} b^{3} c^{7} - 32 \, a^{7} b c^{8}\right)} n^{3} x\right)} x^{-\frac{1}{4} \, n - 1} \sqrt{\sqrt{2} \sqrt{-\frac{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} + b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4}}}} \sqrt{-\frac{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} + b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4}}} - {\left({\left(a^{5} b^{10} - 16 \, a^{6} b^{8} c + 98 \, a^{7} b^{6} c^{2} - 280 \, a^{8} b^{4} c^{3} + 352 \, a^{9} b^{2} c^{4} - 128 \, a^{10} c^{5}\right)} n^{7} x \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} - {\left(b^{11} - 13 \, a b^{9} c + 63 \, a^{2} b^{7} c^{2} - 138 \, a^{3} b^{5} c^{3} + 128 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5}\right)} n^{3} x\right)} \sqrt{\sqrt{2} \sqrt{-\frac{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} + b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4}}}} \sqrt{\frac{4 \, {\left(b^{8} c^{2} - 6 \, a b^{6} c^{3} + 11 \, a^{2} b^{4} c^{4} - 6 \, a^{3} b^{2} c^{5} + a^{4} c^{6}\right)} x^{2} x^{-\frac{1}{2} \, n - 2} - \sqrt{2} {\left({\left(a^{5} b^{11} - 15 \, a^{6} b^{9} c + 85 \, a^{7} b^{7} c^{2} - 220 \, a^{8} b^{5} c^{3} + 240 \, a^{9} b^{3} c^{4} - 64 \, a^{10} b c^{5}\right)} n^{6} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} - {\left(b^{12} - 12 \, a b^{10} c + 55 \, a^{2} b^{8} c^{2} - 120 \, a^{3} b^{6} c^{3} + 125 \, a^{4} b^{4} c^{4} - 54 \, a^{5} b^{2} c^{5} + 8 \, a^{6} c^{6}\right)} n^{2}\right)} \sqrt{-\frac{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} + b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4}}}}{x^{2}}} \sqrt{-\frac{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} + b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4}}}}{8 \, {\left(b^{8} c^{5} - 6 \, a b^{6} c^{6} + 11 \, a^{2} b^{4} c^{7} - 6 \, a^{3} b^{2} c^{8} + a^{4} c^{9}\right)}}\right) + \sqrt{2} a n \sqrt{\sqrt{2} \sqrt{-\frac{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} + b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4}}}} \log\left(\frac{4 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} + a^{2} c^{3}\right)} x x^{-\frac{1}{4} \, n - 1} + \sqrt{2} {\left({\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} n^{5} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} - {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} n\right)} \sqrt{\sqrt{2} \sqrt{-\frac{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} + b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4}}}}}{x}\right) - \sqrt{2} a n \sqrt{\sqrt{2} \sqrt{-\frac{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} + b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4}}}} \log\left(\frac{4 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} + a^{2} c^{3}\right)} x x^{-\frac{1}{4} \, n - 1} - \sqrt{2} {\left({\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} n^{5} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} - {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} n\right)} \sqrt{\sqrt{2} \sqrt{-\frac{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} + b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4}}}}}{x}\right) - \sqrt{2} a n \sqrt{\sqrt{2} \sqrt{\frac{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} - b^{5} + 5 \, a b^{3} c - 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4}}}} \log\left(\frac{4 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} + a^{2} c^{3}\right)} x x^{-\frac{1}{4} \, n - 1} + \sqrt{2} {\left({\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} n^{5} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} + {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} n\right)} \sqrt{\sqrt{2} \sqrt{\frac{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} - b^{5} + 5 \, a b^{3} c - 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4}}}}}{x}\right) + \sqrt{2} a n \sqrt{\sqrt{2} \sqrt{\frac{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} - b^{5} + 5 \, a b^{3} c - 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4}}}} \log\left(\frac{4 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} + a^{2} c^{3}\right)} x x^{-\frac{1}{4} \, n - 1} - \sqrt{2} {\left({\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} n^{5} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} + {\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} n\right)} \sqrt{\sqrt{2} \sqrt{\frac{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4} \sqrt{\frac{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}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} n^{8}}} - b^{5} + 5 \, a b^{3} c - 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} n^{4}}}}}{x}\right) - 8 \, x x^{-\frac{1}{4} \, n - 1}}{2 \, a n}"," ",0,"1/2*(4*sqrt(2)*a*n*sqrt(sqrt(2)*sqrt(((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) - b^5 + 5*a*b^3*c - 5*a^2*b*c^2)/((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4)))*arctan(1/16*sqrt(2)*(2*sqrt(2)*((a^5*b^14*c - 19*a^6*b^12*c^2 + 147*a^7*b^10*c^3 - 590*a^8*b^8*c^4 + 1290*a^9*b^6*c^5 - 1464*a^10*b^4*c^6 + 736*a^11*b^2*c^7 - 128*a^12*c^8)*n^7*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) + (b^15*c - 16*a*b^13*c^2 + 103*a^2*b^11*c^3 - 340*a^3*b^9*c^4 + 605*a^4*b^7*c^5 - 554*a^5*b^5*c^6 + 224*a^6*b^3*c^7 - 32*a^7*b*c^8)*n^3*x)*x^(-1/4*n - 1)*sqrt(((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) - b^5 + 5*a*b^3*c - 5*a^2*b*c^2)/((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4)) - sqrt(2)*((a^5*b^10 - 16*a^6*b^8*c + 98*a^7*b^6*c^2 - 280*a^8*b^4*c^3 + 352*a^9*b^2*c^4 - 128*a^10*c^5)*n^7*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) + (b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 128*a^4*b^3*c^4 - 32*a^5*b*c^5)*n^3*x)*sqrt((4*(b^8*c^2 - 6*a*b^6*c^3 + 11*a^2*b^4*c^4 - 6*a^3*b^2*c^5 + a^4*c^6)*x^2*x^(-1/2*n - 2) + sqrt(2)*((a^5*b^11 - 15*a^6*b^9*c + 85*a^7*b^7*c^2 - 220*a^8*b^5*c^3 + 240*a^9*b^3*c^4 - 64*a^10*b*c^5)*n^6*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) + (b^12 - 12*a*b^10*c + 55*a^2*b^8*c^2 - 120*a^3*b^6*c^3 + 125*a^4*b^4*c^4 - 54*a^5*b^2*c^5 + 8*a^6*c^6)*n^2)*sqrt(((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) - b^5 + 5*a*b^3*c - 5*a^2*b*c^2)/((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4)))/x^2)*sqrt(((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) - b^5 + 5*a*b^3*c - 5*a^2*b*c^2)/((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4)))*sqrt(sqrt(2)*sqrt(((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) - b^5 + 5*a*b^3*c - 5*a^2*b*c^2)/((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4)))/(b^8*c^5 - 6*a*b^6*c^6 + 11*a^2*b^4*c^7 - 6*a^3*b^2*c^8 + a^4*c^9)) - 4*sqrt(2)*a*n*sqrt(sqrt(2)*sqrt(-((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) + b^5 - 5*a*b^3*c + 5*a^2*b*c^2)/((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4)))*arctan(1/8*(2*((a^5*b^14*c - 19*a^6*b^12*c^2 + 147*a^7*b^10*c^3 - 590*a^8*b^8*c^4 + 1290*a^9*b^6*c^5 - 1464*a^10*b^4*c^6 + 736*a^11*b^2*c^7 - 128*a^12*c^8)*n^7*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) - (b^15*c - 16*a*b^13*c^2 + 103*a^2*b^11*c^3 - 340*a^3*b^9*c^4 + 605*a^4*b^7*c^5 - 554*a^5*b^5*c^6 + 224*a^6*b^3*c^7 - 32*a^7*b*c^8)*n^3*x)*x^(-1/4*n - 1)*sqrt(sqrt(2)*sqrt(-((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) + b^5 - 5*a*b^3*c + 5*a^2*b*c^2)/((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4)))*sqrt(-((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) + b^5 - 5*a*b^3*c + 5*a^2*b*c^2)/((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4)) - ((a^5*b^10 - 16*a^6*b^8*c + 98*a^7*b^6*c^2 - 280*a^8*b^4*c^3 + 352*a^9*b^2*c^4 - 128*a^10*c^5)*n^7*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) - (b^11 - 13*a*b^9*c + 63*a^2*b^7*c^2 - 138*a^3*b^5*c^3 + 128*a^4*b^3*c^4 - 32*a^5*b*c^5)*n^3*x)*sqrt(sqrt(2)*sqrt(-((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) + b^5 - 5*a*b^3*c + 5*a^2*b*c^2)/((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4)))*sqrt((4*(b^8*c^2 - 6*a*b^6*c^3 + 11*a^2*b^4*c^4 - 6*a^3*b^2*c^5 + a^4*c^6)*x^2*x^(-1/2*n - 2) - sqrt(2)*((a^5*b^11 - 15*a^6*b^9*c + 85*a^7*b^7*c^2 - 220*a^8*b^5*c^3 + 240*a^9*b^3*c^4 - 64*a^10*b*c^5)*n^6*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) - (b^12 - 12*a*b^10*c + 55*a^2*b^8*c^2 - 120*a^3*b^6*c^3 + 125*a^4*b^4*c^4 - 54*a^5*b^2*c^5 + 8*a^6*c^6)*n^2)*sqrt(-((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) + b^5 - 5*a*b^3*c + 5*a^2*b*c^2)/((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4)))/x^2)*sqrt(-((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) + b^5 - 5*a*b^3*c + 5*a^2*b*c^2)/((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4)))/(b^8*c^5 - 6*a*b^6*c^6 + 11*a^2*b^4*c^7 - 6*a^3*b^2*c^8 + a^4*c^9)) + sqrt(2)*a*n*sqrt(sqrt(2)*sqrt(-((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) + b^5 - 5*a*b^3*c + 5*a^2*b*c^2)/((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4)))*log((4*(b^4*c - 3*a*b^2*c^2 + a^2*c^3)*x*x^(-1/4*n - 1) + sqrt(2)*((a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*n^5*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) - (b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3)*n)*sqrt(sqrt(2)*sqrt(-((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) + b^5 - 5*a*b^3*c + 5*a^2*b*c^2)/((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4))))/x) - sqrt(2)*a*n*sqrt(sqrt(2)*sqrt(-((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) + b^5 - 5*a*b^3*c + 5*a^2*b*c^2)/((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4)))*log((4*(b^4*c - 3*a*b^2*c^2 + a^2*c^3)*x*x^(-1/4*n - 1) - sqrt(2)*((a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*n^5*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) - (b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3)*n)*sqrt(sqrt(2)*sqrt(-((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) + b^5 - 5*a*b^3*c + 5*a^2*b*c^2)/((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4))))/x) - sqrt(2)*a*n*sqrt(sqrt(2)*sqrt(((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) - b^5 + 5*a*b^3*c - 5*a^2*b*c^2)/((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4)))*log((4*(b^4*c - 3*a*b^2*c^2 + a^2*c^3)*x*x^(-1/4*n - 1) + sqrt(2)*((a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*n^5*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) + (b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3)*n)*sqrt(sqrt(2)*sqrt(((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) - b^5 + 5*a*b^3*c - 5*a^2*b*c^2)/((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4))))/x) + sqrt(2)*a*n*sqrt(sqrt(2)*sqrt(((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) - b^5 + 5*a*b^3*c - 5*a^2*b*c^2)/((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4)))*log((4*(b^4*c - 3*a*b^2*c^2 + a^2*c^3)*x*x^(-1/4*n - 1) - sqrt(2)*((a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*n^5*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) + (b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3)*n)*sqrt(sqrt(2)*sqrt(((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4*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)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*n^8)) - b^5 + 5*a*b^3*c - 5*a^2*b*c^2)/((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*n^4))))/x) - 8*x*x^(-1/4*n - 1))/(a*n)","B",0
562,0,0,0,1.263600," ","integrate(x^2/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{c x^{2 \, n} + b x^{n} + a}, x\right)"," ",0,"integral(x^2/(c*x^(2*n) + b*x^n + a), x)","F",0
563,0,0,0,1.247313," ","integrate(x/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{c x^{2 \, n} + b x^{n} + a}, x\right)"," ",0,"integral(x/(c*x^(2*n) + b*x^n + a), x)","F",0
564,0,0,0,0.968314," ","integrate(1/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{c x^{2 \, n} + b x^{n} + a}, x\right)"," ",0,"integral(1/(c*x^(2*n) + b*x^n + a), x)","F",0
565,1,259,0,1.005420," ","integrate(1/x/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} - 4 \, a c\right)} n \log\left(x\right) + \sqrt{b^{2} - 4 \, a c} b \log\left(\frac{2 \, c^{2} x^{2 \, n} + b^{2} - 2 \, a c + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} x^{n} + \sqrt{b^{2} - 4 \, a c} b}{c x^{2 \, n} + b x^{n} + a}\right) - {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{2 \, n} + b x^{n} + a\right)}{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} n}, \frac{2 \, {\left(b^{2} - 4 \, a c\right)} n \log\left(x\right) + 2 \, \sqrt{-b^{2} + 4 \, a c} b \arctan\left(-\frac{2 \, \sqrt{-b^{2} + 4 \, a c} c x^{n} + \sqrt{-b^{2} + 4 \, a c} b}{b^{2} - 4 \, a c}\right) - {\left(b^{2} - 4 \, a c\right)} \log\left(c x^{2 \, n} + b x^{n} + a\right)}{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} n}\right]"," ",0,"[1/2*(2*(b^2 - 4*a*c)*n*log(x) + sqrt(b^2 - 4*a*c)*b*log((2*c^2*x^(2*n) + b^2 - 2*a*c + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*x^n + sqrt(b^2 - 4*a*c)*b)/(c*x^(2*n) + b*x^n + a)) - (b^2 - 4*a*c)*log(c*x^(2*n) + b*x^n + a))/((a*b^2 - 4*a^2*c)*n), 1/2*(2*(b^2 - 4*a*c)*n*log(x) + 2*sqrt(-b^2 + 4*a*c)*b*arctan(-(2*sqrt(-b^2 + 4*a*c)*c*x^n + sqrt(-b^2 + 4*a*c)*b)/(b^2 - 4*a*c)) - (b^2 - 4*a*c)*log(c*x^(2*n) + b*x^n + a))/((a*b^2 - 4*a^2*c)*n)]","A",0
566,0,0,0,0.791053," ","integrate(1/x^2/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{c x^{2} x^{2 \, n} + b x^{2} x^{n} + a x^{2}}, x\right)"," ",0,"integral(1/(c*x^2*x^(2*n) + b*x^2*x^n + a*x^2), x)","F",0
567,0,0,0,1.262501," ","integrate(1/x^3/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{c x^{3} x^{2 \, n} + b x^{3} x^{n} + a x^{3}}, x\right)"," ",0,"integral(1/(c*x^3*x^(2*n) + b*x^3*x^n + a*x^3), x)","F",0
568,-2,0,0,0.000000," ","integrate(x^3*(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
569,-2,0,0,0.000000," ","integrate(x^2*(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
570,-2,0,0,0.000000," ","integrate(x*(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
571,-2,0,0,0.000000," ","integrate((a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
572,1,658,0,1.606303," ","integrate((a+b*x^n+c*x^(2*n))^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{b \sqrt{c} \log\left(-8 \, c^{2} x^{2 \, n} - 8 \, b c x^{n} - b^{2} - 4 \, a c - 4 \, {\left(2 \, c^{\frac{3}{2}} x^{n} + b \sqrt{c}\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}\right) + 2 \, \sqrt{a} c \log\left(-\frac{8 \, a b x^{n} + 8 \, a^{2} + {\left(b^{2} + 4 \, a c\right)} x^{2 \, n} - 4 \, {\left(\sqrt{a} b x^{n} + 2 \, a^{\frac{3}{2}}\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{x^{2 \, n}}\right) + 4 \, \sqrt{c x^{2 \, n} + b x^{n} + a} c}{4 \, c n}, -\frac{b \sqrt{-c} \arctan\left(\frac{{\left(2 \, \sqrt{-c} c x^{n} + b \sqrt{-c}\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{2 \, {\left(c^{2} x^{2 \, n} + b c x^{n} + a c\right)}}\right) - \sqrt{a} c \log\left(-\frac{8 \, a b x^{n} + 8 \, a^{2} + {\left(b^{2} + 4 \, a c\right)} x^{2 \, n} - 4 \, {\left(\sqrt{a} b x^{n} + 2 \, a^{\frac{3}{2}}\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{x^{2 \, n}}\right) - 2 \, \sqrt{c x^{2 \, n} + b x^{n} + a} c}{2 \, c n}, \frac{4 \, \sqrt{-a} c \arctan\left(\frac{{\left(\sqrt{-a} b x^{n} + 2 \, \sqrt{-a} a\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{2 \, {\left(a c x^{2 \, n} + a b x^{n} + a^{2}\right)}}\right) + b \sqrt{c} \log\left(-8 \, c^{2} x^{2 \, n} - 8 \, b c x^{n} - b^{2} - 4 \, a c - 4 \, {\left(2 \, c^{\frac{3}{2}} x^{n} + b \sqrt{c}\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}\right) + 4 \, \sqrt{c x^{2 \, n} + b x^{n} + a} c}{4 \, c n}, \frac{2 \, \sqrt{-a} c \arctan\left(\frac{{\left(\sqrt{-a} b x^{n} + 2 \, \sqrt{-a} a\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{2 \, {\left(a c x^{2 \, n} + a b x^{n} + a^{2}\right)}}\right) - b \sqrt{-c} \arctan\left(\frac{{\left(2 \, \sqrt{-c} c x^{n} + b \sqrt{-c}\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{2 \, {\left(c^{2} x^{2 \, n} + b c x^{n} + a c\right)}}\right) + 2 \, \sqrt{c x^{2 \, n} + b x^{n} + a} c}{2 \, c n}\right]"," ",0,"[1/4*(b*sqrt(c)*log(-8*c^2*x^(2*n) - 8*b*c*x^n - b^2 - 4*a*c - 4*(2*c^(3/2)*x^n + b*sqrt(c))*sqrt(c*x^(2*n) + b*x^n + a)) + 2*sqrt(a)*c*log(-(8*a*b*x^n + 8*a^2 + (b^2 + 4*a*c)*x^(2*n) - 4*(sqrt(a)*b*x^n + 2*a^(3/2))*sqrt(c*x^(2*n) + b*x^n + a))/x^(2*n)) + 4*sqrt(c*x^(2*n) + b*x^n + a)*c)/(c*n), -1/2*(b*sqrt(-c)*arctan(1/2*(2*sqrt(-c)*c*x^n + b*sqrt(-c))*sqrt(c*x^(2*n) + b*x^n + a)/(c^2*x^(2*n) + b*c*x^n + a*c)) - sqrt(a)*c*log(-(8*a*b*x^n + 8*a^2 + (b^2 + 4*a*c)*x^(2*n) - 4*(sqrt(a)*b*x^n + 2*a^(3/2))*sqrt(c*x^(2*n) + b*x^n + a))/x^(2*n)) - 2*sqrt(c*x^(2*n) + b*x^n + a)*c)/(c*n), 1/4*(4*sqrt(-a)*c*arctan(1/2*(sqrt(-a)*b*x^n + 2*sqrt(-a)*a)*sqrt(c*x^(2*n) + b*x^n + a)/(a*c*x^(2*n) + a*b*x^n + a^2)) + b*sqrt(c)*log(-8*c^2*x^(2*n) - 8*b*c*x^n - b^2 - 4*a*c - 4*(2*c^(3/2)*x^n + b*sqrt(c))*sqrt(c*x^(2*n) + b*x^n + a)) + 4*sqrt(c*x^(2*n) + b*x^n + a)*c)/(c*n), 1/2*(2*sqrt(-a)*c*arctan(1/2*(sqrt(-a)*b*x^n + 2*sqrt(-a)*a)*sqrt(c*x^(2*n) + b*x^n + a)/(a*c*x^(2*n) + a*b*x^n + a^2)) - b*sqrt(-c)*arctan(1/2*(2*sqrt(-c)*c*x^n + b*sqrt(-c))*sqrt(c*x^(2*n) + b*x^n + a)/(c^2*x^(2*n) + b*c*x^n + a*c)) + 2*sqrt(c*x^(2*n) + b*x^n + a)*c)/(c*n)]","A",0
573,-2,0,0,0.000000," ","integrate((a+b*x^n+c*x^(2*n))^(1/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
574,-2,0,0,0.000000," ","integrate((a+b*x^n+c*x^(2*n))^(1/2)/x^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
575,-2,0,0,0.000000," ","integrate(x^3*(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
576,-2,0,0,0.000000," ","integrate(x^2*(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
577,-2,0,0,0.000000," ","integrate(x*(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
578,-2,0,0,0.000000," ","integrate((a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
579,1,827,0,1.802722," ","integrate((a+b*x^n+c*x^(2*n))^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{48 \, a^{\frac{3}{2}} c^{2} \log\left(-\frac{8 \, a b x^{n} + 8 \, a^{2} + {\left(b^{2} + 4 \, a c\right)} x^{2 \, n} - 4 \, {\left(\sqrt{a} b x^{n} + 2 \, a^{\frac{3}{2}}\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{x^{2 \, n}}\right) - 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2 \, n} - 8 \, b c x^{n} - b^{2} - 4 \, a c - 4 \, {\left(2 \, c^{\frac{3}{2}} x^{n} + b \sqrt{c}\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}\right) + 4 \, {\left(8 \, c^{3} x^{2 \, n} + 14 \, b c^{2} x^{n} + 3 \, b^{2} c + 32 \, a c^{2}\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{96 \, c^{2} n}, \frac{24 \, a^{\frac{3}{2}} c^{2} \log\left(-\frac{8 \, a b x^{n} + 8 \, a^{2} + {\left(b^{2} + 4 \, a c\right)} x^{2 \, n} - 4 \, {\left(\sqrt{a} b x^{n} + 2 \, a^{\frac{3}{2}}\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{x^{2 \, n}}\right) + 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{-c} \arctan\left(\frac{{\left(2 \, \sqrt{-c} c x^{n} + b \sqrt{-c}\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{2 \, {\left(c^{2} x^{2 \, n} + b c x^{n} + a c\right)}}\right) + 2 \, {\left(8 \, c^{3} x^{2 \, n} + 14 \, b c^{2} x^{n} + 3 \, b^{2} c + 32 \, a c^{2}\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{48 \, c^{2} n}, \frac{96 \, \sqrt{-a} a c^{2} \arctan\left(\frac{{\left(\sqrt{-a} b x^{n} + 2 \, \sqrt{-a} a\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{2 \, {\left(a c x^{2 \, n} + a b x^{n} + a^{2}\right)}}\right) - 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2 \, n} - 8 \, b c x^{n} - b^{2} - 4 \, a c - 4 \, {\left(2 \, c^{\frac{3}{2}} x^{n} + b \sqrt{c}\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}\right) + 4 \, {\left(8 \, c^{3} x^{2 \, n} + 14 \, b c^{2} x^{n} + 3 \, b^{2} c + 32 \, a c^{2}\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{96 \, c^{2} n}, \frac{48 \, \sqrt{-a} a c^{2} \arctan\left(\frac{{\left(\sqrt{-a} b x^{n} + 2 \, \sqrt{-a} a\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{2 \, {\left(a c x^{2 \, n} + a b x^{n} + a^{2}\right)}}\right) + 3 \, {\left(b^{3} - 12 \, a b c\right)} \sqrt{-c} \arctan\left(\frac{{\left(2 \, \sqrt{-c} c x^{n} + b \sqrt{-c}\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{2 \, {\left(c^{2} x^{2 \, n} + b c x^{n} + a c\right)}}\right) + 2 \, {\left(8 \, c^{3} x^{2 \, n} + 14 \, b c^{2} x^{n} + 3 \, b^{2} c + 32 \, a c^{2}\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{48 \, c^{2} n}\right]"," ",0,"[1/96*(48*a^(3/2)*c^2*log(-(8*a*b*x^n + 8*a^2 + (b^2 + 4*a*c)*x^(2*n) - 4*(sqrt(a)*b*x^n + 2*a^(3/2))*sqrt(c*x^(2*n) + b*x^n + a))/x^(2*n)) - 3*(b^3 - 12*a*b*c)*sqrt(c)*log(-8*c^2*x^(2*n) - 8*b*c*x^n - b^2 - 4*a*c - 4*(2*c^(3/2)*x^n + b*sqrt(c))*sqrt(c*x^(2*n) + b*x^n + a)) + 4*(8*c^3*x^(2*n) + 14*b*c^2*x^n + 3*b^2*c + 32*a*c^2)*sqrt(c*x^(2*n) + b*x^n + a))/(c^2*n), 1/48*(24*a^(3/2)*c^2*log(-(8*a*b*x^n + 8*a^2 + (b^2 + 4*a*c)*x^(2*n) - 4*(sqrt(a)*b*x^n + 2*a^(3/2))*sqrt(c*x^(2*n) + b*x^n + a))/x^(2*n)) + 3*(b^3 - 12*a*b*c)*sqrt(-c)*arctan(1/2*(2*sqrt(-c)*c*x^n + b*sqrt(-c))*sqrt(c*x^(2*n) + b*x^n + a)/(c^2*x^(2*n) + b*c*x^n + a*c)) + 2*(8*c^3*x^(2*n) + 14*b*c^2*x^n + 3*b^2*c + 32*a*c^2)*sqrt(c*x^(2*n) + b*x^n + a))/(c^2*n), 1/96*(96*sqrt(-a)*a*c^2*arctan(1/2*(sqrt(-a)*b*x^n + 2*sqrt(-a)*a)*sqrt(c*x^(2*n) + b*x^n + a)/(a*c*x^(2*n) + a*b*x^n + a^2)) - 3*(b^3 - 12*a*b*c)*sqrt(c)*log(-8*c^2*x^(2*n) - 8*b*c*x^n - b^2 - 4*a*c - 4*(2*c^(3/2)*x^n + b*sqrt(c))*sqrt(c*x^(2*n) + b*x^n + a)) + 4*(8*c^3*x^(2*n) + 14*b*c^2*x^n + 3*b^2*c + 32*a*c^2)*sqrt(c*x^(2*n) + b*x^n + a))/(c^2*n), 1/48*(48*sqrt(-a)*a*c^2*arctan(1/2*(sqrt(-a)*b*x^n + 2*sqrt(-a)*a)*sqrt(c*x^(2*n) + b*x^n + a)/(a*c*x^(2*n) + a*b*x^n + a^2)) + 3*(b^3 - 12*a*b*c)*sqrt(-c)*arctan(1/2*(2*sqrt(-c)*c*x^n + b*sqrt(-c))*sqrt(c*x^(2*n) + b*x^n + a)/(c^2*x^(2*n) + b*c*x^n + a*c)) + 2*(8*c^3*x^(2*n) + 14*b*c^2*x^n + 3*b^2*c + 32*a*c^2)*sqrt(c*x^(2*n) + b*x^n + a))/(c^2*n)]","A",0
580,-2,0,0,0.000000," ","integrate((a+b*x^n+c*x^(2*n))^(3/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
581,-2,0,0,0.000000," ","integrate((a+b*x^n+c*x^(2*n))^(3/2)/x^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
582,-2,0,0,0.000000," ","integrate(x^3/(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
583,-2,0,0,0.000000," ","integrate(x^2/(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
584,-2,0,0,0.000000," ","integrate(x/(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
585,-2,0,0,0.000000," ","integrate(1/(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
586,1,148,0,1.335644," ","integrate(1/x/(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{8 \, a b x^{n} + 8 \, a^{2} + {\left(b^{2} + 4 \, a c\right)} x^{2 \, n} - 4 \, {\left(\sqrt{a} b x^{n} + 2 \, a^{\frac{3}{2}}\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{x^{2 \, n}}\right)}{2 \, \sqrt{a} n}, \frac{\sqrt{-a} \arctan\left(\frac{{\left(\sqrt{-a} b x^{n} + 2 \, \sqrt{-a} a\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{2 \, {\left(a c x^{2 \, n} + a b x^{n} + a^{2}\right)}}\right)}{a n}\right]"," ",0,"[1/2*log(-(8*a*b*x^n + 8*a^2 + (b^2 + 4*a*c)*x^(2*n) - 4*(sqrt(a)*b*x^n + 2*a^(3/2))*sqrt(c*x^(2*n) + b*x^n + a))/x^(2*n))/(sqrt(a)*n), sqrt(-a)*arctan(1/2*(sqrt(-a)*b*x^n + 2*sqrt(-a)*a)*sqrt(c*x^(2*n) + b*x^n + a)/(a*c*x^(2*n) + a*b*x^n + a^2))/(a*n)]","A",0
587,-2,0,0,0.000000," ","integrate(1/x^2/(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
588,-2,0,0,0.000000," ","integrate(1/x^3/(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
589,-2,0,0,0.000000," ","integrate(x^3/(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
590,-2,0,0,0.000000," ","integrate(x^2/(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
591,-2,0,0,0.000000," ","integrate(x/(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
592,-2,0,0,0.000000," ","integrate(1/(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
593,1,449,0,1.703202," ","integrate(1/x/(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{a} x^{2 \, n} + {\left(b^{3} - 4 \, a b c\right)} \sqrt{a} x^{n} + {\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{a}\right)} \log\left(-\frac{8 \, a b x^{n} + 8 \, a^{2} + {\left(b^{2} + 4 \, a c\right)} x^{2 \, n} - 4 \, {\left(\sqrt{a} b x^{n} + 2 \, a^{\frac{3}{2}}\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{x^{2 \, n}}\right) + 4 \, {\left(a b c x^{n} + a b^{2} - 2 \, a^{2} c\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{2 \, {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} n x^{2 \, n} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} n x^{n} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} n\right)}}, \frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{-a} x^{2 \, n} + {\left(b^{3} - 4 \, a b c\right)} \sqrt{-a} x^{n} + {\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{-a}\right)} \arctan\left(\frac{{\left(\sqrt{-a} b x^{n} + 2 \, \sqrt{-a} a\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{2 \, {\left(a c x^{2 \, n} + a b x^{n} + a^{2}\right)}}\right) + 2 \, {\left(a b c x^{n} + a b^{2} - 2 \, a^{2} c\right)} \sqrt{c x^{2 \, n} + b x^{n} + a}}{{\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} n x^{2 \, n} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} n x^{n} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} n}\right]"," ",0,"[1/2*(((b^2*c - 4*a*c^2)*sqrt(a)*x^(2*n) + (b^3 - 4*a*b*c)*sqrt(a)*x^n + (a*b^2 - 4*a^2*c)*sqrt(a))*log(-(8*a*b*x^n + 8*a^2 + (b^2 + 4*a*c)*x^(2*n) - 4*(sqrt(a)*b*x^n + 2*a^(3/2))*sqrt(c*x^(2*n) + b*x^n + a))/x^(2*n)) + 4*(a*b*c*x^n + a*b^2 - 2*a^2*c)*sqrt(c*x^(2*n) + b*x^n + a))/((a^2*b^2*c - 4*a^3*c^2)*n*x^(2*n) + (a^2*b^3 - 4*a^3*b*c)*n*x^n + (a^3*b^2 - 4*a^4*c)*n), (((b^2*c - 4*a*c^2)*sqrt(-a)*x^(2*n) + (b^3 - 4*a*b*c)*sqrt(-a)*x^n + (a*b^2 - 4*a^2*c)*sqrt(-a))*arctan(1/2*(sqrt(-a)*b*x^n + 2*sqrt(-a)*a)*sqrt(c*x^(2*n) + b*x^n + a)/(a*c*x^(2*n) + a*b*x^n + a^2)) + 2*(a*b*c*x^n + a*b^2 - 2*a^2*c)*sqrt(c*x^(2*n) + b*x^n + a))/((a^2*b^2*c - 4*a^3*c^2)*n*x^(2*n) + (a^2*b^3 - 4*a^3*b*c)*n*x^n + (a^3*b^2 - 4*a^4*c)*n)]","B",0
594,-2,0,0,0.000000," ","integrate(1/x^2/(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
595,-2,0,0,0.000000," ","integrate(1/x^3/(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
596,1,2303,0,1.390544," ","integrate((d*x)^m*(a+b*x^n+c*x^(2*n))^3,x, algorithm=""fricas"")","\frac{{\left(c^{3} m^{6} + 6 \, c^{3} m^{5} + 15 \, c^{3} m^{4} + 20 \, c^{3} m^{3} + 120 \, {\left(c^{3} m + c^{3}\right)} n^{5} + 15 \, c^{3} m^{2} + 274 \, {\left(c^{3} m^{2} + 2 \, c^{3} m + c^{3}\right)} n^{4} + 6 \, c^{3} m + 225 \, {\left(c^{3} m^{3} + 3 \, c^{3} m^{2} + 3 \, c^{3} m + c^{3}\right)} n^{3} + c^{3} + 85 \, {\left(c^{3} m^{4} + 4 \, c^{3} m^{3} + 6 \, c^{3} m^{2} + 4 \, c^{3} m + c^{3}\right)} n^{2} + 15 \, {\left(c^{3} m^{5} + 5 \, c^{3} m^{4} + 10 \, c^{3} m^{3} + 10 \, c^{3} m^{2} + 5 \, c^{3} m + c^{3}\right)} n\right)} x x^{6 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 3 \, {\left(b c^{2} m^{6} + 6 \, b c^{2} m^{5} + 15 \, b c^{2} m^{4} + 20 \, b c^{2} m^{3} + 144 \, {\left(b c^{2} m + b c^{2}\right)} n^{5} + 15 \, b c^{2} m^{2} + 324 \, {\left(b c^{2} m^{2} + 2 \, b c^{2} m + b c^{2}\right)} n^{4} + 6 \, b c^{2} m + 260 \, {\left(b c^{2} m^{3} + 3 \, b c^{2} m^{2} + 3 \, b c^{2} m + b c^{2}\right)} n^{3} + b c^{2} + 95 \, {\left(b c^{2} m^{4} + 4 \, b c^{2} m^{3} + 6 \, b c^{2} m^{2} + 4 \, b c^{2} m + b c^{2}\right)} n^{2} + 16 \, {\left(b c^{2} m^{5} + 5 \, b c^{2} m^{4} + 10 \, b c^{2} m^{3} + 10 \, b c^{2} m^{2} + 5 \, b c^{2} m + b c^{2}\right)} n\right)} x x^{5 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 3 \, {\left({\left(b^{2} c + a c^{2}\right)} m^{6} + 6 \, {\left(b^{2} c + a c^{2}\right)} m^{5} + 180 \, {\left(b^{2} c + a c^{2} + {\left(b^{2} c + a c^{2}\right)} m\right)} n^{5} + 15 \, {\left(b^{2} c + a c^{2}\right)} m^{4} + 396 \, {\left(b^{2} c + a c^{2} + {\left(b^{2} c + a c^{2}\right)} m^{2} + 2 \, {\left(b^{2} c + a c^{2}\right)} m\right)} n^{4} + 20 \, {\left(b^{2} c + a c^{2}\right)} m^{3} + 307 \, {\left({\left(b^{2} c + a c^{2}\right)} m^{3} + b^{2} c + a c^{2} + 3 \, {\left(b^{2} c + a c^{2}\right)} m^{2} + 3 \, {\left(b^{2} c + a c^{2}\right)} m\right)} n^{3} + b^{2} c + a c^{2} + 15 \, {\left(b^{2} c + a c^{2}\right)} m^{2} + 107 \, {\left({\left(b^{2} c + a c^{2}\right)} m^{4} + 4 \, {\left(b^{2} c + a c^{2}\right)} m^{3} + b^{2} c + a c^{2} + 6 \, {\left(b^{2} c + a c^{2}\right)} m^{2} + 4 \, {\left(b^{2} c + a c^{2}\right)} m\right)} n^{2} + 6 \, {\left(b^{2} c + a c^{2}\right)} m + 17 \, {\left({\left(b^{2} c + a c^{2}\right)} m^{5} + 5 \, {\left(b^{2} c + a c^{2}\right)} m^{4} + 10 \, {\left(b^{2} c + a c^{2}\right)} m^{3} + b^{2} c + a c^{2} + 10 \, {\left(b^{2} c + a c^{2}\right)} m^{2} + 5 \, {\left(b^{2} c + a c^{2}\right)} m\right)} n\right)} x x^{4 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + {\left({\left(b^{3} + 6 \, a b c\right)} m^{6} + 6 \, {\left(b^{3} + 6 \, a b c\right)} m^{5} + 240 \, {\left(b^{3} + 6 \, a b c + {\left(b^{3} + 6 \, a b c\right)} m\right)} n^{5} + 15 \, {\left(b^{3} + 6 \, a b c\right)} m^{4} + 508 \, {\left(b^{3} + 6 \, a b c + {\left(b^{3} + 6 \, a b c\right)} m^{2} + 2 \, {\left(b^{3} + 6 \, a b c\right)} m\right)} n^{4} + 20 \, {\left(b^{3} + 6 \, a b c\right)} m^{3} + 372 \, {\left({\left(b^{3} + 6 \, a b c\right)} m^{3} + b^{3} + 6 \, a b c + 3 \, {\left(b^{3} + 6 \, a b c\right)} m^{2} + 3 \, {\left(b^{3} + 6 \, a b c\right)} m\right)} n^{3} + b^{3} + 6 \, a b c + 15 \, {\left(b^{3} + 6 \, a b c\right)} m^{2} + 121 \, {\left({\left(b^{3} + 6 \, a b c\right)} m^{4} + 4 \, {\left(b^{3} + 6 \, a b c\right)} m^{3} + b^{3} + 6 \, a b c + 6 \, {\left(b^{3} + 6 \, a b c\right)} m^{2} + 4 \, {\left(b^{3} + 6 \, a b c\right)} m\right)} n^{2} + 6 \, {\left(b^{3} + 6 \, a b c\right)} m + 18 \, {\left({\left(b^{3} + 6 \, a b c\right)} m^{5} + 5 \, {\left(b^{3} + 6 \, a b c\right)} m^{4} + 10 \, {\left(b^{3} + 6 \, a b c\right)} m^{3} + b^{3} + 6 \, a b c + 10 \, {\left(b^{3} + 6 \, a b c\right)} m^{2} + 5 \, {\left(b^{3} + 6 \, a b c\right)} m\right)} n\right)} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 3 \, {\left({\left(a b^{2} + a^{2} c\right)} m^{6} + 6 \, {\left(a b^{2} + a^{2} c\right)} m^{5} + 360 \, {\left(a b^{2} + a^{2} c + {\left(a b^{2} + a^{2} c\right)} m\right)} n^{5} + 15 \, {\left(a b^{2} + a^{2} c\right)} m^{4} + 702 \, {\left(a b^{2} + a^{2} c + {\left(a b^{2} + a^{2} c\right)} m^{2} + 2 \, {\left(a b^{2} + a^{2} c\right)} m\right)} n^{4} + 20 \, {\left(a b^{2} + a^{2} c\right)} m^{3} + 461 \, {\left({\left(a b^{2} + a^{2} c\right)} m^{3} + a b^{2} + a^{2} c + 3 \, {\left(a b^{2} + a^{2} c\right)} m^{2} + 3 \, {\left(a b^{2} + a^{2} c\right)} m\right)} n^{3} + a b^{2} + a^{2} c + 15 \, {\left(a b^{2} + a^{2} c\right)} m^{2} + 137 \, {\left({\left(a b^{2} + a^{2} c\right)} m^{4} + 4 \, {\left(a b^{2} + a^{2} c\right)} m^{3} + a b^{2} + a^{2} c + 6 \, {\left(a b^{2} + a^{2} c\right)} m^{2} + 4 \, {\left(a b^{2} + a^{2} c\right)} m\right)} n^{2} + 6 \, {\left(a b^{2} + a^{2} c\right)} m + 19 \, {\left({\left(a b^{2} + a^{2} c\right)} m^{5} + 5 \, {\left(a b^{2} + a^{2} c\right)} m^{4} + 10 \, {\left(a b^{2} + a^{2} c\right)} m^{3} + a b^{2} + a^{2} c + 10 \, {\left(a b^{2} + a^{2} c\right)} m^{2} + 5 \, {\left(a b^{2} + a^{2} c\right)} m\right)} n\right)} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 3 \, {\left(a^{2} b m^{6} + 6 \, a^{2} b m^{5} + 15 \, a^{2} b m^{4} + 20 \, a^{2} b m^{3} + 720 \, {\left(a^{2} b m + a^{2} b\right)} n^{5} + 15 \, a^{2} b m^{2} + 1044 \, {\left(a^{2} b m^{2} + 2 \, a^{2} b m + a^{2} b\right)} n^{4} + 6 \, a^{2} b m + 580 \, {\left(a^{2} b m^{3} + 3 \, a^{2} b m^{2} + 3 \, a^{2} b m + a^{2} b\right)} n^{3} + a^{2} b + 155 \, {\left(a^{2} b m^{4} + 4 \, a^{2} b m^{3} + 6 \, a^{2} b m^{2} + 4 \, a^{2} b m + a^{2} b\right)} n^{2} + 20 \, {\left(a^{2} b m^{5} + 5 \, a^{2} b m^{4} + 10 \, a^{2} b m^{3} + 10 \, a^{2} b m^{2} + 5 \, a^{2} b m + a^{2} b\right)} n\right)} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + {\left(a^{3} m^{6} + 720 \, a^{3} n^{6} + 6 \, a^{3} m^{5} + 15 \, a^{3} m^{4} + 20 \, a^{3} m^{3} + 1764 \, {\left(a^{3} m + a^{3}\right)} n^{5} + 15 \, a^{3} m^{2} + 1624 \, {\left(a^{3} m^{2} + 2 \, a^{3} m + a^{3}\right)} n^{4} + 6 \, a^{3} m + 735 \, {\left(a^{3} m^{3} + 3 \, a^{3} m^{2} + 3 \, a^{3} m + a^{3}\right)} n^{3} + a^{3} + 175 \, {\left(a^{3} m^{4} + 4 \, a^{3} m^{3} + 6 \, a^{3} m^{2} + 4 \, a^{3} m + a^{3}\right)} n^{2} + 21 \, {\left(a^{3} m^{5} + 5 \, a^{3} m^{4} + 10 \, a^{3} m^{3} + 10 \, a^{3} m^{2} + 5 \, a^{3} m + a^{3}\right)} n\right)} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)}}{m^{7} + 720 \, {\left(m + 1\right)} n^{6} + 7 \, m^{6} + 1764 \, {\left(m^{2} + 2 \, m + 1\right)} n^{5} + 21 \, m^{5} + 1624 \, {\left(m^{3} + 3 \, m^{2} + 3 \, m + 1\right)} n^{4} + 35 \, m^{4} + 735 \, {\left(m^{4} + 4 \, m^{3} + 6 \, m^{2} + 4 \, m + 1\right)} n^{3} + 35 \, m^{3} + 175 \, {\left(m^{5} + 5 \, m^{4} + 10 \, m^{3} + 10 \, m^{2} + 5 \, m + 1\right)} n^{2} + 21 \, m^{2} + 21 \, {\left(m^{6} + 6 \, m^{5} + 15 \, m^{4} + 20 \, m^{3} + 15 \, m^{2} + 6 \, m + 1\right)} n + 7 \, m + 1}"," ",0,"((c^3*m^6 + 6*c^3*m^5 + 15*c^3*m^4 + 20*c^3*m^3 + 120*(c^3*m + c^3)*n^5 + 15*c^3*m^2 + 274*(c^3*m^2 + 2*c^3*m + c^3)*n^4 + 6*c^3*m + 225*(c^3*m^3 + 3*c^3*m^2 + 3*c^3*m + c^3)*n^3 + c^3 + 85*(c^3*m^4 + 4*c^3*m^3 + 6*c^3*m^2 + 4*c^3*m + c^3)*n^2 + 15*(c^3*m^5 + 5*c^3*m^4 + 10*c^3*m^3 + 10*c^3*m^2 + 5*c^3*m + c^3)*n)*x*x^(6*n)*e^(m*log(d) + m*log(x)) + 3*(b*c^2*m^6 + 6*b*c^2*m^5 + 15*b*c^2*m^4 + 20*b*c^2*m^3 + 144*(b*c^2*m + b*c^2)*n^5 + 15*b*c^2*m^2 + 324*(b*c^2*m^2 + 2*b*c^2*m + b*c^2)*n^4 + 6*b*c^2*m + 260*(b*c^2*m^3 + 3*b*c^2*m^2 + 3*b*c^2*m + b*c^2)*n^3 + b*c^2 + 95*(b*c^2*m^4 + 4*b*c^2*m^3 + 6*b*c^2*m^2 + 4*b*c^2*m + b*c^2)*n^2 + 16*(b*c^2*m^5 + 5*b*c^2*m^4 + 10*b*c^2*m^3 + 10*b*c^2*m^2 + 5*b*c^2*m + b*c^2)*n)*x*x^(5*n)*e^(m*log(d) + m*log(x)) + 3*((b^2*c + a*c^2)*m^6 + 6*(b^2*c + a*c^2)*m^5 + 180*(b^2*c + a*c^2 + (b^2*c + a*c^2)*m)*n^5 + 15*(b^2*c + a*c^2)*m^4 + 396*(b^2*c + a*c^2 + (b^2*c + a*c^2)*m^2 + 2*(b^2*c + a*c^2)*m)*n^4 + 20*(b^2*c + a*c^2)*m^3 + 307*((b^2*c + a*c^2)*m^3 + b^2*c + a*c^2 + 3*(b^2*c + a*c^2)*m^2 + 3*(b^2*c + a*c^2)*m)*n^3 + b^2*c + a*c^2 + 15*(b^2*c + a*c^2)*m^2 + 107*((b^2*c + a*c^2)*m^4 + 4*(b^2*c + a*c^2)*m^3 + b^2*c + a*c^2 + 6*(b^2*c + a*c^2)*m^2 + 4*(b^2*c + a*c^2)*m)*n^2 + 6*(b^2*c + a*c^2)*m + 17*((b^2*c + a*c^2)*m^5 + 5*(b^2*c + a*c^2)*m^4 + 10*(b^2*c + a*c^2)*m^3 + b^2*c + a*c^2 + 10*(b^2*c + a*c^2)*m^2 + 5*(b^2*c + a*c^2)*m)*n)*x*x^(4*n)*e^(m*log(d) + m*log(x)) + ((b^3 + 6*a*b*c)*m^6 + 6*(b^3 + 6*a*b*c)*m^5 + 240*(b^3 + 6*a*b*c + (b^3 + 6*a*b*c)*m)*n^5 + 15*(b^3 + 6*a*b*c)*m^4 + 508*(b^3 + 6*a*b*c + (b^3 + 6*a*b*c)*m^2 + 2*(b^3 + 6*a*b*c)*m)*n^4 + 20*(b^3 + 6*a*b*c)*m^3 + 372*((b^3 + 6*a*b*c)*m^3 + b^3 + 6*a*b*c + 3*(b^3 + 6*a*b*c)*m^2 + 3*(b^3 + 6*a*b*c)*m)*n^3 + b^3 + 6*a*b*c + 15*(b^3 + 6*a*b*c)*m^2 + 121*((b^3 + 6*a*b*c)*m^4 + 4*(b^3 + 6*a*b*c)*m^3 + b^3 + 6*a*b*c + 6*(b^3 + 6*a*b*c)*m^2 + 4*(b^3 + 6*a*b*c)*m)*n^2 + 6*(b^3 + 6*a*b*c)*m + 18*((b^3 + 6*a*b*c)*m^5 + 5*(b^3 + 6*a*b*c)*m^4 + 10*(b^3 + 6*a*b*c)*m^3 + b^3 + 6*a*b*c + 10*(b^3 + 6*a*b*c)*m^2 + 5*(b^3 + 6*a*b*c)*m)*n)*x*x^(3*n)*e^(m*log(d) + m*log(x)) + 3*((a*b^2 + a^2*c)*m^6 + 6*(a*b^2 + a^2*c)*m^5 + 360*(a*b^2 + a^2*c + (a*b^2 + a^2*c)*m)*n^5 + 15*(a*b^2 + a^2*c)*m^4 + 702*(a*b^2 + a^2*c + (a*b^2 + a^2*c)*m^2 + 2*(a*b^2 + a^2*c)*m)*n^4 + 20*(a*b^2 + a^2*c)*m^3 + 461*((a*b^2 + a^2*c)*m^3 + a*b^2 + a^2*c + 3*(a*b^2 + a^2*c)*m^2 + 3*(a*b^2 + a^2*c)*m)*n^3 + a*b^2 + a^2*c + 15*(a*b^2 + a^2*c)*m^2 + 137*((a*b^2 + a^2*c)*m^4 + 4*(a*b^2 + a^2*c)*m^3 + a*b^2 + a^2*c + 6*(a*b^2 + a^2*c)*m^2 + 4*(a*b^2 + a^2*c)*m)*n^2 + 6*(a*b^2 + a^2*c)*m + 19*((a*b^2 + a^2*c)*m^5 + 5*(a*b^2 + a^2*c)*m^4 + 10*(a*b^2 + a^2*c)*m^3 + a*b^2 + a^2*c + 10*(a*b^2 + a^2*c)*m^2 + 5*(a*b^2 + a^2*c)*m)*n)*x*x^(2*n)*e^(m*log(d) + m*log(x)) + 3*(a^2*b*m^6 + 6*a^2*b*m^5 + 15*a^2*b*m^4 + 20*a^2*b*m^3 + 720*(a^2*b*m + a^2*b)*n^5 + 15*a^2*b*m^2 + 1044*(a^2*b*m^2 + 2*a^2*b*m + a^2*b)*n^4 + 6*a^2*b*m + 580*(a^2*b*m^3 + 3*a^2*b*m^2 + 3*a^2*b*m + a^2*b)*n^3 + a^2*b + 155*(a^2*b*m^4 + 4*a^2*b*m^3 + 6*a^2*b*m^2 + 4*a^2*b*m + a^2*b)*n^2 + 20*(a^2*b*m^5 + 5*a^2*b*m^4 + 10*a^2*b*m^3 + 10*a^2*b*m^2 + 5*a^2*b*m + a^2*b)*n)*x*x^n*e^(m*log(d) + m*log(x)) + (a^3*m^6 + 720*a^3*n^6 + 6*a^3*m^5 + 15*a^3*m^4 + 20*a^3*m^3 + 1764*(a^3*m + a^3)*n^5 + 15*a^3*m^2 + 1624*(a^3*m^2 + 2*a^3*m + a^3)*n^4 + 6*a^3*m + 735*(a^3*m^3 + 3*a^3*m^2 + 3*a^3*m + a^3)*n^3 + a^3 + 175*(a^3*m^4 + 4*a^3*m^3 + 6*a^3*m^2 + 4*a^3*m + a^3)*n^2 + 21*(a^3*m^5 + 5*a^3*m^4 + 10*a^3*m^3 + 10*a^3*m^2 + 5*a^3*m + a^3)*n)*x*e^(m*log(d) + m*log(x)))/(m^7 + 720*(m + 1)*n^6 + 7*m^6 + 1764*(m^2 + 2*m + 1)*n^5 + 21*m^5 + 1624*(m^3 + 3*m^2 + 3*m + 1)*n^4 + 35*m^4 + 735*(m^4 + 4*m^3 + 6*m^2 + 4*m + 1)*n^3 + 35*m^3 + 175*(m^5 + 5*m^4 + 10*m^3 + 10*m^2 + 5*m + 1)*n^2 + 21*m^2 + 21*(m^6 + 6*m^5 + 15*m^4 + 20*m^3 + 15*m^2 + 6*m + 1)*n + 7*m + 1)","B",0
597,1,706,0,1.254639," ","integrate((d*x)^m*(a+b*x^n+c*x^(2*n))^2,x, algorithm=""fricas"")","\frac{{\left(c^{2} m^{4} + 4 \, c^{2} m^{3} + 6 \, c^{2} m^{2} + 6 \, {\left(c^{2} m + c^{2}\right)} n^{3} + 4 \, c^{2} m + 11 \, {\left(c^{2} m^{2} + 2 \, c^{2} m + c^{2}\right)} n^{2} + c^{2} + 6 \, {\left(c^{2} m^{3} + 3 \, c^{2} m^{2} + 3 \, c^{2} m + c^{2}\right)} n\right)} x x^{4 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, {\left(b c m^{4} + 4 \, b c m^{3} + 6 \, b c m^{2} + 8 \, {\left(b c m + b c\right)} n^{3} + 4 \, b c m + 14 \, {\left(b c m^{2} + 2 \, b c m + b c\right)} n^{2} + b c + 7 \, {\left(b c m^{3} + 3 \, b c m^{2} + 3 \, b c m + b c\right)} n\right)} x x^{3 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + {\left({\left(b^{2} + 2 \, a c\right)} m^{4} + 4 \, {\left(b^{2} + 2 \, a c\right)} m^{3} + 12 \, {\left(b^{2} + 2 \, a c + {\left(b^{2} + 2 \, a c\right)} m\right)} n^{3} + 6 \, {\left(b^{2} + 2 \, a c\right)} m^{2} + 19 \, {\left({\left(b^{2} + 2 \, a c\right)} m^{2} + b^{2} + 2 \, a c + 2 \, {\left(b^{2} + 2 \, a c\right)} m\right)} n^{2} + b^{2} + 2 \, a c + 4 \, {\left(b^{2} + 2 \, a c\right)} m + 8 \, {\left({\left(b^{2} + 2 \, a c\right)} m^{3} + 3 \, {\left(b^{2} + 2 \, a c\right)} m^{2} + b^{2} + 2 \, a c + 3 \, {\left(b^{2} + 2 \, a c\right)} m\right)} n\right)} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + 2 \, {\left(a b m^{4} + 4 \, a b m^{3} + 6 \, a b m^{2} + 24 \, {\left(a b m + a b\right)} n^{3} + 4 \, a b m + 26 \, {\left(a b m^{2} + 2 \, a b m + a b\right)} n^{2} + a b + 9 \, {\left(a b m^{3} + 3 \, a b m^{2} + 3 \, a b m + a b\right)} n\right)} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + {\left(a^{2} m^{4} + 24 \, a^{2} n^{4} + 4 \, a^{2} m^{3} + 6 \, a^{2} m^{2} + 50 \, {\left(a^{2} m + a^{2}\right)} n^{3} + 4 \, a^{2} m + 35 \, {\left(a^{2} m^{2} + 2 \, a^{2} m + a^{2}\right)} n^{2} + a^{2} + 10 \, {\left(a^{2} m^{3} + 3 \, a^{2} m^{2} + 3 \, a^{2} m + a^{2}\right)} n\right)} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)}}{m^{5} + 24 \, {\left(m + 1\right)} n^{4} + 5 \, m^{4} + 50 \, {\left(m^{2} + 2 \, m + 1\right)} n^{3} + 10 \, m^{3} + 35 \, {\left(m^{3} + 3 \, m^{2} + 3 \, m + 1\right)} n^{2} + 10 \, m^{2} + 10 \, {\left(m^{4} + 4 \, m^{3} + 6 \, m^{2} + 4 \, m + 1\right)} n + 5 \, m + 1}"," ",0,"((c^2*m^4 + 4*c^2*m^3 + 6*c^2*m^2 + 6*(c^2*m + c^2)*n^3 + 4*c^2*m + 11*(c^2*m^2 + 2*c^2*m + c^2)*n^2 + c^2 + 6*(c^2*m^3 + 3*c^2*m^2 + 3*c^2*m + c^2)*n)*x*x^(4*n)*e^(m*log(d) + m*log(x)) + 2*(b*c*m^4 + 4*b*c*m^3 + 6*b*c*m^2 + 8*(b*c*m + b*c)*n^3 + 4*b*c*m + 14*(b*c*m^2 + 2*b*c*m + b*c)*n^2 + b*c + 7*(b*c*m^3 + 3*b*c*m^2 + 3*b*c*m + b*c)*n)*x*x^(3*n)*e^(m*log(d) + m*log(x)) + ((b^2 + 2*a*c)*m^4 + 4*(b^2 + 2*a*c)*m^3 + 12*(b^2 + 2*a*c + (b^2 + 2*a*c)*m)*n^3 + 6*(b^2 + 2*a*c)*m^2 + 19*((b^2 + 2*a*c)*m^2 + b^2 + 2*a*c + 2*(b^2 + 2*a*c)*m)*n^2 + b^2 + 2*a*c + 4*(b^2 + 2*a*c)*m + 8*((b^2 + 2*a*c)*m^3 + 3*(b^2 + 2*a*c)*m^2 + b^2 + 2*a*c + 3*(b^2 + 2*a*c)*m)*n)*x*x^(2*n)*e^(m*log(d) + m*log(x)) + 2*(a*b*m^4 + 4*a*b*m^3 + 6*a*b*m^2 + 24*(a*b*m + a*b)*n^3 + 4*a*b*m + 26*(a*b*m^2 + 2*a*b*m + a*b)*n^2 + a*b + 9*(a*b*m^3 + 3*a*b*m^2 + 3*a*b*m + a*b)*n)*x*x^n*e^(m*log(d) + m*log(x)) + (a^2*m^4 + 24*a^2*n^4 + 4*a^2*m^3 + 6*a^2*m^2 + 50*(a^2*m + a^2)*n^3 + 4*a^2*m + 35*(a^2*m^2 + 2*a^2*m + a^2)*n^2 + a^2 + 10*(a^2*m^3 + 3*a^2*m^2 + 3*a^2*m + a^2)*n)*x*e^(m*log(d) + m*log(x)))/(m^5 + 24*(m + 1)*n^4 + 5*m^4 + 50*(m^2 + 2*m + 1)*n^3 + 10*m^3 + 35*(m^3 + 3*m^2 + 3*m + 1)*n^2 + 10*m^2 + 10*(m^4 + 4*m^3 + 6*m^2 + 4*m + 1)*n + 5*m + 1)","B",0
598,1,142,0,1.277880," ","integrate((d*x)^m*(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\frac{{\left(c m^{2} + 2 \, c m + {\left(c m + c\right)} n + c\right)} x x^{2 \, n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + {\left(b m^{2} + 2 \, b m + 2 \, {\left(b m + b\right)} n + b\right)} x x^{n} e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)} + {\left(a m^{2} + 2 \, a n^{2} + 2 \, a m + 3 \, {\left(a m + a\right)} n + a\right)} x e^{\left(m \log\left(d\right) + m \log\left(x\right)\right)}}{m^{3} + 2 \, {\left(m + 1\right)} n^{2} + 3 \, m^{2} + 3 \, {\left(m^{2} + 2 \, m + 1\right)} n + 3 \, m + 1}"," ",0,"((c*m^2 + 2*c*m + (c*m + c)*n + c)*x*x^(2*n)*e^(m*log(d) + m*log(x)) + (b*m^2 + 2*b*m + 2*(b*m + b)*n + b)*x*x^n*e^(m*log(d) + m*log(x)) + (a*m^2 + 2*a*n^2 + 2*a*m + 3*(a*m + a)*n + a)*x*e^(m*log(d) + m*log(x)))/(m^3 + 2*(m + 1)*n^2 + 3*m^2 + 3*(m^2 + 2*m + 1)*n + 3*m + 1)","B",0
599,0,0,0,1.501987," ","integrate((d*x)^m/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{c x^{2 \, n} + b x^{n} + a}, x\right)"," ",0,"integral((d*x)^m/(c*x^(2*n) + b*x^n + a), x)","F",0
600,0,0,0,1.577439," ","integrate((d*x)^m/(a+b*x^n+c*x^(2*n))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{c^{2} x^{4 \, n} + b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2} + 2 \, {\left(b c x^{n} + a c\right)} x^{2 \, n}}, x\right)"," ",0,"integral((d*x)^m/(c^2*x^(4*n) + b^2*x^(2*n) + 2*a*b*x^n + a^2 + 2*(b*c*x^n + a*c)*x^(2*n)), x)","F",0
601,0,0,0,1.470650," ","integrate((d*x)^m/(a+b*x^n+c*x^(2*n))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{c^{3} x^{6 \, n} + b^{3} x^{3 \, n} + 3 \, a b^{2} x^{2 \, n} + 3 \, a^{2} b x^{n} + a^{3} + 3 \, {\left(b c^{2} x^{n} + a c^{2}\right)} x^{4 \, n} + 3 \, {\left(b^{2} c x^{2 \, n} + 2 \, a b c x^{n} + a^{2} c\right)} x^{2 \, n}}, x\right)"," ",0,"integral((d*x)^m/(c^3*x^(6*n) + b^3*x^(3*n) + 3*a*b^2*x^(2*n) + 3*a^2*b*x^n + a^3 + 3*(b*c^2*x^n + a*c^2)*x^(4*n) + 3*(b^2*c*x^(2*n) + 2*a*b*c*x^n + a^2*c)*x^(2*n)), x)","F",0
602,-2,0,0,0.000000," ","integrate((d*x)^m*(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
603,-2,0,0,0.000000," ","integrate((d*x)^m*(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
604,-2,0,0,0.000000," ","integrate((d*x)^m/(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
605,-2,0,0,0.000000," ","integrate((d*x)^m/(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
606,0,0,0,1.130593," ","integrate((d*x)^m*(a+b*x^n+c*x^(2*n))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2 \, n} + b x^{n} + a\right)}^{p} \left(d x\right)^{m}, x\right)"," ",0,"integral((c*x^(2*n) + b*x^n + a)^p*(d*x)^m, x)","F",0
607,1,175,0,1.155786," ","integrate((e*x+d)^3*(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""fricas"")","\frac{1}{8} x^{8} e^{7} c + x^{7} e^{6} d c + \frac{7}{2} x^{6} e^{5} d^{2} c + 7 x^{5} e^{4} d^{3} c + \frac{35}{4} x^{4} e^{3} d^{4} c + \frac{1}{6} x^{6} e^{5} b + 7 x^{3} e^{2} d^{5} c + x^{5} e^{4} d b + \frac{7}{2} x^{2} e d^{6} c + \frac{5}{2} x^{4} e^{3} d^{2} b + x d^{7} c + \frac{10}{3} x^{3} e^{2} d^{3} b + \frac{5}{2} x^{2} e d^{4} b + \frac{1}{4} x^{4} e^{3} a + x d^{5} b + x^{3} e^{2} d a + \frac{3}{2} x^{2} e d^{2} a + x d^{3} a"," ",0,"1/8*x^8*e^7*c + x^7*e^6*d*c + 7/2*x^6*e^5*d^2*c + 7*x^5*e^4*d^3*c + 35/4*x^4*e^3*d^4*c + 1/6*x^6*e^5*b + 7*x^3*e^2*d^5*c + x^5*e^4*d*b + 7/2*x^2*e*d^6*c + 5/2*x^4*e^3*d^2*b + x*d^7*c + 10/3*x^3*e^2*d^3*b + 5/2*x^2*e*d^4*b + 1/4*x^4*e^3*a + x*d^5*b + x^3*e^2*d*a + 3/2*x^2*e*d^2*a + x*d^3*a","B",0
608,1,571,0,1.144949," ","integrate((e*x+d)^3*(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""fricas"")","\frac{1}{12} x^{12} e^{11} c^{2} + x^{11} e^{10} d c^{2} + \frac{11}{2} x^{10} e^{9} d^{2} c^{2} + \frac{55}{3} x^{9} e^{8} d^{3} c^{2} + \frac{165}{4} x^{8} e^{7} d^{4} c^{2} + \frac{1}{5} x^{10} e^{9} c b + 66 x^{7} e^{6} d^{5} c^{2} + 2 x^{9} e^{8} d c b + 77 x^{6} e^{5} d^{6} c^{2} + 9 x^{8} e^{7} d^{2} c b + 66 x^{5} e^{4} d^{7} c^{2} + 24 x^{7} e^{6} d^{3} c b + \frac{165}{4} x^{4} e^{3} d^{8} c^{2} + 42 x^{6} e^{5} d^{4} c b + \frac{1}{8} x^{8} e^{7} b^{2} + \frac{1}{4} x^{8} e^{7} c a + \frac{55}{3} x^{3} e^{2} d^{9} c^{2} + \frac{252}{5} x^{5} e^{4} d^{5} c b + x^{7} e^{6} d b^{2} + 2 x^{7} e^{6} d c a + \frac{11}{2} x^{2} e d^{10} c^{2} + 42 x^{4} e^{3} d^{6} c b + \frac{7}{2} x^{6} e^{5} d^{2} b^{2} + 7 x^{6} e^{5} d^{2} c a + x d^{11} c^{2} + 24 x^{3} e^{2} d^{7} c b + 7 x^{5} e^{4} d^{3} b^{2} + 14 x^{5} e^{4} d^{3} c a + 9 x^{2} e d^{8} c b + \frac{35}{4} x^{4} e^{3} d^{4} b^{2} + \frac{35}{2} x^{4} e^{3} d^{4} c a + \frac{1}{3} x^{6} e^{5} b a + 2 x d^{9} c b + 7 x^{3} e^{2} d^{5} b^{2} + 14 x^{3} e^{2} d^{5} c a + 2 x^{5} e^{4} d b a + \frac{7}{2} x^{2} e d^{6} b^{2} + 7 x^{2} e d^{6} c a + 5 x^{4} e^{3} d^{2} b a + x d^{7} b^{2} + 2 x d^{7} c a + \frac{20}{3} x^{3} e^{2} d^{3} b a + 5 x^{2} e d^{4} b a + \frac{1}{4} x^{4} e^{3} a^{2} + 2 x d^{5} b a + x^{3} e^{2} d a^{2} + \frac{3}{2} x^{2} e d^{2} a^{2} + x d^{3} a^{2}"," ",0,"1/12*x^12*e^11*c^2 + x^11*e^10*d*c^2 + 11/2*x^10*e^9*d^2*c^2 + 55/3*x^9*e^8*d^3*c^2 + 165/4*x^8*e^7*d^4*c^2 + 1/5*x^10*e^9*c*b + 66*x^7*e^6*d^5*c^2 + 2*x^9*e^8*d*c*b + 77*x^6*e^5*d^6*c^2 + 9*x^8*e^7*d^2*c*b + 66*x^5*e^4*d^7*c^2 + 24*x^7*e^6*d^3*c*b + 165/4*x^4*e^3*d^8*c^2 + 42*x^6*e^5*d^4*c*b + 1/8*x^8*e^7*b^2 + 1/4*x^8*e^7*c*a + 55/3*x^3*e^2*d^9*c^2 + 252/5*x^5*e^4*d^5*c*b + x^7*e^6*d*b^2 + 2*x^7*e^6*d*c*a + 11/2*x^2*e*d^10*c^2 + 42*x^4*e^3*d^6*c*b + 7/2*x^6*e^5*d^2*b^2 + 7*x^6*e^5*d^2*c*a + x*d^11*c^2 + 24*x^3*e^2*d^7*c*b + 7*x^5*e^4*d^3*b^2 + 14*x^5*e^4*d^3*c*a + 9*x^2*e*d^8*c*b + 35/4*x^4*e^3*d^4*b^2 + 35/2*x^4*e^3*d^4*c*a + 1/3*x^6*e^5*b*a + 2*x*d^9*c*b + 7*x^3*e^2*d^5*b^2 + 14*x^3*e^2*d^5*c*a + 2*x^5*e^4*d*b*a + 7/2*x^2*e*d^6*b^2 + 7*x^2*e*d^6*c*a + 5*x^4*e^3*d^2*b*a + x*d^7*b^2 + 2*x*d^7*c*a + 20/3*x^3*e^2*d^3*b*a + 5*x^2*e*d^4*b*a + 1/4*x^4*e^3*a^2 + 2*x*d^5*b*a + x^3*e^2*d*a^2 + 3/2*x^2*e*d^2*a^2 + x*d^3*a^2","B",0
609,1,1335,0,1.244367," ","integrate((e*x+d)^3*(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""fricas"")","\frac{1}{16} x^{16} e^{15} c^{3} + x^{15} e^{14} d c^{3} + \frac{15}{2} x^{14} e^{13} d^{2} c^{3} + 35 x^{13} e^{12} d^{3} c^{3} + \frac{455}{4} x^{12} e^{11} d^{4} c^{3} + \frac{3}{14} x^{14} e^{13} c^{2} b + 273 x^{11} e^{10} d^{5} c^{3} + 3 x^{13} e^{12} d c^{2} b + \frac{1001}{2} x^{10} e^{9} d^{6} c^{3} + \frac{39}{2} x^{12} e^{11} d^{2} c^{2} b + 715 x^{9} e^{8} d^{7} c^{3} + 78 x^{11} e^{10} d^{3} c^{2} b + \frac{6435}{8} x^{8} e^{7} d^{8} c^{3} + \frac{429}{2} x^{10} e^{9} d^{4} c^{2} b + \frac{1}{4} x^{12} e^{11} c b^{2} + \frac{1}{4} x^{12} e^{11} c^{2} a + 715 x^{7} e^{6} d^{9} c^{3} + 429 x^{9} e^{8} d^{5} c^{2} b + 3 x^{11} e^{10} d c b^{2} + 3 x^{11} e^{10} d c^{2} a + \frac{1001}{2} x^{6} e^{5} d^{10} c^{3} + \frac{1287}{2} x^{8} e^{7} d^{6} c^{2} b + \frac{33}{2} x^{10} e^{9} d^{2} c b^{2} + \frac{33}{2} x^{10} e^{9} d^{2} c^{2} a + 273 x^{5} e^{4} d^{11} c^{3} + \frac{5148}{7} x^{7} e^{6} d^{7} c^{2} b + 55 x^{9} e^{8} d^{3} c b^{2} + 55 x^{9} e^{8} d^{3} c^{2} a + \frac{455}{4} x^{4} e^{3} d^{12} c^{3} + \frac{1287}{2} x^{6} e^{5} d^{8} c^{2} b + \frac{495}{4} x^{8} e^{7} d^{4} c b^{2} + \frac{1}{10} x^{10} e^{9} b^{3} + \frac{495}{4} x^{8} e^{7} d^{4} c^{2} a + \frac{3}{5} x^{10} e^{9} c b a + 35 x^{3} e^{2} d^{13} c^{3} + 429 x^{5} e^{4} d^{9} c^{2} b + 198 x^{7} e^{6} d^{5} c b^{2} + x^{9} e^{8} d b^{3} + 198 x^{7} e^{6} d^{5} c^{2} a + 6 x^{9} e^{8} d c b a + \frac{15}{2} x^{2} e d^{14} c^{3} + \frac{429}{2} x^{4} e^{3} d^{10} c^{2} b + 231 x^{6} e^{5} d^{6} c b^{2} + \frac{9}{2} x^{8} e^{7} d^{2} b^{3} + 231 x^{6} e^{5} d^{6} c^{2} a + 27 x^{8} e^{7} d^{2} c b a + x d^{15} c^{3} + 78 x^{3} e^{2} d^{11} c^{2} b + 198 x^{5} e^{4} d^{7} c b^{2} + 12 x^{7} e^{6} d^{3} b^{3} + 198 x^{5} e^{4} d^{7} c^{2} a + 72 x^{7} e^{6} d^{3} c b a + \frac{39}{2} x^{2} e d^{12} c^{2} b + \frac{495}{4} x^{4} e^{3} d^{8} c b^{2} + 21 x^{6} e^{5} d^{4} b^{3} + \frac{495}{4} x^{4} e^{3} d^{8} c^{2} a + 126 x^{6} e^{5} d^{4} c b a + \frac{3}{8} x^{8} e^{7} b^{2} a + \frac{3}{8} x^{8} e^{7} c a^{2} + 3 x d^{13} c^{2} b + 55 x^{3} e^{2} d^{9} c b^{2} + \frac{126}{5} x^{5} e^{4} d^{5} b^{3} + 55 x^{3} e^{2} d^{9} c^{2} a + \frac{756}{5} x^{5} e^{4} d^{5} c b a + 3 x^{7} e^{6} d b^{2} a + 3 x^{7} e^{6} d c a^{2} + \frac{33}{2} x^{2} e d^{10} c b^{2} + 21 x^{4} e^{3} d^{6} b^{3} + \frac{33}{2} x^{2} e d^{10} c^{2} a + 126 x^{4} e^{3} d^{6} c b a + \frac{21}{2} x^{6} e^{5} d^{2} b^{2} a + \frac{21}{2} x^{6} e^{5} d^{2} c a^{2} + 3 x d^{11} c b^{2} + 12 x^{3} e^{2} d^{7} b^{3} + 3 x d^{11} c^{2} a + 72 x^{3} e^{2} d^{7} c b a + 21 x^{5} e^{4} d^{3} b^{2} a + 21 x^{5} e^{4} d^{3} c a^{2} + \frac{9}{2} x^{2} e d^{8} b^{3} + 27 x^{2} e d^{8} c b a + \frac{105}{4} x^{4} e^{3} d^{4} b^{2} a + \frac{105}{4} x^{4} e^{3} d^{4} c a^{2} + \frac{1}{2} x^{6} e^{5} b a^{2} + x d^{9} b^{3} + 6 x d^{9} c b a + 21 x^{3} e^{2} d^{5} b^{2} a + 21 x^{3} e^{2} d^{5} c a^{2} + 3 x^{5} e^{4} d b a^{2} + \frac{21}{2} x^{2} e d^{6} b^{2} a + \frac{21}{2} x^{2} e d^{6} c a^{2} + \frac{15}{2} x^{4} e^{3} d^{2} b a^{2} + 3 x d^{7} b^{2} a + 3 x d^{7} c a^{2} + 10 x^{3} e^{2} d^{3} b a^{2} + \frac{15}{2} x^{2} e d^{4} b a^{2} + \frac{1}{4} x^{4} e^{3} a^{3} + 3 x d^{5} b a^{2} + x^{3} e^{2} d a^{3} + \frac{3}{2} x^{2} e d^{2} a^{3} + x d^{3} a^{3}"," ",0,"1/16*x^16*e^15*c^3 + x^15*e^14*d*c^3 + 15/2*x^14*e^13*d^2*c^3 + 35*x^13*e^12*d^3*c^3 + 455/4*x^12*e^11*d^4*c^3 + 3/14*x^14*e^13*c^2*b + 273*x^11*e^10*d^5*c^3 + 3*x^13*e^12*d*c^2*b + 1001/2*x^10*e^9*d^6*c^3 + 39/2*x^12*e^11*d^2*c^2*b + 715*x^9*e^8*d^7*c^3 + 78*x^11*e^10*d^3*c^2*b + 6435/8*x^8*e^7*d^8*c^3 + 429/2*x^10*e^9*d^4*c^2*b + 1/4*x^12*e^11*c*b^2 + 1/4*x^12*e^11*c^2*a + 715*x^7*e^6*d^9*c^3 + 429*x^9*e^8*d^5*c^2*b + 3*x^11*e^10*d*c*b^2 + 3*x^11*e^10*d*c^2*a + 1001/2*x^6*e^5*d^10*c^3 + 1287/2*x^8*e^7*d^6*c^2*b + 33/2*x^10*e^9*d^2*c*b^2 + 33/2*x^10*e^9*d^2*c^2*a + 273*x^5*e^4*d^11*c^3 + 5148/7*x^7*e^6*d^7*c^2*b + 55*x^9*e^8*d^3*c*b^2 + 55*x^9*e^8*d^3*c^2*a + 455/4*x^4*e^3*d^12*c^3 + 1287/2*x^6*e^5*d^8*c^2*b + 495/4*x^8*e^7*d^4*c*b^2 + 1/10*x^10*e^9*b^3 + 495/4*x^8*e^7*d^4*c^2*a + 3/5*x^10*e^9*c*b*a + 35*x^3*e^2*d^13*c^3 + 429*x^5*e^4*d^9*c^2*b + 198*x^7*e^6*d^5*c*b^2 + x^9*e^8*d*b^3 + 198*x^7*e^6*d^5*c^2*a + 6*x^9*e^8*d*c*b*a + 15/2*x^2*e*d^14*c^3 + 429/2*x^4*e^3*d^10*c^2*b + 231*x^6*e^5*d^6*c*b^2 + 9/2*x^8*e^7*d^2*b^3 + 231*x^6*e^5*d^6*c^2*a + 27*x^8*e^7*d^2*c*b*a + x*d^15*c^3 + 78*x^3*e^2*d^11*c^2*b + 198*x^5*e^4*d^7*c*b^2 + 12*x^7*e^6*d^3*b^3 + 198*x^5*e^4*d^7*c^2*a + 72*x^7*e^6*d^3*c*b*a + 39/2*x^2*e*d^12*c^2*b + 495/4*x^4*e^3*d^8*c*b^2 + 21*x^6*e^5*d^4*b^3 + 495/4*x^4*e^3*d^8*c^2*a + 126*x^6*e^5*d^4*c*b*a + 3/8*x^8*e^7*b^2*a + 3/8*x^8*e^7*c*a^2 + 3*x*d^13*c^2*b + 55*x^3*e^2*d^9*c*b^2 + 126/5*x^5*e^4*d^5*b^3 + 55*x^3*e^2*d^9*c^2*a + 756/5*x^5*e^4*d^5*c*b*a + 3*x^7*e^6*d*b^2*a + 3*x^7*e^6*d*c*a^2 + 33/2*x^2*e*d^10*c*b^2 + 21*x^4*e^3*d^6*b^3 + 33/2*x^2*e*d^10*c^2*a + 126*x^4*e^3*d^6*c*b*a + 21/2*x^6*e^5*d^2*b^2*a + 21/2*x^6*e^5*d^2*c*a^2 + 3*x*d^11*c*b^2 + 12*x^3*e^2*d^7*b^3 + 3*x*d^11*c^2*a + 72*x^3*e^2*d^7*c*b*a + 21*x^5*e^4*d^3*b^2*a + 21*x^5*e^4*d^3*c*a^2 + 9/2*x^2*e*d^8*b^3 + 27*x^2*e*d^8*c*b*a + 105/4*x^4*e^3*d^4*b^2*a + 105/4*x^4*e^3*d^4*c*a^2 + 1/2*x^6*e^5*b*a^2 + x*d^9*b^3 + 6*x*d^9*c*b*a + 21*x^3*e^2*d^5*b^2*a + 21*x^3*e^2*d^5*c*a^2 + 3*x^5*e^4*d*b*a^2 + 21/2*x^2*e*d^6*b^2*a + 21/2*x^2*e*d^6*c*a^2 + 15/2*x^4*e^3*d^2*b*a^2 + 3*x*d^7*b^2*a + 3*x*d^7*c*a^2 + 10*x^3*e^2*d^3*b*a^2 + 15/2*x^2*e*d^4*b*a^2 + 1/4*x^4*e^3*a^3 + 3*x*d^5*b*a^2 + x^3*e^2*d*a^3 + 3/2*x^2*e*d^2*a^3 + x*d^3*a^3","B",0
610,1,229,0,1.089041," ","integrate((e*f*x+d*f)^3*(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""fricas"")","\frac{1}{8} x^{8} f^{3} e^{7} c + x^{7} f^{3} e^{6} d c + \frac{7}{2} x^{6} f^{3} e^{5} d^{2} c + 7 x^{5} f^{3} e^{4} d^{3} c + \frac{35}{4} x^{4} f^{3} e^{3} d^{4} c + \frac{1}{6} x^{6} f^{3} e^{5} b + 7 x^{3} f^{3} e^{2} d^{5} c + x^{5} f^{3} e^{4} d b + \frac{7}{2} x^{2} f^{3} e d^{6} c + \frac{5}{2} x^{4} f^{3} e^{3} d^{2} b + x f^{3} d^{7} c + \frac{10}{3} x^{3} f^{3} e^{2} d^{3} b + \frac{5}{2} x^{2} f^{3} e d^{4} b + \frac{1}{4} x^{4} f^{3} e^{3} a + x f^{3} d^{5} b + x^{3} f^{3} e^{2} d a + \frac{3}{2} x^{2} f^{3} e d^{2} a + x f^{3} d^{3} a"," ",0,"1/8*x^8*f^3*e^7*c + x^7*f^3*e^6*d*c + 7/2*x^6*f^3*e^5*d^2*c + 7*x^5*f^3*e^4*d^3*c + 35/4*x^4*f^3*e^3*d^4*c + 1/6*x^6*f^3*e^5*b + 7*x^3*f^3*e^2*d^5*c + x^5*f^3*e^4*d*b + 7/2*x^2*f^3*e*d^6*c + 5/2*x^4*f^3*e^3*d^2*b + x*f^3*d^7*c + 10/3*x^3*f^3*e^2*d^3*b + 5/2*x^2*f^3*e*d^4*b + 1/4*x^4*f^3*e^3*a + x*f^3*d^5*b + x^3*f^3*e^2*d*a + 3/2*x^2*f^3*e*d^2*a + x*f^3*d^3*a","B",0
611,1,715,0,1.015545," ","integrate((e*f*x+d*f)^3*(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""fricas"")","\frac{1}{12} x^{12} f^{3} e^{11} c^{2} + x^{11} f^{3} e^{10} d c^{2} + \frac{11}{2} x^{10} f^{3} e^{9} d^{2} c^{2} + \frac{55}{3} x^{9} f^{3} e^{8} d^{3} c^{2} + \frac{165}{4} x^{8} f^{3} e^{7} d^{4} c^{2} + \frac{1}{5} x^{10} f^{3} e^{9} c b + 66 x^{7} f^{3} e^{6} d^{5} c^{2} + 2 x^{9} f^{3} e^{8} d c b + 77 x^{6} f^{3} e^{5} d^{6} c^{2} + 9 x^{8} f^{3} e^{7} d^{2} c b + 66 x^{5} f^{3} e^{4} d^{7} c^{2} + 24 x^{7} f^{3} e^{6} d^{3} c b + \frac{165}{4} x^{4} f^{3} e^{3} d^{8} c^{2} + 42 x^{6} f^{3} e^{5} d^{4} c b + \frac{1}{8} x^{8} f^{3} e^{7} b^{2} + \frac{1}{4} x^{8} f^{3} e^{7} c a + \frac{55}{3} x^{3} f^{3} e^{2} d^{9} c^{2} + \frac{252}{5} x^{5} f^{3} e^{4} d^{5} c b + x^{7} f^{3} e^{6} d b^{2} + 2 x^{7} f^{3} e^{6} d c a + \frac{11}{2} x^{2} f^{3} e d^{10} c^{2} + 42 x^{4} f^{3} e^{3} d^{6} c b + \frac{7}{2} x^{6} f^{3} e^{5} d^{2} b^{2} + 7 x^{6} f^{3} e^{5} d^{2} c a + x f^{3} d^{11} c^{2} + 24 x^{3} f^{3} e^{2} d^{7} c b + 7 x^{5} f^{3} e^{4} d^{3} b^{2} + 14 x^{5} f^{3} e^{4} d^{3} c a + 9 x^{2} f^{3} e d^{8} c b + \frac{35}{4} x^{4} f^{3} e^{3} d^{4} b^{2} + \frac{35}{2} x^{4} f^{3} e^{3} d^{4} c a + \frac{1}{3} x^{6} f^{3} e^{5} b a + 2 x f^{3} d^{9} c b + 7 x^{3} f^{3} e^{2} d^{5} b^{2} + 14 x^{3} f^{3} e^{2} d^{5} c a + 2 x^{5} f^{3} e^{4} d b a + \frac{7}{2} x^{2} f^{3} e d^{6} b^{2} + 7 x^{2} f^{3} e d^{6} c a + 5 x^{4} f^{3} e^{3} d^{2} b a + x f^{3} d^{7} b^{2} + 2 x f^{3} d^{7} c a + \frac{20}{3} x^{3} f^{3} e^{2} d^{3} b a + 5 x^{2} f^{3} e d^{4} b a + \frac{1}{4} x^{4} f^{3} e^{3} a^{2} + 2 x f^{3} d^{5} b a + x^{3} f^{3} e^{2} d a^{2} + \frac{3}{2} x^{2} f^{3} e d^{2} a^{2} + x f^{3} d^{3} a^{2}"," ",0,"1/12*x^12*f^3*e^11*c^2 + x^11*f^3*e^10*d*c^2 + 11/2*x^10*f^3*e^9*d^2*c^2 + 55/3*x^9*f^3*e^8*d^3*c^2 + 165/4*x^8*f^3*e^7*d^4*c^2 + 1/5*x^10*f^3*e^9*c*b + 66*x^7*f^3*e^6*d^5*c^2 + 2*x^9*f^3*e^8*d*c*b + 77*x^6*f^3*e^5*d^6*c^2 + 9*x^8*f^3*e^7*d^2*c*b + 66*x^5*f^3*e^4*d^7*c^2 + 24*x^7*f^3*e^6*d^3*c*b + 165/4*x^4*f^3*e^3*d^8*c^2 + 42*x^6*f^3*e^5*d^4*c*b + 1/8*x^8*f^3*e^7*b^2 + 1/4*x^8*f^3*e^7*c*a + 55/3*x^3*f^3*e^2*d^9*c^2 + 252/5*x^5*f^3*e^4*d^5*c*b + x^7*f^3*e^6*d*b^2 + 2*x^7*f^3*e^6*d*c*a + 11/2*x^2*f^3*e*d^10*c^2 + 42*x^4*f^3*e^3*d^6*c*b + 7/2*x^6*f^3*e^5*d^2*b^2 + 7*x^6*f^3*e^5*d^2*c*a + x*f^3*d^11*c^2 + 24*x^3*f^3*e^2*d^7*c*b + 7*x^5*f^3*e^4*d^3*b^2 + 14*x^5*f^3*e^4*d^3*c*a + 9*x^2*f^3*e*d^8*c*b + 35/4*x^4*f^3*e^3*d^4*b^2 + 35/2*x^4*f^3*e^3*d^4*c*a + 1/3*x^6*f^3*e^5*b*a + 2*x*f^3*d^9*c*b + 7*x^3*f^3*e^2*d^5*b^2 + 14*x^3*f^3*e^2*d^5*c*a + 2*x^5*f^3*e^4*d*b*a + 7/2*x^2*f^3*e*d^6*b^2 + 7*x^2*f^3*e*d^6*c*a + 5*x^4*f^3*e^3*d^2*b*a + x*f^3*d^7*b^2 + 2*x*f^3*d^7*c*a + 20/3*x^3*f^3*e^2*d^3*b*a + 5*x^2*f^3*e*d^4*b*a + 1/4*x^4*f^3*e^3*a^2 + 2*x*f^3*d^5*b*a + x^3*f^3*e^2*d*a^2 + 3/2*x^2*f^3*e*d^2*a^2 + x*f^3*d^3*a^2","B",0
612,1,1635,0,0.726514," ","integrate((e*f*x+d*f)^3*(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""fricas"")","\frac{1}{16} x^{16} f^{3} e^{15} c^{3} + x^{15} f^{3} e^{14} d c^{3} + \frac{15}{2} x^{14} f^{3} e^{13} d^{2} c^{3} + 35 x^{13} f^{3} e^{12} d^{3} c^{3} + \frac{455}{4} x^{12} f^{3} e^{11} d^{4} c^{3} + \frac{3}{14} x^{14} f^{3} e^{13} c^{2} b + 273 x^{11} f^{3} e^{10} d^{5} c^{3} + 3 x^{13} f^{3} e^{12} d c^{2} b + \frac{1001}{2} x^{10} f^{3} e^{9} d^{6} c^{3} + \frac{39}{2} x^{12} f^{3} e^{11} d^{2} c^{2} b + 715 x^{9} f^{3} e^{8} d^{7} c^{3} + 78 x^{11} f^{3} e^{10} d^{3} c^{2} b + \frac{6435}{8} x^{8} f^{3} e^{7} d^{8} c^{3} + \frac{429}{2} x^{10} f^{3} e^{9} d^{4} c^{2} b + \frac{1}{4} x^{12} f^{3} e^{11} c b^{2} + \frac{1}{4} x^{12} f^{3} e^{11} c^{2} a + 715 x^{7} f^{3} e^{6} d^{9} c^{3} + 429 x^{9} f^{3} e^{8} d^{5} c^{2} b + 3 x^{11} f^{3} e^{10} d c b^{2} + 3 x^{11} f^{3} e^{10} d c^{2} a + \frac{1001}{2} x^{6} f^{3} e^{5} d^{10} c^{3} + \frac{1287}{2} x^{8} f^{3} e^{7} d^{6} c^{2} b + \frac{33}{2} x^{10} f^{3} e^{9} d^{2} c b^{2} + \frac{33}{2} x^{10} f^{3} e^{9} d^{2} c^{2} a + 273 x^{5} f^{3} e^{4} d^{11} c^{3} + \frac{5148}{7} x^{7} f^{3} e^{6} d^{7} c^{2} b + 55 x^{9} f^{3} e^{8} d^{3} c b^{2} + 55 x^{9} f^{3} e^{8} d^{3} c^{2} a + \frac{455}{4} x^{4} f^{3} e^{3} d^{12} c^{3} + \frac{1287}{2} x^{6} f^{3} e^{5} d^{8} c^{2} b + \frac{495}{4} x^{8} f^{3} e^{7} d^{4} c b^{2} + \frac{1}{10} x^{10} f^{3} e^{9} b^{3} + \frac{495}{4} x^{8} f^{3} e^{7} d^{4} c^{2} a + \frac{3}{5} x^{10} f^{3} e^{9} c b a + 35 x^{3} f^{3} e^{2} d^{13} c^{3} + 429 x^{5} f^{3} e^{4} d^{9} c^{2} b + 198 x^{7} f^{3} e^{6} d^{5} c b^{2} + x^{9} f^{3} e^{8} d b^{3} + 198 x^{7} f^{3} e^{6} d^{5} c^{2} a + 6 x^{9} f^{3} e^{8} d c b a + \frac{15}{2} x^{2} f^{3} e d^{14} c^{3} + \frac{429}{2} x^{4} f^{3} e^{3} d^{10} c^{2} b + 231 x^{6} f^{3} e^{5} d^{6} c b^{2} + \frac{9}{2} x^{8} f^{3} e^{7} d^{2} b^{3} + 231 x^{6} f^{3} e^{5} d^{6} c^{2} a + 27 x^{8} f^{3} e^{7} d^{2} c b a + x f^{3} d^{15} c^{3} + 78 x^{3} f^{3} e^{2} d^{11} c^{2} b + 198 x^{5} f^{3} e^{4} d^{7} c b^{2} + 12 x^{7} f^{3} e^{6} d^{3} b^{3} + 198 x^{5} f^{3} e^{4} d^{7} c^{2} a + 72 x^{7} f^{3} e^{6} d^{3} c b a + \frac{39}{2} x^{2} f^{3} e d^{12} c^{2} b + \frac{495}{4} x^{4} f^{3} e^{3} d^{8} c b^{2} + 21 x^{6} f^{3} e^{5} d^{4} b^{3} + \frac{495}{4} x^{4} f^{3} e^{3} d^{8} c^{2} a + 126 x^{6} f^{3} e^{5} d^{4} c b a + \frac{3}{8} x^{8} f^{3} e^{7} b^{2} a + \frac{3}{8} x^{8} f^{3} e^{7} c a^{2} + 3 x f^{3} d^{13} c^{2} b + 55 x^{3} f^{3} e^{2} d^{9} c b^{2} + \frac{126}{5} x^{5} f^{3} e^{4} d^{5} b^{3} + 55 x^{3} f^{3} e^{2} d^{9} c^{2} a + \frac{756}{5} x^{5} f^{3} e^{4} d^{5} c b a + 3 x^{7} f^{3} e^{6} d b^{2} a + 3 x^{7} f^{3} e^{6} d c a^{2} + \frac{33}{2} x^{2} f^{3} e d^{10} c b^{2} + 21 x^{4} f^{3} e^{3} d^{6} b^{3} + \frac{33}{2} x^{2} f^{3} e d^{10} c^{2} a + 126 x^{4} f^{3} e^{3} d^{6} c b a + \frac{21}{2} x^{6} f^{3} e^{5} d^{2} b^{2} a + \frac{21}{2} x^{6} f^{3} e^{5} d^{2} c a^{2} + 3 x f^{3} d^{11} c b^{2} + 12 x^{3} f^{3} e^{2} d^{7} b^{3} + 3 x f^{3} d^{11} c^{2} a + 72 x^{3} f^{3} e^{2} d^{7} c b a + 21 x^{5} f^{3} e^{4} d^{3} b^{2} a + 21 x^{5} f^{3} e^{4} d^{3} c a^{2} + \frac{9}{2} x^{2} f^{3} e d^{8} b^{3} + 27 x^{2} f^{3} e d^{8} c b a + \frac{105}{4} x^{4} f^{3} e^{3} d^{4} b^{2} a + \frac{105}{4} x^{4} f^{3} e^{3} d^{4} c a^{2} + \frac{1}{2} x^{6} f^{3} e^{5} b a^{2} + x f^{3} d^{9} b^{3} + 6 x f^{3} d^{9} c b a + 21 x^{3} f^{3} e^{2} d^{5} b^{2} a + 21 x^{3} f^{3} e^{2} d^{5} c a^{2} + 3 x^{5} f^{3} e^{4} d b a^{2} + \frac{21}{2} x^{2} f^{3} e d^{6} b^{2} a + \frac{21}{2} x^{2} f^{3} e d^{6} c a^{2} + \frac{15}{2} x^{4} f^{3} e^{3} d^{2} b a^{2} + 3 x f^{3} d^{7} b^{2} a + 3 x f^{3} d^{7} c a^{2} + 10 x^{3} f^{3} e^{2} d^{3} b a^{2} + \frac{15}{2} x^{2} f^{3} e d^{4} b a^{2} + \frac{1}{4} x^{4} f^{3} e^{3} a^{3} + 3 x f^{3} d^{5} b a^{2} + x^{3} f^{3} e^{2} d a^{3} + \frac{3}{2} x^{2} f^{3} e d^{2} a^{3} + x f^{3} d^{3} a^{3}"," ",0,"1/16*x^16*f^3*e^15*c^3 + x^15*f^3*e^14*d*c^3 + 15/2*x^14*f^3*e^13*d^2*c^3 + 35*x^13*f^3*e^12*d^3*c^3 + 455/4*x^12*f^3*e^11*d^4*c^3 + 3/14*x^14*f^3*e^13*c^2*b + 273*x^11*f^3*e^10*d^5*c^3 + 3*x^13*f^3*e^12*d*c^2*b + 1001/2*x^10*f^3*e^9*d^6*c^3 + 39/2*x^12*f^3*e^11*d^2*c^2*b + 715*x^9*f^3*e^8*d^7*c^3 + 78*x^11*f^3*e^10*d^3*c^2*b + 6435/8*x^8*f^3*e^7*d^8*c^3 + 429/2*x^10*f^3*e^9*d^4*c^2*b + 1/4*x^12*f^3*e^11*c*b^2 + 1/4*x^12*f^3*e^11*c^2*a + 715*x^7*f^3*e^6*d^9*c^3 + 429*x^9*f^3*e^8*d^5*c^2*b + 3*x^11*f^3*e^10*d*c*b^2 + 3*x^11*f^3*e^10*d*c^2*a + 1001/2*x^6*f^3*e^5*d^10*c^3 + 1287/2*x^8*f^3*e^7*d^6*c^2*b + 33/2*x^10*f^3*e^9*d^2*c*b^2 + 33/2*x^10*f^3*e^9*d^2*c^2*a + 273*x^5*f^3*e^4*d^11*c^3 + 5148/7*x^7*f^3*e^6*d^7*c^2*b + 55*x^9*f^3*e^8*d^3*c*b^2 + 55*x^9*f^3*e^8*d^3*c^2*a + 455/4*x^4*f^3*e^3*d^12*c^3 + 1287/2*x^6*f^3*e^5*d^8*c^2*b + 495/4*x^8*f^3*e^7*d^4*c*b^2 + 1/10*x^10*f^3*e^9*b^3 + 495/4*x^8*f^3*e^7*d^4*c^2*a + 3/5*x^10*f^3*e^9*c*b*a + 35*x^3*f^3*e^2*d^13*c^3 + 429*x^5*f^3*e^4*d^9*c^2*b + 198*x^7*f^3*e^6*d^5*c*b^2 + x^9*f^3*e^8*d*b^3 + 198*x^7*f^3*e^6*d^5*c^2*a + 6*x^9*f^3*e^8*d*c*b*a + 15/2*x^2*f^3*e*d^14*c^3 + 429/2*x^4*f^3*e^3*d^10*c^2*b + 231*x^6*f^3*e^5*d^6*c*b^2 + 9/2*x^8*f^3*e^7*d^2*b^3 + 231*x^6*f^3*e^5*d^6*c^2*a + 27*x^8*f^3*e^7*d^2*c*b*a + x*f^3*d^15*c^3 + 78*x^3*f^3*e^2*d^11*c^2*b + 198*x^5*f^3*e^4*d^7*c*b^2 + 12*x^7*f^3*e^6*d^3*b^3 + 198*x^5*f^3*e^4*d^7*c^2*a + 72*x^7*f^3*e^6*d^3*c*b*a + 39/2*x^2*f^3*e*d^12*c^2*b + 495/4*x^4*f^3*e^3*d^8*c*b^2 + 21*x^6*f^3*e^5*d^4*b^3 + 495/4*x^4*f^3*e^3*d^8*c^2*a + 126*x^6*f^3*e^5*d^4*c*b*a + 3/8*x^8*f^3*e^7*b^2*a + 3/8*x^8*f^3*e^7*c*a^2 + 3*x*f^3*d^13*c^2*b + 55*x^3*f^3*e^2*d^9*c*b^2 + 126/5*x^5*f^3*e^4*d^5*b^3 + 55*x^3*f^3*e^2*d^9*c^2*a + 756/5*x^5*f^3*e^4*d^5*c*b*a + 3*x^7*f^3*e^6*d*b^2*a + 3*x^7*f^3*e^6*d*c*a^2 + 33/2*x^2*f^3*e*d^10*c*b^2 + 21*x^4*f^3*e^3*d^6*b^3 + 33/2*x^2*f^3*e*d^10*c^2*a + 126*x^4*f^3*e^3*d^6*c*b*a + 21/2*x^6*f^3*e^5*d^2*b^2*a + 21/2*x^6*f^3*e^5*d^2*c*a^2 + 3*x*f^3*d^11*c*b^2 + 12*x^3*f^3*e^2*d^7*b^3 + 3*x*f^3*d^11*c^2*a + 72*x^3*f^3*e^2*d^7*c*b*a + 21*x^5*f^3*e^4*d^3*b^2*a + 21*x^5*f^3*e^4*d^3*c*a^2 + 9/2*x^2*f^3*e*d^8*b^3 + 27*x^2*f^3*e*d^8*c*b*a + 105/4*x^4*f^3*e^3*d^4*b^2*a + 105/4*x^4*f^3*e^3*d^4*c*a^2 + 1/2*x^6*f^3*e^5*b*a^2 + x*f^3*d^9*b^3 + 6*x*f^3*d^9*c*b*a + 21*x^3*f^3*e^2*d^5*b^2*a + 21*x^3*f^3*e^2*d^5*c*a^2 + 3*x^5*f^3*e^4*d*b*a^2 + 21/2*x^2*f^3*e*d^6*b^2*a + 21/2*x^2*f^3*e*d^6*c*a^2 + 15/2*x^4*f^3*e^3*d^2*b*a^2 + 3*x*f^3*d^7*b^2*a + 3*x*f^3*d^7*c*a^2 + 10*x^3*f^3*e^2*d^3*b*a^2 + 15/2*x^2*f^3*e*d^4*b*a^2 + 1/4*x^4*f^3*e^3*a^3 + 3*x*f^3*d^5*b*a^2 + x^3*f^3*e^2*d*a^3 + 3/2*x^2*f^3*e*d^2*a^3 + x*f^3*d^3*a^3","B",0
613,1,1231,0,2.179187," ","integrate((e*x+d)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} c \sqrt{-\frac{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} + b^{3} - 3 \, a b c}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}} \log\left(-2 \, {\left(a b^{2} - a^{2} c\right)} e x - 2 \, {\left(a b^{2} - a^{2} c\right)} d + \sqrt{\frac{1}{2}} {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e^{3} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} + b^{3} - 3 \, a b c}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}}\right) - \sqrt{\frac{1}{2}} c \sqrt{-\frac{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} + b^{3} - 3 \, a b c}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}} \log\left(-2 \, {\left(a b^{2} - a^{2} c\right)} e x - 2 \, {\left(a b^{2} - a^{2} c\right)} d - \sqrt{\frac{1}{2}} {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e^{3} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} + b^{3} - 3 \, a b c}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}}\right) - \sqrt{\frac{1}{2}} c \sqrt{\frac{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} - b^{3} + 3 \, a b c}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}} \log\left(-2 \, {\left(a b^{2} - a^{2} c\right)} e x - 2 \, {\left(a b^{2} - a^{2} c\right)} d + \sqrt{\frac{1}{2}} {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e^{3} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e\right)} \sqrt{\frac{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} - b^{3} + 3 \, a b c}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}}\right) + \sqrt{\frac{1}{2}} c \sqrt{\frac{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} - b^{3} + 3 \, a b c}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}} \log\left(-2 \, {\left(a b^{2} - a^{2} c\right)} e x - 2 \, {\left(a b^{2} - a^{2} c\right)} d - \sqrt{\frac{1}{2}} {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e^{3} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e\right)} \sqrt{\frac{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} - b^{3} + 3 \, a b c}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}}\right) + 2 \, x}{2 \, c}"," ",0,"1/2*(sqrt(1/2)*c*sqrt(-((b^2*c^3 - 4*a*c^4)*e^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((b^2*c^6 - 4*a*c^7)*e^4)) + b^3 - 3*a*b*c)/((b^2*c^3 - 4*a*c^4)*e^2))*log(-2*(a*b^2 - a^2*c)*e*x - 2*(a*b^2 - a^2*c)*d + sqrt(1/2)*((b^3*c^3 - 4*a*b*c^4)*e^3*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((b^2*c^6 - 4*a*c^7)*e^4)) - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e)*sqrt(-((b^2*c^3 - 4*a*c^4)*e^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((b^2*c^6 - 4*a*c^7)*e^4)) + b^3 - 3*a*b*c)/((b^2*c^3 - 4*a*c^4)*e^2))) - sqrt(1/2)*c*sqrt(-((b^2*c^3 - 4*a*c^4)*e^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((b^2*c^6 - 4*a*c^7)*e^4)) + b^3 - 3*a*b*c)/((b^2*c^3 - 4*a*c^4)*e^2))*log(-2*(a*b^2 - a^2*c)*e*x - 2*(a*b^2 - a^2*c)*d - sqrt(1/2)*((b^3*c^3 - 4*a*b*c^4)*e^3*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((b^2*c^6 - 4*a*c^7)*e^4)) - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e)*sqrt(-((b^2*c^3 - 4*a*c^4)*e^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((b^2*c^6 - 4*a*c^7)*e^4)) + b^3 - 3*a*b*c)/((b^2*c^3 - 4*a*c^4)*e^2))) - sqrt(1/2)*c*sqrt(((b^2*c^3 - 4*a*c^4)*e^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((b^2*c^6 - 4*a*c^7)*e^4)) - b^3 + 3*a*b*c)/((b^2*c^3 - 4*a*c^4)*e^2))*log(-2*(a*b^2 - a^2*c)*e*x - 2*(a*b^2 - a^2*c)*d + sqrt(1/2)*((b^3*c^3 - 4*a*b*c^4)*e^3*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((b^2*c^6 - 4*a*c^7)*e^4)) + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e)*sqrt(((b^2*c^3 - 4*a*c^4)*e^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((b^2*c^6 - 4*a*c^7)*e^4)) - b^3 + 3*a*b*c)/((b^2*c^3 - 4*a*c^4)*e^2))) + sqrt(1/2)*c*sqrt(((b^2*c^3 - 4*a*c^4)*e^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((b^2*c^6 - 4*a*c^7)*e^4)) - b^3 + 3*a*b*c)/((b^2*c^3 - 4*a*c^4)*e^2))*log(-2*(a*b^2 - a^2*c)*e*x - 2*(a*b^2 - a^2*c)*d - sqrt(1/2)*((b^3*c^3 - 4*a*b*c^4)*e^3*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((b^2*c^6 - 4*a*c^7)*e^4)) + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e)*sqrt(((b^2*c^3 - 4*a*c^4)*e^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((b^2*c^6 - 4*a*c^7)*e^4)) - b^3 + 3*a*b*c)/((b^2*c^3 - 4*a*c^4)*e^2))) + 2*x)/c","B",0
614,1,434,0,1.008199," ","integrate((e*x+d)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} - 4 \, a c} b \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c + {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right) + {\left(b^{2} - 4 \, a c\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right)}{4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} e}, \frac{2 \, \sqrt{-b^{2} + 4 \, a c} b \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) + {\left(b^{2} - 4 \, a c\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right)}{4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} e}\right]"," ",0,"[1/4*(sqrt(b^2 - 4*a*c)*b*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c + (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)) + (b^2 - 4*a*c)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a))/((b^2*c - 4*a*c^2)*e), 1/4*(2*sqrt(-b^2 + 4*a*c)*b*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) + (b^2 - 4*a*c)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a))/((b^2*c - 4*a*c^2)*e)]","B",0
615,1,703,0,1.246957," ","integrate((e*x+d)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} \sqrt{\frac{1}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} + b}{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}}} \log\left(\sqrt{\frac{1}{2}} {\left(b^{2} c - 4 \, a c^{2}\right)} e^{3} \sqrt{-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} \sqrt{\frac{1}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} + b}{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}}} \sqrt{\frac{1}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} + e x + d\right) - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} \sqrt{\frac{1}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} + b}{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}}} \log\left(-\sqrt{\frac{1}{2}} {\left(b^{2} c - 4 \, a c^{2}\right)} e^{3} \sqrt{-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} \sqrt{\frac{1}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} + b}{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}}} \sqrt{\frac{1}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} + e x + d\right) - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} \sqrt{\frac{1}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} - b}{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}}} \log\left(\sqrt{\frac{1}{2}} {\left(b^{2} c - 4 \, a c^{2}\right)} e^{3} \sqrt{\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} \sqrt{\frac{1}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} - b}{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}}} \sqrt{\frac{1}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} + e x + d\right) + \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} \sqrt{\frac{1}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} - b}{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}}} \log\left(-\sqrt{\frac{1}{2}} {\left(b^{2} c - 4 \, a c^{2}\right)} e^{3} \sqrt{\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} \sqrt{\frac{1}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} - b}{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}}} \sqrt{\frac{1}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} + e x + d\right)"," ",0,"1/2*sqrt(1/2)*sqrt(-((b^2*c - 4*a*c^2)*e^2*sqrt(1/((b^2*c^2 - 4*a*c^3)*e^4)) + b)/((b^2*c - 4*a*c^2)*e^2))*log(sqrt(1/2)*(b^2*c - 4*a*c^2)*e^3*sqrt(-((b^2*c - 4*a*c^2)*e^2*sqrt(1/((b^2*c^2 - 4*a*c^3)*e^4)) + b)/((b^2*c - 4*a*c^2)*e^2))*sqrt(1/((b^2*c^2 - 4*a*c^3)*e^4)) + e*x + d) - 1/2*sqrt(1/2)*sqrt(-((b^2*c - 4*a*c^2)*e^2*sqrt(1/((b^2*c^2 - 4*a*c^3)*e^4)) + b)/((b^2*c - 4*a*c^2)*e^2))*log(-sqrt(1/2)*(b^2*c - 4*a*c^2)*e^3*sqrt(-((b^2*c - 4*a*c^2)*e^2*sqrt(1/((b^2*c^2 - 4*a*c^3)*e^4)) + b)/((b^2*c - 4*a*c^2)*e^2))*sqrt(1/((b^2*c^2 - 4*a*c^3)*e^4)) + e*x + d) - 1/2*sqrt(1/2)*sqrt(((b^2*c - 4*a*c^2)*e^2*sqrt(1/((b^2*c^2 - 4*a*c^3)*e^4)) - b)/((b^2*c - 4*a*c^2)*e^2))*log(sqrt(1/2)*(b^2*c - 4*a*c^2)*e^3*sqrt(((b^2*c - 4*a*c^2)*e^2*sqrt(1/((b^2*c^2 - 4*a*c^3)*e^4)) - b)/((b^2*c - 4*a*c^2)*e^2))*sqrt(1/((b^2*c^2 - 4*a*c^3)*e^4)) + e*x + d) + 1/2*sqrt(1/2)*sqrt(((b^2*c - 4*a*c^2)*e^2*sqrt(1/((b^2*c^2 - 4*a*c^3)*e^4)) - b)/((b^2*c - 4*a*c^2)*e^2))*log(-sqrt(1/2)*(b^2*c - 4*a*c^2)*e^3*sqrt(((b^2*c - 4*a*c^2)*e^2*sqrt(1/((b^2*c^2 - 4*a*c^3)*e^4)) - b)/((b^2*c - 4*a*c^2)*e^2))*sqrt(1/((b^2*c^2 - 4*a*c^3)*e^4)) + e*x + d)","B",0
616,1,272,0,1.302128," ","integrate((e*x+d)/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c - {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right)}{2 \, \sqrt{b^{2} - 4 \, a c} e}, -\frac{\sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right)}{{\left(b^{2} - 4 \, a c\right)} e}\right]"," ",0,"[1/2*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c - (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a))/(sqrt(b^2 - 4*a*c)*e), -sqrt(-b^2 + 4*a*c)*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c))/((b^2 - 4*a*c)*e)]","A",0
617,1,468,0,1.299088," ","integrate(1/(e*x+d)/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} - 4 \, a c} b \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c + {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right) - {\left(b^{2} - 4 \, a c\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 4 \, {\left(b^{2} - 4 \, a c\right)} \log\left(e x + d\right)}{4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} e}, \frac{2 \, \sqrt{-b^{2} + 4 \, a c} b \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left(b^{2} - 4 \, a c\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 4 \, {\left(b^{2} - 4 \, a c\right)} \log\left(e x + d\right)}{4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} e}\right]"," ",0,"[1/4*(sqrt(b^2 - 4*a*c)*b*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c + (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)) - (b^2 - 4*a*c)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 4*(b^2 - 4*a*c)*log(e*x + d))/((a*b^2 - 4*a^2*c)*e), 1/4*(2*sqrt(-b^2 + 4*a*c)*b*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - (b^2 - 4*a*c)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 4*(b^2 - 4*a*c)*log(e*x + d))/((a*b^2 - 4*a^2*c)*e)]","A",0
618,1,1339,0,1.361101," ","integrate(1/(e*x+d)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} {\left(a e^{2} x + a d e\right)} \sqrt{-\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2}}} \log\left(-2 \, {\left(b^{2} c^{2} - a c^{3}\right)} e x - 2 \, {\left(b^{2} c^{2} - a c^{3}\right)} d + \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} e^{3} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4}}} - {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e\right)} \sqrt{-\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2}}}\right) - \sqrt{\frac{1}{2}} {\left(a e^{2} x + a d e\right)} \sqrt{-\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2}}} \log\left(-2 \, {\left(b^{2} c^{2} - a c^{3}\right)} e x - 2 \, {\left(b^{2} c^{2} - a c^{3}\right)} d - \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} e^{3} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4}}} - {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e\right)} \sqrt{-\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2}}}\right) - \sqrt{\frac{1}{2}} {\left(a e^{2} x + a d e\right)} \sqrt{\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2}}} \log\left(-2 \, {\left(b^{2} c^{2} - a c^{3}\right)} e x - 2 \, {\left(b^{2} c^{2} - a c^{3}\right)} d + \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} e^{3} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4}}} + {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e\right)} \sqrt{\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2}}}\right) + \sqrt{\frac{1}{2}} {\left(a e^{2} x + a d e\right)} \sqrt{\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2}}} \log\left(-2 \, {\left(b^{2} c^{2} - a c^{3}\right)} e x - 2 \, {\left(b^{2} c^{2} - a c^{3}\right)} d - \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} e^{3} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4}}} + {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e\right)} \sqrt{\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2}}}\right) - 2}{2 \, {\left(a e^{2} x + a d e\right)}}"," ",0,"1/2*(sqrt(1/2)*(a*e^2*x + a*d*e)*sqrt(-((a^3*b^2 - 4*a^4*c)*e^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4)) + b^3 - 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*e^2))*log(-2*(b^2*c^2 - a*c^3)*e*x - 2*(b^2*c^2 - a*c^3)*d + sqrt(1/2)*((a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*e^3*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4)) - (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e)*sqrt(-((a^3*b^2 - 4*a^4*c)*e^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4)) + b^3 - 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*e^2))) - sqrt(1/2)*(a*e^2*x + a*d*e)*sqrt(-((a^3*b^2 - 4*a^4*c)*e^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4)) + b^3 - 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*e^2))*log(-2*(b^2*c^2 - a*c^3)*e*x - 2*(b^2*c^2 - a*c^3)*d - sqrt(1/2)*((a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*e^3*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4)) - (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e)*sqrt(-((a^3*b^2 - 4*a^4*c)*e^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4)) + b^3 - 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*e^2))) - sqrt(1/2)*(a*e^2*x + a*d*e)*sqrt(((a^3*b^2 - 4*a^4*c)*e^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4)) - b^3 + 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*e^2))*log(-2*(b^2*c^2 - a*c^3)*e*x - 2*(b^2*c^2 - a*c^3)*d + sqrt(1/2)*((a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*e^3*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4)) + (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e)*sqrt(((a^3*b^2 - 4*a^4*c)*e^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4)) - b^3 + 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*e^2))) + sqrt(1/2)*(a*e^2*x + a*d*e)*sqrt(((a^3*b^2 - 4*a^4*c)*e^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4)) - b^3 + 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*e^2))*log(-2*(b^2*c^2 - a*c^3)*e*x - 2*(b^2*c^2 - a*c^3)*d - sqrt(1/2)*((a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*e^3*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4)) + (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e)*sqrt(((a^3*b^2 - 4*a^4*c)*e^2*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4)) - b^3 + 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*e^2))) - 2)/(a*e^2*x + a*d*e)","B",0
619,1,810,0,1.095909," ","integrate(1/(e*x+d)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""fricas"")","\left[-\frac{2 \, a b^{2} - 8 \, a^{2} c + {\left({\left(b^{2} - 2 \, a c\right)} e^{2} x^{2} + 2 \, {\left(b^{2} - 2 \, a c\right)} d e x + {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c + {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right) - {\left({\left(b^{3} - 4 \, a b c\right)} e^{2} x^{2} + 2 \, {\left(b^{3} - 4 \, a b c\right)} d e x + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 4 \, {\left({\left(b^{3} - 4 \, a b c\right)} e^{2} x^{2} + 2 \, {\left(b^{3} - 4 \, a b c\right)} d e x + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} \log\left(e x + d\right)}{4 \, {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{3} x^{2} + 2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{2} x + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{2} e\right)}}, -\frac{2 \, a b^{2} - 8 \, a^{2} c + 2 \, {\left({\left(b^{2} - 2 \, a c\right)} e^{2} x^{2} + 2 \, {\left(b^{2} - 2 \, a c\right)} d e x + {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left({\left(b^{3} - 4 \, a b c\right)} e^{2} x^{2} + 2 \, {\left(b^{3} - 4 \, a b c\right)} d e x + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 4 \, {\left({\left(b^{3} - 4 \, a b c\right)} e^{2} x^{2} + 2 \, {\left(b^{3} - 4 \, a b c\right)} d e x + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} \log\left(e x + d\right)}{4 \, {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{3} x^{2} + 2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{2} x + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{2} e\right)}}\right]"," ",0,"[-1/4*(2*a*b^2 - 8*a^2*c + ((b^2 - 2*a*c)*e^2*x^2 + 2*(b^2 - 2*a*c)*d*e*x + (b^2 - 2*a*c)*d^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c + (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)) - ((b^3 - 4*a*b*c)*e^2*x^2 + 2*(b^3 - 4*a*b*c)*d*e*x + (b^3 - 4*a*b*c)*d^2)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 4*((b^3 - 4*a*b*c)*e^2*x^2 + 2*(b^3 - 4*a*b*c)*d*e*x + (b^3 - 4*a*b*c)*d^2)*log(e*x + d))/((a^2*b^2 - 4*a^3*c)*e^3*x^2 + 2*(a^2*b^2 - 4*a^3*c)*d*e^2*x + (a^2*b^2 - 4*a^3*c)*d^2*e), -1/4*(2*a*b^2 - 8*a^2*c + 2*((b^2 - 2*a*c)*e^2*x^2 + 2*(b^2 - 2*a*c)*d*e*x + (b^2 - 2*a*c)*d^2)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - ((b^3 - 4*a*b*c)*e^2*x^2 + 2*(b^3 - 4*a*b*c)*d*e*x + (b^3 - 4*a*b*c)*d^2)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 4*((b^3 - 4*a*b*c)*e^2*x^2 + 2*(b^3 - 4*a*b*c)*d*e*x + (b^3 - 4*a*b*c)*d^2)*log(e*x + d))/((a^2*b^2 - 4*a^3*c)*e^3*x^2 + 2*(a^2*b^2 - 4*a^3*c)*d*e^2*x + (a^2*b^2 - 4*a^3*c)*d^2*e)]","B",0
620,1,2044,0,1.224426," ","integrate(1/(e*x+d)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""fricas"")","\frac{6 \, b e^{2} x^{2} + 12 \, b d e x + 6 \, b d^{2} + 3 \, \sqrt{\frac{1}{2}} {\left(a^{2} e^{4} x^{3} + 3 \, a^{2} d e^{3} x^{2} + 3 \, a^{2} d^{2} e^{2} x + a^{2} d^{3} e\right)} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4}}}}{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2}}} \log\left(2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} e x + 2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} d + \sqrt{\frac{1}{2}} {\left({\left(a^{5} b^{5} - 7 \, a^{6} b^{3} c + 12 \, a^{7} b c^{2}\right)} e^{3} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4}}} - {\left(b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 17 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}\right)} e\right)} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4}}}}{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left(a^{2} e^{4} x^{3} + 3 \, a^{2} d e^{3} x^{2} + 3 \, a^{2} d^{2} e^{2} x + a^{2} d^{3} e\right)} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4}}}}{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2}}} \log\left(2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} e x + 2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} d - \sqrt{\frac{1}{2}} {\left({\left(a^{5} b^{5} - 7 \, a^{6} b^{3} c + 12 \, a^{7} b c^{2}\right)} e^{3} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4}}} - {\left(b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 17 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}\right)} e\right)} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4}}}}{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left(a^{2} e^{4} x^{3} + 3 \, a^{2} d e^{3} x^{2} + 3 \, a^{2} d^{2} e^{2} x + a^{2} d^{3} e\right)} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4}}}}{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2}}} \log\left(2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} e x + 2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} d + \sqrt{\frac{1}{2}} {\left({\left(a^{5} b^{5} - 7 \, a^{6} b^{3} c + 12 \, a^{7} b c^{2}\right)} e^{3} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4}}} + {\left(b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 17 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}\right)} e\right)} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4}}}}{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left(a^{2} e^{4} x^{3} + 3 \, a^{2} d e^{3} x^{2} + 3 \, a^{2} d^{2} e^{2} x + a^{2} d^{3} e\right)} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4}}}}{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2}}} \log\left(2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} e x + 2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} d - \sqrt{\frac{1}{2}} {\left({\left(a^{5} b^{5} - 7 \, a^{6} b^{3} c + 12 \, a^{7} b c^{2}\right)} e^{3} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4}}} + {\left(b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 17 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}\right)} e\right)} \sqrt{-\frac{b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2} - {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4}}}}{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2}}}\right) - 2 \, a}{6 \, {\left(a^{2} e^{4} x^{3} + 3 \, a^{2} d e^{3} x^{2} + 3 \, a^{2} d^{2} e^{2} x + a^{2} d^{3} e\right)}}"," ",0,"1/6*(6*b*e^2*x^2 + 12*b*d*e*x + 6*b*d^2 + 3*sqrt(1/2)*(a^2*e^4*x^3 + 3*a^2*d*e^3*x^2 + 3*a^2*d^2*e^2*x + a^2*d^3*e)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^2 - 4*a^6*c)*e^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)/((a^10*b^2 - 4*a^11*c)*e^4)))/((a^5*b^2 - 4*a^6*c)*e^2))*log(2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*e*x + 2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*d + sqrt(1/2)*((a^5*b^5 - 7*a^6*b^3*c + 12*a^7*b*c^2)*e^3*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)/((a^10*b^2 - 4*a^11*c)*e^4)) - (b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 17*a^3*b^2*c^3 + 4*a^4*c^4)*e)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^2 - 4*a^6*c)*e^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)/((a^10*b^2 - 4*a^11*c)*e^4)))/((a^5*b^2 - 4*a^6*c)*e^2))) - 3*sqrt(1/2)*(a^2*e^4*x^3 + 3*a^2*d*e^3*x^2 + 3*a^2*d^2*e^2*x + a^2*d^3*e)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^2 - 4*a^6*c)*e^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)/((a^10*b^2 - 4*a^11*c)*e^4)))/((a^5*b^2 - 4*a^6*c)*e^2))*log(2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*e*x + 2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*d - sqrt(1/2)*((a^5*b^5 - 7*a^6*b^3*c + 12*a^7*b*c^2)*e^3*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)/((a^10*b^2 - 4*a^11*c)*e^4)) - (b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 17*a^3*b^2*c^3 + 4*a^4*c^4)*e)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 + (a^5*b^2 - 4*a^6*c)*e^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)/((a^10*b^2 - 4*a^11*c)*e^4)))/((a^5*b^2 - 4*a^6*c)*e^2))) - 3*sqrt(1/2)*(a^2*e^4*x^3 + 3*a^2*d*e^3*x^2 + 3*a^2*d^2*e^2*x + a^2*d^3*e)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^2 - 4*a^6*c)*e^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)/((a^10*b^2 - 4*a^11*c)*e^4)))/((a^5*b^2 - 4*a^6*c)*e^2))*log(2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*e*x + 2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*d + sqrt(1/2)*((a^5*b^5 - 7*a^6*b^3*c + 12*a^7*b*c^2)*e^3*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)/((a^10*b^2 - 4*a^11*c)*e^4)) + (b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 17*a^3*b^2*c^3 + 4*a^4*c^4)*e)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^2 - 4*a^6*c)*e^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)/((a^10*b^2 - 4*a^11*c)*e^4)))/((a^5*b^2 - 4*a^6*c)*e^2))) + 3*sqrt(1/2)*(a^2*e^4*x^3 + 3*a^2*d*e^3*x^2 + 3*a^2*d^2*e^2*x + a^2*d^3*e)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^2 - 4*a^6*c)*e^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)/((a^10*b^2 - 4*a^11*c)*e^4)))/((a^5*b^2 - 4*a^6*c)*e^2))*log(2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*e*x + 2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*d - sqrt(1/2)*((a^5*b^5 - 7*a^6*b^3*c + 12*a^7*b*c^2)*e^3*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)/((a^10*b^2 - 4*a^11*c)*e^4)) + (b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 17*a^3*b^2*c^3 + 4*a^4*c^4)*e)*sqrt(-(b^5 - 5*a*b^3*c + 5*a^2*b*c^2 - (a^5*b^2 - 4*a^6*c)*e^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)/((a^10*b^2 - 4*a^11*c)*e^4)))/((a^5*b^2 - 4*a^6*c)*e^2))) - 2*a)/(a^2*e^4*x^3 + 3*a^2*d*e^3*x^2 + 3*a^2*d^2*e^2*x + a^2*d^3*e)","B",0
621,1,2454,0,1.110116," ","integrate((e*x+d)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""fricas"")","\frac{2 \, b e^{3} x^{3} + 6 \, b d e^{2} x^{2} + 2 \, b d^{3} + 2 \, {\left(3 \, b d^{2} + 2 \, a\right)} e x + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{4} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{4} x^{3} + {\left(b^{3} - 4 \, a b c + 6 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(b^{3} - 4 \, a b c\right)} d\right)} e^{2} x + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2} \sqrt{\frac{1}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} + b^{3} + 12 \, a b c}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}} \log\left({\left(3 \, b^{2} + 4 \, a c\right)} e x + {\left(3 \, b^{2} + 4 \, a c\right)} d + \sqrt{\frac{1}{2}} {\left(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)} e^{3} \sqrt{\frac{1}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} + {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2} \sqrt{\frac{1}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} + b^{3} + 12 \, a b c}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{4} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{4} x^{3} + {\left(b^{3} - 4 \, a b c + 6 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(b^{3} - 4 \, a b c\right)} d\right)} e^{2} x + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2} \sqrt{\frac{1}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} + b^{3} + 12 \, a b c}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}} \log\left({\left(3 \, b^{2} + 4 \, a c\right)} e x + {\left(3 \, b^{2} + 4 \, a c\right)} d - \sqrt{\frac{1}{2}} {\left(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)} e^{3} \sqrt{\frac{1}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} + {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2} \sqrt{\frac{1}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} + b^{3} + 12 \, a b c}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{4} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{4} x^{3} + {\left(b^{3} - 4 \, a b c + 6 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(b^{3} - 4 \, a b c\right)} d\right)} e^{2} x + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} e\right)} \sqrt{\frac{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2} \sqrt{\frac{1}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} - b^{3} - 12 \, a b c}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}} \log\left({\left(3 \, b^{2} + 4 \, a c\right)} e x + {\left(3 \, b^{2} + 4 \, a c\right)} d + \sqrt{\frac{1}{2}} {\left(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)} e^{3} \sqrt{\frac{1}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} - {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e\right)} \sqrt{\frac{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2} \sqrt{\frac{1}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} - b^{3} - 12 \, a b c}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{4} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{4} x^{3} + {\left(b^{3} - 4 \, a b c + 6 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(b^{3} - 4 \, a b c\right)} d\right)} e^{2} x + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} e\right)} \sqrt{\frac{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2} \sqrt{\frac{1}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} - b^{3} - 12 \, a b c}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}} \log\left({\left(3 \, b^{2} + 4 \, a c\right)} e x + {\left(3 \, b^{2} + 4 \, a c\right)} d - \sqrt{\frac{1}{2}} {\left(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)} e^{3} \sqrt{\frac{1}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} - {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e\right)} \sqrt{\frac{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2} \sqrt{\frac{1}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} - b^{3} - 12 \, a b c}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}}\right) + 4 \, a d}{4 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{4} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{4} x^{3} + {\left(b^{3} - 4 \, a b c + 6 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(b^{3} - 4 \, a b c\right)} d\right)} e^{2} x + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} e\right)}}"," ",0,"1/4*(2*b*e^3*x^3 + 6*b*d*e^2*x^2 + 2*b*d^3 + 2*(3*b*d^2 + 2*a)*e*x + sqrt(1/2)*((b^2*c - 4*a*c^2)*e^5*x^4 + 4*(b^2*c - 4*a*c^2)*d*e^4*x^3 + (b^3 - 4*a*b*c + 6*(b^2*c - 4*a*c^2)*d^2)*e^3*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^3 + (b^3 - 4*a*b*c)*d)*e^2*x + ((b^2*c - 4*a*c^2)*d^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*d^2)*e)*sqrt(-((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2*sqrt(1/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4)) + b^3 + 12*a*b*c)/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2))*log((3*b^2 + 4*a*c)*e*x + (3*b^2 + 4*a*c)*d + sqrt(1/2)*(2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*e^3*sqrt(1/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4)) + (b^4 - 8*a*b^2*c + 16*a^2*c^2)*e)*sqrt(-((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2*sqrt(1/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4)) + b^3 + 12*a*b*c)/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2))) - sqrt(1/2)*((b^2*c - 4*a*c^2)*e^5*x^4 + 4*(b^2*c - 4*a*c^2)*d*e^4*x^3 + (b^3 - 4*a*b*c + 6*(b^2*c - 4*a*c^2)*d^2)*e^3*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^3 + (b^3 - 4*a*b*c)*d)*e^2*x + ((b^2*c - 4*a*c^2)*d^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*d^2)*e)*sqrt(-((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2*sqrt(1/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4)) + b^3 + 12*a*b*c)/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2))*log((3*b^2 + 4*a*c)*e*x + (3*b^2 + 4*a*c)*d - sqrt(1/2)*(2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*e^3*sqrt(1/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4)) + (b^4 - 8*a*b^2*c + 16*a^2*c^2)*e)*sqrt(-((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2*sqrt(1/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4)) + b^3 + 12*a*b*c)/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2))) - sqrt(1/2)*((b^2*c - 4*a*c^2)*e^5*x^4 + 4*(b^2*c - 4*a*c^2)*d*e^4*x^3 + (b^3 - 4*a*b*c + 6*(b^2*c - 4*a*c^2)*d^2)*e^3*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^3 + (b^3 - 4*a*b*c)*d)*e^2*x + ((b^2*c - 4*a*c^2)*d^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*d^2)*e)*sqrt(((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2*sqrt(1/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4)) - b^3 - 12*a*b*c)/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2))*log((3*b^2 + 4*a*c)*e*x + (3*b^2 + 4*a*c)*d + sqrt(1/2)*(2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*e^3*sqrt(1/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4)) - (b^4 - 8*a*b^2*c + 16*a^2*c^2)*e)*sqrt(((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2*sqrt(1/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4)) - b^3 - 12*a*b*c)/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2))) + sqrt(1/2)*((b^2*c - 4*a*c^2)*e^5*x^4 + 4*(b^2*c - 4*a*c^2)*d*e^4*x^3 + (b^3 - 4*a*b*c + 6*(b^2*c - 4*a*c^2)*d^2)*e^3*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^3 + (b^3 - 4*a*b*c)*d)*e^2*x + ((b^2*c - 4*a*c^2)*d^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*d^2)*e)*sqrt(((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2*sqrt(1/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4)) - b^3 - 12*a*b*c)/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2))*log((3*b^2 + 4*a*c)*e*x + (3*b^2 + 4*a*c)*d - sqrt(1/2)*(2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*e^3*sqrt(1/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4)) - (b^4 - 8*a*b^2*c + 16*a^2*c^2)*e)*sqrt(((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2*sqrt(1/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4)) - b^3 - 12*a*b*c)/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2))) + 4*a*d)/((b^2*c - 4*a*c^2)*e^5*x^4 + 4*(b^2*c - 4*a*c^2)*d*e^4*x^3 + (b^3 - 4*a*b*c + 6*(b^2*c - 4*a*c^2)*d^2)*e^3*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^3 + (b^3 - 4*a*b*c)*d)*e^2*x + ((b^2*c - 4*a*c^2)*d^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*d^2)*e)","B",0
622,1,1021,0,1.026052," ","integrate((e*x+d)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""fricas"")","\left[\frac{{\left(b^{3} - 4 \, a b c\right)} e^{2} x^{2} + 2 \, {\left(b^{3} - 4 \, a b c\right)} d e x + 2 \, a b^{2} - 8 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2} - {\left(b c e^{4} x^{4} + 4 \, b c d e^{3} x^{3} + b c d^{4} + {\left(6 \, b c d^{2} + b^{2}\right)} e^{2} x^{2} + b^{2} d^{2} + 2 \, {\left(2 \, b c d^{3} + b^{2} d\right)} e x + a b\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c + {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right)}{2 \, {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{5} x^{4} + 4 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} x^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + 6 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d\right)} e^{2} x + {\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)} d^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2}\right)} e\right)}}, \frac{{\left(b^{3} - 4 \, a b c\right)} e^{2} x^{2} + 2 \, {\left(b^{3} - 4 \, a b c\right)} d e x + 2 \, a b^{2} - 8 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2} - 2 \, {\left(b c e^{4} x^{4} + 4 \, b c d e^{3} x^{3} + b c d^{4} + {\left(6 \, b c d^{2} + b^{2}\right)} e^{2} x^{2} + b^{2} d^{2} + 2 \, {\left(2 \, b c d^{3} + b^{2} d\right)} e x + a b\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right)}{2 \, {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{5} x^{4} + 4 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} x^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + 6 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d\right)} e^{2} x + {\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)} d^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2}\right)} e\right)}}\right]"," ",0,"[1/2*((b^3 - 4*a*b*c)*e^2*x^2 + 2*(b^3 - 4*a*b*c)*d*e*x + 2*a*b^2 - 8*a^2*c + (b^3 - 4*a*b*c)*d^2 - (b*c*e^4*x^4 + 4*b*c*d*e^3*x^3 + b*c*d^4 + (6*b*c*d^2 + b^2)*e^2*x^2 + b^2*d^2 + 2*(2*b*c*d^3 + b^2*d)*e*x + a*b)*sqrt(b^2 - 4*a*c)*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c + (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)))/((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^5*x^4 + 4*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^4*x^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + 6*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2)*e^3*x^2 + 2*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d)*e^2*x + (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)*d^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2)*e), 1/2*((b^3 - 4*a*b*c)*e^2*x^2 + 2*(b^3 - 4*a*b*c)*d*e*x + 2*a*b^2 - 8*a^2*c + (b^3 - 4*a*b*c)*d^2 - 2*(b*c*e^4*x^4 + 4*b*c*d*e^3*x^3 + b*c*d^4 + (6*b*c*d^2 + b^2)*e^2*x^2 + b^2*d^2 + 2*(2*b*c*d^3 + b^2*d)*e*x + a*b)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)))/((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^5*x^4 + 4*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^4*x^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + 6*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2)*e^3*x^2 + 2*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d)*e^2*x + (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)*d^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2)*e)]","B",0
623,1,2474,0,1.323812," ","integrate((e*x+d)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""fricas"")","-\frac{4 \, c e^{3} x^{3} + 12 \, c d e^{2} x^{2} + 4 \, c d^{3} + 2 \, {\left(6 \, c d^{2} + b\right)} e x - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{4} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{4} x^{3} + {\left(b^{3} - 4 \, a b c + 6 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(b^{3} - 4 \, a b c\right)} d\right)} e^{2} x + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} e\right)} \sqrt{-\frac{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2} \sqrt{\frac{1}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} + b^{3} + 12 \, a b c}{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} \log\left({\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e x + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(a b^{8} - 8 \, a^{2} b^{6} c + 128 \, a^{4} b^{2} c^{3} - 256 \, a^{5} c^{4}\right)} e^{3} \sqrt{\frac{1}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e\right)} \sqrt{-\frac{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2} \sqrt{\frac{1}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} + b^{3} + 12 \, a b c}{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{4} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{4} x^{3} + {\left(b^{3} - 4 \, a b c + 6 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(b^{3} - 4 \, a b c\right)} d\right)} e^{2} x + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} e\right)} \sqrt{-\frac{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2} \sqrt{\frac{1}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} + b^{3} + 12 \, a b c}{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} \log\left({\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e x + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(a b^{8} - 8 \, a^{2} b^{6} c + 128 \, a^{4} b^{2} c^{3} - 256 \, a^{5} c^{4}\right)} e^{3} \sqrt{\frac{1}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e\right)} \sqrt{-\frac{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2} \sqrt{\frac{1}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} + b^{3} + 12 \, a b c}{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{4} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{4} x^{3} + {\left(b^{3} - 4 \, a b c + 6 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(b^{3} - 4 \, a b c\right)} d\right)} e^{2} x + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} e\right)} \sqrt{\frac{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2} \sqrt{\frac{1}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} - b^{3} - 12 \, a b c}{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} \log\left({\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e x + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(a b^{8} - 8 \, a^{2} b^{6} c + 128 \, a^{4} b^{2} c^{3} - 256 \, a^{5} c^{4}\right)} e^{3} \sqrt{\frac{1}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e\right)} \sqrt{\frac{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2} \sqrt{\frac{1}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} - b^{3} - 12 \, a b c}{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{4} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{4} x^{3} + {\left(b^{3} - 4 \, a b c + 6 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(b^{3} - 4 \, a b c\right)} d\right)} e^{2} x + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} e\right)} \sqrt{\frac{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2} \sqrt{\frac{1}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} - b^{3} - 12 \, a b c}{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} \log\left({\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e x + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(a b^{8} - 8 \, a^{2} b^{6} c + 128 \, a^{4} b^{2} c^{3} - 256 \, a^{5} c^{4}\right)} e^{3} \sqrt{\frac{1}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e\right)} \sqrt{\frac{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2} \sqrt{\frac{1}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} - b^{3} - 12 \, a b c}{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}}\right) + 2 \, b d}{4 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{4} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{4} x^{3} + {\left(b^{3} - 4 \, a b c + 6 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(b^{3} - 4 \, a b c\right)} d\right)} e^{2} x + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} e\right)}}"," ",0,"-1/4*(4*c*e^3*x^3 + 12*c*d*e^2*x^2 + 4*c*d^3 + 2*(6*c*d^2 + b)*e*x - sqrt(1/2)*((b^2*c - 4*a*c^2)*e^5*x^4 + 4*(b^2*c - 4*a*c^2)*d*e^4*x^3 + (b^3 - 4*a*b*c + 6*(b^2*c - 4*a*c^2)*d^2)*e^3*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^3 + (b^3 - 4*a*b*c)*d)*e^2*x + ((b^2*c - 4*a*c^2)*d^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*d^2)*e)*sqrt(-((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2*sqrt(1/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4)) + b^3 + 12*a*b*c)/((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))*log((3*b^2*c + 4*a*c^2)*e*x + (3*b^2*c + 4*a*c^2)*d + 1/2*sqrt(1/2)*((a*b^8 - 8*a^2*b^6*c + 128*a^4*b^2*c^3 - 256*a^5*c^4)*e^3*sqrt(1/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4)) - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e)*sqrt(-((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2*sqrt(1/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4)) + b^3 + 12*a*b*c)/((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))) + sqrt(1/2)*((b^2*c - 4*a*c^2)*e^5*x^4 + 4*(b^2*c - 4*a*c^2)*d*e^4*x^3 + (b^3 - 4*a*b*c + 6*(b^2*c - 4*a*c^2)*d^2)*e^3*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^3 + (b^3 - 4*a*b*c)*d)*e^2*x + ((b^2*c - 4*a*c^2)*d^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*d^2)*e)*sqrt(-((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2*sqrt(1/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4)) + b^3 + 12*a*b*c)/((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))*log((3*b^2*c + 4*a*c^2)*e*x + (3*b^2*c + 4*a*c^2)*d - 1/2*sqrt(1/2)*((a*b^8 - 8*a^2*b^6*c + 128*a^4*b^2*c^3 - 256*a^5*c^4)*e^3*sqrt(1/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4)) - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e)*sqrt(-((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2*sqrt(1/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4)) + b^3 + 12*a*b*c)/((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))) + sqrt(1/2)*((b^2*c - 4*a*c^2)*e^5*x^4 + 4*(b^2*c - 4*a*c^2)*d*e^4*x^3 + (b^3 - 4*a*b*c + 6*(b^2*c - 4*a*c^2)*d^2)*e^3*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^3 + (b^3 - 4*a*b*c)*d)*e^2*x + ((b^2*c - 4*a*c^2)*d^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*d^2)*e)*sqrt(((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2*sqrt(1/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4)) - b^3 - 12*a*b*c)/((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))*log((3*b^2*c + 4*a*c^2)*e*x + (3*b^2*c + 4*a*c^2)*d + 1/2*sqrt(1/2)*((a*b^8 - 8*a^2*b^6*c + 128*a^4*b^2*c^3 - 256*a^5*c^4)*e^3*sqrt(1/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4)) + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e)*sqrt(((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2*sqrt(1/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4)) - b^3 - 12*a*b*c)/((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))) - sqrt(1/2)*((b^2*c - 4*a*c^2)*e^5*x^4 + 4*(b^2*c - 4*a*c^2)*d*e^4*x^3 + (b^3 - 4*a*b*c + 6*(b^2*c - 4*a*c^2)*d^2)*e^3*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^3 + (b^3 - 4*a*b*c)*d)*e^2*x + ((b^2*c - 4*a*c^2)*d^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*d^2)*e)*sqrt(((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2*sqrt(1/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4)) - b^3 - 12*a*b*c)/((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))*log((3*b^2*c + 4*a*c^2)*e*x + (3*b^2*c + 4*a*c^2)*d - 1/2*sqrt(1/2)*((a*b^8 - 8*a^2*b^6*c + 128*a^4*b^2*c^3 - 256*a^5*c^4)*e^3*sqrt(1/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4)) + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e)*sqrt(((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2*sqrt(1/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4)) - b^3 - 12*a*b*c)/((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))) + 2*b*d)/((b^2*c - 4*a*c^2)*e^5*x^4 + 4*(b^2*c - 4*a*c^2)*d*e^4*x^3 + (b^3 - 4*a*b*c + 6*(b^2*c - 4*a*c^2)*d^2)*e^3*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^3 + (b^3 - 4*a*b*c)*d)*e^2*x + ((b^2*c - 4*a*c^2)*d^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*d^2)*e)","B",0
624,1,1042,0,0.871660," ","integrate((e*x+d)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} x^{2} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e x + b^{3} - 4 \, a b c + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} + 2 \, {\left(c^{2} e^{4} x^{4} + 4 \, c^{2} d e^{3} x^{3} + c^{2} d^{4} + {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + b c d^{2} + 2 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + a c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c - {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right)}{2 \, {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{5} x^{4} + 4 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} x^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + 6 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d\right)} e^{2} x + {\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)} d^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2}\right)} e\right)}}, -\frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} x^{2} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e x + b^{3} - 4 \, a b c + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - 4 \, {\left(c^{2} e^{4} x^{4} + 4 \, c^{2} d e^{3} x^{3} + c^{2} d^{4} + {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + b c d^{2} + 2 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + a c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right)}{2 \, {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{5} x^{4} + 4 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} x^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + 6 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d\right)} e^{2} x + {\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)} d^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2}\right)} e\right)}}\right]"," ",0,"[-1/2*(2*(b^2*c - 4*a*c^2)*e^2*x^2 + 4*(b^2*c - 4*a*c^2)*d*e*x + b^3 - 4*a*b*c + 2*(b^2*c - 4*a*c^2)*d^2 + 2*(c^2*e^4*x^4 + 4*c^2*d*e^3*x^3 + c^2*d^4 + (6*c^2*d^2 + b*c)*e^2*x^2 + b*c*d^2 + 2*(2*c^2*d^3 + b*c*d)*e*x + a*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c - (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)))/((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^5*x^4 + 4*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^4*x^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + 6*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2)*e^3*x^2 + 2*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d)*e^2*x + (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)*d^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2)*e), -1/2*(2*(b^2*c - 4*a*c^2)*e^2*x^2 + 4*(b^2*c - 4*a*c^2)*d*e*x + b^3 - 4*a*b*c + 2*(b^2*c - 4*a*c^2)*d^2 - 4*(c^2*e^4*x^4 + 4*c^2*d*e^3*x^3 + c^2*d^4 + (6*c^2*d^2 + b*c)*e^2*x^2 + b*c*d^2 + 2*(2*c^2*d^3 + b*c*d)*e*x + a*c)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)))/((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^5*x^4 + 4*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^4*x^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + 6*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2)*e^3*x^2 + 2*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d)*e^2*x + (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)*d^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2)*e)]","B",0
625,1,3228,0,1.726256," ","integrate(1/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""fricas"")","\frac{2 \, b c e^{3} x^{3} + 6 \, b c d e^{2} x^{2} + 2 \, b c d^{3} + 2 \, {\left(3 \, b c d^{2} + b^{2} - 2 \, a c\right)} e x - \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} e^{5} x^{4} + 4 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{4} x^{3} + {\left(a b^{3} - 4 \, a^{2} b c + 6 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{3} + {\left(a b^{3} - 4 \, a^{2} b c\right)} d\right)} e^{2} x + {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{2}\right)} e\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} e^{2} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} e^{4}}}}{{\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} e^{2}}} \log\left({\left(5 \, b^{4} c^{2} - 81 \, a b^{2} c^{3} + 324 \, a^{2} c^{4}\right)} e x + {\left(5 \, b^{4} c^{2} - 81 \, a b^{2} c^{3} + 324 \, a^{2} c^{4}\right)} d + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{9} - 20 \, a^{4} b^{7} c + 144 \, a^{5} b^{5} c^{2} - 448 \, a^{6} b^{3} c^{3} + 512 \, a^{7} b c^{4}\right)} e^{3} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} e^{4}}} - {\left(b^{8} - 23 \, a b^{6} c + 190 \, a^{2} b^{4} c^{2} - 672 \, a^{3} b^{2} c^{3} + 864 \, a^{4} c^{4}\right)} e\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} e^{2} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} e^{4}}}}{{\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} e^{2}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} e^{5} x^{4} + 4 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{4} x^{3} + {\left(a b^{3} - 4 \, a^{2} b c + 6 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{3} + {\left(a b^{3} - 4 \, a^{2} b c\right)} d\right)} e^{2} x + {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{2}\right)} e\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} e^{2} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} e^{4}}}}{{\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} e^{2}}} \log\left({\left(5 \, b^{4} c^{2} - 81 \, a b^{2} c^{3} + 324 \, a^{2} c^{4}\right)} e x + {\left(5 \, b^{4} c^{2} - 81 \, a b^{2} c^{3} + 324 \, a^{2} c^{4}\right)} d - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{9} - 20 \, a^{4} b^{7} c + 144 \, a^{5} b^{5} c^{2} - 448 \, a^{6} b^{3} c^{3} + 512 \, a^{7} b c^{4}\right)} e^{3} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} e^{4}}} - {\left(b^{8} - 23 \, a b^{6} c + 190 \, a^{2} b^{4} c^{2} - 672 \, a^{3} b^{2} c^{3} + 864 \, a^{4} c^{4}\right)} e\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} e^{2} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} e^{4}}}}{{\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} e^{2}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} e^{5} x^{4} + 4 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{4} x^{3} + {\left(a b^{3} - 4 \, a^{2} b c + 6 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{3} + {\left(a b^{3} - 4 \, a^{2} b c\right)} d\right)} e^{2} x + {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{2}\right)} e\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} e^{2} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} e^{4}}}}{{\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} e^{2}}} \log\left({\left(5 \, b^{4} c^{2} - 81 \, a b^{2} c^{3} + 324 \, a^{2} c^{4}\right)} e x + {\left(5 \, b^{4} c^{2} - 81 \, a b^{2} c^{3} + 324 \, a^{2} c^{4}\right)} d + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{9} - 20 \, a^{4} b^{7} c + 144 \, a^{5} b^{5} c^{2} - 448 \, a^{6} b^{3} c^{3} + 512 \, a^{7} b c^{4}\right)} e^{3} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} e^{4}}} + {\left(b^{8} - 23 \, a b^{6} c + 190 \, a^{2} b^{4} c^{2} - 672 \, a^{3} b^{2} c^{3} + 864 \, a^{4} c^{4}\right)} e\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} e^{2} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} e^{4}}}}{{\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} e^{2}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} e^{5} x^{4} + 4 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{4} x^{3} + {\left(a b^{3} - 4 \, a^{2} b c + 6 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{3} + {\left(a b^{3} - 4 \, a^{2} b c\right)} d\right)} e^{2} x + {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{2}\right)} e\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} e^{2} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} e^{4}}}}{{\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} e^{2}}} \log\left({\left(5 \, b^{4} c^{2} - 81 \, a b^{2} c^{3} + 324 \, a^{2} c^{4}\right)} e x + {\left(5 \, b^{4} c^{2} - 81 \, a b^{2} c^{3} + 324 \, a^{2} c^{4}\right)} d - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{9} - 20 \, a^{4} b^{7} c + 144 \, a^{5} b^{5} c^{2} - 448 \, a^{6} b^{3} c^{3} + 512 \, a^{7} b c^{4}\right)} e^{3} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} e^{4}}} + {\left(b^{8} - 23 \, a b^{6} c + 190 \, a^{2} b^{4} c^{2} - 672 \, a^{3} b^{2} c^{3} + 864 \, a^{4} c^{4}\right)} e\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} e^{2} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{{\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} e^{4}}}}{{\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} e^{2}}}\right) + 2 \, {\left(b^{2} - 2 \, a c\right)} d}{4 \, {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} e^{5} x^{4} + 4 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{4} x^{3} + {\left(a b^{3} - 4 \, a^{2} b c + 6 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{3} + {\left(a b^{3} - 4 \, a^{2} b c\right)} d\right)} e^{2} x + {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{2}\right)} e\right)}}"," ",0,"1/4*(2*b*c*e^3*x^3 + 6*b*c*d*e^2*x^2 + 2*b*c*d^3 + 2*(3*b*c*d^2 + b^2 - 2*a*c)*e*x - sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*e^5*x^4 + 4*(a*b^2*c - 4*a^2*c^2)*d*e^4*x^3 + (a*b^3 - 4*a^2*b*c + 6*(a*b^2*c - 4*a^2*c^2)*d^2)*e^3*x^2 + 2*(2*(a*b^2*c - 4*a^2*c^2)*d^3 + (a*b^3 - 4*a^2*b*c)*d)*e^2*x + ((a*b^2*c - 4*a^2*c^2)*d^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*d^2)*e)*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*e^2*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*e^4)))/((a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*e^2))*log((5*b^4*c^2 - 81*a*b^2*c^3 + 324*a^2*c^4)*e*x + (5*b^4*c^2 - 81*a*b^2*c^3 + 324*a^2*c^4)*d + 1/2*sqrt(1/2)*((a^3*b^9 - 20*a^4*b^7*c + 144*a^5*b^5*c^2 - 448*a^6*b^3*c^3 + 512*a^7*b*c^4)*e^3*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*e^4)) - (b^8 - 23*a*b^6*c + 190*a^2*b^4*c^2 - 672*a^3*b^2*c^3 + 864*a^4*c^4)*e)*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*e^2*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*e^4)))/((a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*e^2))) + sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*e^5*x^4 + 4*(a*b^2*c - 4*a^2*c^2)*d*e^4*x^3 + (a*b^3 - 4*a^2*b*c + 6*(a*b^2*c - 4*a^2*c^2)*d^2)*e^3*x^2 + 2*(2*(a*b^2*c - 4*a^2*c^2)*d^3 + (a*b^3 - 4*a^2*b*c)*d)*e^2*x + ((a*b^2*c - 4*a^2*c^2)*d^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*d^2)*e)*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*e^2*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*e^4)))/((a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*e^2))*log((5*b^4*c^2 - 81*a*b^2*c^3 + 324*a^2*c^4)*e*x + (5*b^4*c^2 - 81*a*b^2*c^3 + 324*a^2*c^4)*d - 1/2*sqrt(1/2)*((a^3*b^9 - 20*a^4*b^7*c + 144*a^5*b^5*c^2 - 448*a^6*b^3*c^3 + 512*a^7*b*c^4)*e^3*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*e^4)) - (b^8 - 23*a*b^6*c + 190*a^2*b^4*c^2 - 672*a^3*b^2*c^3 + 864*a^4*c^4)*e)*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*e^2*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*e^4)))/((a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*e^2))) + sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*e^5*x^4 + 4*(a*b^2*c - 4*a^2*c^2)*d*e^4*x^3 + (a*b^3 - 4*a^2*b*c + 6*(a*b^2*c - 4*a^2*c^2)*d^2)*e^3*x^2 + 2*(2*(a*b^2*c - 4*a^2*c^2)*d^3 + (a*b^3 - 4*a^2*b*c)*d)*e^2*x + ((a*b^2*c - 4*a^2*c^2)*d^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*d^2)*e)*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*e^2*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*e^4)))/((a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*e^2))*log((5*b^4*c^2 - 81*a*b^2*c^3 + 324*a^2*c^4)*e*x + (5*b^4*c^2 - 81*a*b^2*c^3 + 324*a^2*c^4)*d + 1/2*sqrt(1/2)*((a^3*b^9 - 20*a^4*b^7*c + 144*a^5*b^5*c^2 - 448*a^6*b^3*c^3 + 512*a^7*b*c^4)*e^3*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*e^4)) + (b^8 - 23*a*b^6*c + 190*a^2*b^4*c^2 - 672*a^3*b^2*c^3 + 864*a^4*c^4)*e)*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*e^2*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*e^4)))/((a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*e^2))) - sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*e^5*x^4 + 4*(a*b^2*c - 4*a^2*c^2)*d*e^4*x^3 + (a*b^3 - 4*a^2*b*c + 6*(a*b^2*c - 4*a^2*c^2)*d^2)*e^3*x^2 + 2*(2*(a*b^2*c - 4*a^2*c^2)*d^3 + (a*b^3 - 4*a^2*b*c)*d)*e^2*x + ((a*b^2*c - 4*a^2*c^2)*d^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*d^2)*e)*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*e^2*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*e^4)))/((a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*e^2))*log((5*b^4*c^2 - 81*a*b^2*c^3 + 324*a^2*c^4)*e*x + (5*b^4*c^2 - 81*a*b^2*c^3 + 324*a^2*c^4)*d - 1/2*sqrt(1/2)*((a^3*b^9 - 20*a^4*b^7*c + 144*a^5*b^5*c^2 - 448*a^6*b^3*c^3 + 512*a^7*b*c^4)*e^3*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*e^4)) + (b^8 - 23*a*b^6*c + 190*a^2*b^4*c^2 - 672*a^3*b^2*c^3 + 864*a^4*c^4)*e)*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*e^2*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/((a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*e^4)))/((a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*e^2))) + 2*(b^2 - 2*a*c)*d)/((a*b^2*c - 4*a^2*c^2)*e^5*x^4 + 4*(a*b^2*c - 4*a^2*c^2)*d*e^4*x^3 + (a*b^3 - 4*a^2*b*c + 6*(a*b^2*c - 4*a^2*c^2)*d^2)*e^3*x^2 + 2*(2*(a*b^2*c - 4*a^2*c^2)*d^3 + (a*b^3 - 4*a^2*b*c)*d)*e^2*x + ((a*b^2*c - 4*a^2*c^2)*d^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*d^2)*e)","B",0
626,1,2476,0,1.789010," ","integrate(1/(e*x+d)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a b^{4} - 12 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} e^{2} x^{2} + 4 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e x + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{2} + {\left({\left(b^{3} c - 6 \, a b c^{2}\right)} e^{4} x^{4} + 4 \, {\left(b^{3} c - 6 \, a b c^{2}\right)} d e^{3} x^{3} + {\left(b^{3} c - 6 \, a b c^{2}\right)} d^{4} + {\left(b^{4} - 6 \, a b^{2} c + 6 \, {\left(b^{3} c - 6 \, a b c^{2}\right)} d^{2}\right)} e^{2} x^{2} + a b^{3} - 6 \, a^{2} b c + {\left(b^{4} - 6 \, a b^{2} c\right)} d^{2} + 2 \, {\left(2 \, {\left(b^{3} c - 6 \, a b c^{2}\right)} d^{3} + {\left(b^{4} - 6 \, a b^{2} c\right)} d\right)} e x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c + {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right) - {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{4} x^{4} + 4 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{3} x^{3} + 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)} d^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + 6 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2} + 2 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d\right)} e x\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 4 \, {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{4} x^{4} + 4 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{3} x^{3} + 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)} d^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + 6 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2} + 2 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d\right)} e x\right)} \log\left(e x + d\right)}{4 \, {\left({\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} e^{5} x^{4} + 4 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d e^{4} x^{3} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2} + 6 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d^{3} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d\right)} e^{2} x + {\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)} d^{4} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d^{2}\right)} e\right)}}, \frac{2 \, a b^{4} - 12 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} e^{2} x^{2} + 4 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e x + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{2} + 2 \, {\left({\left(b^{3} c - 6 \, a b c^{2}\right)} e^{4} x^{4} + 4 \, {\left(b^{3} c - 6 \, a b c^{2}\right)} d e^{3} x^{3} + {\left(b^{3} c - 6 \, a b c^{2}\right)} d^{4} + {\left(b^{4} - 6 \, a b^{2} c + 6 \, {\left(b^{3} c - 6 \, a b c^{2}\right)} d^{2}\right)} e^{2} x^{2} + a b^{3} - 6 \, a^{2} b c + {\left(b^{4} - 6 \, a b^{2} c\right)} d^{2} + 2 \, {\left(2 \, {\left(b^{3} c - 6 \, a b c^{2}\right)} d^{3} + {\left(b^{4} - 6 \, a b^{2} c\right)} d\right)} e x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{4} x^{4} + 4 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{3} x^{3} + 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)} d^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + 6 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2} + 2 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d\right)} e x\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 4 \, {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{4} x^{4} + 4 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{3} x^{3} + 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)} d^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + 6 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2} + 2 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d\right)} e x\right)} \log\left(e x + d\right)}{4 \, {\left({\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} e^{5} x^{4} + 4 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d e^{4} x^{3} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2} + 6 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d^{3} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d\right)} e^{2} x + {\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)} d^{4} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d^{2}\right)} e\right)}}\right]"," ",0,"[1/4*(2*a*b^4 - 12*a^2*b^2*c + 16*a^3*c^2 + 2*(a*b^3*c - 4*a^2*b*c^2)*e^2*x^2 + 4*(a*b^3*c - 4*a^2*b*c^2)*d*e*x + 2*(a*b^3*c - 4*a^2*b*c^2)*d^2 + ((b^3*c - 6*a*b*c^2)*e^4*x^4 + 4*(b^3*c - 6*a*b*c^2)*d*e^3*x^3 + (b^3*c - 6*a*b*c^2)*d^4 + (b^4 - 6*a*b^2*c + 6*(b^3*c - 6*a*b*c^2)*d^2)*e^2*x^2 + a*b^3 - 6*a^2*b*c + (b^4 - 6*a*b^2*c)*d^2 + 2*(2*(b^3*c - 6*a*b*c^2)*d^3 + (b^4 - 6*a*b^2*c)*d)*e*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c + (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)) - ((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^4*x^4 + 4*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^3*x^3 + 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)*d^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + 6*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2)*e^2*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2 + 2*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d)*e*x)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 4*((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^4*x^4 + 4*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^3*x^3 + 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)*d^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + 6*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2)*e^2*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2 + 2*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d)*e*x)*log(e*x + d))/((a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*e^5*x^4 + 4*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d*e^4*x^3 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2 + 6*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d^2)*e^3*x^2 + 2*(2*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d^3 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d)*e^2*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)*d^4 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d^2)*e), 1/4*(2*a*b^4 - 12*a^2*b^2*c + 16*a^3*c^2 + 2*(a*b^3*c - 4*a^2*b*c^2)*e^2*x^2 + 4*(a*b^3*c - 4*a^2*b*c^2)*d*e*x + 2*(a*b^3*c - 4*a^2*b*c^2)*d^2 + 2*((b^3*c - 6*a*b*c^2)*e^4*x^4 + 4*(b^3*c - 6*a*b*c^2)*d*e^3*x^3 + (b^3*c - 6*a*b*c^2)*d^4 + (b^4 - 6*a*b^2*c + 6*(b^3*c - 6*a*b*c^2)*d^2)*e^2*x^2 + a*b^3 - 6*a^2*b*c + (b^4 - 6*a*b^2*c)*d^2 + 2*(2*(b^3*c - 6*a*b*c^2)*d^3 + (b^4 - 6*a*b^2*c)*d)*e*x)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - ((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^4*x^4 + 4*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^3*x^3 + 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)*d^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + 6*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2)*e^2*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2 + 2*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d)*e*x)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 4*((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^4*x^4 + 4*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^3*x^3 + 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)*d^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + 6*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2)*e^2*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2 + 2*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d)*e*x)*log(e*x + d))/((a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*e^5*x^4 + 4*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d*e^4*x^3 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2 + 6*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d^2)*e^3*x^2 + 2*(2*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d^3 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d)*e^2*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)*d^4 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d^2)*e)]","B",0
627,1,4330,0,1.860715," ","integrate(1/(e*x+d)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, b^{2} c - 10 \, a c^{2}\right)} e^{4} x^{4} + 8 \, {\left(3 \, b^{2} c - 10 \, a c^{2}\right)} d e^{3} x^{3} + 2 \, {\left(3 \, b^{2} c - 10 \, a c^{2}\right)} d^{4} + 2 \, {\left(3 \, b^{3} - 11 \, a b c + 6 \, {\left(3 \, b^{2} c - 10 \, a c^{2}\right)} d^{2}\right)} e^{2} x^{2} + 4 \, a b^{2} - 16 \, a^{2} c + 2 \, {\left(3 \, b^{3} - 11 \, a b c\right)} d^{2} + 4 \, {\left(2 \, {\left(3 \, b^{2} c - 10 \, a c^{2}\right)} d^{3} + {\left(3 \, b^{3} - 11 \, a b c\right)} d\right)} e x + \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{6} x^{5} + 5 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{5} x^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c + 10 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2}\right)} e^{4} x^{3} + {\left(10 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{3} + 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d\right)} e^{3} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c + 5 \, {\left(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^{2}\right)} e^{2} x + {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d\right)} e\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} + {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4}}}}{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2}}} \log\left(-{\left(189 \, b^{6} c^{3} - 1971 \, a b^{4} c^{4} + 5625 \, a^{2} b^{2} c^{5} - 2500 \, a^{3} c^{6}\right)} e x - {\left(189 \, b^{6} c^{3} - 1971 \, a b^{4} c^{4} + 5625 \, a^{2} b^{2} c^{5} - 2500 \, a^{3} c^{6}\right)} d + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(3 \, a^{5} b^{10} - 55 \, a^{6} b^{8} c + 392 \, a^{7} b^{6} c^{2} - 1344 \, a^{8} b^{4} c^{3} + 2176 \, a^{9} b^{2} c^{4} - 1280 \, a^{10} c^{5}\right)} e^{3} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4}}} - {\left(27 \, b^{11} - 486 \, a b^{9} c + 3330 \, a^{2} b^{7} c^{2} - 10549 \, a^{3} b^{5} c^{3} + 14408 \, a^{4} b^{3} c^{4} - 5200 \, a^{5} b c^{5}\right)} e\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} + {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4}}}}{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{6} x^{5} + 5 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{5} x^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c + 10 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2}\right)} e^{4} x^{3} + {\left(10 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{3} + 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d\right)} e^{3} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c + 5 \, {\left(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^{2}\right)} e^{2} x + {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d\right)} e\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} + {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4}}}}{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2}}} \log\left(-{\left(189 \, b^{6} c^{3} - 1971 \, a b^{4} c^{4} + 5625 \, a^{2} b^{2} c^{5} - 2500 \, a^{3} c^{6}\right)} e x - {\left(189 \, b^{6} c^{3} - 1971 \, a b^{4} c^{4} + 5625 \, a^{2} b^{2} c^{5} - 2500 \, a^{3} c^{6}\right)} d - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(3 \, a^{5} b^{10} - 55 \, a^{6} b^{8} c + 392 \, a^{7} b^{6} c^{2} - 1344 \, a^{8} b^{4} c^{3} + 2176 \, a^{9} b^{2} c^{4} - 1280 \, a^{10} c^{5}\right)} e^{3} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4}}} - {\left(27 \, b^{11} - 486 \, a b^{9} c + 3330 \, a^{2} b^{7} c^{2} - 10549 \, a^{3} b^{5} c^{3} + 14408 \, a^{4} b^{3} c^{4} - 5200 \, a^{5} b c^{5}\right)} e\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} + {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4}}}}{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{6} x^{5} + 5 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{5} x^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c + 10 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2}\right)} e^{4} x^{3} + {\left(10 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{3} + 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d\right)} e^{3} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c + 5 \, {\left(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^{2}\right)} e^{2} x + {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d\right)} e\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} - {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4}}}}{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2}}} \log\left(-{\left(189 \, b^{6} c^{3} - 1971 \, a b^{4} c^{4} + 5625 \, a^{2} b^{2} c^{5} - 2500 \, a^{3} c^{6}\right)} e x - {\left(189 \, b^{6} c^{3} - 1971 \, a b^{4} c^{4} + 5625 \, a^{2} b^{2} c^{5} - 2500 \, a^{3} c^{6}\right)} d + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(3 \, a^{5} b^{10} - 55 \, a^{6} b^{8} c + 392 \, a^{7} b^{6} c^{2} - 1344 \, a^{8} b^{4} c^{3} + 2176 \, a^{9} b^{2} c^{4} - 1280 \, a^{10} c^{5}\right)} e^{3} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4}}} + {\left(27 \, b^{11} - 486 \, a b^{9} c + 3330 \, a^{2} b^{7} c^{2} - 10549 \, a^{3} b^{5} c^{3} + 14408 \, a^{4} b^{3} c^{4} - 5200 \, a^{5} b c^{5}\right)} e\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} - {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4}}}}{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{6} x^{5} + 5 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{5} x^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c + 10 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2}\right)} e^{4} x^{3} + {\left(10 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{3} + 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d\right)} e^{3} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c + 5 \, {\left(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^{2}\right)} e^{2} x + {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d\right)} e\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} - {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4}}}}{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2}}} \log\left(-{\left(189 \, b^{6} c^{3} - 1971 \, a b^{4} c^{4} + 5625 \, a^{2} b^{2} c^{5} - 2500 \, a^{3} c^{6}\right)} e x - {\left(189 \, b^{6} c^{3} - 1971 \, a b^{4} c^{4} + 5625 \, a^{2} b^{2} c^{5} - 2500 \, a^{3} c^{6}\right)} d - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(3 \, a^{5} b^{10} - 55 \, a^{6} b^{8} c + 392 \, a^{7} b^{6} c^{2} - 1344 \, a^{8} b^{4} c^{3} + 2176 \, a^{9} b^{2} c^{4} - 1280 \, a^{10} c^{5}\right)} e^{3} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4}}} + {\left(27 \, b^{11} - 486 \, a b^{9} c + 3330 \, a^{2} b^{7} c^{2} - 10549 \, a^{3} b^{5} c^{3} + 14408 \, a^{4} b^{3} c^{4} - 5200 \, a^{5} b c^{5}\right)} e\right)} \sqrt{-\frac{9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3} - {\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4}}}}{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2}}}\right)}{4 \, {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{6} x^{5} + 5 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{5} x^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c + 10 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2}\right)} e^{4} x^{3} + {\left(10 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{3} + 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d\right)} e^{3} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c + 5 \, {\left(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^{2}\right)} e^{2} x + {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d\right)} e\right)}}"," ",0,"-1/4*(2*(3*b^2*c - 10*a*c^2)*e^4*x^4 + 8*(3*b^2*c - 10*a*c^2)*d*e^3*x^3 + 2*(3*b^2*c - 10*a*c^2)*d^4 + 2*(3*b^3 - 11*a*b*c + 6*(3*b^2*c - 10*a*c^2)*d^2)*e^2*x^2 + 4*a*b^2 - 16*a^2*c + 2*(3*b^3 - 11*a*b*c)*d^2 + 4*(2*(3*b^2*c - 10*a*c^2)*d^3 + (3*b^3 - 11*a*b*c)*d)*e*x + sqrt(1/2)*((a^2*b^2*c - 4*a^3*c^2)*e^6*x^5 + 5*(a^2*b^2*c - 4*a^3*c^2)*d*e^5*x^4 + (a^2*b^3 - 4*a^3*b*c + 10*(a^2*b^2*c - 4*a^3*c^2)*d^2)*e^4*x^3 + (10*(a^2*b^2*c - 4*a^3*c^2)*d^3 + 3*(a^2*b^3 - 4*a^3*b*c)*d)*e^3*x^2 + (a^3*b^2 - 4*a^4*c + 5*(a^2*b^2*c - 4*a^3*c^2)*d^4 + 3*(a^2*b^3 - 4*a^3*b*c)*d^2)*e^2*x + ((a^2*b^2*c - 4*a^3*c^2)*d^5 + (a^2*b^3 - 4*a^3*b*c)*d^3 + (a^3*b^2 - 4*a^4*c)*d)*e)*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 + (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4)))/((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2))*log(-(189*b^6*c^3 - 1971*a*b^4*c^4 + 5625*a^2*b^2*c^5 - 2500*a^3*c^6)*e*x - (189*b^6*c^3 - 1971*a*b^4*c^4 + 5625*a^2*b^2*c^5 - 2500*a^3*c^6)*d + 1/2*sqrt(1/2)*((3*a^5*b^10 - 55*a^6*b^8*c + 392*a^7*b^6*c^2 - 1344*a^8*b^4*c^3 + 2176*a^9*b^2*c^4 - 1280*a^10*c^5)*e^3*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4)) - (27*b^11 - 486*a*b^9*c + 3330*a^2*b^7*c^2 - 10549*a^3*b^5*c^3 + 14408*a^4*b^3*c^4 - 5200*a^5*b*c^5)*e)*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 + (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4)))/((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2))) - sqrt(1/2)*((a^2*b^2*c - 4*a^3*c^2)*e^6*x^5 + 5*(a^2*b^2*c - 4*a^3*c^2)*d*e^5*x^4 + (a^2*b^3 - 4*a^3*b*c + 10*(a^2*b^2*c - 4*a^3*c^2)*d^2)*e^4*x^3 + (10*(a^2*b^2*c - 4*a^3*c^2)*d^3 + 3*(a^2*b^3 - 4*a^3*b*c)*d)*e^3*x^2 + (a^3*b^2 - 4*a^4*c + 5*(a^2*b^2*c - 4*a^3*c^2)*d^4 + 3*(a^2*b^3 - 4*a^3*b*c)*d^2)*e^2*x + ((a^2*b^2*c - 4*a^3*c^2)*d^5 + (a^2*b^3 - 4*a^3*b*c)*d^3 + (a^3*b^2 - 4*a^4*c)*d)*e)*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 + (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4)))/((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2))*log(-(189*b^6*c^3 - 1971*a*b^4*c^4 + 5625*a^2*b^2*c^5 - 2500*a^3*c^6)*e*x - (189*b^6*c^3 - 1971*a*b^4*c^4 + 5625*a^2*b^2*c^5 - 2500*a^3*c^6)*d - 1/2*sqrt(1/2)*((3*a^5*b^10 - 55*a^6*b^8*c + 392*a^7*b^6*c^2 - 1344*a^8*b^4*c^3 + 2176*a^9*b^2*c^4 - 1280*a^10*c^5)*e^3*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4)) - (27*b^11 - 486*a*b^9*c + 3330*a^2*b^7*c^2 - 10549*a^3*b^5*c^3 + 14408*a^4*b^3*c^4 - 5200*a^5*b*c^5)*e)*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 + (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4)))/((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2))) - sqrt(1/2)*((a^2*b^2*c - 4*a^3*c^2)*e^6*x^5 + 5*(a^2*b^2*c - 4*a^3*c^2)*d*e^5*x^4 + (a^2*b^3 - 4*a^3*b*c + 10*(a^2*b^2*c - 4*a^3*c^2)*d^2)*e^4*x^3 + (10*(a^2*b^2*c - 4*a^3*c^2)*d^3 + 3*(a^2*b^3 - 4*a^3*b*c)*d)*e^3*x^2 + (a^3*b^2 - 4*a^4*c + 5*(a^2*b^2*c - 4*a^3*c^2)*d^4 + 3*(a^2*b^3 - 4*a^3*b*c)*d^2)*e^2*x + ((a^2*b^2*c - 4*a^3*c^2)*d^5 + (a^2*b^3 - 4*a^3*b*c)*d^3 + (a^3*b^2 - 4*a^4*c)*d)*e)*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 - (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4)))/((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2))*log(-(189*b^6*c^3 - 1971*a*b^4*c^4 + 5625*a^2*b^2*c^5 - 2500*a^3*c^6)*e*x - (189*b^6*c^3 - 1971*a*b^4*c^4 + 5625*a^2*b^2*c^5 - 2500*a^3*c^6)*d + 1/2*sqrt(1/2)*((3*a^5*b^10 - 55*a^6*b^8*c + 392*a^7*b^6*c^2 - 1344*a^8*b^4*c^3 + 2176*a^9*b^2*c^4 - 1280*a^10*c^5)*e^3*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4)) + (27*b^11 - 486*a*b^9*c + 3330*a^2*b^7*c^2 - 10549*a^3*b^5*c^3 + 14408*a^4*b^3*c^4 - 5200*a^5*b*c^5)*e)*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 - (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4)))/((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2))) + sqrt(1/2)*((a^2*b^2*c - 4*a^3*c^2)*e^6*x^5 + 5*(a^2*b^2*c - 4*a^3*c^2)*d*e^5*x^4 + (a^2*b^3 - 4*a^3*b*c + 10*(a^2*b^2*c - 4*a^3*c^2)*d^2)*e^4*x^3 + (10*(a^2*b^2*c - 4*a^3*c^2)*d^3 + 3*(a^2*b^3 - 4*a^3*b*c)*d)*e^3*x^2 + (a^3*b^2 - 4*a^4*c + 5*(a^2*b^2*c - 4*a^3*c^2)*d^4 + 3*(a^2*b^3 - 4*a^3*b*c)*d^2)*e^2*x + ((a^2*b^2*c - 4*a^3*c^2)*d^5 + (a^2*b^3 - 4*a^3*b*c)*d^3 + (a^3*b^2 - 4*a^4*c)*d)*e)*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 - (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4)))/((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2))*log(-(189*b^6*c^3 - 1971*a*b^4*c^4 + 5625*a^2*b^2*c^5 - 2500*a^3*c^6)*e*x - (189*b^6*c^3 - 1971*a*b^4*c^4 + 5625*a^2*b^2*c^5 - 2500*a^3*c^6)*d - 1/2*sqrt(1/2)*((3*a^5*b^10 - 55*a^6*b^8*c + 392*a^7*b^6*c^2 - 1344*a^8*b^4*c^3 + 2176*a^9*b^2*c^4 - 1280*a^10*c^5)*e^3*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4)) + (27*b^11 - 486*a*b^9*c + 3330*a^2*b^7*c^2 - 10549*a^3*b^5*c^3 + 14408*a^4*b^3*c^4 - 5200*a^5*b*c^5)*e)*sqrt(-(9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3 - (a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4)))/((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2))))/((a^2*b^2*c - 4*a^3*c^2)*e^6*x^5 + 5*(a^2*b^2*c - 4*a^3*c^2)*d*e^5*x^4 + (a^2*b^3 - 4*a^3*b*c + 10*(a^2*b^2*c - 4*a^3*c^2)*d^2)*e^4*x^3 + (10*(a^2*b^2*c - 4*a^3*c^2)*d^3 + 3*(a^2*b^3 - 4*a^3*b*c)*d)*e^3*x^2 + (a^3*b^2 - 4*a^4*c + 5*(a^2*b^2*c - 4*a^3*c^2)*d^4 + 3*(a^2*b^3 - 4*a^3*b*c)*d^2)*e^2*x + ((a^2*b^2*c - 4*a^3*c^2)*d^5 + (a^2*b^3 - 4*a^3*b*c)*d^3 + (a^3*b^2 - 4*a^4*c)*d)*e)","B",0
628,1,4562,0,2.508670," ","integrate(1/(e*x+d)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} e^{4} x^{4} + 8 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d e^{3} x^{3} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + 2 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{4} + {\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2} + 12 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2}\right)} d^{2} + 2 \, {\left(4 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{3} + {\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2}\right)} d\right)} e x + {\left({\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} e^{6} x^{6} + 6 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d e^{5} x^{5} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2} + 15 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{6} + 4 \, {\left(5 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{3} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} d\right)} e^{3} x^{3} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} d^{4} + {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2} + 15 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{4} + 6 \, {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} d^{2} + 2 \, {\left(3 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{5} + 2 \, {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} d^{3} + {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} d\right)} e x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c + {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right) - {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{6} x^{6} + 6 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e^{5} x^{5} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{6} + 4 \, {\left(5 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d\right)} e^{3} x^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{4} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} + 6 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2} + 2 \, {\left(3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} + 2 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{3} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d\right)} e x\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 4 \, {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{6} x^{6} + 6 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e^{5} x^{5} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{6} + 4 \, {\left(5 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d\right)} e^{3} x^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{4} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} + 6 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2} + 2 \, {\left(3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} + 2 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{3} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d\right)} e x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} e^{7} x^{6} + 6 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d e^{6} x^{5} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2} + 15 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(5 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{3} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d\right)} e^{4} x^{3} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 15 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{4} + 6 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(3 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{5} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d^{3} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} d\right)} e^{2} x + {\left({\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{6} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d^{4} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} d^{2}\right)} e\right)}}, -\frac{2 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} e^{4} x^{4} + 8 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d e^{3} x^{3} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + 2 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{4} + {\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2} + 12 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2}\right)} d^{2} + 2 \, {\left(4 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{3} + {\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2}\right)} d\right)} e x + 2 \, {\left({\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} e^{6} x^{6} + 6 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d e^{5} x^{5} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2} + 15 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{6} + 4 \, {\left(5 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{3} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} d\right)} e^{3} x^{3} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} d^{4} + {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2} + 15 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{4} + 6 \, {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} d^{2} + 2 \, {\left(3 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{5} + 2 \, {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} d^{3} + {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} d\right)} e x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{6} x^{6} + 6 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e^{5} x^{5} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{6} + 4 \, {\left(5 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d\right)} e^{3} x^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{4} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} + 6 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2} + 2 \, {\left(3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} + 2 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{3} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d\right)} e x\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 4 \, {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{6} x^{6} + 6 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e^{5} x^{5} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{6} + 4 \, {\left(5 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d\right)} e^{3} x^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{4} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} + 6 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2} + 2 \, {\left(3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} + 2 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{3} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d\right)} e x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} e^{7} x^{6} + 6 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d e^{6} x^{5} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2} + 15 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(5 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{3} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d\right)} e^{4} x^{3} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 15 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{4} + 6 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(3 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{5} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d^{3} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} d\right)} e^{2} x + {\left({\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{6} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d^{4} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} d^{2}\right)} e\right)}}\right]"," ",0,"[-1/2*(2*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*e^4*x^4 + 8*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*d*e^3*x^3 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + 2*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*d^4 + (2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2 + 12*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*d^2)*e^2*x^2 + (2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2)*d^2 + 2*(4*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*d^3 + (2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2)*d)*e*x + ((b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*e^6*x^6 + 6*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d*e^5*x^5 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2 + 15*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^2)*e^4*x^4 + (b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^6 + 4*(5*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^3 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*d)*e^3*x^3 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*d^4 + (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2 + 15*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^4 + 6*(b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*d^2)*e^2*x^2 + (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*d^2 + 2*(3*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^5 + 2*(b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*d^3 + (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*d)*e*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c + (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)) - ((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^6*x^6 + 6*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e^5*x^5 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2)*e^4*x^4 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^6 + 4*(5*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d)*e^3*x^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^4 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^4 + 6*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^2)*e^2*x^2 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2 + 2*(3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^5 + 2*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^3 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d)*e*x)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 4*((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^6*x^6 + 6*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e^5*x^5 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2)*e^4*x^4 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^6 + 4*(5*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d)*e^3*x^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^4 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^4 + 6*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^2)*e^2*x^2 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2 + 2*(3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^5 + 2*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^3 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d)*e*x)*log(e*x + d))/((a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*e^7*x^6 + 6*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d*e^6*x^5 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2 + 15*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^2)*e^5*x^4 + 4*(5*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^3 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d)*e^4*x^3 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 15*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^4 + 6*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d^2)*e^3*x^2 + 2*(3*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^5 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d^3 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*d)*e^2*x + ((a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^6 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d^4 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*d^2)*e), -1/2*(2*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*e^4*x^4 + 8*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*d*e^3*x^3 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + 2*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*d^4 + (2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2 + 12*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*d^2)*e^2*x^2 + (2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2)*d^2 + 2*(4*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*d^3 + (2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2)*d)*e*x + 2*((b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*e^6*x^6 + 6*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d*e^5*x^5 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2 + 15*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^2)*e^4*x^4 + (b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^6 + 4*(5*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^3 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*d)*e^3*x^3 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*d^4 + (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2 + 15*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^4 + 6*(b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*d^2)*e^2*x^2 + (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*d^2 + 2*(3*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^5 + 2*(b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*d^3 + (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*d)*e*x)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - ((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^6*x^6 + 6*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e^5*x^5 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2)*e^4*x^4 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^6 + 4*(5*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d)*e^3*x^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^4 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^4 + 6*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^2)*e^2*x^2 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2 + 2*(3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^5 + 2*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^3 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d)*e*x)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 4*((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^6*x^6 + 6*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e^5*x^5 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2)*e^4*x^4 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^6 + 4*(5*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d)*e^3*x^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^4 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^4 + 6*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^2)*e^2*x^2 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2 + 2*(3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^5 + 2*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^3 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d)*e*x)*log(e*x + d))/((a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*e^7*x^6 + 6*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d*e^6*x^5 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2 + 15*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^2)*e^5*x^4 + 4*(5*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^3 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d)*e^4*x^3 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 15*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^4 + 6*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d^2)*e^3*x^2 + 2*(3*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^5 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d^3 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*d)*e^2*x + ((a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^6 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d^4 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*d^2)*e)]","B",0
629,1,5734,0,2.383289," ","integrate(1/(e*x+d)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""fricas"")","\frac{6 \, {\left(5 \, b^{3} c - 19 \, a b c^{2}\right)} e^{6} x^{6} + 36 \, {\left(5 \, b^{3} c - 19 \, a b c^{2}\right)} d e^{5} x^{5} + 2 \, {\left(15 \, b^{4} - 62 \, a b^{2} c + 14 \, a^{2} c^{2} + 45 \, {\left(5 \, b^{3} c - 19 \, a b c^{2}\right)} d^{2}\right)} e^{4} x^{4} + 6 \, {\left(5 \, b^{3} c - 19 \, a b c^{2}\right)} d^{6} + 8 \, {\left(15 \, {\left(5 \, b^{3} c - 19 \, a b c^{2}\right)} d^{3} + {\left(15 \, b^{4} - 62 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} d\right)} e^{3} x^{3} + 2 \, {\left(15 \, b^{4} - 62 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} d^{4} + 2 \, {\left(45 \, {\left(5 \, b^{3} c - 19 \, a b c^{2}\right)} d^{4} + 10 \, a b^{3} - 40 \, a^{2} b c + 6 \, {\left(15 \, b^{4} - 62 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} d^{2}\right)} e^{2} x^{2} - 4 \, a^{2} b^{2} + 16 \, a^{3} c + 20 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{2} + 4 \, {\left(9 \, {\left(5 \, b^{3} c - 19 \, a b c^{2}\right)} d^{5} + 2 \, {\left(15 \, b^{4} - 62 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} d^{3} + 10 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d\right)} e x - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{8} x^{7} + 7 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d e^{7} x^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c + 21 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2}\right)} e^{6} x^{5} + 5 \, {\left(7 \, {\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\right)} e^{5} x^{4} + {\left(a^{4} b^{2} - 4 \, a^{5} c + 35 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{4} + 10 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2}\right)} e^{4} x^{3} + {\left(21 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{5} + 10 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{3} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d\right)} e^{3} x^{2} + {\left(7 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{6} + 5 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{4} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{2}\right)} e^{2} x + {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{3}\right)} e\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4}}}}{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2}}} \log\left({\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} e x + {\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} d + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(5 \, a^{7} b^{11} - 94 \, a^{8} b^{9} c + 700 \, a^{9} b^{7} c^{2} - 2576 \, a^{10} b^{5} c^{3} + 4672 \, a^{11} b^{3} c^{4} - 3328 \, a^{12} b c^{5}\right)} e^{3} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4}}} - {\left(125 \, b^{14} - 2425 \, a b^{12} c + 18940 \, a^{2} b^{10} c^{2} - 75579 \, a^{3} b^{8} c^{3} + 160932 \, a^{4} b^{6} c^{4} - 172990 \, a^{5} b^{4} c^{5} + 79408 \, a^{6} b^{2} c^{6} - 10976 \, a^{7} c^{7}\right)} e\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4}}}}{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{8} x^{7} + 7 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d e^{7} x^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c + 21 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2}\right)} e^{6} x^{5} + 5 \, {\left(7 \, {\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\right)} e^{5} x^{4} + {\left(a^{4} b^{2} - 4 \, a^{5} c + 35 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{4} + 10 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2}\right)} e^{4} x^{3} + {\left(21 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{5} + 10 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{3} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d\right)} e^{3} x^{2} + {\left(7 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{6} + 5 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{4} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{2}\right)} e^{2} x + {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{3}\right)} e\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4}}}}{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2}}} \log\left({\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} e x + {\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} d - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(5 \, a^{7} b^{11} - 94 \, a^{8} b^{9} c + 700 \, a^{9} b^{7} c^{2} - 2576 \, a^{10} b^{5} c^{3} + 4672 \, a^{11} b^{3} c^{4} - 3328 \, a^{12} b c^{5}\right)} e^{3} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4}}} - {\left(125 \, b^{14} - 2425 \, a b^{12} c + 18940 \, a^{2} b^{10} c^{2} - 75579 \, a^{3} b^{8} c^{3} + 160932 \, a^{4} b^{6} c^{4} - 172990 \, a^{5} b^{4} c^{5} + 79408 \, a^{6} b^{2} c^{6} - 10976 \, a^{7} c^{7}\right)} e\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4}}}}{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{8} x^{7} + 7 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d e^{7} x^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c + 21 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2}\right)} e^{6} x^{5} + 5 \, {\left(7 \, {\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\right)} e^{5} x^{4} + {\left(a^{4} b^{2} - 4 \, a^{5} c + 35 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{4} + 10 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2}\right)} e^{4} x^{3} + {\left(21 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{5} + 10 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{3} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d\right)} e^{3} x^{2} + {\left(7 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{6} + 5 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{4} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{2}\right)} e^{2} x + {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{3}\right)} e\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} - {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4}}}}{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2}}} \log\left({\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} e x + {\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} d + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(5 \, a^{7} b^{11} - 94 \, a^{8} b^{9} c + 700 \, a^{9} b^{7} c^{2} - 2576 \, a^{10} b^{5} c^{3} + 4672 \, a^{11} b^{3} c^{4} - 3328 \, a^{12} b c^{5}\right)} e^{3} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4}}} + {\left(125 \, b^{14} - 2425 \, a b^{12} c + 18940 \, a^{2} b^{10} c^{2} - 75579 \, a^{3} b^{8} c^{3} + 160932 \, a^{4} b^{6} c^{4} - 172990 \, a^{5} b^{4} c^{5} + 79408 \, a^{6} b^{2} c^{6} - 10976 \, a^{7} c^{7}\right)} e\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} - {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4}}}}{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{8} x^{7} + 7 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d e^{7} x^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c + 21 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2}\right)} e^{6} x^{5} + 5 \, {\left(7 \, {\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\right)} e^{5} x^{4} + {\left(a^{4} b^{2} - 4 \, a^{5} c + 35 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{4} + 10 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2}\right)} e^{4} x^{3} + {\left(21 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{5} + 10 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{3} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d\right)} e^{3} x^{2} + {\left(7 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{6} + 5 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{4} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{2}\right)} e^{2} x + {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{3}\right)} e\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} - {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4}}}}{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2}}} \log\left({\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} e x + {\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} d - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(5 \, a^{7} b^{11} - 94 \, a^{8} b^{9} c + 700 \, a^{9} b^{7} c^{2} - 2576 \, a^{10} b^{5} c^{3} + 4672 \, a^{11} b^{3} c^{4} - 3328 \, a^{12} b c^{5}\right)} e^{3} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4}}} + {\left(125 \, b^{14} - 2425 \, a b^{12} c + 18940 \, a^{2} b^{10} c^{2} - 75579 \, a^{3} b^{8} c^{3} + 160932 \, a^{4} b^{6} c^{4} - 172990 \, a^{5} b^{4} c^{5} + 79408 \, a^{6} b^{2} c^{6} - 10976 \, a^{7} c^{7}\right)} e\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} - {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4}}}}{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2}}}\right)}{12 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{8} x^{7} + 7 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d e^{7} x^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c + 21 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2}\right)} e^{6} x^{5} + 5 \, {\left(7 \, {\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\right)} e^{5} x^{4} + {\left(a^{4} b^{2} - 4 \, a^{5} c + 35 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{4} + 10 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2}\right)} e^{4} x^{3} + {\left(21 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{5} + 10 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{3} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d\right)} e^{3} x^{2} + {\left(7 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{6} + 5 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{4} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{2}\right)} e^{2} x + {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{3}\right)} e\right)}}"," ",0,"1/12*(6*(5*b^3*c - 19*a*b*c^2)*e^6*x^6 + 36*(5*b^3*c - 19*a*b*c^2)*d*e^5*x^5 + 2*(15*b^4 - 62*a*b^2*c + 14*a^2*c^2 + 45*(5*b^3*c - 19*a*b*c^2)*d^2)*e^4*x^4 + 6*(5*b^3*c - 19*a*b*c^2)*d^6 + 8*(15*(5*b^3*c - 19*a*b*c^2)*d^3 + (15*b^4 - 62*a*b^2*c + 14*a^2*c^2)*d)*e^3*x^3 + 2*(15*b^4 - 62*a*b^2*c + 14*a^2*c^2)*d^4 + 2*(45*(5*b^3*c - 19*a*b*c^2)*d^4 + 10*a*b^3 - 40*a^2*b*c + 6*(15*b^4 - 62*a*b^2*c + 14*a^2*c^2)*d^2)*e^2*x^2 - 4*a^2*b^2 + 16*a^3*c + 20*(a*b^3 - 4*a^2*b*c)*d^2 + 4*(9*(5*b^3*c - 19*a*b*c^2)*d^5 + 2*(15*b^4 - 62*a*b^2*c + 14*a^2*c^2)*d^3 + 10*(a*b^3 - 4*a^2*b*c)*d)*e*x - 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*e^8*x^7 + 7*(a^3*b^2*c - 4*a^4*c^2)*d*e^7*x^6 + (a^3*b^3 - 4*a^4*b*c + 21*(a^3*b^2*c - 4*a^4*c^2)*d^2)*e^6*x^5 + 5*(7*(a^3*b^2*c - 4*a^4*c^2)*d^3 + (a^3*b^3 - 4*a^4*b*c)*d)*e^5*x^4 + (a^4*b^2 - 4*a^5*c + 35*(a^3*b^2*c - 4*a^4*c^2)*d^4 + 10*(a^3*b^3 - 4*a^4*b*c)*d^2)*e^4*x^3 + (21*(a^3*b^2*c - 4*a^4*c^2)*d^5 + 10*(a^3*b^3 - 4*a^4*b*c)*d^3 + 3*(a^4*b^2 - 4*a^5*c)*d)*e^3*x^2 + (7*(a^3*b^2*c - 4*a^4*c^2)*d^6 + 5*(a^3*b^3 - 4*a^4*b*c)*d^4 + 3*(a^4*b^2 - 4*a^5*c)*d^2)*e^2*x + ((a^3*b^2*c - 4*a^4*c^2)*d^7 + (a^3*b^3 - 4*a^4*b*c)*d^5 + (a^4*b^2 - 4*a^5*c)*d^3)*e)*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4)))/((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2))*log((1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*e*x + (1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*d + 1/2*sqrt(1/2)*((5*a^7*b^11 - 94*a^8*b^9*c + 700*a^9*b^7*c^2 - 2576*a^10*b^5*c^3 + 4672*a^11*b^3*c^4 - 3328*a^12*b*c^5)*e^3*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4)) - (125*b^14 - 2425*a*b^12*c + 18940*a^2*b^10*c^2 - 75579*a^3*b^8*c^3 + 160932*a^4*b^6*c^4 - 172990*a^5*b^4*c^5 + 79408*a^6*b^2*c^6 - 10976*a^7*c^7)*e)*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4)))/((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2))) + 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*e^8*x^7 + 7*(a^3*b^2*c - 4*a^4*c^2)*d*e^7*x^6 + (a^3*b^3 - 4*a^4*b*c + 21*(a^3*b^2*c - 4*a^4*c^2)*d^2)*e^6*x^5 + 5*(7*(a^3*b^2*c - 4*a^4*c^2)*d^3 + (a^3*b^3 - 4*a^4*b*c)*d)*e^5*x^4 + (a^4*b^2 - 4*a^5*c + 35*(a^3*b^2*c - 4*a^4*c^2)*d^4 + 10*(a^3*b^3 - 4*a^4*b*c)*d^2)*e^4*x^3 + (21*(a^3*b^2*c - 4*a^4*c^2)*d^5 + 10*(a^3*b^3 - 4*a^4*b*c)*d^3 + 3*(a^4*b^2 - 4*a^5*c)*d)*e^3*x^2 + (7*(a^3*b^2*c - 4*a^4*c^2)*d^6 + 5*(a^3*b^3 - 4*a^4*b*c)*d^4 + 3*(a^4*b^2 - 4*a^5*c)*d^2)*e^2*x + ((a^3*b^2*c - 4*a^4*c^2)*d^7 + (a^3*b^3 - 4*a^4*b*c)*d^5 + (a^4*b^2 - 4*a^5*c)*d^3)*e)*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4)))/((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2))*log((1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*e*x + (1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*d - 1/2*sqrt(1/2)*((5*a^7*b^11 - 94*a^8*b^9*c + 700*a^9*b^7*c^2 - 2576*a^10*b^5*c^3 + 4672*a^11*b^3*c^4 - 3328*a^12*b*c^5)*e^3*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4)) - (125*b^14 - 2425*a*b^12*c + 18940*a^2*b^10*c^2 - 75579*a^3*b^8*c^3 + 160932*a^4*b^6*c^4 - 172990*a^5*b^4*c^5 + 79408*a^6*b^2*c^6 - 10976*a^7*c^7)*e)*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4)))/((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2))) + 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*e^8*x^7 + 7*(a^3*b^2*c - 4*a^4*c^2)*d*e^7*x^6 + (a^3*b^3 - 4*a^4*b*c + 21*(a^3*b^2*c - 4*a^4*c^2)*d^2)*e^6*x^5 + 5*(7*(a^3*b^2*c - 4*a^4*c^2)*d^3 + (a^3*b^3 - 4*a^4*b*c)*d)*e^5*x^4 + (a^4*b^2 - 4*a^5*c + 35*(a^3*b^2*c - 4*a^4*c^2)*d^4 + 10*(a^3*b^3 - 4*a^4*b*c)*d^2)*e^4*x^3 + (21*(a^3*b^2*c - 4*a^4*c^2)*d^5 + 10*(a^3*b^3 - 4*a^4*b*c)*d^3 + 3*(a^4*b^2 - 4*a^5*c)*d)*e^3*x^2 + (7*(a^3*b^2*c - 4*a^4*c^2)*d^6 + 5*(a^3*b^3 - 4*a^4*b*c)*d^4 + 3*(a^4*b^2 - 4*a^5*c)*d^2)*e^2*x + ((a^3*b^2*c - 4*a^4*c^2)*d^7 + (a^3*b^3 - 4*a^4*b*c)*d^5 + (a^4*b^2 - 4*a^5*c)*d^3)*e)*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 - (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4)))/((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2))*log((1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*e*x + (1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*d + 1/2*sqrt(1/2)*((5*a^7*b^11 - 94*a^8*b^9*c + 700*a^9*b^7*c^2 - 2576*a^10*b^5*c^3 + 4672*a^11*b^3*c^4 - 3328*a^12*b*c^5)*e^3*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4)) + (125*b^14 - 2425*a*b^12*c + 18940*a^2*b^10*c^2 - 75579*a^3*b^8*c^3 + 160932*a^4*b^6*c^4 - 172990*a^5*b^4*c^5 + 79408*a^6*b^2*c^6 - 10976*a^7*c^7)*e)*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 - (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4)))/((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2))) - 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*e^8*x^7 + 7*(a^3*b^2*c - 4*a^4*c^2)*d*e^7*x^6 + (a^3*b^3 - 4*a^4*b*c + 21*(a^3*b^2*c - 4*a^4*c^2)*d^2)*e^6*x^5 + 5*(7*(a^3*b^2*c - 4*a^4*c^2)*d^3 + (a^3*b^3 - 4*a^4*b*c)*d)*e^5*x^4 + (a^4*b^2 - 4*a^5*c + 35*(a^3*b^2*c - 4*a^4*c^2)*d^4 + 10*(a^3*b^3 - 4*a^4*b*c)*d^2)*e^4*x^3 + (21*(a^3*b^2*c - 4*a^4*c^2)*d^5 + 10*(a^3*b^3 - 4*a^4*b*c)*d^3 + 3*(a^4*b^2 - 4*a^5*c)*d)*e^3*x^2 + (7*(a^3*b^2*c - 4*a^4*c^2)*d^6 + 5*(a^3*b^3 - 4*a^4*b*c)*d^4 + 3*(a^4*b^2 - 4*a^5*c)*d^2)*e^2*x + ((a^3*b^2*c - 4*a^4*c^2)*d^7 + (a^3*b^3 - 4*a^4*b*c)*d^5 + (a^4*b^2 - 4*a^5*c)*d^3)*e)*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 - (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4)))/((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2))*log((1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*e*x + (1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*d - 1/2*sqrt(1/2)*((5*a^7*b^11 - 94*a^8*b^9*c + 700*a^9*b^7*c^2 - 2576*a^10*b^5*c^3 + 4672*a^11*b^3*c^4 - 3328*a^12*b*c^5)*e^3*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4)) + (125*b^14 - 2425*a*b^12*c + 18940*a^2*b^10*c^2 - 75579*a^3*b^8*c^3 + 160932*a^4*b^6*c^4 - 172990*a^5*b^4*c^5 + 79408*a^6*b^2*c^6 - 10976*a^7*c^7)*e)*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 - (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4)))/((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2))))/((a^3*b^2*c - 4*a^4*c^2)*e^8*x^7 + 7*(a^3*b^2*c - 4*a^4*c^2)*d*e^7*x^6 + (a^3*b^3 - 4*a^4*b*c + 21*(a^3*b^2*c - 4*a^4*c^2)*d^2)*e^6*x^5 + 5*(7*(a^3*b^2*c - 4*a^4*c^2)*d^3 + (a^3*b^3 - 4*a^4*b*c)*d)*e^5*x^4 + (a^4*b^2 - 4*a^5*c + 35*(a^3*b^2*c - 4*a^4*c^2)*d^4 + 10*(a^3*b^3 - 4*a^4*b*c)*d^2)*e^4*x^3 + (21*(a^3*b^2*c - 4*a^4*c^2)*d^5 + 10*(a^3*b^3 - 4*a^4*b*c)*d^3 + 3*(a^4*b^2 - 4*a^5*c)*d)*e^3*x^2 + (7*(a^3*b^2*c - 4*a^4*c^2)*d^6 + 5*(a^3*b^3 - 4*a^4*b*c)*d^4 + 3*(a^4*b^2 - 4*a^5*c)*d^2)*e^2*x + ((a^3*b^2*c - 4*a^4*c^2)*d^7 + (a^3*b^3 - 4*a^4*b*c)*d^5 + (a^4*b^2 - 4*a^5*c)*d^3)*e)","B",0
630,1,6633,0,2.042979," ","integrate((e*x+d)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""fricas"")","-\frac{24 \, b c^{2} e^{7} x^{7} + 168 \, b c^{2} d e^{6} x^{6} + 2 \, {\left(252 \, b c^{2} d^{2} + 19 \, b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{5} + 24 \, b c^{2} d^{7} + 10 \, {\left(84 \, b c^{2} d^{3} + {\left(19 \, b^{2} c - 4 \, a c^{2}\right)} d\right)} e^{4} x^{4} + 2 \, {\left(420 \, b c^{2} d^{4} + 5 \, b^{3} + 16 \, a b c + 10 \, {\left(19 \, b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{3} + 2 \, {\left(19 \, b^{2} c - 4 \, a c^{2}\right)} d^{5} + 2 \, {\left(252 \, b c^{2} d^{5} + 10 \, {\left(19 \, b^{2} c - 4 \, a c^{2}\right)} d^{3} + 3 \, {\left(5 \, b^{3} + 16 \, a b c\right)} d\right)} e^{2} x^{2} + 2 \, {\left(5 \, b^{3} + 16 \, a b c\right)} d^{3} + 2 \, {\left(84 \, b c^{2} d^{6} + 5 \, {\left(19 \, b^{2} c - 4 \, a c^{2}\right)} d^{4} + 3 \, a b^{2} + 12 \, a^{2} c + 3 \, {\left(5 \, b^{3} + 16 \, a b c\right)} d^{2}\right)} e x - 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{9} x^{8} + 8 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3} + 14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{3} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3} + 70 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{4} + 30 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{5} + 10 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{6} + a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} + 3 \, {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{7} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{3} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{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)} d^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2}\right)} e\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2} \sqrt{\frac{1}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}}}{{\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}} \log\left(3 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e x + 3 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d + \frac{3}{2} \, \sqrt{\frac{1}{2}} {\left({\left(a b^{13} - 8 \, a^{2} b^{11} c - 80 \, a^{3} b^{9} c^{2} + 1280 \, a^{4} b^{7} c^{3} - 6400 \, a^{5} b^{5} c^{4} + 14336 \, a^{6} b^{3} c^{5} - 12288 \, a^{7} b c^{6}\right)} e^{3} \sqrt{\frac{1}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} - {\left(b^{8} - 8 \, a b^{6} c + 128 \, a^{3} b^{2} c^{3} - 256 \, a^{4} c^{4}\right)} e\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2} \sqrt{\frac{1}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}}}{{\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{9} x^{8} + 8 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3} + 14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{3} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3} + 70 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{4} + 30 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{5} + 10 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{6} + a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} + 3 \, {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{7} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{3} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{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)} d^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2}\right)} e\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2} \sqrt{\frac{1}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}}}{{\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}} \log\left(3 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e x + 3 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d - \frac{3}{2} \, \sqrt{\frac{1}{2}} {\left({\left(a b^{13} - 8 \, a^{2} b^{11} c - 80 \, a^{3} b^{9} c^{2} + 1280 \, a^{4} b^{7} c^{3} - 6400 \, a^{5} b^{5} c^{4} + 14336 \, a^{6} b^{3} c^{5} - 12288 \, a^{7} b c^{6}\right)} e^{3} \sqrt{\frac{1}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} - {\left(b^{8} - 8 \, a b^{6} c + 128 \, a^{3} b^{2} c^{3} - 256 \, a^{4} c^{4}\right)} e\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2} \sqrt{\frac{1}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}}}{{\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{9} x^{8} + 8 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3} + 14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{3} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3} + 70 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{4} + 30 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{5} + 10 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{6} + a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} + 3 \, {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{7} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{3} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{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)} d^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2}\right)} e\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} - {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2} \sqrt{\frac{1}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}}}{{\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}} \log\left(3 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e x + 3 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d + \frac{3}{2} \, \sqrt{\frac{1}{2}} {\left({\left(a b^{13} - 8 \, a^{2} b^{11} c - 80 \, a^{3} b^{9} c^{2} + 1280 \, a^{4} b^{7} c^{3} - 6400 \, a^{5} b^{5} c^{4} + 14336 \, a^{6} b^{3} c^{5} - 12288 \, a^{7} b c^{6}\right)} e^{3} \sqrt{\frac{1}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} + {\left(b^{8} - 8 \, a b^{6} c + 128 \, a^{3} b^{2} c^{3} - 256 \, a^{4} c^{4}\right)} e\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} - {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2} \sqrt{\frac{1}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}}}{{\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{9} x^{8} + 8 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3} + 14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{3} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3} + 70 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{4} + 30 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{5} + 10 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{6} + a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} + 3 \, {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{7} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{3} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{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)} d^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2}\right)} e\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} - {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2} \sqrt{\frac{1}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}}}{{\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}} \log\left(3 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e x + 3 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d - \frac{3}{2} \, \sqrt{\frac{1}{2}} {\left({\left(a b^{13} - 8 \, a^{2} b^{11} c - 80 \, a^{3} b^{9} c^{2} + 1280 \, a^{4} b^{7} c^{3} - 6400 \, a^{5} b^{5} c^{4} + 14336 \, a^{6} b^{3} c^{5} - 12288 \, a^{7} b c^{6}\right)} e^{3} \sqrt{\frac{1}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} + {\left(b^{8} - 8 \, a b^{6} c + 128 \, a^{3} b^{2} c^{3} - 256 \, a^{4} c^{4}\right)} e\right)} \sqrt{-\frac{b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2} - {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2} \sqrt{\frac{1}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}}}{{\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}}\right) + 6 \, {\left(a b^{2} + 4 \, a^{2} c\right)} d}{16 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{9} x^{8} + 8 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3} + 14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{3} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3} + 70 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{4} + 30 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{5} + 10 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{6} + a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} + 3 \, {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{7} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{3} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{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)} d^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2}\right)} e\right)}}"," ",0,"-1/16*(24*b*c^2*e^7*x^7 + 168*b*c^2*d*e^6*x^6 + 2*(252*b*c^2*d^2 + 19*b^2*c - 4*a*c^2)*e^5*x^5 + 24*b*c^2*d^7 + 10*(84*b*c^2*d^3 + (19*b^2*c - 4*a*c^2)*d)*e^4*x^4 + 2*(420*b*c^2*d^4 + 5*b^3 + 16*a*b*c + 10*(19*b^2*c - 4*a*c^2)*d^2)*e^3*x^3 + 2*(19*b^2*c - 4*a*c^2)*d^5 + 2*(252*b*c^2*d^5 + 10*(19*b^2*c - 4*a*c^2)*d^3 + 3*(5*b^3 + 16*a*b*c)*d)*e^2*x^2 + 2*(5*b^3 + 16*a*b*c)*d^3 + 2*(84*b*c^2*d^6 + 5*(19*b^2*c - 4*a*c^2)*d^4 + 3*a*b^2 + 12*a^2*c + 3*(5*b^3 + 16*a*b*c)*d^2)*e*x - 3*sqrt(1/2)*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^9*x^8 + 8*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*e^8*x^7 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3 + 14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2)*e^7*x^6 + 4*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^3 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d)*e^6*x^5 + (b^6 - 6*a*b^4*c + 32*a^3*c^3 + 70*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^4 + 30*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2)*e^5*x^4 + 4*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^5 + 10*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d)*e^4*x^3 + 2*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^6 + a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^4 + 3*(b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^2)*e^3*x^2 + 4*(2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^7 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^5 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^3 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d)*e^2*x + ((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^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)*d^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2)*e)*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2*sqrt(1/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4)))/((a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))*log(3*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*e*x + 3*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d + 3/2*sqrt(1/2)*((a*b^13 - 8*a^2*b^11*c - 80*a^3*b^9*c^2 + 1280*a^4*b^7*c^3 - 6400*a^5*b^5*c^4 + 14336*a^6*b^3*c^5 - 12288*a^7*b*c^6)*e^3*sqrt(1/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4)) - (b^8 - 8*a*b^6*c + 128*a^3*b^2*c^3 - 256*a^4*c^4)*e)*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2*sqrt(1/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4)))/((a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))) + 3*sqrt(1/2)*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^9*x^8 + 8*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*e^8*x^7 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3 + 14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2)*e^7*x^6 + 4*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^3 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d)*e^6*x^5 + (b^6 - 6*a*b^4*c + 32*a^3*c^3 + 70*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^4 + 30*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2)*e^5*x^4 + 4*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^5 + 10*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d)*e^4*x^3 + 2*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^6 + a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^4 + 3*(b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^2)*e^3*x^2 + 4*(2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^7 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^5 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^3 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d)*e^2*x + ((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^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)*d^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2)*e)*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2*sqrt(1/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4)))/((a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))*log(3*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*e*x + 3*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d - 3/2*sqrt(1/2)*((a*b^13 - 8*a^2*b^11*c - 80*a^3*b^9*c^2 + 1280*a^4*b^7*c^3 - 6400*a^5*b^5*c^4 + 14336*a^6*b^3*c^5 - 12288*a^7*b*c^6)*e^3*sqrt(1/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4)) - (b^8 - 8*a*b^6*c + 128*a^3*b^2*c^3 - 256*a^4*c^4)*e)*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2*sqrt(1/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4)))/((a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))) + 3*sqrt(1/2)*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^9*x^8 + 8*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*e^8*x^7 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3 + 14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2)*e^7*x^6 + 4*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^3 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d)*e^6*x^5 + (b^6 - 6*a*b^4*c + 32*a^3*c^3 + 70*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^4 + 30*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2)*e^5*x^4 + 4*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^5 + 10*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d)*e^4*x^3 + 2*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^6 + a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^4 + 3*(b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^2)*e^3*x^2 + 4*(2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^7 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^5 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^3 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d)*e^2*x + ((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^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)*d^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2)*e)*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 - (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2*sqrt(1/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4)))/((a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))*log(3*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*e*x + 3*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d + 3/2*sqrt(1/2)*((a*b^13 - 8*a^2*b^11*c - 80*a^3*b^9*c^2 + 1280*a^4*b^7*c^3 - 6400*a^5*b^5*c^4 + 14336*a^6*b^3*c^5 - 12288*a^7*b*c^6)*e^3*sqrt(1/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4)) + (b^8 - 8*a*b^6*c + 128*a^3*b^2*c^3 - 256*a^4*c^4)*e)*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 - (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2*sqrt(1/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4)))/((a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))) - 3*sqrt(1/2)*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^9*x^8 + 8*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*e^8*x^7 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3 + 14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2)*e^7*x^6 + 4*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^3 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d)*e^6*x^5 + (b^6 - 6*a*b^4*c + 32*a^3*c^3 + 70*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^4 + 30*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2)*e^5*x^4 + 4*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^5 + 10*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d)*e^4*x^3 + 2*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^6 + a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^4 + 3*(b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^2)*e^3*x^2 + 4*(2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^7 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^5 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^3 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d)*e^2*x + ((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^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)*d^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2)*e)*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 - (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2*sqrt(1/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4)))/((a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))*log(3*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*e*x + 3*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d - 3/2*sqrt(1/2)*((a*b^13 - 8*a^2*b^11*c - 80*a^3*b^9*c^2 + 1280*a^4*b^7*c^3 - 6400*a^5*b^5*c^4 + 14336*a^6*b^3*c^5 - 12288*a^7*b*c^6)*e^3*sqrt(1/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4)) + (b^8 - 8*a*b^6*c + 128*a^3*b^2*c^3 - 256*a^4*c^4)*e)*sqrt(-(b^5 + 40*a*b^3*c + 80*a^2*b*c^2 - (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2*sqrt(1/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4)))/((a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))) + 6*(a*b^2 + 4*a^2*c)*d)/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^9*x^8 + 8*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*e^8*x^7 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3 + 14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2)*e^7*x^6 + 4*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^3 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d)*e^6*x^5 + (b^6 - 6*a*b^4*c + 32*a^3*c^3 + 70*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^4 + 30*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2)*e^5*x^4 + 4*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^5 + 10*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d)*e^4*x^3 + 2*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^6 + a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^4 + 3*(b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^2)*e^3*x^2 + 4*(2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^7 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^5 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^3 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d)*e^2*x + ((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^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)*d^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2)*e)","B",0
631,1,3739,0,1.531108," ","integrate((e*x+d)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{6} x^{6} + 36 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{5} x^{5} + 9 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 10 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2}\right)} e^{4} x^{4} + 6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{6} + 12 \, {\left(10 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} + 3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d\right)} e^{3} x^{3} + a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2} + 9 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{4} + 2 \, {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2} + 45 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} + 27 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{2}\right)} e^{2} x^{2} + 2 \, {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} d^{2} + 4 \, {\left(9 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} + 9 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} + {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} d\right)} e x - 6 \, {\left(b c^{3} e^{8} x^{8} + 8 \, b c^{3} d e^{7} x^{7} + 2 \, {\left(14 \, b c^{3} d^{2} + b^{2} c^{2}\right)} e^{6} x^{6} + b c^{3} d^{8} + 4 \, {\left(14 \, b c^{3} d^{3} + 3 \, b^{2} c^{2} d\right)} e^{5} x^{5} + 2 \, b^{2} c^{2} d^{6} + {\left(70 \, b c^{3} d^{4} + 30 \, b^{2} c^{2} d^{2} + b^{3} c + 2 \, a b c^{2}\right)} e^{4} x^{4} + 4 \, {\left(14 \, b c^{3} d^{5} + 10 \, b^{2} c^{2} d^{3} + {\left(b^{3} c + 2 \, a b c^{2}\right)} d\right)} e^{3} x^{3} + 2 \, a b^{2} c d^{2} + {\left(b^{3} c + 2 \, a b c^{2}\right)} d^{4} + 2 \, {\left(14 \, b c^{3} d^{6} + 15 \, b^{2} c^{2} d^{4} + a b^{2} c + 3 \, {\left(b^{3} c + 2 \, a b c^{2}\right)} d^{2}\right)} e^{2} x^{2} + a^{2} b c + 4 \, {\left(2 \, b c^{3} d^{7} + 3 \, b^{2} c^{2} d^{5} + a b^{2} c d + {\left(b^{3} c + 2 \, a b c^{2}\right)} d^{3}\right)} e x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c + {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right)}{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)} e^{9} x^{8} + 8 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d e^{8} x^{7} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{3} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d\right)} e^{6} x^{5} + {\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} + 70 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} + 30 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{5} + 10 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} + {\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)} d\right)} e^{4} x^{3} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{6} + 15 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{4} + 3 \, {\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)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{7} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{5} + {\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)} d^{3} + {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d\right)} e^{2} x + {\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)} d^{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)} d^{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)} d^{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)} d^{2}\right)} e\right)}}, -\frac{6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{6} x^{6} + 36 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{5} x^{5} + 9 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 10 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2}\right)} e^{4} x^{4} + 6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{6} + 12 \, {\left(10 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} + 3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d\right)} e^{3} x^{3} + a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2} + 9 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{4} + 2 \, {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2} + 45 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} + 27 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{2}\right)} e^{2} x^{2} + 2 \, {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} d^{2} + 4 \, {\left(9 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} + 9 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} + {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} d\right)} e x - 12 \, {\left(b c^{3} e^{8} x^{8} + 8 \, b c^{3} d e^{7} x^{7} + 2 \, {\left(14 \, b c^{3} d^{2} + b^{2} c^{2}\right)} e^{6} x^{6} + b c^{3} d^{8} + 4 \, {\left(14 \, b c^{3} d^{3} + 3 \, b^{2} c^{2} d\right)} e^{5} x^{5} + 2 \, b^{2} c^{2} d^{6} + {\left(70 \, b c^{3} d^{4} + 30 \, b^{2} c^{2} d^{2} + b^{3} c + 2 \, a b c^{2}\right)} e^{4} x^{4} + 4 \, {\left(14 \, b c^{3} d^{5} + 10 \, b^{2} c^{2} d^{3} + {\left(b^{3} c + 2 \, a b c^{2}\right)} d\right)} e^{3} x^{3} + 2 \, a b^{2} c d^{2} + {\left(b^{3} c + 2 \, a b c^{2}\right)} d^{4} + 2 \, {\left(14 \, b c^{3} d^{6} + 15 \, b^{2} c^{2} d^{4} + a b^{2} c + 3 \, {\left(b^{3} c + 2 \, a b c^{2}\right)} d^{2}\right)} e^{2} x^{2} + a^{2} b c + 4 \, {\left(2 \, b c^{3} d^{7} + 3 \, b^{2} c^{2} d^{5} + a b^{2} c d + {\left(b^{3} c + 2 \, a b c^{2}\right)} d^{3}\right)} e x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right)}{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)} e^{9} x^{8} + 8 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d e^{8} x^{7} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{3} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d\right)} e^{6} x^{5} + {\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} + 70 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} + 30 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{5} + 10 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} + {\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)} d\right)} e^{4} x^{3} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{6} + 15 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{4} + 3 \, {\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)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{7} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{5} + {\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)} d^{3} + {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d\right)} e^{2} x + {\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)} d^{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)} d^{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)} d^{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)} d^{2}\right)} e\right)}}\right]"," ",0,"[-1/4*(6*(b^3*c^2 - 4*a*b*c^3)*e^6*x^6 + 36*(b^3*c^2 - 4*a*b*c^3)*d*e^5*x^5 + 9*(b^4*c - 4*a*b^2*c^2 + 10*(b^3*c^2 - 4*a*b*c^3)*d^2)*e^4*x^4 + 6*(b^3*c^2 - 4*a*b*c^3)*d^6 + 12*(10*(b^3*c^2 - 4*a*b*c^3)*d^3 + 3*(b^4*c - 4*a*b^2*c^2)*d)*e^3*x^3 + a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2 + 9*(b^4*c - 4*a*b^2*c^2)*d^4 + 2*(b^5 + a*b^3*c - 20*a^2*b*c^2 + 45*(b^3*c^2 - 4*a*b*c^3)*d^4 + 27*(b^4*c - 4*a*b^2*c^2)*d^2)*e^2*x^2 + 2*(b^5 + a*b^3*c - 20*a^2*b*c^2)*d^2 + 4*(9*(b^3*c^2 - 4*a*b*c^3)*d^5 + 9*(b^4*c - 4*a*b^2*c^2)*d^3 + (b^5 + a*b^3*c - 20*a^2*b*c^2)*d)*e*x - 6*(b*c^3*e^8*x^8 + 8*b*c^3*d*e^7*x^7 + 2*(14*b*c^3*d^2 + b^2*c^2)*e^6*x^6 + b*c^3*d^8 + 4*(14*b*c^3*d^3 + 3*b^2*c^2*d)*e^5*x^5 + 2*b^2*c^2*d^6 + (70*b*c^3*d^4 + 30*b^2*c^2*d^2 + b^3*c + 2*a*b*c^2)*e^4*x^4 + 4*(14*b*c^3*d^5 + 10*b^2*c^2*d^3 + (b^3*c + 2*a*b*c^2)*d)*e^3*x^3 + 2*a*b^2*c*d^2 + (b^3*c + 2*a*b*c^2)*d^4 + 2*(14*b*c^3*d^6 + 15*b^2*c^2*d^4 + a*b^2*c + 3*(b^3*c + 2*a*b*c^2)*d^2)*e^2*x^2 + a^2*b*c + 4*(2*b*c^3*d^7 + 3*b^2*c^2*d^5 + a*b^2*c*d + (b^3*c + 2*a*b*c^2)*d^3)*e*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c + (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)))/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^9*x^8 + 8*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d*e^8*x^7 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2)*e^7*x^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^3 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d)*e^6*x^5 + (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 + 70*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 + 30*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2)*e^5*x^4 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^5 + 10*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3 + (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)*d)*e^4*x^3 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^6 + 15*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^4 + 3*(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)*d^2)*e^3*x^2 + 4*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^7 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^5 + (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)*d^3 + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d)*e^2*x + ((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^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)*d^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)*d^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2)*e), -1/4*(6*(b^3*c^2 - 4*a*b*c^3)*e^6*x^6 + 36*(b^3*c^2 - 4*a*b*c^3)*d*e^5*x^5 + 9*(b^4*c - 4*a*b^2*c^2 + 10*(b^3*c^2 - 4*a*b*c^3)*d^2)*e^4*x^4 + 6*(b^3*c^2 - 4*a*b*c^3)*d^6 + 12*(10*(b^3*c^2 - 4*a*b*c^3)*d^3 + 3*(b^4*c - 4*a*b^2*c^2)*d)*e^3*x^3 + a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2 + 9*(b^4*c - 4*a*b^2*c^2)*d^4 + 2*(b^5 + a*b^3*c - 20*a^2*b*c^2 + 45*(b^3*c^2 - 4*a*b*c^3)*d^4 + 27*(b^4*c - 4*a*b^2*c^2)*d^2)*e^2*x^2 + 2*(b^5 + a*b^3*c - 20*a^2*b*c^2)*d^2 + 4*(9*(b^3*c^2 - 4*a*b*c^3)*d^5 + 9*(b^4*c - 4*a*b^2*c^2)*d^3 + (b^5 + a*b^3*c - 20*a^2*b*c^2)*d)*e*x - 12*(b*c^3*e^8*x^8 + 8*b*c^3*d*e^7*x^7 + 2*(14*b*c^3*d^2 + b^2*c^2)*e^6*x^6 + b*c^3*d^8 + 4*(14*b*c^3*d^3 + 3*b^2*c^2*d)*e^5*x^5 + 2*b^2*c^2*d^6 + (70*b*c^3*d^4 + 30*b^2*c^2*d^2 + b^3*c + 2*a*b*c^2)*e^4*x^4 + 4*(14*b*c^3*d^5 + 10*b^2*c^2*d^3 + (b^3*c + 2*a*b*c^2)*d)*e^3*x^3 + 2*a*b^2*c*d^2 + (b^3*c + 2*a*b*c^2)*d^4 + 2*(14*b*c^3*d^6 + 15*b^2*c^2*d^4 + a*b^2*c + 3*(b^3*c + 2*a*b*c^2)*d^2)*e^2*x^2 + a^2*b*c + 4*(2*b*c^3*d^7 + 3*b^2*c^2*d^5 + a*b^2*c*d + (b^3*c + 2*a*b*c^2)*d^3)*e*x)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)))/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^9*x^8 + 8*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d*e^8*x^7 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2)*e^7*x^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^3 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d)*e^6*x^5 + (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 + 70*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 + 30*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2)*e^5*x^4 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^5 + 10*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3 + (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)*d)*e^4*x^3 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^6 + 15*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^4 + 3*(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)*d^2)*e^3*x^2 + 4*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^7 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^5 + (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)*d^3 + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d)*e^2*x + ((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^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)*d^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)*d^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2)*e)]","B",0
632,1,7701,0,2.258109," ","integrate((e*x+d)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} e^{7} x^{7} + 14 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} d e^{6} x^{6} + 2 \, {\left(2 \, b^{3} c + 28 \, a b c^{2} + 21 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} d^{2}\right)} e^{5} x^{5} + 10 \, {\left(7 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} d^{3} + 2 \, {\left(b^{3} c + 14 \, a b c^{2}\right)} d\right)} e^{4} x^{4} + 2 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} d^{7} + 2 \, {\left(35 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} d^{4} + b^{4} + 5 \, a b^{2} c + 36 \, a^{2} c^{2} + 20 \, {\left(b^{3} c + 14 \, a b c^{2}\right)} d^{2}\right)} e^{3} x^{3} + 4 \, {\left(b^{3} c + 14 \, a b c^{2}\right)} d^{5} + 2 \, {\left(21 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} d^{5} + 20 \, {\left(b^{3} c + 14 \, a b c^{2}\right)} d^{3} + 3 \, {\left(b^{4} + 5 \, a b^{2} c + 36 \, a^{2} c^{2}\right)} d\right)} e^{2} x^{2} + 2 \, {\left(b^{4} + 5 \, a b^{2} c + 36 \, a^{2} c^{2}\right)} d^{3} + 2 \, {\left(7 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} d^{6} + 10 \, {\left(b^{3} c + 14 \, a b c^{2}\right)} d^{4} - a b^{3} + 16 \, a^{2} b c + 3 \, {\left(b^{4} + 5 \, a b^{2} c + 36 \, a^{2} c^{2}\right)} d^{2}\right)} e x - \sqrt{\frac{1}{2}} {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} e^{9} x^{8} + 8 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3} + 14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{3} + 3 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3} + 70 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{4} + 30 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{5} + 10 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{3} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2} + 14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{6} + 15 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{4} + 3 \, {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{7} + 3 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{5} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{3} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{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)} d^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d^{2}\right)} e\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} + {\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)} e^{2} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{{\left(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)} e^{4}}}}{{\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)} e^{2}}} \log\left({\left(35 \, b^{6} c^{2} - 1491 \, a b^{4} c^{3} + 15000 \, a^{2} b^{2} c^{4} + 10000 \, a^{3} c^{5}\right)} e x + {\left(35 \, b^{6} c^{2} - 1491 \, a b^{4} c^{3} + 15000 \, a^{2} b^{2} c^{4} + 10000 \, a^{3} c^{5}\right)} d + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{14} - 38 \, a^{4} b^{12} c + 480 \, a^{5} b^{10} c^{2} - 2720 \, a^{6} b^{8} c^{3} + 6400 \, a^{7} b^{6} c^{4} + 1536 \, a^{8} b^{4} c^{5} - 32768 \, a^{9} b^{2} c^{6} + 40960 \, a^{10} c^{7}\right)} e^{3} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{{\left(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)} e^{4}}} - {\left(b^{11} - 53 \, a b^{9} c + 940 \, a^{2} b^{7} c^{2} - 6832 \, a^{3} b^{5} c^{3} + 21824 \, a^{4} b^{3} c^{4} - 25600 \, a^{5} b c^{5}\right)} e\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} + {\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)} e^{2} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{{\left(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)} e^{4}}}}{{\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)} e^{2}}}\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)} e^{9} x^{8} + 8 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3} + 14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{3} + 3 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3} + 70 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{4} + 30 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{5} + 10 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{3} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2} + 14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{6} + 15 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{4} + 3 \, {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{7} + 3 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{5} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{3} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{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)} d^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d^{2}\right)} e\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} + {\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)} e^{2} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{{\left(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)} e^{4}}}}{{\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)} e^{2}}} \log\left({\left(35 \, b^{6} c^{2} - 1491 \, a b^{4} c^{3} + 15000 \, a^{2} b^{2} c^{4} + 10000 \, a^{3} c^{5}\right)} e x + {\left(35 \, b^{6} c^{2} - 1491 \, a b^{4} c^{3} + 15000 \, a^{2} b^{2} c^{4} + 10000 \, a^{3} c^{5}\right)} d - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{14} - 38 \, a^{4} b^{12} c + 480 \, a^{5} b^{10} c^{2} - 2720 \, a^{6} b^{8} c^{3} + 6400 \, a^{7} b^{6} c^{4} + 1536 \, a^{8} b^{4} c^{5} - 32768 \, a^{9} b^{2} c^{6} + 40960 \, a^{10} c^{7}\right)} e^{3} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{{\left(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)} e^{4}}} - {\left(b^{11} - 53 \, a b^{9} c + 940 \, a^{2} b^{7} c^{2} - 6832 \, a^{3} b^{5} c^{3} + 21824 \, a^{4} b^{3} c^{4} - 25600 \, a^{5} b c^{5}\right)} e\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} + {\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)} e^{2} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{{\left(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)} e^{4}}}}{{\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)} e^{2}}}\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)} e^{9} x^{8} + 8 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3} + 14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{3} + 3 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3} + 70 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{4} + 30 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{5} + 10 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{3} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2} + 14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{6} + 15 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{4} + 3 \, {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{7} + 3 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{5} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{3} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{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)} d^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d^{2}\right)} e\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} - {\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)} e^{2} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{{\left(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)} e^{4}}}}{{\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)} e^{2}}} \log\left({\left(35 \, b^{6} c^{2} - 1491 \, a b^{4} c^{3} + 15000 \, a^{2} b^{2} c^{4} + 10000 \, a^{3} c^{5}\right)} e x + {\left(35 \, b^{6} c^{2} - 1491 \, a b^{4} c^{3} + 15000 \, a^{2} b^{2} c^{4} + 10000 \, a^{3} c^{5}\right)} d + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{14} - 38 \, a^{4} b^{12} c + 480 \, a^{5} b^{10} c^{2} - 2720 \, a^{6} b^{8} c^{3} + 6400 \, a^{7} b^{6} c^{4} + 1536 \, a^{8} b^{4} c^{5} - 32768 \, a^{9} b^{2} c^{6} + 40960 \, a^{10} c^{7}\right)} e^{3} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{{\left(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)} e^{4}}} + {\left(b^{11} - 53 \, a b^{9} c + 940 \, a^{2} b^{7} c^{2} - 6832 \, a^{3} b^{5} c^{3} + 21824 \, a^{4} b^{3} c^{4} - 25600 \, a^{5} b c^{5}\right)} e\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} - {\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)} e^{2} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{{\left(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)} e^{4}}}}{{\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)} e^{2}}}\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)} e^{9} x^{8} + 8 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3} + 14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{3} + 3 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3} + 70 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{4} + 30 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{5} + 10 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{3} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2} + 14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{6} + 15 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{4} + 3 \, {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{7} + 3 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{5} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{3} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{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)} d^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d^{2}\right)} e\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} - {\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)} e^{2} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{{\left(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)} e^{4}}}}{{\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)} e^{2}}} \log\left({\left(35 \, b^{6} c^{2} - 1491 \, a b^{4} c^{3} + 15000 \, a^{2} b^{2} c^{4} + 10000 \, a^{3} c^{5}\right)} e x + {\left(35 \, b^{6} c^{2} - 1491 \, a b^{4} c^{3} + 15000 \, a^{2} b^{2} c^{4} + 10000 \, a^{3} c^{5}\right)} d - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{14} - 38 \, a^{4} b^{12} c + 480 \, a^{5} b^{10} c^{2} - 2720 \, a^{6} b^{8} c^{3} + 6400 \, a^{7} b^{6} c^{4} + 1536 \, a^{8} b^{4} c^{5} - 32768 \, a^{9} b^{2} c^{6} + 40960 \, a^{10} c^{7}\right)} e^{3} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{{\left(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)} e^{4}}} + {\left(b^{11} - 53 \, a b^{9} c + 940 \, a^{2} b^{7} c^{2} - 6832 \, a^{3} b^{5} c^{3} + 21824 \, a^{4} b^{3} c^{4} - 25600 \, a^{5} b c^{5}\right)} e\right)} \sqrt{-\frac{b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3} - {\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)} e^{2} \sqrt{\frac{b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}}{{\left(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)} e^{4}}}}{{\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)} e^{2}}}\right) - 2 \, {\left(a b^{3} - 16 \, a^{2} b c\right)} d}{16 \, {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} e^{9} x^{8} + 8 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3} + 14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{3} + 3 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3} + 70 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{4} + 30 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{5} + 10 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{3} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2} + 14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{6} + 15 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{4} + 3 \, {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{7} + 3 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{5} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{3} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{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)} d^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d^{2}\right)} e\right)}}"," ",0,"1/16*(2*(b^2*c^2 + 20*a*c^3)*e^7*x^7 + 14*(b^2*c^2 + 20*a*c^3)*d*e^6*x^6 + 2*(2*b^3*c + 28*a*b*c^2 + 21*(b^2*c^2 + 20*a*c^3)*d^2)*e^5*x^5 + 10*(7*(b^2*c^2 + 20*a*c^3)*d^3 + 2*(b^3*c + 14*a*b*c^2)*d)*e^4*x^4 + 2*(b^2*c^2 + 20*a*c^3)*d^7 + 2*(35*(b^2*c^2 + 20*a*c^3)*d^4 + b^4 + 5*a*b^2*c + 36*a^2*c^2 + 20*(b^3*c + 14*a*b*c^2)*d^2)*e^3*x^3 + 4*(b^3*c + 14*a*b*c^2)*d^5 + 2*(21*(b^2*c^2 + 20*a*c^3)*d^5 + 20*(b^3*c + 14*a*b*c^2)*d^3 + 3*(b^4 + 5*a*b^2*c + 36*a^2*c^2)*d)*e^2*x^2 + 2*(b^4 + 5*a*b^2*c + 36*a^2*c^2)*d^3 + 2*(7*(b^2*c^2 + 20*a*c^3)*d^6 + 10*(b^3*c + 14*a*b*c^2)*d^4 - a*b^3 + 16*a^2*b*c + 3*(b^4 + 5*a*b^2*c + 36*a^2*c^2)*d^2)*e*x - sqrt(1/2)*((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*e^9*x^8 + 8*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d*e^8*x^7 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3 + 14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^2)*e^7*x^6 + 4*(14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^3 + 3*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d)*e^6*x^5 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3 + 70*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^4 + 30*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^2)*e^5*x^4 + 4*(14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^5 + 10*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^3 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d)*e^4*x^3 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2 + 14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^6 + 15*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^4 + 3*(a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^2)*e^3*x^2 + 4*(2*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^7 + 3*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^5 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^3 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d)*e^2*x + ((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^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)*d^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d^2)*e)*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 + (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)*e^2*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/((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)*e^4)))/((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)*e^2))*log((35*b^6*c^2 - 1491*a*b^4*c^3 + 15000*a^2*b^2*c^4 + 10000*a^3*c^5)*e*x + (35*b^6*c^2 - 1491*a*b^4*c^3 + 15000*a^2*b^2*c^4 + 10000*a^3*c^5)*d + 1/2*sqrt(1/2)*((a^3*b^14 - 38*a^4*b^12*c + 480*a^5*b^10*c^2 - 2720*a^6*b^8*c^3 + 6400*a^7*b^6*c^4 + 1536*a^8*b^4*c^5 - 32768*a^9*b^2*c^6 + 40960*a^10*c^7)*e^3*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/((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)*e^4)) - (b^11 - 53*a*b^9*c + 940*a^2*b^7*c^2 - 6832*a^3*b^5*c^3 + 21824*a^4*b^3*c^4 - 25600*a^5*b*c^5)*e)*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 + (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)*e^2*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/((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)*e^4)))/((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)*e^2))) + sqrt(1/2)*((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*e^9*x^8 + 8*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d*e^8*x^7 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3 + 14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^2)*e^7*x^6 + 4*(14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^3 + 3*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d)*e^6*x^5 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3 + 70*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^4 + 30*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^2)*e^5*x^4 + 4*(14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^5 + 10*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^3 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d)*e^4*x^3 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2 + 14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^6 + 15*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^4 + 3*(a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^2)*e^3*x^2 + 4*(2*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^7 + 3*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^5 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^3 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d)*e^2*x + ((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^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)*d^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d^2)*e)*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 + (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)*e^2*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/((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)*e^4)))/((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)*e^2))*log((35*b^6*c^2 - 1491*a*b^4*c^3 + 15000*a^2*b^2*c^4 + 10000*a^3*c^5)*e*x + (35*b^6*c^2 - 1491*a*b^4*c^3 + 15000*a^2*b^2*c^4 + 10000*a^3*c^5)*d - 1/2*sqrt(1/2)*((a^3*b^14 - 38*a^4*b^12*c + 480*a^5*b^10*c^2 - 2720*a^6*b^8*c^3 + 6400*a^7*b^6*c^4 + 1536*a^8*b^4*c^5 - 32768*a^9*b^2*c^6 + 40960*a^10*c^7)*e^3*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/((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)*e^4)) - (b^11 - 53*a*b^9*c + 940*a^2*b^7*c^2 - 6832*a^3*b^5*c^3 + 21824*a^4*b^3*c^4 - 25600*a^5*b*c^5)*e)*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 + (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)*e^2*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/((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)*e^4)))/((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)*e^2))) + sqrt(1/2)*((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*e^9*x^8 + 8*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d*e^8*x^7 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3 + 14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^2)*e^7*x^6 + 4*(14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^3 + 3*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d)*e^6*x^5 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3 + 70*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^4 + 30*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^2)*e^5*x^4 + 4*(14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^5 + 10*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^3 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d)*e^4*x^3 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2 + 14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^6 + 15*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^4 + 3*(a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^2)*e^3*x^2 + 4*(2*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^7 + 3*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^5 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^3 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d)*e^2*x + ((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^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)*d^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d^2)*e)*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 - (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)*e^2*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/((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)*e^4)))/((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)*e^2))*log((35*b^6*c^2 - 1491*a*b^4*c^3 + 15000*a^2*b^2*c^4 + 10000*a^3*c^5)*e*x + (35*b^6*c^2 - 1491*a*b^4*c^3 + 15000*a^2*b^2*c^4 + 10000*a^3*c^5)*d + 1/2*sqrt(1/2)*((a^3*b^14 - 38*a^4*b^12*c + 480*a^5*b^10*c^2 - 2720*a^6*b^8*c^3 + 6400*a^7*b^6*c^4 + 1536*a^8*b^4*c^5 - 32768*a^9*b^2*c^6 + 40960*a^10*c^7)*e^3*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/((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)*e^4)) + (b^11 - 53*a*b^9*c + 940*a^2*b^7*c^2 - 6832*a^3*b^5*c^3 + 21824*a^4*b^3*c^4 - 25600*a^5*b*c^5)*e)*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 - (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)*e^2*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/((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)*e^4)))/((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)*e^2))) - sqrt(1/2)*((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*e^9*x^8 + 8*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d*e^8*x^7 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3 + 14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^2)*e^7*x^6 + 4*(14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^3 + 3*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d)*e^6*x^5 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3 + 70*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^4 + 30*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^2)*e^5*x^4 + 4*(14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^5 + 10*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^3 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d)*e^4*x^3 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2 + 14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^6 + 15*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^4 + 3*(a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^2)*e^3*x^2 + 4*(2*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^7 + 3*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^5 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^3 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d)*e^2*x + ((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^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)*d^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d^2)*e)*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 - (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)*e^2*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/((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)*e^4)))/((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)*e^2))*log((35*b^6*c^2 - 1491*a*b^4*c^3 + 15000*a^2*b^2*c^4 + 10000*a^3*c^5)*e*x + (35*b^6*c^2 - 1491*a*b^4*c^3 + 15000*a^2*b^2*c^4 + 10000*a^3*c^5)*d - 1/2*sqrt(1/2)*((a^3*b^14 - 38*a^4*b^12*c + 480*a^5*b^10*c^2 - 2720*a^6*b^8*c^3 + 6400*a^7*b^6*c^4 + 1536*a^8*b^4*c^5 - 32768*a^9*b^2*c^6 + 40960*a^10*c^7)*e^3*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/((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)*e^4)) + (b^11 - 53*a*b^9*c + 940*a^2*b^7*c^2 - 6832*a^3*b^5*c^3 + 21824*a^4*b^3*c^4 - 25600*a^5*b*c^5)*e)*sqrt(-(b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3 - (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)*e^2*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)/((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)*e^4)))/((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)*e^2))) - 2*(a*b^3 - 16*a^2*b*c)*d)/((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*e^9*x^8 + 8*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d*e^8*x^7 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3 + 14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^2)*e^7*x^6 + 4*(14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^3 + 3*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d)*e^6*x^5 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3 + 70*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^4 + 30*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^2)*e^5*x^4 + 4*(14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^5 + 10*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^3 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d)*e^4*x^3 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2 + 14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^6 + 15*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^4 + 3*(a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^2)*e^3*x^2 + 4*(2*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^7 + 3*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^5 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^3 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d)*e^2*x + ((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^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)*d^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d^2)*e)","B",0
633,1,3708,0,1.469527," ","integrate((e*x+d)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{6} x^{6} + 72 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d e^{5} x^{5} + 18 \, {\left(b^{3} c^{2} - 4 \, a b c^{3} + 10 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2}\right)} e^{4} x^{4} + 12 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} + 24 \, {\left(10 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} + 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d\right)} e^{3} x^{3} - b^{5} + 14 \, a b^{3} c - 40 \, a^{2} b c^{2} + 18 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} + 4 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3} + 45 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} + 27 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2}\right)} e^{2} x^{2} + 4 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} d^{2} + 8 \, {\left(9 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{5} + 9 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} + {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} d\right)} e x + 12 \, {\left(c^{4} e^{8} x^{8} + 8 \, c^{4} d e^{7} x^{7} + 2 \, {\left(14 \, c^{4} d^{2} + b c^{3}\right)} e^{6} x^{6} + c^{4} d^{8} + 4 \, {\left(14 \, c^{4} d^{3} + 3 \, b c^{3} d\right)} e^{5} x^{5} + 2 \, b c^{3} d^{6} + {\left(70 \, c^{4} d^{4} + 30 \, b c^{3} d^{2} + b^{2} c^{2} + 2 \, a c^{3}\right)} e^{4} x^{4} + 4 \, {\left(14 \, c^{4} d^{5} + 10 \, b c^{3} d^{3} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d\right)} e^{3} x^{3} + 2 \, a b c^{2} d^{2} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} + 2 \, {\left(14 \, c^{4} d^{6} + 15 \, b c^{3} d^{4} + a b c^{2} + 3 \, {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2}\right)} e^{2} x^{2} + a^{2} c^{2} + 4 \, {\left(2 \, c^{4} d^{7} + 3 \, b c^{3} d^{5} + a b c^{2} d + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3}\right)} e x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c - {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right)}{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)} e^{9} x^{8} + 8 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d e^{8} x^{7} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{3} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d\right)} e^{6} x^{5} + {\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} + 70 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} + 30 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{5} + 10 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} + {\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)} d\right)} e^{4} x^{3} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{6} + 15 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{4} + 3 \, {\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)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{7} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{5} + {\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)} d^{3} + {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d\right)} e^{2} x + {\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)} d^{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)} d^{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)} d^{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)} d^{2}\right)} e\right)}}, \frac{12 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{6} x^{6} + 72 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d e^{5} x^{5} + 18 \, {\left(b^{3} c^{2} - 4 \, a b c^{3} + 10 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2}\right)} e^{4} x^{4} + 12 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} + 24 \, {\left(10 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} + 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d\right)} e^{3} x^{3} - b^{5} + 14 \, a b^{3} c - 40 \, a^{2} b c^{2} + 18 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} + 4 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3} + 45 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} + 27 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2}\right)} e^{2} x^{2} + 4 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} d^{2} + 8 \, {\left(9 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{5} + 9 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} + {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} d\right)} e x - 24 \, {\left(c^{4} e^{8} x^{8} + 8 \, c^{4} d e^{7} x^{7} + 2 \, {\left(14 \, c^{4} d^{2} + b c^{3}\right)} e^{6} x^{6} + c^{4} d^{8} + 4 \, {\left(14 \, c^{4} d^{3} + 3 \, b c^{3} d\right)} e^{5} x^{5} + 2 \, b c^{3} d^{6} + {\left(70 \, c^{4} d^{4} + 30 \, b c^{3} d^{2} + b^{2} c^{2} + 2 \, a c^{3}\right)} e^{4} x^{4} + 4 \, {\left(14 \, c^{4} d^{5} + 10 \, b c^{3} d^{3} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d\right)} e^{3} x^{3} + 2 \, a b c^{2} d^{2} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} + 2 \, {\left(14 \, c^{4} d^{6} + 15 \, b c^{3} d^{4} + a b c^{2} + 3 \, {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2}\right)} e^{2} x^{2} + a^{2} c^{2} + 4 \, {\left(2 \, c^{4} d^{7} + 3 \, b c^{3} d^{5} + a b c^{2} d + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3}\right)} e x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right)}{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)} e^{9} x^{8} + 8 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d e^{8} x^{7} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{3} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d\right)} e^{6} x^{5} + {\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} + 70 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} + 30 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{5} + 10 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} + {\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)} d\right)} e^{4} x^{3} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{6} + 15 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{4} + 3 \, {\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)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{7} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{5} + {\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)} d^{3} + {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d\right)} e^{2} x + {\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)} d^{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)} d^{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)} d^{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)} d^{2}\right)} e\right)}}\right]"," ",0,"[1/4*(12*(b^2*c^3 - 4*a*c^4)*e^6*x^6 + 72*(b^2*c^3 - 4*a*c^4)*d*e^5*x^5 + 18*(b^3*c^2 - 4*a*b*c^3 + 10*(b^2*c^3 - 4*a*c^4)*d^2)*e^4*x^4 + 12*(b^2*c^3 - 4*a*c^4)*d^6 + 24*(10*(b^2*c^3 - 4*a*c^4)*d^3 + 3*(b^3*c^2 - 4*a*b*c^3)*d)*e^3*x^3 - b^5 + 14*a*b^3*c - 40*a^2*b*c^2 + 18*(b^3*c^2 - 4*a*b*c^3)*d^4 + 4*(b^4*c + a*b^2*c^2 - 20*a^2*c^3 + 45*(b^2*c^3 - 4*a*c^4)*d^4 + 27*(b^3*c^2 - 4*a*b*c^3)*d^2)*e^2*x^2 + 4*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*d^2 + 8*(9*(b^2*c^3 - 4*a*c^4)*d^5 + 9*(b^3*c^2 - 4*a*b*c^3)*d^3 + (b^4*c + a*b^2*c^2 - 20*a^2*c^3)*d)*e*x + 12*(c^4*e^8*x^8 + 8*c^4*d*e^7*x^7 + 2*(14*c^4*d^2 + b*c^3)*e^6*x^6 + c^4*d^8 + 4*(14*c^4*d^3 + 3*b*c^3*d)*e^5*x^5 + 2*b*c^3*d^6 + (70*c^4*d^4 + 30*b*c^3*d^2 + b^2*c^2 + 2*a*c^3)*e^4*x^4 + 4*(14*c^4*d^5 + 10*b*c^3*d^3 + (b^2*c^2 + 2*a*c^3)*d)*e^3*x^3 + 2*a*b*c^2*d^2 + (b^2*c^2 + 2*a*c^3)*d^4 + 2*(14*c^4*d^6 + 15*b*c^3*d^4 + a*b*c^2 + 3*(b^2*c^2 + 2*a*c^3)*d^2)*e^2*x^2 + a^2*c^2 + 4*(2*c^4*d^7 + 3*b*c^3*d^5 + a*b*c^2*d + (b^2*c^2 + 2*a*c^3)*d^3)*e*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c - (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)))/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^9*x^8 + 8*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d*e^8*x^7 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2)*e^7*x^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^3 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d)*e^6*x^5 + (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 + 70*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 + 30*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2)*e^5*x^4 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^5 + 10*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3 + (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)*d)*e^4*x^3 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^6 + 15*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^4 + 3*(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)*d^2)*e^3*x^2 + 4*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^7 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^5 + (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)*d^3 + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d)*e^2*x + ((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^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)*d^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)*d^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2)*e), 1/4*(12*(b^2*c^3 - 4*a*c^4)*e^6*x^6 + 72*(b^2*c^3 - 4*a*c^4)*d*e^5*x^5 + 18*(b^3*c^2 - 4*a*b*c^3 + 10*(b^2*c^3 - 4*a*c^4)*d^2)*e^4*x^4 + 12*(b^2*c^3 - 4*a*c^4)*d^6 + 24*(10*(b^2*c^3 - 4*a*c^4)*d^3 + 3*(b^3*c^2 - 4*a*b*c^3)*d)*e^3*x^3 - b^5 + 14*a*b^3*c - 40*a^2*b*c^2 + 18*(b^3*c^2 - 4*a*b*c^3)*d^4 + 4*(b^4*c + a*b^2*c^2 - 20*a^2*c^3 + 45*(b^2*c^3 - 4*a*c^4)*d^4 + 27*(b^3*c^2 - 4*a*b*c^3)*d^2)*e^2*x^2 + 4*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*d^2 + 8*(9*(b^2*c^3 - 4*a*c^4)*d^5 + 9*(b^3*c^2 - 4*a*b*c^3)*d^3 + (b^4*c + a*b^2*c^2 - 20*a^2*c^3)*d)*e*x - 24*(c^4*e^8*x^8 + 8*c^4*d*e^7*x^7 + 2*(14*c^4*d^2 + b*c^3)*e^6*x^6 + c^4*d^8 + 4*(14*c^4*d^3 + 3*b*c^3*d)*e^5*x^5 + 2*b*c^3*d^6 + (70*c^4*d^4 + 30*b*c^3*d^2 + b^2*c^2 + 2*a*c^3)*e^4*x^4 + 4*(14*c^4*d^5 + 10*b*c^3*d^3 + (b^2*c^2 + 2*a*c^3)*d)*e^3*x^3 + 2*a*b*c^2*d^2 + (b^2*c^2 + 2*a*c^3)*d^4 + 2*(14*c^4*d^6 + 15*b*c^3*d^4 + a*b*c^2 + 3*(b^2*c^2 + 2*a*c^3)*d^2)*e^2*x^2 + a^2*c^2 + 4*(2*c^4*d^7 + 3*b*c^3*d^5 + a*b*c^2*d + (b^2*c^2 + 2*a*c^3)*d^3)*e*x)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)))/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^9*x^8 + 8*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d*e^8*x^7 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2)*e^7*x^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^3 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d)*e^6*x^5 + (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 + 70*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 + 30*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2)*e^5*x^4 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^5 + 10*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3 + (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)*d)*e^4*x^3 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^6 + 15*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^4 + 3*(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)*d^2)*e^3*x^2 + 4*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^7 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^5 + (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)*d^3 + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d)*e^2*x + ((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^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)*d^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)*d^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2)*e)]","B",0
634,1,8554,0,2.545974," ","integrate(1/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""fricas"")","\frac{6 \, {\left(b^{3} c^{2} - 8 \, a b c^{3}\right)} e^{7} x^{7} + 42 \, {\left(b^{3} c^{2} - 8 \, a b c^{3}\right)} d e^{6} x^{6} + 2 \, {\left(6 \, b^{4} c - 49 \, a b^{2} c^{2} + 28 \, a^{2} c^{3} + 63 \, {\left(b^{3} c^{2} - 8 \, a b c^{3}\right)} d^{2}\right)} e^{5} x^{5} + 10 \, {\left(21 \, {\left(b^{3} c^{2} - 8 \, a b c^{3}\right)} d^{3} + {\left(6 \, b^{4} c - 49 \, a b^{2} c^{2} + 28 \, a^{2} c^{3}\right)} d\right)} e^{4} x^{4} + 6 \, {\left(b^{3} c^{2} - 8 \, a b c^{3}\right)} d^{7} + 2 \, {\left(3 \, b^{5} - 20 \, a b^{3} c - 4 \, a^{2} b c^{2} + 105 \, {\left(b^{3} c^{2} - 8 \, a b c^{3}\right)} d^{4} + 10 \, {\left(6 \, b^{4} c - 49 \, a b^{2} c^{2} + 28 \, a^{2} c^{3}\right)} d^{2}\right)} e^{3} x^{3} + 2 \, {\left(6 \, b^{4} c - 49 \, a b^{2} c^{2} + 28 \, a^{2} c^{3}\right)} d^{5} + 2 \, {\left(63 \, {\left(b^{3} c^{2} - 8 \, a b c^{3}\right)} d^{5} + 10 \, {\left(6 \, b^{4} c - 49 \, a b^{2} c^{2} + 28 \, a^{2} c^{3}\right)} d^{3} + 3 \, {\left(3 \, b^{5} - 20 \, a b^{3} c - 4 \, a^{2} b c^{2}\right)} d\right)} e^{2} x^{2} + 2 \, {\left(3 \, b^{5} - 20 \, a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} + 2 \, {\left(21 \, {\left(b^{3} c^{2} - 8 \, a b c^{3}\right)} d^{6} + 5 \, a b^{4} - 37 \, a^{2} b^{2} c + 44 \, a^{3} c^{2} + 5 \, {\left(6 \, b^{4} c - 49 \, a b^{2} c^{2} + 28 \, a^{2} c^{3}\right)} d^{4} + 3 \, {\left(3 \, b^{5} - 20 \, a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{2}\right)} e 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)} e^{9} x^{8} + 8 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3} + 14 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{3} + 3 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3} + 70 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{4} + 30 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{5} + 10 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{3} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2} + 14 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{6} + 15 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{4} + 3 \, {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{7} + 3 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{5} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} d^{3} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{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)} d^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} d^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d^{2}\right)} e\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} + {\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)} e^{2} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{{\left(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)} e^{4}}}}{{\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)} e^{2}}} \log\left(27 \, {\left(21 \, b^{8} c^{3} - 447 \, a b^{6} c^{4} + 4189 \, a^{2} b^{4} c^{5} - 19208 \, a^{3} b^{2} c^{6} + 38416 \, a^{4} c^{7}\right)} e x + 27 \, {\left(21 \, b^{8} c^{3} - 447 \, a b^{6} c^{4} + 4189 \, a^{2} b^{4} c^{5} - 19208 \, a^{3} b^{2} c^{6} + 38416 \, a^{4} c^{7}\right)} d + \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left({\left(a^{5} b^{15} - 31 \, a^{6} b^{13} c + 424 \, a^{7} b^{11} c^{2} - 3280 \, a^{8} b^{9} c^{3} + 15360 \, a^{9} b^{7} c^{4} - 43264 \, a^{10} b^{5} c^{5} + 67584 \, a^{11} b^{3} c^{6} - 45056 \, a^{12} b c^{7}\right)} e^{3} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{{\left(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)} e^{4}}} - {\left(b^{14} - 32 \, a b^{12} c + 464 \, a^{2} b^{10} c^{2} - 3885 \, a^{3} b^{8} c^{3} + 20088 \, a^{4} b^{6} c^{4} - 63680 \, a^{5} b^{4} c^{5} + 113792 \, a^{6} b^{2} c^{6} - 87808 \, a^{7} c^{7}\right)} e\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} + {\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)} e^{2} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{{\left(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)} e^{4}}}}{{\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)} e^{2}}}\right) - 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)} e^{9} x^{8} + 8 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3} + 14 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{3} + 3 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3} + 70 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{4} + 30 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{5} + 10 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{3} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2} + 14 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{6} + 15 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{4} + 3 \, {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{7} + 3 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{5} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} d^{3} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{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)} d^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} d^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d^{2}\right)} e\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} + {\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)} e^{2} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{{\left(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)} e^{4}}}}{{\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)} e^{2}}} \log\left(27 \, {\left(21 \, b^{8} c^{3} - 447 \, a b^{6} c^{4} + 4189 \, a^{2} b^{4} c^{5} - 19208 \, a^{3} b^{2} c^{6} + 38416 \, a^{4} c^{7}\right)} e x + 27 \, {\left(21 \, b^{8} c^{3} - 447 \, a b^{6} c^{4} + 4189 \, a^{2} b^{4} c^{5} - 19208 \, a^{3} b^{2} c^{6} + 38416 \, a^{4} c^{7}\right)} d - \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left({\left(a^{5} b^{15} - 31 \, a^{6} b^{13} c + 424 \, a^{7} b^{11} c^{2} - 3280 \, a^{8} b^{9} c^{3} + 15360 \, a^{9} b^{7} c^{4} - 43264 \, a^{10} b^{5} c^{5} + 67584 \, a^{11} b^{3} c^{6} - 45056 \, a^{12} b c^{7}\right)} e^{3} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{{\left(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)} e^{4}}} - {\left(b^{14} - 32 \, a b^{12} c + 464 \, a^{2} b^{10} c^{2} - 3885 \, a^{3} b^{8} c^{3} + 20088 \, a^{4} b^{6} c^{4} - 63680 \, a^{5} b^{4} c^{5} + 113792 \, a^{6} b^{2} c^{6} - 87808 \, a^{7} c^{7}\right)} e\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} + {\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)} e^{2} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{{\left(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)} e^{4}}}}{{\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)} e^{2}}}\right) - 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)} e^{9} x^{8} + 8 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3} + 14 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{3} + 3 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3} + 70 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{4} + 30 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{5} + 10 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{3} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2} + 14 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{6} + 15 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{4} + 3 \, {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{7} + 3 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{5} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} d^{3} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{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)} d^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} d^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d^{2}\right)} e\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} - {\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)} e^{2} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{{\left(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)} e^{4}}}}{{\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)} e^{2}}} \log\left(27 \, {\left(21 \, b^{8} c^{3} - 447 \, a b^{6} c^{4} + 4189 \, a^{2} b^{4} c^{5} - 19208 \, a^{3} b^{2} c^{6} + 38416 \, a^{4} c^{7}\right)} e x + 27 \, {\left(21 \, b^{8} c^{3} - 447 \, a b^{6} c^{4} + 4189 \, a^{2} b^{4} c^{5} - 19208 \, a^{3} b^{2} c^{6} + 38416 \, a^{4} c^{7}\right)} d + \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left({\left(a^{5} b^{15} - 31 \, a^{6} b^{13} c + 424 \, a^{7} b^{11} c^{2} - 3280 \, a^{8} b^{9} c^{3} + 15360 \, a^{9} b^{7} c^{4} - 43264 \, a^{10} b^{5} c^{5} + 67584 \, a^{11} b^{3} c^{6} - 45056 \, a^{12} b c^{7}\right)} e^{3} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{{\left(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)} e^{4}}} + {\left(b^{14} - 32 \, a b^{12} c + 464 \, a^{2} b^{10} c^{2} - 3885 \, a^{3} b^{8} c^{3} + 20088 \, a^{4} b^{6} c^{4} - 63680 \, a^{5} b^{4} c^{5} + 113792 \, a^{6} b^{2} c^{6} - 87808 \, a^{7} c^{7}\right)} e\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} - {\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)} e^{2} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{{\left(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)} e^{4}}}}{{\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)} e^{2}}}\right) + 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)} e^{9} x^{8} + 8 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3} + 14 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{3} + 3 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3} + 70 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{4} + 30 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{5} + 10 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{3} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2} + 14 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{6} + 15 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{4} + 3 \, {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{7} + 3 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{5} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} d^{3} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{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)} d^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} d^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d^{2}\right)} e\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} - {\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)} e^{2} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{{\left(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)} e^{4}}}}{{\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)} e^{2}}} \log\left(27 \, {\left(21 \, b^{8} c^{3} - 447 \, a b^{6} c^{4} + 4189 \, a^{2} b^{4} c^{5} - 19208 \, a^{3} b^{2} c^{6} + 38416 \, a^{4} c^{7}\right)} e x + 27 \, {\left(21 \, b^{8} c^{3} - 447 \, a b^{6} c^{4} + 4189 \, a^{2} b^{4} c^{5} - 19208 \, a^{3} b^{2} c^{6} + 38416 \, a^{4} c^{7}\right)} d - \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left({\left(a^{5} b^{15} - 31 \, a^{6} b^{13} c + 424 \, a^{7} b^{11} c^{2} - 3280 \, a^{8} b^{9} c^{3} + 15360 \, a^{9} b^{7} c^{4} - 43264 \, a^{10} b^{5} c^{5} + 67584 \, a^{11} b^{3} c^{6} - 45056 \, a^{12} b c^{7}\right)} e^{3} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{{\left(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)} e^{4}}} + {\left(b^{14} - 32 \, a b^{12} c + 464 \, a^{2} b^{10} c^{2} - 3885 \, a^{3} b^{8} c^{3} + 20088 \, a^{4} b^{6} c^{4} - 63680 \, a^{5} b^{4} c^{5} + 113792 \, a^{6} b^{2} c^{6} - 87808 \, a^{7} c^{7}\right)} e\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} - {\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)} e^{2} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{{\left(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)} e^{4}}}}{{\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)} e^{2}}}\right) + 2 \, {\left(5 \, a b^{4} - 37 \, a^{2} b^{2} c + 44 \, a^{3} c^{2}\right)} d}{16 \, {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} e^{9} x^{8} + 8 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3} + 14 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{3} + 3 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3} + 70 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{4} + 30 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{5} + 10 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{3} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2} + 14 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{6} + 15 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{4} + 3 \, {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{7} + 3 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{5} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} d^{3} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{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)} d^{6} + {\left(a^{2} b^{6} - 6 \, a^{3} b^{4} c + 32 \, a^{5} c^{3}\right)} d^{4} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d^{2}\right)} e\right)}}"," ",0,"1/16*(6*(b^3*c^2 - 8*a*b*c^3)*e^7*x^7 + 42*(b^3*c^2 - 8*a*b*c^3)*d*e^6*x^6 + 2*(6*b^4*c - 49*a*b^2*c^2 + 28*a^2*c^3 + 63*(b^3*c^2 - 8*a*b*c^3)*d^2)*e^5*x^5 + 10*(21*(b^3*c^2 - 8*a*b*c^3)*d^3 + (6*b^4*c - 49*a*b^2*c^2 + 28*a^2*c^3)*d)*e^4*x^4 + 6*(b^3*c^2 - 8*a*b*c^3)*d^7 + 2*(3*b^5 - 20*a*b^3*c - 4*a^2*b*c^2 + 105*(b^3*c^2 - 8*a*b*c^3)*d^4 + 10*(6*b^4*c - 49*a*b^2*c^2 + 28*a^2*c^3)*d^2)*e^3*x^3 + 2*(6*b^4*c - 49*a*b^2*c^2 + 28*a^2*c^3)*d^5 + 2*(63*(b^3*c^2 - 8*a*b*c^3)*d^5 + 10*(6*b^4*c - 49*a*b^2*c^2 + 28*a^2*c^3)*d^3 + 3*(3*b^5 - 20*a*b^3*c - 4*a^2*b*c^2)*d)*e^2*x^2 + 2*(3*b^5 - 20*a*b^3*c - 4*a^2*b*c^2)*d^3 + 2*(21*(b^3*c^2 - 8*a*b*c^3)*d^6 + 5*a*b^4 - 37*a^2*b^2*c + 44*a^3*c^2 + 5*(6*b^4*c - 49*a*b^2*c^2 + 28*a^2*c^3)*d^4 + 3*(3*b^5 - 20*a*b^3*c - 4*a^2*b*c^2)*d^2)*e*x + 3*sqrt(1/2)*((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*e^9*x^8 + 8*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d*e^8*x^7 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3 + 14*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^2)*e^7*x^6 + 4*(14*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^3 + 3*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d)*e^6*x^5 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3 + 70*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^4 + 30*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^2)*e^5*x^4 + 4*(14*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^5 + 10*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^3 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*d)*e^4*x^3 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2 + 14*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^6 + 15*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^4 + 3*(a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*d^2)*e^3*x^2 + 4*(2*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^7 + 3*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^5 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*d^3 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d)*e^2*x + ((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^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)*d^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*d^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d^2)*e)*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 + (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)*e^2*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/((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)*e^4)))/((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)*e^2))*log(27*(21*b^8*c^3 - 447*a*b^6*c^4 + 4189*a^2*b^4*c^5 - 19208*a^3*b^2*c^6 + 38416*a^4*c^7)*e*x + 27*(21*b^8*c^3 - 447*a*b^6*c^4 + 4189*a^2*b^4*c^5 - 19208*a^3*b^2*c^6 + 38416*a^4*c^7)*d + 27/2*sqrt(1/2)*((a^5*b^15 - 31*a^6*b^13*c + 424*a^7*b^11*c^2 - 3280*a^8*b^9*c^3 + 15360*a^9*b^7*c^4 - 43264*a^10*b^5*c^5 + 67584*a^11*b^3*c^6 - 45056*a^12*b*c^7)*e^3*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/((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)*e^4)) - (b^14 - 32*a*b^12*c + 464*a^2*b^10*c^2 - 3885*a^3*b^8*c^3 + 20088*a^4*b^6*c^4 - 63680*a^5*b^4*c^5 + 113792*a^6*b^2*c^6 - 87808*a^7*c^7)*e)*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 + (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)*e^2*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/((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)*e^4)))/((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)*e^2))) - 3*sqrt(1/2)*((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*e^9*x^8 + 8*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d*e^8*x^7 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3 + 14*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^2)*e^7*x^6 + 4*(14*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^3 + 3*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d)*e^6*x^5 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3 + 70*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^4 + 30*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^2)*e^5*x^4 + 4*(14*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^5 + 10*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^3 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*d)*e^4*x^3 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2 + 14*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^6 + 15*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^4 + 3*(a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*d^2)*e^3*x^2 + 4*(2*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^7 + 3*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^5 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*d^3 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d)*e^2*x + ((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^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)*d^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*d^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d^2)*e)*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 + (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)*e^2*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/((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)*e^4)))/((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)*e^2))*log(27*(21*b^8*c^3 - 447*a*b^6*c^4 + 4189*a^2*b^4*c^5 - 19208*a^3*b^2*c^6 + 38416*a^4*c^7)*e*x + 27*(21*b^8*c^3 - 447*a*b^6*c^4 + 4189*a^2*b^4*c^5 - 19208*a^3*b^2*c^6 + 38416*a^4*c^7)*d - 27/2*sqrt(1/2)*((a^5*b^15 - 31*a^6*b^13*c + 424*a^7*b^11*c^2 - 3280*a^8*b^9*c^3 + 15360*a^9*b^7*c^4 - 43264*a^10*b^5*c^5 + 67584*a^11*b^3*c^6 - 45056*a^12*b*c^7)*e^3*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/((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)*e^4)) - (b^14 - 32*a*b^12*c + 464*a^2*b^10*c^2 - 3885*a^3*b^8*c^3 + 20088*a^4*b^6*c^4 - 63680*a^5*b^4*c^5 + 113792*a^6*b^2*c^6 - 87808*a^7*c^7)*e)*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 + (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)*e^2*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/((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)*e^4)))/((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)*e^2))) - 3*sqrt(1/2)*((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*e^9*x^8 + 8*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d*e^8*x^7 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3 + 14*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^2)*e^7*x^6 + 4*(14*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^3 + 3*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d)*e^6*x^5 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3 + 70*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^4 + 30*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^2)*e^5*x^4 + 4*(14*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^5 + 10*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^3 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*d)*e^4*x^3 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2 + 14*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^6 + 15*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^4 + 3*(a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*d^2)*e^3*x^2 + 4*(2*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^7 + 3*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^5 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*d^3 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d)*e^2*x + ((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^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)*d^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*d^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d^2)*e)*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 - (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)*e^2*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/((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)*e^4)))/((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)*e^2))*log(27*(21*b^8*c^3 - 447*a*b^6*c^4 + 4189*a^2*b^4*c^5 - 19208*a^3*b^2*c^6 + 38416*a^4*c^7)*e*x + 27*(21*b^8*c^3 - 447*a*b^6*c^4 + 4189*a^2*b^4*c^5 - 19208*a^3*b^2*c^6 + 38416*a^4*c^7)*d + 27/2*sqrt(1/2)*((a^5*b^15 - 31*a^6*b^13*c + 424*a^7*b^11*c^2 - 3280*a^8*b^9*c^3 + 15360*a^9*b^7*c^4 - 43264*a^10*b^5*c^5 + 67584*a^11*b^3*c^6 - 45056*a^12*b*c^7)*e^3*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/((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)*e^4)) + (b^14 - 32*a*b^12*c + 464*a^2*b^10*c^2 - 3885*a^3*b^8*c^3 + 20088*a^4*b^6*c^4 - 63680*a^5*b^4*c^5 + 113792*a^6*b^2*c^6 - 87808*a^7*c^7)*e)*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 - (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)*e^2*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/((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)*e^4)))/((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)*e^2))) + 3*sqrt(1/2)*((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*e^9*x^8 + 8*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d*e^8*x^7 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3 + 14*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^2)*e^7*x^6 + 4*(14*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^3 + 3*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d)*e^6*x^5 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3 + 70*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^4 + 30*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^2)*e^5*x^4 + 4*(14*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^5 + 10*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^3 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*d)*e^4*x^3 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2 + 14*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^6 + 15*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^4 + 3*(a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*d^2)*e^3*x^2 + 4*(2*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^7 + 3*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^5 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*d^3 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d)*e^2*x + ((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^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)*d^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*d^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d^2)*e)*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 - (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)*e^2*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/((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)*e^4)))/((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)*e^2))*log(27*(21*b^8*c^3 - 447*a*b^6*c^4 + 4189*a^2*b^4*c^5 - 19208*a^3*b^2*c^6 + 38416*a^4*c^7)*e*x + 27*(21*b^8*c^3 - 447*a*b^6*c^4 + 4189*a^2*b^4*c^5 - 19208*a^3*b^2*c^6 + 38416*a^4*c^7)*d - 27/2*sqrt(1/2)*((a^5*b^15 - 31*a^6*b^13*c + 424*a^7*b^11*c^2 - 3280*a^8*b^9*c^3 + 15360*a^9*b^7*c^4 - 43264*a^10*b^5*c^5 + 67584*a^11*b^3*c^6 - 45056*a^12*b*c^7)*e^3*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/((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)*e^4)) + (b^14 - 32*a*b^12*c + 464*a^2*b^10*c^2 - 3885*a^3*b^8*c^3 + 20088*a^4*b^6*c^4 - 63680*a^5*b^4*c^5 + 113792*a^6*b^2*c^6 - 87808*a^7*c^7)*e)*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 - (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)*e^2*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/((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)*e^4)))/((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)*e^2))) + 2*(5*a*b^4 - 37*a^2*b^2*c + 44*a^3*c^2)*d)/((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*e^9*x^8 + 8*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d*e^8*x^7 + 2*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3 + 14*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^2)*e^7*x^6 + 4*(14*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^3 + 3*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d)*e^6*x^5 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3 + 70*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^4 + 30*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^2)*e^5*x^4 + 4*(14*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^5 + 10*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^3 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*d)*e^4*x^3 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2 + 14*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^6 + 15*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^4 + 3*(a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*d^2)*e^3*x^2 + 4*(2*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^7 + 3*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^5 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*d^3 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d)*e^2*x + ((a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^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)*d^6 + (a^2*b^6 - 6*a^3*b^4*c + 32*a^5*c^3)*d^4 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d^2)*e)","B",0
635,1,9908,0,4.114468," ","integrate(1/(e*x+d)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} e^{6} x^{6} + 12 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d e^{5} x^{5} + {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4} + 30 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + 3 \, a^{2} b^{6} - 33 \, a^{3} b^{4} c + 108 \, a^{4} b^{2} c^{2} - 96 \, a^{5} c^{3} + 2 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d^{6} + 4 \, {\left(10 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d^{3} + {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} d\right)} e^{3} x^{3} + {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} d^{4} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 23 \, a^{3} b^{3} c^{2} + 4 \, a^{4} b c^{3} + 15 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d^{4} + 3 \, {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} d^{2}\right)} e^{2} x^{2} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 23 \, a^{3} b^{3} c^{2} + 4 \, a^{4} b c^{3}\right)} d^{2} + 4 \, {\left(3 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d^{5} + {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} d^{3} + {\left(a b^{7} - 10 \, a^{2} b^{5} c + 23 \, a^{3} b^{3} c^{2} + 4 \, a^{4} b c^{3}\right)} d\right)} e x + {\left({\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} e^{8} x^{8} + 8 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d e^{7} x^{7} + 2 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3} + 14 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{2}\right)} e^{6} x^{6} + 4 \, {\left(14 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{3} + 3 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d\right)} e^{5} x^{5} + {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{8} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3} + 70 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{4} + 30 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d^{2}\right)} e^{4} x^{4} + a^{2} b^{5} - 10 \, a^{3} b^{3} c + 30 \, a^{4} b c^{2} + 2 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d^{6} + 4 \, {\left(14 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{5} + 10 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d^{3} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} d\right)} e^{3} x^{3} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} d^{4} + 2 \, {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2} + 14 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{6} + 15 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d^{4} + 3 \, {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} d^{2}\right)} e^{2} x^{2} + 2 \, {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2}\right)} d^{2} + 4 \, {\left(2 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{7} + 3 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d^{5} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} d^{3} + {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2}\right)} d\right)} e x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c + {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right) - {\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)} e^{8} x^{8} + 8 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d e^{7} x^{7} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2}\right)} e^{6} x^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{3} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d\right)} e^{5} x^{5} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{8} + {\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} + 70 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} + 30 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + 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)} d^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{5} + 10 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} + {\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)} d\right)} e^{3} x^{3} + {\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)} d^{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} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{6} + 15 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{4} + 3 \, {\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)} d^{2}\right)} e^{2} x^{2} + 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)} d^{2} + 4 \, {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{7} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{5} + {\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)} d^{3} + {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d\right)} e x\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 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)} e^{8} x^{8} + 8 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d e^{7} x^{7} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2}\right)} e^{6} x^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{3} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d\right)} e^{5} x^{5} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{8} + {\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} + 70 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} + 30 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + 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)} d^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{5} + 10 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} + {\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)} d\right)} e^{3} x^{3} + {\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)} d^{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} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{6} + 15 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{4} + 3 \, {\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)} d^{2}\right)} e^{2} x^{2} + 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)} d^{2} + 4 \, {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{7} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{5} + {\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)} d^{3} + {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d\right)} e x\right)} \log\left(e x + d\right)}{4 \, {\left({\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)} e^{9} x^{8} + 8 \, {\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)} d e^{8} x^{7} + 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} + 14 \, {\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)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\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)} d^{3} + 3 \, {\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)} d\right)} e^{6} x^{5} + {\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} + 70 \, {\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)} d^{4} + 30 \, {\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)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\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)} d^{5} + 10 \, {\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)} d^{3} + {\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)} d\right)} e^{4} x^{3} + 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} + 14 \, {\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)} d^{6} + 15 \, {\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)} d^{4} + 3 \, {\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)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\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)} d^{7} + 3 \, {\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)} d^{5} + {\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)} d^{3} + {\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)} d\right)} e^{2} x + {\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)} d^{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)} d^{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)} d^{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)} d^{2}\right)} e\right)}}, \frac{2 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} e^{6} x^{6} + 12 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d e^{5} x^{5} + {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4} + 30 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + 3 \, a^{2} b^{6} - 33 \, a^{3} b^{4} c + 108 \, a^{4} b^{2} c^{2} - 96 \, a^{5} c^{3} + 2 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d^{6} + 4 \, {\left(10 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d^{3} + {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} d\right)} e^{3} x^{3} + {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} d^{4} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 23 \, a^{3} b^{3} c^{2} + 4 \, a^{4} b c^{3} + 15 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d^{4} + 3 \, {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} d^{2}\right)} e^{2} x^{2} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 23 \, a^{3} b^{3} c^{2} + 4 \, a^{4} b c^{3}\right)} d^{2} + 4 \, {\left(3 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d^{5} + {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} d^{3} + {\left(a b^{7} - 10 \, a^{2} b^{5} c + 23 \, a^{3} b^{3} c^{2} + 4 \, a^{4} b c^{3}\right)} d\right)} e x + 2 \, {\left({\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} e^{8} x^{8} + 8 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d e^{7} x^{7} + 2 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3} + 14 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{2}\right)} e^{6} x^{6} + 4 \, {\left(14 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{3} + 3 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d\right)} e^{5} x^{5} + {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{8} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3} + 70 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{4} + 30 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d^{2}\right)} e^{4} x^{4} + a^{2} b^{5} - 10 \, a^{3} b^{3} c + 30 \, a^{4} b c^{2} + 2 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d^{6} + 4 \, {\left(14 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{5} + 10 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d^{3} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} d\right)} e^{3} x^{3} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} d^{4} + 2 \, {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2} + 14 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{6} + 15 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d^{4} + 3 \, {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} d^{2}\right)} e^{2} x^{2} + 2 \, {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2}\right)} d^{2} + 4 \, {\left(2 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{7} + 3 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d^{5} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} d^{3} + {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2}\right)} d\right)} e x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\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)} e^{8} x^{8} + 8 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d e^{7} x^{7} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2}\right)} e^{6} x^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{3} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d\right)} e^{5} x^{5} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{8} + {\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} + 70 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} + 30 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + 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)} d^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{5} + 10 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} + {\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)} d\right)} e^{3} x^{3} + {\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)} d^{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} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{6} + 15 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{4} + 3 \, {\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)} d^{2}\right)} e^{2} x^{2} + 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)} d^{2} + 4 \, {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{7} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{5} + {\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)} d^{3} + {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d\right)} e x\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 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)} e^{8} x^{8} + 8 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d e^{7} x^{7} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2}\right)} e^{6} x^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{3} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d\right)} e^{5} x^{5} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{8} + {\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} + 70 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} + 30 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + 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)} d^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{5} + 10 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} + {\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)} d\right)} e^{3} x^{3} + {\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)} d^{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} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{6} + 15 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{4} + 3 \, {\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)} d^{2}\right)} e^{2} x^{2} + 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)} d^{2} + 4 \, {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{7} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{5} + {\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)} d^{3} + {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d\right)} e x\right)} \log\left(e x + d\right)}{4 \, {\left({\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)} e^{9} x^{8} + 8 \, {\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)} d e^{8} x^{7} + 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} + 14 \, {\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)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\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)} d^{3} + 3 \, {\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)} d\right)} e^{6} x^{5} + {\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} + 70 \, {\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)} d^{4} + 30 \, {\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)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\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)} d^{5} + 10 \, {\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)} d^{3} + {\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)} d\right)} e^{4} x^{3} + 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} + 14 \, {\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)} d^{6} + 15 \, {\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)} d^{4} + 3 \, {\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)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\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)} d^{7} + 3 \, {\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)} d^{5} + {\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)} d^{3} + {\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)} d\right)} e^{2} x + {\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)} d^{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)} d^{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)} d^{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)} d^{2}\right)} e\right)}}\right]"," ",0,"[1/4*(2*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*e^6*x^6 + 12*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d*e^5*x^5 + (4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4 + 30*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d^2)*e^4*x^4 + 3*a^2*b^6 - 33*a^3*b^4*c + 108*a^4*b^2*c^2 - 96*a^5*c^3 + 2*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d^6 + 4*(10*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d^3 + (4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4)*d)*e^3*x^3 + (4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4)*d^4 + 2*(a*b^7 - 10*a^2*b^5*c + 23*a^3*b^3*c^2 + 4*a^4*b*c^3 + 15*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d^4 + 3*(4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4)*d^2)*e^2*x^2 + 2*(a*b^7 - 10*a^2*b^5*c + 23*a^3*b^3*c^2 + 4*a^4*b*c^3)*d^2 + 4*(3*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d^5 + (4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4)*d^3 + (a*b^7 - 10*a^2*b^5*c + 23*a^3*b^3*c^2 + 4*a^4*b*c^3)*d)*e*x + ((b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*e^8*x^8 + 8*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d*e^7*x^7 + 2*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3 + 14*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^2)*e^6*x^6 + 4*(14*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^3 + 3*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d)*e^5*x^5 + (b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^8 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3 + 70*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^4 + 30*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d^2)*e^4*x^4 + a^2*b^5 - 10*a^3*b^3*c + 30*a^4*b*c^2 + 2*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d^6 + 4*(14*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^5 + 10*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d^3 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*d)*e^3*x^3 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*d^4 + 2*(a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2 + 14*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^6 + 15*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d^4 + 3*(b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*d^2)*e^2*x^2 + 2*(a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2)*d^2 + 4*(2*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^7 + 3*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d^5 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*d^3 + (a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2)*d)*e*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c + (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)) - ((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^8*x^8 + 8*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d*e^7*x^7 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2)*e^6*x^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^3 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d)*e^5*x^5 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^8 + (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 + 70*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 + 30*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2)*e^4*x^4 + 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)*d^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^5 + 10*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3 + (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)*d)*e^3*x^3 + (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)*d^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^6 + 15*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^4 + 3*(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)*d^2)*e^2*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2 + 4*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^7 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^5 + (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)*d^3 + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d)*e*x)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 4*((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^8*x^8 + 8*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d*e^7*x^7 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2)*e^6*x^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^3 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d)*e^5*x^5 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^8 + (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 + 70*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 + 30*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2)*e^4*x^4 + 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)*d^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^5 + 10*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3 + (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)*d)*e^3*x^3 + (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)*d^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^6 + 15*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^4 + 3*(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)*d^2)*e^2*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2 + 4*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^7 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^5 + (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)*d^3 + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d)*e*x)*log(e*x + d))/((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)*e^9*x^8 + 8*(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)*d*e^8*x^7 + 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 + 14*(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)*d^2)*e^7*x^6 + 4*(14*(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)*d^3 + 3*(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)*d)*e^6*x^5 + (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 + 70*(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)*d^4 + 30*(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)*d^2)*e^5*x^4 + 4*(14*(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)*d^5 + 10*(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)*d^3 + (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)*d)*e^4*x^3 + 2*(a^4*b^7 - 12*a^5*b^5*c + 48*a^6*b^3*c^2 - 64*a^7*b*c^3 + 14*(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)*d^6 + 15*(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)*d^4 + 3*(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)*d^2)*e^3*x^2 + 4*(2*(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)*d^7 + 3*(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)*d^5 + (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)*d^3 + (a^4*b^7 - 12*a^5*b^5*c + 48*a^6*b^3*c^2 - 64*a^7*b*c^3)*d)*e^2*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)*d^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)*d^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)*d^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)*d^2)*e), 1/4*(2*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*e^6*x^6 + 12*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d*e^5*x^5 + (4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4 + 30*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d^2)*e^4*x^4 + 3*a^2*b^6 - 33*a^3*b^4*c + 108*a^4*b^2*c^2 - 96*a^5*c^3 + 2*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d^6 + 4*(10*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d^3 + (4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4)*d)*e^3*x^3 + (4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4)*d^4 + 2*(a*b^7 - 10*a^2*b^5*c + 23*a^3*b^3*c^2 + 4*a^4*b*c^3 + 15*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d^4 + 3*(4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4)*d^2)*e^2*x^2 + 2*(a*b^7 - 10*a^2*b^5*c + 23*a^3*b^3*c^2 + 4*a^4*b*c^3)*d^2 + 4*(3*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d^5 + (4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4)*d^3 + (a*b^7 - 10*a^2*b^5*c + 23*a^3*b^3*c^2 + 4*a^4*b*c^3)*d)*e*x + 2*((b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*e^8*x^8 + 8*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d*e^7*x^7 + 2*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3 + 14*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^2)*e^6*x^6 + 4*(14*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^3 + 3*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d)*e^5*x^5 + (b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^8 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3 + 70*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^4 + 30*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d^2)*e^4*x^4 + a^2*b^5 - 10*a^3*b^3*c + 30*a^4*b*c^2 + 2*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d^6 + 4*(14*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^5 + 10*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d^3 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*d)*e^3*x^3 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*d^4 + 2*(a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2 + 14*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^6 + 15*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d^4 + 3*(b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*d^2)*e^2*x^2 + 2*(a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2)*d^2 + 4*(2*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^7 + 3*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d^5 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*d^3 + (a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2)*d)*e*x)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - ((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^8*x^8 + 8*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d*e^7*x^7 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2)*e^6*x^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^3 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d)*e^5*x^5 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^8 + (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 + 70*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 + 30*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2)*e^4*x^4 + 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)*d^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^5 + 10*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3 + (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)*d)*e^3*x^3 + (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)*d^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^6 + 15*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^4 + 3*(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)*d^2)*e^2*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2 + 4*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^7 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^5 + (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)*d^3 + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d)*e*x)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 4*((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^8*x^8 + 8*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d*e^7*x^7 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2)*e^6*x^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^3 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d)*e^5*x^5 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^8 + (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 + 70*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 + 30*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2)*e^4*x^4 + 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)*d^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^5 + 10*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3 + (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)*d)*e^3*x^3 + (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)*d^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^6 + 15*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^4 + 3*(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)*d^2)*e^2*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2 + 4*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^7 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^5 + (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)*d^3 + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d)*e*x)*log(e*x + d))/((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)*e^9*x^8 + 8*(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)*d*e^8*x^7 + 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 + 14*(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)*d^2)*e^7*x^6 + 4*(14*(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)*d^3 + 3*(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)*d)*e^6*x^5 + (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 + 70*(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)*d^4 + 30*(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)*d^2)*e^5*x^4 + 4*(14*(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)*d^5 + 10*(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)*d^3 + (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)*d)*e^4*x^3 + 2*(a^4*b^7 - 12*a^5*b^5*c + 48*a^6*b^3*c^2 - 64*a^7*b*c^3 + 14*(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)*d^6 + 15*(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)*d^4 + 3*(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)*d^2)*e^3*x^2 + 4*(2*(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)*d^7 + 3*(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)*d^5 + (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)*d^3 + (a^4*b^7 - 12*a^5*b^5*c + 48*a^6*b^3*c^2 - 64*a^7*b*c^3)*d)*e^2*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)*d^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)*d^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)*d^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)*d^2)*e)]","B",0
636,1,10260,0,3.916872," ","integrate(1/(e*x+d)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""fricas"")","-\frac{6 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} e^{8} x^{8} + 48 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} d e^{7} x^{7} + 2 \, {\left(30 \, b^{5} c - 227 \, a b^{3} c^{2} + 392 \, a^{2} b c^{3} + 84 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} d^{2}\right)} e^{6} x^{6} + 12 \, {\left(28 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} d^{3} + {\left(30 \, b^{5} c - 227 \, a b^{3} c^{2} + 392 \, a^{2} b c^{3}\right)} d\right)} e^{5} x^{5} + 6 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} d^{8} + 2 \, {\left(15 \, b^{6} - 91 \, a b^{4} c + 25 \, a^{2} b^{2} c^{2} + 324 \, a^{3} c^{3} + 210 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} d^{4} + 15 \, {\left(30 \, b^{5} c - 227 \, a b^{3} c^{2} + 392 \, a^{2} b c^{3}\right)} d^{2}\right)} e^{4} x^{4} + 2 \, {\left(30 \, b^{5} c - 227 \, a b^{3} c^{2} + 392 \, a^{2} b c^{3}\right)} d^{6} + 8 \, {\left(42 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} d^{5} + 5 \, {\left(30 \, b^{5} c - 227 \, a b^{3} c^{2} + 392 \, a^{2} b c^{3}\right)} d^{3} + {\left(15 \, b^{6} - 91 \, a b^{4} c + 25 \, a^{2} b^{2} c^{2} + 324 \, a^{3} c^{3}\right)} d\right)} e^{3} x^{3} + 16 \, a^{2} b^{4} - 128 \, a^{3} b^{2} c + 256 \, a^{4} c^{2} + 2 \, {\left(15 \, b^{6} - 91 \, a b^{4} c + 25 \, a^{2} b^{2} c^{2} + 324 \, a^{3} c^{3}\right)} d^{4} + 2 \, {\left(84 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} d^{6} + 25 \, a b^{5} - 194 \, a^{2} b^{3} c + 364 \, a^{3} b c^{2} + 15 \, {\left(30 \, b^{5} c - 227 \, a b^{3} c^{2} + 392 \, a^{2} b c^{3}\right)} d^{4} + 6 \, {\left(15 \, b^{6} - 91 \, a b^{4} c + 25 \, a^{2} b^{2} c^{2} + 324 \, a^{3} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + 2 \, {\left(25 \, a b^{5} - 194 \, a^{2} b^{3} c + 364 \, a^{3} b c^{2}\right)} d^{2} + 4 \, {\left(12 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} d^{7} + 3 \, {\left(30 \, b^{5} c - 227 \, a b^{3} c^{2} + 392 \, a^{2} b c^{3}\right)} d^{5} + 2 \, {\left(15 \, b^{6} - 91 \, a b^{4} c + 25 \, a^{2} b^{2} c^{2} + 324 \, a^{3} c^{3}\right)} d^{3} + {\left(25 \, a b^{5} - 194 \, a^{2} b^{3} c + 364 \, a^{3} b c^{2}\right)} d\right)} e x - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} e^{10} x^{9} + 9 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d e^{9} x^{8} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3} + 18 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{2}\right)} e^{8} x^{7} + 14 \, {\left(6 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{3} + {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d\right)} e^{7} x^{6} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3} + 126 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{4} + 42 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{2}\right)} e^{6} x^{5} + {\left(126 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{5} + 70 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{3} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d\right)} e^{5} x^{4} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2} + 42 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{6} + 35 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{4} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{2}\right)} e^{4} x^{3} + 2 \, {\left(18 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{7} + 21 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{5} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{3} + 3 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d\right)} e^{3} x^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2} + 9 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{8} + 14 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{6} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{4} + 6 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d^{2}\right)} e^{2} x + {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{9} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{7} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{5} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d^{3} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} d\right)} e\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} + {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4}}}}{{\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2}}} \log\left(-27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} e x - 27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} d + \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left({\left(5 \, a^{7} b^{16} - 152 \, a^{8} b^{14} c + 2006 \, a^{9} b^{12} c^{2} - 14960 \, a^{10} b^{10} c^{3} + 68640 \, a^{11} b^{8} c^{4} - 197120 \, a^{12} b^{6} c^{5} + 342528 \, a^{13} b^{4} c^{6} - 323584 \, a^{14} b^{2} c^{7} + 122880 \, a^{15} c^{8}\right)} e^{3} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4}}} - {\left(125 \, b^{17} - 3775 \, a b^{15} c + 49360 \, a^{2} b^{13} c^{2} - 362733 \, a^{3} b^{11} c^{3} + 1623534 \, a^{4} b^{9} c^{4} - 4463140 \, a^{5} b^{7} c^{5} + 7146736 \, a^{6} b^{5} c^{6} - 5684672 \, a^{7} b^{3} c^{7} + 1324800 \, a^{8} b c^{8}\right)} e\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} + {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4}}}}{{\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} e^{10} x^{9} + 9 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d e^{9} x^{8} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3} + 18 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{2}\right)} e^{8} x^{7} + 14 \, {\left(6 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{3} + {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d\right)} e^{7} x^{6} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3} + 126 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{4} + 42 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{2}\right)} e^{6} x^{5} + {\left(126 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{5} + 70 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{3} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d\right)} e^{5} x^{4} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2} + 42 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{6} + 35 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{4} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{2}\right)} e^{4} x^{3} + 2 \, {\left(18 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{7} + 21 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{5} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{3} + 3 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d\right)} e^{3} x^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2} + 9 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{8} + 14 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{6} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{4} + 6 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d^{2}\right)} e^{2} x + {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{9} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{7} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{5} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d^{3} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} d\right)} e\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} + {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4}}}}{{\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2}}} \log\left(-27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} e x - 27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} d - \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left({\left(5 \, a^{7} b^{16} - 152 \, a^{8} b^{14} c + 2006 \, a^{9} b^{12} c^{2} - 14960 \, a^{10} b^{10} c^{3} + 68640 \, a^{11} b^{8} c^{4} - 197120 \, a^{12} b^{6} c^{5} + 342528 \, a^{13} b^{4} c^{6} - 323584 \, a^{14} b^{2} c^{7} + 122880 \, a^{15} c^{8}\right)} e^{3} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4}}} - {\left(125 \, b^{17} - 3775 \, a b^{15} c + 49360 \, a^{2} b^{13} c^{2} - 362733 \, a^{3} b^{11} c^{3} + 1623534 \, a^{4} b^{9} c^{4} - 4463140 \, a^{5} b^{7} c^{5} + 7146736 \, a^{6} b^{5} c^{6} - 5684672 \, a^{7} b^{3} c^{7} + 1324800 \, a^{8} b c^{8}\right)} e\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} + {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4}}}}{{\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} e^{10} x^{9} + 9 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d e^{9} x^{8} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3} + 18 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{2}\right)} e^{8} x^{7} + 14 \, {\left(6 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{3} + {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d\right)} e^{7} x^{6} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3} + 126 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{4} + 42 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{2}\right)} e^{6} x^{5} + {\left(126 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{5} + 70 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{3} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d\right)} e^{5} x^{4} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2} + 42 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{6} + 35 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{4} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{2}\right)} e^{4} x^{3} + 2 \, {\left(18 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{7} + 21 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{5} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{3} + 3 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d\right)} e^{3} x^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2} + 9 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{8} + 14 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{6} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{4} + 6 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d^{2}\right)} e^{2} x + {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{9} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{7} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{5} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d^{3} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} d\right)} e\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} - {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4}}}}{{\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2}}} \log\left(-27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} e x - 27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} d + \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left({\left(5 \, a^{7} b^{16} - 152 \, a^{8} b^{14} c + 2006 \, a^{9} b^{12} c^{2} - 14960 \, a^{10} b^{10} c^{3} + 68640 \, a^{11} b^{8} c^{4} - 197120 \, a^{12} b^{6} c^{5} + 342528 \, a^{13} b^{4} c^{6} - 323584 \, a^{14} b^{2} c^{7} + 122880 \, a^{15} c^{8}\right)} e^{3} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4}}} + {\left(125 \, b^{17} - 3775 \, a b^{15} c + 49360 \, a^{2} b^{13} c^{2} - 362733 \, a^{3} b^{11} c^{3} + 1623534 \, a^{4} b^{9} c^{4} - 4463140 \, a^{5} b^{7} c^{5} + 7146736 \, a^{6} b^{5} c^{6} - 5684672 \, a^{7} b^{3} c^{7} + 1324800 \, a^{8} b c^{8}\right)} e\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} - {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4}}}}{{\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} e^{10} x^{9} + 9 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d e^{9} x^{8} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3} + 18 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{2}\right)} e^{8} x^{7} + 14 \, {\left(6 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{3} + {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d\right)} e^{7} x^{6} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3} + 126 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{4} + 42 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{2}\right)} e^{6} x^{5} + {\left(126 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{5} + 70 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{3} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d\right)} e^{5} x^{4} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2} + 42 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{6} + 35 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{4} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{2}\right)} e^{4} x^{3} + 2 \, {\left(18 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{7} + 21 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{5} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{3} + 3 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d\right)} e^{3} x^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2} + 9 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{8} + 14 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{6} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{4} + 6 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d^{2}\right)} e^{2} x + {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{9} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{7} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{5} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d^{3} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} d\right)} e\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} - {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4}}}}{{\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2}}} \log\left(-27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} e x - 27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} d - \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left({\left(5 \, a^{7} b^{16} - 152 \, a^{8} b^{14} c + 2006 \, a^{9} b^{12} c^{2} - 14960 \, a^{10} b^{10} c^{3} + 68640 \, a^{11} b^{8} c^{4} - 197120 \, a^{12} b^{6} c^{5} + 342528 \, a^{13} b^{4} c^{6} - 323584 \, a^{14} b^{2} c^{7} + 122880 \, a^{15} c^{8}\right)} e^{3} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4}}} + {\left(125 \, b^{17} - 3775 \, a b^{15} c + 49360 \, a^{2} b^{13} c^{2} - 362733 \, a^{3} b^{11} c^{3} + 1623534 \, a^{4} b^{9} c^{4} - 4463140 \, a^{5} b^{7} c^{5} + 7146736 \, a^{6} b^{5} c^{6} - 5684672 \, a^{7} b^{3} c^{7} + 1324800 \, a^{8} b c^{8}\right)} e\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} - {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4}}}}{{\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2}}}\right)}{16 \, {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} e^{10} x^{9} + 9 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d e^{9} x^{8} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3} + 18 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{2}\right)} e^{8} x^{7} + 14 \, {\left(6 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{3} + {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d\right)} e^{7} x^{6} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3} + 126 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{4} + 42 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{2}\right)} e^{6} x^{5} + {\left(126 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{5} + 70 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{3} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d\right)} e^{5} x^{4} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2} + 42 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{6} + 35 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{4} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{2}\right)} e^{4} x^{3} + 2 \, {\left(18 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{7} + 21 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{5} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{3} + 3 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d\right)} e^{3} x^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2} + 9 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{8} + 14 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{6} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{4} + 6 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d^{2}\right)} e^{2} x + {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{9} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{7} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{5} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d^{3} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} d\right)} e\right)}}"," ",0,"-1/16*(6*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*e^8*x^8 + 48*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d*e^7*x^7 + 2*(30*b^5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3 + 84*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^2)*e^6*x^6 + 12*(28*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^3 + (30*b^5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3)*d)*e^5*x^5 + 6*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^8 + 2*(15*b^6 - 91*a*b^4*c + 25*a^2*b^2*c^2 + 324*a^3*c^3 + 210*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^4 + 15*(30*b^5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3)*d^2)*e^4*x^4 + 2*(30*b^5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3)*d^6 + 8*(42*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^5 + 5*(30*b^5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3)*d^3 + (15*b^6 - 91*a*b^4*c + 25*a^2*b^2*c^2 + 324*a^3*c^3)*d)*e^3*x^3 + 16*a^2*b^4 - 128*a^3*b^2*c + 256*a^4*c^2 + 2*(15*b^6 - 91*a*b^4*c + 25*a^2*b^2*c^2 + 324*a^3*c^3)*d^4 + 2*(84*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^6 + 25*a*b^5 - 194*a^2*b^3*c + 364*a^3*b*c^2 + 15*(30*b^5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3)*d^4 + 6*(15*b^6 - 91*a*b^4*c + 25*a^2*b^2*c^2 + 324*a^3*c^3)*d^2)*e^2*x^2 + 2*(25*a*b^5 - 194*a^2*b^3*c + 364*a^3*b*c^2)*d^2 + 4*(12*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^7 + 3*(30*b^5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3)*d^5 + 2*(15*b^6 - 91*a*b^4*c + 25*a^2*b^2*c^2 + 324*a^3*c^3)*d^3 + (25*a*b^5 - 194*a^2*b^3*c + 364*a^3*b*c^2)*d)*e*x - 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^10*x^9 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d*e^9*x^8 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3 + 18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^2)*e^8*x^7 + 14*(6*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^3 + (a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d)*e^7*x^6 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3 + 126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^4 + 42*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^2)*e^6*x^5 + (126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^5 + 70*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d)*e^5*x^4 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2 + 42*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^6 + 35*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^4 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^2)*e^4*x^3 + 2*(18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^7 + 21*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^5 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^3 + 3*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d)*e^3*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^8 + 14*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^6 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^4 + 6*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^2)*e^2*x + ((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^9 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^7 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^5 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*d)*e)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4)))/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2))*log(-27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*e*x - 27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*d + 27/2*sqrt(1/2)*((5*a^7*b^16 - 152*a^8*b^14*c + 2006*a^9*b^12*c^2 - 14960*a^10*b^10*c^3 + 68640*a^11*b^8*c^4 - 197120*a^12*b^6*c^5 + 342528*a^13*b^4*c^6 - 323584*a^14*b^2*c^7 + 122880*a^15*c^8)*e^3*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4)) - (125*b^17 - 3775*a*b^15*c + 49360*a^2*b^13*c^2 - 362733*a^3*b^11*c^3 + 1623534*a^4*b^9*c^4 - 4463140*a^5*b^7*c^5 + 7146736*a^6*b^5*c^6 - 5684672*a^7*b^3*c^7 + 1324800*a^8*b*c^8)*e)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4)))/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2))) + 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^10*x^9 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d*e^9*x^8 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3 + 18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^2)*e^8*x^7 + 14*(6*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^3 + (a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d)*e^7*x^6 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3 + 126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^4 + 42*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^2)*e^6*x^5 + (126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^5 + 70*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d)*e^5*x^4 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2 + 42*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^6 + 35*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^4 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^2)*e^4*x^3 + 2*(18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^7 + 21*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^5 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^3 + 3*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d)*e^3*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^8 + 14*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^6 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^4 + 6*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^2)*e^2*x + ((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^9 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^7 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^5 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*d)*e)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4)))/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2))*log(-27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*e*x - 27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*d - 27/2*sqrt(1/2)*((5*a^7*b^16 - 152*a^8*b^14*c + 2006*a^9*b^12*c^2 - 14960*a^10*b^10*c^3 + 68640*a^11*b^8*c^4 - 197120*a^12*b^6*c^5 + 342528*a^13*b^4*c^6 - 323584*a^14*b^2*c^7 + 122880*a^15*c^8)*e^3*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4)) - (125*b^17 - 3775*a*b^15*c + 49360*a^2*b^13*c^2 - 362733*a^3*b^11*c^3 + 1623534*a^4*b^9*c^4 - 4463140*a^5*b^7*c^5 + 7146736*a^6*b^5*c^6 - 5684672*a^7*b^3*c^7 + 1324800*a^8*b*c^8)*e)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4)))/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2))) + 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^10*x^9 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d*e^9*x^8 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3 + 18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^2)*e^8*x^7 + 14*(6*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^3 + (a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d)*e^7*x^6 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3 + 126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^4 + 42*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^2)*e^6*x^5 + (126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^5 + 70*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d)*e^5*x^4 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2 + 42*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^6 + 35*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^4 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^2)*e^4*x^3 + 2*(18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^7 + 21*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^5 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^3 + 3*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d)*e^3*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^8 + 14*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^6 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^4 + 6*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^2)*e^2*x + ((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^9 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^7 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^5 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*d)*e)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4)))/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2))*log(-27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*e*x - 27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*d + 27/2*sqrt(1/2)*((5*a^7*b^16 - 152*a^8*b^14*c + 2006*a^9*b^12*c^2 - 14960*a^10*b^10*c^3 + 68640*a^11*b^8*c^4 - 197120*a^12*b^6*c^5 + 342528*a^13*b^4*c^6 - 323584*a^14*b^2*c^7 + 122880*a^15*c^8)*e^3*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4)) + (125*b^17 - 3775*a*b^15*c + 49360*a^2*b^13*c^2 - 362733*a^3*b^11*c^3 + 1623534*a^4*b^9*c^4 - 4463140*a^5*b^7*c^5 + 7146736*a^6*b^5*c^6 - 5684672*a^7*b^3*c^7 + 1324800*a^8*b*c^8)*e)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4)))/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2))) - 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^10*x^9 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d*e^9*x^8 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3 + 18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^2)*e^8*x^7 + 14*(6*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^3 + (a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d)*e^7*x^6 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3 + 126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^4 + 42*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^2)*e^6*x^5 + (126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^5 + 70*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d)*e^5*x^4 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2 + 42*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^6 + 35*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^4 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^2)*e^4*x^3 + 2*(18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^7 + 21*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^5 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^3 + 3*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d)*e^3*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^8 + 14*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^6 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^4 + 6*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^2)*e^2*x + ((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^9 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^7 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^5 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*d)*e)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4)))/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2))*log(-27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*e*x - 27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*d - 27/2*sqrt(1/2)*((5*a^7*b^16 - 152*a^8*b^14*c + 2006*a^9*b^12*c^2 - 14960*a^10*b^10*c^3 + 68640*a^11*b^8*c^4 - 197120*a^12*b^6*c^5 + 342528*a^13*b^4*c^6 - 323584*a^14*b^2*c^7 + 122880*a^15*c^8)*e^3*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4)) + (125*b^17 - 3775*a*b^15*c + 49360*a^2*b^13*c^2 - 362733*a^3*b^11*c^3 + 1623534*a^4*b^9*c^4 - 4463140*a^5*b^7*c^5 + 7146736*a^6*b^5*c^6 - 5684672*a^7*b^3*c^7 + 1324800*a^8*b*c^8)*e)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4)))/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2))))/((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^10*x^9 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d*e^9*x^8 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3 + 18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^2)*e^8*x^7 + 14*(6*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^3 + (a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d)*e^7*x^6 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3 + 126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^4 + 42*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^2)*e^6*x^5 + (126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^5 + 70*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d)*e^5*x^4 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2 + 42*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^6 + 35*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^4 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^2)*e^4*x^3 + 2*(18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^7 + 21*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^5 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^3 + 3*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d)*e^3*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^8 + 14*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^6 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^4 + 6*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^2)*e^2*x + ((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^9 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^7 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^5 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*d)*e)","B",0
637,1,15165,0,7.534361," ","integrate(1/(e*x+d)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} e^{8} x^{8} + 48 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d e^{7} x^{7} + 3 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4} + 56 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{2}\right)} e^{6} x^{6} + 6 \, {\left(56 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{3} + 3 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d\right)} e^{5} x^{5} + 2 \, a^{3} b^{6} - 24 \, a^{4} b^{4} c + 96 \, a^{5} b^{2} c^{2} - 128 \, a^{6} c^{3} + 6 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{8} + {\left(6 \, a b^{8} - 60 \, a^{2} b^{6} c + 158 \, a^{3} b^{4} c^{2} + 44 \, a^{4} b^{2} c^{3} - 400 \, a^{5} c^{4} + 420 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{4} + 45 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + 3 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d^{6} + 4 \, {\left(84 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{5} + 15 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d^{3} + 2 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} d\right)} e^{3} x^{3} + 2 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} d^{4} + {\left(9 \, a^{2} b^{7} - 104 \, a^{3} b^{5} c + 394 \, a^{4} b^{3} c^{2} - 488 \, a^{5} b c^{3} + 168 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{6} + 45 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d^{4} + 12 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} d^{2}\right)} e^{2} x^{2} + {\left(9 \, a^{2} b^{7} - 104 \, a^{3} b^{5} c + 394 \, a^{4} b^{3} c^{2} - 488 \, a^{5} b c^{3}\right)} d^{2} + 2 \, {\left(24 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{7} + 9 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d^{5} + 4 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} d^{3} + {\left(9 \, a^{2} b^{7} - 104 \, a^{3} b^{5} c + 394 \, a^{4} b^{3} c^{2} - 488 \, a^{5} b c^{3}\right)} d\right)} e x + 3 \, {\left({\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} e^{10} x^{10} + 10 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d e^{9} x^{9} + {\left(2 \, b^{7} c - 20 \, a b^{5} c^{2} + 60 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4} + 45 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{2}\right)} e^{8} x^{8} + 8 \, {\left(15 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{3} + 2 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d\right)} e^{7} x^{7} + {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4} + 210 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{4} + 56 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{6} x^{6} + {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{10} + 2 \, {\left(126 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{5} + 56 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{3} + 3 \, {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d\right)} e^{5} x^{5} + 2 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{8} + {\left(2 \, a b^{7} - 20 \, a^{2} b^{5} c + 60 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3} + 210 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{6} + 140 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{4} + 15 \, {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d^{6} + 4 \, {\left(30 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{7} + 28 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{5} + 5 \, {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d^{3} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} d\right)} e^{3} x^{3} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} d^{4} + {\left(45 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{8} + a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3} + 56 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{6} + 15 \, {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d^{4} + 12 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3}\right)} d^{2} + 2 \, {\left(5 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{9} + 8 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{7} + 3 \, {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d^{5} + 4 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} d^{3} + {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3}\right)} d\right)} e x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c + {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right) - 3 \, {\left({\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)} e^{10} x^{10} + 10 \, {\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)} d e^{9} x^{9} + {\left(2 \, b^{8} c - 24 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 128 \, a^{3} b^{2} c^{4} + 45 \, {\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)} d^{2}\right)} e^{8} x^{8} + 8 \, {\left(15 \, {\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)} d^{3} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d\right)} e^{7} x^{7} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4} + 210 \, {\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)} d^{4} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{2}\right)} e^{6} x^{6} + {\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)} d^{10} + 2 \, {\left(126 \, {\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)} d^{5} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{3} + 3 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d\right)} e^{5} x^{5} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{8} + {\left(2 \, a b^{8} - 24 \, a^{2} b^{6} c + 96 \, a^{3} b^{4} c^{2} - 128 \, a^{4} b^{2} c^{3} + 210 \, {\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)} d^{6} + 140 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{4} + 15 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{6} + 4 \, {\left(30 \, {\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)} d^{7} + 28 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{5} + 5 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d\right)} e^{3} x^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{4} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3} + 45 \, {\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)} d^{8} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{6} + 15 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{4} + 12 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} d^{2} + 2 \, {\left(5 \, {\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)} d^{9} + 8 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{7} + 3 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{5} + 4 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{3} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} d\right)} e x\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 12 \, {\left({\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)} e^{10} x^{10} + 10 \, {\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)} d e^{9} x^{9} + {\left(2 \, b^{8} c - 24 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 128 \, a^{3} b^{2} c^{4} + 45 \, {\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)} d^{2}\right)} e^{8} x^{8} + 8 \, {\left(15 \, {\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)} d^{3} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d\right)} e^{7} x^{7} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4} + 210 \, {\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)} d^{4} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{2}\right)} e^{6} x^{6} + {\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)} d^{10} + 2 \, {\left(126 \, {\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)} d^{5} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{3} + 3 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d\right)} e^{5} x^{5} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{8} + {\left(2 \, a b^{8} - 24 \, a^{2} b^{6} c + 96 \, a^{3} b^{4} c^{2} - 128 \, a^{4} b^{2} c^{3} + 210 \, {\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)} d^{6} + 140 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{4} + 15 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{6} + 4 \, {\left(30 \, {\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)} d^{7} + 28 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{5} + 5 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d\right)} e^{3} x^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{4} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3} + 45 \, {\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)} d^{8} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{6} + 15 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{4} + 12 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} d^{2} + 2 \, {\left(5 \, {\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)} d^{9} + 8 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{7} + 3 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{5} + 4 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{3} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} d\right)} e x\right)} \log\left(e x + d\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)} e^{11} x^{10} + 10 \, {\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)} d e^{10} x^{9} + {\left(2 \, a^{4} b^{7} c - 24 \, a^{5} b^{5} c^{2} + 96 \, a^{6} b^{3} c^{3} - 128 \, a^{7} b c^{4} + 45 \, {\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)} d^{2}\right)} e^{9} x^{8} + 8 \, {\left(15 \, {\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)} d^{3} + 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)} d\right)} e^{8} x^{7} + {\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} + 210 \, {\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)} d^{4} + 56 \, {\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)} d^{2}\right)} e^{7} x^{6} + 2 \, {\left(126 \, {\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)} d^{5} + 56 \, {\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)} d^{3} + 3 \, {\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)} d\right)} e^{6} x^{5} + {\left(2 \, a^{5} b^{7} - 24 \, a^{6} b^{5} c + 96 \, a^{7} b^{3} c^{2} - 128 \, a^{8} b c^{3} + 210 \, {\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)} d^{6} + 140 \, {\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)} d^{4} + 15 \, {\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)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(30 \, {\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)} d^{7} + 28 \, {\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)} d^{5} + 5 \, {\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)} d^{3} + 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)} d\right)} e^{4} x^{3} + {\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3} + 45 \, {\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)} d^{8} + 56 \, {\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)} d^{6} + 15 \, {\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)} d^{4} + 12 \, {\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)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(5 \, {\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)} d^{9} + 8 \, {\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)} d^{7} + 3 \, {\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)} d^{5} + 4 \, {\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)} d^{3} + {\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} d\right)} e^{2} x + {\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)} d^{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)} d^{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)} d^{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)} d^{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)} d^{2}\right)} e\right)}}, -\frac{6 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} e^{8} x^{8} + 48 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d e^{7} x^{7} + 3 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4} + 56 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{2}\right)} e^{6} x^{6} + 6 \, {\left(56 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{3} + 3 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d\right)} e^{5} x^{5} + 2 \, a^{3} b^{6} - 24 \, a^{4} b^{4} c + 96 \, a^{5} b^{2} c^{2} - 128 \, a^{6} c^{3} + 6 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{8} + {\left(6 \, a b^{8} - 60 \, a^{2} b^{6} c + 158 \, a^{3} b^{4} c^{2} + 44 \, a^{4} b^{2} c^{3} - 400 \, a^{5} c^{4} + 420 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{4} + 45 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + 3 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d^{6} + 4 \, {\left(84 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{5} + 15 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d^{3} + 2 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} d\right)} e^{3} x^{3} + 2 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} d^{4} + {\left(9 \, a^{2} b^{7} - 104 \, a^{3} b^{5} c + 394 \, a^{4} b^{3} c^{2} - 488 \, a^{5} b c^{3} + 168 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{6} + 45 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d^{4} + 12 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} d^{2}\right)} e^{2} x^{2} + {\left(9 \, a^{2} b^{7} - 104 \, a^{3} b^{5} c + 394 \, a^{4} b^{3} c^{2} - 488 \, a^{5} b c^{3}\right)} d^{2} + 2 \, {\left(24 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{7} + 9 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d^{5} + 4 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} d^{3} + {\left(9 \, a^{2} b^{7} - 104 \, a^{3} b^{5} c + 394 \, a^{4} b^{3} c^{2} - 488 \, a^{5} b c^{3}\right)} d\right)} e x + 6 \, {\left({\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} e^{10} x^{10} + 10 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d e^{9} x^{9} + {\left(2 \, b^{7} c - 20 \, a b^{5} c^{2} + 60 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4} + 45 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{2}\right)} e^{8} x^{8} + 8 \, {\left(15 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{3} + 2 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d\right)} e^{7} x^{7} + {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4} + 210 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{4} + 56 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{6} x^{6} + {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{10} + 2 \, {\left(126 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{5} + 56 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{3} + 3 \, {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d\right)} e^{5} x^{5} + 2 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{8} + {\left(2 \, a b^{7} - 20 \, a^{2} b^{5} c + 60 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3} + 210 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{6} + 140 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{4} + 15 \, {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d^{6} + 4 \, {\left(30 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{7} + 28 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{5} + 5 \, {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d^{3} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} d\right)} e^{3} x^{3} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} d^{4} + {\left(45 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{8} + a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3} + 56 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{6} + 15 \, {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d^{4} + 12 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3}\right)} d^{2} + 2 \, {\left(5 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{9} + 8 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{7} + 3 \, {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d^{5} + 4 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} d^{3} + {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3}\right)} d\right)} e x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - 3 \, {\left({\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)} e^{10} x^{10} + 10 \, {\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)} d e^{9} x^{9} + {\left(2 \, b^{8} c - 24 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 128 \, a^{3} b^{2} c^{4} + 45 \, {\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)} d^{2}\right)} e^{8} x^{8} + 8 \, {\left(15 \, {\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)} d^{3} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d\right)} e^{7} x^{7} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4} + 210 \, {\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)} d^{4} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{2}\right)} e^{6} x^{6} + {\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)} d^{10} + 2 \, {\left(126 \, {\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)} d^{5} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{3} + 3 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d\right)} e^{5} x^{5} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{8} + {\left(2 \, a b^{8} - 24 \, a^{2} b^{6} c + 96 \, a^{3} b^{4} c^{2} - 128 \, a^{4} b^{2} c^{3} + 210 \, {\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)} d^{6} + 140 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{4} + 15 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{6} + 4 \, {\left(30 \, {\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)} d^{7} + 28 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{5} + 5 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d\right)} e^{3} x^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{4} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3} + 45 \, {\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)} d^{8} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{6} + 15 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{4} + 12 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} d^{2} + 2 \, {\left(5 \, {\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)} d^{9} + 8 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{7} + 3 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{5} + 4 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{3} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} d\right)} e x\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 12 \, {\left({\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)} e^{10} x^{10} + 10 \, {\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)} d e^{9} x^{9} + {\left(2 \, b^{8} c - 24 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 128 \, a^{3} b^{2} c^{4} + 45 \, {\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)} d^{2}\right)} e^{8} x^{8} + 8 \, {\left(15 \, {\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)} d^{3} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d\right)} e^{7} x^{7} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4} + 210 \, {\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)} d^{4} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{2}\right)} e^{6} x^{6} + {\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)} d^{10} + 2 \, {\left(126 \, {\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)} d^{5} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{3} + 3 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d\right)} e^{5} x^{5} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{8} + {\left(2 \, a b^{8} - 24 \, a^{2} b^{6} c + 96 \, a^{3} b^{4} c^{2} - 128 \, a^{4} b^{2} c^{3} + 210 \, {\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)} d^{6} + 140 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{4} + 15 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{6} + 4 \, {\left(30 \, {\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)} d^{7} + 28 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{5} + 5 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d\right)} e^{3} x^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{4} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3} + 45 \, {\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)} d^{8} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{6} + 15 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{4} + 12 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} d^{2} + 2 \, {\left(5 \, {\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)} d^{9} + 8 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{7} + 3 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{5} + 4 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{3} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} d\right)} e x\right)} \log\left(e x + d\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)} e^{11} x^{10} + 10 \, {\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)} d e^{10} x^{9} + {\left(2 \, a^{4} b^{7} c - 24 \, a^{5} b^{5} c^{2} + 96 \, a^{6} b^{3} c^{3} - 128 \, a^{7} b c^{4} + 45 \, {\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)} d^{2}\right)} e^{9} x^{8} + 8 \, {\left(15 \, {\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)} d^{3} + 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)} d\right)} e^{8} x^{7} + {\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} + 210 \, {\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)} d^{4} + 56 \, {\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)} d^{2}\right)} e^{7} x^{6} + 2 \, {\left(126 \, {\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)} d^{5} + 56 \, {\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)} d^{3} + 3 \, {\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)} d\right)} e^{6} x^{5} + {\left(2 \, a^{5} b^{7} - 24 \, a^{6} b^{5} c + 96 \, a^{7} b^{3} c^{2} - 128 \, a^{8} b c^{3} + 210 \, {\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)} d^{6} + 140 \, {\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)} d^{4} + 15 \, {\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)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(30 \, {\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)} d^{7} + 28 \, {\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)} d^{5} + 5 \, {\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)} d^{3} + 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)} d\right)} e^{4} x^{3} + {\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3} + 45 \, {\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)} d^{8} + 56 \, {\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)} d^{6} + 15 \, {\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)} d^{4} + 12 \, {\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)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(5 \, {\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)} d^{9} + 8 \, {\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)} d^{7} + 3 \, {\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)} d^{5} + 4 \, {\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)} d^{3} + {\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} d\right)} e^{2} x + {\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)} d^{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)} d^{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)} d^{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)} d^{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)} d^{2}\right)} e\right)}}\right]"," ",0,"[-1/4*(6*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*e^8*x^8 + 48*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d*e^7*x^7 + 3*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4 + 56*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^2)*e^6*x^6 + 6*(56*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^3 + 3*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d)*e^5*x^5 + 2*a^3*b^6 - 24*a^4*b^4*c + 96*a^5*b^2*c^2 - 128*a^6*c^3 + 6*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^8 + (6*a*b^8 - 60*a^2*b^6*c + 158*a^3*b^4*c^2 + 44*a^4*b^2*c^3 - 400*a^5*c^4 + 420*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^4 + 45*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d^2)*e^4*x^4 + 3*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d^6 + 4*(84*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^5 + 15*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d^3 + 2*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*d)*e^3*x^3 + 2*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*d^4 + (9*a^2*b^7 - 104*a^3*b^5*c + 394*a^4*b^3*c^2 - 488*a^5*b*c^3 + 168*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^6 + 45*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d^4 + 12*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*d^2)*e^2*x^2 + (9*a^2*b^7 - 104*a^3*b^5*c + 394*a^4*b^3*c^2 - 488*a^5*b*c^3)*d^2 + 2*(24*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^7 + 9*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d^5 + 4*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*d^3 + (9*a^2*b^7 - 104*a^3*b^5*c + 394*a^4*b^3*c^2 - 488*a^5*b*c^3)*d)*e*x + 3*((b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*e^10*x^10 + 10*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d*e^9*x^9 + (2*b^7*c - 20*a*b^5*c^2 + 60*a^2*b^3*c^3 - 40*a^3*b*c^4 + 45*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^2)*e^8*x^8 + 8*(15*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^3 + 2*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d)*e^7*x^7 + (b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4 + 210*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^4 + 56*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^2)*e^6*x^6 + (b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^10 + 2*(126*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^5 + 56*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^3 + 3*(b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d)*e^5*x^5 + 2*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^8 + (2*a*b^7 - 20*a^2*b^5*c + 60*a^3*b^3*c^2 - 40*a^4*b*c^3 + 210*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^6 + 140*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^4 + 15*(b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d^2)*e^4*x^4 + (b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d^6 + 4*(30*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^7 + 28*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^5 + 5*(b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d^3 + 2*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*d)*e^3*x^3 + 2*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*d^4 + (45*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^8 + a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3 + 56*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^6 + 15*(b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d^4 + 12*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*d^2)*e^2*x^2 + (a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3)*d^2 + 2*(5*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^9 + 8*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^7 + 3*(b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d^5 + 4*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*d^3 + (a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3)*d)*e*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c + (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)) - 3*((b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*e^10*x^10 + 10*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d*e^9*x^9 + (2*b^8*c - 24*a*b^6*c^2 + 96*a^2*b^4*c^3 - 128*a^3*b^2*c^4 + 45*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^2)*e^8*x^8 + 8*(15*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^3 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d)*e^7*x^7 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4 + 210*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^4 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^2)*e^6*x^6 + (b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^10 + 2*(126*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^5 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^3 + 3*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d)*e^5*x^5 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^8 + (2*a*b^8 - 24*a^2*b^6*c + 96*a^3*b^4*c^2 - 128*a^4*b^2*c^3 + 210*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^6 + 140*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^4 + 15*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^2)*e^4*x^4 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^6 + 4*(30*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^7 + 28*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^5 + 5*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d)*e^3*x^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^4 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3 + 45*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^8 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^6 + 15*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^4 + 12*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^2)*e^2*x^2 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d^2 + 2*(5*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^9 + 8*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^7 + 3*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^5 + 4*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^3 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d)*e*x)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 12*((b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*e^10*x^10 + 10*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d*e^9*x^9 + (2*b^8*c - 24*a*b^6*c^2 + 96*a^2*b^4*c^3 - 128*a^3*b^2*c^4 + 45*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^2)*e^8*x^8 + 8*(15*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^3 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d)*e^7*x^7 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4 + 210*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^4 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^2)*e^6*x^6 + (b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^10 + 2*(126*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^5 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^3 + 3*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d)*e^5*x^5 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^8 + (2*a*b^8 - 24*a^2*b^6*c + 96*a^3*b^4*c^2 - 128*a^4*b^2*c^3 + 210*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^6 + 140*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^4 + 15*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^2)*e^4*x^4 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^6 + 4*(30*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^7 + 28*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^5 + 5*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d)*e^3*x^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^4 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3 + 45*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^8 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^6 + 15*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^4 + 12*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^2)*e^2*x^2 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d^2 + 2*(5*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^9 + 8*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^7 + 3*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^5 + 4*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^3 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d)*e*x)*log(e*x + d))/((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)*e^11*x^10 + 10*(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)*d*e^10*x^9 + (2*a^4*b^7*c - 24*a^5*b^5*c^2 + 96*a^6*b^3*c^3 - 128*a^7*b*c^4 + 45*(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)*d^2)*e^9*x^8 + 8*(15*(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)*d^3 + 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)*d)*e^8*x^7 + (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 + 210*(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)*d^4 + 56*(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)*d^2)*e^7*x^6 + 2*(126*(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)*d^5 + 56*(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)*d^3 + 3*(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)*d)*e^6*x^5 + (2*a^5*b^7 - 24*a^6*b^5*c + 96*a^7*b^3*c^2 - 128*a^8*b*c^3 + 210*(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)*d^6 + 140*(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)*d^4 + 15*(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)*d^2)*e^5*x^4 + 4*(30*(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)*d^7 + 28*(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)*d^5 + 5*(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)*d^3 + 2*(a^5*b^7 - 12*a^6*b^5*c + 48*a^7*b^3*c^2 - 64*a^8*b*c^3)*d)*e^4*x^3 + (a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3 + 45*(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)*d^8 + 56*(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)*d^6 + 15*(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)*d^4 + 12*(a^5*b^7 - 12*a^6*b^5*c + 48*a^7*b^3*c^2 - 64*a^8*b*c^3)*d^2)*e^3*x^2 + 2*(5*(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)*d^9 + 8*(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)*d^7 + 3*(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)*d^5 + 4*(a^5*b^7 - 12*a^6*b^5*c + 48*a^7*b^3*c^2 - 64*a^8*b*c^3)*d^3 + (a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*d)*e^2*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)*d^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)*d^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)*d^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)*d^4 + (a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*d^2)*e), -1/4*(6*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*e^8*x^8 + 48*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d*e^7*x^7 + 3*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4 + 56*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^2)*e^6*x^6 + 6*(56*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^3 + 3*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d)*e^5*x^5 + 2*a^3*b^6 - 24*a^4*b^4*c + 96*a^5*b^2*c^2 - 128*a^6*c^3 + 6*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^8 + (6*a*b^8 - 60*a^2*b^6*c + 158*a^3*b^4*c^2 + 44*a^4*b^2*c^3 - 400*a^5*c^4 + 420*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^4 + 45*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d^2)*e^4*x^4 + 3*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d^6 + 4*(84*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^5 + 15*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d^3 + 2*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*d)*e^3*x^3 + 2*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*d^4 + (9*a^2*b^7 - 104*a^3*b^5*c + 394*a^4*b^3*c^2 - 488*a^5*b*c^3 + 168*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^6 + 45*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d^4 + 12*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*d^2)*e^2*x^2 + (9*a^2*b^7 - 104*a^3*b^5*c + 394*a^4*b^3*c^2 - 488*a^5*b*c^3)*d^2 + 2*(24*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^7 + 9*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d^5 + 4*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*d^3 + (9*a^2*b^7 - 104*a^3*b^5*c + 394*a^4*b^3*c^2 - 488*a^5*b*c^3)*d)*e*x + 6*((b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*e^10*x^10 + 10*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d*e^9*x^9 + (2*b^7*c - 20*a*b^5*c^2 + 60*a^2*b^3*c^3 - 40*a^3*b*c^4 + 45*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^2)*e^8*x^8 + 8*(15*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^3 + 2*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d)*e^7*x^7 + (b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4 + 210*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^4 + 56*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^2)*e^6*x^6 + (b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^10 + 2*(126*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^5 + 56*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^3 + 3*(b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d)*e^5*x^5 + 2*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^8 + (2*a*b^7 - 20*a^2*b^5*c + 60*a^3*b^3*c^2 - 40*a^4*b*c^3 + 210*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^6 + 140*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^4 + 15*(b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d^2)*e^4*x^4 + (b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d^6 + 4*(30*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^7 + 28*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^5 + 5*(b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d^3 + 2*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*d)*e^3*x^3 + 2*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*d^4 + (45*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^8 + a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3 + 56*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^6 + 15*(b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d^4 + 12*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*d^2)*e^2*x^2 + (a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3)*d^2 + 2*(5*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^9 + 8*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^7 + 3*(b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d^5 + 4*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*d^3 + (a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3)*d)*e*x)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - 3*((b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*e^10*x^10 + 10*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d*e^9*x^9 + (2*b^8*c - 24*a*b^6*c^2 + 96*a^2*b^4*c^3 - 128*a^3*b^2*c^4 + 45*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^2)*e^8*x^8 + 8*(15*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^3 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d)*e^7*x^7 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4 + 210*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^4 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^2)*e^6*x^6 + (b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^10 + 2*(126*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^5 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^3 + 3*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d)*e^5*x^5 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^8 + (2*a*b^8 - 24*a^2*b^6*c + 96*a^3*b^4*c^2 - 128*a^4*b^2*c^3 + 210*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^6 + 140*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^4 + 15*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^2)*e^4*x^4 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^6 + 4*(30*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^7 + 28*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^5 + 5*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d)*e^3*x^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^4 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3 + 45*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^8 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^6 + 15*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^4 + 12*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^2)*e^2*x^2 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d^2 + 2*(5*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^9 + 8*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^7 + 3*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^5 + 4*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^3 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d)*e*x)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 12*((b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*e^10*x^10 + 10*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d*e^9*x^9 + (2*b^8*c - 24*a*b^6*c^2 + 96*a^2*b^4*c^3 - 128*a^3*b^2*c^4 + 45*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^2)*e^8*x^8 + 8*(15*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^3 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d)*e^7*x^7 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4 + 210*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^4 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^2)*e^6*x^6 + (b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^10 + 2*(126*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^5 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^3 + 3*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d)*e^5*x^5 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^8 + (2*a*b^8 - 24*a^2*b^6*c + 96*a^3*b^4*c^2 - 128*a^4*b^2*c^3 + 210*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^6 + 140*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^4 + 15*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^2)*e^4*x^4 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^6 + 4*(30*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^7 + 28*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^5 + 5*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d)*e^3*x^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^4 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3 + 45*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^8 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^6 + 15*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^4 + 12*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^2)*e^2*x^2 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d^2 + 2*(5*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^9 + 8*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^7 + 3*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^5 + 4*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^3 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d)*e*x)*log(e*x + d))/((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)*e^11*x^10 + 10*(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)*d*e^10*x^9 + (2*a^4*b^7*c - 24*a^5*b^5*c^2 + 96*a^6*b^3*c^3 - 128*a^7*b*c^4 + 45*(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)*d^2)*e^9*x^8 + 8*(15*(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)*d^3 + 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)*d)*e^8*x^7 + (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 + 210*(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)*d^4 + 56*(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)*d^2)*e^7*x^6 + 2*(126*(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)*d^5 + 56*(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)*d^3 + 3*(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)*d)*e^6*x^5 + (2*a^5*b^7 - 24*a^6*b^5*c + 96*a^7*b^3*c^2 - 128*a^8*b*c^3 + 210*(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)*d^6 + 140*(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)*d^4 + 15*(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)*d^2)*e^5*x^4 + 4*(30*(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)*d^7 + 28*(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)*d^5 + 5*(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)*d^3 + 2*(a^5*b^7 - 12*a^6*b^5*c + 48*a^7*b^3*c^2 - 64*a^8*b*c^3)*d)*e^4*x^3 + (a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3 + 45*(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)*d^8 + 56*(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)*d^6 + 15*(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)*d^4 + 12*(a^5*b^7 - 12*a^6*b^5*c + 48*a^7*b^3*c^2 - 64*a^8*b*c^3)*d^2)*e^3*x^2 + 2*(5*(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)*d^9 + 8*(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)*d^7 + 3*(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)*d^5 + 4*(a^5*b^7 - 12*a^6*b^5*c + 48*a^7*b^3*c^2 - 64*a^8*b*c^3)*d^3 + (a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*d)*e^2*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)*d^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)*d^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)*d^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)*d^4 + (a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*d^2)*e)]","B",0
638,1,1346,0,1.322279," ","integrate((e*f*x+d*f)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""fricas"")","\frac{2 \, f^{4} x - \sqrt{\frac{1}{2}} c \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} f^{8} + \sqrt{\frac{{\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} f^{16}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}} \log\left(-2 \, {\left(a b^{2} - a^{2} c\right)} e f^{12} x - 2 \, {\left(a b^{2} - a^{2} c\right)} d f^{12} + \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e f^{8} - \sqrt{\frac{{\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} f^{16}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e^{3}\right)} \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} f^{8} + \sqrt{\frac{{\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} f^{16}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}}\right) + \sqrt{\frac{1}{2}} c \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} f^{8} + \sqrt{\frac{{\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} f^{16}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}} \log\left(-2 \, {\left(a b^{2} - a^{2} c\right)} e f^{12} x - 2 \, {\left(a b^{2} - a^{2} c\right)} d f^{12} - \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e f^{8} - \sqrt{\frac{{\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} f^{16}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e^{3}\right)} \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} f^{8} + \sqrt{\frac{{\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} f^{16}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}}\right) - \sqrt{\frac{1}{2}} c \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} f^{8} - \sqrt{\frac{{\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} f^{16}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}} \log\left(-2 \, {\left(a b^{2} - a^{2} c\right)} e f^{12} x - 2 \, {\left(a b^{2} - a^{2} c\right)} d f^{12} + \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e f^{8} + \sqrt{\frac{{\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} f^{16}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e^{3}\right)} \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} f^{8} - \sqrt{\frac{{\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} f^{16}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}}\right) + \sqrt{\frac{1}{2}} c \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} f^{8} - \sqrt{\frac{{\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} f^{16}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}} \log\left(-2 \, {\left(a b^{2} - a^{2} c\right)} e f^{12} x - 2 \, {\left(a b^{2} - a^{2} c\right)} d f^{12} - \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e f^{8} + \sqrt{\frac{{\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} f^{16}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e^{3}\right)} \sqrt{-\frac{{\left(b^{3} - 3 \, a b c\right)} f^{8} - \sqrt{\frac{{\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} f^{16}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} e^{4}}} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2}}}\right)}{2 \, c}"," ",0,"1/2*(2*f^4*x - sqrt(1/2)*c*sqrt(-((b^3 - 3*a*b*c)*f^8 + sqrt((b^4 - 2*a*b^2*c + a^2*c^2)*f^16/((b^2*c^6 - 4*a*c^7)*e^4))*(b^2*c^3 - 4*a*c^4)*e^2)/((b^2*c^3 - 4*a*c^4)*e^2))*log(-2*(a*b^2 - a^2*c)*e*f^12*x - 2*(a*b^2 - a^2*c)*d*f^12 + sqrt(1/2)*((b^4 - 5*a*b^2*c + 4*a^2*c^2)*e*f^8 - sqrt((b^4 - 2*a*b^2*c + a^2*c^2)*f^16/((b^2*c^6 - 4*a*c^7)*e^4))*(b^3*c^3 - 4*a*b*c^4)*e^3)*sqrt(-((b^3 - 3*a*b*c)*f^8 + sqrt((b^4 - 2*a*b^2*c + a^2*c^2)*f^16/((b^2*c^6 - 4*a*c^7)*e^4))*(b^2*c^3 - 4*a*c^4)*e^2)/((b^2*c^3 - 4*a*c^4)*e^2))) + sqrt(1/2)*c*sqrt(-((b^3 - 3*a*b*c)*f^8 + sqrt((b^4 - 2*a*b^2*c + a^2*c^2)*f^16/((b^2*c^6 - 4*a*c^7)*e^4))*(b^2*c^3 - 4*a*c^4)*e^2)/((b^2*c^3 - 4*a*c^4)*e^2))*log(-2*(a*b^2 - a^2*c)*e*f^12*x - 2*(a*b^2 - a^2*c)*d*f^12 - sqrt(1/2)*((b^4 - 5*a*b^2*c + 4*a^2*c^2)*e*f^8 - sqrt((b^4 - 2*a*b^2*c + a^2*c^2)*f^16/((b^2*c^6 - 4*a*c^7)*e^4))*(b^3*c^3 - 4*a*b*c^4)*e^3)*sqrt(-((b^3 - 3*a*b*c)*f^8 + sqrt((b^4 - 2*a*b^2*c + a^2*c^2)*f^16/((b^2*c^6 - 4*a*c^7)*e^4))*(b^2*c^3 - 4*a*c^4)*e^2)/((b^2*c^3 - 4*a*c^4)*e^2))) - sqrt(1/2)*c*sqrt(-((b^3 - 3*a*b*c)*f^8 - sqrt((b^4 - 2*a*b^2*c + a^2*c^2)*f^16/((b^2*c^6 - 4*a*c^7)*e^4))*(b^2*c^3 - 4*a*c^4)*e^2)/((b^2*c^3 - 4*a*c^4)*e^2))*log(-2*(a*b^2 - a^2*c)*e*f^12*x - 2*(a*b^2 - a^2*c)*d*f^12 + sqrt(1/2)*((b^4 - 5*a*b^2*c + 4*a^2*c^2)*e*f^8 + sqrt((b^4 - 2*a*b^2*c + a^2*c^2)*f^16/((b^2*c^6 - 4*a*c^7)*e^4))*(b^3*c^3 - 4*a*b*c^4)*e^3)*sqrt(-((b^3 - 3*a*b*c)*f^8 - sqrt((b^4 - 2*a*b^2*c + a^2*c^2)*f^16/((b^2*c^6 - 4*a*c^7)*e^4))*(b^2*c^3 - 4*a*c^4)*e^2)/((b^2*c^3 - 4*a*c^4)*e^2))) + sqrt(1/2)*c*sqrt(-((b^3 - 3*a*b*c)*f^8 - sqrt((b^4 - 2*a*b^2*c + a^2*c^2)*f^16/((b^2*c^6 - 4*a*c^7)*e^4))*(b^2*c^3 - 4*a*c^4)*e^2)/((b^2*c^3 - 4*a*c^4)*e^2))*log(-2*(a*b^2 - a^2*c)*e*f^12*x - 2*(a*b^2 - a^2*c)*d*f^12 - sqrt(1/2)*((b^4 - 5*a*b^2*c + 4*a^2*c^2)*e*f^8 + sqrt((b^4 - 2*a*b^2*c + a^2*c^2)*f^16/((b^2*c^6 - 4*a*c^7)*e^4))*(b^3*c^3 - 4*a*b*c^4)*e^3)*sqrt(-((b^3 - 3*a*b*c)*f^8 - sqrt((b^4 - 2*a*b^2*c + a^2*c^2)*f^16/((b^2*c^6 - 4*a*c^7)*e^4))*(b^2*c^3 - 4*a*c^4)*e^2)/((b^2*c^3 - 4*a*c^4)*e^2))))/c","B",0
639,1,446,0,1.186504," ","integrate((e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} - 4 \, a c} b f^{3} \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c + {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right) + {\left(b^{2} - 4 \, a c\right)} f^{3} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right)}{4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} e}, \frac{2 \, \sqrt{-b^{2} + 4 \, a c} b f^{3} \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) + {\left(b^{2} - 4 \, a c\right)} f^{3} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right)}{4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} e}\right]"," ",0,"[1/4*(sqrt(b^2 - 4*a*c)*b*f^3*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c + (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)) + (b^2 - 4*a*c)*f^3*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a))/((b^2*c - 4*a*c^2)*e), 1/4*(2*sqrt(-b^2 + 4*a*c)*b*f^3*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) + (b^2 - 4*a*c)*f^3*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a))/((b^2*c - 4*a*c^2)*e)]","A",0
640,1,799,0,1.102779," ","integrate((e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b f^{4} + {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{f^{8}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} e^{2}}{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}}} \log\left(e f^{6} x + d f^{6} + \sqrt{\frac{1}{2}} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{f^{8}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} e^{3} \sqrt{-\frac{b f^{4} + {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{f^{8}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} e^{2}}{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}}}\right) - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b f^{4} + {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{f^{8}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} e^{2}}{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}}} \log\left(e f^{6} x + d f^{6} - \sqrt{\frac{1}{2}} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{f^{8}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} e^{3} \sqrt{-\frac{b f^{4} + {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{f^{8}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} e^{2}}{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}}}\right) - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b f^{4} - {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{f^{8}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} e^{2}}{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}}} \log\left(e f^{6} x + d f^{6} + \sqrt{\frac{1}{2}} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{f^{8}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} e^{3} \sqrt{-\frac{b f^{4} - {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{f^{8}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} e^{2}}{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}}}\right) + \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b f^{4} - {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{f^{8}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} e^{2}}{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}}} \log\left(e f^{6} x + d f^{6} - \sqrt{\frac{1}{2}} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{f^{8}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} e^{3} \sqrt{-\frac{b f^{4} - {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{f^{8}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{4}}} e^{2}}{{\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}}}\right)"," ",0,"1/2*sqrt(1/2)*sqrt(-(b*f^4 + (b^2*c - 4*a*c^2)*sqrt(f^8/((b^2*c^2 - 4*a*c^3)*e^4))*e^2)/((b^2*c - 4*a*c^2)*e^2))*log(e*f^6*x + d*f^6 + sqrt(1/2)*(b^2*c - 4*a*c^2)*sqrt(f^8/((b^2*c^2 - 4*a*c^3)*e^4))*e^3*sqrt(-(b*f^4 + (b^2*c - 4*a*c^2)*sqrt(f^8/((b^2*c^2 - 4*a*c^3)*e^4))*e^2)/((b^2*c - 4*a*c^2)*e^2))) - 1/2*sqrt(1/2)*sqrt(-(b*f^4 + (b^2*c - 4*a*c^2)*sqrt(f^8/((b^2*c^2 - 4*a*c^3)*e^4))*e^2)/((b^2*c - 4*a*c^2)*e^2))*log(e*f^6*x + d*f^6 - sqrt(1/2)*(b^2*c - 4*a*c^2)*sqrt(f^8/((b^2*c^2 - 4*a*c^3)*e^4))*e^3*sqrt(-(b*f^4 + (b^2*c - 4*a*c^2)*sqrt(f^8/((b^2*c^2 - 4*a*c^3)*e^4))*e^2)/((b^2*c - 4*a*c^2)*e^2))) - 1/2*sqrt(1/2)*sqrt(-(b*f^4 - (b^2*c - 4*a*c^2)*sqrt(f^8/((b^2*c^2 - 4*a*c^3)*e^4))*e^2)/((b^2*c - 4*a*c^2)*e^2))*log(e*f^6*x + d*f^6 + sqrt(1/2)*(b^2*c - 4*a*c^2)*sqrt(f^8/((b^2*c^2 - 4*a*c^3)*e^4))*e^3*sqrt(-(b*f^4 - (b^2*c - 4*a*c^2)*sqrt(f^8/((b^2*c^2 - 4*a*c^3)*e^4))*e^2)/((b^2*c - 4*a*c^2)*e^2))) + 1/2*sqrt(1/2)*sqrt(-(b*f^4 - (b^2*c - 4*a*c^2)*sqrt(f^8/((b^2*c^2 - 4*a*c^3)*e^4))*e^2)/((b^2*c - 4*a*c^2)*e^2))*log(e*f^6*x + d*f^6 - sqrt(1/2)*(b^2*c - 4*a*c^2)*sqrt(f^8/((b^2*c^2 - 4*a*c^3)*e^4))*e^3*sqrt(-(b*f^4 - (b^2*c - 4*a*c^2)*sqrt(f^8/((b^2*c^2 - 4*a*c^3)*e^4))*e^2)/((b^2*c - 4*a*c^2)*e^2)))","B",0
641,1,274,0,1.220254," ","integrate((e*f*x+d*f)/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""fricas"")","\left[\frac{f \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c - {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right)}{2 \, \sqrt{b^{2} - 4 \, a c} e}, -\frac{\sqrt{-b^{2} + 4 \, a c} f \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right)}{{\left(b^{2} - 4 \, a c\right)} e}\right]"," ",0,"[1/2*f*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c - (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a))/(sqrt(b^2 - 4*a*c)*e), -sqrt(-b^2 + 4*a*c)*f*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c))/((b^2 - 4*a*c)*e)]","A",0
642,1,474,0,1.184368," ","integrate(1/(e*f*x+d*f)/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} - 4 \, a c} b \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c + {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right) - {\left(b^{2} - 4 \, a c\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 4 \, {\left(b^{2} - 4 \, a c\right)} \log\left(e x + d\right)}{4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} e f}, \frac{2 \, \sqrt{-b^{2} + 4 \, a c} b \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left(b^{2} - 4 \, a c\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 4 \, {\left(b^{2} - 4 \, a c\right)} \log\left(e x + d\right)}{4 \, {\left(a b^{2} - 4 \, a^{2} c\right)} e f}\right]"," ",0,"[1/4*(sqrt(b^2 - 4*a*c)*b*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c + (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)) - (b^2 - 4*a*c)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 4*(b^2 - 4*a*c)*log(e*x + d))/((a*b^2 - 4*a^2*c)*e*f), 1/4*(2*sqrt(-b^2 + 4*a*c)*b*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - (b^2 - 4*a*c)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 4*(b^2 - 4*a*c)*log(e*x + d))/((a*b^2 - 4*a^2*c)*e*f)]","A",0
643,1,1477,0,1.447975," ","integrate(1/(e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} {\left(a e^{2} f^{2} x + a d e f^{2}\right)} \sqrt{-\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} f^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4} f^{8}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} f^{4}}} \log\left(-2 \, {\left(b^{2} c^{2} - a c^{3}\right)} e x - 2 \, {\left(b^{2} c^{2} - a c^{3}\right)} d + \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} e^{3} f^{6} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4} f^{8}}} - {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e f^{2}\right)} \sqrt{-\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} f^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4} f^{8}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} f^{4}}}\right) - \sqrt{\frac{1}{2}} {\left(a e^{2} f^{2} x + a d e f^{2}\right)} \sqrt{-\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} f^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4} f^{8}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} f^{4}}} \log\left(-2 \, {\left(b^{2} c^{2} - a c^{3}\right)} e x - 2 \, {\left(b^{2} c^{2} - a c^{3}\right)} d - \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} e^{3} f^{6} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4} f^{8}}} - {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e f^{2}\right)} \sqrt{-\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} f^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4} f^{8}}} + b^{3} - 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} f^{4}}}\right) - \sqrt{\frac{1}{2}} {\left(a e^{2} f^{2} x + a d e f^{2}\right)} \sqrt{\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} f^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4} f^{8}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} f^{4}}} \log\left(-2 \, {\left(b^{2} c^{2} - a c^{3}\right)} e x - 2 \, {\left(b^{2} c^{2} - a c^{3}\right)} d + \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} e^{3} f^{6} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4} f^{8}}} + {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e f^{2}\right)} \sqrt{\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} f^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4} f^{8}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} f^{4}}}\right) + \sqrt{\frac{1}{2}} {\left(a e^{2} f^{2} x + a d e f^{2}\right)} \sqrt{\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} f^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4} f^{8}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} f^{4}}} \log\left(-2 \, {\left(b^{2} c^{2} - a c^{3}\right)} e x - 2 \, {\left(b^{2} c^{2} - a c^{3}\right)} d - \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} e^{3} f^{6} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4} f^{8}}} + {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e f^{2}\right)} \sqrt{\frac{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} f^{4} \sqrt{\frac{b^{4} - 2 \, a b^{2} c + a^{2} c^{2}}{{\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{4} f^{8}}} - b^{3} + 3 \, a b c}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{2} f^{4}}}\right) - 2}{2 \, {\left(a e^{2} f^{2} x + a d e f^{2}\right)}}"," ",0,"1/2*(sqrt(1/2)*(a*e^2*f^2*x + a*d*e*f^2)*sqrt(-((a^3*b^2 - 4*a^4*c)*e^2*f^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4*f^8)) + b^3 - 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*e^2*f^4))*log(-2*(b^2*c^2 - a*c^3)*e*x - 2*(b^2*c^2 - a*c^3)*d + sqrt(1/2)*((a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*e^3*f^6*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4*f^8)) - (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e*f^2)*sqrt(-((a^3*b^2 - 4*a^4*c)*e^2*f^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4*f^8)) + b^3 - 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*e^2*f^4))) - sqrt(1/2)*(a*e^2*f^2*x + a*d*e*f^2)*sqrt(-((a^3*b^2 - 4*a^4*c)*e^2*f^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4*f^8)) + b^3 - 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*e^2*f^4))*log(-2*(b^2*c^2 - a*c^3)*e*x - 2*(b^2*c^2 - a*c^3)*d - sqrt(1/2)*((a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*e^3*f^6*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4*f^8)) - (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e*f^2)*sqrt(-((a^3*b^2 - 4*a^4*c)*e^2*f^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4*f^8)) + b^3 - 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*e^2*f^4))) - sqrt(1/2)*(a*e^2*f^2*x + a*d*e*f^2)*sqrt(((a^3*b^2 - 4*a^4*c)*e^2*f^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4*f^8)) - b^3 + 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*e^2*f^4))*log(-2*(b^2*c^2 - a*c^3)*e*x - 2*(b^2*c^2 - a*c^3)*d + sqrt(1/2)*((a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*e^3*f^6*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4*f^8)) + (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e*f^2)*sqrt(((a^3*b^2 - 4*a^4*c)*e^2*f^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4*f^8)) - b^3 + 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*e^2*f^4))) + sqrt(1/2)*(a*e^2*f^2*x + a*d*e*f^2)*sqrt(((a^3*b^2 - 4*a^4*c)*e^2*f^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4*f^8)) - b^3 + 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*e^2*f^4))*log(-2*(b^2*c^2 - a*c^3)*e*x - 2*(b^2*c^2 - a*c^3)*d - sqrt(1/2)*((a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*e^3*f^6*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4*f^8)) + (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e*f^2)*sqrt(((a^3*b^2 - 4*a^4*c)*e^2*f^4*sqrt((b^4 - 2*a*b^2*c + a^2*c^2)/((a^6*b^2 - 4*a^7*c)*e^4*f^8)) - b^3 + 3*a*b*c)/((a^3*b^2 - 4*a^4*c)*e^2*f^4))) - 2)/(a*e^2*f^2*x + a*d*e*f^2)","B",0
644,1,828,0,1.934735," ","integrate(1/(e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""fricas"")","\left[-\frac{2 \, a b^{2} - 8 \, a^{2} c + {\left({\left(b^{2} - 2 \, a c\right)} e^{2} x^{2} + 2 \, {\left(b^{2} - 2 \, a c\right)} d e x + {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c + {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right) - {\left({\left(b^{3} - 4 \, a b c\right)} e^{2} x^{2} + 2 \, {\left(b^{3} - 4 \, a b c\right)} d e x + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 4 \, {\left({\left(b^{3} - 4 \, a b c\right)} e^{2} x^{2} + 2 \, {\left(b^{3} - 4 \, a b c\right)} d e x + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} \log\left(e x + d\right)}{4 \, {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{3} f^{3} x^{2} + 2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{2} f^{3} x + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{2} e f^{3}\right)}}, -\frac{2 \, a b^{2} - 8 \, a^{2} c + 2 \, {\left({\left(b^{2} - 2 \, a c\right)} e^{2} x^{2} + 2 \, {\left(b^{2} - 2 \, a c\right)} d e x + {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left({\left(b^{3} - 4 \, a b c\right)} e^{2} x^{2} + 2 \, {\left(b^{3} - 4 \, a b c\right)} d e x + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 4 \, {\left({\left(b^{3} - 4 \, a b c\right)} e^{2} x^{2} + 2 \, {\left(b^{3} - 4 \, a b c\right)} d e x + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} \log\left(e x + d\right)}{4 \, {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{3} f^{3} x^{2} + 2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{2} f^{3} x + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{2} e f^{3}\right)}}\right]"," ",0,"[-1/4*(2*a*b^2 - 8*a^2*c + ((b^2 - 2*a*c)*e^2*x^2 + 2*(b^2 - 2*a*c)*d*e*x + (b^2 - 2*a*c)*d^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c + (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)) - ((b^3 - 4*a*b*c)*e^2*x^2 + 2*(b^3 - 4*a*b*c)*d*e*x + (b^3 - 4*a*b*c)*d^2)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 4*((b^3 - 4*a*b*c)*e^2*x^2 + 2*(b^3 - 4*a*b*c)*d*e*x + (b^3 - 4*a*b*c)*d^2)*log(e*x + d))/((a^2*b^2 - 4*a^3*c)*e^3*f^3*x^2 + 2*(a^2*b^2 - 4*a^3*c)*d*e^2*f^3*x + (a^2*b^2 - 4*a^3*c)*d^2*e*f^3), -1/4*(2*a*b^2 - 8*a^2*c + 2*((b^2 - 2*a*c)*e^2*x^2 + 2*(b^2 - 2*a*c)*d*e*x + (b^2 - 2*a*c)*d^2)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - ((b^3 - 4*a*b*c)*e^2*x^2 + 2*(b^3 - 4*a*b*c)*d*e*x + (b^3 - 4*a*b*c)*d^2)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 4*((b^3 - 4*a*b*c)*e^2*x^2 + 2*(b^3 - 4*a*b*c)*d*e*x + (b^3 - 4*a*b*c)*d^2)*log(e*x + d))/((a^2*b^2 - 4*a^3*c)*e^3*f^3*x^2 + 2*(a^2*b^2 - 4*a^3*c)*d*e^2*f^3*x + (a^2*b^2 - 4*a^3*c)*d^2*e*f^3)]","B",0
645,1,2212,0,1.316229," ","integrate(1/(e*f*x+d*f)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4),x, algorithm=""fricas"")","\frac{6 \, b e^{2} x^{2} + 12 \, b d e x + 6 \, b d^{2} + 3 \, \sqrt{\frac{1}{2}} {\left(a^{2} e^{4} f^{4} x^{3} + 3 \, a^{2} d e^{3} f^{4} x^{2} + 3 \, a^{2} d^{2} e^{2} f^{4} x + a^{2} d^{3} e f^{4}\right)} \sqrt{-\frac{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} f^{8} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4} f^{16}}} + b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} f^{8}}} \log\left(2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} e x + 2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} d + \sqrt{\frac{1}{2}} {\left({\left(a^{5} b^{5} - 7 \, a^{6} b^{3} c + 12 \, a^{7} b c^{2}\right)} e^{3} f^{12} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4} f^{16}}} - {\left(b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 17 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}\right)} e f^{4}\right)} \sqrt{-\frac{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} f^{8} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4} f^{16}}} + b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} f^{8}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left(a^{2} e^{4} f^{4} x^{3} + 3 \, a^{2} d e^{3} f^{4} x^{2} + 3 \, a^{2} d^{2} e^{2} f^{4} x + a^{2} d^{3} e f^{4}\right)} \sqrt{-\frac{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} f^{8} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4} f^{16}}} + b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} f^{8}}} \log\left(2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} e x + 2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} d - \sqrt{\frac{1}{2}} {\left({\left(a^{5} b^{5} - 7 \, a^{6} b^{3} c + 12 \, a^{7} b c^{2}\right)} e^{3} f^{12} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4} f^{16}}} - {\left(b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 17 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}\right)} e f^{4}\right)} \sqrt{-\frac{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} f^{8} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4} f^{16}}} + b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} f^{8}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left(a^{2} e^{4} f^{4} x^{3} + 3 \, a^{2} d e^{3} f^{4} x^{2} + 3 \, a^{2} d^{2} e^{2} f^{4} x + a^{2} d^{3} e f^{4}\right)} \sqrt{\frac{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} f^{8} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4} f^{16}}} - b^{5} + 5 \, a b^{3} c - 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} f^{8}}} \log\left(2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} e x + 2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} d + \sqrt{\frac{1}{2}} {\left({\left(a^{5} b^{5} - 7 \, a^{6} b^{3} c + 12 \, a^{7} b c^{2}\right)} e^{3} f^{12} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4} f^{16}}} + {\left(b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 17 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}\right)} e f^{4}\right)} \sqrt{\frac{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} f^{8} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4} f^{16}}} - b^{5} + 5 \, a b^{3} c - 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} f^{8}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left(a^{2} e^{4} f^{4} x^{3} + 3 \, a^{2} d e^{3} f^{4} x^{2} + 3 \, a^{2} d^{2} e^{2} f^{4} x + a^{2} d^{3} e f^{4}\right)} \sqrt{\frac{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} f^{8} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4} f^{16}}} - b^{5} + 5 \, a b^{3} c - 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} f^{8}}} \log\left(2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} e x + 2 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} + a^{2} c^{5}\right)} d - \sqrt{\frac{1}{2}} {\left({\left(a^{5} b^{5} - 7 \, a^{6} b^{3} c + 12 \, a^{7} b c^{2}\right)} e^{3} f^{12} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4} f^{16}}} + {\left(b^{8} - 8 \, a b^{6} c + 20 \, a^{2} b^{4} c^{2} - 17 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}\right)} e f^{4}\right)} \sqrt{\frac{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} f^{8} \sqrt{\frac{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}}{{\left(a^{10} b^{2} - 4 \, a^{11} c\right)} e^{4} f^{16}}} - b^{5} + 5 \, a b^{3} c - 5 \, a^{2} b c^{2}}{{\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{2} f^{8}}}\right) - 2 \, a}{6 \, {\left(a^{2} e^{4} f^{4} x^{3} + 3 \, a^{2} d e^{3} f^{4} x^{2} + 3 \, a^{2} d^{2} e^{2} f^{4} x + a^{2} d^{3} e f^{4}\right)}}"," ",0,"1/6*(6*b*e^2*x^2 + 12*b*d*e*x + 6*b*d^2 + 3*sqrt(1/2)*(a^2*e^4*f^4*x^3 + 3*a^2*d*e^3*f^4*x^2 + 3*a^2*d^2*e^2*f^4*x + a^2*d^3*e*f^4)*sqrt(-((a^5*b^2 - 4*a^6*c)*e^2*f^8*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)/((a^10*b^2 - 4*a^11*c)*e^4*f^16)) + b^5 - 5*a*b^3*c + 5*a^2*b*c^2)/((a^5*b^2 - 4*a^6*c)*e^2*f^8))*log(2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*e*x + 2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*d + sqrt(1/2)*((a^5*b^5 - 7*a^6*b^3*c + 12*a^7*b*c^2)*e^3*f^12*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)/((a^10*b^2 - 4*a^11*c)*e^4*f^16)) - (b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 17*a^3*b^2*c^3 + 4*a^4*c^4)*e*f^4)*sqrt(-((a^5*b^2 - 4*a^6*c)*e^2*f^8*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)/((a^10*b^2 - 4*a^11*c)*e^4*f^16)) + b^5 - 5*a*b^3*c + 5*a^2*b*c^2)/((a^5*b^2 - 4*a^6*c)*e^2*f^8))) - 3*sqrt(1/2)*(a^2*e^4*f^4*x^3 + 3*a^2*d*e^3*f^4*x^2 + 3*a^2*d^2*e^2*f^4*x + a^2*d^3*e*f^4)*sqrt(-((a^5*b^2 - 4*a^6*c)*e^2*f^8*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)/((a^10*b^2 - 4*a^11*c)*e^4*f^16)) + b^5 - 5*a*b^3*c + 5*a^2*b*c^2)/((a^5*b^2 - 4*a^6*c)*e^2*f^8))*log(2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*e*x + 2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*d - sqrt(1/2)*((a^5*b^5 - 7*a^6*b^3*c + 12*a^7*b*c^2)*e^3*f^12*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)/((a^10*b^2 - 4*a^11*c)*e^4*f^16)) - (b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 17*a^3*b^2*c^3 + 4*a^4*c^4)*e*f^4)*sqrt(-((a^5*b^2 - 4*a^6*c)*e^2*f^8*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)/((a^10*b^2 - 4*a^11*c)*e^4*f^16)) + b^5 - 5*a*b^3*c + 5*a^2*b*c^2)/((a^5*b^2 - 4*a^6*c)*e^2*f^8))) - 3*sqrt(1/2)*(a^2*e^4*f^4*x^3 + 3*a^2*d*e^3*f^4*x^2 + 3*a^2*d^2*e^2*f^4*x + a^2*d^3*e*f^4)*sqrt(((a^5*b^2 - 4*a^6*c)*e^2*f^8*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)/((a^10*b^2 - 4*a^11*c)*e^4*f^16)) - b^5 + 5*a*b^3*c - 5*a^2*b*c^2)/((a^5*b^2 - 4*a^6*c)*e^2*f^8))*log(2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*e*x + 2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*d + sqrt(1/2)*((a^5*b^5 - 7*a^6*b^3*c + 12*a^7*b*c^2)*e^3*f^12*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)/((a^10*b^2 - 4*a^11*c)*e^4*f^16)) + (b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 17*a^3*b^2*c^3 + 4*a^4*c^4)*e*f^4)*sqrt(((a^5*b^2 - 4*a^6*c)*e^2*f^8*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)/((a^10*b^2 - 4*a^11*c)*e^4*f^16)) - b^5 + 5*a*b^3*c - 5*a^2*b*c^2)/((a^5*b^2 - 4*a^6*c)*e^2*f^8))) + 3*sqrt(1/2)*(a^2*e^4*f^4*x^3 + 3*a^2*d*e^3*f^4*x^2 + 3*a^2*d^2*e^2*f^4*x + a^2*d^3*e*f^4)*sqrt(((a^5*b^2 - 4*a^6*c)*e^2*f^8*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)/((a^10*b^2 - 4*a^11*c)*e^4*f^16)) - b^5 + 5*a*b^3*c - 5*a^2*b*c^2)/((a^5*b^2 - 4*a^6*c)*e^2*f^8))*log(2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*e*x + 2*(b^4*c^3 - 3*a*b^2*c^4 + a^2*c^5)*d - sqrt(1/2)*((a^5*b^5 - 7*a^6*b^3*c + 12*a^7*b*c^2)*e^3*f^12*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)/((a^10*b^2 - 4*a^11*c)*e^4*f^16)) + (b^8 - 8*a*b^6*c + 20*a^2*b^4*c^2 - 17*a^3*b^2*c^3 + 4*a^4*c^4)*e*f^4)*sqrt(((a^5*b^2 - 4*a^6*c)*e^2*f^8*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)/((a^10*b^2 - 4*a^11*c)*e^4*f^16)) - b^5 + 5*a*b^3*c - 5*a^2*b*c^2)/((a^5*b^2 - 4*a^6*c)*e^2*f^8))) - 2*a)/(a^2*e^4*f^4*x^3 + 3*a^2*d*e^3*f^4*x^2 + 3*a^2*d^2*e^2*f^4*x + a^2*d^3*e*f^4)","B",0
646,1,2578,0,1.255686," ","integrate((e*f*x+d*f)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""fricas"")","\frac{2 \, b e^{3} f^{4} x^{3} + 6 \, b d e^{2} f^{4} x^{2} + 2 \, {\left(3 \, b d^{2} + 2 \, a\right)} e f^{4} x + 2 \, {\left(b d^{3} + 2 \, a d\right)} f^{4} + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{4} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{4} x^{3} + {\left(b^{3} - 4 \, a b c + 6 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(b^{3} - 4 \, a b c\right)} d\right)} e^{2} x + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{3} + 12 \, a b c\right)} f^{8} + \sqrt{\frac{f^{16}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}} \log\left({\left(3 \, b^{2} + 4 \, a c\right)} e f^{12} x + {\left(3 \, b^{2} + 4 \, a c\right)} d f^{12} + \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e f^{8} + 2 \, \sqrt{\frac{f^{16}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e^{3}\right)} \sqrt{-\frac{{\left(b^{3} + 12 \, a b c\right)} f^{8} + \sqrt{\frac{f^{16}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{4} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{4} x^{3} + {\left(b^{3} - 4 \, a b c + 6 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(b^{3} - 4 \, a b c\right)} d\right)} e^{2} x + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{3} + 12 \, a b c\right)} f^{8} + \sqrt{\frac{f^{16}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}} \log\left({\left(3 \, b^{2} + 4 \, a c\right)} e f^{12} x + {\left(3 \, b^{2} + 4 \, a c\right)} d f^{12} - \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e f^{8} + 2 \, \sqrt{\frac{f^{16}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e^{3}\right)} \sqrt{-\frac{{\left(b^{3} + 12 \, a b c\right)} f^{8} + \sqrt{\frac{f^{16}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{4} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{4} x^{3} + {\left(b^{3} - 4 \, a b c + 6 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(b^{3} - 4 \, a b c\right)} d\right)} e^{2} x + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{3} + 12 \, a b c\right)} f^{8} - \sqrt{\frac{f^{16}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}} \log\left({\left(3 \, b^{2} + 4 \, a c\right)} e f^{12} x + {\left(3 \, b^{2} + 4 \, a c\right)} d f^{12} + \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e f^{8} - 2 \, \sqrt{\frac{f^{16}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e^{3}\right)} \sqrt{-\frac{{\left(b^{3} + 12 \, a b c\right)} f^{8} - \sqrt{\frac{f^{16}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{4} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{4} x^{3} + {\left(b^{3} - 4 \, a b c + 6 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(b^{3} - 4 \, a b c\right)} d\right)} e^{2} x + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{3} + 12 \, a b c\right)} f^{8} - \sqrt{\frac{f^{16}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}} \log\left({\left(3 \, b^{2} + 4 \, a c\right)} e f^{12} x + {\left(3 \, b^{2} + 4 \, a c\right)} d f^{12} - \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e f^{8} - 2 \, \sqrt{\frac{f^{16}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e^{3}\right)} \sqrt{-\frac{{\left(b^{3} + 12 \, a b c\right)} f^{8} - \sqrt{\frac{f^{16}}{{\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{4}}} {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}}}\right)}{4 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{4} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{4} x^{3} + {\left(b^{3} - 4 \, a b c + 6 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(b^{3} - 4 \, a b c\right)} d\right)} e^{2} x + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} e\right)}}"," ",0,"1/4*(2*b*e^3*f^4*x^3 + 6*b*d*e^2*f^4*x^2 + 2*(3*b*d^2 + 2*a)*e*f^4*x + 2*(b*d^3 + 2*a*d)*f^4 + sqrt(1/2)*((b^2*c - 4*a*c^2)*e^5*x^4 + 4*(b^2*c - 4*a*c^2)*d*e^4*x^3 + (b^3 - 4*a*b*c + 6*(b^2*c - 4*a*c^2)*d^2)*e^3*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^3 + (b^3 - 4*a*b*c)*d)*e^2*x + ((b^2*c - 4*a*c^2)*d^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*d^2)*e)*sqrt(-((b^3 + 12*a*b*c)*f^8 + sqrt(f^16/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4))*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2)/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2))*log((3*b^2 + 4*a*c)*e*f^12*x + (3*b^2 + 4*a*c)*d*f^12 + sqrt(1/2)*((b^4 - 8*a*b^2*c + 16*a^2*c^2)*e*f^8 + 2*sqrt(f^16/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4))*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*e^3)*sqrt(-((b^3 + 12*a*b*c)*f^8 + sqrt(f^16/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4))*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2)/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2))) - sqrt(1/2)*((b^2*c - 4*a*c^2)*e^5*x^4 + 4*(b^2*c - 4*a*c^2)*d*e^4*x^3 + (b^3 - 4*a*b*c + 6*(b^2*c - 4*a*c^2)*d^2)*e^3*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^3 + (b^3 - 4*a*b*c)*d)*e^2*x + ((b^2*c - 4*a*c^2)*d^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*d^2)*e)*sqrt(-((b^3 + 12*a*b*c)*f^8 + sqrt(f^16/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4))*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2)/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2))*log((3*b^2 + 4*a*c)*e*f^12*x + (3*b^2 + 4*a*c)*d*f^12 - sqrt(1/2)*((b^4 - 8*a*b^2*c + 16*a^2*c^2)*e*f^8 + 2*sqrt(f^16/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4))*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*e^3)*sqrt(-((b^3 + 12*a*b*c)*f^8 + sqrt(f^16/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4))*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2)/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2))) + sqrt(1/2)*((b^2*c - 4*a*c^2)*e^5*x^4 + 4*(b^2*c - 4*a*c^2)*d*e^4*x^3 + (b^3 - 4*a*b*c + 6*(b^2*c - 4*a*c^2)*d^2)*e^3*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^3 + (b^3 - 4*a*b*c)*d)*e^2*x + ((b^2*c - 4*a*c^2)*d^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*d^2)*e)*sqrt(-((b^3 + 12*a*b*c)*f^8 - sqrt(f^16/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4))*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2)/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2))*log((3*b^2 + 4*a*c)*e*f^12*x + (3*b^2 + 4*a*c)*d*f^12 + sqrt(1/2)*((b^4 - 8*a*b^2*c + 16*a^2*c^2)*e*f^8 - 2*sqrt(f^16/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4))*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*e^3)*sqrt(-((b^3 + 12*a*b*c)*f^8 - sqrt(f^16/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4))*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2)/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2))) - sqrt(1/2)*((b^2*c - 4*a*c^2)*e^5*x^4 + 4*(b^2*c - 4*a*c^2)*d*e^4*x^3 + (b^3 - 4*a*b*c + 6*(b^2*c - 4*a*c^2)*d^2)*e^3*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^3 + (b^3 - 4*a*b*c)*d)*e^2*x + ((b^2*c - 4*a*c^2)*d^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*d^2)*e)*sqrt(-((b^3 + 12*a*b*c)*f^8 - sqrt(f^16/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4))*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2)/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2))*log((3*b^2 + 4*a*c)*e*f^12*x + (3*b^2 + 4*a*c)*d*f^12 - sqrt(1/2)*((b^4 - 8*a*b^2*c + 16*a^2*c^2)*e*f^8 - 2*sqrt(f^16/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4))*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*e^3)*sqrt(-((b^3 + 12*a*b*c)*f^8 - sqrt(f^16/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^4))*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2)/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*e^2))))/((b^2*c - 4*a*c^2)*e^5*x^4 + 4*(b^2*c - 4*a*c^2)*d*e^4*x^3 + (b^3 - 4*a*b*c + 6*(b^2*c - 4*a*c^2)*d^2)*e^3*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^3 + (b^3 - 4*a*b*c)*d)*e^2*x + ((b^2*c - 4*a*c^2)*d^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*d^2)*e)","B",0
647,1,1077,0,1.209067," ","integrate((e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""fricas"")","\left[\frac{{\left(b^{3} - 4 \, a b c\right)} e^{2} f^{3} x^{2} + 2 \, {\left(b^{3} - 4 \, a b c\right)} d e f^{3} x + {\left(2 \, a b^{2} - 8 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} f^{3} - {\left(b c e^{4} f^{3} x^{4} + 4 \, b c d e^{3} f^{3} x^{3} + {\left(6 \, b c d^{2} + b^{2}\right)} e^{2} f^{3} x^{2} + 2 \, {\left(2 \, b c d^{3} + b^{2} d\right)} e f^{3} x + {\left(b c d^{4} + b^{2} d^{2} + a b\right)} f^{3}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c + {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right)}{2 \, {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{5} x^{4} + 4 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} x^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + 6 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d\right)} e^{2} x + {\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)} d^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2}\right)} e\right)}}, \frac{{\left(b^{3} - 4 \, a b c\right)} e^{2} f^{3} x^{2} + 2 \, {\left(b^{3} - 4 \, a b c\right)} d e f^{3} x + {\left(2 \, a b^{2} - 8 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} f^{3} - 2 \, {\left(b c e^{4} f^{3} x^{4} + 4 \, b c d e^{3} f^{3} x^{3} + {\left(6 \, b c d^{2} + b^{2}\right)} e^{2} f^{3} x^{2} + 2 \, {\left(2 \, b c d^{3} + b^{2} d\right)} e f^{3} x + {\left(b c d^{4} + b^{2} d^{2} + a b\right)} f^{3}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right)}{2 \, {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{5} x^{4} + 4 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} x^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + 6 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d\right)} e^{2} x + {\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)} d^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2}\right)} e\right)}}\right]"," ",0,"[1/2*((b^3 - 4*a*b*c)*e^2*f^3*x^2 + 2*(b^3 - 4*a*b*c)*d*e*f^3*x + (2*a*b^2 - 8*a^2*c + (b^3 - 4*a*b*c)*d^2)*f^3 - (b*c*e^4*f^3*x^4 + 4*b*c*d*e^3*f^3*x^3 + (6*b*c*d^2 + b^2)*e^2*f^3*x^2 + 2*(2*b*c*d^3 + b^2*d)*e*f^3*x + (b*c*d^4 + b^2*d^2 + a*b)*f^3)*sqrt(b^2 - 4*a*c)*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c + (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)))/((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^5*x^4 + 4*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^4*x^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + 6*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2)*e^3*x^2 + 2*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d)*e^2*x + (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)*d^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2)*e), 1/2*((b^3 - 4*a*b*c)*e^2*f^3*x^2 + 2*(b^3 - 4*a*b*c)*d*e*f^3*x + (2*a*b^2 - 8*a^2*c + (b^3 - 4*a*b*c)*d^2)*f^3 - 2*(b*c*e^4*f^3*x^4 + 4*b*c*d*e^3*f^3*x^3 + (6*b*c*d^2 + b^2)*e^2*f^3*x^2 + 2*(2*b*c*d^3 + b^2*d)*e*f^3*x + (b*c*d^4 + b^2*d^2 + a*b)*f^3)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)))/((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^5*x^4 + 4*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^4*x^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + 6*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2)*e^3*x^2 + 2*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d)*e^2*x + (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)*d^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2)*e)]","B",0
648,1,2600,0,1.315925," ","integrate((e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""fricas"")","-\frac{4 \, c e^{3} f^{2} x^{3} + 12 \, c d e^{2} f^{2} x^{2} + 2 \, {\left(6 \, c d^{2} + b\right)} e f^{2} x + 2 \, {\left(2 \, c d^{3} + b d\right)} f^{2} + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{4} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{4} x^{3} + {\left(b^{3} - 4 \, a b c + 6 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(b^{3} - 4 \, a b c\right)} d\right)} e^{2} x + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{3} + 12 \, a b c\right)} f^{4} + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} \sqrt{\frac{f^{8}}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} e^{2}}{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} \log\left({\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e f^{6} x + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d f^{6} + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e f^{4} - {\left(a b^{8} - 8 \, a^{2} b^{6} c + 128 \, a^{4} b^{2} c^{3} - 256 \, a^{5} c^{4}\right)} \sqrt{\frac{f^{8}}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} e^{3}\right)} \sqrt{-\frac{{\left(b^{3} + 12 \, a b c\right)} f^{4} + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} \sqrt{\frac{f^{8}}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} e^{2}}{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{4} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{4} x^{3} + {\left(b^{3} - 4 \, a b c + 6 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(b^{3} - 4 \, a b c\right)} d\right)} e^{2} x + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{3} + 12 \, a b c\right)} f^{4} + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} \sqrt{\frac{f^{8}}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} e^{2}}{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} \log\left({\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e f^{6} x + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d f^{6} - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e f^{4} - {\left(a b^{8} - 8 \, a^{2} b^{6} c + 128 \, a^{4} b^{2} c^{3} - 256 \, a^{5} c^{4}\right)} \sqrt{\frac{f^{8}}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} e^{3}\right)} \sqrt{-\frac{{\left(b^{3} + 12 \, a b c\right)} f^{4} + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} \sqrt{\frac{f^{8}}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} e^{2}}{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{4} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{4} x^{3} + {\left(b^{3} - 4 \, a b c + 6 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(b^{3} - 4 \, a b c\right)} d\right)} e^{2} x + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{3} + 12 \, a b c\right)} f^{4} - {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} \sqrt{\frac{f^{8}}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} e^{2}}{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} \log\left({\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e f^{6} x + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d f^{6} + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e f^{4} + {\left(a b^{8} - 8 \, a^{2} b^{6} c + 128 \, a^{4} b^{2} c^{3} - 256 \, a^{5} c^{4}\right)} \sqrt{\frac{f^{8}}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} e^{3}\right)} \sqrt{-\frac{{\left(b^{3} + 12 \, a b c\right)} f^{4} - {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} \sqrt{\frac{f^{8}}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} e^{2}}{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{4} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{4} x^{3} + {\left(b^{3} - 4 \, a b c + 6 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(b^{3} - 4 \, a b c\right)} d\right)} e^{2} x + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{3} + 12 \, a b c\right)} f^{4} - {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} \sqrt{\frac{f^{8}}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} e^{2}}{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} \log\left({\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e f^{6} x + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d f^{6} - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e f^{4} + {\left(a b^{8} - 8 \, a^{2} b^{6} c + 128 \, a^{4} b^{2} c^{3} - 256 \, a^{5} c^{4}\right)} \sqrt{\frac{f^{8}}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} e^{3}\right)} \sqrt{-\frac{{\left(b^{3} + 12 \, a b c\right)} f^{4} - {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} \sqrt{\frac{f^{8}}{{\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} e^{2}}{{\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}}\right)}{4 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{5} x^{4} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{4} x^{3} + {\left(b^{3} - 4 \, a b c + 6 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} + {\left(b^{3} - 4 \, a b c\right)} d\right)} e^{2} x + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} + a b^{2} - 4 \, a^{2} c + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} e\right)}}"," ",0,"-1/4*(4*c*e^3*f^2*x^3 + 12*c*d*e^2*f^2*x^2 + 2*(6*c*d^2 + b)*e*f^2*x + 2*(2*c*d^3 + b*d)*f^2 + sqrt(1/2)*((b^2*c - 4*a*c^2)*e^5*x^4 + 4*(b^2*c - 4*a*c^2)*d*e^4*x^3 + (b^3 - 4*a*b*c + 6*(b^2*c - 4*a*c^2)*d^2)*e^3*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^3 + (b^3 - 4*a*b*c)*d)*e^2*x + ((b^2*c - 4*a*c^2)*d^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*d^2)*e)*sqrt(-((b^3 + 12*a*b*c)*f^4 + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*sqrt(f^8/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*e^2)/((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))*log((3*b^2*c + 4*a*c^2)*e*f^6*x + (3*b^2*c + 4*a*c^2)*d*f^6 + 1/2*sqrt(1/2)*((b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e*f^4 - (a*b^8 - 8*a^2*b^6*c + 128*a^4*b^2*c^3 - 256*a^5*c^4)*sqrt(f^8/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*e^3)*sqrt(-((b^3 + 12*a*b*c)*f^4 + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*sqrt(f^8/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*e^2)/((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))) - sqrt(1/2)*((b^2*c - 4*a*c^2)*e^5*x^4 + 4*(b^2*c - 4*a*c^2)*d*e^4*x^3 + (b^3 - 4*a*b*c + 6*(b^2*c - 4*a*c^2)*d^2)*e^3*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^3 + (b^3 - 4*a*b*c)*d)*e^2*x + ((b^2*c - 4*a*c^2)*d^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*d^2)*e)*sqrt(-((b^3 + 12*a*b*c)*f^4 + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*sqrt(f^8/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*e^2)/((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))*log((3*b^2*c + 4*a*c^2)*e*f^6*x + (3*b^2*c + 4*a*c^2)*d*f^6 - 1/2*sqrt(1/2)*((b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e*f^4 - (a*b^8 - 8*a^2*b^6*c + 128*a^4*b^2*c^3 - 256*a^5*c^4)*sqrt(f^8/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*e^3)*sqrt(-((b^3 + 12*a*b*c)*f^4 + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*sqrt(f^8/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*e^2)/((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))) + sqrt(1/2)*((b^2*c - 4*a*c^2)*e^5*x^4 + 4*(b^2*c - 4*a*c^2)*d*e^4*x^3 + (b^3 - 4*a*b*c + 6*(b^2*c - 4*a*c^2)*d^2)*e^3*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^3 + (b^3 - 4*a*b*c)*d)*e^2*x + ((b^2*c - 4*a*c^2)*d^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*d^2)*e)*sqrt(-((b^3 + 12*a*b*c)*f^4 - (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*sqrt(f^8/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*e^2)/((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))*log((3*b^2*c + 4*a*c^2)*e*f^6*x + (3*b^2*c + 4*a*c^2)*d*f^6 + 1/2*sqrt(1/2)*((b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e*f^4 + (a*b^8 - 8*a^2*b^6*c + 128*a^4*b^2*c^3 - 256*a^5*c^4)*sqrt(f^8/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*e^3)*sqrt(-((b^3 + 12*a*b*c)*f^4 - (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*sqrt(f^8/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*e^2)/((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))) - sqrt(1/2)*((b^2*c - 4*a*c^2)*e^5*x^4 + 4*(b^2*c - 4*a*c^2)*d*e^4*x^3 + (b^3 - 4*a*b*c + 6*(b^2*c - 4*a*c^2)*d^2)*e^3*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^3 + (b^3 - 4*a*b*c)*d)*e^2*x + ((b^2*c - 4*a*c^2)*d^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*d^2)*e)*sqrt(-((b^3 + 12*a*b*c)*f^4 - (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*sqrt(f^8/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*e^2)/((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))*log((3*b^2*c + 4*a*c^2)*e*f^6*x + (3*b^2*c + 4*a*c^2)*d*f^6 - 1/2*sqrt(1/2)*((b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e*f^4 + (a*b^8 - 8*a^2*b^6*c + 128*a^4*b^2*c^3 - 256*a^5*c^4)*sqrt(f^8/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*e^3)*sqrt(-((b^3 + 12*a*b*c)*f^4 - (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*sqrt(f^8/((a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*e^2)/((a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))))/((b^2*c - 4*a*c^2)*e^5*x^4 + 4*(b^2*c - 4*a*c^2)*d*e^4*x^3 + (b^3 - 4*a*b*c + 6*(b^2*c - 4*a*c^2)*d^2)*e^3*x^2 + 2*(2*(b^2*c - 4*a*c^2)*d^3 + (b^3 - 4*a*b*c)*d)*e^2*x + ((b^2*c - 4*a*c^2)*d^4 + a*b^2 - 4*a^2*c + (b^3 - 4*a*b*c)*d^2)*e)","B",0
649,1,1066,0,1.114996," ","integrate((e*f*x+d*f)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} f x^{2} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e f x + 2 \, {\left(c^{2} e^{4} f x^{4} + 4 \, c^{2} d e^{3} f x^{3} + {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} f x^{2} + 2 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e f x + {\left(c^{2} d^{4} + b c d^{2} + a c\right)} f\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c - {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right) + {\left(b^{3} - 4 \, a b c + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} f}{2 \, {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{5} x^{4} + 4 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} x^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + 6 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d\right)} e^{2} x + {\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)} d^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2}\right)} e\right)}}, -\frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} f x^{2} + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e f x - 4 \, {\left(c^{2} e^{4} f x^{4} + 4 \, c^{2} d e^{3} f x^{3} + {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} f x^{2} + 2 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e f x + {\left(c^{2} d^{4} + b c d^{2} + a c\right)} f\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) + {\left(b^{3} - 4 \, a b c + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} f}{2 \, {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{5} x^{4} + 4 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} x^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + 6 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 2 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d\right)} e^{2} x + {\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)} d^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2}\right)} e\right)}}\right]"," ",0,"[-1/2*(2*(b^2*c - 4*a*c^2)*e^2*f*x^2 + 4*(b^2*c - 4*a*c^2)*d*e*f*x + 2*(c^2*e^4*f*x^4 + 4*c^2*d*e^3*f*x^3 + (6*c^2*d^2 + b*c)*e^2*f*x^2 + 2*(2*c^2*d^3 + b*c*d)*e*f*x + (c^2*d^4 + b*c*d^2 + a*c)*f)*sqrt(b^2 - 4*a*c)*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c - (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)) + (b^3 - 4*a*b*c + 2*(b^2*c - 4*a*c^2)*d^2)*f)/((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^5*x^4 + 4*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^4*x^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + 6*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2)*e^3*x^2 + 2*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d)*e^2*x + (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)*d^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2)*e), -1/2*(2*(b^2*c - 4*a*c^2)*e^2*f*x^2 + 4*(b^2*c - 4*a*c^2)*d*e*f*x - 4*(c^2*e^4*f*x^4 + 4*c^2*d*e^3*f*x^3 + (6*c^2*d^2 + b*c)*e^2*f*x^2 + 2*(2*c^2*d^3 + b*c*d)*e*f*x + (c^2*d^4 + b*c*d^2 + a*c)*f)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) + (b^3 - 4*a*b*c + 2*(b^2*c - 4*a*c^2)*d^2)*f)/((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^5*x^4 + 4*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^4*x^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + 6*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2)*e^3*x^2 + 2*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d)*e^2*x + (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)*d^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2)*e)]","B",0
650,1,2486,0,2.338344," ","integrate(1/(e*f*x+d*f)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a b^{4} - 12 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} e^{2} x^{2} + 4 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e x + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{2} + {\left({\left(b^{3} c - 6 \, a b c^{2}\right)} e^{4} x^{4} + 4 \, {\left(b^{3} c - 6 \, a b c^{2}\right)} d e^{3} x^{3} + {\left(b^{3} c - 6 \, a b c^{2}\right)} d^{4} + {\left(b^{4} - 6 \, a b^{2} c + 6 \, {\left(b^{3} c - 6 \, a b c^{2}\right)} d^{2}\right)} e^{2} x^{2} + a b^{3} - 6 \, a^{2} b c + {\left(b^{4} - 6 \, a b^{2} c\right)} d^{2} + 2 \, {\left(2 \, {\left(b^{3} c - 6 \, a b c^{2}\right)} d^{3} + {\left(b^{4} - 6 \, a b^{2} c\right)} d\right)} e x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c + {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right) - {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{4} x^{4} + 4 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{3} x^{3} + 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)} d^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + 6 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2} + 2 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d\right)} e x\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 4 \, {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{4} x^{4} + 4 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{3} x^{3} + 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)} d^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + 6 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2} + 2 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d\right)} e x\right)} \log\left(e x + d\right)}{4 \, {\left({\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} e^{5} f x^{4} + 4 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d e^{4} f x^{3} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2} + 6 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d^{2}\right)} e^{3} f x^{2} + 2 \, {\left(2 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d^{3} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d\right)} e^{2} f x + {\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)} d^{4} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d^{2}\right)} e f\right)}}, \frac{2 \, a b^{4} - 12 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} e^{2} x^{2} + 4 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e x + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{2} + 2 \, {\left({\left(b^{3} c - 6 \, a b c^{2}\right)} e^{4} x^{4} + 4 \, {\left(b^{3} c - 6 \, a b c^{2}\right)} d e^{3} x^{3} + {\left(b^{3} c - 6 \, a b c^{2}\right)} d^{4} + {\left(b^{4} - 6 \, a b^{2} c + 6 \, {\left(b^{3} c - 6 \, a b c^{2}\right)} d^{2}\right)} e^{2} x^{2} + a b^{3} - 6 \, a^{2} b c + {\left(b^{4} - 6 \, a b^{2} c\right)} d^{2} + 2 \, {\left(2 \, {\left(b^{3} c - 6 \, a b c^{2}\right)} d^{3} + {\left(b^{4} - 6 \, a b^{2} c\right)} d\right)} e x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{4} x^{4} + 4 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{3} x^{3} + 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)} d^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + 6 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2} + 2 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d\right)} e x\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 4 \, {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{4} x^{4} + 4 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{3} x^{3} + 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)} d^{4} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + 6 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2} + 2 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d\right)} e x\right)} \log\left(e x + d\right)}{4 \, {\left({\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} e^{5} f x^{4} + 4 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d e^{4} f x^{3} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2} + 6 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d^{2}\right)} e^{3} f x^{2} + 2 \, {\left(2 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d^{3} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d\right)} e^{2} f x + {\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)} d^{4} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d^{2}\right)} e f\right)}}\right]"," ",0,"[1/4*(2*a*b^4 - 12*a^2*b^2*c + 16*a^3*c^2 + 2*(a*b^3*c - 4*a^2*b*c^2)*e^2*x^2 + 4*(a*b^3*c - 4*a^2*b*c^2)*d*e*x + 2*(a*b^3*c - 4*a^2*b*c^2)*d^2 + ((b^3*c - 6*a*b*c^2)*e^4*x^4 + 4*(b^3*c - 6*a*b*c^2)*d*e^3*x^3 + (b^3*c - 6*a*b*c^2)*d^4 + (b^4 - 6*a*b^2*c + 6*(b^3*c - 6*a*b*c^2)*d^2)*e^2*x^2 + a*b^3 - 6*a^2*b*c + (b^4 - 6*a*b^2*c)*d^2 + 2*(2*(b^3*c - 6*a*b*c^2)*d^3 + (b^4 - 6*a*b^2*c)*d)*e*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c + (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)) - ((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^4*x^4 + 4*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^3*x^3 + 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)*d^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + 6*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2)*e^2*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2 + 2*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d)*e*x)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 4*((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^4*x^4 + 4*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^3*x^3 + 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)*d^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + 6*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2)*e^2*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2 + 2*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d)*e*x)*log(e*x + d))/((a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*e^5*f*x^4 + 4*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d*e^4*f*x^3 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2 + 6*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d^2)*e^3*f*x^2 + 2*(2*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d^3 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d)*e^2*f*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)*d^4 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d^2)*e*f), 1/4*(2*a*b^4 - 12*a^2*b^2*c + 16*a^3*c^2 + 2*(a*b^3*c - 4*a^2*b*c^2)*e^2*x^2 + 4*(a*b^3*c - 4*a^2*b*c^2)*d*e*x + 2*(a*b^3*c - 4*a^2*b*c^2)*d^2 + 2*((b^3*c - 6*a*b*c^2)*e^4*x^4 + 4*(b^3*c - 6*a*b*c^2)*d*e^3*x^3 + (b^3*c - 6*a*b*c^2)*d^4 + (b^4 - 6*a*b^2*c + 6*(b^3*c - 6*a*b*c^2)*d^2)*e^2*x^2 + a*b^3 - 6*a^2*b*c + (b^4 - 6*a*b^2*c)*d^2 + 2*(2*(b^3*c - 6*a*b*c^2)*d^3 + (b^4 - 6*a*b^2*c)*d)*e*x)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - ((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^4*x^4 + 4*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^3*x^3 + 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)*d^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + 6*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2)*e^2*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2 + 2*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d)*e*x)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 4*((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^4*x^4 + 4*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^3*x^3 + 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)*d^4 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + 6*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2)*e^2*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2 + 2*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d)*e*x)*log(e*x + d))/((a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*e^5*f*x^4 + 4*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d*e^4*f*x^3 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2 + 6*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d^2)*e^3*f*x^2 + 2*(2*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d^3 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d)*e^2*f*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)*d^4 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d^2)*e*f)]","B",0
651,1,4520,0,1.762564," ","integrate(1/(e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, b^{2} c - 10 \, a c^{2}\right)} e^{4} x^{4} + 8 \, {\left(3 \, b^{2} c - 10 \, a c^{2}\right)} d e^{3} x^{3} + 2 \, {\left(3 \, b^{2} c - 10 \, a c^{2}\right)} d^{4} + 2 \, {\left(3 \, b^{3} - 11 \, a b c + 6 \, {\left(3 \, b^{2} c - 10 \, a c^{2}\right)} d^{2}\right)} e^{2} x^{2} + 4 \, a b^{2} - 16 \, a^{2} c + 2 \, {\left(3 \, b^{3} - 11 \, a b c\right)} d^{2} + 4 \, {\left(2 \, {\left(3 \, b^{2} c - 10 \, a c^{2}\right)} d^{3} + {\left(3 \, b^{3} - 11 \, a b c\right)} d\right)} e x + \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{6} f^{2} x^{5} + 5 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{5} f^{2} x^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c + 10 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2}\right)} e^{4} f^{2} x^{3} + {\left(10 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{3} + 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d\right)} e^{3} f^{2} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c + 5 \, {\left(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^{2}\right)} e^{2} f^{2} x + {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d\right)} e f^{2}\right)} \sqrt{-\frac{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} f^{4} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4} f^{8}}} + 9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3}}{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} f^{4}}} \log\left(-{\left(189 \, b^{6} c^{3} - 1971 \, a b^{4} c^{4} + 5625 \, a^{2} b^{2} c^{5} - 2500 \, a^{3} c^{6}\right)} e x - {\left(189 \, b^{6} c^{3} - 1971 \, a b^{4} c^{4} + 5625 \, a^{2} b^{2} c^{5} - 2500 \, a^{3} c^{6}\right)} d + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(3 \, a^{5} b^{10} - 55 \, a^{6} b^{8} c + 392 \, a^{7} b^{6} c^{2} - 1344 \, a^{8} b^{4} c^{3} + 2176 \, a^{9} b^{2} c^{4} - 1280 \, a^{10} c^{5}\right)} e^{3} f^{6} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4} f^{8}}} - {\left(27 \, b^{11} - 486 \, a b^{9} c + 3330 \, a^{2} b^{7} c^{2} - 10549 \, a^{3} b^{5} c^{3} + 14408 \, a^{4} b^{3} c^{4} - 5200 \, a^{5} b c^{5}\right)} e f^{2}\right)} \sqrt{-\frac{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} f^{4} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4} f^{8}}} + 9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3}}{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} f^{4}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{6} f^{2} x^{5} + 5 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{5} f^{2} x^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c + 10 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2}\right)} e^{4} f^{2} x^{3} + {\left(10 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{3} + 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d\right)} e^{3} f^{2} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c + 5 \, {\left(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^{2}\right)} e^{2} f^{2} x + {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d\right)} e f^{2}\right)} \sqrt{-\frac{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} f^{4} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4} f^{8}}} + 9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3}}{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} f^{4}}} \log\left(-{\left(189 \, b^{6} c^{3} - 1971 \, a b^{4} c^{4} + 5625 \, a^{2} b^{2} c^{5} - 2500 \, a^{3} c^{6}\right)} e x - {\left(189 \, b^{6} c^{3} - 1971 \, a b^{4} c^{4} + 5625 \, a^{2} b^{2} c^{5} - 2500 \, a^{3} c^{6}\right)} d - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(3 \, a^{5} b^{10} - 55 \, a^{6} b^{8} c + 392 \, a^{7} b^{6} c^{2} - 1344 \, a^{8} b^{4} c^{3} + 2176 \, a^{9} b^{2} c^{4} - 1280 \, a^{10} c^{5}\right)} e^{3} f^{6} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4} f^{8}}} - {\left(27 \, b^{11} - 486 \, a b^{9} c + 3330 \, a^{2} b^{7} c^{2} - 10549 \, a^{3} b^{5} c^{3} + 14408 \, a^{4} b^{3} c^{4} - 5200 \, a^{5} b c^{5}\right)} e f^{2}\right)} \sqrt{-\frac{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} f^{4} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4} f^{8}}} + 9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3}}{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} f^{4}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{6} f^{2} x^{5} + 5 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{5} f^{2} x^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c + 10 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2}\right)} e^{4} f^{2} x^{3} + {\left(10 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{3} + 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d\right)} e^{3} f^{2} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c + 5 \, {\left(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^{2}\right)} e^{2} f^{2} x + {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d\right)} e f^{2}\right)} \sqrt{\frac{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} f^{4} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4} f^{8}}} - 9 \, b^{7} + 105 \, a b^{5} c - 385 \, a^{2} b^{3} c^{2} + 420 \, a^{3} b c^{3}}{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} f^{4}}} \log\left(-{\left(189 \, b^{6} c^{3} - 1971 \, a b^{4} c^{4} + 5625 \, a^{2} b^{2} c^{5} - 2500 \, a^{3} c^{6}\right)} e x - {\left(189 \, b^{6} c^{3} - 1971 \, a b^{4} c^{4} + 5625 \, a^{2} b^{2} c^{5} - 2500 \, a^{3} c^{6}\right)} d + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(3 \, a^{5} b^{10} - 55 \, a^{6} b^{8} c + 392 \, a^{7} b^{6} c^{2} - 1344 \, a^{8} b^{4} c^{3} + 2176 \, a^{9} b^{2} c^{4} - 1280 \, a^{10} c^{5}\right)} e^{3} f^{6} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4} f^{8}}} + {\left(27 \, b^{11} - 486 \, a b^{9} c + 3330 \, a^{2} b^{7} c^{2} - 10549 \, a^{3} b^{5} c^{3} + 14408 \, a^{4} b^{3} c^{4} - 5200 \, a^{5} b c^{5}\right)} e f^{2}\right)} \sqrt{\frac{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} f^{4} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4} f^{8}}} - 9 \, b^{7} + 105 \, a b^{5} c - 385 \, a^{2} b^{3} c^{2} + 420 \, a^{3} b c^{3}}{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} f^{4}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{6} f^{2} x^{5} + 5 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{5} f^{2} x^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c + 10 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2}\right)} e^{4} f^{2} x^{3} + {\left(10 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{3} + 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d\right)} e^{3} f^{2} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c + 5 \, {\left(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^{2}\right)} e^{2} f^{2} x + {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d\right)} e f^{2}\right)} \sqrt{\frac{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} f^{4} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4} f^{8}}} - 9 \, b^{7} + 105 \, a b^{5} c - 385 \, a^{2} b^{3} c^{2} + 420 \, a^{3} b c^{3}}{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} f^{4}}} \log\left(-{\left(189 \, b^{6} c^{3} - 1971 \, a b^{4} c^{4} + 5625 \, a^{2} b^{2} c^{5} - 2500 \, a^{3} c^{6}\right)} e x - {\left(189 \, b^{6} c^{3} - 1971 \, a b^{4} c^{4} + 5625 \, a^{2} b^{2} c^{5} - 2500 \, a^{3} c^{6}\right)} d - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(3 \, a^{5} b^{10} - 55 \, a^{6} b^{8} c + 392 \, a^{7} b^{6} c^{2} - 1344 \, a^{8} b^{4} c^{3} + 2176 \, a^{9} b^{2} c^{4} - 1280 \, a^{10} c^{5}\right)} e^{3} f^{6} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4} f^{8}}} + {\left(27 \, b^{11} - 486 \, a b^{9} c + 3330 \, a^{2} b^{7} c^{2} - 10549 \, a^{3} b^{5} c^{3} + 14408 \, a^{4} b^{3} c^{4} - 5200 \, a^{5} b c^{5}\right)} e f^{2}\right)} \sqrt{\frac{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} f^{4} \sqrt{\frac{81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}}{{\left(a^{10} b^{6} - 12 \, a^{11} b^{4} c + 48 \, a^{12} b^{2} c^{2} - 64 \, a^{13} c^{3}\right)} e^{4} f^{8}}} - 9 \, b^{7} + 105 \, a b^{5} c - 385 \, a^{2} b^{3} c^{2} + 420 \, a^{3} b c^{3}}{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} e^{2} f^{4}}}\right)}{4 \, {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{6} f^{2} x^{5} + 5 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d e^{5} f^{2} x^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c + 10 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2}\right)} e^{4} f^{2} x^{3} + {\left(10 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{3} + 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d\right)} e^{3} f^{2} x^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c + 5 \, {\left(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^{2}\right)} e^{2} f^{2} x + {\left({\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{5} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d\right)} e f^{2}\right)}}"," ",0,"-1/4*(2*(3*b^2*c - 10*a*c^2)*e^4*x^4 + 8*(3*b^2*c - 10*a*c^2)*d*e^3*x^3 + 2*(3*b^2*c - 10*a*c^2)*d^4 + 2*(3*b^3 - 11*a*b*c + 6*(3*b^2*c - 10*a*c^2)*d^2)*e^2*x^2 + 4*a*b^2 - 16*a^2*c + 2*(3*b^3 - 11*a*b*c)*d^2 + 4*(2*(3*b^2*c - 10*a*c^2)*d^3 + (3*b^3 - 11*a*b*c)*d)*e*x + sqrt(1/2)*((a^2*b^2*c - 4*a^3*c^2)*e^6*f^2*x^5 + 5*(a^2*b^2*c - 4*a^3*c^2)*d*e^5*f^2*x^4 + (a^2*b^3 - 4*a^3*b*c + 10*(a^2*b^2*c - 4*a^3*c^2)*d^2)*e^4*f^2*x^3 + (10*(a^2*b^2*c - 4*a^3*c^2)*d^3 + 3*(a^2*b^3 - 4*a^3*b*c)*d)*e^3*f^2*x^2 + (a^3*b^2 - 4*a^4*c + 5*(a^2*b^2*c - 4*a^3*c^2)*d^4 + 3*(a^2*b^3 - 4*a^3*b*c)*d^2)*e^2*f^2*x + ((a^2*b^2*c - 4*a^3*c^2)*d^5 + (a^2*b^3 - 4*a^3*b*c)*d^3 + (a^3*b^2 - 4*a^4*c)*d)*e*f^2)*sqrt(-((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*f^4*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4*f^8)) + 9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3)/((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*f^4))*log(-(189*b^6*c^3 - 1971*a*b^4*c^4 + 5625*a^2*b^2*c^5 - 2500*a^3*c^6)*e*x - (189*b^6*c^3 - 1971*a*b^4*c^4 + 5625*a^2*b^2*c^5 - 2500*a^3*c^6)*d + 1/2*sqrt(1/2)*((3*a^5*b^10 - 55*a^6*b^8*c + 392*a^7*b^6*c^2 - 1344*a^8*b^4*c^3 + 2176*a^9*b^2*c^4 - 1280*a^10*c^5)*e^3*f^6*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4*f^8)) - (27*b^11 - 486*a*b^9*c + 3330*a^2*b^7*c^2 - 10549*a^3*b^5*c^3 + 14408*a^4*b^3*c^4 - 5200*a^5*b*c^5)*e*f^2)*sqrt(-((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*f^4*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4*f^8)) + 9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3)/((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*f^4))) - sqrt(1/2)*((a^2*b^2*c - 4*a^3*c^2)*e^6*f^2*x^5 + 5*(a^2*b^2*c - 4*a^3*c^2)*d*e^5*f^2*x^4 + (a^2*b^3 - 4*a^3*b*c + 10*(a^2*b^2*c - 4*a^3*c^2)*d^2)*e^4*f^2*x^3 + (10*(a^2*b^2*c - 4*a^3*c^2)*d^3 + 3*(a^2*b^3 - 4*a^3*b*c)*d)*e^3*f^2*x^2 + (a^3*b^2 - 4*a^4*c + 5*(a^2*b^2*c - 4*a^3*c^2)*d^4 + 3*(a^2*b^3 - 4*a^3*b*c)*d^2)*e^2*f^2*x + ((a^2*b^2*c - 4*a^3*c^2)*d^5 + (a^2*b^3 - 4*a^3*b*c)*d^3 + (a^3*b^2 - 4*a^4*c)*d)*e*f^2)*sqrt(-((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*f^4*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4*f^8)) + 9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3)/((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*f^4))*log(-(189*b^6*c^3 - 1971*a*b^4*c^4 + 5625*a^2*b^2*c^5 - 2500*a^3*c^6)*e*x - (189*b^6*c^3 - 1971*a*b^4*c^4 + 5625*a^2*b^2*c^5 - 2500*a^3*c^6)*d - 1/2*sqrt(1/2)*((3*a^5*b^10 - 55*a^6*b^8*c + 392*a^7*b^6*c^2 - 1344*a^8*b^4*c^3 + 2176*a^9*b^2*c^4 - 1280*a^10*c^5)*e^3*f^6*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4*f^8)) - (27*b^11 - 486*a*b^9*c + 3330*a^2*b^7*c^2 - 10549*a^3*b^5*c^3 + 14408*a^4*b^3*c^4 - 5200*a^5*b*c^5)*e*f^2)*sqrt(-((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*f^4*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4*f^8)) + 9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3)/((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*f^4))) - sqrt(1/2)*((a^2*b^2*c - 4*a^3*c^2)*e^6*f^2*x^5 + 5*(a^2*b^2*c - 4*a^3*c^2)*d*e^5*f^2*x^4 + (a^2*b^3 - 4*a^3*b*c + 10*(a^2*b^2*c - 4*a^3*c^2)*d^2)*e^4*f^2*x^3 + (10*(a^2*b^2*c - 4*a^3*c^2)*d^3 + 3*(a^2*b^3 - 4*a^3*b*c)*d)*e^3*f^2*x^2 + (a^3*b^2 - 4*a^4*c + 5*(a^2*b^2*c - 4*a^3*c^2)*d^4 + 3*(a^2*b^3 - 4*a^3*b*c)*d^2)*e^2*f^2*x + ((a^2*b^2*c - 4*a^3*c^2)*d^5 + (a^2*b^3 - 4*a^3*b*c)*d^3 + (a^3*b^2 - 4*a^4*c)*d)*e*f^2)*sqrt(((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*f^4*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4*f^8)) - 9*b^7 + 105*a*b^5*c - 385*a^2*b^3*c^2 + 420*a^3*b*c^3)/((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*f^4))*log(-(189*b^6*c^3 - 1971*a*b^4*c^4 + 5625*a^2*b^2*c^5 - 2500*a^3*c^6)*e*x - (189*b^6*c^3 - 1971*a*b^4*c^4 + 5625*a^2*b^2*c^5 - 2500*a^3*c^6)*d + 1/2*sqrt(1/2)*((3*a^5*b^10 - 55*a^6*b^8*c + 392*a^7*b^6*c^2 - 1344*a^8*b^4*c^3 + 2176*a^9*b^2*c^4 - 1280*a^10*c^5)*e^3*f^6*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4*f^8)) + (27*b^11 - 486*a*b^9*c + 3330*a^2*b^7*c^2 - 10549*a^3*b^5*c^3 + 14408*a^4*b^3*c^4 - 5200*a^5*b*c^5)*e*f^2)*sqrt(((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*f^4*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4*f^8)) - 9*b^7 + 105*a*b^5*c - 385*a^2*b^3*c^2 + 420*a^3*b*c^3)/((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*f^4))) + sqrt(1/2)*((a^2*b^2*c - 4*a^3*c^2)*e^6*f^2*x^5 + 5*(a^2*b^2*c - 4*a^3*c^2)*d*e^5*f^2*x^4 + (a^2*b^3 - 4*a^3*b*c + 10*(a^2*b^2*c - 4*a^3*c^2)*d^2)*e^4*f^2*x^3 + (10*(a^2*b^2*c - 4*a^3*c^2)*d^3 + 3*(a^2*b^3 - 4*a^3*b*c)*d)*e^3*f^2*x^2 + (a^3*b^2 - 4*a^4*c + 5*(a^2*b^2*c - 4*a^3*c^2)*d^4 + 3*(a^2*b^3 - 4*a^3*b*c)*d^2)*e^2*f^2*x + ((a^2*b^2*c - 4*a^3*c^2)*d^5 + (a^2*b^3 - 4*a^3*b*c)*d^3 + (a^3*b^2 - 4*a^4*c)*d)*e*f^2)*sqrt(((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*f^4*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4*f^8)) - 9*b^7 + 105*a*b^5*c - 385*a^2*b^3*c^2 + 420*a^3*b*c^3)/((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*f^4))*log(-(189*b^6*c^3 - 1971*a*b^4*c^4 + 5625*a^2*b^2*c^5 - 2500*a^3*c^6)*e*x - (189*b^6*c^3 - 1971*a*b^4*c^4 + 5625*a^2*b^2*c^5 - 2500*a^3*c^6)*d - 1/2*sqrt(1/2)*((3*a^5*b^10 - 55*a^6*b^8*c + 392*a^7*b^6*c^2 - 1344*a^8*b^4*c^3 + 2176*a^9*b^2*c^4 - 1280*a^10*c^5)*e^3*f^6*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4*f^8)) + (27*b^11 - 486*a*b^9*c + 3330*a^2*b^7*c^2 - 10549*a^3*b^5*c^3 + 14408*a^4*b^3*c^4 - 5200*a^5*b*c^5)*e*f^2)*sqrt(((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*f^4*sqrt((81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)/((a^10*b^6 - 12*a^11*b^4*c + 48*a^12*b^2*c^2 - 64*a^13*c^3)*e^4*f^8)) - 9*b^7 + 105*a*b^5*c - 385*a^2*b^3*c^2 + 420*a^3*b*c^3)/((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*e^2*f^4))))/((a^2*b^2*c - 4*a^3*c^2)*e^6*f^2*x^5 + 5*(a^2*b^2*c - 4*a^3*c^2)*d*e^5*f^2*x^4 + (a^2*b^3 - 4*a^3*b*c + 10*(a^2*b^2*c - 4*a^3*c^2)*d^2)*e^4*f^2*x^3 + (10*(a^2*b^2*c - 4*a^3*c^2)*d^3 + 3*(a^2*b^3 - 4*a^3*b*c)*d)*e^3*f^2*x^2 + (a^3*b^2 - 4*a^4*c + 5*(a^2*b^2*c - 4*a^3*c^2)*d^4 + 3*(a^2*b^3 - 4*a^3*b*c)*d^2)*e^2*f^2*x + ((a^2*b^2*c - 4*a^3*c^2)*d^5 + (a^2*b^3 - 4*a^3*b*c)*d^3 + (a^3*b^2 - 4*a^4*c)*d)*e*f^2)","B",0
652,1,4604,0,5.904333," ","integrate(1/(e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} e^{4} x^{4} + 8 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d e^{3} x^{3} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + 2 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{4} + {\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2} + 12 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2}\right)} d^{2} + 2 \, {\left(4 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{3} + {\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2}\right)} d\right)} e x + {\left({\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} e^{6} x^{6} + 6 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d e^{5} x^{5} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2} + 15 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{6} + 4 \, {\left(5 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{3} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} d\right)} e^{3} x^{3} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} d^{4} + {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2} + 15 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{4} + 6 \, {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} d^{2} + 2 \, {\left(3 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{5} + 2 \, {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} d^{3} + {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} d\right)} e x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c + {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right) - {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{6} x^{6} + 6 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e^{5} x^{5} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{6} + 4 \, {\left(5 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d\right)} e^{3} x^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{4} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} + 6 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2} + 2 \, {\left(3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} + 2 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{3} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d\right)} e x\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 4 \, {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{6} x^{6} + 6 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e^{5} x^{5} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{6} + 4 \, {\left(5 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d\right)} e^{3} x^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{4} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} + 6 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2} + 2 \, {\left(3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} + 2 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{3} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d\right)} e x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} e^{7} f^{3} x^{6} + 6 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d e^{6} f^{3} x^{5} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2} + 15 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{2}\right)} e^{5} f^{3} x^{4} + 4 \, {\left(5 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{3} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d\right)} e^{4} f^{3} x^{3} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 15 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{4} + 6 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d^{2}\right)} e^{3} f^{3} x^{2} + 2 \, {\left(3 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{5} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d^{3} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} d\right)} e^{2} f^{3} x + {\left({\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{6} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d^{4} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} d^{2}\right)} e f^{3}\right)}}, -\frac{2 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} e^{4} x^{4} + 8 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d e^{3} x^{3} + a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + 2 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{4} + {\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2} + 12 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2}\right)} d^{2} + 2 \, {\left(4 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{3} + {\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2}\right)} d\right)} e x + 2 \, {\left({\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} e^{6} x^{6} + 6 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d e^{5} x^{5} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2} + 15 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{6} + 4 \, {\left(5 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{3} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} d\right)} e^{3} x^{3} + {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} d^{4} + {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2} + 15 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{4} + 6 \, {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} d^{2} + 2 \, {\left(3 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{5} + 2 \, {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} d^{3} + {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} d\right)} e x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{6} x^{6} + 6 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e^{5} x^{5} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{6} + 4 \, {\left(5 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d\right)} e^{3} x^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{4} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} + 6 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2} + 2 \, {\left(3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} + 2 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{3} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d\right)} e x\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 4 \, {\left({\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{6} x^{6} + 6 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e^{5} x^{5} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{6} + 4 \, {\left(5 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d\right)} e^{3} x^{3} + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{4} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} + 6 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2} + 2 \, {\left(3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} + 2 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{3} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d\right)} e x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} e^{7} f^{3} x^{6} + 6 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d e^{6} f^{3} x^{5} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2} + 15 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{2}\right)} e^{5} f^{3} x^{4} + 4 \, {\left(5 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{3} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d\right)} e^{4} f^{3} x^{3} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2} + 15 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{4} + 6 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d^{2}\right)} e^{3} f^{3} x^{2} + 2 \, {\left(3 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{5} + 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d^{3} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} d\right)} e^{2} f^{3} x + {\left({\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{6} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d^{4} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} d^{2}\right)} e f^{3}\right)}}\right]"," ",0,"[-1/2*(2*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*e^4*x^4 + 8*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*d*e^3*x^3 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + 2*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*d^4 + (2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2 + 12*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*d^2)*e^2*x^2 + (2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2)*d^2 + 2*(4*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*d^3 + (2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2)*d)*e*x + ((b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*e^6*x^6 + 6*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d*e^5*x^5 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2 + 15*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^2)*e^4*x^4 + (b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^6 + 4*(5*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^3 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*d)*e^3*x^3 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*d^4 + (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2 + 15*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^4 + 6*(b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*d^2)*e^2*x^2 + (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*d^2 + 2*(3*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^5 + 2*(b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*d^3 + (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*d)*e*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c + (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)) - ((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^6*x^6 + 6*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e^5*x^5 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2)*e^4*x^4 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^6 + 4*(5*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d)*e^3*x^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^4 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^4 + 6*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^2)*e^2*x^2 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2 + 2*(3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^5 + 2*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^3 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d)*e*x)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 4*((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^6*x^6 + 6*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e^5*x^5 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2)*e^4*x^4 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^6 + 4*(5*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d)*e^3*x^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^4 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^4 + 6*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^2)*e^2*x^2 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2 + 2*(3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^5 + 2*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^3 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d)*e*x)*log(e*x + d))/((a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*e^7*f^3*x^6 + 6*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d*e^6*f^3*x^5 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2 + 15*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^2)*e^5*f^3*x^4 + 4*(5*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^3 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d)*e^4*f^3*x^3 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 15*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^4 + 6*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d^2)*e^3*f^3*x^2 + 2*(3*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^5 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d^3 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*d)*e^2*f^3*x + ((a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^6 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d^4 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*d^2)*e*f^3), -1/2*(2*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*e^4*x^4 + 8*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*d*e^3*x^3 + a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + 2*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*d^4 + (2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2 + 12*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*d^2)*e^2*x^2 + (2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2)*d^2 + 2*(4*(a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*d^3 + (2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2)*d)*e*x + 2*((b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*e^6*x^6 + 6*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d*e^5*x^5 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2 + 15*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^2)*e^4*x^4 + (b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^6 + 4*(5*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^3 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*d)*e^3*x^3 + (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*d^4 + (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2 + 15*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^4 + 6*(b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*d^2)*e^2*x^2 + (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*d^2 + 2*(3*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^5 + 2*(b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*d^3 + (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*d)*e*x)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - ((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^6*x^6 + 6*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e^5*x^5 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2)*e^4*x^4 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^6 + 4*(5*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d)*e^3*x^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^4 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^4 + 6*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^2)*e^2*x^2 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2 + 2*(3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^5 + 2*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^3 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d)*e*x)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 4*((b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^6*x^6 + 6*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e^5*x^5 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2)*e^4*x^4 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^6 + 4*(5*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d)*e^3*x^3 + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^4 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^4 + 6*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^2)*e^2*x^2 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2 + 2*(3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^5 + 2*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^3 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d)*e*x)*log(e*x + d))/((a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*e^7*f^3*x^6 + 6*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d*e^6*f^3*x^5 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2 + 15*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^2)*e^5*f^3*x^4 + 4*(5*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^3 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d)*e^4*f^3*x^3 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2 + 15*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^4 + 6*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d^2)*e^3*f^3*x^2 + 2*(3*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^5 + 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d^3 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*d)*e^2*f^3*x + ((a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^6 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d^4 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*d^2)*e*f^3)]","B",0
653,1,5954,0,2.131159," ","integrate(1/(e*f*x+d*f)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x, algorithm=""fricas"")","\frac{6 \, {\left(5 \, b^{3} c - 19 \, a b c^{2}\right)} e^{6} x^{6} + 36 \, {\left(5 \, b^{3} c - 19 \, a b c^{2}\right)} d e^{5} x^{5} + 2 \, {\left(15 \, b^{4} - 62 \, a b^{2} c + 14 \, a^{2} c^{2} + 45 \, {\left(5 \, b^{3} c - 19 \, a b c^{2}\right)} d^{2}\right)} e^{4} x^{4} + 6 \, {\left(5 \, b^{3} c - 19 \, a b c^{2}\right)} d^{6} + 8 \, {\left(15 \, {\left(5 \, b^{3} c - 19 \, a b c^{2}\right)} d^{3} + {\left(15 \, b^{4} - 62 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} d\right)} e^{3} x^{3} + 2 \, {\left(15 \, b^{4} - 62 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} d^{4} + 2 \, {\left(45 \, {\left(5 \, b^{3} c - 19 \, a b c^{2}\right)} d^{4} + 10 \, a b^{3} - 40 \, a^{2} b c + 6 \, {\left(15 \, b^{4} - 62 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} d^{2}\right)} e^{2} x^{2} - 4 \, a^{2} b^{2} + 16 \, a^{3} c + 20 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{2} + 4 \, {\left(9 \, {\left(5 \, b^{3} c - 19 \, a b c^{2}\right)} d^{5} + 2 \, {\left(15 \, b^{4} - 62 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} d^{3} + 10 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d\right)} e x - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{8} f^{4} x^{7} + 7 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d e^{7} f^{4} x^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c + 21 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2}\right)} e^{6} f^{4} x^{5} + 5 \, {\left(7 \, {\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\right)} e^{5} f^{4} x^{4} + {\left(a^{4} b^{2} - 4 \, a^{5} c + 35 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{4} + 10 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2}\right)} e^{4} f^{4} x^{3} + {\left(21 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{5} + 10 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{3} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d\right)} e^{3} f^{4} x^{2} + {\left(7 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{6} + 5 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{4} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{2}\right)} e^{2} f^{4} x + {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{3}\right)} e f^{4}\right)} \sqrt{-\frac{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} f^{8} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4} f^{16}}} + 25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4}}{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} f^{8}}} \log\left({\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} e x + {\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} d + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(5 \, a^{7} b^{11} - 94 \, a^{8} b^{9} c + 700 \, a^{9} b^{7} c^{2} - 2576 \, a^{10} b^{5} c^{3} + 4672 \, a^{11} b^{3} c^{4} - 3328 \, a^{12} b c^{5}\right)} e^{3} f^{12} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4} f^{16}}} - {\left(125 \, b^{14} - 2425 \, a b^{12} c + 18940 \, a^{2} b^{10} c^{2} - 75579 \, a^{3} b^{8} c^{3} + 160932 \, a^{4} b^{6} c^{4} - 172990 \, a^{5} b^{4} c^{5} + 79408 \, a^{6} b^{2} c^{6} - 10976 \, a^{7} c^{7}\right)} e f^{4}\right)} \sqrt{-\frac{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} f^{8} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4} f^{16}}} + 25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4}}{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} f^{8}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{8} f^{4} x^{7} + 7 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d e^{7} f^{4} x^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c + 21 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2}\right)} e^{6} f^{4} x^{5} + 5 \, {\left(7 \, {\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\right)} e^{5} f^{4} x^{4} + {\left(a^{4} b^{2} - 4 \, a^{5} c + 35 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{4} + 10 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2}\right)} e^{4} f^{4} x^{3} + {\left(21 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{5} + 10 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{3} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d\right)} e^{3} f^{4} x^{2} + {\left(7 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{6} + 5 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{4} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{2}\right)} e^{2} f^{4} x + {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{3}\right)} e f^{4}\right)} \sqrt{-\frac{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} f^{8} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4} f^{16}}} + 25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4}}{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} f^{8}}} \log\left({\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} e x + {\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} d - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(5 \, a^{7} b^{11} - 94 \, a^{8} b^{9} c + 700 \, a^{9} b^{7} c^{2} - 2576 \, a^{10} b^{5} c^{3} + 4672 \, a^{11} b^{3} c^{4} - 3328 \, a^{12} b c^{5}\right)} e^{3} f^{12} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4} f^{16}}} - {\left(125 \, b^{14} - 2425 \, a b^{12} c + 18940 \, a^{2} b^{10} c^{2} - 75579 \, a^{3} b^{8} c^{3} + 160932 \, a^{4} b^{6} c^{4} - 172990 \, a^{5} b^{4} c^{5} + 79408 \, a^{6} b^{2} c^{6} - 10976 \, a^{7} c^{7}\right)} e f^{4}\right)} \sqrt{-\frac{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} f^{8} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4} f^{16}}} + 25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4}}{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} f^{8}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{8} f^{4} x^{7} + 7 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d e^{7} f^{4} x^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c + 21 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2}\right)} e^{6} f^{4} x^{5} + 5 \, {\left(7 \, {\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\right)} e^{5} f^{4} x^{4} + {\left(a^{4} b^{2} - 4 \, a^{5} c + 35 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{4} + 10 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2}\right)} e^{4} f^{4} x^{3} + {\left(21 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{5} + 10 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{3} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d\right)} e^{3} f^{4} x^{2} + {\left(7 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{6} + 5 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{4} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{2}\right)} e^{2} f^{4} x + {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{3}\right)} e f^{4}\right)} \sqrt{\frac{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} f^{8} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4} f^{16}}} - 25 \, b^{9} + 315 \, a b^{7} c - 1386 \, a^{2} b^{5} c^{2} + 2415 \, a^{3} b^{3} c^{3} - 1260 \, a^{4} b c^{4}}{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} f^{8}}} \log\left({\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} e x + {\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} d + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(5 \, a^{7} b^{11} - 94 \, a^{8} b^{9} c + 700 \, a^{9} b^{7} c^{2} - 2576 \, a^{10} b^{5} c^{3} + 4672 \, a^{11} b^{3} c^{4} - 3328 \, a^{12} b c^{5}\right)} e^{3} f^{12} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4} f^{16}}} + {\left(125 \, b^{14} - 2425 \, a b^{12} c + 18940 \, a^{2} b^{10} c^{2} - 75579 \, a^{3} b^{8} c^{3} + 160932 \, a^{4} b^{6} c^{4} - 172990 \, a^{5} b^{4} c^{5} + 79408 \, a^{6} b^{2} c^{6} - 10976 \, a^{7} c^{7}\right)} e f^{4}\right)} \sqrt{\frac{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} f^{8} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4} f^{16}}} - 25 \, b^{9} + 315 \, a b^{7} c - 1386 \, a^{2} b^{5} c^{2} + 2415 \, a^{3} b^{3} c^{3} - 1260 \, a^{4} b c^{4}}{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} f^{8}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{8} f^{4} x^{7} + 7 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d e^{7} f^{4} x^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c + 21 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2}\right)} e^{6} f^{4} x^{5} + 5 \, {\left(7 \, {\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\right)} e^{5} f^{4} x^{4} + {\left(a^{4} b^{2} - 4 \, a^{5} c + 35 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{4} + 10 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2}\right)} e^{4} f^{4} x^{3} + {\left(21 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{5} + 10 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{3} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d\right)} e^{3} f^{4} x^{2} + {\left(7 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{6} + 5 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{4} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{2}\right)} e^{2} f^{4} x + {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{3}\right)} e f^{4}\right)} \sqrt{\frac{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} f^{8} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4} f^{16}}} - 25 \, b^{9} + 315 \, a b^{7} c - 1386 \, a^{2} b^{5} c^{2} + 2415 \, a^{3} b^{3} c^{3} - 1260 \, a^{4} b c^{4}}{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} f^{8}}} \log\left({\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} e x + {\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} d - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(5 \, a^{7} b^{11} - 94 \, a^{8} b^{9} c + 700 \, a^{9} b^{7} c^{2} - 2576 \, a^{10} b^{5} c^{3} + 4672 \, a^{11} b^{3} c^{4} - 3328 \, a^{12} b c^{5}\right)} e^{3} f^{12} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4} f^{16}}} + {\left(125 \, b^{14} - 2425 \, a b^{12} c + 18940 \, a^{2} b^{10} c^{2} - 75579 \, a^{3} b^{8} c^{3} + 160932 \, a^{4} b^{6} c^{4} - 172990 \, a^{5} b^{4} c^{5} + 79408 \, a^{6} b^{2} c^{6} - 10976 \, a^{7} c^{7}\right)} e f^{4}\right)} \sqrt{\frac{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} f^{8} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{{\left(a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}\right)} e^{4} f^{16}}} - 25 \, b^{9} + 315 \, a b^{7} c - 1386 \, a^{2} b^{5} c^{2} + 2415 \, a^{3} b^{3} c^{3} - 1260 \, a^{4} b c^{4}}{{\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} e^{2} f^{8}}}\right)}{12 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{8} f^{4} x^{7} + 7 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d e^{7} f^{4} x^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c + 21 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2}\right)} e^{6} f^{4} x^{5} + 5 \, {\left(7 \, {\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\right)} e^{5} f^{4} x^{4} + {\left(a^{4} b^{2} - 4 \, a^{5} c + 35 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{4} + 10 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2}\right)} e^{4} f^{4} x^{3} + {\left(21 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{5} + 10 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{3} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d\right)} e^{3} f^{4} x^{2} + {\left(7 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{6} + 5 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{4} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{2}\right)} e^{2} f^{4} x + {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{7} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{3}\right)} e f^{4}\right)}}"," ",0,"1/12*(6*(5*b^3*c - 19*a*b*c^2)*e^6*x^6 + 36*(5*b^3*c - 19*a*b*c^2)*d*e^5*x^5 + 2*(15*b^4 - 62*a*b^2*c + 14*a^2*c^2 + 45*(5*b^3*c - 19*a*b*c^2)*d^2)*e^4*x^4 + 6*(5*b^3*c - 19*a*b*c^2)*d^6 + 8*(15*(5*b^3*c - 19*a*b*c^2)*d^3 + (15*b^4 - 62*a*b^2*c + 14*a^2*c^2)*d)*e^3*x^3 + 2*(15*b^4 - 62*a*b^2*c + 14*a^2*c^2)*d^4 + 2*(45*(5*b^3*c - 19*a*b*c^2)*d^4 + 10*a*b^3 - 40*a^2*b*c + 6*(15*b^4 - 62*a*b^2*c + 14*a^2*c^2)*d^2)*e^2*x^2 - 4*a^2*b^2 + 16*a^3*c + 20*(a*b^3 - 4*a^2*b*c)*d^2 + 4*(9*(5*b^3*c - 19*a*b*c^2)*d^5 + 2*(15*b^4 - 62*a*b^2*c + 14*a^2*c^2)*d^3 + 10*(a*b^3 - 4*a^2*b*c)*d)*e*x - 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*e^8*f^4*x^7 + 7*(a^3*b^2*c - 4*a^4*c^2)*d*e^7*f^4*x^6 + (a^3*b^3 - 4*a^4*b*c + 21*(a^3*b^2*c - 4*a^4*c^2)*d^2)*e^6*f^4*x^5 + 5*(7*(a^3*b^2*c - 4*a^4*c^2)*d^3 + (a^3*b^3 - 4*a^4*b*c)*d)*e^5*f^4*x^4 + (a^4*b^2 - 4*a^5*c + 35*(a^3*b^2*c - 4*a^4*c^2)*d^4 + 10*(a^3*b^3 - 4*a^4*b*c)*d^2)*e^4*f^4*x^3 + (21*(a^3*b^2*c - 4*a^4*c^2)*d^5 + 10*(a^3*b^3 - 4*a^4*b*c)*d^3 + 3*(a^4*b^2 - 4*a^5*c)*d)*e^3*f^4*x^2 + (7*(a^3*b^2*c - 4*a^4*c^2)*d^6 + 5*(a^3*b^3 - 4*a^4*b*c)*d^4 + 3*(a^4*b^2 - 4*a^5*c)*d^2)*e^2*f^4*x + ((a^3*b^2*c - 4*a^4*c^2)*d^7 + (a^3*b^3 - 4*a^4*b*c)*d^5 + (a^4*b^2 - 4*a^5*c)*d^3)*e*f^4)*sqrt(-((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*f^8*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4*f^16)) + 25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4)/((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*f^8))*log((1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*e*x + (1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*d + 1/2*sqrt(1/2)*((5*a^7*b^11 - 94*a^8*b^9*c + 700*a^9*b^7*c^2 - 2576*a^10*b^5*c^3 + 4672*a^11*b^3*c^4 - 3328*a^12*b*c^5)*e^3*f^12*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4*f^16)) - (125*b^14 - 2425*a*b^12*c + 18940*a^2*b^10*c^2 - 75579*a^3*b^8*c^3 + 160932*a^4*b^6*c^4 - 172990*a^5*b^4*c^5 + 79408*a^6*b^2*c^6 - 10976*a^7*c^7)*e*f^4)*sqrt(-((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*f^8*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4*f^16)) + 25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4)/((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*f^8))) + 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*e^8*f^4*x^7 + 7*(a^3*b^2*c - 4*a^4*c^2)*d*e^7*f^4*x^6 + (a^3*b^3 - 4*a^4*b*c + 21*(a^3*b^2*c - 4*a^4*c^2)*d^2)*e^6*f^4*x^5 + 5*(7*(a^3*b^2*c - 4*a^4*c^2)*d^3 + (a^3*b^3 - 4*a^4*b*c)*d)*e^5*f^4*x^4 + (a^4*b^2 - 4*a^5*c + 35*(a^3*b^2*c - 4*a^4*c^2)*d^4 + 10*(a^3*b^3 - 4*a^4*b*c)*d^2)*e^4*f^4*x^3 + (21*(a^3*b^2*c - 4*a^4*c^2)*d^5 + 10*(a^3*b^3 - 4*a^4*b*c)*d^3 + 3*(a^4*b^2 - 4*a^5*c)*d)*e^3*f^4*x^2 + (7*(a^3*b^2*c - 4*a^4*c^2)*d^6 + 5*(a^3*b^3 - 4*a^4*b*c)*d^4 + 3*(a^4*b^2 - 4*a^5*c)*d^2)*e^2*f^4*x + ((a^3*b^2*c - 4*a^4*c^2)*d^7 + (a^3*b^3 - 4*a^4*b*c)*d^5 + (a^4*b^2 - 4*a^5*c)*d^3)*e*f^4)*sqrt(-((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*f^8*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4*f^16)) + 25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4)/((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*f^8))*log((1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*e*x + (1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*d - 1/2*sqrt(1/2)*((5*a^7*b^11 - 94*a^8*b^9*c + 700*a^9*b^7*c^2 - 2576*a^10*b^5*c^3 + 4672*a^11*b^3*c^4 - 3328*a^12*b*c^5)*e^3*f^12*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4*f^16)) - (125*b^14 - 2425*a*b^12*c + 18940*a^2*b^10*c^2 - 75579*a^3*b^8*c^3 + 160932*a^4*b^6*c^4 - 172990*a^5*b^4*c^5 + 79408*a^6*b^2*c^6 - 10976*a^7*c^7)*e*f^4)*sqrt(-((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*f^8*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4*f^16)) + 25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4)/((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*f^8))) + 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*e^8*f^4*x^7 + 7*(a^3*b^2*c - 4*a^4*c^2)*d*e^7*f^4*x^6 + (a^3*b^3 - 4*a^4*b*c + 21*(a^3*b^2*c - 4*a^4*c^2)*d^2)*e^6*f^4*x^5 + 5*(7*(a^3*b^2*c - 4*a^4*c^2)*d^3 + (a^3*b^3 - 4*a^4*b*c)*d)*e^5*f^4*x^4 + (a^4*b^2 - 4*a^5*c + 35*(a^3*b^2*c - 4*a^4*c^2)*d^4 + 10*(a^3*b^3 - 4*a^4*b*c)*d^2)*e^4*f^4*x^3 + (21*(a^3*b^2*c - 4*a^4*c^2)*d^5 + 10*(a^3*b^3 - 4*a^4*b*c)*d^3 + 3*(a^4*b^2 - 4*a^5*c)*d)*e^3*f^4*x^2 + (7*(a^3*b^2*c - 4*a^4*c^2)*d^6 + 5*(a^3*b^3 - 4*a^4*b*c)*d^4 + 3*(a^4*b^2 - 4*a^5*c)*d^2)*e^2*f^4*x + ((a^3*b^2*c - 4*a^4*c^2)*d^7 + (a^3*b^3 - 4*a^4*b*c)*d^5 + (a^4*b^2 - 4*a^5*c)*d^3)*e*f^4)*sqrt(((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*f^8*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4*f^16)) - 25*b^9 + 315*a*b^7*c - 1386*a^2*b^5*c^2 + 2415*a^3*b^3*c^3 - 1260*a^4*b*c^4)/((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*f^8))*log((1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*e*x + (1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*d + 1/2*sqrt(1/2)*((5*a^7*b^11 - 94*a^8*b^9*c + 700*a^9*b^7*c^2 - 2576*a^10*b^5*c^3 + 4672*a^11*b^3*c^4 - 3328*a^12*b*c^5)*e^3*f^12*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4*f^16)) + (125*b^14 - 2425*a*b^12*c + 18940*a^2*b^10*c^2 - 75579*a^3*b^8*c^3 + 160932*a^4*b^6*c^4 - 172990*a^5*b^4*c^5 + 79408*a^6*b^2*c^6 - 10976*a^7*c^7)*e*f^4)*sqrt(((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*f^8*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4*f^16)) - 25*b^9 + 315*a*b^7*c - 1386*a^2*b^5*c^2 + 2415*a^3*b^3*c^3 - 1260*a^4*b*c^4)/((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*f^8))) - 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*e^8*f^4*x^7 + 7*(a^3*b^2*c - 4*a^4*c^2)*d*e^7*f^4*x^6 + (a^3*b^3 - 4*a^4*b*c + 21*(a^3*b^2*c - 4*a^4*c^2)*d^2)*e^6*f^4*x^5 + 5*(7*(a^3*b^2*c - 4*a^4*c^2)*d^3 + (a^3*b^3 - 4*a^4*b*c)*d)*e^5*f^4*x^4 + (a^4*b^2 - 4*a^5*c + 35*(a^3*b^2*c - 4*a^4*c^2)*d^4 + 10*(a^3*b^3 - 4*a^4*b*c)*d^2)*e^4*f^4*x^3 + (21*(a^3*b^2*c - 4*a^4*c^2)*d^5 + 10*(a^3*b^3 - 4*a^4*b*c)*d^3 + 3*(a^4*b^2 - 4*a^5*c)*d)*e^3*f^4*x^2 + (7*(a^3*b^2*c - 4*a^4*c^2)*d^6 + 5*(a^3*b^3 - 4*a^4*b*c)*d^4 + 3*(a^4*b^2 - 4*a^5*c)*d^2)*e^2*f^4*x + ((a^3*b^2*c - 4*a^4*c^2)*d^7 + (a^3*b^3 - 4*a^4*b*c)*d^5 + (a^4*b^2 - 4*a^5*c)*d^3)*e*f^4)*sqrt(((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*f^8*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4*f^16)) - 25*b^9 + 315*a*b^7*c - 1386*a^2*b^5*c^2 + 2415*a^3*b^3*c^3 - 1260*a^4*b*c^4)/((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*f^8))*log((1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*e*x + (1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*d - 1/2*sqrt(1/2)*((5*a^7*b^11 - 94*a^8*b^9*c + 700*a^9*b^7*c^2 - 2576*a^10*b^5*c^3 + 4672*a^11*b^3*c^4 - 3328*a^12*b*c^5)*e^3*f^12*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4*f^16)) + (125*b^14 - 2425*a*b^12*c + 18940*a^2*b^10*c^2 - 75579*a^3*b^8*c^3 + 160932*a^4*b^6*c^4 - 172990*a^5*b^4*c^5 + 79408*a^6*b^2*c^6 - 10976*a^7*c^7)*e*f^4)*sqrt(((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*f^8*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/((a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)*e^4*f^16)) - 25*b^9 + 315*a*b^7*c - 1386*a^2*b^5*c^2 + 2415*a^3*b^3*c^3 - 1260*a^4*b*c^4)/((a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*e^2*f^8))))/((a^3*b^2*c - 4*a^4*c^2)*e^8*f^4*x^7 + 7*(a^3*b^2*c - 4*a^4*c^2)*d*e^7*f^4*x^6 + (a^3*b^3 - 4*a^4*b*c + 21*(a^3*b^2*c - 4*a^4*c^2)*d^2)*e^6*f^4*x^5 + 5*(7*(a^3*b^2*c - 4*a^4*c^2)*d^3 + (a^3*b^3 - 4*a^4*b*c)*d)*e^5*f^4*x^4 + (a^4*b^2 - 4*a^5*c + 35*(a^3*b^2*c - 4*a^4*c^2)*d^4 + 10*(a^3*b^3 - 4*a^4*b*c)*d^2)*e^4*f^4*x^3 + (21*(a^3*b^2*c - 4*a^4*c^2)*d^5 + 10*(a^3*b^3 - 4*a^4*b*c)*d^3 + 3*(a^4*b^2 - 4*a^5*c)*d)*e^3*f^4*x^2 + (7*(a^3*b^2*c - 4*a^4*c^2)*d^6 + 5*(a^3*b^3 - 4*a^4*b*c)*d^4 + 3*(a^4*b^2 - 4*a^5*c)*d^2)*e^2*f^4*x + ((a^3*b^2*c - 4*a^4*c^2)*d^7 + (a^3*b^3 - 4*a^4*b*c)*d^5 + (a^4*b^2 - 4*a^5*c)*d^3)*e*f^4)","B",0
654,1,6770,0,1.412432," ","integrate((e*f*x+d*f)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""fricas"")","-\frac{24 \, b c^{2} e^{7} f^{4} x^{7} + 168 \, b c^{2} d e^{6} f^{4} x^{6} + 2 \, {\left(252 \, b c^{2} d^{2} + 19 \, b^{2} c - 4 \, a c^{2}\right)} e^{5} f^{4} x^{5} + 10 \, {\left(84 \, b c^{2} d^{3} + {\left(19 \, b^{2} c - 4 \, a c^{2}\right)} d\right)} e^{4} f^{4} x^{4} + 2 \, {\left(420 \, b c^{2} d^{4} + 5 \, b^{3} + 16 \, a b c + 10 \, {\left(19 \, b^{2} c - 4 \, a c^{2}\right)} d^{2}\right)} e^{3} f^{4} x^{3} + 2 \, {\left(252 \, b c^{2} d^{5} + 10 \, {\left(19 \, b^{2} c - 4 \, a c^{2}\right)} d^{3} + 3 \, {\left(5 \, b^{3} + 16 \, a b c\right)} d\right)} e^{2} f^{4} x^{2} + 2 \, {\left(84 \, b c^{2} d^{6} + 5 \, {\left(19 \, b^{2} c - 4 \, a c^{2}\right)} d^{4} + 3 \, a b^{2} + 12 \, a^{2} c + 3 \, {\left(5 \, b^{3} + 16 \, a b c\right)} d^{2}\right)} e f^{4} x + 2 \, {\left(12 \, b c^{2} d^{7} + {\left(19 \, b^{2} c - 4 \, a c^{2}\right)} d^{5} + {\left(5 \, b^{3} + 16 \, a b c\right)} d^{3} + 3 \, {\left(a b^{2} + 4 \, a^{2} c\right)} d\right)} f^{4} + 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{9} x^{8} + 8 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3} + 14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{3} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3} + 70 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{4} + 30 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{5} + 10 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{6} + a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} + 3 \, {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{7} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{3} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{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)} d^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} f^{8} + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} \sqrt{\frac{f^{16}}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} e^{2}}{{\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}} \log\left(27 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e f^{12} x + 27 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d f^{12} + \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{8} - 8 \, a b^{6} c + 128 \, a^{3} b^{2} c^{3} - 256 \, a^{4} c^{4}\right)} e f^{8} - {\left(a b^{13} - 8 \, a^{2} b^{11} c - 80 \, a^{3} b^{9} c^{2} + 1280 \, a^{4} b^{7} c^{3} - 6400 \, a^{5} b^{5} c^{4} + 14336 \, a^{6} b^{3} c^{5} - 12288 \, a^{7} b c^{6}\right)} \sqrt{\frac{f^{16}}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} e^{3}\right)} \sqrt{-\frac{{\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} f^{8} + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} \sqrt{\frac{f^{16}}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} e^{2}}{{\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{9} x^{8} + 8 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3} + 14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{3} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3} + 70 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{4} + 30 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{5} + 10 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{6} + a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} + 3 \, {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{7} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{3} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{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)} d^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} f^{8} + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} \sqrt{\frac{f^{16}}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} e^{2}}{{\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}} \log\left(27 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e f^{12} x + 27 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d f^{12} - \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{8} - 8 \, a b^{6} c + 128 \, a^{3} b^{2} c^{3} - 256 \, a^{4} c^{4}\right)} e f^{8} - {\left(a b^{13} - 8 \, a^{2} b^{11} c - 80 \, a^{3} b^{9} c^{2} + 1280 \, a^{4} b^{7} c^{3} - 6400 \, a^{5} b^{5} c^{4} + 14336 \, a^{6} b^{3} c^{5} - 12288 \, a^{7} b c^{6}\right)} \sqrt{\frac{f^{16}}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} e^{3}\right)} \sqrt{-\frac{{\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} f^{8} + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} \sqrt{\frac{f^{16}}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} e^{2}}{{\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{9} x^{8} + 8 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3} + 14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{3} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3} + 70 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{4} + 30 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{5} + 10 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{6} + a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} + 3 \, {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{7} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{3} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{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)} d^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} f^{8} - {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} \sqrt{\frac{f^{16}}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} e^{2}}{{\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}} \log\left(27 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e f^{12} x + 27 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d f^{12} + \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{8} - 8 \, a b^{6} c + 128 \, a^{3} b^{2} c^{3} - 256 \, a^{4} c^{4}\right)} e f^{8} + {\left(a b^{13} - 8 \, a^{2} b^{11} c - 80 \, a^{3} b^{9} c^{2} + 1280 \, a^{4} b^{7} c^{3} - 6400 \, a^{5} b^{5} c^{4} + 14336 \, a^{6} b^{3} c^{5} - 12288 \, a^{7} b c^{6}\right)} \sqrt{\frac{f^{16}}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} e^{3}\right)} \sqrt{-\frac{{\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} f^{8} - {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} \sqrt{\frac{f^{16}}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} e^{2}}{{\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{9} x^{8} + 8 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3} + 14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{3} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3} + 70 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{4} + 30 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{5} + 10 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{6} + a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} + 3 \, {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{7} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{3} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{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)} d^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} f^{8} - {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} \sqrt{\frac{f^{16}}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} e^{2}}{{\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}} \log\left(27 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e f^{12} x + 27 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d f^{12} - \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{8} - 8 \, a b^{6} c + 128 \, a^{3} b^{2} c^{3} - 256 \, a^{4} c^{4}\right)} e f^{8} + {\left(a b^{13} - 8 \, a^{2} b^{11} c - 80 \, a^{3} b^{9} c^{2} + 1280 \, a^{4} b^{7} c^{3} - 6400 \, a^{5} b^{5} c^{4} + 14336 \, a^{6} b^{3} c^{5} - 12288 \, a^{7} b c^{6}\right)} \sqrt{\frac{f^{16}}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} e^{3}\right)} \sqrt{-\frac{{\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} f^{8} - {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} \sqrt{\frac{f^{16}}{{\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} e^{2}}{{\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}}\right)}{16 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{9} x^{8} + 8 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3} + 14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{3} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3} + 70 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{4} + 30 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{5} + 10 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(14 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{6} + a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2} + 15 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} + 3 \, {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{7} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{3} + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{8} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{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)} d^{4} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2}\right)} e\right)}}"," ",0,"-1/16*(24*b*c^2*e^7*f^4*x^7 + 168*b*c^2*d*e^6*f^4*x^6 + 2*(252*b*c^2*d^2 + 19*b^2*c - 4*a*c^2)*e^5*f^4*x^5 + 10*(84*b*c^2*d^3 + (19*b^2*c - 4*a*c^2)*d)*e^4*f^4*x^4 + 2*(420*b*c^2*d^4 + 5*b^3 + 16*a*b*c + 10*(19*b^2*c - 4*a*c^2)*d^2)*e^3*f^4*x^3 + 2*(252*b*c^2*d^5 + 10*(19*b^2*c - 4*a*c^2)*d^3 + 3*(5*b^3 + 16*a*b*c)*d)*e^2*f^4*x^2 + 2*(84*b*c^2*d^6 + 5*(19*b^2*c - 4*a*c^2)*d^4 + 3*a*b^2 + 12*a^2*c + 3*(5*b^3 + 16*a*b*c)*d^2)*e*f^4*x + 2*(12*b*c^2*d^7 + (19*b^2*c - 4*a*c^2)*d^5 + (5*b^3 + 16*a*b*c)*d^3 + 3*(a*b^2 + 4*a^2*c)*d)*f^4 + 3*sqrt(1/2)*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^9*x^8 + 8*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*e^8*x^7 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3 + 14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2)*e^7*x^6 + 4*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^3 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d)*e^6*x^5 + (b^6 - 6*a*b^4*c + 32*a^3*c^3 + 70*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^4 + 30*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2)*e^5*x^4 + 4*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^5 + 10*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d)*e^4*x^3 + 2*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^6 + a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^4 + 3*(b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^2)*e^3*x^2 + 4*(2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^7 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^5 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^3 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d)*e^2*x + ((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^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)*d^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2)*e)*sqrt(-((b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*f^8 + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*sqrt(f^16/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*e^2)/((a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))*log(27*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*e*f^12*x + 27*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d*f^12 + 27/2*sqrt(1/2)*((b^8 - 8*a*b^6*c + 128*a^3*b^2*c^3 - 256*a^4*c^4)*e*f^8 - (a*b^13 - 8*a^2*b^11*c - 80*a^3*b^9*c^2 + 1280*a^4*b^7*c^3 - 6400*a^5*b^5*c^4 + 14336*a^6*b^3*c^5 - 12288*a^7*b*c^6)*sqrt(f^16/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*e^3)*sqrt(-((b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*f^8 + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*sqrt(f^16/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*e^2)/((a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))) - 3*sqrt(1/2)*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^9*x^8 + 8*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*e^8*x^7 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3 + 14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2)*e^7*x^6 + 4*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^3 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d)*e^6*x^5 + (b^6 - 6*a*b^4*c + 32*a^3*c^3 + 70*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^4 + 30*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2)*e^5*x^4 + 4*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^5 + 10*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d)*e^4*x^3 + 2*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^6 + a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^4 + 3*(b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^2)*e^3*x^2 + 4*(2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^7 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^5 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^3 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d)*e^2*x + ((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^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)*d^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2)*e)*sqrt(-((b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*f^8 + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*sqrt(f^16/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*e^2)/((a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))*log(27*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*e*f^12*x + 27*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d*f^12 - 27/2*sqrt(1/2)*((b^8 - 8*a*b^6*c + 128*a^3*b^2*c^3 - 256*a^4*c^4)*e*f^8 - (a*b^13 - 8*a^2*b^11*c - 80*a^3*b^9*c^2 + 1280*a^4*b^7*c^3 - 6400*a^5*b^5*c^4 + 14336*a^6*b^3*c^5 - 12288*a^7*b*c^6)*sqrt(f^16/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*e^3)*sqrt(-((b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*f^8 + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*sqrt(f^16/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*e^2)/((a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))) + 3*sqrt(1/2)*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^9*x^8 + 8*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*e^8*x^7 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3 + 14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2)*e^7*x^6 + 4*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^3 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d)*e^6*x^5 + (b^6 - 6*a*b^4*c + 32*a^3*c^3 + 70*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^4 + 30*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2)*e^5*x^4 + 4*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^5 + 10*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d)*e^4*x^3 + 2*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^6 + a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^4 + 3*(b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^2)*e^3*x^2 + 4*(2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^7 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^5 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^3 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d)*e^2*x + ((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^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)*d^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2)*e)*sqrt(-((b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*f^8 - (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*sqrt(f^16/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*e^2)/((a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))*log(27*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*e*f^12*x + 27*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d*f^12 + 27/2*sqrt(1/2)*((b^8 - 8*a*b^6*c + 128*a^3*b^2*c^3 - 256*a^4*c^4)*e*f^8 + (a*b^13 - 8*a^2*b^11*c - 80*a^3*b^9*c^2 + 1280*a^4*b^7*c^3 - 6400*a^5*b^5*c^4 + 14336*a^6*b^3*c^5 - 12288*a^7*b*c^6)*sqrt(f^16/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*e^3)*sqrt(-((b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*f^8 - (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*sqrt(f^16/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*e^2)/((a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))) - 3*sqrt(1/2)*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^9*x^8 + 8*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*e^8*x^7 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3 + 14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2)*e^7*x^6 + 4*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^3 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d)*e^6*x^5 + (b^6 - 6*a*b^4*c + 32*a^3*c^3 + 70*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^4 + 30*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2)*e^5*x^4 + 4*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^5 + 10*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d)*e^4*x^3 + 2*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^6 + a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^4 + 3*(b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^2)*e^3*x^2 + 4*(2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^7 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^5 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^3 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d)*e^2*x + ((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^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)*d^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2)*e)*sqrt(-((b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*f^8 - (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*sqrt(f^16/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*e^2)/((a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))*log(27*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*e*f^12*x + 27*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d*f^12 - 27/2*sqrt(1/2)*((b^8 - 8*a*b^6*c + 128*a^3*b^2*c^3 - 256*a^4*c^4)*e*f^8 + (a*b^13 - 8*a^2*b^11*c - 80*a^3*b^9*c^2 + 1280*a^4*b^7*c^3 - 6400*a^5*b^5*c^4 + 14336*a^6*b^3*c^5 - 12288*a^7*b*c^6)*sqrt(f^16/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*e^3)*sqrt(-((b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*f^8 - (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*sqrt(f^16/((a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*e^2)/((a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))))/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^9*x^8 + 8*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*e^8*x^7 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3 + 14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2)*e^7*x^6 + 4*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^3 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d)*e^6*x^5 + (b^6 - 6*a*b^4*c + 32*a^3*c^3 + 70*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^4 + 30*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2)*e^5*x^4 + 4*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^5 + 10*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d)*e^4*x^3 + 2*(14*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^6 + a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2 + 15*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^4 + 3*(b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^2)*e^3*x^2 + 4*(2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^7 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^5 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^3 + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d)*e^2*x + ((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^8 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^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)*d^4 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2)*e)","B",0
655,1,3843,0,1.443226," ","integrate((e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{6} f^{3} x^{6} + 36 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{5} f^{3} x^{5} + 9 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 10 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2}\right)} e^{4} f^{3} x^{4} + 12 \, {\left(10 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} + 3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d\right)} e^{3} f^{3} x^{3} + 2 \, {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2} + 45 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} + 27 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{2}\right)} e^{2} f^{3} x^{2} + 4 \, {\left(9 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} + 9 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} + {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} d\right)} e f^{3} x + {\left(6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{6} + a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2} + 9 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{4} + 2 \, {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} d^{2}\right)} f^{3} - 6 \, {\left(b c^{3} e^{8} f^{3} x^{8} + 8 \, b c^{3} d e^{7} f^{3} x^{7} + 2 \, {\left(14 \, b c^{3} d^{2} + b^{2} c^{2}\right)} e^{6} f^{3} x^{6} + 4 \, {\left(14 \, b c^{3} d^{3} + 3 \, b^{2} c^{2} d\right)} e^{5} f^{3} x^{5} + {\left(70 \, b c^{3} d^{4} + 30 \, b^{2} c^{2} d^{2} + b^{3} c + 2 \, a b c^{2}\right)} e^{4} f^{3} x^{4} + 4 \, {\left(14 \, b c^{3} d^{5} + 10 \, b^{2} c^{2} d^{3} + {\left(b^{3} c + 2 \, a b c^{2}\right)} d\right)} e^{3} f^{3} x^{3} + 2 \, {\left(14 \, b c^{3} d^{6} + 15 \, b^{2} c^{2} d^{4} + a b^{2} c + 3 \, {\left(b^{3} c + 2 \, a b c^{2}\right)} d^{2}\right)} e^{2} f^{3} x^{2} + 4 \, {\left(2 \, b c^{3} d^{7} + 3 \, b^{2} c^{2} d^{5} + a b^{2} c d + {\left(b^{3} c + 2 \, a b c^{2}\right)} d^{3}\right)} e f^{3} x + {\left(b c^{3} d^{8} + 2 \, b^{2} c^{2} d^{6} + 2 \, a b^{2} c d^{2} + {\left(b^{3} c + 2 \, a b c^{2}\right)} d^{4} + a^{2} b c\right)} f^{3}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c + {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right)}{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)} e^{9} x^{8} + 8 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d e^{8} x^{7} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{3} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d\right)} e^{6} x^{5} + {\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} + 70 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} + 30 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{5} + 10 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} + {\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)} d\right)} e^{4} x^{3} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{6} + 15 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{4} + 3 \, {\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)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{7} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{5} + {\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)} d^{3} + {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d\right)} e^{2} x + {\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)} d^{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)} d^{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)} d^{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)} d^{2}\right)} e\right)}}, -\frac{6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{6} f^{3} x^{6} + 36 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{5} f^{3} x^{5} + 9 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 10 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2}\right)} e^{4} f^{3} x^{4} + 12 \, {\left(10 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} + 3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d\right)} e^{3} f^{3} x^{3} + 2 \, {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2} + 45 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} + 27 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{2}\right)} e^{2} f^{3} x^{2} + 4 \, {\left(9 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} + 9 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} + {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} d\right)} e f^{3} x + {\left(6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{6} + a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2} + 9 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{4} + 2 \, {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} d^{2}\right)} f^{3} - 12 \, {\left(b c^{3} e^{8} f^{3} x^{8} + 8 \, b c^{3} d e^{7} f^{3} x^{7} + 2 \, {\left(14 \, b c^{3} d^{2} + b^{2} c^{2}\right)} e^{6} f^{3} x^{6} + 4 \, {\left(14 \, b c^{3} d^{3} + 3 \, b^{2} c^{2} d\right)} e^{5} f^{3} x^{5} + {\left(70 \, b c^{3} d^{4} + 30 \, b^{2} c^{2} d^{2} + b^{3} c + 2 \, a b c^{2}\right)} e^{4} f^{3} x^{4} + 4 \, {\left(14 \, b c^{3} d^{5} + 10 \, b^{2} c^{2} d^{3} + {\left(b^{3} c + 2 \, a b c^{2}\right)} d\right)} e^{3} f^{3} x^{3} + 2 \, {\left(14 \, b c^{3} d^{6} + 15 \, b^{2} c^{2} d^{4} + a b^{2} c + 3 \, {\left(b^{3} c + 2 \, a b c^{2}\right)} d^{2}\right)} e^{2} f^{3} x^{2} + 4 \, {\left(2 \, b c^{3} d^{7} + 3 \, b^{2} c^{2} d^{5} + a b^{2} c d + {\left(b^{3} c + 2 \, a b c^{2}\right)} d^{3}\right)} e f^{3} x + {\left(b c^{3} d^{8} + 2 \, b^{2} c^{2} d^{6} + 2 \, a b^{2} c d^{2} + {\left(b^{3} c + 2 \, a b c^{2}\right)} d^{4} + a^{2} b c\right)} f^{3}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right)}{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)} e^{9} x^{8} + 8 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d e^{8} x^{7} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{3} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d\right)} e^{6} x^{5} + {\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} + 70 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} + 30 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{5} + 10 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} + {\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)} d\right)} e^{4} x^{3} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{6} + 15 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{4} + 3 \, {\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)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{7} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{5} + {\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)} d^{3} + {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d\right)} e^{2} x + {\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)} d^{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)} d^{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)} d^{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)} d^{2}\right)} e\right)}}\right]"," ",0,"[-1/4*(6*(b^3*c^2 - 4*a*b*c^3)*e^6*f^3*x^6 + 36*(b^3*c^2 - 4*a*b*c^3)*d*e^5*f^3*x^5 + 9*(b^4*c - 4*a*b^2*c^2 + 10*(b^3*c^2 - 4*a*b*c^3)*d^2)*e^4*f^3*x^4 + 12*(10*(b^3*c^2 - 4*a*b*c^3)*d^3 + 3*(b^4*c - 4*a*b^2*c^2)*d)*e^3*f^3*x^3 + 2*(b^5 + a*b^3*c - 20*a^2*b*c^2 + 45*(b^3*c^2 - 4*a*b*c^3)*d^4 + 27*(b^4*c - 4*a*b^2*c^2)*d^2)*e^2*f^3*x^2 + 4*(9*(b^3*c^2 - 4*a*b*c^3)*d^5 + 9*(b^4*c - 4*a*b^2*c^2)*d^3 + (b^5 + a*b^3*c - 20*a^2*b*c^2)*d)*e*f^3*x + (6*(b^3*c^2 - 4*a*b*c^3)*d^6 + a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2 + 9*(b^4*c - 4*a*b^2*c^2)*d^4 + 2*(b^5 + a*b^3*c - 20*a^2*b*c^2)*d^2)*f^3 - 6*(b*c^3*e^8*f^3*x^8 + 8*b*c^3*d*e^7*f^3*x^7 + 2*(14*b*c^3*d^2 + b^2*c^2)*e^6*f^3*x^6 + 4*(14*b*c^3*d^3 + 3*b^2*c^2*d)*e^5*f^3*x^5 + (70*b*c^3*d^4 + 30*b^2*c^2*d^2 + b^3*c + 2*a*b*c^2)*e^4*f^3*x^4 + 4*(14*b*c^3*d^5 + 10*b^2*c^2*d^3 + (b^3*c + 2*a*b*c^2)*d)*e^3*f^3*x^3 + 2*(14*b*c^3*d^6 + 15*b^2*c^2*d^4 + a*b^2*c + 3*(b^3*c + 2*a*b*c^2)*d^2)*e^2*f^3*x^2 + 4*(2*b*c^3*d^7 + 3*b^2*c^2*d^5 + a*b^2*c*d + (b^3*c + 2*a*b*c^2)*d^3)*e*f^3*x + (b*c^3*d^8 + 2*b^2*c^2*d^6 + 2*a*b^2*c*d^2 + (b^3*c + 2*a*b*c^2)*d^4 + a^2*b*c)*f^3)*sqrt(b^2 - 4*a*c)*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c + (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)))/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^9*x^8 + 8*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d*e^8*x^7 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2)*e^7*x^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^3 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d)*e^6*x^5 + (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 + 70*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 + 30*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2)*e^5*x^4 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^5 + 10*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3 + (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)*d)*e^4*x^3 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^6 + 15*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^4 + 3*(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)*d^2)*e^3*x^2 + 4*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^7 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^5 + (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)*d^3 + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d)*e^2*x + ((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^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)*d^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)*d^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2)*e), -1/4*(6*(b^3*c^2 - 4*a*b*c^3)*e^6*f^3*x^6 + 36*(b^3*c^2 - 4*a*b*c^3)*d*e^5*f^3*x^5 + 9*(b^4*c - 4*a*b^2*c^2 + 10*(b^3*c^2 - 4*a*b*c^3)*d^2)*e^4*f^3*x^4 + 12*(10*(b^3*c^2 - 4*a*b*c^3)*d^3 + 3*(b^4*c - 4*a*b^2*c^2)*d)*e^3*f^3*x^3 + 2*(b^5 + a*b^3*c - 20*a^2*b*c^2 + 45*(b^3*c^2 - 4*a*b*c^3)*d^4 + 27*(b^4*c - 4*a*b^2*c^2)*d^2)*e^2*f^3*x^2 + 4*(9*(b^3*c^2 - 4*a*b*c^3)*d^5 + 9*(b^4*c - 4*a*b^2*c^2)*d^3 + (b^5 + a*b^3*c - 20*a^2*b*c^2)*d)*e*f^3*x + (6*(b^3*c^2 - 4*a*b*c^3)*d^6 + a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2 + 9*(b^4*c - 4*a*b^2*c^2)*d^4 + 2*(b^5 + a*b^3*c - 20*a^2*b*c^2)*d^2)*f^3 - 12*(b*c^3*e^8*f^3*x^8 + 8*b*c^3*d*e^7*f^3*x^7 + 2*(14*b*c^3*d^2 + b^2*c^2)*e^6*f^3*x^6 + 4*(14*b*c^3*d^3 + 3*b^2*c^2*d)*e^5*f^3*x^5 + (70*b*c^3*d^4 + 30*b^2*c^2*d^2 + b^3*c + 2*a*b*c^2)*e^4*f^3*x^4 + 4*(14*b*c^3*d^5 + 10*b^2*c^2*d^3 + (b^3*c + 2*a*b*c^2)*d)*e^3*f^3*x^3 + 2*(14*b*c^3*d^6 + 15*b^2*c^2*d^4 + a*b^2*c + 3*(b^3*c + 2*a*b*c^2)*d^2)*e^2*f^3*x^2 + 4*(2*b*c^3*d^7 + 3*b^2*c^2*d^5 + a*b^2*c*d + (b^3*c + 2*a*b*c^2)*d^3)*e*f^3*x + (b*c^3*d^8 + 2*b^2*c^2*d^6 + 2*a*b^2*c*d^2 + (b^3*c + 2*a*b*c^2)*d^4 + a^2*b*c)*f^3)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)))/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^9*x^8 + 8*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d*e^8*x^7 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2)*e^7*x^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^3 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d)*e^6*x^5 + (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 + 70*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 + 30*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2)*e^5*x^4 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^5 + 10*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3 + (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)*d)*e^4*x^3 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^6 + 15*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^4 + 3*(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)*d^2)*e^3*x^2 + 4*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^7 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^5 + (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)*d^3 + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d)*e^2*x + ((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^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)*d^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)*d^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2)*e)]","B",0
656,1,7838,0,2.198558," ","integrate((e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} e^{7} f^{2} x^{7} + 14 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} d e^{6} f^{2} x^{6} + 2 \, {\left(2 \, b^{3} c + 28 \, a b c^{2} + 21 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} d^{2}\right)} e^{5} f^{2} x^{5} + 10 \, {\left(7 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} d^{3} + 2 \, {\left(b^{3} c + 14 \, a b c^{2}\right)} d\right)} e^{4} f^{2} x^{4} + 2 \, {\left(35 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} d^{4} + b^{4} + 5 \, a b^{2} c + 36 \, a^{2} c^{2} + 20 \, {\left(b^{3} c + 14 \, a b c^{2}\right)} d^{2}\right)} e^{3} f^{2} x^{3} + 2 \, {\left(21 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} d^{5} + 20 \, {\left(b^{3} c + 14 \, a b c^{2}\right)} d^{3} + 3 \, {\left(b^{4} + 5 \, a b^{2} c + 36 \, a^{2} c^{2}\right)} d\right)} e^{2} f^{2} x^{2} + 2 \, {\left(7 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} d^{6} + 10 \, {\left(b^{3} c + 14 \, a b c^{2}\right)} d^{4} - a b^{3} + 16 \, a^{2} b c + 3 \, {\left(b^{4} + 5 \, a b^{2} c + 36 \, a^{2} c^{2}\right)} d^{2}\right)} e f^{2} x + 2 \, {\left({\left(b^{2} c^{2} + 20 \, a c^{3}\right)} d^{7} + 2 \, {\left(b^{3} c + 14 \, a b c^{2}\right)} d^{5} + {\left(b^{4} + 5 \, a b^{2} c + 36 \, a^{2} c^{2}\right)} d^{3} - {\left(a b^{3} - 16 \, a^{2} b c\right)} d\right)} f^{2} + \sqrt{\frac{1}{2}} {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} e^{9} x^{8} + 8 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3} + 14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{3} + 3 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3} + 70 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{4} + 30 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{5} + 10 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{3} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2} + 14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{6} + 15 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{4} + 3 \, {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{7} + 3 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{5} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{3} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{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)} d^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3}\right)} f^{4} + {\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{{\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} f^{8}}{{\left(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)} e^{4}}} e^{2}}{{\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)} e^{2}}} \log\left({\left(35 \, b^{6} c^{2} - 1491 \, a b^{4} c^{3} + 15000 \, a^{2} b^{2} c^{4} + 10000 \, a^{3} c^{5}\right)} e f^{6} x + {\left(35 \, b^{6} c^{2} - 1491 \, a b^{4} c^{3} + 15000 \, a^{2} b^{2} c^{4} + 10000 \, a^{3} c^{5}\right)} d f^{6} + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{11} - 53 \, a b^{9} c + 940 \, a^{2} b^{7} c^{2} - 6832 \, a^{3} b^{5} c^{3} + 21824 \, a^{4} b^{3} c^{4} - 25600 \, a^{5} b c^{5}\right)} e f^{4} - {\left(a^{3} b^{14} - 38 \, a^{4} b^{12} c + 480 \, a^{5} b^{10} c^{2} - 2720 \, a^{6} b^{8} c^{3} + 6400 \, a^{7} b^{6} c^{4} + 1536 \, a^{8} b^{4} c^{5} - 32768 \, a^{9} b^{2} c^{6} + 40960 \, a^{10} c^{7}\right)} \sqrt{\frac{{\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} f^{8}}{{\left(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)} e^{4}}} e^{3}\right)} \sqrt{-\frac{{\left(b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3}\right)} f^{4} + {\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{{\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} f^{8}}{{\left(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)} e^{4}}} e^{2}}{{\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)} e^{2}}}\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)} e^{9} x^{8} + 8 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3} + 14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{3} + 3 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3} + 70 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{4} + 30 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{5} + 10 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{3} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2} + 14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{6} + 15 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{4} + 3 \, {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{7} + 3 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{5} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{3} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{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)} d^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3}\right)} f^{4} + {\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{{\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} f^{8}}{{\left(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)} e^{4}}} e^{2}}{{\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)} e^{2}}} \log\left({\left(35 \, b^{6} c^{2} - 1491 \, a b^{4} c^{3} + 15000 \, a^{2} b^{2} c^{4} + 10000 \, a^{3} c^{5}\right)} e f^{6} x + {\left(35 \, b^{6} c^{2} - 1491 \, a b^{4} c^{3} + 15000 \, a^{2} b^{2} c^{4} + 10000 \, a^{3} c^{5}\right)} d f^{6} - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{11} - 53 \, a b^{9} c + 940 \, a^{2} b^{7} c^{2} - 6832 \, a^{3} b^{5} c^{3} + 21824 \, a^{4} b^{3} c^{4} - 25600 \, a^{5} b c^{5}\right)} e f^{4} - {\left(a^{3} b^{14} - 38 \, a^{4} b^{12} c + 480 \, a^{5} b^{10} c^{2} - 2720 \, a^{6} b^{8} c^{3} + 6400 \, a^{7} b^{6} c^{4} + 1536 \, a^{8} b^{4} c^{5} - 32768 \, a^{9} b^{2} c^{6} + 40960 \, a^{10} c^{7}\right)} \sqrt{\frac{{\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} f^{8}}{{\left(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)} e^{4}}} e^{3}\right)} \sqrt{-\frac{{\left(b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3}\right)} f^{4} + {\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{{\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} f^{8}}{{\left(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)} e^{4}}} e^{2}}{{\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)} e^{2}}}\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)} e^{9} x^{8} + 8 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3} + 14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{3} + 3 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3} + 70 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{4} + 30 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{5} + 10 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{3} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2} + 14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{6} + 15 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{4} + 3 \, {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{7} + 3 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{5} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{3} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{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)} d^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3}\right)} f^{4} - {\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{{\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} f^{8}}{{\left(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)} e^{4}}} e^{2}}{{\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)} e^{2}}} \log\left({\left(35 \, b^{6} c^{2} - 1491 \, a b^{4} c^{3} + 15000 \, a^{2} b^{2} c^{4} + 10000 \, a^{3} c^{5}\right)} e f^{6} x + {\left(35 \, b^{6} c^{2} - 1491 \, a b^{4} c^{3} + 15000 \, a^{2} b^{2} c^{4} + 10000 \, a^{3} c^{5}\right)} d f^{6} + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{11} - 53 \, a b^{9} c + 940 \, a^{2} b^{7} c^{2} - 6832 \, a^{3} b^{5} c^{3} + 21824 \, a^{4} b^{3} c^{4} - 25600 \, a^{5} b c^{5}\right)} e f^{4} + {\left(a^{3} b^{14} - 38 \, a^{4} b^{12} c + 480 \, a^{5} b^{10} c^{2} - 2720 \, a^{6} b^{8} c^{3} + 6400 \, a^{7} b^{6} c^{4} + 1536 \, a^{8} b^{4} c^{5} - 32768 \, a^{9} b^{2} c^{6} + 40960 \, a^{10} c^{7}\right)} \sqrt{\frac{{\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} f^{8}}{{\left(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)} e^{4}}} e^{3}\right)} \sqrt{-\frac{{\left(b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3}\right)} f^{4} - {\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{{\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} f^{8}}{{\left(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)} e^{4}}} e^{2}}{{\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)} e^{2}}}\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)} e^{9} x^{8} + 8 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3} + 14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{3} + 3 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3} + 70 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{4} + 30 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{5} + 10 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{3} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2} + 14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{6} + 15 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{4} + 3 \, {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{7} + 3 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{5} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{3} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{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)} d^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d^{2}\right)} e\right)} \sqrt{-\frac{{\left(b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3}\right)} f^{4} - {\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{{\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} f^{8}}{{\left(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)} e^{4}}} e^{2}}{{\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)} e^{2}}} \log\left({\left(35 \, b^{6} c^{2} - 1491 \, a b^{4} c^{3} + 15000 \, a^{2} b^{2} c^{4} + 10000 \, a^{3} c^{5}\right)} e f^{6} x + {\left(35 \, b^{6} c^{2} - 1491 \, a b^{4} c^{3} + 15000 \, a^{2} b^{2} c^{4} + 10000 \, a^{3} c^{5}\right)} d f^{6} - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{11} - 53 \, a b^{9} c + 940 \, a^{2} b^{7} c^{2} - 6832 \, a^{3} b^{5} c^{3} + 21824 \, a^{4} b^{3} c^{4} - 25600 \, a^{5} b c^{5}\right)} e f^{4} + {\left(a^{3} b^{14} - 38 \, a^{4} b^{12} c + 480 \, a^{5} b^{10} c^{2} - 2720 \, a^{6} b^{8} c^{3} + 6400 \, a^{7} b^{6} c^{4} + 1536 \, a^{8} b^{4} c^{5} - 32768 \, a^{9} b^{2} c^{6} + 40960 \, a^{10} c^{7}\right)} \sqrt{\frac{{\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} f^{8}}{{\left(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)} e^{4}}} e^{3}\right)} \sqrt{-\frac{{\left(b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3}\right)} f^{4} - {\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{{\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} f^{8}}{{\left(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)} e^{4}}} e^{2}}{{\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)} e^{2}}}\right)}{16 \, {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} e^{9} x^{8} + 8 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d e^{8} x^{7} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3} + 14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{3} + 3 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d\right)} e^{6} x^{5} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3} + 70 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{4} + 30 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{5} + 10 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{3} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d\right)} e^{4} x^{3} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2} + 14 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{6} + 15 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{4} + 3 \, {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{7} + 3 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{5} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{3} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d\right)} e^{2} x + {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{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)} d^{6} + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{4} + 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d^{2}\right)} e\right)}}"," ",0,"1/16*(2*(b^2*c^2 + 20*a*c^3)*e^7*f^2*x^7 + 14*(b^2*c^2 + 20*a*c^3)*d*e^6*f^2*x^6 + 2*(2*b^3*c + 28*a*b*c^2 + 21*(b^2*c^2 + 20*a*c^3)*d^2)*e^5*f^2*x^5 + 10*(7*(b^2*c^2 + 20*a*c^3)*d^3 + 2*(b^3*c + 14*a*b*c^2)*d)*e^4*f^2*x^4 + 2*(35*(b^2*c^2 + 20*a*c^3)*d^4 + b^4 + 5*a*b^2*c + 36*a^2*c^2 + 20*(b^3*c + 14*a*b*c^2)*d^2)*e^3*f^2*x^3 + 2*(21*(b^2*c^2 + 20*a*c^3)*d^5 + 20*(b^3*c + 14*a*b*c^2)*d^3 + 3*(b^4 + 5*a*b^2*c + 36*a^2*c^2)*d)*e^2*f^2*x^2 + 2*(7*(b^2*c^2 + 20*a*c^3)*d^6 + 10*(b^3*c + 14*a*b*c^2)*d^4 - a*b^3 + 16*a^2*b*c + 3*(b^4 + 5*a*b^2*c + 36*a^2*c^2)*d^2)*e*f^2*x + 2*((b^2*c^2 + 20*a*c^3)*d^7 + 2*(b^3*c + 14*a*b*c^2)*d^5 + (b^4 + 5*a*b^2*c + 36*a^2*c^2)*d^3 - (a*b^3 - 16*a^2*b*c)*d)*f^2 + sqrt(1/2)*((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*e^9*x^8 + 8*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d*e^8*x^7 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3 + 14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^2)*e^7*x^6 + 4*(14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^3 + 3*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d)*e^6*x^5 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3 + 70*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^4 + 30*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^2)*e^5*x^4 + 4*(14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^5 + 10*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^3 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d)*e^4*x^3 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2 + 14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^6 + 15*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^4 + 3*(a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^2)*e^3*x^2 + 4*(2*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^7 + 3*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^5 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^3 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d)*e^2*x + ((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^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)*d^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d^2)*e)*sqrt(-((b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3)*f^4 + (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((b^4 - 50*a*b^2*c + 625*a^2*c^2)*f^8/((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)*e^4))*e^2)/((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)*e^2))*log((35*b^6*c^2 - 1491*a*b^4*c^3 + 15000*a^2*b^2*c^4 + 10000*a^3*c^5)*e*f^6*x + (35*b^6*c^2 - 1491*a*b^4*c^3 + 15000*a^2*b^2*c^4 + 10000*a^3*c^5)*d*f^6 + 1/2*sqrt(1/2)*((b^11 - 53*a*b^9*c + 940*a^2*b^7*c^2 - 6832*a^3*b^5*c^3 + 21824*a^4*b^3*c^4 - 25600*a^5*b*c^5)*e*f^4 - (a^3*b^14 - 38*a^4*b^12*c + 480*a^5*b^10*c^2 - 2720*a^6*b^8*c^3 + 6400*a^7*b^6*c^4 + 1536*a^8*b^4*c^5 - 32768*a^9*b^2*c^6 + 40960*a^10*c^7)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)*f^8/((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)*e^4))*e^3)*sqrt(-((b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3)*f^4 + (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((b^4 - 50*a*b^2*c + 625*a^2*c^2)*f^8/((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)*e^4))*e^2)/((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)*e^2))) - sqrt(1/2)*((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*e^9*x^8 + 8*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d*e^8*x^7 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3 + 14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^2)*e^7*x^6 + 4*(14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^3 + 3*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d)*e^6*x^5 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3 + 70*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^4 + 30*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^2)*e^5*x^4 + 4*(14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^5 + 10*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^3 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d)*e^4*x^3 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2 + 14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^6 + 15*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^4 + 3*(a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^2)*e^3*x^2 + 4*(2*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^7 + 3*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^5 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^3 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d)*e^2*x + ((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^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)*d^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d^2)*e)*sqrt(-((b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3)*f^4 + (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((b^4 - 50*a*b^2*c + 625*a^2*c^2)*f^8/((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)*e^4))*e^2)/((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)*e^2))*log((35*b^6*c^2 - 1491*a*b^4*c^3 + 15000*a^2*b^2*c^4 + 10000*a^3*c^5)*e*f^6*x + (35*b^6*c^2 - 1491*a*b^4*c^3 + 15000*a^2*b^2*c^4 + 10000*a^3*c^5)*d*f^6 - 1/2*sqrt(1/2)*((b^11 - 53*a*b^9*c + 940*a^2*b^7*c^2 - 6832*a^3*b^5*c^3 + 21824*a^4*b^3*c^4 - 25600*a^5*b*c^5)*e*f^4 - (a^3*b^14 - 38*a^4*b^12*c + 480*a^5*b^10*c^2 - 2720*a^6*b^8*c^3 + 6400*a^7*b^6*c^4 + 1536*a^8*b^4*c^5 - 32768*a^9*b^2*c^6 + 40960*a^10*c^7)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)*f^8/((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)*e^4))*e^3)*sqrt(-((b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3)*f^4 + (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((b^4 - 50*a*b^2*c + 625*a^2*c^2)*f^8/((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)*e^4))*e^2)/((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)*e^2))) + sqrt(1/2)*((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*e^9*x^8 + 8*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d*e^8*x^7 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3 + 14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^2)*e^7*x^6 + 4*(14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^3 + 3*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d)*e^6*x^5 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3 + 70*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^4 + 30*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^2)*e^5*x^4 + 4*(14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^5 + 10*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^3 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d)*e^4*x^3 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2 + 14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^6 + 15*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^4 + 3*(a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^2)*e^3*x^2 + 4*(2*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^7 + 3*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^5 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^3 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d)*e^2*x + ((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^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)*d^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d^2)*e)*sqrt(-((b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3)*f^4 - (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((b^4 - 50*a*b^2*c + 625*a^2*c^2)*f^8/((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)*e^4))*e^2)/((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)*e^2))*log((35*b^6*c^2 - 1491*a*b^4*c^3 + 15000*a^2*b^2*c^4 + 10000*a^3*c^5)*e*f^6*x + (35*b^6*c^2 - 1491*a*b^4*c^3 + 15000*a^2*b^2*c^4 + 10000*a^3*c^5)*d*f^6 + 1/2*sqrt(1/2)*((b^11 - 53*a*b^9*c + 940*a^2*b^7*c^2 - 6832*a^3*b^5*c^3 + 21824*a^4*b^3*c^4 - 25600*a^5*b*c^5)*e*f^4 + (a^3*b^14 - 38*a^4*b^12*c + 480*a^5*b^10*c^2 - 2720*a^6*b^8*c^3 + 6400*a^7*b^6*c^4 + 1536*a^8*b^4*c^5 - 32768*a^9*b^2*c^6 + 40960*a^10*c^7)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)*f^8/((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)*e^4))*e^3)*sqrt(-((b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3)*f^4 - (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((b^4 - 50*a*b^2*c + 625*a^2*c^2)*f^8/((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)*e^4))*e^2)/((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)*e^2))) - sqrt(1/2)*((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*e^9*x^8 + 8*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d*e^8*x^7 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3 + 14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^2)*e^7*x^6 + 4*(14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^3 + 3*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d)*e^6*x^5 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3 + 70*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^4 + 30*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^2)*e^5*x^4 + 4*(14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^5 + 10*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^3 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d)*e^4*x^3 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2 + 14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^6 + 15*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^4 + 3*(a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^2)*e^3*x^2 + 4*(2*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^7 + 3*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^5 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^3 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d)*e^2*x + ((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^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)*d^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d^2)*e)*sqrt(-((b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3)*f^4 - (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((b^4 - 50*a*b^2*c + 625*a^2*c^2)*f^8/((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)*e^4))*e^2)/((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)*e^2))*log((35*b^6*c^2 - 1491*a*b^4*c^3 + 15000*a^2*b^2*c^4 + 10000*a^3*c^5)*e*f^6*x + (35*b^6*c^2 - 1491*a*b^4*c^3 + 15000*a^2*b^2*c^4 + 10000*a^3*c^5)*d*f^6 - 1/2*sqrt(1/2)*((b^11 - 53*a*b^9*c + 940*a^2*b^7*c^2 - 6832*a^3*b^5*c^3 + 21824*a^4*b^3*c^4 - 25600*a^5*b*c^5)*e*f^4 + (a^3*b^14 - 38*a^4*b^12*c + 480*a^5*b^10*c^2 - 2720*a^6*b^8*c^3 + 6400*a^7*b^6*c^4 + 1536*a^8*b^4*c^5 - 32768*a^9*b^2*c^6 + 40960*a^10*c^7)*sqrt((b^4 - 50*a*b^2*c + 625*a^2*c^2)*f^8/((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)*e^4))*e^3)*sqrt(-((b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3)*f^4 - (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((b^4 - 50*a*b^2*c + 625*a^2*c^2)*f^8/((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)*e^4))*e^2)/((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)*e^2))))/((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*e^9*x^8 + 8*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d*e^8*x^7 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3 + 14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^2)*e^7*x^6 + 4*(14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^3 + 3*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d)*e^6*x^5 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3 + 70*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^4 + 30*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^2)*e^5*x^4 + 4*(14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^5 + 10*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^3 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d)*e^4*x^3 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2 + 14*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^6 + 15*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^4 + 3*(a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^2)*e^3*x^2 + 4*(2*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^7 + 3*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^5 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^3 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d)*e^2*x + ((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^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)*d^6 + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^4 + 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d^2)*e)","B",0
657,1,3748,0,1.590734," ","integrate((e*f*x+d*f)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{6} f x^{6} + 72 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d e^{5} f x^{5} + 18 \, {\left(b^{3} c^{2} - 4 \, a b c^{3} + 10 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2}\right)} e^{4} f x^{4} + 24 \, {\left(10 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} + 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d\right)} e^{3} f x^{3} + 4 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3} + 45 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} + 27 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2}\right)} e^{2} f x^{2} + 8 \, {\left(9 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{5} + 9 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} + {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} d\right)} e f x + 12 \, {\left(c^{4} e^{8} f x^{8} + 8 \, c^{4} d e^{7} f x^{7} + 2 \, {\left(14 \, c^{4} d^{2} + b c^{3}\right)} e^{6} f x^{6} + 4 \, {\left(14 \, c^{4} d^{3} + 3 \, b c^{3} d\right)} e^{5} f x^{5} + {\left(70 \, c^{4} d^{4} + 30 \, b c^{3} d^{2} + b^{2} c^{2} + 2 \, a c^{3}\right)} e^{4} f x^{4} + 4 \, {\left(14 \, c^{4} d^{5} + 10 \, b c^{3} d^{3} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d\right)} e^{3} f x^{3} + 2 \, {\left(14 \, c^{4} d^{6} + 15 \, b c^{3} d^{4} + a b c^{2} + 3 \, {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2}\right)} e^{2} f x^{2} + 4 \, {\left(2 \, c^{4} d^{7} + 3 \, b c^{3} d^{5} + a b c^{2} d + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3}\right)} e f x + {\left(c^{4} d^{8} + 2 \, b c^{3} d^{6} + 2 \, a b c^{2} d^{2} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} + a^{2} c^{2}\right)} f\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c - {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right) + {\left(12 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - b^{5} + 14 \, a b^{3} c - 40 \, a^{2} b c^{2} + 18 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} + 4 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} d^{2}\right)} f}{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)} e^{9} x^{8} + 8 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d e^{8} x^{7} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{3} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d\right)} e^{6} x^{5} + {\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} + 70 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} + 30 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{5} + 10 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} + {\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)} d\right)} e^{4} x^{3} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{6} + 15 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{4} + 3 \, {\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)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{7} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{5} + {\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)} d^{3} + {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d\right)} e^{2} x + {\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)} d^{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)} d^{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)} d^{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)} d^{2}\right)} e\right)}}, \frac{12 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{6} f x^{6} + 72 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d e^{5} f x^{5} + 18 \, {\left(b^{3} c^{2} - 4 \, a b c^{3} + 10 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2}\right)} e^{4} f x^{4} + 24 \, {\left(10 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} + 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d\right)} e^{3} f x^{3} + 4 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3} + 45 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} + 27 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2}\right)} e^{2} f x^{2} + 8 \, {\left(9 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{5} + 9 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} + {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} d\right)} e f x - 24 \, {\left(c^{4} e^{8} f x^{8} + 8 \, c^{4} d e^{7} f x^{7} + 2 \, {\left(14 \, c^{4} d^{2} + b c^{3}\right)} e^{6} f x^{6} + 4 \, {\left(14 \, c^{4} d^{3} + 3 \, b c^{3} d\right)} e^{5} f x^{5} + {\left(70 \, c^{4} d^{4} + 30 \, b c^{3} d^{2} + b^{2} c^{2} + 2 \, a c^{3}\right)} e^{4} f x^{4} + 4 \, {\left(14 \, c^{4} d^{5} + 10 \, b c^{3} d^{3} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d\right)} e^{3} f x^{3} + 2 \, {\left(14 \, c^{4} d^{6} + 15 \, b c^{3} d^{4} + a b c^{2} + 3 \, {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2}\right)} e^{2} f x^{2} + 4 \, {\left(2 \, c^{4} d^{7} + 3 \, b c^{3} d^{5} + a b c^{2} d + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3}\right)} e f x + {\left(c^{4} d^{8} + 2 \, b c^{3} d^{6} + 2 \, a b c^{2} d^{2} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} + a^{2} c^{2}\right)} f\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) + {\left(12 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - b^{5} + 14 \, a b^{3} c - 40 \, a^{2} b c^{2} + 18 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} + 4 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} d^{2}\right)} f}{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)} e^{9} x^{8} + 8 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d e^{8} x^{7} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2}\right)} e^{7} x^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{3} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d\right)} e^{6} x^{5} + {\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} + 70 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} + 30 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{5} x^{4} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{5} + 10 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} + {\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)} d\right)} e^{4} x^{3} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{6} + 15 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{4} + 3 \, {\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)} d^{2}\right)} e^{3} x^{2} + 4 \, {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{7} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{5} + {\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)} d^{3} + {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d\right)} e^{2} x + {\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)} d^{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)} d^{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)} d^{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)} d^{2}\right)} e\right)}}\right]"," ",0,"[1/4*(12*(b^2*c^3 - 4*a*c^4)*e^6*f*x^6 + 72*(b^2*c^3 - 4*a*c^4)*d*e^5*f*x^5 + 18*(b^3*c^2 - 4*a*b*c^3 + 10*(b^2*c^3 - 4*a*c^4)*d^2)*e^4*f*x^4 + 24*(10*(b^2*c^3 - 4*a*c^4)*d^3 + 3*(b^3*c^2 - 4*a*b*c^3)*d)*e^3*f*x^3 + 4*(b^4*c + a*b^2*c^2 - 20*a^2*c^3 + 45*(b^2*c^3 - 4*a*c^4)*d^4 + 27*(b^3*c^2 - 4*a*b*c^3)*d^2)*e^2*f*x^2 + 8*(9*(b^2*c^3 - 4*a*c^4)*d^5 + 9*(b^3*c^2 - 4*a*b*c^3)*d^3 + (b^4*c + a*b^2*c^2 - 20*a^2*c^3)*d)*e*f*x + 12*(c^4*e^8*f*x^8 + 8*c^4*d*e^7*f*x^7 + 2*(14*c^4*d^2 + b*c^3)*e^6*f*x^6 + 4*(14*c^4*d^3 + 3*b*c^3*d)*e^5*f*x^5 + (70*c^4*d^4 + 30*b*c^3*d^2 + b^2*c^2 + 2*a*c^3)*e^4*f*x^4 + 4*(14*c^4*d^5 + 10*b*c^3*d^3 + (b^2*c^2 + 2*a*c^3)*d)*e^3*f*x^3 + 2*(14*c^4*d^6 + 15*b*c^3*d^4 + a*b*c^2 + 3*(b^2*c^2 + 2*a*c^3)*d^2)*e^2*f*x^2 + 4*(2*c^4*d^7 + 3*b*c^3*d^5 + a*b*c^2*d + (b^2*c^2 + 2*a*c^3)*d^3)*e*f*x + (c^4*d^8 + 2*b*c^3*d^6 + 2*a*b*c^2*d^2 + (b^2*c^2 + 2*a*c^3)*d^4 + a^2*c^2)*f)*sqrt(b^2 - 4*a*c)*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c - (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)) + (12*(b^2*c^3 - 4*a*c^4)*d^6 - b^5 + 14*a*b^3*c - 40*a^2*b*c^2 + 18*(b^3*c^2 - 4*a*b*c^3)*d^4 + 4*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*d^2)*f)/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^9*x^8 + 8*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d*e^8*x^7 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2)*e^7*x^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^3 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d)*e^6*x^5 + (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 + 70*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 + 30*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2)*e^5*x^4 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^5 + 10*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3 + (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)*d)*e^4*x^3 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^6 + 15*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^4 + 3*(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)*d^2)*e^3*x^2 + 4*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^7 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^5 + (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)*d^3 + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d)*e^2*x + ((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^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)*d^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)*d^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2)*e), 1/4*(12*(b^2*c^3 - 4*a*c^4)*e^6*f*x^6 + 72*(b^2*c^3 - 4*a*c^4)*d*e^5*f*x^5 + 18*(b^3*c^2 - 4*a*b*c^3 + 10*(b^2*c^3 - 4*a*c^4)*d^2)*e^4*f*x^4 + 24*(10*(b^2*c^3 - 4*a*c^4)*d^3 + 3*(b^3*c^2 - 4*a*b*c^3)*d)*e^3*f*x^3 + 4*(b^4*c + a*b^2*c^2 - 20*a^2*c^3 + 45*(b^2*c^3 - 4*a*c^4)*d^4 + 27*(b^3*c^2 - 4*a*b*c^3)*d^2)*e^2*f*x^2 + 8*(9*(b^2*c^3 - 4*a*c^4)*d^5 + 9*(b^3*c^2 - 4*a*b*c^3)*d^3 + (b^4*c + a*b^2*c^2 - 20*a^2*c^3)*d)*e*f*x - 24*(c^4*e^8*f*x^8 + 8*c^4*d*e^7*f*x^7 + 2*(14*c^4*d^2 + b*c^3)*e^6*f*x^6 + 4*(14*c^4*d^3 + 3*b*c^3*d)*e^5*f*x^5 + (70*c^4*d^4 + 30*b*c^3*d^2 + b^2*c^2 + 2*a*c^3)*e^4*f*x^4 + 4*(14*c^4*d^5 + 10*b*c^3*d^3 + (b^2*c^2 + 2*a*c^3)*d)*e^3*f*x^3 + 2*(14*c^4*d^6 + 15*b*c^3*d^4 + a*b*c^2 + 3*(b^2*c^2 + 2*a*c^3)*d^2)*e^2*f*x^2 + 4*(2*c^4*d^7 + 3*b*c^3*d^5 + a*b*c^2*d + (b^2*c^2 + 2*a*c^3)*d^3)*e*f*x + (c^4*d^8 + 2*b*c^3*d^6 + 2*a*b*c^2*d^2 + (b^2*c^2 + 2*a*c^3)*d^4 + a^2*c^2)*f)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) + (12*(b^2*c^3 - 4*a*c^4)*d^6 - b^5 + 14*a*b^3*c - 40*a^2*b*c^2 + 18*(b^3*c^2 - 4*a*b*c^3)*d^4 + 4*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*d^2)*f)/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^9*x^8 + 8*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d*e^8*x^7 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2)*e^7*x^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^3 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d)*e^6*x^5 + (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 + 70*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 + 30*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2)*e^5*x^4 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^5 + 10*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3 + (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)*d)*e^4*x^3 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^6 + 15*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^4 + 3*(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)*d^2)*e^3*x^2 + 4*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^7 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^5 + (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)*d^3 + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d)*e^2*x + ((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^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)*d^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)*d^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2)*e)]","B",0
658,1,9926,0,7.393731," ","integrate(1/(e*f*x+d*f)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} e^{6} x^{6} + 12 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d e^{5} x^{5} + {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4} + 30 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + 3 \, a^{2} b^{6} - 33 \, a^{3} b^{4} c + 108 \, a^{4} b^{2} c^{2} - 96 \, a^{5} c^{3} + 2 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d^{6} + 4 \, {\left(10 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d^{3} + {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} d\right)} e^{3} x^{3} + {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} d^{4} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 23 \, a^{3} b^{3} c^{2} + 4 \, a^{4} b c^{3} + 15 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d^{4} + 3 \, {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} d^{2}\right)} e^{2} x^{2} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 23 \, a^{3} b^{3} c^{2} + 4 \, a^{4} b c^{3}\right)} d^{2} + 4 \, {\left(3 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d^{5} + {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} d^{3} + {\left(a b^{7} - 10 \, a^{2} b^{5} c + 23 \, a^{3} b^{3} c^{2} + 4 \, a^{4} b c^{3}\right)} d\right)} e x + {\left({\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} e^{8} x^{8} + 8 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d e^{7} x^{7} + 2 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3} + 14 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{2}\right)} e^{6} x^{6} + 4 \, {\left(14 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{3} + 3 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d\right)} e^{5} x^{5} + {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{8} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3} + 70 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{4} + 30 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d^{2}\right)} e^{4} x^{4} + a^{2} b^{5} - 10 \, a^{3} b^{3} c + 30 \, a^{4} b c^{2} + 2 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d^{6} + 4 \, {\left(14 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{5} + 10 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d^{3} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} d\right)} e^{3} x^{3} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} d^{4} + 2 \, {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2} + 14 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{6} + 15 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d^{4} + 3 \, {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} d^{2}\right)} e^{2} x^{2} + 2 \, {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2}\right)} d^{2} + 4 \, {\left(2 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{7} + 3 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d^{5} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} d^{3} + {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2}\right)} d\right)} e x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c + {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right) - {\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)} e^{8} x^{8} + 8 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d e^{7} x^{7} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2}\right)} e^{6} x^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{3} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d\right)} e^{5} x^{5} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{8} + {\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} + 70 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} + 30 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + 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)} d^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{5} + 10 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} + {\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)} d\right)} e^{3} x^{3} + {\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)} d^{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} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{6} + 15 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{4} + 3 \, {\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)} d^{2}\right)} e^{2} x^{2} + 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)} d^{2} + 4 \, {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{7} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{5} + {\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)} d^{3} + {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d\right)} e x\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 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)} e^{8} x^{8} + 8 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d e^{7} x^{7} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2}\right)} e^{6} x^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{3} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d\right)} e^{5} x^{5} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{8} + {\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} + 70 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} + 30 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + 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)} d^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{5} + 10 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} + {\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)} d\right)} e^{3} x^{3} + {\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)} d^{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} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{6} + 15 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{4} + 3 \, {\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)} d^{2}\right)} e^{2} x^{2} + 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)} d^{2} + 4 \, {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{7} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{5} + {\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)} d^{3} + {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d\right)} e x\right)} \log\left(e x + d\right)}{4 \, {\left({\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)} e^{9} f x^{8} + 8 \, {\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)} d e^{8} f x^{7} + 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} + 14 \, {\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)} d^{2}\right)} e^{7} f x^{6} + 4 \, {\left(14 \, {\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)} d^{3} + 3 \, {\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)} d\right)} e^{6} f x^{5} + {\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} + 70 \, {\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)} d^{4} + 30 \, {\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)} d^{2}\right)} e^{5} f x^{4} + 4 \, {\left(14 \, {\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)} d^{5} + 10 \, {\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)} d^{3} + {\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)} d\right)} e^{4} f x^{3} + 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} + 14 \, {\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)} d^{6} + 15 \, {\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)} d^{4} + 3 \, {\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)} d^{2}\right)} e^{3} f x^{2} + 4 \, {\left(2 \, {\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)} d^{7} + 3 \, {\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)} d^{5} + {\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)} d^{3} + {\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)} d\right)} e^{2} f x + {\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)} d^{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)} d^{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)} d^{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)} d^{2}\right)} e f\right)}}, \frac{2 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} e^{6} x^{6} + 12 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d e^{5} x^{5} + {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4} + 30 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + 3 \, a^{2} b^{6} - 33 \, a^{3} b^{4} c + 108 \, a^{4} b^{2} c^{2} - 96 \, a^{5} c^{3} + 2 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d^{6} + 4 \, {\left(10 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d^{3} + {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} d\right)} e^{3} x^{3} + {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} d^{4} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 23 \, a^{3} b^{3} c^{2} + 4 \, a^{4} b c^{3} + 15 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d^{4} + 3 \, {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} d^{2}\right)} e^{2} x^{2} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 23 \, a^{3} b^{3} c^{2} + 4 \, a^{4} b c^{3}\right)} d^{2} + 4 \, {\left(3 \, {\left(a b^{5} c^{2} - 11 \, a^{2} b^{3} c^{3} + 28 \, a^{3} b c^{4}\right)} d^{5} + {\left(4 \, a b^{6} c - 45 \, a^{2} b^{4} c^{2} + 132 \, a^{3} b^{2} c^{3} - 64 \, a^{4} c^{4}\right)} d^{3} + {\left(a b^{7} - 10 \, a^{2} b^{5} c + 23 \, a^{3} b^{3} c^{2} + 4 \, a^{4} b c^{3}\right)} d\right)} e x + 2 \, {\left({\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} e^{8} x^{8} + 8 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d e^{7} x^{7} + 2 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3} + 14 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{2}\right)} e^{6} x^{6} + 4 \, {\left(14 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{3} + 3 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d\right)} e^{5} x^{5} + {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{8} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3} + 70 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{4} + 30 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d^{2}\right)} e^{4} x^{4} + a^{2} b^{5} - 10 \, a^{3} b^{3} c + 30 \, a^{4} b c^{2} + 2 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d^{6} + 4 \, {\left(14 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{5} + 10 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d^{3} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} d\right)} e^{3} x^{3} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} d^{4} + 2 \, {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2} + 14 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{6} + 15 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d^{4} + 3 \, {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} d^{2}\right)} e^{2} x^{2} + 2 \, {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2}\right)} d^{2} + 4 \, {\left(2 \, {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} d^{7} + 3 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} d^{5} + {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} d^{3} + {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2}\right)} d\right)} e x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\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)} e^{8} x^{8} + 8 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d e^{7} x^{7} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2}\right)} e^{6} x^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{3} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d\right)} e^{5} x^{5} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{8} + {\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} + 70 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} + 30 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + 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)} d^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{5} + 10 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} + {\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)} d\right)} e^{3} x^{3} + {\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)} d^{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} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{6} + 15 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{4} + 3 \, {\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)} d^{2}\right)} e^{2} x^{2} + 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)} d^{2} + 4 \, {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{7} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{5} + {\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)} d^{3} + {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d\right)} e x\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 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)} e^{8} x^{8} + 8 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d e^{7} x^{7} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2}\right)} e^{6} x^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{3} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d\right)} e^{5} x^{5} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{8} + {\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} + 70 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{4} + 30 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + 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)} d^{6} + 4 \, {\left(14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{5} + 10 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} + {\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)} d\right)} e^{3} x^{3} + {\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)} d^{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} + 14 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{6} + 15 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{4} + 3 \, {\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)} d^{2}\right)} e^{2} x^{2} + 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)} d^{2} + 4 \, {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{7} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{5} + {\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)} d^{3} + {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d\right)} e x\right)} \log\left(e x + d\right)}{4 \, {\left({\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)} e^{9} f x^{8} + 8 \, {\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)} d e^{8} f x^{7} + 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} + 14 \, {\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)} d^{2}\right)} e^{7} f x^{6} + 4 \, {\left(14 \, {\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)} d^{3} + 3 \, {\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)} d\right)} e^{6} f x^{5} + {\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} + 70 \, {\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)} d^{4} + 30 \, {\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)} d^{2}\right)} e^{5} f x^{4} + 4 \, {\left(14 \, {\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)} d^{5} + 10 \, {\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)} d^{3} + {\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)} d\right)} e^{4} f x^{3} + 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} + 14 \, {\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)} d^{6} + 15 \, {\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)} d^{4} + 3 \, {\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)} d^{2}\right)} e^{3} f x^{2} + 4 \, {\left(2 \, {\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)} d^{7} + 3 \, {\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)} d^{5} + {\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)} d^{3} + {\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)} d\right)} e^{2} f x + {\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)} d^{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)} d^{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)} d^{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)} d^{2}\right)} e f\right)}}\right]"," ",0,"[1/4*(2*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*e^6*x^6 + 12*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d*e^5*x^5 + (4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4 + 30*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d^2)*e^4*x^4 + 3*a^2*b^6 - 33*a^3*b^4*c + 108*a^4*b^2*c^2 - 96*a^5*c^3 + 2*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d^6 + 4*(10*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d^3 + (4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4)*d)*e^3*x^3 + (4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4)*d^4 + 2*(a*b^7 - 10*a^2*b^5*c + 23*a^3*b^3*c^2 + 4*a^4*b*c^3 + 15*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d^4 + 3*(4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4)*d^2)*e^2*x^2 + 2*(a*b^7 - 10*a^2*b^5*c + 23*a^3*b^3*c^2 + 4*a^4*b*c^3)*d^2 + 4*(3*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d^5 + (4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4)*d^3 + (a*b^7 - 10*a^2*b^5*c + 23*a^3*b^3*c^2 + 4*a^4*b*c^3)*d)*e*x + ((b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*e^8*x^8 + 8*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d*e^7*x^7 + 2*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3 + 14*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^2)*e^6*x^6 + 4*(14*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^3 + 3*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d)*e^5*x^5 + (b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^8 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3 + 70*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^4 + 30*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d^2)*e^4*x^4 + a^2*b^5 - 10*a^3*b^3*c + 30*a^4*b*c^2 + 2*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d^6 + 4*(14*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^5 + 10*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d^3 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*d)*e^3*x^3 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*d^4 + 2*(a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2 + 14*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^6 + 15*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d^4 + 3*(b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*d^2)*e^2*x^2 + 2*(a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2)*d^2 + 4*(2*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^7 + 3*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d^5 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*d^3 + (a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2)*d)*e*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c + (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)) - ((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^8*x^8 + 8*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d*e^7*x^7 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2)*e^6*x^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^3 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d)*e^5*x^5 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^8 + (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 + 70*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 + 30*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2)*e^4*x^4 + 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)*d^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^5 + 10*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3 + (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)*d)*e^3*x^3 + (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)*d^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^6 + 15*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^4 + 3*(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)*d^2)*e^2*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2 + 4*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^7 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^5 + (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)*d^3 + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d)*e*x)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 4*((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^8*x^8 + 8*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d*e^7*x^7 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2)*e^6*x^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^3 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d)*e^5*x^5 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^8 + (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 + 70*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 + 30*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2)*e^4*x^4 + 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)*d^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^5 + 10*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3 + (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)*d)*e^3*x^3 + (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)*d^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^6 + 15*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^4 + 3*(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)*d^2)*e^2*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2 + 4*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^7 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^5 + (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)*d^3 + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d)*e*x)*log(e*x + d))/((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)*e^9*f*x^8 + 8*(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)*d*e^8*f*x^7 + 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 + 14*(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)*d^2)*e^7*f*x^6 + 4*(14*(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)*d^3 + 3*(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)*d)*e^6*f*x^5 + (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 + 70*(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)*d^4 + 30*(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)*d^2)*e^5*f*x^4 + 4*(14*(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)*d^5 + 10*(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)*d^3 + (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)*d)*e^4*f*x^3 + 2*(a^4*b^7 - 12*a^5*b^5*c + 48*a^6*b^3*c^2 - 64*a^7*b*c^3 + 14*(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)*d^6 + 15*(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)*d^4 + 3*(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)*d^2)*e^3*f*x^2 + 4*(2*(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)*d^7 + 3*(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)*d^5 + (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)*d^3 + (a^4*b^7 - 12*a^5*b^5*c + 48*a^6*b^3*c^2 - 64*a^7*b*c^3)*d)*e^2*f*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)*d^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)*d^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)*d^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)*d^2)*e*f), 1/4*(2*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*e^6*x^6 + 12*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d*e^5*x^5 + (4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4 + 30*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d^2)*e^4*x^4 + 3*a^2*b^6 - 33*a^3*b^4*c + 108*a^4*b^2*c^2 - 96*a^5*c^3 + 2*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d^6 + 4*(10*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d^3 + (4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4)*d)*e^3*x^3 + (4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4)*d^4 + 2*(a*b^7 - 10*a^2*b^5*c + 23*a^3*b^3*c^2 + 4*a^4*b*c^3 + 15*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d^4 + 3*(4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4)*d^2)*e^2*x^2 + 2*(a*b^7 - 10*a^2*b^5*c + 23*a^3*b^3*c^2 + 4*a^4*b*c^3)*d^2 + 4*(3*(a*b^5*c^2 - 11*a^2*b^3*c^3 + 28*a^3*b*c^4)*d^5 + (4*a*b^6*c - 45*a^2*b^4*c^2 + 132*a^3*b^2*c^3 - 64*a^4*c^4)*d^3 + (a*b^7 - 10*a^2*b^5*c + 23*a^3*b^3*c^2 + 4*a^4*b*c^3)*d)*e*x + 2*((b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*e^8*x^8 + 8*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d*e^7*x^7 + 2*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3 + 14*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^2)*e^6*x^6 + 4*(14*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^3 + 3*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d)*e^5*x^5 + (b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^8 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3 + 70*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^4 + 30*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d^2)*e^4*x^4 + a^2*b^5 - 10*a^3*b^3*c + 30*a^4*b*c^2 + 2*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d^6 + 4*(14*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^5 + 10*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d^3 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*d)*e^3*x^3 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*d^4 + 2*(a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2 + 14*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^6 + 15*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d^4 + 3*(b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*d^2)*e^2*x^2 + 2*(a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2)*d^2 + 4*(2*(b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*d^7 + 3*(b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*d^5 + (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*d^3 + (a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2)*d)*e*x)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - ((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^8*x^8 + 8*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d*e^7*x^7 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2)*e^6*x^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^3 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d)*e^5*x^5 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^8 + (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 + 70*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 + 30*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2)*e^4*x^4 + 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)*d^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^5 + 10*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3 + (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)*d)*e^3*x^3 + (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)*d^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^6 + 15*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^4 + 3*(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)*d^2)*e^2*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2 + 4*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^7 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^5 + (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)*d^3 + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d)*e*x)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 4*((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^8*x^8 + 8*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d*e^7*x^7 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2)*e^6*x^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^3 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d)*e^5*x^5 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^8 + (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 + 70*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 + 30*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2)*e^4*x^4 + 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)*d^6 + 4*(14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^5 + 10*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3 + (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)*d)*e^3*x^3 + (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)*d^4 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3 + 14*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^6 + 15*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^4 + 3*(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)*d^2)*e^2*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2 + 4*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^7 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^5 + (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)*d^3 + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d)*e*x)*log(e*x + d))/((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)*e^9*f*x^8 + 8*(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)*d*e^8*f*x^7 + 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 + 14*(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)*d^2)*e^7*f*x^6 + 4*(14*(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)*d^3 + 3*(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)*d)*e^6*f*x^5 + (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 + 70*(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)*d^4 + 30*(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)*d^2)*e^5*f*x^4 + 4*(14*(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)*d^5 + 10*(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)*d^3 + (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)*d)*e^4*f*x^3 + 2*(a^4*b^7 - 12*a^5*b^5*c + 48*a^6*b^3*c^2 - 64*a^7*b*c^3 + 14*(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)*d^6 + 15*(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)*d^4 + 3*(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)*d^2)*e^3*f*x^2 + 4*(2*(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)*d^7 + 3*(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)*d^5 + (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)*d^3 + (a^4*b^7 - 12*a^5*b^5*c + 48*a^6*b^3*c^2 - 64*a^7*b*c^3)*d)*e^2*f*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)*d^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)*d^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)*d^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)*d^2)*e*f)]","B",0
659,1,10518,0,3.605061," ","integrate(1/(e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""fricas"")","-\frac{6 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} e^{8} x^{8} + 48 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} d e^{7} x^{7} + 2 \, {\left(30 \, b^{5} c - 227 \, a b^{3} c^{2} + 392 \, a^{2} b c^{3} + 84 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} d^{2}\right)} e^{6} x^{6} + 12 \, {\left(28 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} d^{3} + {\left(30 \, b^{5} c - 227 \, a b^{3} c^{2} + 392 \, a^{2} b c^{3}\right)} d\right)} e^{5} x^{5} + 6 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} d^{8} + 2 \, {\left(15 \, b^{6} - 91 \, a b^{4} c + 25 \, a^{2} b^{2} c^{2} + 324 \, a^{3} c^{3} + 210 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} d^{4} + 15 \, {\left(30 \, b^{5} c - 227 \, a b^{3} c^{2} + 392 \, a^{2} b c^{3}\right)} d^{2}\right)} e^{4} x^{4} + 2 \, {\left(30 \, b^{5} c - 227 \, a b^{3} c^{2} + 392 \, a^{2} b c^{3}\right)} d^{6} + 8 \, {\left(42 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} d^{5} + 5 \, {\left(30 \, b^{5} c - 227 \, a b^{3} c^{2} + 392 \, a^{2} b c^{3}\right)} d^{3} + {\left(15 \, b^{6} - 91 \, a b^{4} c + 25 \, a^{2} b^{2} c^{2} + 324 \, a^{3} c^{3}\right)} d\right)} e^{3} x^{3} + 16 \, a^{2} b^{4} - 128 \, a^{3} b^{2} c + 256 \, a^{4} c^{2} + 2 \, {\left(15 \, b^{6} - 91 \, a b^{4} c + 25 \, a^{2} b^{2} c^{2} + 324 \, a^{3} c^{3}\right)} d^{4} + 2 \, {\left(84 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} d^{6} + 25 \, a b^{5} - 194 \, a^{2} b^{3} c + 364 \, a^{3} b c^{2} + 15 \, {\left(30 \, b^{5} c - 227 \, a b^{3} c^{2} + 392 \, a^{2} b c^{3}\right)} d^{4} + 6 \, {\left(15 \, b^{6} - 91 \, a b^{4} c + 25 \, a^{2} b^{2} c^{2} + 324 \, a^{3} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + 2 \, {\left(25 \, a b^{5} - 194 \, a^{2} b^{3} c + 364 \, a^{3} b c^{2}\right)} d^{2} + 4 \, {\left(12 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} d^{7} + 3 \, {\left(30 \, b^{5} c - 227 \, a b^{3} c^{2} + 392 \, a^{2} b c^{3}\right)} d^{5} + 2 \, {\left(15 \, b^{6} - 91 \, a b^{4} c + 25 \, a^{2} b^{2} c^{2} + 324 \, a^{3} c^{3}\right)} d^{3} + {\left(25 \, a b^{5} - 194 \, a^{2} b^{3} c + 364 \, a^{3} b c^{2}\right)} d\right)} e x - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} e^{10} f^{2} x^{9} + 9 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d e^{9} f^{2} x^{8} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3} + 18 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{2}\right)} e^{8} f^{2} x^{7} + 14 \, {\left(6 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{3} + {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d\right)} e^{7} f^{2} x^{6} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3} + 126 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{4} + 42 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{2}\right)} e^{6} f^{2} x^{5} + {\left(126 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{5} + 70 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{3} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d\right)} e^{5} f^{2} x^{4} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2} + 42 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{6} + 35 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{4} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{2}\right)} e^{4} f^{2} x^{3} + 2 \, {\left(18 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{7} + 21 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{5} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{3} + 3 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d\right)} e^{3} f^{2} x^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2} + 9 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{8} + 14 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{6} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{4} + 6 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d^{2}\right)} e^{2} f^{2} x + {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{9} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{7} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{5} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d^{3} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} d\right)} e f^{2}\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} + {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} f^{4} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4} f^{8}}}}{{\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} f^{4}}} \log\left(-27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} e x - 27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} d + \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left({\left(5 \, a^{7} b^{16} - 152 \, a^{8} b^{14} c + 2006 \, a^{9} b^{12} c^{2} - 14960 \, a^{10} b^{10} c^{3} + 68640 \, a^{11} b^{8} c^{4} - 197120 \, a^{12} b^{6} c^{5} + 342528 \, a^{13} b^{4} c^{6} - 323584 \, a^{14} b^{2} c^{7} + 122880 \, a^{15} c^{8}\right)} e^{3} f^{6} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4} f^{8}}} - {\left(125 \, b^{17} - 3775 \, a b^{15} c + 49360 \, a^{2} b^{13} c^{2} - 362733 \, a^{3} b^{11} c^{3} + 1623534 \, a^{4} b^{9} c^{4} - 4463140 \, a^{5} b^{7} c^{5} + 7146736 \, a^{6} b^{5} c^{6} - 5684672 \, a^{7} b^{3} c^{7} + 1324800 \, a^{8} b c^{8}\right)} e f^{2}\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} + {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} f^{4} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4} f^{8}}}}{{\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} f^{4}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} e^{10} f^{2} x^{9} + 9 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d e^{9} f^{2} x^{8} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3} + 18 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{2}\right)} e^{8} f^{2} x^{7} + 14 \, {\left(6 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{3} + {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d\right)} e^{7} f^{2} x^{6} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3} + 126 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{4} + 42 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{2}\right)} e^{6} f^{2} x^{5} + {\left(126 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{5} + 70 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{3} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d\right)} e^{5} f^{2} x^{4} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2} + 42 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{6} + 35 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{4} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{2}\right)} e^{4} f^{2} x^{3} + 2 \, {\left(18 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{7} + 21 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{5} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{3} + 3 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d\right)} e^{3} f^{2} x^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2} + 9 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{8} + 14 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{6} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{4} + 6 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d^{2}\right)} e^{2} f^{2} x + {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{9} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{7} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{5} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d^{3} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} d\right)} e f^{2}\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} + {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} f^{4} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4} f^{8}}}}{{\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} f^{4}}} \log\left(-27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} e x - 27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} d - \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left({\left(5 \, a^{7} b^{16} - 152 \, a^{8} b^{14} c + 2006 \, a^{9} b^{12} c^{2} - 14960 \, a^{10} b^{10} c^{3} + 68640 \, a^{11} b^{8} c^{4} - 197120 \, a^{12} b^{6} c^{5} + 342528 \, a^{13} b^{4} c^{6} - 323584 \, a^{14} b^{2} c^{7} + 122880 \, a^{15} c^{8}\right)} e^{3} f^{6} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4} f^{8}}} - {\left(125 \, b^{17} - 3775 \, a b^{15} c + 49360 \, a^{2} b^{13} c^{2} - 362733 \, a^{3} b^{11} c^{3} + 1623534 \, a^{4} b^{9} c^{4} - 4463140 \, a^{5} b^{7} c^{5} + 7146736 \, a^{6} b^{5} c^{6} - 5684672 \, a^{7} b^{3} c^{7} + 1324800 \, a^{8} b c^{8}\right)} e f^{2}\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} + {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} f^{4} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4} f^{8}}}}{{\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} f^{4}}}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} e^{10} f^{2} x^{9} + 9 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d e^{9} f^{2} x^{8} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3} + 18 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{2}\right)} e^{8} f^{2} x^{7} + 14 \, {\left(6 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{3} + {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d\right)} e^{7} f^{2} x^{6} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3} + 126 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{4} + 42 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{2}\right)} e^{6} f^{2} x^{5} + {\left(126 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{5} + 70 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{3} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d\right)} e^{5} f^{2} x^{4} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2} + 42 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{6} + 35 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{4} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{2}\right)} e^{4} f^{2} x^{3} + 2 \, {\left(18 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{7} + 21 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{5} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{3} + 3 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d\right)} e^{3} f^{2} x^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2} + 9 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{8} + 14 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{6} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{4} + 6 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d^{2}\right)} e^{2} f^{2} x + {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{9} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{7} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{5} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d^{3} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} d\right)} e f^{2}\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} - {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} f^{4} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4} f^{8}}}}{{\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} f^{4}}} \log\left(-27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} e x - 27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} d + \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left({\left(5 \, a^{7} b^{16} - 152 \, a^{8} b^{14} c + 2006 \, a^{9} b^{12} c^{2} - 14960 \, a^{10} b^{10} c^{3} + 68640 \, a^{11} b^{8} c^{4} - 197120 \, a^{12} b^{6} c^{5} + 342528 \, a^{13} b^{4} c^{6} - 323584 \, a^{14} b^{2} c^{7} + 122880 \, a^{15} c^{8}\right)} e^{3} f^{6} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4} f^{8}}} + {\left(125 \, b^{17} - 3775 \, a b^{15} c + 49360 \, a^{2} b^{13} c^{2} - 362733 \, a^{3} b^{11} c^{3} + 1623534 \, a^{4} b^{9} c^{4} - 4463140 \, a^{5} b^{7} c^{5} + 7146736 \, a^{6} b^{5} c^{6} - 5684672 \, a^{7} b^{3} c^{7} + 1324800 \, a^{8} b c^{8}\right)} e f^{2}\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} - {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} f^{4} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4} f^{8}}}}{{\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} f^{4}}}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} e^{10} f^{2} x^{9} + 9 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d e^{9} f^{2} x^{8} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3} + 18 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{2}\right)} e^{8} f^{2} x^{7} + 14 \, {\left(6 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{3} + {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d\right)} e^{7} f^{2} x^{6} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3} + 126 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{4} + 42 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{2}\right)} e^{6} f^{2} x^{5} + {\left(126 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{5} + 70 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{3} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d\right)} e^{5} f^{2} x^{4} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2} + 42 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{6} + 35 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{4} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{2}\right)} e^{4} f^{2} x^{3} + 2 \, {\left(18 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{7} + 21 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{5} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{3} + 3 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d\right)} e^{3} f^{2} x^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2} + 9 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{8} + 14 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{6} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{4} + 6 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d^{2}\right)} e^{2} f^{2} x + {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{9} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{7} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{5} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d^{3} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} d\right)} e f^{2}\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} - {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} f^{4} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4} f^{8}}}}{{\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} f^{4}}} \log\left(-27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} e x - 27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} d - \frac{27}{2} \, \sqrt{\frac{1}{2}} {\left({\left(5 \, a^{7} b^{16} - 152 \, a^{8} b^{14} c + 2006 \, a^{9} b^{12} c^{2} - 14960 \, a^{10} b^{10} c^{3} + 68640 \, a^{11} b^{8} c^{4} - 197120 \, a^{12} b^{6} c^{5} + 342528 \, a^{13} b^{4} c^{6} - 323584 \, a^{14} b^{2} c^{7} + 122880 \, a^{15} c^{8}\right)} e^{3} f^{6} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4} f^{8}}} + {\left(125 \, b^{17} - 3775 \, a b^{15} c + 49360 \, a^{2} b^{13} c^{2} - 362733 \, a^{3} b^{11} c^{3} + 1623534 \, a^{4} b^{9} c^{4} - 4463140 \, a^{5} b^{7} c^{5} + 7146736 \, a^{6} b^{5} c^{6} - 5684672 \, a^{7} b^{3} c^{7} + 1324800 \, a^{8} b c^{8}\right)} e f^{2}\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} - {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} f^{4} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{{\left(a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}\right)} e^{4} f^{8}}}}{{\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} e^{2} f^{4}}}\right)}{16 \, {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} e^{10} f^{2} x^{9} + 9 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d e^{9} f^{2} x^{8} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3} + 18 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{2}\right)} e^{8} f^{2} x^{7} + 14 \, {\left(6 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{3} + {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d\right)} e^{7} f^{2} x^{6} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3} + 126 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{4} + 42 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{2}\right)} e^{6} f^{2} x^{5} + {\left(126 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{5} + 70 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{3} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d\right)} e^{5} f^{2} x^{4} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2} + 42 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{6} + 35 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{4} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{2}\right)} e^{4} f^{2} x^{3} + 2 \, {\left(18 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{7} + 21 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{5} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{3} + 3 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d\right)} e^{3} f^{2} x^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2} + 9 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{8} + 14 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{6} + 5 \, {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{4} + 6 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d^{2}\right)} e^{2} f^{2} x + {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{9} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{7} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} d^{5} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d^{3} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} d\right)} e f^{2}\right)}}"," ",0,"-1/16*(6*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*e^8*x^8 + 48*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d*e^7*x^7 + 2*(30*b^5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3 + 84*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^2)*e^6*x^6 + 12*(28*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^3 + (30*b^5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3)*d)*e^5*x^5 + 6*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^8 + 2*(15*b^6 - 91*a*b^4*c + 25*a^2*b^2*c^2 + 324*a^3*c^3 + 210*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^4 + 15*(30*b^5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3)*d^2)*e^4*x^4 + 2*(30*b^5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3)*d^6 + 8*(42*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^5 + 5*(30*b^5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3)*d^3 + (15*b^6 - 91*a*b^4*c + 25*a^2*b^2*c^2 + 324*a^3*c^3)*d)*e^3*x^3 + 16*a^2*b^4 - 128*a^3*b^2*c + 256*a^4*c^2 + 2*(15*b^6 - 91*a*b^4*c + 25*a^2*b^2*c^2 + 324*a^3*c^3)*d^4 + 2*(84*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^6 + 25*a*b^5 - 194*a^2*b^3*c + 364*a^3*b*c^2 + 15*(30*b^5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3)*d^4 + 6*(15*b^6 - 91*a*b^4*c + 25*a^2*b^2*c^2 + 324*a^3*c^3)*d^2)*e^2*x^2 + 2*(25*a*b^5 - 194*a^2*b^3*c + 364*a^3*b*c^2)*d^2 + 4*(12*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*d^7 + 3*(30*b^5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3)*d^5 + 2*(15*b^6 - 91*a*b^4*c + 25*a^2*b^2*c^2 + 324*a^3*c^3)*d^3 + (25*a*b^5 - 194*a^2*b^3*c + 364*a^3*b*c^2)*d)*e*x - 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^10*f^2*x^9 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d*e^9*f^2*x^8 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3 + 18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^2)*e^8*f^2*x^7 + 14*(6*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^3 + (a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d)*e^7*f^2*x^6 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3 + 126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^4 + 42*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^2)*e^6*f^2*x^5 + (126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^5 + 70*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d)*e^5*f^2*x^4 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2 + 42*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^6 + 35*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^4 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^2)*e^4*f^2*x^3 + 2*(18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^7 + 21*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^5 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^3 + 3*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d)*e^3*f^2*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^8 + 14*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^6 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^4 + 6*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^2)*e^2*f^2*x + ((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^9 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^7 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^5 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*d)*e*f^2)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8)))/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4))*log(-27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*e*x - 27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*d + 27/2*sqrt(1/2)*((5*a^7*b^16 - 152*a^8*b^14*c + 2006*a^9*b^12*c^2 - 14960*a^10*b^10*c^3 + 68640*a^11*b^8*c^4 - 197120*a^12*b^6*c^5 + 342528*a^13*b^4*c^6 - 323584*a^14*b^2*c^7 + 122880*a^15*c^8)*e^3*f^6*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8)) - (125*b^17 - 3775*a*b^15*c + 49360*a^2*b^13*c^2 - 362733*a^3*b^11*c^3 + 1623534*a^4*b^9*c^4 - 4463140*a^5*b^7*c^5 + 7146736*a^6*b^5*c^6 - 5684672*a^7*b^3*c^7 + 1324800*a^8*b*c^8)*e*f^2)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8)))/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4))) + 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^10*f^2*x^9 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d*e^9*f^2*x^8 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3 + 18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^2)*e^8*f^2*x^7 + 14*(6*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^3 + (a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d)*e^7*f^2*x^6 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3 + 126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^4 + 42*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^2)*e^6*f^2*x^5 + (126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^5 + 70*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d)*e^5*f^2*x^4 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2 + 42*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^6 + 35*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^4 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^2)*e^4*f^2*x^3 + 2*(18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^7 + 21*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^5 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^3 + 3*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d)*e^3*f^2*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^8 + 14*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^6 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^4 + 6*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^2)*e^2*f^2*x + ((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^9 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^7 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^5 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*d)*e*f^2)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8)))/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4))*log(-27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*e*x - 27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*d - 27/2*sqrt(1/2)*((5*a^7*b^16 - 152*a^8*b^14*c + 2006*a^9*b^12*c^2 - 14960*a^10*b^10*c^3 + 68640*a^11*b^8*c^4 - 197120*a^12*b^6*c^5 + 342528*a^13*b^4*c^6 - 323584*a^14*b^2*c^7 + 122880*a^15*c^8)*e^3*f^6*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8)) - (125*b^17 - 3775*a*b^15*c + 49360*a^2*b^13*c^2 - 362733*a^3*b^11*c^3 + 1623534*a^4*b^9*c^4 - 4463140*a^5*b^7*c^5 + 7146736*a^6*b^5*c^6 - 5684672*a^7*b^3*c^7 + 1324800*a^8*b*c^8)*e*f^2)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8)))/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4))) + 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^10*f^2*x^9 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d*e^9*f^2*x^8 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3 + 18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^2)*e^8*f^2*x^7 + 14*(6*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^3 + (a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d)*e^7*f^2*x^6 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3 + 126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^4 + 42*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^2)*e^6*f^2*x^5 + (126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^5 + 70*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d)*e^5*f^2*x^4 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2 + 42*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^6 + 35*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^4 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^2)*e^4*f^2*x^3 + 2*(18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^7 + 21*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^5 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^3 + 3*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d)*e^3*f^2*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^8 + 14*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^6 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^4 + 6*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^2)*e^2*f^2*x + ((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^9 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^7 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^5 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*d)*e*f^2)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8)))/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4))*log(-27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*e*x - 27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*d + 27/2*sqrt(1/2)*((5*a^7*b^16 - 152*a^8*b^14*c + 2006*a^9*b^12*c^2 - 14960*a^10*b^10*c^3 + 68640*a^11*b^8*c^4 - 197120*a^12*b^6*c^5 + 342528*a^13*b^4*c^6 - 323584*a^14*b^2*c^7 + 122880*a^15*c^8)*e^3*f^6*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8)) + (125*b^17 - 3775*a*b^15*c + 49360*a^2*b^13*c^2 - 362733*a^3*b^11*c^3 + 1623534*a^4*b^9*c^4 - 4463140*a^5*b^7*c^5 + 7146736*a^6*b^5*c^6 - 5684672*a^7*b^3*c^7 + 1324800*a^8*b*c^8)*e*f^2)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8)))/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4))) - 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^10*f^2*x^9 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d*e^9*f^2*x^8 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3 + 18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^2)*e^8*f^2*x^7 + 14*(6*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^3 + (a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d)*e^7*f^2*x^6 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3 + 126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^4 + 42*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^2)*e^6*f^2*x^5 + (126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^5 + 70*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d)*e^5*f^2*x^4 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2 + 42*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^6 + 35*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^4 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^2)*e^4*f^2*x^3 + 2*(18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^7 + 21*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^5 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^3 + 3*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d)*e^3*f^2*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^8 + 14*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^6 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^4 + 6*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^2)*e^2*f^2*x + ((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^9 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^7 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^5 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*d)*e*f^2)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8)))/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4))*log(-27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*e*x - 27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*d - 27/2*sqrt(1/2)*((5*a^7*b^16 - 152*a^8*b^14*c + 2006*a^9*b^12*c^2 - 14960*a^10*b^10*c^3 + 68640*a^11*b^8*c^4 - 197120*a^12*b^6*c^5 + 342528*a^13*b^4*c^6 - 323584*a^14*b^2*c^7 + 122880*a^15*c^8)*e^3*f^6*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8)) + (125*b^17 - 3775*a*b^15*c + 49360*a^2*b^13*c^2 - 362733*a^3*b^11*c^3 + 1623534*a^4*b^9*c^4 - 4463140*a^5*b^7*c^5 + 7146736*a^6*b^5*c^6 - 5684672*a^7*b^3*c^7 + 1324800*a^8*b*c^8)*e*f^2)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/((a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)*e^4*f^8)))/((a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*e^2*f^4))))/((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^10*f^2*x^9 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d*e^9*f^2*x^8 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3 + 18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^2)*e^8*f^2*x^7 + 14*(6*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^3 + (a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d)*e^7*f^2*x^6 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3 + 126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^4 + 42*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^2)*e^6*f^2*x^5 + (126*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^5 + 70*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d)*e^5*f^2*x^4 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2 + 42*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^6 + 35*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^4 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^2)*e^4*f^2*x^3 + 2*(18*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^7 + 21*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^5 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^3 + 3*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d)*e^3*f^2*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2 + 9*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^8 + 14*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^6 + 5*(a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^4 + 6*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^2)*e^2*f^2*x + ((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^9 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^7 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*d^5 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d^3 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*d)*e*f^2)","B",0
660,1,15231,0,22.606726," ","integrate(1/(e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} e^{8} x^{8} + 48 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d e^{7} x^{7} + 3 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4} + 56 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{2}\right)} e^{6} x^{6} + 6 \, {\left(56 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{3} + 3 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d\right)} e^{5} x^{5} + 2 \, a^{3} b^{6} - 24 \, a^{4} b^{4} c + 96 \, a^{5} b^{2} c^{2} - 128 \, a^{6} c^{3} + 6 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{8} + {\left(6 \, a b^{8} - 60 \, a^{2} b^{6} c + 158 \, a^{3} b^{4} c^{2} + 44 \, a^{4} b^{2} c^{3} - 400 \, a^{5} c^{4} + 420 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{4} + 45 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + 3 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d^{6} + 4 \, {\left(84 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{5} + 15 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d^{3} + 2 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} d\right)} e^{3} x^{3} + 2 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} d^{4} + {\left(9 \, a^{2} b^{7} - 104 \, a^{3} b^{5} c + 394 \, a^{4} b^{3} c^{2} - 488 \, a^{5} b c^{3} + 168 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{6} + 45 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d^{4} + 12 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} d^{2}\right)} e^{2} x^{2} + {\left(9 \, a^{2} b^{7} - 104 \, a^{3} b^{5} c + 394 \, a^{4} b^{3} c^{2} - 488 \, a^{5} b c^{3}\right)} d^{2} + 2 \, {\left(24 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{7} + 9 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d^{5} + 4 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} d^{3} + {\left(9 \, a^{2} b^{7} - 104 \, a^{3} b^{5} c + 394 \, a^{4} b^{3} c^{2} - 488 \, a^{5} b c^{3}\right)} d\right)} e x + 3 \, {\left({\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} e^{10} x^{10} + 10 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d e^{9} x^{9} + {\left(2 \, b^{7} c - 20 \, a b^{5} c^{2} + 60 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4} + 45 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{2}\right)} e^{8} x^{8} + 8 \, {\left(15 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{3} + 2 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d\right)} e^{7} x^{7} + {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4} + 210 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{4} + 56 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{6} x^{6} + {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{10} + 2 \, {\left(126 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{5} + 56 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{3} + 3 \, {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d\right)} e^{5} x^{5} + 2 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{8} + {\left(2 \, a b^{7} - 20 \, a^{2} b^{5} c + 60 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3} + 210 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{6} + 140 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{4} + 15 \, {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d^{6} + 4 \, {\left(30 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{7} + 28 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{5} + 5 \, {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d^{3} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} d\right)} e^{3} x^{3} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} d^{4} + {\left(45 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{8} + a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3} + 56 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{6} + 15 \, {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d^{4} + 12 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3}\right)} d^{2} + 2 \, {\left(5 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{9} + 8 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{7} + 3 \, {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d^{5} + 4 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} d^{3} + {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3}\right)} d\right)} e x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} e^{4} x^{4} + 8 \, c^{2} d e^{3} x^{3} + 2 \, c^{2} d^{4} + 2 \, {\left(6 \, c^{2} d^{2} + b c\right)} e^{2} x^{2} + 2 \, b c d^{2} + 4 \, {\left(2 \, c^{2} d^{3} + b c d\right)} e x + b^{2} - 2 \, a c + {\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a}\right) - 3 \, {\left({\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)} e^{10} x^{10} + 10 \, {\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)} d e^{9} x^{9} + {\left(2 \, b^{8} c - 24 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 128 \, a^{3} b^{2} c^{4} + 45 \, {\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)} d^{2}\right)} e^{8} x^{8} + 8 \, {\left(15 \, {\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)} d^{3} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d\right)} e^{7} x^{7} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4} + 210 \, {\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)} d^{4} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{2}\right)} e^{6} x^{6} + {\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)} d^{10} + 2 \, {\left(126 \, {\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)} d^{5} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{3} + 3 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d\right)} e^{5} x^{5} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{8} + {\left(2 \, a b^{8} - 24 \, a^{2} b^{6} c + 96 \, a^{3} b^{4} c^{2} - 128 \, a^{4} b^{2} c^{3} + 210 \, {\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)} d^{6} + 140 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{4} + 15 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{6} + 4 \, {\left(30 \, {\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)} d^{7} + 28 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{5} + 5 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d\right)} e^{3} x^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{4} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3} + 45 \, {\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)} d^{8} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{6} + 15 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{4} + 12 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} d^{2} + 2 \, {\left(5 \, {\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)} d^{9} + 8 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{7} + 3 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{5} + 4 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{3} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} d\right)} e x\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 12 \, {\left({\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)} e^{10} x^{10} + 10 \, {\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)} d e^{9} x^{9} + {\left(2 \, b^{8} c - 24 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 128 \, a^{3} b^{2} c^{4} + 45 \, {\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)} d^{2}\right)} e^{8} x^{8} + 8 \, {\left(15 \, {\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)} d^{3} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d\right)} e^{7} x^{7} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4} + 210 \, {\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)} d^{4} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{2}\right)} e^{6} x^{6} + {\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)} d^{10} + 2 \, {\left(126 \, {\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)} d^{5} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{3} + 3 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d\right)} e^{5} x^{5} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{8} + {\left(2 \, a b^{8} - 24 \, a^{2} b^{6} c + 96 \, a^{3} b^{4} c^{2} - 128 \, a^{4} b^{2} c^{3} + 210 \, {\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)} d^{6} + 140 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{4} + 15 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{6} + 4 \, {\left(30 \, {\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)} d^{7} + 28 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{5} + 5 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d\right)} e^{3} x^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{4} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3} + 45 \, {\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)} d^{8} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{6} + 15 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{4} + 12 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} d^{2} + 2 \, {\left(5 \, {\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)} d^{9} + 8 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{7} + 3 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{5} + 4 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{3} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} d\right)} e x\right)} \log\left(e x + d\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)} e^{11} f^{3} x^{10} + 10 \, {\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)} d e^{10} f^{3} x^{9} + {\left(2 \, a^{4} b^{7} c - 24 \, a^{5} b^{5} c^{2} + 96 \, a^{6} b^{3} c^{3} - 128 \, a^{7} b c^{4} + 45 \, {\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)} d^{2}\right)} e^{9} f^{3} x^{8} + 8 \, {\left(15 \, {\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)} d^{3} + 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)} d\right)} e^{8} f^{3} x^{7} + {\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} + 210 \, {\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)} d^{4} + 56 \, {\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)} d^{2}\right)} e^{7} f^{3} x^{6} + 2 \, {\left(126 \, {\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)} d^{5} + 56 \, {\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)} d^{3} + 3 \, {\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)} d\right)} e^{6} f^{3} x^{5} + {\left(2 \, a^{5} b^{7} - 24 \, a^{6} b^{5} c + 96 \, a^{7} b^{3} c^{2} - 128 \, a^{8} b c^{3} + 210 \, {\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)} d^{6} + 140 \, {\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)} d^{4} + 15 \, {\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)} d^{2}\right)} e^{5} f^{3} x^{4} + 4 \, {\left(30 \, {\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)} d^{7} + 28 \, {\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)} d^{5} + 5 \, {\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)} d^{3} + 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)} d\right)} e^{4} f^{3} x^{3} + {\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3} + 45 \, {\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)} d^{8} + 56 \, {\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)} d^{6} + 15 \, {\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)} d^{4} + 12 \, {\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)} d^{2}\right)} e^{3} f^{3} x^{2} + 2 \, {\left(5 \, {\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)} d^{9} + 8 \, {\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)} d^{7} + 3 \, {\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)} d^{5} + 4 \, {\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)} d^{3} + {\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} d\right)} e^{2} f^{3} x + {\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)} d^{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)} d^{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)} d^{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)} d^{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)} d^{2}\right)} e f^{3}\right)}}, -\frac{6 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} e^{8} x^{8} + 48 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d e^{7} x^{7} + 3 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4} + 56 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{2}\right)} e^{6} x^{6} + 6 \, {\left(56 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{3} + 3 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d\right)} e^{5} x^{5} + 2 \, a^{3} b^{6} - 24 \, a^{4} b^{4} c + 96 \, a^{5} b^{2} c^{2} - 128 \, a^{6} c^{3} + 6 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{8} + {\left(6 \, a b^{8} - 60 \, a^{2} b^{6} c + 158 \, a^{3} b^{4} c^{2} + 44 \, a^{4} b^{2} c^{3} - 400 \, a^{5} c^{4} + 420 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{4} + 45 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + 3 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d^{6} + 4 \, {\left(84 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{5} + 15 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d^{3} + 2 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} d\right)} e^{3} x^{3} + 2 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} d^{4} + {\left(9 \, a^{2} b^{7} - 104 \, a^{3} b^{5} c + 394 \, a^{4} b^{3} c^{2} - 488 \, a^{5} b c^{3} + 168 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{6} + 45 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d^{4} + 12 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} d^{2}\right)} e^{2} x^{2} + {\left(9 \, a^{2} b^{7} - 104 \, a^{3} b^{5} c + 394 \, a^{4} b^{3} c^{2} - 488 \, a^{5} b c^{3}\right)} d^{2} + 2 \, {\left(24 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} d^{7} + 9 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} d^{5} + 4 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} d^{3} + {\left(9 \, a^{2} b^{7} - 104 \, a^{3} b^{5} c + 394 \, a^{4} b^{3} c^{2} - 488 \, a^{5} b c^{3}\right)} d\right)} e x + 6 \, {\left({\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} e^{10} x^{10} + 10 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d e^{9} x^{9} + {\left(2 \, b^{7} c - 20 \, a b^{5} c^{2} + 60 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4} + 45 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{2}\right)} e^{8} x^{8} + 8 \, {\left(15 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{3} + 2 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d\right)} e^{7} x^{7} + {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4} + 210 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{4} + 56 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{2}\right)} e^{6} x^{6} + {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{10} + 2 \, {\left(126 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{5} + 56 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{3} + 3 \, {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d\right)} e^{5} x^{5} + 2 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{8} + {\left(2 \, a b^{7} - 20 \, a^{2} b^{5} c + 60 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3} + 210 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{6} + 140 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{4} + 15 \, {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d^{6} + 4 \, {\left(30 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{7} + 28 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{5} + 5 \, {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d^{3} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} d\right)} e^{3} x^{3} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} d^{4} + {\left(45 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{8} + a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3} + 56 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{6} + 15 \, {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d^{4} + 12 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3}\right)} d^{2} + 2 \, {\left(5 \, {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} d^{9} + 8 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{7} + 3 \, {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} d^{5} + 4 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} d^{3} + {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3}\right)} d\right)} e x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c e^{2} x^{2} + 4 \, c d e x + 2 \, c d^{2} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - 3 \, {\left({\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)} e^{10} x^{10} + 10 \, {\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)} d e^{9} x^{9} + {\left(2 \, b^{8} c - 24 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 128 \, a^{3} b^{2} c^{4} + 45 \, {\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)} d^{2}\right)} e^{8} x^{8} + 8 \, {\left(15 \, {\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)} d^{3} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d\right)} e^{7} x^{7} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4} + 210 \, {\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)} d^{4} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{2}\right)} e^{6} x^{6} + {\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)} d^{10} + 2 \, {\left(126 \, {\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)} d^{5} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{3} + 3 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d\right)} e^{5} x^{5} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{8} + {\left(2 \, a b^{8} - 24 \, a^{2} b^{6} c + 96 \, a^{3} b^{4} c^{2} - 128 \, a^{4} b^{2} c^{3} + 210 \, {\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)} d^{6} + 140 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{4} + 15 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{6} + 4 \, {\left(30 \, {\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)} d^{7} + 28 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{5} + 5 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d\right)} e^{3} x^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{4} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3} + 45 \, {\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)} d^{8} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{6} + 15 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{4} + 12 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} d^{2} + 2 \, {\left(5 \, {\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)} d^{9} + 8 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{7} + 3 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{5} + 4 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{3} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} d\right)} e x\right)} \log\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + c d^{4} + {\left(6 \, c d^{2} + b\right)} e^{2} x^{2} + b d^{2} + 2 \, {\left(2 \, c d^{3} + b d\right)} e x + a\right) + 12 \, {\left({\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)} e^{10} x^{10} + 10 \, {\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)} d e^{9} x^{9} + {\left(2 \, b^{8} c - 24 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 128 \, a^{3} b^{2} c^{4} + 45 \, {\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)} d^{2}\right)} e^{8} x^{8} + 8 \, {\left(15 \, {\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)} d^{3} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d\right)} e^{7} x^{7} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4} + 210 \, {\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)} d^{4} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{2}\right)} e^{6} x^{6} + {\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)} d^{10} + 2 \, {\left(126 \, {\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)} d^{5} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{3} + 3 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d\right)} e^{5} x^{5} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{8} + {\left(2 \, a b^{8} - 24 \, a^{2} b^{6} c + 96 \, a^{3} b^{4} c^{2} - 128 \, a^{4} b^{2} c^{3} + 210 \, {\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)} d^{6} + 140 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{4} + 15 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{2}\right)} e^{4} x^{4} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{6} + 4 \, {\left(30 \, {\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)} d^{7} + 28 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{5} + 5 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d\right)} e^{3} x^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{4} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3} + 45 \, {\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)} d^{8} + 56 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{6} + 15 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{4} + 12 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{2}\right)} e^{2} x^{2} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} d^{2} + 2 \, {\left(5 \, {\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)} d^{9} + 8 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{7} + 3 \, {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} d^{5} + 4 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{3} + {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} d\right)} e x\right)} \log\left(e x + d\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)} e^{11} f^{3} x^{10} + 10 \, {\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)} d e^{10} f^{3} x^{9} + {\left(2 \, a^{4} b^{7} c - 24 \, a^{5} b^{5} c^{2} + 96 \, a^{6} b^{3} c^{3} - 128 \, a^{7} b c^{4} + 45 \, {\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)} d^{2}\right)} e^{9} f^{3} x^{8} + 8 \, {\left(15 \, {\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)} d^{3} + 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)} d\right)} e^{8} f^{3} x^{7} + {\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} + 210 \, {\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)} d^{4} + 56 \, {\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)} d^{2}\right)} e^{7} f^{3} x^{6} + 2 \, {\left(126 \, {\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)} d^{5} + 56 \, {\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)} d^{3} + 3 \, {\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)} d\right)} e^{6} f^{3} x^{5} + {\left(2 \, a^{5} b^{7} - 24 \, a^{6} b^{5} c + 96 \, a^{7} b^{3} c^{2} - 128 \, a^{8} b c^{3} + 210 \, {\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)} d^{6} + 140 \, {\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)} d^{4} + 15 \, {\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)} d^{2}\right)} e^{5} f^{3} x^{4} + 4 \, {\left(30 \, {\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)} d^{7} + 28 \, {\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)} d^{5} + 5 \, {\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)} d^{3} + 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)} d\right)} e^{4} f^{3} x^{3} + {\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3} + 45 \, {\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)} d^{8} + 56 \, {\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)} d^{6} + 15 \, {\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)} d^{4} + 12 \, {\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)} d^{2}\right)} e^{3} f^{3} x^{2} + 2 \, {\left(5 \, {\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)} d^{9} + 8 \, {\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)} d^{7} + 3 \, {\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)} d^{5} + 4 \, {\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)} d^{3} + {\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} d\right)} e^{2} f^{3} x + {\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)} d^{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)} d^{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)} d^{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)} d^{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)} d^{2}\right)} e f^{3}\right)}}\right]"," ",0,"[-1/4*(6*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*e^8*x^8 + 48*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d*e^7*x^7 + 3*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4 + 56*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^2)*e^6*x^6 + 6*(56*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^3 + 3*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d)*e^5*x^5 + 2*a^3*b^6 - 24*a^4*b^4*c + 96*a^5*b^2*c^2 - 128*a^6*c^3 + 6*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^8 + (6*a*b^8 - 60*a^2*b^6*c + 158*a^3*b^4*c^2 + 44*a^4*b^2*c^3 - 400*a^5*c^4 + 420*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^4 + 45*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d^2)*e^4*x^4 + 3*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d^6 + 4*(84*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^5 + 15*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d^3 + 2*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*d)*e^3*x^3 + 2*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*d^4 + (9*a^2*b^7 - 104*a^3*b^5*c + 394*a^4*b^3*c^2 - 488*a^5*b*c^3 + 168*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^6 + 45*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d^4 + 12*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*d^2)*e^2*x^2 + (9*a^2*b^7 - 104*a^3*b^5*c + 394*a^4*b^3*c^2 - 488*a^5*b*c^3)*d^2 + 2*(24*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^7 + 9*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d^5 + 4*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*d^3 + (9*a^2*b^7 - 104*a^3*b^5*c + 394*a^4*b^3*c^2 - 488*a^5*b*c^3)*d)*e*x + 3*((b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*e^10*x^10 + 10*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d*e^9*x^9 + (2*b^7*c - 20*a*b^5*c^2 + 60*a^2*b^3*c^3 - 40*a^3*b*c^4 + 45*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^2)*e^8*x^8 + 8*(15*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^3 + 2*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d)*e^7*x^7 + (b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4 + 210*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^4 + 56*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^2)*e^6*x^6 + (b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^10 + 2*(126*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^5 + 56*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^3 + 3*(b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d)*e^5*x^5 + 2*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^8 + (2*a*b^7 - 20*a^2*b^5*c + 60*a^3*b^3*c^2 - 40*a^4*b*c^3 + 210*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^6 + 140*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^4 + 15*(b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d^2)*e^4*x^4 + (b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d^6 + 4*(30*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^7 + 28*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^5 + 5*(b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d^3 + 2*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*d)*e^3*x^3 + 2*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*d^4 + (45*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^8 + a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3 + 56*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^6 + 15*(b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d^4 + 12*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*d^2)*e^2*x^2 + (a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3)*d^2 + 2*(5*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^9 + 8*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^7 + 3*(b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d^5 + 4*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*d^3 + (a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3)*d)*e*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*e^4*x^4 + 8*c^2*d*e^3*x^3 + 2*c^2*d^4 + 2*(6*c^2*d^2 + b*c)*e^2*x^2 + 2*b*c*d^2 + 4*(2*c^2*d^3 + b*c*d)*e*x + b^2 - 2*a*c + (2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(b^2 - 4*a*c))/(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a)) - 3*((b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*e^10*x^10 + 10*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d*e^9*x^9 + (2*b^8*c - 24*a*b^6*c^2 + 96*a^2*b^4*c^3 - 128*a^3*b^2*c^4 + 45*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^2)*e^8*x^8 + 8*(15*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^3 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d)*e^7*x^7 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4 + 210*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^4 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^2)*e^6*x^6 + (b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^10 + 2*(126*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^5 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^3 + 3*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d)*e^5*x^5 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^8 + (2*a*b^8 - 24*a^2*b^6*c + 96*a^3*b^4*c^2 - 128*a^4*b^2*c^3 + 210*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^6 + 140*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^4 + 15*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^2)*e^4*x^4 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^6 + 4*(30*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^7 + 28*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^5 + 5*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d)*e^3*x^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^4 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3 + 45*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^8 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^6 + 15*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^4 + 12*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^2)*e^2*x^2 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d^2 + 2*(5*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^9 + 8*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^7 + 3*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^5 + 4*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^3 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d)*e*x)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 12*((b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*e^10*x^10 + 10*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d*e^9*x^9 + (2*b^8*c - 24*a*b^6*c^2 + 96*a^2*b^4*c^3 - 128*a^3*b^2*c^4 + 45*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^2)*e^8*x^8 + 8*(15*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^3 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d)*e^7*x^7 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4 + 210*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^4 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^2)*e^6*x^6 + (b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^10 + 2*(126*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^5 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^3 + 3*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d)*e^5*x^5 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^8 + (2*a*b^8 - 24*a^2*b^6*c + 96*a^3*b^4*c^2 - 128*a^4*b^2*c^3 + 210*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^6 + 140*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^4 + 15*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^2)*e^4*x^4 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^6 + 4*(30*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^7 + 28*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^5 + 5*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d)*e^3*x^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^4 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3 + 45*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^8 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^6 + 15*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^4 + 12*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^2)*e^2*x^2 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d^2 + 2*(5*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^9 + 8*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^7 + 3*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^5 + 4*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^3 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d)*e*x)*log(e*x + d))/((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)*e^11*f^3*x^10 + 10*(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)*d*e^10*f^3*x^9 + (2*a^4*b^7*c - 24*a^5*b^5*c^2 + 96*a^6*b^3*c^3 - 128*a^7*b*c^4 + 45*(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)*d^2)*e^9*f^3*x^8 + 8*(15*(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)*d^3 + 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)*d)*e^8*f^3*x^7 + (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 + 210*(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)*d^4 + 56*(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)*d^2)*e^7*f^3*x^6 + 2*(126*(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)*d^5 + 56*(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)*d^3 + 3*(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)*d)*e^6*f^3*x^5 + (2*a^5*b^7 - 24*a^6*b^5*c + 96*a^7*b^3*c^2 - 128*a^8*b*c^3 + 210*(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)*d^6 + 140*(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)*d^4 + 15*(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)*d^2)*e^5*f^3*x^4 + 4*(30*(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)*d^7 + 28*(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)*d^5 + 5*(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)*d^3 + 2*(a^5*b^7 - 12*a^6*b^5*c + 48*a^7*b^3*c^2 - 64*a^8*b*c^3)*d)*e^4*f^3*x^3 + (a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3 + 45*(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)*d^8 + 56*(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)*d^6 + 15*(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)*d^4 + 12*(a^5*b^7 - 12*a^6*b^5*c + 48*a^7*b^3*c^2 - 64*a^8*b*c^3)*d^2)*e^3*f^3*x^2 + 2*(5*(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)*d^9 + 8*(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)*d^7 + 3*(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)*d^5 + 4*(a^5*b^7 - 12*a^6*b^5*c + 48*a^7*b^3*c^2 - 64*a^8*b*c^3)*d^3 + (a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*d)*e^2*f^3*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)*d^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)*d^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)*d^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)*d^4 + (a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*d^2)*e*f^3), -1/4*(6*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*e^8*x^8 + 48*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d*e^7*x^7 + 3*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4 + 56*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^2)*e^6*x^6 + 6*(56*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^3 + 3*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d)*e^5*x^5 + 2*a^3*b^6 - 24*a^4*b^4*c + 96*a^5*b^2*c^2 - 128*a^6*c^3 + 6*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^8 + (6*a*b^8 - 60*a^2*b^6*c + 158*a^3*b^4*c^2 + 44*a^4*b^2*c^3 - 400*a^5*c^4 + 420*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^4 + 45*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d^2)*e^4*x^4 + 3*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d^6 + 4*(84*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^5 + 15*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d^3 + 2*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*d)*e^3*x^3 + 2*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*d^4 + (9*a^2*b^7 - 104*a^3*b^5*c + 394*a^4*b^3*c^2 - 488*a^5*b*c^3 + 168*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^6 + 45*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d^4 + 12*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*d^2)*e^2*x^2 + (9*a^2*b^7 - 104*a^3*b^5*c + 394*a^4*b^3*c^2 - 488*a^5*b*c^3)*d^2 + 2*(24*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*d^7 + 9*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*d^5 + 4*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*d^3 + (9*a^2*b^7 - 104*a^3*b^5*c + 394*a^4*b^3*c^2 - 488*a^5*b*c^3)*d)*e*x + 6*((b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*e^10*x^10 + 10*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d*e^9*x^9 + (2*b^7*c - 20*a*b^5*c^2 + 60*a^2*b^3*c^3 - 40*a^3*b*c^4 + 45*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^2)*e^8*x^8 + 8*(15*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^3 + 2*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d)*e^7*x^7 + (b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4 + 210*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^4 + 56*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^2)*e^6*x^6 + (b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^10 + 2*(126*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^5 + 56*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^3 + 3*(b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d)*e^5*x^5 + 2*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^8 + (2*a*b^7 - 20*a^2*b^5*c + 60*a^3*b^3*c^2 - 40*a^4*b*c^3 + 210*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^6 + 140*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^4 + 15*(b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d^2)*e^4*x^4 + (b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d^6 + 4*(30*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^7 + 28*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^5 + 5*(b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d^3 + 2*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*d)*e^3*x^3 + 2*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*d^4 + (45*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^8 + a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3 + 56*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^6 + 15*(b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d^4 + 12*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*d^2)*e^2*x^2 + (a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3)*d^2 + 2*(5*(b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*d^9 + 8*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*d^7 + 3*(b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*d^5 + 4*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*d^3 + (a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3)*d)*e*x)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*e^2*x^2 + 4*c*d*e*x + 2*c*d^2 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - 3*((b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*e^10*x^10 + 10*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d*e^9*x^9 + (2*b^8*c - 24*a*b^6*c^2 + 96*a^2*b^4*c^3 - 128*a^3*b^2*c^4 + 45*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^2)*e^8*x^8 + 8*(15*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^3 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d)*e^7*x^7 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4 + 210*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^4 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^2)*e^6*x^6 + (b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^10 + 2*(126*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^5 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^3 + 3*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d)*e^5*x^5 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^8 + (2*a*b^8 - 24*a^2*b^6*c + 96*a^3*b^4*c^2 - 128*a^4*b^2*c^3 + 210*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^6 + 140*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^4 + 15*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^2)*e^4*x^4 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^6 + 4*(30*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^7 + 28*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^5 + 5*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d)*e^3*x^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^4 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3 + 45*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^8 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^6 + 15*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^4 + 12*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^2)*e^2*x^2 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d^2 + 2*(5*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^9 + 8*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^7 + 3*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^5 + 4*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^3 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d)*e*x)*log(c*e^4*x^4 + 4*c*d*e^3*x^3 + c*d^4 + (6*c*d^2 + b)*e^2*x^2 + b*d^2 + 2*(2*c*d^3 + b*d)*e*x + a) + 12*((b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*e^10*x^10 + 10*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d*e^9*x^9 + (2*b^8*c - 24*a*b^6*c^2 + 96*a^2*b^4*c^3 - 128*a^3*b^2*c^4 + 45*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^2)*e^8*x^8 + 8*(15*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^3 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d)*e^7*x^7 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4 + 210*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^4 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^2)*e^6*x^6 + (b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^10 + 2*(126*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^5 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^3 + 3*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d)*e^5*x^5 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^8 + (2*a*b^8 - 24*a^2*b^6*c + 96*a^3*b^4*c^2 - 128*a^4*b^2*c^3 + 210*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^6 + 140*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^4 + 15*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^2)*e^4*x^4 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^6 + 4*(30*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^7 + 28*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^5 + 5*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d)*e^3*x^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^4 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3 + 45*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^8 + 56*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^6 + 15*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^4 + 12*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^2)*e^2*x^2 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d^2 + 2*(5*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^9 + 8*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^7 + 3*(b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*d^5 + 4*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^3 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d)*e*x)*log(e*x + d))/((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)*e^11*f^3*x^10 + 10*(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)*d*e^10*f^3*x^9 + (2*a^4*b^7*c - 24*a^5*b^5*c^2 + 96*a^6*b^3*c^3 - 128*a^7*b*c^4 + 45*(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)*d^2)*e^9*f^3*x^8 + 8*(15*(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)*d^3 + 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)*d)*e^8*f^3*x^7 + (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 + 210*(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)*d^4 + 56*(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)*d^2)*e^7*f^3*x^6 + 2*(126*(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)*d^5 + 56*(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)*d^3 + 3*(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)*d)*e^6*f^3*x^5 + (2*a^5*b^7 - 24*a^6*b^5*c + 96*a^7*b^3*c^2 - 128*a^8*b*c^3 + 210*(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)*d^6 + 140*(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)*d^4 + 15*(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)*d^2)*e^5*f^3*x^4 + 4*(30*(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)*d^7 + 28*(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)*d^5 + 5*(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)*d^3 + 2*(a^5*b^7 - 12*a^6*b^5*c + 48*a^7*b^3*c^2 - 64*a^8*b*c^3)*d)*e^4*f^3*x^3 + (a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3 + 45*(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)*d^8 + 56*(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)*d^6 + 15*(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)*d^4 + 12*(a^5*b^7 - 12*a^6*b^5*c + 48*a^7*b^3*c^2 - 64*a^8*b*c^3)*d^2)*e^3*f^3*x^2 + 2*(5*(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)*d^9 + 8*(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)*d^7 + 3*(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)*d^5 + 4*(a^5*b^7 - 12*a^6*b^5*c + 48*a^7*b^3*c^2 - 64*a^8*b*c^3)*d^3 + (a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*d)*e^2*f^3*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)*d^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)*d^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)*d^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)*d^4 + (a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*d^2)*e*f^3)]","B",0
661,0,0,0,1.106877," ","integrate(x/(a+b*(e*x+d)^3+c*(e*x+d)^6)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\sqrt{c e^{6} x^{6} + 6 \, c d e^{5} x^{5} + 15 \, c d^{2} e^{4} x^{4} + c d^{6} + {\left(20 \, c d^{3} + b\right)} e^{3} x^{3} + 3 \, {\left(5 \, c d^{4} + b d\right)} e^{2} x^{2} + b d^{3} + 3 \, {\left(2 \, c d^{5} + b d^{2}\right)} e x + a}}, x\right)"," ",0,"integral(x/sqrt(c*e^6*x^6 + 6*c*d*e^5*x^5 + 15*c*d^2*e^4*x^4 + c*d^6 + (20*c*d^3 + b)*e^3*x^3 + 3*(5*c*d^4 + b*d)*e^2*x^2 + b*d^3 + 3*(2*c*d^5 + b*d^2)*e*x + a), x)","F",0
662,0,0,0,17.251716," ","integrate(x^2/(a+b*(e*x+d)^3+c*(e*x+d)^6)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{\sqrt{c e^{6} x^{6} + 6 \, c d e^{5} x^{5} + 15 \, c d^{2} e^{4} x^{4} + c d^{6} + {\left(20 \, c d^{3} + b\right)} e^{3} x^{3} + 3 \, {\left(5 \, c d^{4} + b d\right)} e^{2} x^{2} + b d^{3} + 3 \, {\left(2 \, c d^{5} + b d^{2}\right)} e x + a}}, x\right)"," ",0,"integral(x^2/sqrt(c*e^6*x^6 + 6*c*d*e^5*x^5 + 15*c*d^2*e^4*x^4 + c*d^6 + (20*c*d^3 + b)*e^3*x^3 + 3*(5*c*d^4 + b*d)*e^2*x^2 + b*d^3 + 3*(2*c*d^5 + b*d^2)*e*x + a), x)","F",0
663,1,104,0,1.170706," ","integrate((2+3*x)^6*(1+(2+3*x)^7+(2+3*x)^14),x, algorithm=""fricas"")","\frac{1162261467}{7} x^{21} + 2324522934 x^{20} + 15496819560 x^{19} + 65431015920 x^{18} + 196293047760 x^{17} + 444930908256 x^{16} + 790988281344 x^{15} + \frac{15819767221203}{14} x^{14} + 1318314865122 x^{13} + 1269491970942 x^{12} + 1015602174288 x^{11} + 677082445416 x^{10} + 376174427616 x^{9} + 173635132896 x^{8} + 66158154783 x^{7} + 20588764518 x^{6} + 5149786572 x^{5} + 1010576952 x^{4} + 149902032 x^{3} + 15808800 x^{2} + 1056832 x"," ",0,"1162261467/7*x^21 + 2324522934*x^20 + 15496819560*x^19 + 65431015920*x^18 + 196293047760*x^17 + 444930908256*x^16 + 790988281344*x^15 + 15819767221203/14*x^14 + 1318314865122*x^13 + 1269491970942*x^12 + 1015602174288*x^11 + 677082445416*x^10 + 376174427616*x^9 + 173635132896*x^8 + 66158154783*x^7 + 20588764518*x^6 + 5149786572*x^5 + 1010576952*x^4 + 149902032*x^3 + 15808800*x^2 + 1056832*x","B",0
664,1,174,0,0.995730," ","integrate((2+3*x)^6*(1+(2+3*x)^7+(2+3*x)^14)^2,x, algorithm=""fricas"")","\frac{16677181699666569}{35} x^{35} + 11118121133111046 x^{34} + 126005372841925188 x^{33} + 924039400840784712 x^{32} + 4928210137817518464 x^{31} + \frac{101849676181562048256}{5} x^{30} + 67899784121041365504 x^{29} + \frac{2625458326972530284475}{14} x^{28} + 437576396725285446564 x^{27} + 875152864622814086340 x^{26} + \frac{7584660010542711771792}{5} x^{25} + 2298383223254096766840 x^{24} + 3064515076512846852480 x^{23} + 3614565944605222108800 x^{22} + \frac{26506949038858918036881}{7} x^{21} + 3534290697929473864098 x^{20} + 2945285062308448290360 x^{19} + 2194577166014752240080 x^{18} + 1463104032160519033200 x^{17} + 872775774067455498528 x^{16} + 465517091041681015296 x^{15} + 221699757548270194389 x^{14} + 94069263918929616324 x^{13} + 35454069480572048124 x^{12} + 11821487501620716192 x^{11} + \frac{17344958593049772048}{5} x^{10} + 889942562270387136 x^{9} + 197897276851452864 x^{8} + 37727143432895007 x^{7} + 6077684727888102 x^{6} + \frac{4057390785756924}{5} x^{5} + 87406679578680 x^{4} + 7299544818384 x^{3} + 443569828128 x^{2} + 17451466816 x"," ",0,"16677181699666569/35*x^35 + 11118121133111046*x^34 + 126005372841925188*x^33 + 924039400840784712*x^32 + 4928210137817518464*x^31 + 101849676181562048256/5*x^30 + 67899784121041365504*x^29 + 2625458326972530284475/14*x^28 + 437576396725285446564*x^27 + 875152864622814086340*x^26 + 7584660010542711771792/5*x^25 + 2298383223254096766840*x^24 + 3064515076512846852480*x^23 + 3614565944605222108800*x^22 + 26506949038858918036881/7*x^21 + 3534290697929473864098*x^20 + 2945285062308448290360*x^19 + 2194577166014752240080*x^18 + 1463104032160519033200*x^17 + 872775774067455498528*x^16 + 465517091041681015296*x^15 + 221699757548270194389*x^14 + 94069263918929616324*x^13 + 35454069480572048124*x^12 + 11821487501620716192*x^11 + 17344958593049772048/5*x^10 + 889942562270387136*x^9 + 197897276851452864*x^8 + 37727143432895007*x^7 + 6077684727888102*x^6 + 4057390785756924/5*x^5 + 87406679578680*x^4 + 7299544818384*x^3 + 443569828128*x^2 + 17451466816*x","B",0
